Big44
As discussed I’m going to give you a lot of information and some links for further reading
First pick the type of unit (armor, armored infantry, armored engineers etc) then pick the Armored Division (or a cavalry Group, Separate Tank Battalion, etc - basically an armored unit that would have a HT...). From there go on line and research the units assigned to that division/unit during the war.
In WW2, a total of 16 armored divisions were organized (1st-14th, 16th, and 20th). In 1943, the US Army reorganized the Table of Organization and Equipment (TO&E) for the Armored Divisions from a “Heavy” regimental system to a “Light” battalion system. Of these, only two, the 2nd and the 3rd retained the "heavy" organization throughout the war. All of the other divisions were reorganized as light divisions prior to leaving the US (except the 1st, which converted to the light organization while in Italy during July 1944). All of the armored divisions served in the ETO or in Italy.
1st Armored Division “Old Ironsides”: Formed in 1940, the 1st served in North Africa from November 1942 to May 1943 and in Italy from October 1943 to the end of the war.
2nd Armored Division “Hell On Wheels”: Formed in 1940, the 2nd served in North Africa from November 1942 to May 1943, landed in Sicily in July 1943, and participated in the liberation of France from June 1944 to the end of the war.
3rd Armored Division “Spearhead”: Formed in 1941, the 3rd served in NW Europe from June 1944 to the end of the war.
4th Armored Division: Formed in 1941, the 4th served in NW Europe from July 1944 to the end of the war.
5th Armored Division “Victory”: Formed in 1941, the 5th served in NW Europe from July 1944 to the end of the war.
6th Armored Division “Super Sixth”: Formed in 1942, the 6th served in NW Europe from July 1944 to the end of the war.
7th Armored Division “Lucky Seventh”: Formed in 1942, the 7th served in NW Europe from August 1944 to the end of the war.
8th Armored Division “Thunder Herd” or “Iron Snake” or “Tornado”: Formed in 1942, the 8th served in NW Europe from January 1945 to the end of the war.
9th Armored Division “Phantom” (I’ve also seen this unit called “Remagen” : Formed in 1942, the 9th served in NW Europe from December 1944 to the end of the war.
10th Armored Division “Tiger”: Formed in 1942, the 10th served in NW Europe from September 1944 to the end of the war.
11th Armored Division “Thunderbolt”: Formed in 1942, the 11th served in NW Europe from December 1944 to the end of the war.
12th Armored Division “Hellcat”: Formed in 1942, the 12th served in NW Europe from November 1944 to the end of the war.
13th Armored Division “The Black Cats”: Formed in 1942, the 13th served in NW Europe from January 1945 to the end of the war.
14th Armored Division “Liberators” : Formed in 1942, the 14th served in NW Europe from October 1944 to the end of the war.
16th Armored Division “Armadillo”: Formed in 1942, the 16th served in NW Europe from February 1945 to the end of the war.
20th Armored Division “Armoraiders” or “Liberators”: Formed in 1942, the 20th served in NW Europe from February 1945 to the end of the war.
As first organized, the armored regiments medium tank was the M3A1 or M3A4 Grant, the light tank was the M3 or M3A1 Stuart, and the assault gun was the T30 Howitzer Motor Carriage. In early 1943 the M4 Sherman replaced the M3 series. Later in 1943 the M5 Stuart replaced the M3 and a purpose designed assault gun, the M8 HMC 75mm, replaced the T30. The M4 105mm assault gun in turn replaced the M8 in early 1944, except in the light tank battalions.
The light armor division organization (TO&E 17-2, dated 15 September 1943) included a Division Headquarters and Headquarters (H&H) Company, two Combat Command Headquarters (CCA and CCB), a Reserve Combat Command Headquarters (CCR), three tank battalions (of three medium and one light tank companies), three armored infantry battalions, three eighteen-gun artillery battalions, a cavalry reconnaissance squadron (battalion), an engineer battalion, and division services. The division included 77 light tanks, 168 medium tanks, 18 M4 105mm assault guns, 54 M7 105mm SP artillery pieces, 54 M8 armored cars,
450 halftracks, 1,031 motor vehicles, and 8 light observation aircraft. Total personnel strength was 10,754.
The heavy armored division organization (TO&E 17-1, dated 1 March 1942, with Changes 1 & 2, dated to 29 October 1942) included two three-battalion tank regiments (the 1st battalion was light, with three light tank companies, the 2nd and 3rd battalions were medium, each with three medium tank companies), a three-battalion armored infantry regiment, and only two combat commands, the rest of the divisional units were nearly identical to those in the light division. The heavy division included 158 light tanks, 232 medium tanks, 24 M4 105mm assault guns, 17 M8 assault guns, 54 M7 105mm SP artillery pieces, 54 M8 armored cars,
640 halftracks, 1,242 motor vehicles, and 8 light observation aircraft. The total personnel strength of the division was 14,664.
One-hundred-and-eighteen tank battalions were eventually formed. Sixty-one of those were separate tank battalions and not assigned to the Armored Divisions.
I pulled a lot of the above from this link – excellent source of the TO&E.
http://www.warandtactics.com/smf/toe-world-war-2-allied/us-armored-divsion-toes/?wap2For Tank Battalions, (they would have 13 Halftracks) - U.S. Army's T/O & E (Table of Organization and Equipment) 17-25. The last wartime update for this table was November 18th, 1944. One should note that a T/O & E was a guide. During the war, the battalions usually fought with less. Less personnel, less tanks, and some variations in equipment to what was required by the T/O & E.
For Armored infantry Battalions - (they would have over 72 halftracks) T/O&E 7-25 Armored Infantry Battalion (15 September 1943) Notes: Three of these battalions were assigned to each Armored Division. This type of battalion could also be a separate battalion attached to a separate Armored Group, or attached directly to a Corps or Army, although this was very rare.
For a List of TO&E (and free downloads of the tables) and how each type of unit was equipped (including armored engineers, artillery etc) go here to MRS archive of ‘41-45 TO&E:
http://www.militaryresearch.org/freebies.htm