I've addressed elements of this question in earlier answers;

• "Who got what weapons in ww2?"

• "Why did some US infantry in WW2 have Thompsons or BARs and not M1 Garands?"

• "Who got what gear in ww2 (U.S Army, European theater)"

• "How much rifle ammunition was the average infantry soldier issued during WWI & WWII?"

Here is the table of organization and equipment of a U.S. airborne rifle company from February 17, 1942. This basic TO&E was in effect until August 1, 1944, and would have been used during the D-Day landings.

Hi there -- you may be interested in this older answer about the various model of Thompsons from u/the_howling_cow:

https://www.reddit.com/r/AskHistorians/comments/67hk2e/was_the_thompson_model_1921_ever_used_in_world/