Iraq ORBAT, but it’s a bit dated and hard to read. Try this - I don’t think the numbers have significantly changed since August although I could be wrong.
Also, there are sometimes some funky counts going on. They sometimes count combat units that are assigned to the theatre but not ‘in’ theatre in the classic sense (i.e. B-52 crews) but don’t count troops who are in theatre but not in combat roles (i.e. rear-echelon support troops like supply and maintenance) so that number might be significantly higher or lower. Also not counted are private contractors in the AO, most famously Blackwater, who are ‘de facto’ US troops but not counted as such.