Search on the airforcehistoryindex site mentioned above for 0082 Fighter Group between dates 12/01/1944 and 12/31/1944 gives this:
http://airforcehistoryindex.org/data/000/080/894.xml
Sometimes searching for the individual squadrons, i.e. 0095 0096 or 0097 Fighter Squadrons in the same date range will give more possibilities.