Most historians do not believe that HUAC operated independent from Mccarthy’s “Permanent Subcommittee on Investigations” because as soon as Mccarthy’s prestige tumbled HUAC did right along with his even though yes he did not run that committee too.
But technically you may be correct.
Scratching head. McCarthy was a senator from Wisconsin, first elected in in 1946. HUAC was a house committee (not Senate) that first began looking at Hollywood commies fully ten years eariler in 1936. The famous "Hollywood Ten" HUAC hearing happened in 1947 while McCarthy was still in his freshman year in the Senate.
No one outside of Wisconsin know McCarthy's name until 1950 with his Wheeling (WV) speech were he said he had a list of commies in the State Department.