On huppert's conjecture for the conway and fischer families of sporadic simple groups

Let G denote a finite group and \mathrm{cd} (G) the set of irreducible character degrees of G. Huppert conjectured that if H is a finite nonabelian simple group such that \mathrm{cd} (G)= \mathrm{cd} (H), then G\cong H\times A, where A is an abelian group. He verified the conjecture for many of the sporadic simple groups and we complete its verification for the remainder.