Determining group structure from the sets of character degrees

Let cd(G) be the set of all irreducible complex characters of a finite group G. In [4], Lewis proved that if p, q, r, and s are distinct primes and cd(G)={1,p,q,r,pq,pr} or cd(G)={1,p,q,r,s,pr,ps,qr,qs}, then G is the direct product of two normal non-abelian subgroups of G. We generalize Lewis' results by loosening the primeness hypothesis of cd(G).