[seqfan] Symmetric groups

[Frank Adams-Watters]

If n divides m!, does the symmetric group S_m always have a subgroup of order n?

If so, a comment should be added to A002034 that a(n) is the genus of the smallest symmetric group with a subgroup of order n. If not, where is the first exception? (8 in S_4?) Is the sequence so described in the OEIS? If not, it should be added.

Franklin T. Adams-Watters