Maximal subgroups of symmetric groups

Martin W. Liebeck*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We show that Sn has at most n6/11 + o(1) conjugacy classes of primitive maximal subgroups. This improves an nclog3n bound given by Babai. We conclude that the number of conjugacy classes of maximal subgroups of Sn is of the form (1/2 + o(1))n. It also follows that, for large n, Sn has less than n! maximal subgroups. This confirms a special case of a conjecture of Wall. Improving a recent result from [MSh], we also show that any finite almost simple group has at most n17/11+o(1) maximal subgroups of index n.

Original languageAmerican English
Pages (from-to)341-352
Number of pages12
JournalJournal of Combinatorial Theory. Series A
Issue number2
StatePublished - Aug 1996

Bibliographical note

Funding Information:
The second author thanks the department of mathematics of the University of Chicago for its support and hospitality while this work was carried out.


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