# Maximal subgroups of the sporadic almost-simple groups

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## Abstract

Let S be one of the sporadic groups
M_{12},
M_{22},
HS,
McL,
J_{2},
J_{3},
Suz,
He,
HN,
O'N,
Fi_{22},
Fi_{24}'
and let G = Aut(S). Using
a permutation representation of G on a computer, we calculate
explicit generators for the maximal subgroups of G. The generators of
the maximal subgroups are presented as
straight line programs in
standard generators of G, making it easy to produce each maximal subgroup
for any choice of representation and generators for G. All these straight
line programs have been made available on the World Wide Web. In the proof
that the generators we produce are correct, we tabulate the orbit shapes
of each maximal subgroup in the smallest faithful permutation representation
of G, which are useful data when attempting to identify subgroups of G.

## Full text

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