Baby Monster Group - Maximal Subgroups

Maximal Subgroups

Wilson (1999) gave the 30 classes of maximal subgroups of the baby monster as follows:

2.2E₆(2):2 This is the centralizer of an involution, and is the subgroup fixing a point of the smallest permutation representation on 13 571 955 000 points.

21+22.Co₂

Fi₂₃

29+16.S₈(2)

Th

(22 × F₄(2)):2

22+10+20.(M₂₂:2 × S₃)

.L₅(2)

S₃ × Fi₂₂:2

.(S₅ × L₃(2))

HN:2

O₈+(3):S₄

31+8.21+6.U₄(2).2

(32:D₈ × U₄(3).2.2).2

5:4 × HS:2

S₄ × 2F₄(2)

.(S₄ × 2S₄)

S₅ × M₂₂:2

(S₆ × L₃(4):2).2

53.L₃(5)

51+4.21+4.A₅.4

(S₆ × S₆).4

52:4S₄ × S₅

L₂(49).2₃

L₂(31)

M₁₁

L₃(3)

L₂(17):2

L₂(11):2

47:23