Subgroups — PSL(2,𝔽₂₃) #72209616

Order 6072.

23 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃⋊C₁₁	—	24	1	no	maximal, Hall
2	S₄	—	253	2	no	maximal, Hall
3	D₁₂	—	253	1	no	maximal, Hall
4	C₂₃	—	24	1	no	Sylow
5	D₁₁	—	276	1	no	maximal
6	C₂×D₃	—	253	2	no	—
7	A₄	—	253	2	no	—
8	C₃×C₄	—	253	1	no	—
9	C₁₁	—	276	1	no	Sylow
10	D₄	—	759	1	no	Sylow
11	C₂×C₃	—	253	1	no	—
12	D₃	—	506	2	no	—
13	C₂²	—	253	2	no	—
14	C₄	—	253	1	no	—
15	C₃	—	253	1	no	Sylow
16	C₂	—	253	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.