Subgroups — C₁₁⋊S₄ #63164

Order 264.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₁₁	—	3	1	no	maximal, Hall
3	D₃₃	—	4	1	no	maximal
4	C₂²×C₁₁	D₃	1	1	yes	characteristic, complemented
5	C₂×D₁₁	—	3	1	no	—
6	Dic₁₁	—	3	1	no	—
7	C₃×C₁₁	—	4	1	no	Hall
8	S₄	—	11	1	no	maximal, Hall
9	C₂×C₁₁	—	3	1	no	—
10	D₁₁	—	6	1	no	—
11	A₄	D₁₁	1	1	yes	characteristic, complemented
12	C₁₁	S₄	1	1	yes	characteristic, complemented, Sylow
13	D₄	—	33	1	no	Sylow
14	D₃	—	44	1	no	—
15	C₂²	—	33	1	no	—
16	C₂²	D₃₃	1	1	yes	characteristic, complemented
17	C₄	—	33	1	no	—
18	C₃	—	4	1	no	Sylow
19	C₂	—	3	1	no	—
20	C₂	—	66	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₁×A₄	C₂
Fitting, socle	C₂²×C₁₁	D₃
LCS	G ▷ C₁₁×A₄
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

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