Subgroups — C₁₁⋊(#10597845⋊C₃) #35208564

Order 20724.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₅₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊#10597845	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₅₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₁₅₇	C₂×C₃	1	1	yes	characteristic
5	#10597845⋊C₃	—	11	1	no	maximal, Hall
6	C₁₁×C₁₅₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	D₁₅₇⋊C₃	D₁₁	1	1	yes	characteristic
8	#10597845	—	11	1	no	Hall
9	C₁₅₇⋊C₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	D₁₅₇	C₃×D₁₁	1	1	yes	characteristic
11	C₁₅₇	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
12	C₃×Dic₁₁	—	157	1	no	maximal, Hall
13	C₂×C₃×C₁₁	—	157	1	no	—
14	Dic₁₁	—	157	1	no	Hall
15	C₃×C₁₁	—	628	1	no	Hall
16	C₂×C₁₁	—	157	1	no	—
17	C₃×C₄	—	1727	1	no	Hall
18	C₁₁	#10597845⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	157	1	no	—
20	C₄	—	1727	1	no	Sylow
21	C₃	—	628	1	no	Sylow
22	C₂	—	157	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₁₅₇	C₃×C₄
prime radical	C₁₁×D₁₅₇⋊C₃	C₂
cosocle	C₁₁×D₁₅₇	C₂×C₃
LCS	G ▷ C₁₁×C₁₅₇
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.