Subgroups — D₁₁×C₁₅₇⋊C₉ #44527264

Order 31086.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₅₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₁×C₁₅₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₁×C₁₅₇	C₂×C₃	1	1	yes	characteristic
4	D₁₁×C₁₅₇	C₉	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₅₇⋊C₉	—	11	1	no	maximal, Hall
6	C₁₁×C₁₅₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₁₅₇⋊C₉	D₁₁	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₁₅₇	—	11	1	no	—
9	C₃×C₁₅₇	C₃×D₁₁	1	1	yes	characteristic
10	C₂×C₁₅₇	—	11	1	no	Hall
11	C₉×D₁₁	—	157	1	no	maximal, Hall
12	C₁₅₇	C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
13	C₉×C₁₁	—	157	1	no	Hall
14	C₃×D₁₁	C₁₅₇⋊C₃	1	1	yes	characteristic
15	C₃×C₁₁	C₂×C₁₅₇⋊C₃	1	1	yes	characteristic
16	D₁₁	C₁₅₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₉	—	1727	1	no	Hall
18	C₁₁	C₂×C₁₅₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₉	—	157	1	no	Sylow
20	C₂×C₃	—	11	1	no	—
21	C₃	D₁₁×C₁₅₇⋊C₃	1	1	yes	characteristic
22	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₁₁×C₁₅₇⋊C₃
commutator, hypocenter	C₁₁×C₁₅₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₁₁×C₁₅₇	C₂×C₃
prime radical	C₃×D₁₁×C₁₅₇	C₃
LCS	G ▷ C₁₁×C₁₅₇
UCS	C₁ ◁ C₃

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.