Subgroups — C₉⋊(C₃₁⋊#1181) #44569039

Order 32364.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃₁×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃₁⋊#1181)	—	3	1	no	maximal
3	C₉×C₂₉×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₁×D₂₉	D₃	1	1	yes	characteristic
5	C₃₁⋊#1181	—	9	1	no	Hall
6	C₃×C₂₉×C₃₁	Dic₃	1	1	yes	characteristic
7	C₃₁×D₂₉	D₉	1	1	yes	characteristic
8	Dic₂₇₉	—	29	1	no	maximal, Hall
9	C₉⋊#1181	—	31	1	no	maximal, Hall
10	C₂₉×C₃₁	Dic₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₉×C₃₁	—	29	1	no	—
12	C₉×D₂₉	D₃₁	1	1	yes	characteristic
13	Dic₉₃	—	87	1	no	—
14	C₃⋊#1181	—	93	1	no	—
15	C₉×C₃₁	#1181	1	1	yes	characteristic, complemented, Hall
16	C₉×C₂₉	Dic₃₁	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₃₁	—	29	1	no	—
18	C₃×D₂₉	D₉₃	1	1	yes	characteristic
19	Dic₃₁	—	261	1	no	Hall
20	#1181	—	279	1	no	Hall
21	C₃×C₃₁	C₃⋊#1181	1	1	yes	characteristic
22	C₃×C₂₉	Dic₉₃	1	1	yes	characteristic
23	C₂×C₃₁	—	29	1	no	—
24	D₂₉	D₂₇₉	1	1	yes	characteristic
25	Dic₉	—	899	1	no	Hall
26	C₃₁	C₉⋊#1181	1	1	yes	characteristic, complemented, Sylow
27	C₂₉	Dic₂₇₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	29	1	no	—
29	Dic₃	—	2697	1	no	—
30	C₉	C₃₁⋊#1181	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	29	1	no	—
32	C₄	—	8091	1	no	Sylow
33	C₃	C₃⋊(C₃₁⋊#1181)	1	1	yes	characteristic
34	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₂₉×C₃₁	C₄
Frattini	C₃	C₃⋊(C₃₁⋊#1181)
socle	C₃×C₂₉×C₃₁	Dic₃
prime radical	C₃×C₃₁×D₂₉	D₃
cosocle	C₉×C₃₁×D₂₉	C₂
LCS	G ▷ C₉×C₂₉×C₃₁
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.