Subgroups — C₃⋊((C₃₁⋊C₃)⋊#1181) #44569080

Order 32364.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₉×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃₁⋊#1181)	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₃₁⋊C₃)⋊#1181	—	3	1	no	maximal
4	C₃×C₂₉×C₃₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	D₂₉×C₃₁⋊C₃	—	2	1	no	—
6	D₂₉×C₃₁⋊C₃	D₃	1	1	yes	characteristic
7	C₃×C₃₁×D₂₉	C₂×C₃	1	1	yes	characteristic
8	C₃₁⋊#1181	—	3	1	no	Hall
9	C₃×C₂₉×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented
10	C₂₉×C₃₁⋊C₃	—	2	1	no	—
11	C₂₉×C₃₁⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	C₃₁×D₂₉	C₃×D₃	1	1	yes	characteristic
13	C₃⋊((C₃₁⋊C₃)⋊C₄)	—	29	1	no	maximal, Hall
14	C₃×C₃⋊#1181	—	31	1	no	maximal, Hall
15	C₂₉×C₃₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₃₁⋊C₃	—	29	1	no	—
17	C₃²×D₂₉	—	31	1	no	—
18	Dic₉₃	—	29	1	no	—
19	(C₃₁⋊C₃)⋊C₄	—	87	1	no	—
20	C₃⋊#1181	—	31	1	no	—
21	C₃×#1181	—	93	1	no	—
22	C₃×C₃₁⋊C₃	#1181	1	1	yes	characteristic, complemented, Hall
23	C₃²×C₂₉	—	31	1	no	Hall
24	C₂×C₃×C₃₁	—	29	1	no	—
25	C₂×C₃₁⋊C₃	—	29	1	no	—
26	C₂×C₃₁⋊C₃	—	58	1	no	—
27	C₃×D₂₉	—	31	1	no	—
28	C₃×D₂₉	—	62	1	no	—
29	C₃×D₂₉	D₃₁⋊C₃	1	1	yes	characteristic
30	Dic₃₁	—	87	1	no	Hall
31	#1181	—	93	1	no	Hall
32	C₃×C₃₁	C₃×#1181	1	1	yes	characteristic, complemented
33	C₃₁⋊C₃	—	2	1	no	—
34	C₃₁⋊C₃	C₃⋊#1181	1	1	yes	characteristic, complemented
35	C₃×C₂₉	—	31	1	no	—
36	C₃×C₂₉	—	62	1	no	—
37	C₃×C₂₉	(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
38	C₂×C₃₁	—	29	1	no	—
39	D₂₉	C₃⋊(D₃₁⋊C₃)	1	1	yes	characteristic
40	C₃×Dic₃	—	899	1	no	Hall
41	C₃₁	C₃×C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
42	C₂₉	C₃⋊((C₃₁⋊C₃)⋊C₄)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃²	—	899	1	no	—
44	C₃×C₄	—	2697	1	no	—
45	Dic₃	—	899	1	no	—
46	C₃²	—	31	1	no	Sylow
47	C₂×C₃	—	1798	1	no	—
48	C₂×C₃	—	29	1	no	—
49	C₂×C₃	—	899	1	no	—
50	C₄	—	2697	1	no	Sylow
51	C₃	—	31	1	no	—
52	C₃	—	62	1	no	—
53	C₃	(C₃₁⋊C₃)⋊#1181	1	1	yes	characteristic, complemented
54	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₂₉×C₃₁	C₃×C₄
prime radical	C₃×D₂₉×C₃₁⋊C₃	C₂
cosocle	C₃×C₃₁×D₂₉	C₂×C₃
LCS	G ▷ C₃×C₂₉×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃₁⋊#1181)	C₃	semidirect
4. C₃×C₂₉×C₃₁⋊C₃	C₄	semidirect
9. C₃×C₂₉×C₃₁	C₃×C₄	semidirect
11. C₂₉×C₃₁⋊C₃	Dic₃	semidirect
15. C₂₉×C₃₁	C₃×Dic₃	semidirect
22. C₃×C₃₁⋊C₃	#1181	semidirect
32. C₃×C₃₁	C₃×#1181	semidirect
34. C₃₁⋊C₃	C₃⋊#1181	semidirect
37. C₃×C₂₉	(C₃₁⋊C₃)⋊C₄	semidirect
41. C₃₁	C₃×C₃⋊#1181	semidirect
42. C₂₉	C₃⋊((C₃₁⋊C₃)⋊C₄)	semidirect
53. C₃	(C₃₁⋊C₃)⋊#1181	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₂₉×C₃₁⋊C₃	2
C₃⋊(C₃₁⋊#1181)	3
(C₃₁⋊C₃)⋊#1181	3
C₃⋊((C₃₁⋊C₃)⋊C₄)	29
C₃×C₃⋊#1181	31

Subgroups — C3⋊((C31⋊C3)⋊#1181) #44569080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊((C₃₁⋊C₃)⋊#1181) #44569080