Subgroups — #13097100

Order 1584.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃₂	C₂	1	2	yes	maximal, complemented
2	C₁₁×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	#10587142	—	3	2	no	maximal
4	C₂×C₃×D₃₃	—	2	2	no	—
5	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	D₁₃₂	D₃	1	2	yes	complemented
7	C₃×D₄₄	—	3	2	no	—
8	C₁₁×C₃⋊C₈	—	3	2	no	—
9	C₁₁×C₃⋊C₈	—	6	1	no	—
10	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
11	C₃×D₃₃	—	4	2	no	—
12	D₈₈	—	9	1	no	Hall
13	#3713	—	11	1	no	maximal, Hall
14	C₂×D₃₃	—	2	2	no	—
15	C₂×C₃×D₁₁	—	6	2	no	—
16	C₃×C₄×C₁₁	—	2	1	no	—
17	C₃×C₄×C₁₁	C₂×D₃	1	2	yes	—
18	C₃²×C₁₁	D₈	1	1	yes	characteristic, complemented, Hall
19	D₄₄	—	3	2	no	—
20	C₈×C₁₁	—	9	1	no	—
21	C₃×D₁₂	—	11	2	no	—
22	C₃⋊(C₃⋊C₈)	D₁₁	1	1	yes	characteristic, complemented
23	C₂×C₃×C₁₁	—	2	1	no	—
24	C₂×C₃×C₁₁	#67	1	2	yes	—
25	D₃₃	—	4	2	no	—
26	C₃×D₁₁	—	12	2	no	—
27	#213	—	33	2	no	—
28	C₂×D₁₁	—	6	2	no	—
29	C₄×C₁₁	D₃²	1	1	yes	characteristic
30	C₂×C₃×D₃	—	22	2	no	—
31	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
32	C₃×C₁₁	—	2	1	no	—
33	C₃×C₁₁	#213	1	2	yes	complemented
34	C₃×D₄	—	33	2	no	—
35	D₁₂	—	11	2	no	—
36	C₃⋊C₈	—	3	2	no	—
37	C₃⋊C₈	—	6	1	no	—
38	C₂×C₁₁	#625	1	1	yes	characteristic
39	D₁₁	—	12	2	no	—
40	C₂×C₃²	D₄₄	1	1	yes	characteristic
41	C₃×D₃	—	44	2	no	—
42	D₈	—	99	1	no	Sylow
43	C₂²×C₃	—	66	2	no	—
44	C₂×D₃	—	22	2	no	—
45	C₃×C₄	—	2	1	no	—
46	C₃×C₄	D₃×D₁₁	1	2	yes	—
47	C₁₁	#3713	1	1	yes	characteristic, complemented, Sylow
48	C₃²	D₈₈	1	1	yes	characteristic, complemented, Sylow
49	D₄	—	33	2	no	—
50	C₈	—	9	1	no	—
51	C₂×C₃	—	2	1	no	—
52	C₂×C₃	—	132	2	no	—
53	C₂×C₃	#63141	1	2	yes	—
54	D₃	—	44	2	no	—
55	C₂²	—	66	2	no	—
56	C₄	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic
57	C₃	—	2	1	no	—
58	C₃	#10587142	1	2	yes	complemented
59	C₂	—	132	2	no	—
60	C₂	#11716247	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716247
commutator, Fitting, cosocle	C₃²×C₄×C₁₁	C₂²
Frattini, hypercenter	C₄	(C₃⋊D₃)⋊D₁₁
socle	C₂×C₃²×C₁₁	D₄
hypocenter	C₃²×C₁₁	D₈
LCS	G ▷ C₃²×C₄×C₁₁ ▷ C₂×C₃²×C₁₁ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₃₂	C₂	semidirect
2. C₁₁×C₃⋊(C₃⋊C₈)	C₂	semidirect
6. D₁₃₂	D₃	semidirect
18. C₃²×C₁₁	D₈	semidirect
22. C₃⋊(C₃⋊C₈)	D₁₁	semidirect
33. C₃×C₁₁	#213	semidirect
47. C₁₁	#3713	semidirect
48. C₃²	D₈₈	semidirect
58. C₃	#10587142	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₁₃₂	2
C₁₁×C₃⋊(C₃⋊C₈)	2
#10587142	3
#3713	11