Subgroups — #13097087

Order 1584.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11716270	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₁×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₃⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#10587207	—	3	1	no	maximal
5	#10587152	—	3	1	no	maximal
6	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₃₃	—	2	1	no	—
8	C₃×C₁₁×Dic₃	—	2	1	no	—
9	C₃×Q₈×C₁₁	—	3	1	no	—
10	Dic₆₆	—	3	1	no	—
11	Dic₆₆	—	3	1	no	—
12	Dic₆₆	—	6	1	no	—
13	C₁₁×Dic₆	D₃	1	1	yes	characteristic
14	C₃⋊(C₁₁⋊C₈)	D₃	1	1	yes	characteristic
15	C₃×C₁₁⋊C₈	—	3	1	no	—
16	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
17	#4326	—	9	1	no	Hall
18	#3719	—	11	1	no	maximal, Hall
19	C₃×C₄×C₁₁	—	2	1	no	—
20	C₃×C₄×C₁₁	—	6	1	no	—
21	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
22	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
23	Dic₃₃	—	6	2	no	—
24	Dic₃₃	—	6	1	no	—
25	Dic₃₃	—	6	1	no	—
26	C₁₁×Dic₃	—	2	1	no	—
27	C₃²×C₁₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
28	Q₈×C₁₁	—	3	1	no	—
29	Dic₂₂	—	9	1	no	—
30	C₁₁⋊C₈	—	3	1	no	—
31	#634	—	11	1	no	—
32	C₃×Dic₆	D₁₁	1	1	yes	characteristic
33	C₃×C₃⋊C₈	—	11	1	no	—
34	C₂×C₃×C₁₁	—	2	1	no	—
35	C₂×C₃×C₁₁	D₁₂	1	1	yes	characteristic
36	C₂×C₃×C₁₁	#67	1	1	yes	characteristic
37	#216	—	33	1	no	—
38	Dic₁₂	—	33	1	no	—
39	C₄×C₁₁	—	6	1	no	—
40	C₄×C₁₁	D₃²	1	1	yes	characteristic
41	Dic₁₁	—	18	1	no	—
42	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
43	C₃⋊Dic₃	—	22	1	no	—
44	C₃×Dic₃	—	2	1	no	—
45	C₃×C₁₁	—	2	1	no	—
46	C₃×C₁₁	Dic₁₂	1	1	yes	characteristic, complemented
47	C₃×C₁₁	#216	1	1	yes	characteristic, complemented
48	C₃×Q₈	—	3	1	no	—
49	Dic₆	—	33	1	no	—
50	Dic₆	—	33	1	no	—
51	Dic₆	—	66	1	no	—
52	Dic₆	D₃₃	1	1	yes	characteristic
53	C₃×C₈	—	33	1	no	—
54	C₃⋊C₈	—	11	1	no	—
55	C₂×C₁₁	#626	1	1	yes	characteristic
56	C₂×C₃²	C₂²⋊D₁₁	1	1	yes	characteristic
57	Q₁₆	—	99	1	no	Sylow
58	C₃×C₄	—	2	1	no	—
59	C₃×C₄	—	6	1	no	—
60	C₃×C₄	D₃×D₁₁	1	1	yes	characteristic
61	C₃×C₄	C₂×D₃₃	1	1	yes	characteristic
62	Dic₃	—	2	1	no	—
63	Dic₃	—	66	2	no	—
64	Dic₃	—	66	1	no	—
65	Dic₃	—	66	1	no	—
66	C₁₁	#3719	1	1	yes	characteristic, complemented, Sylow
67	C₃²	#4326	1	1	yes	characteristic, complemented, Sylow
68	Q₈	—	3	1	no	—
69	Q₈	—	99	1	no	—
70	C₈	—	33	1	no	—
71	C₂×C₃	—	2	1	no	—
72	C₂×C₃	#63142	1	1	yes	characteristic
73	C₂×C₃	#63159	1	1	yes	characteristic
74	C₄	—	6	1	no	—
75	C₄	—	198	1	no	—
76	C₄	D₃×D₃₃	1	1	yes	characteristic
77	C₃	—	2	1	no	—
78	C₃	#10587152	1	1	yes	characteristic, complemented
79	C₃	#10587207	1	1	yes	characteristic, complemented
80	C₂	#11716242	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716242
commutator, Fitting, cosocle	C₃²×C₄×C₁₁	C₂²
Frattini, hypercenter	C₄	D₃×D₃₃
socle, prime radical	C₂×C₃²×C₁₁	D₄
hypocenter	C₃²×C₁₁	Q₁₆
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
27. C₃²×C₁₁	Q₁₆	semidirect
46. C₃×C₁₁	Dic₁₂	semidirect
47. C₃×C₁₁	#216	semidirect
66. C₁₁	#3719	semidirect
67. C₃²	#4326	semidirect
78. C₃	#10587152	semidirect
79. C₃	#10587207	semidirect

Maximal subgroups

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

subgroup	index
#11716270	2
C₃×C₁₁×Dic₆	2
C₃×C₃⋊(C₁₁⋊C₈)	2
#10587207	3
#10587152	3
#3719	11