Subgroups — #11760886

Order 1056.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63142	C₂	1	4	yes	maximal, complemented
4	C₃×C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#66993	—	3	1	no	maximal, Hall
6	C₂²×D₃₃	C₂²	1	2	yes	—
7	C₂²×D₃×C₁₁	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₁	C₂²	1	1	yes	characteristic
9	D₁₃₂	—	2	2	no	—
10	C₁₁×D₁₂	—	2	2	no	—
11	C₂×C₃×Dic₁₁	C₂²	1	2	yes	—
12	#63142	—	2	8	no	—
13	C₂×D₄×C₁₁	—	3	1	no	—
14	C₂×C₂²⋊D₁₁	—	3	4	no	—
15	C₂×D₄₄	—	3	1	no	—
16	C₄×Dic₁₁	D₃	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×D₃₃	—	2	4	no	—
19	C₂×D₃₃	—	2	2	no	—
20	C₂×D₃×C₁₁	—	2	4	no	—
21	C₂×D₃×C₁₁	—	2	2	no	—
22	C₃×C₄×C₁₁	D₄	1	2	yes	complemented
23	C₃×Dic₁₁	D₄	1	4	yes	complemented
24	#874	—	11	1	no	maximal, Hall
25	C₂³×C₁₁	—	3	2	no	—
26	C₂²×D₁₁	—	3	2	no	—
27	D₄×C₁₁	—	6	2	no	—
28	C₂×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
29	C₂²⋊D₁₁	—	6	8	no	—
30	C₂×Dic₁₁	C₂×D₃	1	2	yes	—
31	D₄₄	—	6	2	no	—
32	C₂×C₃×C₁₁	C₂×D₄	1	2	yes	—
33	C₂×C₃×C₁₁	C₂×D₄	1	1	yes	characteristic
34	D₃₃	—	4	2	no	—
35	D₃×C₁₁	—	4	2	no	—
36	C₂×D₁₂	—	11	4	no	—
37	C₂×D₁₂	—	11	1	no	—
38	C₂×D₁₂	D₁₁	1	1	yes	characteristic, complemented
39	C₃×C₄²	—	11	1	no	—
40	C₂²×C₁₁	—	6	2	no	—
41	C₂²×C₁₁	—	6	4	no	—
42	C₂²×C₁₁	C₂²×D₃	1	1	yes	characteristic
43	C₂×D₁₁	—	6	2	no	—
44	C₂×D₁₁	—	6	4	no	—
45	C₄×C₁₁	D₁₂	1	2	yes	complemented
46	Dic₁₁	D₁₂	1	4	yes	complemented
47	C₃×C₁₁	#127	1	1	yes	characteristic, complemented, Hall
48	#127	—	33	1	no	Sylow
49	C₂²×D₃	—	11	2	no	—
50	C₂²×D₃	C₂×D₁₁	1	2	yes	—
51	C₂×C₃×C₄	—	11	2	no	—
52	C₂×C₃×C₄	C₂×D₁₁	1	1	yes	characteristic
53	D₁₂	—	2	2	no	—
54	D₁₂	—	22	8	no	—
55	D₁₂	—	22	2	no	—
56	C₂×C₁₁	—	12	2	no	—
57	C₂×C₁₁	C₂×D₁₂	1	2	yes	—
58	C₂×C₁₁	C₂×D₁₂	1	1	yes	characteristic
59	D₁₁	—	12	2	no	—
60	C₂×D₄	—	3	1	no	—
61	C₂×D₄	—	33	4	no	—
62	C₂×D₄	—	33	1	no	—
63	C₄²	—	11	1	no	—
64	C₂²×C₃	C₂²×D₁₁	1	1	yes	characteristic
65	C₂×D₃	—	2	4	no	—
66	C₂×D₃	—	2	2	no	—
67	C₂×D₃	—	22	4	no	—
68	C₂×D₃	—	22	2	no	—
69	C₃×C₄	—	11	4	no	—
70	C₃×C₄	C₂²⋊D₁₁	1	2	yes	complemented
71	C₁₁	#874	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	3	2	no	—
73	C₂³	—	33	2	no	—
74	D₄	—	6	2	no	—
75	D₄	—	66	8	no	—
76	D₄	—	66	2	no	—
77	C₂×C₄	—	11	2	no	—
78	C₂×C₄	D₃×D₁₁	1	1	yes	characteristic
79	C₂×C₃	D₄×D₁₁	1	2	yes	—
80	C₂×C₃	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
81	D₃	—	4	2	no	—
82	D₃	—	44	2	no	—
83	C₂²	—	6	4	no	—
84	C₂²	—	6	2	no	—
85	C₂²	—	66	4	no	—
86	C₂²	—	66	2	no	—
87	C₂²	C₂×D₃×D₁₁	1	1	yes	characteristic
88	C₄	—	11	4	no	—
89	C₄	#63142	1	2	yes	complemented
90	C₃	#66993	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	12	2	no	—
92	C₂	—	132	2	no	—
93	C₂	D₁₁×D₁₂	1	2	yes	—
94	C₂	C₂×#63142	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₁
commutator, socle, cosocle	C₂²×C₃×C₁₁	C₂³
Fitting	C₂×C₃×C₄×C₁₁	C₂²
hypercenter	C₂×C₄	D₃×D₁₁
hypocenter	C₃×C₁₁	#127
LCS	G ▷ C₂²×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₃₂	C₂	semidirect
2. C₂×C₁₁×D₁₂	C₂	semidirect
3. C₂×#63142	C₂	semidirect
4. C₃×C₄×Dic₁₁	C₂	semidirect
16. C₄×Dic₁₁	D₃	semidirect
22. C₃×C₄×C₁₁	D₄	semidirect
23. C₃×Dic₁₁	D₄	semidirect
38. C₂×D₁₂	D₁₁	semidirect
45. C₄×C₁₁	D₁₂	semidirect
46. Dic₁₁	D₁₂	semidirect
47. C₃×C₁₁	#127	semidirect
70. C₃×C₄	C₂²⋊D₁₁	semidirect
71. C₁₁	#874	semidirect
89. C₄	#63142	semidirect
90. C₃	#66993	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃₂	2
C₂×C₁₁×D₁₂	2
C₂×#63142	2
C₃×C₄×Dic₁₁	2
#66993	3
#874	11