Subgroups — #13070873

Order 1408.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#66892	C₂	1	4	yes	maximal, complemented
3	#10622308	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×Q₁₆	—	2	1	no	—
6	C₂×C₁₁×Q₁₆	C₂²	1	2	yes	—
7	C₁₁×C₄⋊Q₈	—	2	1	no	—
8	C₂×D₈₈	—	2	1	no	—
9	C₂×D₈₈	C₂²	1	2	yes	—
10	#66927	—	2	1	no	—
11	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	#66892	—	2	8	no	—
13	C₂×C₁₁⋊C₁₆	C₂²	1	2	yes	—
14	C₂×Q₈×C₁₁	—	2	2	no	—
15	C₂×D₄₄	—	2	2	no	—
16	C₂×D₄₄	—	4	2	no	—
17	C₁₁×Q₁₆	—	2	4	no	—
18	C₁₁×Q₁₆	—	4	2	no	—
19	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
21	C₁₁×C₄⋊C₄	—	4	2	no	—
22	C₄²×C₁₁	D₄	1	1	yes	characteristic
23	D₈₈	—	2	4	no	—
24	D₈₈	—	4	2	no	—
25	C₁₁⋊C₁₆	D₄	1	4	yes	complemented
26	#2248	—	11	1	no	maximal, Sylow
27	C₂²×D₁₁	—	4	2	no	—
28	Q₈×C₁₁	—	4	2	no	—
29	Q₈×C₁₁	—	4	2	no	—
30	C₂×C₄×C₁₁	—	4	2	no	—
31	C₂×C₄×C₁₁	D₈	1	2	yes	—
32	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
33	D₄₄	—	4	2	no	—
34	D₄₄	—	4	2	no	—
35	D₄₄	—	8	4	no	—
36	C₈×C₁₁	D₈	1	2	yes	—
37	C₈×C₁₁	C₂×D₄	1	2	yes	—
38	C₂×SD₃₂	—	11	4	no	—
39	#494	D₁₁	1	1	yes	characteristic, complemented
40	#493	—	11	1	no	—
41	C₄×C₁₆	—	11	1	no	—
42	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
43	C₂×D₁₁	—	8	2	no	—
44	C₂×D₁₁	—	8	4	no	—
45	C₄×C₁₁	—	8	2	no	—
46	C₄×C₁₁	SD₃₂	1	4	yes	complemented
47	C₄×C₁₁	#127	1	1	yes	characteristic
48	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
49	C₂×Q₁₆	—	2	1	no	—
50	C₂×Q₁₆	C₂×D₁₁	1	2	yes	—
51	C₂×D₈	—	11	2	no	—
52	C₂×D₈	—	22	1	no	—
53	C₄⋊Q₈	—	2	1	no	—
54	#127	—	22	1	no	—
55	SD₃₂	—	22	8	no	—
56	C₂×C₁₆	—	11	2	no	—
57	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
58	C₂×C₁₁	#493	1	1	yes	characteristic
59	C₂×C₁₁	C₂×SD₃₂	1	2	yes	—
60	D₁₁	—	16	2	no	—
61	C₂×Q₈	—	2	2	no	—
62	C₂×D₄	—	22	2	no	—
63	C₂×D₄	—	44	2	no	—
64	Q₁₆	—	2	4	no	—
65	Q₁₆	—	4	2	no	—
66	D₈	—	22	4	no	—
67	D₈	—	44	2	no	—
68	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
69	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
70	C₄⋊C₄	—	4	2	no	—
71	C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
72	C₁₆	—	11	4	no	—
73	C₁₁	#2248	1	1	yes	characteristic, complemented, Sylow
74	C₂³	—	44	2	no	—
75	Q₈	—	4	2	no	—
76	Q₈	—	4	2	no	—
77	D₄	—	44	2	no	—
78	D₄	—	44	2	no	—
79	D₄	—	88	4	no	—
80	C₂×C₄	—	4	2	no	—
81	C₂×C₄	#4323	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
83	C₈	#4323	1	2	yes	—
84	C₈	D₄×D₁₁	1	2	yes	—
85	C₂²	—	88	4	no	—
86	C₂²	—	88	2	no	—
87	C₂²	C₂×#4323	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	#66892	1	4	yes	complemented
90	C₄	C₂×#4323	1	1	yes	characteristic
91	C₄	#66993	1	1	yes	characteristic
92	C₂	—	176	2	no	—
93	C₂	#10622686	1	1	yes	characteristic
94	C₂	C₂×#66892	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#4323
commutator, cosocle	C₂×C₈×C₁₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₁₁×#494	C₂
socle	C₂²×C₁₁	C₂×D₈
prime radical	#10622308	C₂
hypercenter	#494	D₁₁
hypocenter	C₁₁	#2248
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
1. C₁₁×#494	C₂	semidirect
2. C₂×#66892	C₂	semidirect
4. C₄×C₁₁⋊C₁₆	C₂	semidirect
25. C₁₁⋊C₁₆	D₄	semidirect
39. #494	D₁₁	semidirect
46. C₄×C₁₁	SD₃₂	semidirect
73. C₁₁	#2248	semidirect
89. C₄	#66892	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#494	2
C₂×#66892	2
#10622308	2
C₄×C₁₁⋊C₁₆	2
#2248	11