Subgroups — #14641664

Order 2816.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₅₂	C₂	1	1	yes	maximal, characteristic
2	#13066820	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₇₆	—	2	1	no	—
5	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	#10622144	—	2	1	no	—
7	D₃₅₂	—	2	1	no	—
8	D₃₅₂	C₄	1	2	yes	—
9	C₁₁×C₆₄	—	2	1	no	—
10	C₂×D₈₈	—	4	1	no	—
11	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
12	#66883	—	4	1	no	—
13	D₁₇₆	—	2	2	no	—
14	D₁₇₆	—	4	1	no	—
15	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₁×C₃₂	D₄	1	1	yes	characteristic
17	#7541	—	11	1	no	maximal, Sylow
18	C₂×D₄₄	—	8	1	no	—
19	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
20	#4318	—	8	1	no	—
21	D₈₈	—	4	2	no	—
22	D₈₈	—	8	1	no	—
23	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
25	C₂×D₃₂	—	11	1	no	—
26	M₁₂₈	D₁₁	1	1	yes	characteristic, complemented
27	#1425	—	11	1	no	—
28	C₂²×D₁₁	—	16	1	no	—
29	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
30	D₄₄	—	8	2	no	—
31	D₄₄	—	16	1	no	—
32	C₈×C₁₁	#102	1	1	yes	characteristic
33	C₈×C₁₁	SD₃₂	1	1	yes	characteristic
34	C₁₁⋊C₈	—	16	1	no	—
35	C₂×D₁₆	—	22	1	no	—
36	D₃₂	—	11	2	no	—
37	D₃₂	—	22	1	no	—
38	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
39	#368	—	22	1	no	—
40	C₆₄	—	2	1	no	—
41	C₂²×C₁₁	SD₆₄	1	1	yes	characteristic
42	C₂×D₁₁	—	16	2	no	—
43	C₂×D₁₁	—	32	2	no	—
44	C₄×C₁₁	#357	1	1	yes	characteristic
45	C₄×C₁₁	D₃₂	1	1	yes	characteristic
46	C₂×D₈	—	44	1	no	—
47	D₁₆	—	22	2	no	—
48	D₁₆	—	44	1	no	—
49	C₂×C₁₆	D₄₄	1	1	yes	characteristic
50	#108	—	44	1	no	—
51	C₃₂	C₄×D₁₁	1	1	yes	characteristic
52	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
53	C₂×C₁₁	—	2	1	no	—
54	C₂×C₁₁	#1415	1	1	yes	characteristic
55	D₁₁	—	32	2	no	—
56	C₂×D₄	—	88	1	no	—
57	D₈	—	44	2	no	—
58	D₈	—	88	1	no	—
59	M₁₆	—	88	1	no	—
60	C₂×C₈	D₈₈	1	1	yes	characteristic
61	C₁₆	#4314	1	1	yes	characteristic
62	C₁₆	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
63	C₁₁	#7541	1	1	yes	characteristic, complemented, Sylow
64	C₂³	—	176	1	no	—
65	D₄	—	88	2	no	—
66	D₄	—	176	1	no	—
67	C₂×C₄	D₁₇₆	1	1	yes	characteristic
68	C₈	—	176	1	no	—
69	C₈	#66864	1	1	yes	characteristic
70	C₈	#66885	1	1	yes	characteristic
71	C₂²	—	352	2	no	—
72	C₂²	—	176	2	no	—
73	C₂²	#10622087	1	1	yes	characteristic
74	C₄	D₃₅₂	1	1	yes	characteristic
75	C₄	#10622147	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	352	2	no	—
78	C₂	#13066795	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13066795
commutator	C₁₁×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₁₁×M₁₂₈	C₂
socle	C₂×C₁₁	#1415
prime radical	C₂×D₃₅₂	C₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₁
hypocenter	C₁₁	#7541
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #13066820	C₂	semidirect
3. C₁₁×M₁₂₈	C₂	semidirect
26. M₁₂₈	D₁₁	semidirect
63. C₁₁	#7541	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₅₂	2
#13066820	2
C₁₁×M₁₂₈	2
#7541	11