Subgroups — #14641667

Order 2816.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₆	C₂	1	1	yes	maximal, characteristic
2	#13066820	C₂	1	1	yes	maximal, characteristic
3	C₁₁×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₈	—	2	1	no	—
5	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	#10622144	—	2	1	no	—
7	Dic₁₇₆	—	2	1	no	—
8	Dic₁₇₆	C₄	1	2	yes	—
9	C₁₁×C₆₄	—	2	1	no	—
10	C₂×Dic₄₄	—	4	1	no	—
11	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
12	#66883	—	4	1	no	—
13	Dic₈₈	—	2	2	no	—
14	Dic₈₈	—	4	1	no	—
15	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₁×C₃₂	D₄	1	1	yes	characteristic
17	#7542	—	11	1	no	maximal, Sylow
18	C₂×Dic₂₂	—	8	1	no	—
19	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
20	#4318	—	8	1	no	—
21	Dic₄₄	—	4	2	no	—
22	Dic₄₄	—	8	1	no	—
23	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
25	C₂×Q₆₄	—	11	1	no	—
26	M₁₂₈	D₁₁	1	1	yes	characteristic
27	#1425	—	11	1	no	—
28	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
29	C₂×Dic₁₁	—	16	1	no	—
30	Dic₂₂	—	8	2	no	—
31	Dic₂₂	—	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×Q₃₂	—	22	1	no	—
36	Q₆₄	—	11	2	no	—
37	Q₆₄	—	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	C₄×C₁₁	#357	1	1	yes	characteristic
43	C₄×C₁₁	D₃₂	1	1	yes	characteristic
44	Dic₁₁	—	16	2	no	—
45	C₂×Q₁₆	—	44	1	no	—
46	Q₃₂	—	22	2	no	—
47	Q₃₂	—	44	1	no	—
48	C₂×C₁₆	D₄₄	1	1	yes	characteristic
49	#108	—	44	1	no	—
50	C₃₂	C₄×D₁₁	1	1	yes	characteristic
51	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
52	C₂×C₁₁	—	2	1	no	—
53	C₂×C₁₁	#1415	1	1	yes	characteristic
54	C₂×Q₈	—	88	1	no	—
55	Q₁₆	—	44	2	no	—
56	Q₁₆	—	88	1	no	—
57	M₁₆	—	88	1	no	—
58	C₂×C₈	D₈₈	1	1	yes	characteristic
59	C₁₆	#4314	1	1	yes	characteristic
60	C₁₆	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
61	C₁₁	#7542	1	1	yes	characteristic, complemented, Sylow
62	Q₈	—	88	2	no	—
63	Q₈	—	176	1	no	—
64	C₂×C₄	—	176	1	no	—
65	C₂×C₄	D₁₇₆	1	1	yes	characteristic
66	C₈	—	176	1	no	—
67	C₈	#66864	1	1	yes	characteristic
68	C₈	#66885	1	1	yes	characteristic
69	C₂²	#10622087	1	1	yes	characteristic
70	C₄	—	176	2	no	—
71	C₄	D₃₅₂	1	1	yes	characteristic
72	C₄	#10622147	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	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	C₂²×C₁₁	SD₆₄
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₁
hypocenter	C₁₁	#7542
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
61. C₁₁	#7542	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₇₆	2
#13066820	2
C₁₁×M₁₂₈	2
#7542	11