Subgroups — #14641658

Order 2816.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070925	C₂	1	1	yes	maximal, characteristic
2	#13066820	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622517	—	2	1	no	—
5	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	#10622144	—	2	1	no	—
7	Dic₁₇₆	C₄	1	1	yes	characteristic
8	#10622087	—	2	1	no	—
9	D₃₅₂	C₄	1	1	yes	characteristic
10	C₁₁×C₆₄	—	2	1	no	—
11	#66957	—	4	1	no	—
12	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
13	#66883	—	4	1	no	—
14	Dic₈₈	—	2	1	no	—
15	#66864	—	4	1	no	—
16	D₁₇₆	—	2	1	no	—
17	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₁₁×C₃₂	D₄	1	1	yes	characteristic
19	#7539	—	11	1	no	maximal, Sylow
20	#4339	—	8	1	no	—
21	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
22	#4318	—	8	1	no	—
23	Dic₄₄	—	4	1	no	—
24	D₈₈	—	4	1	no	—
25	#4314	—	8	1	no	—
26	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
28	#2262	—	11	1	no	—
29	C₂×C₆₄	D₁₁	1	1	yes	characteristic, complemented
30	#1425	—	11	1	no	—
31	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
32	C₂²⋊D₁₁	—	16	1	no	—
33	D₄₄	—	8	1	no	—
34	C₄×D₁₁	—	16	1	no	—
35	Dic₂₂	—	8	1	no	—
36	C₈×C₁₁	#102	1	1	yes	characteristic
37	C₈×C₁₁	SD₃₂	1	1	yes	characteristic
38	C₁₁⋊C₈	—	16	1	no	—
39	#508	—	22	1	no	—
40	Q₆₄	—	11	1	no	—
41	SD₆₄	—	22	1	no	—
42	D₃₂	—	11	1	no	—
43	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
44	#368	—	22	1	no	—
45	C₆₄	—	2	1	no	—
46	C₂²×C₁₁	SD₆₄	1	1	yes	characteristic
47	C₂×D₁₁	—	16	1	no	—
48	C₄×C₁₁	#357	1	1	yes	characteristic
49	C₄×C₁₁	D₃₂	1	1	yes	characteristic
50	Dic₁₁	—	16	1	no	—
51	#135	—	44	1	no	—
52	Q₃₂	—	22	1	no	—
53	SD₃₂	—	44	1	no	—
54	D₁₆	—	22	1	no	—
55	C₂×C₁₆	D₄₄	1	1	yes	characteristic
56	#108	—	44	1	no	—
57	C₃₂	C₄×D₁₁	1	1	yes	characteristic
58	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
59	C₂×C₁₁	—	2	1	no	—
60	C₂×C₁₁	#1415	1	1	yes	characteristic
61	D₁₁	—	32	1	no	—
62	#41	—	88	1	no	—
63	Q₁₆	—	44	1	no	—
64	SD₁₆	—	88	1	no	—
65	D₈	—	44	1	no	—
66	M₁₆	—	88	1	no	—
67	C₂×C₈	D₈₈	1	1	yes	characteristic
68	C₁₆	#4314	1	1	yes	characteristic
69	C₁₆	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
70	C₁₁	#7539	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	88	1	no	—
72	D₄	—	88	1	no	—
73	D₄	—	176	1	no	—
74	C₂×C₄	—	176	1	no	—
75	C₂×C₄	D₁₇₆	1	1	yes	characteristic
76	C₈	—	176	1	no	—
77	C₈	#66864	1	1	yes	characteristic
78	C₈	#66885	1	1	yes	characteristic
79	C₂²	—	176	1	no	—
80	C₂²	#10622087	1	1	yes	characteristic
81	C₄	—	176	1	no	—
82	C₄	D₃₅₂	1	1	yes	characteristic
83	C₄	#10622147	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	352	1	no	—
86	C₂	#13066795	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃₅₂
commutator	C₁₁×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₂×C₁₁×C₆₄	C₂
socle	C₂×C₁₁	#1415
prime radical	#13070925	C₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	C₂×C₆₄	D₁₁
hypocenter	C₁₁	#7539
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. #13066820	C₂	semidirect
3. C₂×C₁₁×C₆₄	C₂	semidirect
29. C₂×C₆₄	D₁₁	semidirect
70. C₁₁	#7539	semidirect

Maximal subgroups

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

subgroup	index
#13070925	2
#13066820	2
C₂×C₁₁×C₆₄	2
#7539	11