Subgroups — #20266095

Order 6464.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692330	C₂	1	1	yes	maximal, characteristic, complemented
2	#15692325	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#13108084	—	2	1	no	—
5	#13108077	—	2	1	no	—
6	D₄×D₁₀₁	—	2	1	no	—
7	D₈₀₈	C₄	1	1	yes	characteristic
8	#13108059	—	2	1	no	—
9	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
10	D₈×C₁₀₁	C₄	1	1	yes	characteristic
11	C₂²×D₁₀₁	—	4	1	no	—
12	D₄×C₁₀₁	—	2	1	no	—
13	C₂²⋊D₁₀₁	—	4	1	no	—
14	D₄₀₄	—	2	1	no	—
15	C₄×D₁₀₁	D₄	1	1	yes	characteristic
16	#11717581	—	4	1	no	—
17	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	#11717579	D₄	1	1	yes	characteristic
19	C₂²×C₁₀₁	—	4	1	no	—
20	C₂×D₁₀₁	—	4	1	no	—
21	C₂×D₁₀₁	—	8	2	no	—
22	C₂×D₁₀₁	SD₁₆	1	1	yes	characteristic
23	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₀₁	D₈	1	1	yes	characteristic
25	C₂×C₁₀₁	—	8	1	no	—
26	C₂×C₁₀₁	#102	1	1	yes	characteristic
27	D₁₀₁	—	2	1	no	—
28	D₁₀₁	—	8	1	no	—
29	C₁₀₁	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	101	1	no	maximal, Sylow
31	C₂×D₈	—	101	1	no	—
32	M₃₂	—	101	1	no	—
33	#108	—	101	1	no	—
34	C₂×D₄	—	202	1	no	—
35	D₈	—	101	1	no	—
36	D₈	—	202	1	no	—
37	D₈	#87938	1	1	yes	characteristic
38	M₁₆	—	202	1	no	—
39	C₂×C₈	—	101	1	no	—
40	C₁₆	—	202	1	no	—
41	C₂³	—	404	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	404	1	no	—
44	D₄	—	202	1	no	—
45	C₂×C₄	—	101	1	no	—
46	C₈	—	101	1	no	—
47	C₈	—	404	1	no	—
48	C₈	C₂×#87938	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	808	2	no	—
51	C₂²	—	101	1	no	—
52	C₂²	—	404	1	no	—
53	C₄	—	101	1	no	—
54	C₄	C₂²⋊#87938	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	808	1	no	—
57	C₂	—	202	1	no	—
58	C₂	#15692317	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692317
commutator	C₈×C₁₀₁	C₂×C₄
Frattini	C₈	C₂×#87938
Fitting	D₈×C₁₀₁	C₄
socle	C₂×C₁₀₁	#102
hypercenter	D₈	#87938
hypocenter	C₁₀₁	#361
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #15692330	C₂	semidirect
2. #15692325	C₂	semidirect
29. C₁₀₁	#361	semidirect