Subgroups — #20266089

Order 6464.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#15692324	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#87938	—	2	1	no	—
5	#13108077	—	2	1	no	—
6	D₄×D₁₀₁	—	2	1	no	—
7	D₈₀₈	C₄	1	1	yes	characteristic, complemented
8	#13108059	—	2	1	no	—
9	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
10	D₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
11	C₂²×D₁₀₁	—	4	1	no	—
12	C₂×#87938	—	4	1	no	—
13	D₄×C₁₀₁	—	2	1	no	—
14	C₂²⋊D₁₀₁	—	4	1	no	—
15	D₄₀₄	—	2	1	no	—
16	C₄×D₁₀₁	D₄	1	1	yes	characteristic
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	1	no	—
22	C₂×D₁₀₁	—	8	1	no	—
23	C₂×D₁₀₁	D₈	1	1	yes	characteristic
24	#87938	—	8	1	no	—
25	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
26	Dic₁₀₁	SD₁₆	1	1	yes	characteristic
27	C₂×C₁₀₁	—	8	1	no	—
28	C₂×C₁₀₁	#102	1	1	yes	characteristic
29	D₁₀₁	—	8	1	no	—
30	D₁₀₁	D₁₆	1	1	yes	characteristic
31	D₁₀₁	SD₃₂	1	1	yes	characteristic
32	C₁₀₁	#357	1	1	yes	characteristic, complemented, Sylow
33	#357	—	101	1	no	maximal, Sylow
34	C₂×D₈	—	101	1	no	—
35	C₂×C₁₆	—	101	1	no	—
36	#107	—	101	1	no	—
37	C₂×D₄	—	202	1	no	—
38	D₈	—	101	1	no	—
39	D₈	—	202	1	no	—
40	D₈	#87938	1	1	yes	characteristic, complemented
41	C₂×C₈	—	101	1	no	—
42	C₄⋊C₄	—	202	1	no	—
43	C₁₆	—	202	1	no	—
44	C₂³	—	404	1	no	—
45	D₄	—	2	1	no	—
46	D₄	—	404	1	no	—
47	D₄	—	202	1	no	—
48	C₂×C₄	—	101	1	no	—
49	C₂×C₄	—	404	1	no	—
50	C₈	—	101	1	no	—
51	C₈	C₂×#87938	1	1	yes	characteristic
52	C₂²	—	4	1	no	—
53	C₂²	—	808	1	no	—
54	C₂²	—	808	1	no	—
55	C₂²	—	101	1	no	—
56	C₂²	—	404	1	no	—
57	C₄	—	808	1	no	—
58	C₄	—	101	1	no	—
59	C₄	C₂²⋊#87938	1	1	yes	characteristic
60	C₂	—	8	1	no	—
61	C₂	—	808	1	no	—
62	C₂	—	101	1	no	—
63	C₂	—	101	1	no	—
64	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	#357
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. D₁₀₁⋊C₁₆	C₂	semidirect
2. #15692324	C₂	semidirect
7. D₈₀₈	C₄	semidirect
10. D₈×C₁₀₁	C₄	semidirect
32. C₁₀₁	#357	semidirect
40. D₈	#87938	semidirect