Subgroups — #20264983

Order 6464.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692277	C₂	1	1	yes	maximal, characteristic
2	C₂×#13108049	C₂	1	1	yes	maximal, characteristic, complemented
3	#108×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#13108074	—	2	1	no	—
5	Dic₄₀₄	C₄	1	1	yes	characteristic
6	#13108063	—	2	1	no	—
7	D₈₀₈	C₄	1	1	yes	characteristic
8	#13108049	—	2	1	no	—
9	M₁₆×C₁₀₁	—	2	1	no	—
10	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
12	C₂²⋊D₁₀₁	—	4	1	no	—
13	D₄₀₄	—	2	1	no	—
14	C₄×D₁₀₁	—	4	1	no	—
15	Dic₂₀₂	—	2	1	no	—
16	C₈×C₁₀₁	—	4	1	no	—
17	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₁₀₁	D₄	1	1	yes	characteristic
19	C₂²×C₁₀₁	SD₁₆	1	1	yes	characteristic
20	C₂×D₁₀₁	—	4	1	no	—
21	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₀₁	D₈	1	1	yes	characteristic
23	Dic₁₀₁	—	4	1	no	—
24	C₂×C₁₀₁	—	2	1	no	—
25	C₂×C₁₀₁	#102	1	1	yes	characteristic
26	D₁₀₁	—	8	1	no	—
27	C₁₀₁	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	101	1	no	maximal, Sylow
29	#135	—	101	1	no	—
30	C₂×C₁₆	—	101	1	no	—
31	#108	D₁₀₁	1	1	yes	characteristic, complemented
32	#41	—	202	1	no	—
33	Q₁₆	—	101	1	no	—
34	SD₁₆	—	202	1	no	—
35	D₈	—	101	1	no	—
36	M₁₆	—	2	1	no	—
37	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
38	C₁₆	—	202	1	no	—
39	Q₈	—	202	1	no	—
40	D₄	—	404	1	no	—
41	D₄	—	202	1	no	—
42	C₂×C₄	—	404	1	no	—
43	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
44	C₈	—	4	1	no	—
45	C₈	C₄×D₁₀₁	1	1	yes	characteristic
46	C₈	D₄₀₄	1	1	yes	characteristic
47	C₂²	—	404	1	no	—
48	C₂²	#13108061	1	1	yes	characteristic
49	C₄	—	404	1	no	—
50	C₄	#13108051	1	1	yes	characteristic
51	C₄	#13108059	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	808	1	no	—
54	C₂	#15692175	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13108059
commutator	C₈×C₁₀₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₁
Fitting	#108×C₁₀₁	C₂
socle	C₂×C₁₀₁	#102
hypercenter	#108	D₁₀₁
hypocenter	C₁₀₁	#359
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×#13108049	C₂	semidirect
3. #108×C₁₀₁	C₂	semidirect
27. C₁₀₁	#359	semidirect
31. #108	D₁₀₁	semidirect