Subgroups — #20264988

Order 6464.

58 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	#15692187	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#13108074	—	2	1	no	—
5	Dic₄₀₄	C₄	1	1	yes	characteristic, complemented
6	#13108063	—	2	1	no	—
7	D₈₀₈	C₄	1	1	yes	characteristic, complemented
8	C₄⋊Dic₁₀₁	—	2	1	no	—
9	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₀₁	—	2	1	no	—
11	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
12	C₂²⋊D₁₀₁	—	4	1	no	—
13	C₂×Dic₁₀₁	—	4	1	no	—
14	D₄₀₄	—	2	1	no	—
15	C₄×D₁₀₁	—	4	1	no	—
16	Dic₂₀₂	—	2	1	no	—
17	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₁₀₁	D₄	1	1	yes	characteristic
19	C₂²×C₁₀₁	D₈	1	1	yes	characteristic
20	C₂×D₁₀₁	—	4	1	no	—
21	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₀₁	SD₁₆	1	1	yes	characteristic
23	Dic₁₀₁	—	4	1	no	—
24	Dic₁₀₁	—	8	1	no	—
25	C₂×C₁₀₁	—	2	1	no	—
26	C₂×C₁₀₁	#102	1	1	yes	characteristic
27	D₁₀₁	—	8	1	no	—
28	C₁₀₁	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	101	1	no	maximal, Sylow
30	#135	—	101	1	no	—
31	M₃₂	D₁₀₁	1	1	yes	characteristic, complemented
32	#106	—	101	1	no	—
33	#41	—	202	1	no	—
34	Q₁₆	—	101	1	no	—
35	SD₁₆	—	202	1	no	—
36	D₈	—	101	1	no	—
37	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
38	C₄⋊C₄	—	202	1	no	—
39	C₁₆	—	2	1	no	—
40	Q₈	—	202	1	no	—
41	D₄	—	404	1	no	—
42	D₄	—	202	1	no	—
43	C₂×C₄	—	404	1	no	—
44	C₂×C₄	—	404	1	no	—
45	C₂×C₄	D₄₀₄	1	1	yes	characteristic
46	C₈	C₄×D₁₀₁	1	1	yes	characteristic
47	C₈	C₂²⋊D₁₀₁	1	1	yes	characteristic
48	C₂²	—	404	1	no	—
49	C₂²	D₈₀₈	1	1	yes	characteristic
50	C₄	—	808	1	no	—
51	C₄	—	404	1	no	—
52	C₄	#13108051	1	1	yes	characteristic
53	C₄	#13108063	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	808	1	no	—
56	C₂	#15692177	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692177
commutator	C₈×C₁₀₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₁
Fitting	M₃₂×C₁₀₁	C₂
socle	C₂×C₁₀₁	#102
hypercenter	M₃₂	D₁₀₁
hypocenter	C₁₀₁	#360
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #15692187	C₂	semidirect
3. M₃₂×C₁₀₁	C₂	semidirect
5. Dic₄₀₄	C₄	semidirect
7. D₈₀₈	C₄	semidirect
28. C₁₀₁	#360	semidirect
31. M₃₂	D₁₀₁	semidirect