Subgroups — #20265004

Order 6464.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108049	C₂	1	1	yes	maximal, characteristic
2	#15692189	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₀₁	—	2	1	no	—
5	#13108049	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₀₁	—	2	1	no	—
8	C₂×C₄×C₁₀₁	—	4	1	no	—
9	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
10	C₂×Dic₁₀₁	—	4	1	no	—
11	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₀₁	Q₈	1	1	yes	characteristic
13	C₂²×C₁₀₁	D₈	1	1	yes	characteristic
14	C₄×C₁₀₁	—	8	1	no	—
15	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₀₁	Q₁₆	1	1	yes	characteristic
17	Dic₁₀₁	—	8	1	no	—
18	C₂×C₁₀₁	#107	1	1	yes	characteristic
19	C₂×C₁₀₁	SD₃₂	1	1	yes	characteristic
20	C₂×C₁₀₁	SD₃₂	1	1	yes	characteristic
21	C₁₀₁	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	101	1	no	maximal, Sylow
23	C₂×C₁₆	—	101	1	no	—
24	#107	—	101	1	no	—
25	#107	D₁₀₁	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	202	1	no	—
29	C₁₆	—	101	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	404	1	no	—
32	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
33	C₈	Dic₂₀₂	1	1	yes	characteristic
34	C₈	C₄×D₁₀₁	1	1	yes	characteristic
35	C₂²	#13108059	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	808	1	no	—
38	C₄	#13108053	1	1	yes	characteristic
39	C₄	#13108064	1	1	yes	characteristic
40	C₂	#15692188	1	1	yes	characteristic
41	C₂	#15692198	1	1	yes	characteristic
42	C₂	#15692199	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13108059
commutator	C₈×C₁₀₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₁
Fitting	#107×C₁₀₁	C₂
socle	C₂²×C₁₀₁	D₈
hypercenter	#107	D₁₀₁
hypocenter	C₁₀₁	#367
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. #13108049	C₄	semidirect
21. C₁₀₁	#367	semidirect