Subgroups — #20264992

Order 6464.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₀₄	C₂	1	1	yes	maximal, characteristic
2	#15692195	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₀₂	—	2	1	no	—
5	Dic₄₀₄	—	2	1	no	—
6	Dic₄₀₄	C₄	1	2	yes	—
7	#13108049	—	2	1	no	—
8	M₁₆×C₁₀₁	—	2	1	no	—
9	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
11	C₂×Dic₁₀₁	—	4	1	no	—
12	Dic₂₀₂	—	2	2	no	—
13	Dic₂₀₂	—	4	1	no	—
14	C₈×C₁₀₁	—	4	1	no	—
15	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₀₁	D₄	1	1	yes	characteristic
17	C₂²×C₁₀₁	SD₁₆	1	1	yes	characteristic
18	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₁	D₈	1	1	yes	characteristic
20	Dic₁₀₁	—	4	2	no	—
21	C₂×C₁₀₁	—	2	1	no	—
22	C₂×C₁₀₁	#102	1	1	yes	characteristic
23	C₁₀₁	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	101	1	no	maximal, Sylow
25	C₂×Q₁₆	—	101	1	no	—
26	M₃₂	—	101	1	no	—
27	#108	D₁₀₁	1	1	yes	characteristic
28	C₂×Q₈	—	202	1	no	—
29	Q₁₆	—	101	2	no	—
30	Q₁₆	—	202	1	no	—
31	M₁₆	—	2	1	no	—
32	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
33	C₁₆	—	202	1	no	—
34	Q₈	—	404	1	no	—
35	Q₈	—	202	2	no	—
36	C₂×C₄	—	404	1	no	—
37	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	C₄×D₁₀₁	1	1	yes	characteristic
40	C₈	D₄₀₄	1	1	yes	characteristic
41	C₂²	#13108061	1	1	yes	characteristic
42	C₄	—	404	2	no	—
43	C₄	#13108051	1	1	yes	characteristic
44	C₄	#13108059	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#15692175	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692175
commutator	C₈×C₁₀₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₁
Fitting	#108×C₁₀₁	C₂
socle	C₂×C₁₀₁	#102
hypercenter	#108	D₁₀₁
hypocenter	C₁₀₁	#362
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
23. C₁₀₁	#362	semidirect