Subgroups — #20266092

Order 6464.

56 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	#15692326	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692278	C₂	1	1	yes	maximal, characteristic
4	#13108084	—	2	1	no	—
5	#13108077	—	2	1	no	—
6	#13108075	—	2	1	no	—
7	#13108061	—	2	1	no	—
8	D₈₀₈	C₄	1	1	yes	characteristic
9	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₀₁	C₄	1	1	yes	characteristic
11	Q₈×C₁₀₁	—	2	1	no	—
12	D₄₀₄	—	2	1	no	—
13	D₄₀₄	—	4	1	no	—
14	C₄×D₁₀₁	—	4	1	no	—
15	C₄×D₁₀₁	D₄	1	1	yes	characteristic
16	#11717581	—	4	1	no	—
17	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	#11717579	D₄	1	1	yes	characteristic
19	C₂×D₁₀₁	—	4	1	no	—
20	C₂×D₁₀₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₀₁	—	4	1	no	—
22	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₀₁	D₈	1	1	yes	characteristic
24	C₂×C₁₀₁	#102	1	1	yes	characteristic
25	D₁₀₁	—	2	1	no	—
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	—	101	1	no	—
32	#41	—	202	1	no	—
33	Q₁₆	#87938	1	1	yes	characteristic
34	SD₁₆	—	202	1	no	—
35	D₈	—	101	1	no	—
36	M₁₆	—	202	1	no	—
37	C₂×C₈	—	101	1	no	—
38	C₁₆	—	202	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	404	1	no	—
41	D₄	—	202	1	no	—
42	C₂×C₄	—	101	1	no	—
43	C₂×C₄	—	404	1	no	—
44	C₈	—	101	1	no	—
45	C₈	—	404	1	no	—
46	C₈	C₂×#87938	1	1	yes	characteristic
47	C₂²	—	101	1	no	—
48	C₂²	—	404	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	101	1	no	—
51	C₄	C₂²⋊#87938	1	1	yes	characteristic
52	C₂	—	808	1	no	—
53	C₂	—	202	1	no	—
54	C₂	#15692317	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692317
commutator	C₈×C₁₀₁	C₂×C₄
Frattini	C₈	C₂×#87938
Fitting	Q₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	#102
hypercenter	Q₁₆	#87938
hypocenter	C₁₀₁	#359
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. D₁₀₁⋊C₁₆	C₂	semidirect
2. #15692326	C₂	semidirect
27. C₁₀₁	#359	semidirect