Subgroups — #20264982

Order 6464.

58 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	#15692189	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₀₂	—	2	1	no	—
5	Dic₄₀₄	—	2	1	no	—
6	Dic₄₀₄	C₄	1	2	yes	complemented
7	C₄⋊Dic₁₀₁	—	2	1	no	—
8	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₀₁	—	2	1	no	—
10	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
11	C₂×Dic₁₀₁	—	4	1	no	—
12	C₂×Dic₁₀₁	—	4	1	no	—
13	Dic₂₀₂	—	2	2	no	—
14	Dic₂₀₂	—	4	1	no	—
15	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₀₁	D₄	1	1	yes	characteristic
17	C₂²×C₁₀₁	D₈	1	1	yes	characteristic
18	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₁	SD₁₆	1	1	yes	characteristic
20	Dic₁₀₁	—	4	2	no	—
21	Dic₁₀₁	—	8	1	no	—
22	C₂×C₁₀₁	#102	1	1	yes	characteristic
23	C₂×C₁₀₁	SD₃₂	1	1	yes	characteristic
24	C₂×C₁₀₁	Q₃₂	1	1	yes	characteristic
25	C₁₀₁	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	101	1	no	maximal, Sylow
27	C₂×Q₁₆	—	101	1	no	—
28	C₂×C₁₆	D₁₀₁	1	1	yes	characteristic
29	#107	—	101	1	no	—
30	C₂×Q₈	—	202	1	no	—
31	Q₁₆	—	101	2	no	—
32	Q₁₆	—	202	1	no	—
33	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
34	C₄⋊C₄	—	202	1	no	—
35	C₁₆	—	2	1	no	—
36	Q₈	—	404	1	no	—
37	Q₈	—	202	2	no	—
38	C₂×C₄	—	404	1	no	—
39	C₂×C₄	—	404	1	no	—
40	C₂×C₄	D₄₀₄	1	1	yes	characteristic
41	C₈	C₄×D₁₀₁	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₀₁	1	1	yes	characteristic
43	C₂²	D₈₀₈	1	1	yes	characteristic
44	C₄	—	808	1	no	—
45	C₄	—	404	2	no	—
46	C₄	#13108051	1	1	yes	characteristic
47	C₄	#13108063	1	1	yes	characteristic
48	C₂	#15692177	1	1	yes	characteristic
49	C₂	#15692200	1	1	yes	characteristic
50	C₂	Dic₈₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈₀₈
commutator	C₈×C₁₀₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₁
Fitting	C₂×C₁₆×C₁₀₁	C₂
socle	C₂²×C₁₀₁	D₈
hypercenter	C₂×C₁₆	D₁₀₁
hypocenter	C₁₀₁	#358
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. Dic₄₀₄	C₄	semidirect
25. C₁₀₁	#358	semidirect