Subgroups — #20264960

Order 6464.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692261	C₂	1	1	yes	maximal, characteristic
2	#15692195	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#13108074	C₄	1	1	yes	characteristic
5	#13108058	C₄	1	1	yes	characteristic
6	#13108057	—	2	1	no	—
7	C₈×D₁₀₁	—	2	1	no	—
8	#13108049	—	2	1	no	—
9	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₁₆×C₁₀₁	—	2	1	no	—
11	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₁₀₁	—	2	1	no	—
13	D₄₀₄	C₈	1	1	yes	characteristic
14	C₄×D₁₀₁	—	2	1	no	—
15	Dic₂₀₂	C₈	1	1	yes	characteristic
16	C₈×C₁₀₁	D₄	1	1	yes	characteristic
17	C₈×C₁₀₁	D₄	1	1	yes	characteristic
18	#11717579	—	2	1	no	—
19	C₂²×C₁₀₁	M₁₆	1	1	yes	characteristic
20	C₂×D₁₀₁	—	2	1	no	—
21	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
23	Dic₁₀₁	—	2	1	no	—
24	C₂×C₁₀₁	—	2	1	no	—
25	C₂×C₁₀₁	C₂²⋊C₈	1	1	yes	characteristic
26	D₁₀₁	—	4	1	no	—
27	C₁₀₁	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	101	1	no	maximal, Sylow
29	#131	—	101	1	no	—
30	M₃₂	—	101	1	no	—
31	C₂×C₁₆	D₁₀₁	1	1	yes	characteristic, complemented
32	#41	—	101	1	no	—
33	M₁₆	—	101	1	no	—
34	M₁₆	—	202	1	no	—
35	C₂×C₈	—	202	1	no	—
36	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	—	202	1	no	—
39	Q₈	—	101	1	no	—
40	D₄	—	101	1	no	—
41	D₄	—	202	1	no	—
42	C₂×C₄	—	202	1	no	—
43	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
44	C₈	—	202	1	no	—
45	C₈	D₄₀₄	1	1	yes	characteristic
46	C₈	C₂²⋊D₁₀₁	1	1	yes	characteristic
47	C₂²	—	202	1	no	—
48	C₂²	#13108057	1	1	yes	characteristic
49	C₄	—	202	1	no	—
50	C₄	#13108051	1	1	yes	characteristic
51	C₄	C₈×D₁₀₁	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	404	1	no	—
54	C₂	#15692167	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₄₀₄
commutator	C₄×C₁₀₁	C₂×C₈
Frattini	C₂×C₈	C₂×D₁₀₁
Fitting	C₂×C₁₆×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₂²⋊C₈
hypercenter	C₂×C₁₆	D₁₀₁
hypocenter	C₁₀₁	#350
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #15692195	C₂	semidirect
3. C₂×C₁₆×C₁₀₁	C₂	semidirect
27. C₁₀₁	#350	semidirect
31. C₂×C₁₆	D₁₀₁	semidirect