Subgroups — #20266076

Order 6464.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692329	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13108077	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692263	C₂	1	1	yes	maximal, characteristic
4	#13108077	—	2	1	no	—
5	#13108077	—	2	1	no	—
6	#13108074	C₄	1	1	yes	characteristic
7	#13108057	—	2	1	no	—
8	C₂×#11717579	C₂²	1	1	yes	characteristic
9	C₈×D₁₀₁	—	2	1	no	—
10	M₁₆×C₁₀₁	C₄	1	1	yes	characteristic
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	—	2	1	no	—
17	#11717579	D₄	1	1	yes	characteristic
18	#11717579	D₄	1	1	yes	characteristic
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	—	101	1	no	—
32	#41	—	101	1	no	—
33	M₁₆	—	202	1	no	—
34	M₁₆	#87938	1	1	yes	characteristic
35	C₂×C₈	—	101	1	no	—
36	C₂×C₈	—	202	1	no	—
37	C₁₆	—	202	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	C₂×#87938	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	101	1	no	—
46	C₈	—	101	1	no	—
47	C₂²	—	202	1	no	—
48	C₂²	#13108084	1	1	yes	characteristic
49	C₄	—	202	1	no	—
50	C₄	C₂²⋊#87938	1	1	yes	characteristic
51	C₄	D₁₀₁⋊C₈	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	404	1	no	—
54	C₂	#15692312	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#87938
commutator	C₄×C₁₀₁	C₂×C₈
Frattini	C₂×C₄	C₂×#87938
Fitting	M₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	C₂²⋊C₈
hypercenter	M₁₆	#87938
hypocenter	C₁₀₁	#350
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #15692329	C₂	semidirect
2. C₂×#13108077	C₂	semidirect
27. C₁₀₁	#350	semidirect