Subgroups — #20266098

Order 6464.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108077	C₂	1	2	yes	maximal
2	C₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#13108077	—	2	2	no	—
4	C₂×#11717579	C₂²	1	1	yes	characteristic
5	C₄×Dic₁₀₁	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₀₁	C₈	1	1	yes	characteristic
9	C₂×Dic₁₀₁	C₈	1	1	yes	characteristic
10	C₈×C₁₀₁	—	2	1	no	—
11	#11717579	D₄	1	1	yes	characteristic
12	#11717579	Q₈	1	1	yes	characteristic
13	C₂²×C₁₀₁	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
16	Dic₁₀₁	—	2	1	no	—
17	Dic₁₀₁	C₁₆	1	2	yes	complemented
18	C₂×C₁₀₁	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₀₁	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₀₁	M₃₂	1	1	yes	characteristic
21	C₁₀₁	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	101	1	no	maximal, Sylow
23	C₂×C₁₆	—	101	2	no	—
24	C₄×C₈	—	101	1	no	—
25	C₂×C₈	—	101	1	no	—
26	C₂×C₈	#87938	1	1	yes	characteristic
27	C₄²	—	101	1	no	—
28	C₁₆	—	202	2	no	—
29	C₂×C₄	—	101	1	no	—
30	C₂×C₄	—	101	1	no	—
31	C₂×C₄	C₂×#87938	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	101	1	no	—
34	C₈	—	101	1	no	—
35	C₂²	D₁₀₁⋊C₈	1	1	yes	characteristic
36	C₄	—	101	2	no	—
37	C₄	—	202	1	no	—
38	C₄	C₄⋊#87938	1	1	yes	characteristic
39	C₄	#13108083	1	1	yes	characteristic
40	C₂	#15692322	1	1	yes	characteristic
41	C₂	D₁₀₁⋊C₁₆	1	1	yes	characteristic
42	C₂	#15692330	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#87938
commutator	C₂×C₁₀₁	C₂×C₁₆
Fitting	C₂×C₈×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂×C₈
hypercenter	C₂×C₈	#87938
hypocenter	C₁₀₁	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
17. Dic₁₀₁	C₁₆	semidirect
21. C₁₀₁	C₄⋊C₁₆	semidirect