Subgroups — #20264930

Order 6464.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11717579	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#11717579	—	2	2	no	—
4	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic
6	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
9	C₂×C₄×C₁₀₁	Q₈	1	1	yes	characteristic
10	C₈×C₁₀₁	—	2	1	no	—
11	C₈×C₁₀₁	C₈	1	2	yes	complemented
12	#11717579	—	4	2	no	—
13	C₂²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₀₁	—	2	1	no	—
15	C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
17	C₄×C₁₀₁	D₈	1	1	yes	characteristic
18	C₄×C₁₀₁	Q₁₆	1	1	yes	characteristic
19	C₂×C₁₀₁	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₁₀₁	#107	1	1	yes	characteristic
21	C₂×C₁₀₁	#108	1	1	yes	characteristic
22	C₁₀₁	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	101	1	no	maximal, Sylow
24	C₄⋊C₈	—	101	2	no	—
25	C₄×C₈	D₁₀₁	1	1	yes	characteristic
26	C₂×C₈	—	202	2	no	—
27	C₂×C₈	Dic₁₀₁	1	1	yes	characteristic
28	C₂×C₈	Dic₁₀₁	1	1	yes	characteristic
29	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
30	C₂×C₄	Dic₂₀₂	1	1	yes	characteristic
31	C₂×C₄	D₄₀₄	1	1	yes	characteristic
32	C₂×C₄	C₂×Dic₁₀₁	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	404	2	no	—
35	C₈	#11717579	1	2	yes	complemented
36	C₂²	C₄⋊Dic₁₀₁	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	C₂×#11717579	1	1	yes	characteristic
39	C₄	#13108058	1	1	yes	characteristic
40	C₄	D₈₀₈	1	1	yes	characteristic
41	C₄	Dic₄₀₄	1	1	yes	characteristic
42	C₂	C₄⋊#11717579	1	1	yes	characteristic
43	C₂	#15692189	1	1	yes	characteristic
44	C₂	#15692191	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄₀₄
commutator	C₄×C₁₀₁	C₂×C₈
Frattini	C₄²	C₂×D₁₀₁
Fitting	C₄×C₈×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₄⋊C₄
hypercenter	C₄×C₈	D₁₀₁
hypocenter	C₁₀₁	#335
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
11. C₈×C₁₀₁	C₈	semidirect
22. C₁₀₁	#335	semidirect
35. C₈	#11717579	semidirect