Subgroups — #20264927

Order 6464.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11717579	C₂	1	1	yes	maximal, characteristic
2	C₄×#11717579	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11717579	—	2	1	no	—
5	C₂×#11717579	C₄	1	1	yes	characteristic
6	C₂×#11717579	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₀₁	—	2	1	no	—
8	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
11	C₂×C₄×C₁₀₁	Q₈	1	1	yes	characteristic
12	C₈×C₁₀₁	—	4	1	no	—
13	#11717579	—	2	1	no	—
14	#11717579	—	4	1	no	—
15	#11717579	C₈	1	2	yes	complemented
16	C₂²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₀₁	—	2	1	no	—
18	C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
19	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
20	C₄×C₁₀₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₀₁	SD₁₆	1	1	yes	characteristic
22	C₂×C₁₀₁	C₄⋊C₈	1	1	yes	characteristic
23	C₂×C₁₀₁	#106	1	1	yes	characteristic
24	C₂×C₁₀₁	#108	1	1	yes	characteristic
25	C₁₀₁	#334	1	1	yes	characteristic, complemented, Sylow
26	#334	—	101	1	no	maximal, Sylow
27	C₄⋊C₈	—	101	1	no	—
28	C₄⋊C₈	D₁₀₁	1	1	yes	characteristic
29	C₄×C₈	—	101	1	no	—
30	C₂×C₈	—	2	1	no	—
31	C₂×C₈	—	101	1	no	—
32	C₂×C₈	—	101	1	no	—
33	C₂×C₈	—	202	1	no	—
34	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
35	C₂×C₄	Dic₂₀₂	1	1	yes	characteristic
36	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
37	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	—	101	2	no	—
40	C₈	—	404	1	no	—
41	C₈	—	202	1	no	—
42	C₂²	#13108053	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₈×D₁₀₁	1	1	yes	characteristic
45	C₄	#13108057	1	1	yes	characteristic
46	C₄	#13108061	1	1	yes	characteristic
47	C₄	#13108062	1	1	yes	characteristic
48	C₂	#15692184	1	1	yes	characteristic
49	C₂	#15692186	1	1	yes	characteristic
50	C₂	#15692190	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₀₁
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	#334
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
15. #11717579	C₈	semidirect
25. C₁₀₁	#334	semidirect