Subgroups — #20266090

Order 6464.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#15692324	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#87938	—	2	1	no	—
5	#13108077	—	2	1	no	—
6	Q₈×D₁₀₁	—	2	1	no	—
7	Dic₄₀₄	C₄	1	1	yes	characteristic, complemented
8	#13108064	—	2	1	no	—
9	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₀₁	C₄	1	1	yes	characteristic, complemented
11	C₂×#87938	—	4	1	no	—
12	Q₈×C₁₀₁	—	2	1	no	—
13	C₄×D₁₀₁	—	4	1	no	—
14	C₄×D₁₀₁	D₄	1	1	yes	characteristic
15	Dic₂₀₂	—	2	1	no	—
16	Dic₂₀₂	—	4	1	no	—
17	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	#11717579	D₄	1	1	yes	characteristic
19	C₂×D₁₀₁	D₈	1	1	yes	characteristic
20	#87938	—	8	1	no	—
21	C₄×C₁₀₁	—	4	1	no	—
22	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₀₁	—	4	1	no	—
24	Dic₁₀₁	SD₁₆	1	1	yes	characteristic
25	C₂×C₁₀₁	#102	1	1	yes	characteristic
26	D₁₀₁	SD₃₂	1	1	yes	characteristic
27	D₁₀₁	Q₃₂	1	1	yes	characteristic
28	C₁₀₁	#358	1	1	yes	characteristic, complemented, Sylow
29	#358	—	101	1	no	maximal, Sylow
30	C₂×Q₁₆	—	101	1	no	—
31	C₂×C₁₆	—	101	1	no	—
32	#107	—	101	1	no	—
33	C₂×Q₈	—	202	1	no	—
34	Q₁₆	—	101	1	no	—
35	Q₁₆	—	202	1	no	—
36	Q₁₆	#87938	1	1	yes	characteristic, complemented
37	C₂×C₈	—	101	1	no	—
38	C₄⋊C₄	—	202	1	no	—
39	C₁₆	—	202	1	no	—
40	Q₈	—	2	1	no	—
41	Q₈	—	404	1	no	—
42	Q₈	—	202	1	no	—
43	C₂×C₄	—	101	1	no	—
44	C₂×C₄	—	404	1	no	—
45	C₂×C₄	—	404	1	no	—
46	C₈	—	101	1	no	—
47	C₈	C₂×#87938	1	1	yes	characteristic
48	C₂²	—	101	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	808	1	no	—
51	C₄	—	101	1	no	—
52	C₄	—	404	1	no	—
53	C₄	C₂²⋊#87938	1	1	yes	characteristic
54	C₂	—	101	1	no	—
55	C₂	—	101	1	no	—
56	C₂	#15692317	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692317
commutator	C₈×C₁₀₁	C₂×C₄
Frattini	C₈	C₂×#87938
Fitting	Q₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	#102
hypercenter	Q₁₆	#87938
hypocenter	C₁₀₁	#358
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
7. Dic₄₀₄	C₄	semidirect
10. Q₁₆×C₁₀₁	C₄	semidirect
28. C₁₀₁	#358	semidirect
36. Q₁₆	#87938	semidirect