Subgroups — #20266096

Order 6464.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692330	C₂	1	1	yes	maximal, characteristic
2	#15692325	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#13108084	—	2	1	no	—
5	#13108077	—	2	1	no	—
6	Q₈×D₁₀₁	—	2	1	no	—
7	Dic₄₀₄	C₄	1	1	yes	characteristic
8	#13108064	—	2	1	no	—
9	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₀₁	C₄	1	1	yes	characteristic
11	Q₈×C₁₀₁	—	2	1	no	—
12	C₄×D₁₀₁	—	4	1	no	—
13	C₄×D₁₀₁	D₄	1	1	yes	characteristic
14	Dic₂₀₂	—	2	1	no	—
15	Dic₂₀₂	—	4	1	no	—
16	#11717581	—	4	1	no	—
17	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	#11717579	D₄	1	1	yes	characteristic
19	C₂×D₁₀₁	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₀₁	—	4	1	no	—
21	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₁₀₁	—	4	1	no	—
23	Dic₁₀₁	D₈	1	1	yes	characteristic
24	C₂×C₁₀₁	#102	1	1	yes	characteristic
25	D₁₀₁	—	2	1	no	—
26	C₁₀₁	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	101	1	no	maximal, Sylow
28	C₂×Q₁₆	—	101	1	no	—
29	M₃₂	—	101	1	no	—
30	#108	—	101	1	no	—
31	C₂×Q₈	—	202	1	no	—
32	Q₁₆	—	101	1	no	—
33	Q₁₆	—	202	1	no	—
34	Q₁₆	#87938	1	1	yes	characteristic
35	M₁₆	—	202	1	no	—
36	C₂×C₈	—	101	1	no	—
37	C₁₆	—	202	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	404	1	no	—
40	Q₈	—	202	1	no	—
41	C₂×C₄	—	101	1	no	—
42	C₂×C₄	—	404	1	no	—
43	C₈	—	101	1	no	—
44	C₈	—	404	1	no	—
45	C₈	C₂×#87938	1	1	yes	characteristic
46	C₂²	—	101	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	101	1	no	—
49	C₄	—	404	1	no	—
50	C₄	C₂²⋊#87938	1	1	yes	characteristic
51	C₂	—	202	1	no	—
52	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	#362
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
26. C₁₀₁	#362	semidirect