Subgroups — #20265620

Order 6464.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692277	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₄₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₈₀₈	C₂	1	2	yes	maximal, complemented
4	#15692200	C₂	1	2	yes	maximal, complemented
5	M₃₂×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#13108074	—	2	1	no	—
7	C₂×Dic₂₀₂	—	2	1	no	—
8	Dic₄₀₄	—	2	1	no	—
9	Dic₄₀₄	C₂²	1	2	yes	—
10	Dic₄₀₄	C₂²	1	1	yes	characteristic
11	#13108063	—	2	1	no	—
12	D₈₀₈	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₁₆×C₁₀₁	C₂²	1	2	yes	—
15	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
16	C₂²⋊D₁₀₁	—	4	1	no	—
17	C₂×Dic₁₀₁	—	4	1	no	—
18	D₄₀₄	—	2	1	no	—
19	C₄×D₁₀₁	—	4	1	no	—
20	Dic₂₀₂	—	2	1	no	—
21	Dic₂₀₂	—	2	2	no	—
22	Dic₂₀₂	—	4	1	no	—
23	C₈×C₁₀₁	D₄	1	1	yes	characteristic
24	C₈×C₁₀₁	C₂³	1	1	yes	characteristic
25	C₂²×C₁₀₁	D₈	1	1	yes	characteristic
26	C₂×D₁₀₁	—	4	1	no	—
27	C₄×C₁₀₁	D₈	1	1	yes	characteristic
28	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
29	Dic₁₀₁	—	4	2	no	—
30	Dic₁₀₁	—	4	1	no	—
31	C₂×C₁₀₁	—	2	1	no	—
32	C₂×C₁₀₁	C₂×D₈	1	1	yes	characteristic
33	D₁₀₁	—	8	1	no	—
34	C₁₀₁	#510	1	1	yes	characteristic, complemented, Sylow
35	#510	—	101	1	no	maximal, Sylow
36	#135	—	101	1	no	—
37	C₂×Q₁₆	—	101	1	no	—
38	Q₃₂	—	101	2	no	—
39	SD₃₂	—	101	2	no	—
40	M₃₂	D₁₀₁	1	1	yes	characteristic, complemented
41	#41	—	202	1	no	—
42	C₂×Q₈	—	202	1	no	—
43	Q₁₆	—	101	2	no	—
44	Q₁₆	—	101	1	no	—
45	Q₁₆	—	202	1	no	—
46	SD₁₆	—	202	1	no	—
47	D₈	—	101	1	no	—
48	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
49	C₁₆	C₂×D₁₀₁	1	2	yes	—
50	Q₈	—	404	1	no	—
51	Q₈	—	202	1	no	—
52	Q₈	—	202	2	no	—
53	D₄	—	404	1	no	—
54	D₄	—	202	1	no	—
55	C₂×C₄	—	404	1	no	—
56	C₂×C₄	—	404	1	no	—
57	C₂×C₄	D₄₀₄	1	1	yes	characteristic
58	C₈	D₄₀₄	1	1	yes	characteristic
59	C₈	C₂²×D₁₀₁	1	1	yes	characteristic
60	C₂²	—	404	1	no	—
61	C₂²	D₈₀₈	1	1	yes	characteristic
62	C₄	—	404	1	no	—
63	C₄	—	404	2	no	—
64	C₄	D₈₀₈	1	1	yes	characteristic
65	C₄	C₂×D₄₀₄	1	1	yes	characteristic
66	C₂	—	2	1	no	—
67	C₂	—	808	1	no	—
68	C₂	C₂×D₈₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₈₀₈
commutator	C₈×C₁₀₁	C₂³
Frattini	C₈	C₂²×D₁₀₁
Fitting	M₃₂×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₂×D₈
hypercenter	M₃₂	D₁₀₁
hypocenter	C₁₀₁	#510
LCS	G ▷ C₈×C₁₀₁ ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₄₀₄	C₂	semidirect
3. Dic₈₀₈	C₂	semidirect
4. #15692200	C₂	semidirect
5. M₃₂×C₁₀₁	C₂	semidirect
34. C₁₀₁	#510	semidirect
40. M₃₂	D₁₀₁	semidirect