Subgroups — #20265994

Order 6464.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692302	C₂	1	2	yes	maximal, complemented
2	#15692288	C₂	1	6	yes	maximal, complemented
3	#15692277	C₂	1	3	yes	maximal, complemented
4	C₂×Dic₄₀₄	C₂	1	3	yes	maximal, complemented
5	#131×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#13108074	C₂²	1	6	yes	—
7	#13108073	—	2	6	no	—
8	C₂×Dic₂₀₂	C₂²	1	6	yes	—
9	Q₈×D₁₀₁	—	2	2	no	—
10	Dic₄₀₄	C₂²	1	6	yes	—
11	Dic₄₀₄	C₂²	1	3	yes	—
12	#13108063	C₂²	1	6	yes	—
13	D₈₀₈	C₂²	1	1	yes	characteristic
14	#41×C₁₀₁	C₂²	1	1	yes	characteristic
15	M₁₆×C₁₀₁	C₂²	1	3	yes	—
16	C₂×C₈×C₁₀₁	C₂²	1	3	yes	—
17	Q₈×C₁₀₁	D₄	1	1	yes	characteristic
18	D₄×C₁₀₁	D₄	1	3	yes	—
19	C₂×C₄×C₁₀₁	C₂³	1	3	yes	—
20	C₂²⋊D₁₀₁	—	2	6	no	—
21	C₂×Dic₁₀₁	—	2	6	no	—
22	D₄₀₄	C₂³	1	2	yes	—
23	C₄×D₁₀₁	—	2	6	no	—
24	Dic₂₀₂	—	2	6	no	—
25	Dic₂₀₂	C₂³	1	6	yes	—
26	C₈×C₁₀₁	C₂³	1	1	yes	characteristic
27	C₈×C₁₀₁	C₂³	1	3	yes	—
28	C₂²×C₁₀₁	C₂×D₄	1	3	yes	—
29	C₂×D₁₀₁	—	2	2	no	—
30	C₄×C₁₀₁	C₂×D₄	1	3	yes	—
31	C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
32	Dic₁₀₁	—	2	6	no	—
33	C₂×C₁₀₁	—	2	3	no	—
34	C₂×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
35	D₁₀₁	—	4	2	no	—
36	C₁₀₁	#578	1	1	yes	characteristic, complemented, Sylow
37	#578	—	101	1	no	maximal, Sylow
38	2₋¹⁺⁴	—	101	2	no	—
39	#137	—	101	6	no	—
40	#135	—	101	3	no	—
41	C₂×Q₁₆	—	101	3	no	—
42	#131	D₁₀₁	1	1	yes	characteristic, complemented
43	#41	—	101	6	no	—
44	#41	—	202	6	no	—
45	#41	C₂×D₁₀₁	1	1	yes	characteristic
46	C₂×Q₈	—	101	6	no	—
47	C₂×Q₈	—	202	2	no	—
48	Q₁₆	—	101	3	no	—
49	Q₁₆	—	101	6	no	—
50	SD₁₆	—	101	6	no	—
51	D₈	—	101	1	no	—
52	M₁₆	C₂×D₁₀₁	1	3	yes	—
53	C₂×C₈	C₂×D₁₀₁	1	3	yes	—
54	Q₈	—	101	6	no	—
55	Q₈	—	202	6	no	—
56	Q₈	D₄₀₄	1	1	yes	characteristic
57	D₄	—	101	2	no	—
58	D₄	—	202	6	no	—
59	D₄	D₄₀₄	1	3	yes	—
60	C₂×C₄	—	202	6	no	—
61	C₂×C₄	—	202	6	no	—
62	C₂×C₄	C₂²×D₁₀₁	1	3	yes	—
63	C₈	C₂²×D₁₀₁	1	1	yes	characteristic
64	C₈	C₂²×D₁₀₁	1	3	yes	—
65	C₂²	—	202	2	no	—
66	C₂²	C₂×D₄₀₄	1	3	yes	—
67	C₄	—	202	6	no	—
68	C₄	C₂×D₄₀₄	1	3	yes	—
69	C₄	C₂³×D₁₀₁	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	404	2	no	—
72	C₂	C₂²×D₄₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄₀₄
commutator	C₄×C₁₀₁	C₂⁴
Frattini	C₄	C₂³×D₁₀₁
Fitting	#131×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₂²×D₄
hypercenter	#131	D₁₀₁
hypocenter	C₁₀₁	#578
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #15692302	C₂	semidirect
2. #15692288	C₂	semidirect
3. #15692277	C₂	semidirect
4. C₂×Dic₄₀₄	C₂	semidirect
5. #131×C₁₀₁	C₂	semidirect
36. C₁₀₁	#578	semidirect
42. #131	D₁₀₁	semidirect