Subgroups — #20265295

Order 6464.

106 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	#15692261	C₂	1	2	yes	maximal, complemented
3	#15692191	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692183	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#13108074	C₂²	1	2	yes	—
7	Dic₄₀₄	C₄	1	1	yes	characteristic, complemented
8	#13108063	C₄	1	2	yes	complemented
9	D₈₀₈	C₄	1	1	yes	characteristic, complemented
10	#13108058	C₂²	1	2	yes	—
11	#13108057	—	2	2	no	—
12	C₈×D₁₀₁	—	2	2	no	—
13	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	—	2	1	no	—
17	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
18	C₂²⋊D₁₀₁	—	2	2	no	—
19	D₄₀₄	C₂×C₄	1	2	yes	—
20	C₄×D₁₀₁	—	2	2	no	—
21	Dic₂₀₂	C₂×C₄	1	2	yes	—
22	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
23	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
24	C₈×C₁₀₁	D₄	1	1	yes	characteristic
25	C₈×C₁₀₁	D₄	1	1	yes	characteristic
26	#11717579	—	2	2	no	—
27	C₂²×C₁₀₁	#41	1	1	yes	characteristic
28	C₂×D₁₀₁	—	2	2	no	—
29	C₄×C₁₀₁	—	2	2	no	—
30	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
32	Dic₁₀₁	—	2	2	no	—
33	C₂×C₁₀₁	—	2	1	no	—
34	C₂×C₁₀₁	C₄×D₄	1	1	yes	characteristic
35	D₁₀₁	—	4	2	no	—
36	C₁₀₁	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	101	1	no	maximal, Sylow
38	#135	—	101	1	no	—
39	#131	—	101	2	no	—
40	#108	—	101	1	no	—
41	#104	—	101	2	no	—
42	C₄×C₈	D₁₀₁	1	1	yes	characteristic, complemented
43	#41	—	101	2	no	—
44	Q₁₆	—	101	1	no	—
45	SD₁₆	—	101	2	no	—
46	D₈	—	101	1	no	—
47	M₁₆	—	101	2	no	—
48	M₁₆	—	202	2	no	—
49	C₂×C₈	—	202	2	no	—
50	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
51	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
52	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
53	Q₈	—	101	2	no	—
54	D₄	—	101	2	no	—
55	D₄	—	202	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	202	2	no	—
58	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
59	C₈	—	202	2	no	—
60	C₈	C₄×D₁₀₁	1	1	yes	characteristic
61	C₈	C₄×D₁₀₁	1	1	yes	characteristic
62	C₈	D₄₀₄	1	1	yes	characteristic
63	C₈	D₄₀₄	1	1	yes	characteristic
64	C₂²	—	202	2	no	—
65	C₂²	#13108074	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	202	2	no	—
68	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
69	C₄	C₂×D₄₀₄	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	404	2	no	—
72	C₂	C₄×D₄₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₄₀₄
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₄×C₈×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₄×D₄
hypercenter	C₄×C₈	D₁₀₁
hypocenter	C₁₀₁	#443
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #15692261	C₂	semidirect
3. #15692191	C₂	semidirect
4. #15692183	C₂	semidirect
5. C₄×C₈×C₁₀₁	C₂	semidirect
7. Dic₄₀₄	C₄	semidirect
8. #13108063	C₄	semidirect
9. D₈₀₈	C₄	semidirect
36. C₁₀₁	#443	semidirect
42. C₄×C₈	D₁₀₁	semidirect