Subgroups — #20266218

Order 6464.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#87938	C₂	1	2	yes	maximal, complemented
2	#15692323	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692317	C₂	1	2	yes	maximal, complemented
4	#15692309	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×#87938	—	2	2	no	—
7	D₁₀₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊#87938	C₂²	1	2	yes	—
9	C₂²⋊#87938	—	2	2	no	—
10	C₄×#87938	C₂²	1	1	yes	characteristic
11	D₄×D₁₀₁	C₂²	1	2	yes	—
12	D₈₀₈	C₄	1	1	yes	characteristic, complemented
13	#13108059	C₄	1	2	yes	complemented
14	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
15	D₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
16	C₂²×D₁₀₁	—	2	2	no	—
17	C₂×#87938	—	2	2	no	—
18	C₂×#87938	—	4	4	no	—
19	C₂×#87938	D₄	1	2	yes	—
20	D₄×C₁₀₁	C₂×C₄	1	2	yes	complemented
21	C₂²⋊D₁₀₁	—	2	2	no	—
22	D₄₀₄	C₂×C₄	1	2	yes	complemented
23	C₄×D₁₀₁	C₂³	1	1	yes	characteristic
24	#11717581	—	2	1	no	—
25	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
26	#11717579	C₂×C₄	1	1	yes	characteristic, complemented
27	C₂²×C₁₀₁	—	2	2	no	—
28	C₂×D₁₀₁	—	2	2	no	—
29	C₂×D₁₀₁	—	4	2	no	—
30	C₂×D₁₀₁	—	4	2	no	—
31	C₂×D₁₀₁	C₂×D₄	1	1	yes	characteristic
32	#87938	—	2	2	no	—
33	#87938	—	4	2	no	—
34	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
35	Dic₁₀₁	#41	1	1	yes	characteristic
36	C₂×C₁₀₁	—	4	2	no	—
37	C₂×C₁₀₁	C₄×D₄	1	1	yes	characteristic
38	D₁₀₁	—	4	2	no	—
39	D₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
40	C₁₀₁	#442	1	1	yes	characteristic, complemented, Sylow
41	#442	—	101	1	no	maximal, Sylow
42	C₂×D₈	—	101	1	no	—
43	C₄×D₄	—	101	2	no	—
44	#106	—	101	1	no	—
45	#102	—	101	2	no	—
46	#97	—	101	1	no	—
47	C₂×D₄	—	101	2	no	—
48	C₂²×C₄	—	202	2	no	—
49	D₈	—	101	2	no	—
50	D₈	—	101	1	no	—
51	D₈	#87938	1	1	yes	characteristic, complemented
52	C₂×C₈	—	101	1	no	—
53	C₂×C₈	—	101	1	no	—
54	C₄⋊C₄	—	101	2	no	—
55	C₂²⋊C₄	—	202	2	no	—
56	C₄²	—	101	1	no	—
57	C₂³	—	202	2	no	—
58	D₄	—	101	2	no	—
59	D₄	—	202	2	no	—
60	D₄	C₂×#87938	1	2	yes	complemented
61	C₂×C₄	—	101	1	no	—
62	C₂×C₄	—	101	2	no	—
63	C₂×C₄	—	404	4	no	—
64	C₂×C₄	—	202	2	no	—
65	C₈	—	101	1	no	—
66	C₈	—	202	1	no	—
67	C₈	C₂×#87938	1	1	yes	characteristic, complemented
68	C₂²	—	2	2	no	—
69	C₂²	—	101	1	no	—
70	C₂²	—	404	2	no	—
71	C₂²	—	404	2	no	—
72	C₂²	—	202	2	no	—
73	C₄	—	101	1	no	—
74	C₄	—	404	2	no	—
75	C₄	—	202	2	no	—
76	C₄	C₂²×#87938	1	1	yes	characteristic
77	C₂	—	4	2	no	—
78	C₂	—	101	2	no	—
79	C₂	—	404	2	no	—
80	C₂	D₄×#87938	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#87938
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₄	C₂²×#87938
Fitting	D₈×C₁₀₁	C₄
socle	C₂×C₁₀₁	C₄×D₄
hypercenter	D₈	#87938
hypocenter	C₁₀₁	#442
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#87938	C₂	semidirect
2. #15692323	C₂	semidirect
3. #15692317	C₂	semidirect
4. #15692309	C₂	semidirect
12. D₈₀₈	C₄	semidirect
13. #13108059	C₄	semidirect
15. D₈×C₁₀₁	C₄	semidirect
20. D₄×C₁₀₁	C₂×C₄	semidirect
22. D₄₀₄	C₂×C₄	semidirect
25. C₈×C₁₀₁	C₂×C₄	semidirect
26. #11717579	C₂×C₄	semidirect
40. C₁₀₁	#442	semidirect
51. D₈	#87938	semidirect
60. D₄	C₂×#87938	semidirect
67. C₈	C₂×#87938	semidirect