Subgroups — #20265585

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692254	C₂	1	1	yes	maximal, characteristic
2	#15692246	C₂	1	1	yes	maximal, characteristic
3	#15692188	C₂	1	1	yes	maximal, characteristic
4	#15692187	C₂	1	1	yes	maximal, characteristic
5	#15692186	C₂	1	1	yes	maximal, characteristic
6	#15692165	C₂	1	1	yes	maximal, characteristic
7	#107×C₁₀₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₀₂	—	2	1	no	—
9	C₂×#11717579	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₀₁	—	2	1	no	—
11	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
13	#13108053	—	2	1	no	—
14	#13108053	—	2	1	no	—
15	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	—	2	1	no	—
20	C₂×C₄×C₁₀₁	—	2	1	no	—
21	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₀₁	—	2	1	no	—
23	C₂×Dic₁₀₁	—	2	1	no	—
24	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
25	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
26	Dic₂₀₂	—	4	2	no	—
27	C₈×C₁₀₁	Q₈	1	2	yes	complemented
28	#11717579	Q₈	1	2	yes	complemented
29	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₀₁	—	4	1	no	—
31	C₄×C₁₀₁	—	4	1	no	—
32	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
34	Dic₁₀₁	—	2	1	no	—
35	Dic₁₀₁	—	2	1	no	—
36	Dic₁₀₁	—	4	1	no	—
37	Dic₁₀₁	—	4	1	no	—
38	C₂×C₁₀₁	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₁₀₁	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₁₀₁	#137	1	1	yes	characteristic
41	C₁₀₁	#501	1	1	yes	characteristic, complemented, Sylow
42	#501	—	101	1	no	maximal, Sylow
43	C₄⋊Q₈	—	101	1	no	—
44	#125	—	101	1	no	—
45	#107	—	101	1	no	—
46	#107	D₁₀₁	1	1	yes	characteristic
47	#106	—	101	1	no	—
48	#106	—	101	1	no	—
49	#97	—	101	1	no	—
50	C₂×Q₈	—	202	1	no	—
51	C₂×C₈	—	101	1	no	—
52	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
53	C₄⋊C₄	—	101	1	no	—
54	C₄⋊C₄	—	101	1	no	—
55	C₄⋊C₄	—	202	1	no	—
56	C₄⋊C₄	—	202	1	no	—
57	C₄⋊C₄	—	202	1	no	—
58	C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
60	C₄²	—	101	1	no	—
61	Q₈	—	404	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	101	1	no	—
65	C₂×C₄	—	101	1	no	—
66	C₂×C₄	—	202	1	no	—
67	C₂×C₄	—	202	1	no	—
68	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
69	C₈	—	101	2	no	—
70	C₈	Dic₂₀₂	1	2	yes	complemented
71	C₂²	D₄×D₁₀₁	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	404	1	no	—
75	C₄	—	404	1	no	—
76	C₄	—	202	1	no	—
77	C₄	—	202	1	no	—
78	C₄	Q₈×D₁₀₁	1	1	yes	characteristic
79	C₄	C₂×Dic₂₀₂	1	1	yes	characteristic
80	C₂	#15692254	1	1	yes	characteristic
81	C₂	#15692279	1	1	yes	characteristic
82	C₂	#15692287	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#107×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#107	D₁₀₁
hypocenter	C₁₀₁	#501
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
27. C₈×C₁₀₁	Q₈	semidirect
28. #11717579	Q₈	semidirect
41. C₁₀₁	#501	semidirect
70. C₈	Dic₂₀₂	semidirect