Subgroups — #20265461

Order 6464.

96 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	#15692220	C₂	1	1	yes	maximal, characteristic
3	#15692186	C₂	1	1	yes	maximal, characteristic
4	#15692184	C₂	1	1	yes	maximal, characteristic
5	#15692180	C₂	1	1	yes	maximal, characteristic
6	#15692178	C₂	1	1	yes	maximal, characteristic
7	#106×C₁₀₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₀₂	—	2	1	no	—
9	C₂×Dic₂₀₂	C₂²	1	1	yes	characteristic
10	C₂×#11717579	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
12	#13108053	—	2	1	no	—
13	#13108053	—	2	1	no	—
14	C₄×Dic₁₀₁	—	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	—	2	1	no	—
27	Dic₂₀₂	—	4	2	no	—
28	Dic₂₀₂	Q₈	1	2	yes	complemented
29	C₈×C₁₀₁	—	2	1	no	—
30	#11717579	—	2	1	no	—
31	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
32	C₄×C₁₀₁	—	4	1	no	—
33	C₄×C₁₀₁	—	4	1	no	—
34	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₁₀₁	#41	1	1	yes	characteristic
36	Dic₁₀₁	—	2	2	no	—
37	Dic₁₀₁	—	2	1	no	—
38	Dic₁₀₁	—	4	1	no	—
39	Dic₁₀₁	SD₁₆	1	2	yes	—
40	C₂×C₁₀₁	C₂²⋊Q₈	1	1	yes	characteristic
41	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₁₀₁	#137	1	1	yes	characteristic
43	C₁₀₁	#475	1	1	yes	characteristic, complemented, Sylow
44	#475	—	101	1	no	maximal, Sylow
45	C₄⋊Q₈	—	101	1	no	—
46	C₄×Q₈	—	101	1	no	—
47	#106	—	101	1	no	—
48	#106	D₁₀₁	1	1	yes	characteristic
49	C₄⋊C₈	—	101	1	no	—
50	#103	—	101	1	no	—
51	#103	—	101	1	no	—
52	C₂×Q₈	—	101	1	no	—
53	C₂×Q₈	—	202	1	no	—
54	C₂×C₈	—	101	1	no	—
55	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
56	C₄⋊C₄	—	101	1	no	—
57	C₄⋊C₄	—	202	1	no	—
58	C₄⋊C₄	—	202	1	no	—
59	C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
60	C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
61	C₄²	—	101	1	no	—
62	C₄²	—	202	1	no	—
63	Q₈	—	101	2	no	—
64	Q₈	—	404	2	no	—
65	Q₈	—	202	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	101	1	no	—
69	C₂×C₄	—	101	1	no	—
70	C₂×C₄	—	202	1	no	—
71	C₂×C₄	—	202	1	no	—
72	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	202	1	no	—
75	C₂²	D₄×D₁₀₁	1	1	yes	characteristic
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	101	2	no	—
79	C₄	—	404	1	no	—
80	C₄	—	202	2	no	—
81	C₄	—	202	1	no	—
82	C₄	Q₈×D₁₀₁	1	1	yes	characteristic
83	C₄	#13108074	1	1	yes	characteristic
84	C₂	#15692233	1	1	yes	characteristic
85	C₂	SD₁₆×D₁₀₁	1	1	yes	characteristic
86	C₂	#15692284	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#106×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#106	D₁₀₁
hypocenter	C₁₀₁	#475
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
28. Dic₂₀₂	Q₈	semidirect
43. C₁₀₁	#475	semidirect