Subgroups — #20265486

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692246	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#15692189	C₂	1	1	yes	maximal, characteristic
4	#15692186	C₂	1	1	yes	maximal, characteristic
5	#15692184	C₂	1	1	yes	maximal, characteristic
6	#15692179	C₂	1	1	yes	maximal, characteristic
7	#103×C₁₀₁	C₂	1	1	yes	maximal, characteristic
8	C₂×#11717579	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₀₁	—	2	1	no	—
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	C₄×Dic₁₀₁	—	2	1	no	—
15	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
19	Q₈×C₁₀₁	—	2	1	no	—
20	Q₈×C₁₀₁	Q₈	1	2	yes	—
21	C₂×C₄×C₁₀₁	—	2	1	no	—
22	C₂×C₄×C₁₀₁	—	2	1	no	—
23	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₀₁	—	2	1	no	—
25	C₂×Dic₁₀₁	—	2	1	no	—
26	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
27	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
28	C₈×C₁₀₁	—	2	1	no	—
29	#11717579	—	2	1	no	—
30	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₀₁	—	2	2	no	—
32	C₄×C₁₀₁	—	4	1	no	—
33	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₁₀₁	#41	1	1	yes	characteristic
35	Dic₁₀₁	—	2	1	no	—
36	Dic₁₀₁	—	2	1	no	—
37	Dic₁₀₁	—	4	1	no	—
38	Dic₁₀₁	—	4	1	no	—
39	C₂×C₁₀₁	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₁₀₁	#135	1	1	yes	characteristic
41	C₂×C₁₀₁	#137	1	1	yes	characteristic
42	C₁₀₁	#479	1	1	yes	characteristic, complemented, Sylow
43	#479	—	101	1	no	maximal, Sylow
44	#125	—	101	1	no	—
45	C₄×Q₈	—	101	1	no	—
46	#107	—	101	1	no	—
47	#106	—	101	1	no	—
48	C₄⋊C₈	—	101	1	no	—
49	#103	—	101	1	no	—
50	#103	D₁₀₁	1	1	yes	characteristic
51	C₂×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
52	C₂×C₈	—	101	1	no	—
53	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
54	C₄⋊C₄	—	101	1	no	—
55	C₄⋊C₄	—	101	1	no	—
56	C₄⋊C₄	—	202	1	no	—
57	C₄⋊C₄	—	202	1	no	—
58	C₄⋊C₄	—	202	1	no	—
59	C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
60	C₄²	—	101	1	no	—
61	C₄²	—	202	1	no	—
62	Q₈	—	2	1	no	—
63	Q₈	Dic₂₀₂	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	101	1	no	—
67	C₂×C₄	—	101	1	no	—
68	C₂×C₄	—	202	1	no	—
69	C₂×C₄	—	202	1	no	—
70	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	202	1	no	—
73	C₂²	D₄×D₁₀₁	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	4	1	no	—
76	C₄	—	404	1	no	—
77	C₄	—	404	1	no	—
78	C₄	—	202	1	no	—
79	C₄	—	202	1	no	—
80	C₄	C₂×Dic₂₀₂	1	1	yes	characteristic
81	C₄	#13108073	1	1	yes	characteristic
82	C₂	#15692232	1	1	yes	characteristic
83	C₂	#15692278	1	1	yes	characteristic
84	C₂	#15692284	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#103×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#103	D₁₀₁
hypocenter	C₁₀₁	#479
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
42. C₁₀₁	#479	semidirect