Subgroups — #20265414

Order 6464.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₀₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692230	C₂	1	2	yes	maximal, complemented
4	#15692175	C₂	1	2	yes	maximal, complemented
5	#107×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₀₄	—	2	2	no	—
7	C₂×D₄₀₄	C₂²	1	2	yes	—
8	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
9	D₈₀₈	—	2	2	no	—
10	C₂×#11717579	C₂²	1	1	yes	characteristic
11	C₈×D₁₀₁	—	2	2	no	—
12	#13108051	—	2	2	no	—
13	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×D₁₀₁	—	2	2	no	—
16	C₂²×D₁₀₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	—	2	2	no	—
18	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
20	D₄₀₄	—	2	2	no	—
21	D₄₀₄	—	2	2	no	—
22	D₄₀₄	—	4	4	no	—
23	C₄×D₁₀₁	—	2	1	no	—
24	C₄×D₁₀₁	—	2	1	no	—
25	C₈×C₁₀₁	D₄	1	2	yes	complemented
26	#11717579	—	2	1	no	—
27	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
28	C₂×D₁₀₁	—	2	1	no	—
29	C₂×D₁₀₁	—	2	1	no	—
30	C₂×D₁₀₁	—	4	2	no	—
31	C₂×D₁₀₁	—	4	2	no	—
32	C₂×D₁₀₁	—	4	2	no	—
33	C₂×D₁₀₁	D₈	1	2	yes	complemented
34	C₄×C₁₀₁	—	4	2	no	—
35	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₀₁	#41	1	1	yes	characteristic
37	Dic₁₀₁	—	2	1	no	—
38	C₂×C₁₀₁	#121	1	1	yes	characteristic
39	C₂×C₁₀₁	C₂×D₈	1	1	yes	characteristic
40	C₂×C₁₀₁	#135	1	1	yes	characteristic
41	D₁₀₁	—	2	2	no	—
42	D₁₀₁	—	8	2	no	—
43	C₁₀₁	#466	1	1	yes	characteristic, complemented, Sylow
44	#466	—	101	1	no	maximal, Sylow
45	C₂×D₈	—	101	1	no	—
46	C₂²×C₈	—	101	1	no	—
47	#121	—	101	2	no	—
48	#107	D₁₀₁	1	1	yes	characteristic, complemented
49	#102	—	101	2	no	—
50	C₂×D₄	—	101	2	no	—
51	C₂×D₄	—	202	2	no	—
52	C₂²×C₄	—	101	1	no	—
53	D₈	—	202	2	no	—
54	C₂×C₈	—	101	1	no	—
55	C₂×C₈	—	202	2	no	—
56	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
57	C₄⋊C₄	C₂×D₁₀₁	1	2	yes	—
58	C₂²⋊C₄	—	202	2	no	—
59	C₂³	—	101	1	no	—
60	C₂³	—	202	2	no	—
61	D₄	—	404	4	no	—
62	D₄	—	202	2	no	—
63	D₄	—	202	2	no	—
64	C₂×C₄	—	2	2	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	—	202	1	no	—
70	C₈	D₄₀₄	1	2	yes	complemented
71	C₂²	—	101	2	no	—
72	C₂²	—	404	2	no	—
73	C₂²	—	404	2	no	—
74	C₂²	—	404	2	no	—
75	C₂²	—	202	1	no	—
76	C₂²	—	202	1	no	—
77	C₂²	D₄×D₁₀₁	1	1	yes	characteristic
78	C₄	—	4	2	no	—
79	C₄	—	202	1	no	—
80	C₄	C₂×D₄₀₄	1	1	yes	characteristic
81	C₄	#13108075	1	1	yes	characteristic
82	C₂	—	808	2	no	—
83	C₂	—	202	2	no	—
84	C₂	#15692230	1	1	yes	characteristic
85	C₂	D₈×D₁₀₁	1	1	yes	characteristic
86	C₂	#15692278	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	#466
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
1. C₂×D₈₀₈	C₂	semidirect
2. C₂×C₈×D₁₀₁	C₂	semidirect
3. #15692230	C₂	semidirect
4. #15692175	C₂	semidirect
5. #107×C₁₀₁	C₂	semidirect
25. C₈×C₁₀₁	D₄	semidirect
33. C₂×D₁₀₁	D₈	semidirect
43. C₁₀₁	#466	semidirect
48. #107	D₁₀₁	semidirect
70. C₈	D₄₀₄	semidirect