Subgroups — #20265114

Order 6464.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₁₀₁	C₂	1	3	yes	maximal, complemented
2	C₂×#13108051	C₂	1	3	yes	maximal
3	#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₁₀₁	C₂²	1	1	yes	characteristic
5	C₂²×Dic₁₀₁	C₂²	1	3	yes	—
6	C₄⋊Dic₁₀₁	—	2	6	no	—
7	#13108051	—	2	6	no	—
8	C₂²×C₄×C₁₀₁	C₂²	1	3	yes	—
9	C₂³×C₁₀₁	C₂³	1	1	yes	characteristic
10	C₂²×D₁₀₁	—	2	3	no	—
11	C₂²×D₁₀₁	—	2	3	no	—
12	C₂²×D₁₀₁	Q₈	1	2	yes	—
13	C₂×C₄×C₁₀₁	—	2	6	no	—
14	C₂×C₄×C₁₀₁	D₄	1	6	yes	—
15	C₂×Dic₁₀₁	—	2	3	no	—
16	C₂×Dic₁₀₁	—	2	6	no	—
17	C₂²×C₁₀₁	C₂×D₄	1	3	yes	—
18	C₂²×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
19	C₂²×C₁₀₁	#41	1	3	yes	—
20	C₂×D₁₀₁	—	2	6	no	—
21	C₂×D₁₀₁	—	4	3	no	—
22	C₂×D₁₀₁	—	4	1	no	—
23	C₄×C₁₀₁	—	2	6	no	—
24	Dic₁₀₁	—	4	3	no	—
25	C₂×C₁₀₁	C₂²⋊Q₈	1	3	yes	—
26	C₂×C₁₀₁	#123	1	3	yes	—
27	C₂×C₁₀₁	#127	1	1	yes	characteristic
28	D₁₀₁	—	4	2	no	—
29	C₁₀₁	#399	1	1	yes	characteristic, complemented, Sylow
30	#399	—	101	1	no	maximal, Sylow
31	C₂×C₄⋊C₄	—	101	3	no	—
32	C₂×C₂²⋊C₄	—	101	3	no	—
33	#95	D₁₀₁	1	1	yes	characteristic, complemented
34	C₂⁴	—	101	1	no	—
35	C₂²×C₄	—	101	3	no	—
36	C₂²×C₄	C₂×D₁₀₁	1	3	yes	—
37	C₄⋊C₄	—	202	6	no	—
38	C₂²⋊C₄	—	202	6	no	—
39	C₂³	—	101	2	no	—
40	C₂³	—	202	3	no	—
41	C₂³	—	202	3	no	—
42	C₂³	C₂²×D₁₀₁	1	1	yes	characteristic
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	—	202	3	no	—
45	C₂×C₄	—	202	6	no	—
46	C₂×C₄	D₄₀₄	1	6	yes	—
47	C₂²	—	404	3	no	—
48	C₂²	—	404	1	no	—
49	C₂²	—	202	6	no	—
50	C₂²	C₂×D₄₀₄	1	3	yes	—
51	C₂²	Q₈×D₁₀₁	1	1	yes	characteristic
52	C₂²	#13108073	1	3	yes	—
53	C₄	—	2	6	no	—
54	C₄	—	404	3	no	—
55	C₂	—	404	2	no	—
56	C₂	#15692235	1	3	yes	—
57	C₂	#15692239	1	3	yes	—
58	C₂	#15692252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₁
commutator, socle	C₂³×C₁₀₁	C₂³
Fitting	#95×C₁₀₁	C₂
hypercenter	#95	D₁₀₁
hypocenter	C₁₀₁	#399
LCS	G ▷ C₂³×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
1. C₂×C₄⋊Dic₁₀₁	C₂	semidirect
3. #95×C₁₀₁	C₂	semidirect
29. C₁₀₁	#399	semidirect
33. #95	D₁₀₁	semidirect