Subgroups — #20266079

Order 6464.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692315	C₂	1	1	yes	maximal, characteristic
2	#15692313	C₂	1	1	yes	maximal, characteristic
3	#15692238	C₂	1	1	yes	maximal, characteristic
4	#13108083	—	2	1	no	—
5	C₂²⋊#87938	—	2	1	no	—
6	C₂×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
7	#13108053	—	2	1	no	—
8	C₂²⋊Dic₁₀₁	C₄	1	1	yes	characteristic, complemented
9	#13108051	—	2	1	no	—
10	C₂²×C₄×C₁₀₁	C₄	1	1	yes	characteristic, complemented
11	C₂³×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₁₀₁	D₄	1	1	yes	characteristic
13	C₂×#87938	—	4	1	no	—
14	C₂×C₄×C₁₀₁	—	2	1	no	—
15	C₂×C₄×C₁₀₁	—	4	1	no	—
16	C₂²⋊D₁₀₁	—	4	1	no	—
17	C₂×Dic₁₀₁	—	2	1	no	—
18	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
19	#11717581	—	4	1	no	—
20	C₂²×C₁₀₁	—	2	1	no	—
21	C₂²×C₁₀₁	—	4	1	no	—
22	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₀₁	—	2	1	no	—
24	C₂×D₁₀₁	—	4	1	no	—
25	#87938	—	8	1	no	—
26	C₄×C₁₀₁	—	4	1	no	—
27	Dic₁₀₁	—	2	1	no	—
28	Dic₁₀₁	—	4	1	no	—
29	C₂×C₁₀₁	—	2	1	no	—
30	C₂×C₁₀₁	—	4	1	no	—
31	C₂×C₁₀₁	#99	1	1	yes	characteristic
32	D₁₀₁	—	4	1	no	—
33	C₁₀₁	#352	1	1	yes	characteristic, complemented, Sylow
34	#352	—	101	1	no	maximal, Sylow
35	#123	—	101	1	no	—
36	#100	—	101	1	no	—
37	#99	—	101	1	no	—
38	C₂×D₄	—	101	1	no	—
39	C₂²×C₄	#87938	1	1	yes	characteristic, complemented
40	M₁₆	—	202	1	no	—
41	C₄⋊C₄	—	202	1	no	—
42	C₂²⋊C₄	—	101	1	no	—
43	C₂²⋊C₄	—	202	1	no	—
44	C₂²⋊C₄	—	202	1	no	—
45	C₂³	—	101	1	no	—
46	C₂³	C₂×#87938	1	1	yes	characteristic
47	D₄	—	404	1	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	4	1	no	—
50	C₂×C₄	—	101	1	no	—
51	C₂×C₄	—	404	1	no	—
52	C₂×C₄	—	202	1	no	—
53	C₈	—	404	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	4	1	no	—
56	C₂²	—	404	1	no	—
57	C₂²	—	202	1	no	—
58	C₂²	C₂²⋊#87938	1	1	yes	characteristic
59	C₄	—	4	1	no	—
60	C₄	—	808	1	no	—
61	C₄	—	404	1	no	—
62	C₄	—	202	1	no	—
63	C₂	—	2	1	no	—
64	C₂	—	4	1	no	—
65	C₂	—	404	1	no	—
66	C₂	#15692313	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692313
commutator	C₂³×C₁₀₁	C₂×C₄
Frattini	C₂³	C₂×#87938
Fitting	C₂²×C₄×C₁₀₁	C₄
socle	C₂×C₁₀₁	#99
hypercenter	C₂²×C₄	#87938
hypocenter	C₁₀₁	#352
LCS	G ▷ C₂³×C₁₀₁ ▷ C₂²×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
8. C₂²⋊Dic₁₀₁	C₄	semidirect
10. C₂²×C₄×C₁₀₁	C₄	semidirect
33. C₁₀₁	#352	semidirect
39. C₂²×C₄	#87938	semidirect