Subgroups — #20264925

Order 6464.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692255	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11717579	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₀₂	C₄	1	2	yes	—
5	C₂×#11717579	—	2	1	no	—
6	C₄⋊Dic₁₀₁	—	2	1	no	—
7	C₄⋊Dic₁₀₁	—	2	1	no	—
8	C₂×C₈×C₁₀₁	—	2	1	no	—
9	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
13	C₂×Dic₁₀₁	—	2	2	no	—
14	Dic₂₀₂	—	4	2	no	—
15	C₈×C₁₀₁	—	4	1	no	—
16	#11717579	—	4	1	no	—
17	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₁₀₁	—	2	1	no	—
19	C₄×C₁₀₁	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₀₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₀₁	Q₁₆	1	1	yes	characteristic
22	C₄×C₁₀₁	Q₁₆	1	1	yes	characteristic
23	Dic₁₀₁	—	4	2	no	—
24	C₂×C₁₀₁	#100	1	1	yes	characteristic
25	C₂×C₁₀₁	#103	1	1	yes	characteristic
26	C₂×C₁₀₁	#103	1	1	yes	characteristic
27	C₁₀₁	#333	1	1	yes	characteristic, complemented, Sylow
28	#333	—	101	1	no	maximal, Sylow
29	C₄⋊Q₈	—	101	1	no	—
30	C₄⋊C₈	—	101	1	no	—
31	C₄⋊C₈	D₁₀₁	1	1	yes	characteristic
32	C₂×Q₈	—	101	2	no	—
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	—	202	1	no	—
35	C₄⋊C₄	—	202	1	no	—
36	C₄⋊C₄	—	202	1	no	—
37	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
38	Q₈	—	404	2	no	—
39	C₂×C₄	—	202	2	no	—
40	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
41	C₂×C₄	D₄₀₄	1	1	yes	characteristic
42	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
43	C₈	—	4	1	no	—
44	C₈	—	404	1	no	—
45	C₂²	#13108051	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	404	2	no	—
48	C₄	#13108062	1	1	yes	characteristic
49	C₄	#13108063	1	1	yes	characteristic
50	C₄	#13108064	1	1	yes	characteristic
51	C₄	Dic₄₀₄	1	1	yes	characteristic
52	C₂	#15692171	1	1	yes	characteristic
53	C₂	#15692178	1	1	yes	characteristic
54	C₂	#15692180	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13108051
commutator	C₂×C₄×C₁₀₁	C₂×C₄
Frattini	C₄²	C₂×D₁₀₁
Fitting	C₄⋊C₈×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂²⋊C₄
hypercenter	C₄⋊C₈	D₁₀₁
hypocenter	C₁₀₁	#333
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
27. C₁₀₁	#333	semidirect