Subgroups — #20264935

Order 6464.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108058	C₂	1	2	yes	maximal
2	C₂×M₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#13108058	—	2	2	no	—
4	#13108058	—	2	2	no	—
5	C₂×#11717579	C₄	1	4	yes	—
6	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
7	M₁₆×C₁₀₁	—	2	2	no	—
8	C₂×C₈×C₁₀₁	C₄	1	2	yes	—
9	C₂³×C₁₀₁	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
14	C₈×C₁₀₁	—	2	2	no	—
15	#11717579	—	2	4	no	—
16	C₂²×C₁₀₁	—	4	1	no	—
17	C₂²×C₁₀₁	C₄⋊C₄	1	2	yes	—
18	C₂²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₁	C₄²	1	1	yes	characteristic
20	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
21	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₁₀₁	—	2	2	no	—
23	C₂×C₁₀₁	—	2	1	no	—
24	C₂×C₁₀₁	#95	1	1	yes	characteristic
25	C₁₀₁	#338	1	1	yes	characteristic, complemented, Sylow
26	#338	—	101	1	no	maximal, Sylow
27	C₂×M₁₆	—	101	2	no	—
28	C₂×M₁₆	D₁₀₁	1	1	yes	characteristic
29	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
30	M₁₆	—	2	2	no	—
31	M₁₆	—	202	2	no	—
32	M₁₆	—	202	2	no	—
33	C₂×C₈	—	101	4	no	—
34	C₂×C₈	Dic₁₀₁	1	2	yes	—
35	C₂³	Dic₂₀₂	1	1	yes	characteristic
36	C₂×C₄	C₄×D₁₀₁	1	2	yes	—
37	C₂×C₄	D₄₀₄	1	1	yes	characteristic
38	C₂×C₄	C₂×Dic₁₀₁	1	1	yes	characteristic
39	C₂×C₄	C₂²⋊D₁₀₁	1	2	yes	—
40	C₈	—	2	2	no	—
41	C₈	—	202	4	no	—
42	C₂²	—	4	1	no	—
43	C₂²	#13108053	1	2	yes	—
44	C₂²	C₄⋊Dic₁₀₁	1	1	yes	characteristic
45	C₄	C₄×Dic₁₀₁	1	1	yes	characteristic
46	C₄	#13108051	1	2	yes	—
47	C₄	C₂²⋊Dic₁₀₁	1	1	yes	characteristic
48	C₂	—	2	2	no	—
49	C₂	—	2	1	no	—
50	C₂	#15692162	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₁₀₁
commutator	C₄×C₁₀₁	C₄²
Frattini	C₂²×C₄	C₂×D₁₀₁
Fitting	C₂×M₁₆×C₁₀₁	C₂
socle	C₂×C₁₀₁	#95
hypercenter	C₂×M₁₆	D₁₀₁
hypocenter	C₁₀₁	#338
LCS	G ▷ C₄×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
25. C₁₀₁	#338	semidirect