Subgroups — #20264995

Order 6464.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108049	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11717579	C₄	1	1	yes	characteristic
5	C₄×Dic₁₀₁	C₄	1	1	yes	characteristic
6	#13108049	—	2	1	no	—
7	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₀₁	—	2	1	no	—
9	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₀₁	C₈	1	1	yes	characteristic
11	C₂×Dic₁₀₁	C₈	1	1	yes	characteristic
12	C₈×C₁₀₁	D₄	1	1	yes	characteristic
13	C₈×C₁₀₁	Q₈	1	1	yes	characteristic
14	#11717579	—	2	1	no	—
15	C₂²×C₁₀₁	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
18	Dic₁₀₁	—	2	1	no	—
19	Dic₁₀₁	C₁₆	1	2	yes	complemented
20	C₂×C₁₀₁	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₁₀₁	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₀₁	M₃₂	1	1	yes	characteristic
23	C₁₀₁	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	101	1	no	maximal, Sylow
25	C₂×C₁₆	—	101	1	no	—
26	C₂×C₁₆	D₁₀₁	1	1	yes	characteristic
27	C₄×C₈	—	101	1	no	—
28	C₂×C₈	—	101	1	no	—
29	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
30	C₄²	—	101	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	202	1	no	—
33	C₂×C₄	—	101	1	no	—
34	C₂×C₄	—	101	1	no	—
35	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
36	C₈	—	202	1	no	—
37	C₈	Dic₂₀₂	1	1	yes	characteristic
38	C₈	C₂²⋊D₁₀₁	1	1	yes	characteristic
39	C₂²	C₈×D₁₀₁	1	1	yes	characteristic
40	C₄	—	101	2	no	—
41	C₄	—	202	1	no	—
42	C₄	#13108053	1	1	yes	characteristic
43	C₄	#13108057	1	1	yes	characteristic
44	C₂	#15692184	1	1	yes	characteristic
45	C₂	C₁₆×D₁₀₁	1	1	yes	characteristic
46	C₂	#15692194	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×C₈
hypercenter	C₂×C₁₆	D₁₀₁
hypocenter	C₁₀₁	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₁₀₁	C₁₆	semidirect
23. C₁₀₁	C₄⋊C₁₆	semidirect