Subgroups — #11717581⋊C₈ #20266019

Order 6464.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11717581	C₂	1	1	yes	maximal, characteristic
2	C₄×#11717581	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11717581	C₄	1	2	yes	—
5	C₂×#11717581	C₄	1	2	yes	—
6	C₂×#11717579	C₄	1	1	yes	characteristic
7	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
12	#11717581	—	2	2	no	—
13	#11717581	C₈	1	4	yes	complemented
14	C₈×C₁₀₁	—	2	1	no	—
15	#11717579	—	2	1	no	—
16	C₂²×C₁₀₁	C₄²	1	1	yes	characteristic
17	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
18	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
19	Dic₁₀₁	C₂×C₈	1	2	yes	—
20	Dic₁₀₁	M₁₆	1	2	yes	—
21	C₂×C₁₀₁	C₄×C₈	1	1	yes	characteristic
22	C₂×C₁₀₁	#97	1	1	yes	characteristic
23	C₂×C₁₀₁	#97	1	1	yes	characteristic
24	C₁₀₁	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	101	1	no	maximal, Sylow
26	C₄×C₈	—	101	1	no	—
27	C₄×C₈	—	101	1	no	—
28	C₄×C₈	—	101	1	no	—
29	C₂×C₈	—	101	2	no	—
30	C₂×C₈	—	101	2	no	—
31	C₂×C₈	—	101	1	no	—
32	C₂×C₈	#87938	1	1	yes	characteristic
33	C₄²	—	101	1	no	—
34	C₂×C₄	—	101	1	no	—
35	C₂×C₄	—	101	1	no	—
36	C₂×C₄	C₂×#87938	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	101	4	no	—
39	C₈	—	202	2	no	—
40	C₈	—	202	1	no	—
41	C₂²	C₄×#87938	1	1	yes	characteristic
42	C₄	—	101	2	no	—
43	C₄	—	101	2	no	—
44	C₄	#13108083	1	1	yes	characteristic
45	C₄	#13108084	1	1	yes	characteristic
46	C₂	C₈×#87938	1	1	yes	characteristic
47	C₂	#15692309	1	1	yes	characteristic
48	C₂	#15692310	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#87938
commutator	C₂×C₁₀₁	C₄×C₈
Fitting	C₂×C₈×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₄²
hypercenter	C₂×C₈	#87938
hypocenter	C₁₀₁	#322
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
13. #11717581	C₈	semidirect
24. C₁₀₁	#322	semidirect

Subgroups — #11717581⋊C8 #20266019

Conjugacy classes of subgroups

Complements

Subgroups — #11717581⋊C₈ #20266019