Subgroups — D₈×D₁₉₁ #20259331

Order 6112.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₁₉₁	C₂	1	2	yes	maximal, complemented
2	D₁₅₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#15690272	C₂	1	2	yes	maximal, complemented
4	C₈×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₉₁	—	2	2	no	—
7	D₇₆₄	C₂²	1	2	yes	complemented
8	C₂²⋊D₁₉₁	—	2	2	no	—
9	C₄×D₁₉₁	C₂²	1	1	yes	characteristic
10	C₁₉₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
11	D₄×C₁₉₁	C₂²	1	2	yes	complemented
12	C₈×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₁₉₁	—	2	2	no	—
14	C₂×D₁₉₁	—	2	2	no	—
15	C₂×D₁₉₁	—	4	4	no	—
16	C₂×D₁₉₁	D₄	1	1	yes	characteristic
17	C₄×C₁₉₁	C₂³	1	1	yes	characteristic
18	Dic₁₉₁	D₄	1	1	yes	characteristic
19	C₂×C₁₉₁	—	4	2	no	—
20	C₂×C₁₉₁	C₂×D₄	1	1	yes	characteristic
21	D₁₉₁	—	4	2	no	—
22	D₁₉₁	D₈	1	2	yes	direct product factor
23	C₁₉₁	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₈	—	191	1	no	maximal, Sylow
25	C₂×D₄	—	191	2	no	—
26	D₈	—	191	2	no	—
27	D₈	—	191	1	no	—
28	D₈	D₁₉₁	1	1	yes	characteristic, direct product factor
29	C₂×C₈	—	191	1	no	—
30	C₂³	—	382	2	no	—
31	D₄	—	382	2	no	—
32	D₄	—	191	2	no	—
33	D₄	C₂×D₁₉₁	1	2	yes	complemented
34	C₂×C₄	—	191	1	no	—
35	C₈	—	191	1	no	—
36	C₈	C₂×D₁₉₁	1	1	yes	characteristic, complemented
37	C₂²	—	2	2	no	—
38	C₂²	—	382	2	no	—
39	C₂²	—	191	1	no	—
40	C₂²	—	764	4	no	—
41	C₄	—	191	1	no	—
42	C₄	C₂²×D₁₉₁	1	1	yes	characteristic
43	C₂	—	4	2	no	—
44	C₂	—	191	2	no	—
45	C₂	—	764	2	no	—
46	C₂	D₄×D₁₉₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₉₁
commutator	C₄×C₁₉₁	C₂³
Frattini	C₄	C₂²×D₁₉₁
Fitting	D₈×C₁₉₁	C₂
socle	C₂×C₁₉₁	C₂×D₄
hypercenter	D₈	D₁₉₁
hypocenter	C₁₉₁	C₂×D₈
LCS	G ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₁₉₁	C₂	semidirect
2. D₁₅₂₈	C₂	semidirect
3. #15690272	C₂	semidirect
4. C₈×D₁₉₁	C₂	semidirect
5. D₈×C₁₉₁	C₂	semidirect
7. D₇₆₄	C₂²	semidirect
10. C₁₉₁⋊C₈	C₂²	semidirect
11. D₄×C₁₉₁	C₂²	semidirect
12. C₈×C₁₉₁	C₂²	semidirect
22. D₁₉₁	D₈	direct (N × H)
23. C₁₉₁	C₂×D₈	semidirect
28. D₈	D₁₉₁	direct (N × H)
33. D₄	C₂×D₁₉₁	semidirect
36. C₈	C₂×D₁₉₁	semidirect

Subgroups — D8×D191 #20259331

Conjugacy classes of subgroups

Complements

Subgroups — D₈×D₁₉₁ #20259331