Subgroups — (C₂×D₉₉₁)⋊C₈ #44540362

Order 31712.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₉₉₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉₉₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₉₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₉₉₁	C₄	1	1	yes	characteristic
5	C₂×Dic₉₉₁	C₄	1	1	yes	characteristic
6	C₄×D₉₉₁	—	2	1	no	—
7	C₄×D₉₉₁	—	2	1	no	—
8	C₉₉₁⋊C₈	—	2	1	no	—
9	C₂×C₄×C₉₉₁	C₂²	1	1	yes	characteristic
10	C₈×C₉₉₁	—	2	1	no	—
11	C₂²×C₉₉₁	C₂×C₄	1	1	yes	characteristic
12	C₂×D₉₉₁	—	2	1	no	—
13	C₂×D₉₉₁	—	2	1	no	—
14	C₂×D₉₉₁	C₈	1	2	yes	complemented
15	C₄×C₉₉₁	D₄	1	1	yes	characteristic
16	C₄×C₉₉₁	D₄	1	1	yes	characteristic
17	Dic₉₉₁	—	2	1	no	—
18	C₂×C₉₉₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₉₉₁	C₂×C₈	1	1	yes	characteristic
20	C₂×C₉₉₁	M₁₆	1	1	yes	characteristic
21	D₉₉₁	—	2	2	no	—
22	C₉₉₁	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
23	C₂²⋊C₈	—	991	1	no	maximal, Sylow
24	C₂²×C₄	—	991	1	no	—
25	C₂×C₈	—	991	1	no	—
26	C₂×C₈	D₉₉₁	1	1	yes	characteristic, complemented
27	C₂³	—	991	1	no	—
28	C₂×C₄	—	1982	1	no	—
29	C₂×C₄	—	1982	1	no	—
30	C₂×C₄	—	991	1	no	—
31	C₂×C₄	C₂×D₉₉₁	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	1982	1	no	—
34	C₂²	—	1982	1	no	—
35	C₂²	—	1982	1	no	—
36	C₂²	—	991	2	no	—
37	C₂²	C₄×D₉₉₁	1	1	yes	characteristic
38	C₄	—	1982	1	no	—
39	C₄	C₂²⋊D₉₉₁	1	1	yes	characteristic
40	C₄	D₃₉₆₄	1	1	yes	characteristic
41	C₂	—	1982	2	no	—
42	C₂	(C₂×D₉₉₁)⋊C₄	1	1	yes	characteristic
43	C₂	C₈×D₉₉₁	1	1	yes	characteristic
44	C₂	#30629375	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₉₉₁
commutator	C₂×C₉₉₁	C₂×C₈
Fitting	C₂×C₈×C₉₉₁	C₂
socle	C₂²×C₉₉₁	C₂×C₄
prime radical	C₂²×D₉₉₁	C₄
cosocle	C₂×C₄×C₉₉₁	C₂²
hypercenter	C₂×C₈	D₉₉₁
hypocenter	C₉₉₁	C₂²⋊C₈
LCS	G ▷ C₂×C₉₉₁ ▷ C₉₉₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₉₉₁⋊C₈	C₂	semidirect
3. C₂×C₈×C₉₉₁	C₂	semidirect
14. C₂×D₉₉₁	C₈	semidirect
22. C₉₉₁	C₂²⋊C₈	semidirect
26. C₂×C₈	D₉₉₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×D₉₉₁	2
C₂×C₉₉₁⋊C₈	2
C₂×C₈×C₉₉₁	2
C₂²⋊C₈	991

Subgroups — (C2×D991)⋊C8 #44540362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₉₉₁)⋊C₈ #44540362