Subgroups — Dic₉₉₁⋊C₈ #44540379

Order 31712.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉₉₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₉₉₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₉₉₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₉₁	C₄	1	1	yes	characteristic
5	C₂×Dic₉₉₁	C₄	1	1	yes	characteristic
6	C₉₉₁⋊C₈	—	2	1	no	—
7	C₂×C₄×C₉₉₁	C₂²	1	1	yes	characteristic
8	C₈×C₉₉₁	—	2	1	no	—
9	C₂²×C₉₉₁	C₂×C₄	1	1	yes	characteristic
10	C₄×C₉₉₁	D₄	1	1	yes	characteristic
11	C₄×C₉₉₁	Q₈	1	1	yes	characteristic
12	Dic₉₉₁	—	2	1	no	—
13	Dic₉₉₁	C₈	1	2	yes	complemented
14	C₂×C₉₉₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₉₉₁	C₂×C₈	1	1	yes	characteristic
16	C₂×C₉₉₁	M₁₆	1	1	yes	characteristic
17	C₉₉₁	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
18	C₄⋊C₈	—	991	1	no	maximal, Sylow
19	C₂×C₈	—	991	1	no	—
20	C₂×C₈	D₉₉₁	1	1	yes	characteristic
21	C₄²	—	991	1	no	—
22	C₂×C₄	—	991	1	no	—
23	C₂×C₄	—	991	1	no	—
24	C₂×C₄	C₂×D₉₉₁	1	1	yes	characteristic
25	C₈	—	2	1	no	—
26	C₈	—	1982	1	no	—
27	C₂²	C₄×D₉₉₁	1	1	yes	characteristic
28	C₄	—	1982	1	no	—
29	C₄	—	991	2	no	—
30	C₄	C₂²⋊D₉₉₁	1	1	yes	characteristic
31	C₄	Dic₁₉₈₂	1	1	yes	characteristic
32	C₂	Dic₉₉₁⋊C₄	1	1	yes	characteristic
33	C₂	C₈×D₉₉₁	1	1	yes	characteristic
34	C₂	#30629375	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. Dic₉₉₁	C₈	semidirect
17. C₉₉₁	C₄⋊C₈	semidirect

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