Subgroups — C₈×Dic₉₉₁ #44540358

Order 31712.

44 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	2	yes	—
5	C₉₉₁⋊C₈	C₄	1	2	yes	complemented
6	C₂×C₄×C₉₉₁	C₂²	1	1	yes	characteristic
7	C₈×C₉₉₁	C₄	1	2	yes	complemented
8	C₂²×C₉₉₁	C₂×C₄	1	1	yes	characteristic
9	C₄×C₉₉₁	C₂×C₄	1	1	yes	characteristic
10	C₄×C₉₉₁	C₂×C₄	1	1	yes	characteristic
11	Dic₉₉₁	C₈	1	4	yes	direct product factor
12	C₂×C₉₉₁	C₄²	1	1	yes	characteristic
13	C₂×C₉₉₁	C₂×C₈	1	2	yes	—
14	C₉₉₁	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₈	—	991	1	no	maximal, Sylow
16	C₂×C₈	—	991	1	no	—
17	C₂×C₈	D₉₉₁	1	1	yes	characteristic
18	C₄²	—	991	1	no	—
19	C₂×C₄	—	991	2	no	—
20	C₂×C₄	C₂×D₉₉₁	1	1	yes	characteristic
21	C₈	—	991	2	no	—
22	C₈	Dic₉₉₁	1	2	yes	direct product factor
23	C₂²	C₄×D₉₉₁	1	1	yes	characteristic
24	C₄	—	991	4	no	—
25	C₄	C₄×D₉₉₁	1	1	yes	characteristic
26	C₄	C₂×Dic₉₉₁	1	1	yes	characteristic
27	C₂	C₄×Dic₉₉₁	1	1	yes	characteristic
28	C₂	C₈×D₉₉₁	1	2	yes	—

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

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