Subgroups — #44540385

Order 31712.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30629376	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉₉₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	M₁₆×C₉₉₁	C₂	1	1	yes	maximal, characteristic
4	C₉₉₁⋊C₈	—	2	1	no	—
5	C₉₉₁⋊C₈	C₄	1	2	yes	—
6	C₂×C₄×C₉₉₁	C₂²	1	1	yes	characteristic
7	C₈×C₉₉₁	—	2	1	no	—
8	C₂²×C₉₉₁	Q₈	1	1	yes	characteristic
9	C₄×C₉₉₁	C₂×C₄	1	1	yes	characteristic
10	C₄×C₉₉₁	D₄	1	1	yes	characteristic
11	C₂×C₉₉₁	—	2	1	no	—
12	C₂×C₉₉₁	C₄⋊C₄	1	1	yes	characteristic
13	C₉₉₁	#108	1	1	yes	characteristic, complemented, Sylow
14	#108	—	991	1	no	maximal, Sylow
15	M₁₆	—	991	1	no	—
16	M₁₆	D₉₉₁	1	1	yes	characteristic
17	C₂×C₈	—	991	1	no	—
18	C₂×C₄	C₂×D₉₉₁	1	1	yes	characteristic
19	C₈	—	2	1	no	—
20	C₈	—	1982	1	no	—
21	C₈	—	991	2	no	—
22	C₂²	Dic₁₉₈₂	1	1	yes	characteristic
23	C₄	C₄×D₉₉₁	1	1	yes	characteristic
24	C₄	C₂²⋊D₉₉₁	1	1	yes	characteristic
25	C₂	—	2	1	no	—
26	C₂	Dic₉₉₁⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₉₉₁	#108	semidirect

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