Subgroups — #22582879

Order 8992.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₆₂	C₂	1	2	yes	maximal
2	C₄⋊Dic₂₈₁	C₂	1	4	yes	maximal
3	C₄²×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	Dic₅₆₂	—	2	4	no	—
5	C₂×Dic₂₈₁	C₂²	1	4	yes	—
6	C₂×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₂₈₁	C₂²	1	2	yes	—
8	C₂²×C₂₈₁	C₂³	1	1	yes	characteristic
9	C₄×C₂₈₁	D₄	1	2	yes	—
10	C₄×C₂₈₁	Q₈	1	4	yes	complemented
11	Dic₂₈₁	—	2	4	no	—
12	C₂×C₂₈₁	C₂×D₄	1	1	yes	characteristic
13	C₂×C₂₈₁	C₂×Q₈	1	2	yes	—
14	C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₄⋊Q₈	—	281	1	no	maximal, Sylow
16	C₂×Q₈	—	281	2	no	—
17	C₄⋊C₄	—	281	4	no	—
18	C₄²	D₂₈₁	1	1	yes	characteristic
19	Q₈	—	562	4	no	—
20	C₂×C₄	—	281	4	no	—
21	C₂×C₄	C₂×D₂₈₁	1	1	yes	characteristic
22	C₂×C₄	C₂×D₂₈₁	1	2	yes	—
23	C₂²	C₂²×D₂₈₁	1	1	yes	characteristic
24	C₄	—	562	4	no	—
25	C₄	D₁₁₂₄	1	2	yes	—
26	C₄	Dic₅₆₂	1	4	yes	complemented
27	C₂	C₂×D₁₁₂₄	1	1	yes	characteristic
28	C₂	C₂×Dic₅₆₂	1	2	yes	—

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