Subgroups — #22582867

Order 8992.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₆₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₁₂₄	C₂	1	1	yes	maximal, characteristic
3	#17985115	C₂	1	4	yes	maximal, complemented
4	C₄²×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₂₈₁	C₂²	1	2	yes	—
6	Dic₅₆₂	—	2	2	no	—
7	D₁₁₂₄	—	2	2	no	—
8	C₂×Dic₂₈₁	C₂²	1	2	yes	—
9	C₂×C₄×C₂₈₁	C₂²	1	2	yes	—
10	C₂×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₂²×C₂₈₁	C₂³	1	1	yes	characteristic
12	C₂×D₂₈₁	—	2	2	no	—
13	C₂×D₂₈₁	—	2	4	no	—
14	C₄×C₂₈₁	—	2	2	no	—
15	C₄×C₂₈₁	D₄	1	2	yes	—
16	Dic₂₈₁	—	2	2	no	—
17	C₂×C₂₈₁	C₂×D₄	1	1	yes	characteristic
18	C₂×C₂₈₁	#41	1	2	yes	—
19	D₂₈₁	—	4	2	no	—
20	C₂₈₁	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	281	1	no	maximal, Sylow
22	C₂×Q₈	—	281	1	no	—
23	C₂×D₄	—	281	1	no	—
24	C₂²⋊C₄	—	281	4	no	—
25	C₄²	D₂₈₁	1	1	yes	characteristic, complemented
26	C₂³	—	281	2	no	—
27	Q₈	—	562	2	no	—
28	D₄	—	562	2	no	—
29	C₂×C₄	—	281	2	no	—
30	C₂×C₄	C₂×D₂₈₁	1	2	yes	—
31	C₂×C₄	C₂×D₂₈₁	1	1	yes	characteristic
32	C₂²	—	562	2	no	—
33	C₂²	—	562	4	no	—
34	C₂²	C₂²×D₂₈₁	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	562	2	no	—
37	C₄	D₁₁₂₄	1	2	yes	—
38	C₂	—	1124	2	no	—
39	C₂	C₂×D₁₁₂₄	1	1	yes	characteristic
40	C₂	#17985138	1	2	yes	—

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