Subgroups — C₂×#17985128 #22582896

Order 8992.

60 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
2	#17985128	C₂	1	4	yes	maximal, direct product factor
3	C₂×#14555886	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	Dic₅₆₂	—	2	1	no	—
6	Dic₅₆₂	C₂²	1	2	yes	—
7	C₂×Dic₂₈₁	—	2	1	no	—
8	#14555886	C₂²	1	2	yes	—
9	Q₈×C₂₈₁	—	2	1	no	—
10	Q₈×C₂₈₁	C₂²	1	2	yes	—
11	C₂×C₄×C₂₈₁	—	2	1	no	—
12	C₂×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₂²×C₂₈₁	D₄	1	1	yes	characteristic
14	C₄×C₂₈₁	—	2	2	no	—
15	C₄×C₂₈₁	D₄	1	1	yes	characteristic
16	C₄×C₂₈₁	C₂³	1	1	yes	characteristic
17	Dic₂₈₁	—	2	2	no	—
18	C₂×C₂₈₁	Q₁₆	1	2	yes	complemented
19	C₂×C₂₈₁	C₂×D₄	1	1	yes	characteristic
20	C₂₈₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	281	1	no	maximal, Sylow
22	C₂×Q₈	—	281	1	no	—
23	C₂×Q₈	D₂₈₁	1	1	yes	characteristic
24	Q₁₆	—	281	4	no	—
25	C₂×C₈	—	281	1	no	—
26	Q₈	—	2	1	no	—
27	Q₈	—	281	2	no	—
28	Q₈	—	562	1	no	—
29	Q₈	C₂×D₂₈₁	1	2	yes	—
30	C₂×C₄	—	2	1	no	—
31	C₂×C₄	—	562	1	no	—
32	C₂×C₄	C₂×D₂₈₁	1	1	yes	characteristic
33	C₈	—	281	2	no	—
34	C₂²	C₂²⋊D₂₈₁	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	562	2	no	—
37	C₄	C₂²⋊D₂₈₁	1	1	yes	characteristic
38	C₄	C₂²×D₂₈₁	1	1	yes	characteristic
39	C₂	#17985128	1	2	yes	direct product factor
40	C₂	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic

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