Subgroups — #22548639

Order 8032.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₂₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₂₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₅₁	—	2	1	no	—
5	C₂₅₁⋊C₈	—	2	1	no	—
6	Q₈×C₂₅₁	—	2	1	no	—
7	Q₈×C₂₅₁	C₄	1	2	yes	complemented
8	C₂×C₄×C₂₅₁	—	2	1	no	—
9	C₂×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
10	C₂²×C₂₅₁	D₄	1	1	yes	characteristic
11	C₄×C₂₅₁	—	2	2	no	—
12	C₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic
13	C₄×C₂₅₁	D₄	1	1	yes	characteristic
14	Dic₂₅₁	—	4	1	no	—
15	C₂×C₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₂₅₁	SD₁₆	1	1	yes	characteristic
17	C₂×C₂₅₁	Q₁₆	1	1	yes	characteristic
18	C₂₅₁	#103	1	1	yes	characteristic, complemented, Sylow
19	#103	—	251	1	no	maximal, Sylow
20	C₂×Q₈	D₂₅₁	1	1	yes	characteristic
21	C₂×C₈	—	251	1	no	—
22	C₄⋊C₄	—	251	1	no	—
23	Q₈	—	2	1	no	—
24	Q₈	Dic₂₅₁	1	2	yes	complemented
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	502	1	no	—
27	C₂×C₄	C₂×D₂₅₁	1	1	yes	characteristic
28	C₈	—	502	1	no	—
29	C₂²	C₂²⋊D₂₅₁	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	—	1004	1	no	—
32	C₄	C₂×Dic₂₅₁	1	1	yes	characteristic
33	C₄	C₂²⋊D₂₅₁	1	1	yes	characteristic
34	C₂	C₂²⋊Dic₂₅₁	1	1	yes	characteristic
35	C₂	#16860797	1	1	yes	characteristic
36	C₂	#16860800	1	1	yes	characteristic

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