Subgroups — #22548715

Order 8032.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₀₂	C₂	1	2	yes	maximal
2	C₄⋊Dic₂₅₁	C₂	1	4	yes	maximal
3	C₄²×C₂₅₁	C₂	1	1	yes	maximal, characteristic
4	Dic₅₀₂	—	2	4	no	—
5	C₂×Dic₂₅₁	C₂²	1	4	yes	—
6	C₂×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₂₅₁	C₂²	1	2	yes	—
8	C₂²×C₂₅₁	C₂³	1	1	yes	characteristic
9	C₄×C₂₅₁	D₄	1	2	yes	—
10	C₄×C₂₅₁	Q₈	1	4	yes	complemented
11	Dic₂₅₁	—	2	4	no	—
12	C₂×C₂₅₁	C₂×D₄	1	1	yes	characteristic
13	C₂×C₂₅₁	C₂×Q₈	1	2	yes	—
14	C₂₅₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₄⋊Q₈	—	251	1	no	maximal, Sylow
16	C₂×Q₈	—	251	2	no	—
17	C₄⋊C₄	—	251	4	no	—
18	C₄²	D₂₅₁	1	1	yes	characteristic
19	Q₈	—	502	4	no	—
20	C₂×C₄	—	251	4	no	—
21	C₂×C₄	C₂×D₂₅₁	1	1	yes	characteristic
22	C₂×C₄	C₂×D₂₅₁	1	2	yes	—
23	C₂²	C₂²×D₂₅₁	1	1	yes	characteristic
24	C₄	—	502	4	no	—
25	C₄	D₁₀₀₄	1	2	yes	—
26	C₄	Dic₅₀₂	1	4	yes	complemented
27	C₂	C₂×D₁₀₀₄	1	1	yes	characteristic
28	C₂	C₂×Dic₅₀₂	1	2	yes	—

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