Subgroups — C₂×#16860799 #22548730

Order 8032.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₀₀₄	C₂	1	1	yes	maximal, characteristic
3	#16860799	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₂₅₁	—	2	1	no	—
6	Dic₅₀₂	—	2	1	no	—
7	Dic₅₀₂	C₂²	1	2	yes	complemented
8	D₁₀₀₄	—	2	1	no	—
9	D₁₀₀₄	C₂²	1	2	yes	—
10	C₂×Dic₂₅₁	—	2	1	no	—
11	C₂×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
12	C₈×C₂₅₁	C₂²	1	2	yes	complemented
13	C₂²×C₂₅₁	D₄	1	1	yes	characteristic
14	C₂×D₂₅₁	—	2	2	no	—
15	C₂×D₂₅₁	—	4	2	no	—
16	C₄×C₂₅₁	D₄	1	1	yes	characteristic
17	C₄×C₂₅₁	C₂³	1	1	yes	characteristic
18	Dic₂₅₁	—	2	2	no	—
19	C₂×C₂₅₁	SD₁₆	1	2	yes	complemented
20	C₂×C₂₅₁	C₂×D₄	1	1	yes	characteristic
21	D₂₅₁	—	4	2	no	—
22	C₂₅₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×SD₁₆	—	251	1	no	maximal, Sylow
24	C₂×Q₈	—	251	1	no	—
25	C₂×D₄	—	251	1	no	—
26	SD₁₆	—	251	4	no	—
27	C₂×C₈	D₂₅₁	1	1	yes	characteristic, complemented
28	C₂³	—	502	1	no	—
29	Q₈	—	502	1	no	—
30	Q₈	—	251	2	no	—
31	D₄	—	502	1	no	—
32	D₄	—	251	2	no	—
33	C₂×C₄	—	502	1	no	—
34	C₂×C₄	C₂×D₂₅₁	1	1	yes	characteristic
35	C₈	C₂×D₂₅₁	1	2	yes	complemented
36	C₂²	—	1004	2	no	—
37	C₂²	—	502	2	no	—
38	C₂²	D₁₀₀₄	1	1	yes	characteristic
39	C₄	—	502	2	no	—
40	C₄	D₁₀₀₄	1	1	yes	characteristic
41	C₄	C₂²×D₂₅₁	1	1	yes	characteristic
42	C₂	—	1004	2	no	—
43	C₂	#16860799	1	2	yes	direct product factor
44	C₂	C₂×D₁₀₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₀₀₄
commutator	C₄×C₂₅₁	C₂³
Frattini	C₄	C₂²×D₂₅₁
Fitting	C₂×C₈×C₂₅₁	C₂
socle	C₂²×C₂₅₁	D₄
hypercenter	C₂×C₈	D₂₅₁
hypocenter	C₂₅₁	C₂×SD₁₆
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₅₀₂	C₂	semidirect
3. #16860799	C₂	direct (N × H)
4. C₂×C₈×C₂₅₁	C₂	semidirect
7. Dic₅₀₂	C₂²	semidirect
12. C₈×C₂₅₁	C₂²	semidirect
19. C₂×C₂₅₁	SD₁₆	semidirect
22. C₂₅₁	C₂×SD₁₆	semidirect
27. C₂×C₈	D₂₅₁	semidirect
35. C₈	C₂×D₂₅₁	semidirect
43. C₂	#16860799	direct (N × H)

Subgroups — C2×#16860799 #22548730

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16860799 #22548730