Subgroups — C₄×D₁₁₂₄ #22582843

Order 8992.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₄	C₂×D₂₈₁
commutator	C₂×C₂₈₁	C₂²×C₄
Frattini	C₂²	C₂²×D₂₈₁
Fitting	C₄²×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂³
hypercenter	C₄²	D₂₈₁
hypocenter	C₂₈₁	C₄×D₄
LCS	G ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₂₈₁	C₂	semidirect
3. C₄⋊Dic₂₈₁	C₂	semidirect
4. #17985115	C₂	semidirect
5. C₄²×C₂₈₁	C₂	semidirect
7. D₁₁₂₄	C₄	direct (N × H)
16. C₂×D₂₈₁	C₂×C₄	semidirect
18. C₄×C₂₈₁	C₂×C₄	semidirect
19. C₄×C₂₈₁	D₄	semidirect
25. C₂₈₁	C₄×D₄	semidirect
31. C₄²	D₂₈₁	semidirect
45. C₄	C₄×D₂₈₁	semidirect
46. C₄	D₁₁₂₄	direct (N × H)

Subgroups — C4×D1124 #22582843

Conjugacy classes of subgroups

Complements

Subgroups — C₄×D₁₁₂₄ #22582843