Subgroups — #22582874

Order 8992.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#17985117	C₂	1	1	yes	maximal, characteristic, complemented
3	#17985115	C₂	1	1	yes	maximal, characteristic
4	#17985115	C₂	1	1	yes	maximal, characteristic
5	#17985115	C₂	1	1	yes	maximal, characteristic
6	C₄×Dic₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₄×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₂₈₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₈₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₂₈₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₈₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
15	C₂²×C₂₈₁	C₂³	1	1	yes	characteristic
16	C₂×D₂₈₁	—	2	1	no	—
17	C₂×D₂₈₁	—	2	1	no	—
18	C₂×D₂₈₁	—	2	1	no	—
19	C₄×C₂₈₁	—	2	1	no	—
20	C₄×C₂₈₁	—	2	1	no	—
21	C₄×C₂₈₁	—	2	1	no	—
22	Dic₂₈₁	—	2	1	no	—
23	Dic₂₈₁	—	2	1	no	—
24	Dic₂₈₁	—	2	1	no	—
25	C₂×C₂₈₁	#41	1	1	yes	characteristic
26	C₂×C₂₈₁	#41	1	1	yes	characteristic
27	C₂×C₂₈₁	#41	1	1	yes	characteristic
28	D₂₈₁	—	4	1	no	—
29	C₂₈₁	#126	1	1	yes	characteristic, complemented, Sylow
30	#126	—	281	1	no	maximal, Sylow
31	C₄⋊C₄	—	281	1	no	—
32	C₄⋊C₄	—	281	1	no	—
33	C₄⋊C₄	D₂₈₁	1	1	yes	characteristic, complemented
34	C₂²⋊C₄	—	281	1	no	—
35	C₂²⋊C₄	—	281	1	no	—
36	C₂²⋊C₄	—	281	1	no	—
37	C₄²	—	281	1	no	—
38	C₂³	—	281	1	no	—
39	C₂×C₄	—	281	1	no	—
40	C₂×C₄	—	281	1	no	—
41	C₂×C₄	—	281	1	no	—
42	C₂×C₄	C₂×D₂₈₁	1	1	yes	characteristic
43	C₂×C₄	C₂×D₂₈₁	1	1	yes	characteristic
44	C₂×C₄	C₂×D₂₈₁	1	1	yes	characteristic
45	C₂²	—	562	1	no	—
46	C₂²	—	562	1	no	—
47	C₂²	—	562	1	no	—
48	C₂²	C₂²×D₂₈₁	1	1	yes	characteristic
49	C₄	—	2	1	no	—
50	C₄	—	2	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	562	1	no	—
53	C₄	—	562	1	no	—
54	C₄	—	562	1	no	—
55	C₂	—	1124	1	no	—
56	C₂	#17985137	1	1	yes	characteristic
57	C₂	#17985138	1	1	yes	characteristic
58	C₂	#17985139	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₂₈₁
commutator, socle	C₂²×C₂₈₁	C₂³
Fitting	C₄⋊C₄×C₂₈₁	C₂
hypercenter	C₄⋊C₄	D₂₈₁
hypocenter	C₂₈₁	#126
LCS	G ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊Dic₂₈₁	C₂	semidirect
2. #17985117	C₂	semidirect
6. C₄×Dic₂₈₁	C₂	semidirect
7. C₄⋊C₄×C₂₈₁	C₂	semidirect
29. C₂₈₁	#126	semidirect
33. C₄⋊C₄	D₂₈₁	semidirect