Subgroups — #22582911

Order 8992.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985139	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#17985128	C₂	1	1	yes	maximal, characteristic, complemented
4	#17985127	C₂	1	1	yes	maximal, characteristic, complemented
5	#17985125	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985121	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₅₆₂	—	2	1	no	—
9	Dic₅₆₂	C₂²	1	1	yes	characteristic
10	D₁₁₂₄	—	2	1	no	—
11	D₁₁₂₄	C₂²	1	1	yes	characteristic
12	C₄×D₂₈₁	—	2	1	no	—
13	C₄×D₂₈₁	—	2	1	no	—
14	C₄×D₂₈₁	C₂²	1	1	yes	characteristic
15	#14555886	C₂²	1	1	yes	characteristic
16	Q₈×C₂₈₁	C₂²	1	1	yes	characteristic
17	Q₈×C₂₈₁	C₂²	1	1	yes	characteristic
18	C₈×C₂₈₁	C₂²	1	1	yes	characteristic
19	C₂×D₂₈₁	—	2	1	no	—
20	C₂×D₂₈₁	D₄	1	1	yes	characteristic
21	C₄×C₂₈₁	—	2	1	no	—
22	C₄×C₂₈₁	—	2	1	no	—
23	C₄×C₂₈₁	C₂³	1	1	yes	characteristic
24	Dic₂₈₁	—	2	1	no	—
25	Dic₂₈₁	D₄	1	1	yes	characteristic
26	C₂×C₂₈₁	C₂×D₄	1	1	yes	characteristic
27	D₂₈₁	—	2	1	no	—
28	D₂₈₁	—	4	1	no	—
29	C₂₈₁	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	281	1	no	maximal, Sylow
31	#41	—	281	1	no	—
32	C₂×Q₈	—	281	1	no	—
33	Q₁₆	—	281	1	no	—
34	Q₁₆	D₂₈₁	1	1	yes	characteristic, complemented
35	SD₁₆	—	281	1	no	—
36	SD₁₆	—	281	1	no	—
37	M₁₆	—	281	1	no	—
38	Q₈	—	281	1	no	—
39	Q₈	—	562	1	no	—
40	Q₈	C₂×D₂₈₁	1	1	yes	characteristic
41	Q₈	C₂×D₂₈₁	1	1	yes	characteristic
42	D₄	—	281	1	no	—
43	D₄	—	562	1	no	—
44	C₂×C₄	—	281	1	no	—
45	C₂×C₄	—	562	1	no	—
46	C₂×C₄	—	562	1	no	—
47	C₈	—	281	1	no	—
48	C₈	C₂×D₂₈₁	1	1	yes	characteristic
49	C₂²	—	281	1	no	—
50	C₂²	—	562	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	281	1	no	—
54	C₄	—	562	1	no	—
55	C₄	C₂²×D₂₈₁	1	1	yes	characteristic
56	C₂	—	562	1	no	—
57	C₂	—	1124	1	no	—
58	C₂	D₄×D₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₂₈₁
commutator	C₄×C₂₈₁	C₂³
Frattini	C₄	C₂²×D₂₈₁
Fitting	Q₁₆×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₂×D₄
hypercenter	Q₁₆	D₂₈₁
hypocenter	C₂₈₁	#137
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₂₈₁	C₂	semidirect
3. #17985128	C₂	semidirect
4. #17985127	C₂	semidirect
5. #17985125	C₂	semidirect
6. #17985121	C₂	semidirect
7. Q₁₆×C₂₈₁	C₂	semidirect
29. C₂₈₁	#137	semidirect
34. Q₁₆	D₂₈₁	semidirect