Subgroups — #31823281

Order 17984.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17985113	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₂₈₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#14555886	C₄	1	1	yes	characteristic
5	C₄×Dic₂₈₁	C₄	1	1	yes	characteristic
6	#17985113	—	2	1	no	—
7	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
8	C₁₆×C₂₈₁	—	2	1	no	—
9	C₂×Dic₂₈₁	C₈	1	1	yes	characteristic
10	C₂×Dic₂₈₁	C₈	1	1	yes	characteristic
11	#14555886	—	2	1	no	—
12	C₂×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
13	C₈×C₂₈₁	D₄	1	1	yes	characteristic
14	C₈×C₂₈₁	Q₈	1	1	yes	characteristic
15	C₂²×C₂₈₁	C₂×C₈	1	1	yes	characteristic
16	C₄×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₂₈₁	M₁₆	1	1	yes	characteristic
18	Dic₂₈₁	—	2	1	no	—
19	Dic₂₈₁	C₁₆	1	2	yes	complemented
20	C₂×C₂₈₁	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₂₈₁	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₂₈₁	M₃₂	1	1	yes	characteristic
23	C₂₈₁	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	281	1	no	maximal, Sylow
25	C₂×C₁₆	—	281	1	no	—
26	C₂×C₁₆	D₂₈₁	1	1	yes	characteristic
27	C₄×C₈	—	281	1	no	—
28	C₂×C₈	—	281	1	no	—
29	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
30	C₄²	—	281	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	562	1	no	—
33	C₂×C₄	—	281	1	no	—
34	C₂×C₄	—	281	1	no	—
35	C₂×C₄	C₄×D₂₈₁	1	1	yes	characteristic
36	C₈	—	562	1	no	—
37	C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
38	C₈	Dic₅₆₂	1	1	yes	characteristic
39	C₂²	C₈×D₂₈₁	1	1	yes	characteristic
40	C₄	—	281	2	no	—
41	C₄	—	562	1	no	—
42	C₄	#17985117	1	1	yes	characteristic
43	C₄	#17985121	1	1	yes	characteristic
44	C₂	#22582808	1	1	yes	characteristic
45	C₂	C₁₆×D₂₈₁	1	1	yes	characteristic
46	C₂	#22582818	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₂₈₁
commutator	C₂×C₂₈₁	C₂×C₁₆
Fitting	C₂×C₁₆×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₂×C₈
cosocle	C₂×C₈×C₂₈₁	C₂²
hypercenter	C₂×C₁₆	D₂₈₁
hypocenter	C₂₈₁	C₄⋊C₁₆
LCS	G ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₂₈₁	C₁₆	semidirect
23. C₂₈₁	C₄⋊C₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#17985113	2
C₈×Dic₂₈₁	2
C₂×C₁₆×C₂₈₁	2
C₄⋊C₁₆	281