Subgroups — #31823587

Order 17984.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₅₆₂	C₂	1	1	yes	maximal, characteristic
2	#22582808	C₂	1	2	yes	maximal
3	C₄×#14555886	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₂₈₁	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₆₂	C₄	1	1	yes	characteristic
7	C₂×#14555886	C₂²	1	1	yes	characteristic
8	C₂×#14555886	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₈₁	C₄	1	1	yes	characteristic
10	#17985117	C₄	1	2	yes	—
11	C₄×Dic₂₈₁	C₂²	1	2	yes	—
12	C₂×C₈×C₂₈₁	C₂²	1	2	yes	—
13	C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
14	Dic₅₆₂	C₈	1	4	yes	complemented
15	C₂×Dic₂₈₁	C₂×C₄	1	2	yes	—
16	C₂×Dic₂₈₁	C₂×C₄	1	2	yes	—
17	#14555886	—	2	1	no	—
18	#14555886	Q₈	1	2	yes	complemented
19	C₂×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
22	C₈×C₂₈₁	—	2	2	no	—
23	C₂²×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₂₈₁	—	2	1	no	—
25	C₄×C₂₈₁	C₂×C₈	1	2	yes	—
26	C₄×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₂₈₁	#41	1	1	yes	characteristic
28	Dic₂₈₁	—	2	2	no	—
29	Dic₂₈₁	C₂×C₈	1	4	yes	—
30	C₂×C₂₈₁	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₂₈₁	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₂₈₁	#131	1	1	yes	characteristic
33	C₂₈₁	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
34	C₈×Q₈	—	281	1	no	maximal, Sylow
35	C₄×Q₈	—	281	1	no	—
36	C₄⋊C₈	—	281	2	no	—
37	C₄⋊C₈	D₂₈₁	1	1	yes	characteristic
38	C₄×C₈	—	281	2	no	—
39	C₄×C₈	—	281	1	no	—
40	C₂×Q₈	—	281	1	no	—
41	C₂×C₈	—	281	1	no	—
42	C₂×C₈	—	281	1	no	—
43	C₂×C₈	C₂×D₂₈₁	1	2	yes	—
44	C₄⋊C₄	—	281	2	no	—
45	C₄⋊C₄	—	281	1	no	—
46	C₄²	—	281	2	no	—
47	C₄²	C₂×D₂₈₁	1	1	yes	characteristic
48	Q₈	—	281	4	no	—
49	C₂×C₄	—	281	2	no	—
50	C₂×C₄	—	281	2	no	—
51	C₂×C₄	C₄×D₂₈₁	1	1	yes	characteristic
52	C₂×C₄	C₄×D₂₈₁	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	281	2	no	—
56	C₈	—	562	1	no	—
57	C₂²	C₂×C₄×D₂₈₁	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	281	4	no	—
60	C₄	—	562	2	no	—
61	C₄	C₈×D₂₈₁	1	2	yes	—
62	C₄	Q₈×D₂₈₁	1	1	yes	characteristic
63	C₄	#17985137	1	1	yes	characteristic
64	C₂	#22582844	1	1	yes	characteristic
65	C₂	C₂×C₈×D₂₈₁	1	1	yes	characteristic
66	C₂	#22582887	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₈₁
commutator	C₂×C₂₈₁	C₂²×C₈
Fitting	C₄⋊C₈×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₂²×C₄
cosocle	C₂×C₄×C₂₈₁	C₂³
hypercenter	C₄⋊C₈	D₂₈₁
hypocenter	C₂₈₁	C₈×Q₈
LCS	G ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
14. Dic₅₆₂	C₈	semidirect
18. #14555886	Q₈	semidirect
33. C₂₈₁	C₈×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₅₆₂	2
#22582808	2
C₄×#14555886	2
C₈×Dic₂₈₁	2
C₄⋊C₈×C₂₈₁	2
C₈×Q₈	281