Subgroups — #31823831

Order 17984.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582871	C₂	1	1	yes	maximal, characteristic
2	#22582803	C₂	1	4	yes	maximal
3	#22582790	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#14555886	C₂²	1	2	yes	—
6	C₄⋊Dic₂₈₁	C₂²	1	2	yes	—
7	#17985117	—	2	2	no	—
8	C₂×Q₈×C₂₈₁	C₂²	1	2	yes	—
9	C₄⋊C₄×C₂₈₁	—	2	2	no	—
10	C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₈₁	—	2	2	no	—
12	#14555886	—	2	2	no	—
13	Q₈×C₂₈₁	—	2	4	no	—
14	C₂×C₄×C₂₈₁	—	2	2	no	—
15	C₂×C₄×C₂₈₁	D₄	1	2	yes	—
16	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
17	C₂²×C₂₈₁	C₂×D₄	1	1	yes	characteristic
18	C₄×C₂₈₁	—	2	2	no	—
19	C₄×C₂₈₁	—	4	2	no	—
20	C₄×C₂₈₁	#41	1	2	yes	—
21	Dic₂₈₁	—	4	2	no	—
22	C₂×C₂₈₁	#124	1	1	yes	characteristic
23	C₂×C₂₈₁	#137	1	2	yes	—
24	C₂₈₁	#491	1	1	yes	characteristic, complemented, Sylow
25	#491	—	281	1	no	maximal, Sylow
26	C₄⋊Q₈	D₂₈₁	1	1	yes	characteristic
27	#125	—	281	1	no	—
28	#103	—	281	4	no	—
29	#97	—	281	1	no	—
30	C₂×Q₈	C₂×D₂₈₁	1	2	yes	—
31	C₂×C₈	—	281	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	281	2	no	—
34	C₄⋊C₄	—	562	2	no	—
35	C₄²	C₂×D₂₈₁	1	1	yes	characteristic
36	Q₈	—	2	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	562	2	no	—
39	C₂×C₄	C₂²⋊D₂₈₁	1	2	yes	—
40	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
41	C₈	—	562	2	no	—
42	C₂²	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	1124	2	no	—
46	C₄	#17985137	1	2	yes	—
47	C₂	#22582866	1	1	yes	characteristic
48	C₂	#22582910	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₈₁
commutator, cosocle	C₂×C₄×C₂₈₁	C₂³
Frattini	C₂×C₄	C₂²×D₂₈₁
Fitting	C₄⋊Q₈×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₂×D₄
hypercenter	C₄⋊Q₈	D₂₈₁
hypocenter	C₂₈₁	#491
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
24. C₂₈₁	#491	semidirect

Maximal subgroups

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

subgroup	index
#22582871	2
#22582803	2
#22582790	2
C₄⋊Q₈×C₂₈₁	2
#491	281