Subgroups — C₂×#22582871 #31823985

Order 17984.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582871	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊Dic₂₈₁	C₂	1	2	yes	maximal
3	C₂×#17985117	C₂	1	4	yes	maximal
4	C₂×C₄²×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₂₈₁	C₂²	1	4	yes	—
6	C₄⋊Dic₂₈₁	C₂²	1	8	yes	—
7	#17985117	C₂²	1	16	yes	—
8	C₂²×C₄×C₂₈₁	C₂²	1	2	yes	—
9	C₂²×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₄²×C₂₈₁	C₂²	1	4	yes	—
11	C₂×Dic₂₈₁	—	2	8	no	—
12	C₂×Dic₂₈₁	C₂³	1	8	yes	—
13	C₂³×C₂₈₁	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₂₈₁	—	2	4	no	—
15	C₂×C₄×C₂₈₁	Q₈	1	4	yes	—
16	C₂×C₄×C₂₈₁	C₂³	1	4	yes	—
17	C₂×C₄×C₂₈₁	C₂³	1	2	yes	—
18	C₂²×C₂₈₁	C₂×Q₈	1	2	yes	—
19	C₂²×C₂₈₁	#41	1	4	yes	—
20	C₂²×C₂₈₁	C₂⁴	1	1	yes	characteristic
21	C₄×C₂₈₁	—	2	4	no	—
22	C₄×C₂₈₁	C₂×Q₈	1	4	yes	—
23	Dic₂₈₁	—	2	8	no	—
24	C₂×C₂₈₁	#125	1	4	yes	complemented
25	C₂×C₂₈₁	C₂²×Q₈	1	1	yes	characteristic
26	C₂×C₂₈₁	C₂×#41	1	2	yes	—
27	C₂₈₁	C₂×#125	1	1	yes	characteristic, complemented, Sylow
28	C₂×#125	—	281	1	no	maximal, Sylow
29	#125	—	281	8	no	—
30	C₂×C₄⋊C₄	—	281	4	no	—
31	C₂×C₄⋊C₄	—	281	2	no	—
32	C₂×C₄²	D₂₈₁	1	1	yes	characteristic
33	C₂²×C₄	—	281	4	no	—
34	C₂²×C₄	C₂×D₂₈₁	1	2	yes	—
35	C₂²×C₄	C₂×D₂₈₁	1	1	yes	characteristic
36	C₄⋊C₄	—	281	16	no	—
37	C₄⋊C₄	—	281	8	no	—
38	C₄²	C₂×D₂₈₁	1	4	yes	—
39	C₂³	C₂²×D₂₈₁	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	—	281	8	no	—
42	C₂×C₄	—	562	8	no	—
43	C₂×C₄	Dic₅₆₂	1	4	yes	—
44	C₂×C₄	C₂²×D₂₈₁	1	4	yes	—
45	C₂×C₄	C₂²×D₂₈₁	1	2	yes	—
46	C₂²	C₂×Dic₅₆₂	1	2	yes	—
47	C₂²	#17985138	1	4	yes	—
48	C₂²	C₂³×D₂₈₁	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	562	8	no	—
51	C₄	C₂×Dic₅₆₂	1	4	yes	—
52	C₂	#22582871	1	4	yes	direct product factor
53	C₂	C₂²×Dic₅₆₂	1	1	yes	characteristic
54	C₂	C₂×#17985138	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₈₁
commutator, cosocle	C₂²×C₂₈₁	C₂⁴
Frattini	C₂²	C₂³×D₂₈₁
Fitting	C₂×C₄²×C₂₈₁	C₂
socle, prime radical	C₂³×C₂₈₁	C₂³
hypercenter	C₂×C₄²	D₂₈₁
hypocenter	C₂₈₁	C₂×#125
LCS	G ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #22582871	C₂	direct (N × H)
24. C₂×C₂₈₁	#125	semidirect
27. C₂₈₁	C₂×#125	semidirect
52. C₂	#22582871	direct (N × H)

Maximal subgroups

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

subgroup	index
#22582871	2
C₂×C₄⋊Dic₂₈₁	2
C₂×#17985117	2
C₂×C₄²×C₂₈₁	2
C₂×#125	281

Subgroups — C2×#22582871 #31823985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22582871 #31823985