Subgroups — C₂×#22582811 #31823494

Order 17984.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₂₈₁	C₂	1	2	yes	maximal
2	#22582811	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₂₈₁	—	2	2	no	—
5	C₄⋊Dic₂₈₁	—	2	2	no	—
6	C₄⋊Dic₂₈₁	C₂²	1	4	yes	—
7	C₂²×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₂₈₁	C₄	1	4	yes	complemented
9	C₂×C₈×C₂₈₁	C₂²	1	2	yes	—
10	C₂×Dic₂₈₁	—	2	4	no	—
11	C₂×Dic₂₈₁	—	4	4	no	—
12	C₂³×C₂₈₁	D₄	1	1	yes	characteristic
13	C₂×C₄×C₂₈₁	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₈₁	Q₈	1	2	yes	—
16	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
17	C₈×C₂₈₁	C₂×C₄	1	4	yes	complemented
18	C₂²×C₂₈₁	C₄⋊C₄	1	2	yes	—
19	C₂²×C₂₈₁	SD₁₆	1	4	yes	—
20	C₂²×C₂₈₁	C₂×D₄	1	1	yes	characteristic
21	C₄×C₂₈₁	C₄⋊C₄	1	2	yes	—
22	C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
24	Dic₂₈₁	—	4	4	no	—
25	C₂×C₂₈₁	#106	1	4	yes	complemented
26	C₂×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₂₈₁	C₂×SD₁₆	1	2	yes	—
28	C₂₈₁	C₂×#106	1	1	yes	characteristic, complemented, Sylow
29	C₂×#106	—	281	1	no	maximal, Sylow
30	C₂²×C₈	D₂₈₁	1	1	yes	characteristic
31	C₂×C₄⋊C₄	—	281	2	no	—
32	#106	—	281	4	no	—
33	C₂²×C₄	—	562	2	no	—
34	C₂²×C₄	C₂×D₂₈₁	1	1	yes	characteristic
35	C₂×C₈	Dic₂₈₁	1	4	yes	complemented
36	C₂×C₈	C₂×D₂₈₁	1	2	yes	—
37	C₄⋊C₄	—	281	4	no	—
38	C₄⋊C₄	—	562	2	no	—
39	C₂³	D₁₁₂₄	1	1	yes	characteristic
40	C₂×C₄	—	562	4	no	—
41	C₂×C₄	—	1124	4	no	—
42	C₂×C₄	C₂×Dic₂₈₁	1	2	yes	—
43	C₂×C₄	D₁₁₂₄	1	1	yes	characteristic
44	C₂×C₄	Dic₅₆₂	1	2	yes	—
45	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
46	C₈	C₂×Dic₂₈₁	1	4	yes	complemented
47	C₂²	C₄⋊Dic₂₈₁	1	2	yes	—
48	C₂²	#17985127	1	4	yes	—
49	C₂²	C₂×D₁₁₂₄	1	1	yes	characteristic
50	C₄	—	1124	4	no	—
51	C₄	C₄⋊Dic₂₈₁	1	2	yes	—
52	C₄	C₂²×Dic₂₈₁	1	1	yes	characteristic
53	C₄	C₂×Dic₅₆₂	1	1	yes	characteristic
54	C₂	#22582811	1	4	yes	direct product factor
55	C₂	C₂×C₄⋊Dic₂₈₁	1	1	yes	characteristic
56	C₂	C₂×#17985127	1	2	yes	—

	subgroup	G/H
center	C₂³	D₁₁₂₄
commutator	C₄×C₂₈₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₈₁
Fitting	C₂²×C₈×C₂₈₁	C₂
socle, prime radical	C₂³×C₂₈₁	D₄
cosocle	C₂×C₄×C₂₈₁	C₂³
hypercenter	C₂²×C₈	D₂₈₁
hypocenter	C₂₈₁	C₂×#106
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #22582811	C₂	direct (N × H)
8. C₂×C₈×C₂₈₁	C₄	semidirect
17. C₈×C₂₈₁	C₂×C₄	semidirect
25. C₂×C₂₈₁	#106	semidirect
28. C₂₈₁	C₂×#106	semidirect
35. C₂×C₈	Dic₂₈₁	semidirect
46. C₈	C₂×Dic₂₈₁	semidirect
54. C₂	#22582811	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₂₈₁	2
#22582811	2
C₂²×C₈×C₂₈₁	2
C₂×#106	281

Subgroups — C2×#22582811 #31823494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22582811 #31823494