Subgroups — C₂×#22583554 #31826889

Order 18112.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#22583554	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₈₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₂₈₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₅₆₆	—	2	1	no	—
6	Dic₁₁₃₂	—	2	1	no	—
7	Dic₁₁₃₂	C₂²	1	2	yes	complemented
8	C₂₈₃⋊C₁₆	C₂²	1	2	yes	complemented
9	C₂×D₄×C₂₈₃	—	2	1	no	—
10	D₈×C₂₈₃	—	2	1	no	—
11	D₈×C₂₈₃	C₂²	1	2	yes	—
12	C₂×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
13	Dic₅₆₆	—	2	2	no	—
14	Dic₅₆₆	—	4	1	no	—
15	C₂×Dic₂₈₃	—	4	1	no	—
16	C₂³×C₂₈₃	—	4	1	no	—
17	D₄×C₂₈₃	—	2	2	no	—
18	D₄×C₂₈₃	—	4	1	no	—
19	C₂×C₄×C₂₈₃	D₄	1	1	yes	characteristic
20	C₈×C₂₈₃	D₄	1	1	yes	characteristic
21	C₈×C₂₈₃	C₂³	1	1	yes	characteristic
22	C₂²×C₂₈₃	—	4	2	no	—
23	C₂²×C₂₈₃	—	8	2	no	—
24	C₂²×C₂₈₃	D₈	1	1	yes	characteristic
25	C₄×C₂₈₃	D₈	1	1	yes	characteristic
26	C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
27	Dic₂₈₃	—	4	2	no	—
28	C₂×C₂₈₃	—	8	2	no	—
29	C₂×C₂₈₃	SD₃₂	1	2	yes	complemented
30	C₂×C₂₈₃	C₂×D₈	1	1	yes	characteristic
31	C₂₈₃	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₃₂	—	283	1	no	maximal, Sylow
33	C₂×Q₁₆	—	283	1	no	—
34	C₂×D₈	D₂₈₃	1	1	yes	characteristic
35	SD₃₂	—	283	4	no	—
36	C₂×C₁₆	—	283	1	no	—
37	C₂×Q₈	—	566	1	no	—
38	C₂×D₄	—	2	1	no	—
39	Q₁₆	—	283	2	no	—
40	Q₁₆	—	566	1	no	—
41	D₈	—	2	1	no	—
42	D₈	C₂×D₂₈₃	1	2	yes	—
43	C₂×C₈	C₂×D₂₈₃	1	1	yes	characteristic
44	C₁₆	—	283	2	no	—
45	C₂³	—	4	1	no	—
46	Q₈	—	566	2	no	—
47	Q₈	—	1132	1	no	—
48	D₄	—	2	2	no	—
49	D₄	—	4	1	no	—
50	C₂×C₄	—	1132	1	no	—
51	C₂×C₄	C₂²⋊D₂₈₃	1	1	yes	characteristic
52	C₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
53	C₈	C₂²×D₂₈₃	1	1	yes	characteristic
54	C₂²	—	4	2	no	—
55	C₂²	—	8	2	no	—
56	C₂²	#17985377	1	1	yes	characteristic
57	C₄	—	1132	2	no	—
58	C₄	#17985377	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₂₈₃	1	1	yes	characteristic
60	C₂	—	8	2	no	—
61	C₂	#22583554	1	2	yes	direct product factor
62	C₂	C₂×#17985377	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17985377
commutator, cosocle	C₈×C₂₈₃	C₂³
Frattini	C₈	C₂²×D₂₈₃
Fitting, prime radical	C₂×D₈×C₂₈₃	C₂
socle	C₂²×C₂₈₃	D₈
hypercenter	C₂×D₈	D₂₈₃
hypocenter	C₂₈₃	C₂×SD₃₂
LCS	G ▷ C₈×C₂₈₃ ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₁₃₂	C₂	semidirect
2. #22583554	C₂	direct (N × H)
3. C₂×C₂₈₃⋊C₁₆	C₂	semidirect
7. Dic₁₁₃₂	C₂²	semidirect
8. C₂₈₃⋊C₁₆	C₂²	semidirect
29. C₂×C₂₈₃	SD₃₂	semidirect
31. C₂₈₃	C₂×SD₃₂	semidirect
61. C₂	#22583554	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×Dic₁₁₃₂	2
#22583554	2
C₂×C₂₈₃⋊C₁₆	2
C₂×D₈×C₂₈₃	2
C₂×SD₃₂	283

Subgroups — C2×#22583554 #31826889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22583554 #31826889