Subgroups — #31827282

Order 18112.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22583657	C₂	1	2	yes	maximal, complemented
2	#22583643	C₂	1	6	yes	maximal, complemented
3	#22583632	C₂	1	3	yes	maximal, complemented
4	C₂×Dic₁₁₃₂	C₂	1	3	yes	maximal, complemented
5	#131×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985392	C₂²	1	6	yes	—
7	#17985391	—	2	6	no	—
8	C₂×Dic₅₆₆	C₂²	1	6	yes	—
9	Q₈×D₂₈₃	—	2	2	no	—
10	Dic₁₁₃₂	C₂²	1	3	yes	—
11	Dic₁₁₃₂	C₂²	1	6	yes	—
12	#17985381	C₂²	1	6	yes	—
13	D₂₂₆₄	C₂²	1	1	yes	characteristic
14	#41×C₂₈₃	C₂²	1	1	yes	characteristic
15	M₁₆×C₂₈₃	C₂²	1	3	yes	—
16	C₂×C₈×C₂₈₃	C₂²	1	3	yes	—
17	Dic₅₆₆	—	2	6	no	—
18	Dic₅₆₆	C₂³	1	6	yes	—
19	D₁₁₃₂	C₂³	1	2	yes	—
20	C₂²⋊D₂₈₃	—	2	6	no	—
21	C₂×Dic₂₈₃	—	2	6	no	—
22	C₄×D₂₈₃	—	2	6	no	—
23	Q₈×C₂₈₃	D₄	1	1	yes	characteristic
24	D₄×C₂₈₃	D₄	1	3	yes	—
25	C₂×C₄×C₂₈₃	C₂³	1	3	yes	—
26	C₈×C₂₈₃	C₂³	1	1	yes	characteristic
27	C₈×C₂₈₃	C₂³	1	3	yes	—
28	C₂²×C₂₈₃	C₂×D₄	1	3	yes	—
29	C₂×D₂₈₃	—	2	2	no	—
30	C₄×C₂₈₃	C₂×D₄	1	3	yes	—
31	C₄×C₂₈₃	C₂⁴	1	1	yes	characteristic
32	Dic₂₈₃	—	2	6	no	—
33	C₂×C₂₈₃	—	2	3	no	—
34	C₂×C₂₈₃	C₂²×D₄	1	1	yes	characteristic
35	D₂₈₃	—	4	2	no	—
36	C₂₈₃	#578	1	1	yes	characteristic, complemented, Sylow
37	#578	—	283	1	no	maximal, Sylow
38	2₋¹⁺⁴	—	283	2	no	—
39	#137	—	283	6	no	—
40	#135	—	283	3	no	—
41	C₂×Q₁₆	—	283	3	no	—
42	#131	D₂₈₃	1	1	yes	characteristic, complemented
43	#41	—	283	6	no	—
44	#41	—	566	6	no	—
45	#41	C₂×D₂₈₃	1	1	yes	characteristic
46	C₂×Q₈	—	283	6	no	—
47	C₂×Q₈	—	566	2	no	—
48	Q₁₆	—	283	3	no	—
49	Q₁₆	—	283	6	no	—
50	SD₁₆	—	283	6	no	—
51	D₈	—	283	1	no	—
52	M₁₆	C₂×D₂₈₃	1	3	yes	—
53	C₂×C₈	C₂×D₂₈₃	1	3	yes	—
54	Q₈	—	283	6	no	—
55	Q₈	—	566	6	no	—
56	Q₈	D₁₁₃₂	1	1	yes	characteristic
57	D₄	—	283	2	no	—
58	D₄	—	566	6	no	—
59	D₄	D₁₁₃₂	1	3	yes	—
60	C₂×C₄	—	566	6	no	—
61	C₂×C₄	—	566	6	no	—
62	C₂×C₄	C₂²×D₂₈₃	1	3	yes	—
63	C₈	C₂²×D₂₈₃	1	1	yes	characteristic
64	C₈	C₂²×D₂₈₃	1	3	yes	—
65	C₂²	—	566	2	no	—
66	C₂²	C₂×D₁₁₃₂	1	3	yes	—
67	C₄	—	566	6	no	—
68	C₄	C₂×D₁₁₃₂	1	3	yes	—
69	C₄	C₂³×D₂₈₃	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	1132	2	no	—
72	C₂	C₂²×D₁₁₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₁₁₃₂
commutator, cosocle	C₄×C₂₈₃	C₂⁴
Frattini	C₄	C₂³×D₂₈₃
Fitting	#131×C₂₈₃	C₂
socle	C₂×C₂₈₃	C₂²×D₄
hypercenter	#131	D₂₈₃
hypocenter	C₂₈₃	#578
LCS	G ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #22583657	C₂	semidirect
2. #22583643	C₂	semidirect
3. #22583632	C₂	semidirect
4. C₂×Dic₁₁₃₂	C₂	semidirect
5. #131×C₂₈₃	C₂	semidirect
36. C₂₈₃	#578	semidirect
42. #131	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#22583657	2
#22583643	2
#22583632	2
C₂×Dic₁₁₃₂	2
#131×C₂₈₃	2
#578	283