Subgroups — #31826795

Order 18112.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22583589	C₂	1	1	yes	maximal, characteristic
2	#22583541	C₂	1	2	yes	maximal, complemented
3	#22583533	C₂	1	2	yes	maximal, complemented
4	C₂²⋊(C₂₈₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×C₂₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₅₆₆	C₂²	1	1	yes	characteristic
7	C₂×C₂₈₃⋊C₈	C₂²	1	2	yes	—
8	C₄⋊Dic₂₈₃	C₂²	1	1	yes	characteristic
9	Dic₂₈₃⋊C₄	—	2	1	no	—
10	C₂²⋊Dic₂₈₃	—	2	1	no	—
11	C₂²×C₄×C₂₈₃	—	2	1	no	—
12	C₂²×C₄×C₂₈₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₂₈₃	—	2	1	no	—
14	C₄⋊C₄×C₂₈₃	C₂²	1	2	yes	—
15	Dic₅₆₆	—	2	2	no	—
16	C₂×Dic₂₈₃	—	2	1	no	—
17	C₂×Dic₂₈₃	—	2	1	no	—
18	C₂₈₃⋊C₈	—	2	2	no	—
19	C₂³×C₂₈₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₈₃	—	2	2	no	—
21	C₂×C₄×C₂₈₃	—	2	2	no	—
22	C₂×C₄×C₂₈₃	—	4	2	no	—
23	C₂×C₄×C₂₈₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₈₃	C₂³	1	1	yes	characteristic
25	C₂²×C₂₈₃	—	2	1	no	—
26	C₂²×C₂₈₃	—	2	1	no	—
27	C₂²×C₂₈₃	SD₁₆	1	2	yes	—
28	C₂²×C₂₈₃	C₂×D₄	1	1	yes	characteristic
29	C₄×C₂₈₃	—	2	1	no	—
30	C₄×C₂₈₃	—	4	2	no	—
31	C₄×C₂₈₃	#41	1	2	yes	—
32	Dic₂₈₃	—	4	1	no	—
33	Dic₂₈₃	—	4	1	no	—
34	C₂×C₂₈₃	—	2	2	no	—
35	C₂×C₂₈₃	#123	1	1	yes	characteristic
36	C₂×C₂₈₃	C₂×SD₁₆	1	1	yes	characteristic
37	C₂×C₂₈₃	#137	1	1	yes	characteristic
38	C₂₈₃	#483	1	1	yes	characteristic, complemented, Sylow
39	#483	—	283	1	no	maximal, Sylow
40	C₂²⋊Q₈	—	283	1	no	—
41	C₂×C₄⋊C₄	D₂₈₃	1	1	yes	characteristic
42	#106	—	283	2	no	—
43	#103	—	283	2	no	—
44	C₂²⋊C₈	—	283	1	no	—
45	C₂×Q₈	—	283	1	no	—
46	C₂²×C₄	—	2	1	no	—
47	C₂²×C₄	C₂×D₂₈₃	1	1	yes	characteristic
48	C₂×C₈	—	283	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	283	1	no	—
51	C₄⋊C₄	—	566	1	no	—
52	C₄⋊C₄	C₂×D₂₈₃	1	2	yes	—
53	C₂²⋊C₄	—	566	1	no	—
54	C₂³	C₂²⋊D₂₈₃	1	1	yes	characteristic
55	Q₈	—	566	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	4	2	no	—
59	C₂×C₄	—	566	1	no	—
60	C₂×C₄	—	566	1	no	—
61	C₂×C₄	C₂²⋊D₂₈₃	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₂₈₃	1	1	yes	characteristic
63	C₈	—	566	2	no	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	#17985380	1	2	yes	—
67	C₂²	C₂×C₂²⋊D₂₈₃	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	4	2	no	—
70	C₄	—	1132	1	no	—
71	C₄	—	1132	1	no	—
72	C₄	#17985392	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	#22583593	1	1	yes	characteristic
75	C₂	C₂×#17985380	1	1	yes	characteristic
76	C₂	#22583641	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₈₃
commutator, cosocle	C₂×C₄×C₂₈₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₈₃
Fitting	C₂×C₄⋊C₄×C₂₈₃	C₂
socle	C₂²×C₂₈₃	C₂×D₄
prime radical	C₂³×C₂₈₃	D₄
hypercenter	C₂×C₄⋊C₄	D₂₈₃
hypocenter	C₂₈₃	#483
LCS	G ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #22583541	C₂	semidirect
3. #22583533	C₂	semidirect
38. C₂₈₃	#483	semidirect

Maximal subgroups

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

subgroup	index
#22583589	2
#22583541	2
#22583533	2
C₂²⋊(C₂₈₃⋊C₈)	2
C₂×C₄⋊C₄×C₂₈₃	2
#483	283