Subgroups — #31826587

Order 18112.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22583617	C₂	1	2	yes	maximal, complemented
2	#22583546	C₂	1	1	yes	maximal, characteristic, complemented
3	#22583537	C₂	1	2	yes	maximal, complemented
4	#22583520	C₂	1	1	yes	maximal, characteristic, complemented
5	#135×C₂₈₃	C₂	1	1	yes	maximal, characteristic
6	#17985376	—	2	2	no	—
7	#17985376	C₂²	1	2	yes	—
8	C₂×C₂₈₃⋊C₈	—	2	2	no	—
9	C₂×C₂₈₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×Dic₂₈₃	C₂²	1	1	yes	characteristic
11	#41×C₂₈₃	C₂²	1	2	yes	—
12	Q₁₆×C₂₈₃	C₄	1	1	yes	characteristic, complemented
13	SD₁₆×C₂₈₃	C₄	1	2	yes	complemented
14	D₈×C₂₈₃	C₄	1	1	yes	characteristic, complemented
15	C₂×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₂₈₃	—	2	1	no	—
17	C₂₈₃⋊C₈	—	2	2	no	—
18	C₂₈₃⋊C₈	D₄	1	2	yes	—
19	Q₈×C₂₈₃	C₂×C₄	1	2	yes	—
20	D₄×C₂₈₃	—	2	2	no	—
21	D₄×C₂₈₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₂₈₃	—	2	2	no	—
23	C₂×C₄×C₂₈₃	C₂³	1	1	yes	characteristic
24	C₈×C₂₈₃	C₂×C₄	1	1	yes	characteristic
25	C₈×C₂₈₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₂₈₃	—	2	2	no	—
27	C₂²×C₂₈₃	#41	1	1	yes	characteristic
28	C₄×C₂₈₃	—	2	2	no	—
29	C₄×C₂₈₃	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
31	Dic₂₈₃	—	4	1	no	—
32	C₂×C₂₈₃	—	2	1	no	—
33	C₂×C₂₈₃	—	4	2	no	—
34	C₂×C₂₈₃	C₄×D₄	1	1	yes	characteristic
35	C₂₈₃	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	283	1	no	maximal, Sylow
37	#135	D₂₈₃	1	1	yes	characteristic
38	#131	—	283	2	no	—
39	#108	—	283	1	no	—
40	#104	—	283	2	no	—
41	#97	—	283	1	no	—
42	#41	C₂×D₂₈₃	1	2	yes	—
43	Q₁₆	Dic₂₈₃	1	1	yes	characteristic, complemented
44	SD₁₆	Dic₂₈₃	1	2	yes	complemented
45	D₈	Dic₂₈₃	1	1	yes	characteristic, complemented
46	M₁₆	—	283	2	no	—
47	M₁₆	—	566	2	no	—
48	C₂×C₈	—	283	1	no	—
49	C₂×C₈	—	566	2	no	—
50	C₂×C₈	C₂×D₂₈₃	1	1	yes	characteristic
51	C₄²	—	283	1	no	—
52	Q₈	C₂×Dic₂₈₃	1	2	yes	—
53	D₄	—	2	2	no	—
54	D₄	C₂×Dic₂₈₃	1	2	yes	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	566	1	no	—
57	C₂×C₄	C₂²×D₂₈₃	1	1	yes	characteristic
58	C₈	—	283	2	no	—
59	C₈	—	566	2	no	—
60	C₈	C₂×Dic₂₈₃	1	1	yes	characteristic
61	C₈	C₂×Dic₂₈₃	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	#17985391	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	1132	1	no	—
66	C₄	C₂²×Dic₂₈₃	1	1	yes	characteristic
67	C₄	D₄×D₂₈₃	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	2	no	—
70	C₂	D₄×Dic₂₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₂₈₃
commutator	C₄×C₂₈₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₈₃
Fitting, prime radical	#135×C₂₈₃	C₂
socle	C₂×C₂₈₃	C₄×D₄
cosocle	C₂×C₄×C₂₈₃	C₂³
hypercenter	#135	D₂₈₃
hypocenter	C₂₈₃	#444
LCS	G ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #22583617	C₂	semidirect
2. #22583546	C₂	semidirect
3. #22583537	C₂	semidirect
4. #22583520	C₂	semidirect
12. Q₁₆×C₂₈₃	C₄	semidirect
13. SD₁₆×C₂₈₃	C₄	semidirect
14. D₈×C₂₈₃	C₄	semidirect
35. C₂₈₃	#444	semidirect
43. Q₁₆	Dic₂₈₃	semidirect
44. SD₁₆	Dic₂₈₃	semidirect
45. D₈	Dic₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#22583617	2
#22583546	2
#22583537	2
#22583520	2
#135×C₂₈₃	2
#444	283