Subgroups — #31826741

Order 18112.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22583643	C₂	1	2	yes	maximal
2	C₂×Dic₁₁₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#22583616	C₂	1	1	yes	maximal, characteristic
4	#22583528	C₂	1	2	yes	maximal, complemented
5	#108×C₂₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985392	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₆₆	C₂²	1	2	yes	—
8	Dic₁₁₃₂	—	2	2	no	—
9	Dic₁₁₃₂	—	2	1	no	—
10	Dic₁₁₃₂	—	2	1	no	—
11	#17985381	—	2	2	no	—
12	#17985376	C₂²	1	1	yes	characteristic
13	#17985375	—	2	1	no	—
14	C₈×D₂₈₃	—	2	1	no	—
15	M₁₆×C₂₈₃	C₂²	1	2	yes	—
16	C₂×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
17	Dic₅₆₆	—	2	2	no	—
18	Dic₅₆₆	—	2	2	no	—
19	Dic₅₆₆	D₄	1	1	yes	characteristic
20	D₁₁₃₂	D₄	1	1	yes	characteristic
21	C₂²⋊D₂₈₃	—	2	1	no	—
22	C₂×Dic₂₈₃	—	2	2	no	—
23	C₄×D₂₈₃	—	2	1	no	—
24	C₂₈₃⋊C₈	—	2	1	no	—
25	C₂×C₄×C₂₈₃	C₂³	1	1	yes	characteristic
26	C₈×C₂₈₃	—	2	2	no	—
27	C₈×C₂₈₃	D₄	1	1	yes	characteristic
28	C₈×C₂₈₃	D₄	1	1	yes	characteristic
29	C₂²×C₂₈₃	#41	1	1	yes	characteristic
30	C₂×D₂₈₃	—	2	1	no	—
31	C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
33	Dic₂₈₃	—	2	1	no	—
34	Dic₂₈₃	—	4	2	no	—
35	C₂×C₂₈₃	—	2	1	no	—
36	C₂×C₂₈₃	#121	1	1	yes	characteristic
37	D₂₈₃	—	4	1	no	—
38	C₂₈₃	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	283	1	no	maximal, Sylow
40	#137	—	283	2	no	—
41	C₂×Q₁₆	—	283	1	no	—
42	#131	—	283	1	no	—
43	#108	D₂₈₃	1	1	yes	characteristic, complemented
44	#101	—	283	2	no	—
45	#41	—	283	1	no	—
46	C₂×Q₈	—	283	2	no	—
47	Q₁₆	—	566	2	no	—
48	Q₁₆	—	566	1	no	—
49	Q₁₆	—	566	1	no	—
50	SD₁₆	—	566	2	no	—
51	M₁₆	—	283	1	no	—
52	M₁₆	—	566	1	no	—
53	M₁₆	C₂×D₂₈₃	1	2	yes	—
54	C₂×C₈	—	566	1	no	—
55	C₂×C₈	C₂×D₂₈₃	1	1	yes	characteristic
56	Q₈	—	283	1	no	—
57	Q₈	—	566	2	no	—
58	Q₈	—	566	2	no	—
59	D₄	—	283	1	no	—
60	D₄	—	566	1	no	—
61	C₂×C₄	—	566	1	no	—
62	C₂×C₄	—	566	2	no	—
63	C₂×C₄	C₂²×D₂₈₃	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	566	1	no	—
66	C₈	D₁₁₃₂	1	1	yes	characteristic
67	C₈	D₁₁₃₂	1	1	yes	characteristic
68	C₂²	—	566	1	no	—
69	C₂²	#17985393	1	1	yes	characteristic
70	C₄	—	566	1	no	—
71	C₄	—	1132	2	no	—
72	C₄	D₄×D₂₈₃	1	1	yes	characteristic
73	C₄	C₂×D₁₁₃₂	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	1132	1	no	—
76	C₂	#22583585	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22583585
commutator, cosocle	C₂×C₄×C₂₈₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₈₃
Fitting	#108×C₂₈₃	C₂
socle	C₂×C₂₈₃	#121
prime radical	#17985392	C₂²
hypercenter	#108	D₂₈₃
hypocenter	C₂₈₃	#473
LCS	G ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₁₃₂	C₂	semidirect
4. #22583528	C₂	semidirect
5. #108×C₂₈₃	C₂	semidirect
38. C₂₈₃	#473	semidirect
43. #108	D₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#22583643	2
C₂×Dic₁₁₃₂	2
#22583616	2
#22583528	2
#108×C₂₈₃	2
#473	283