Subgroups — #49119467

Order 36224.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826295	C₂	1	1	yes	maximal, characteristic
2	#31826293	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₂₈₃	C₂	1	1	yes	maximal, characteristic
4	#22583546	—	2	1	no	—
5	#22583544	—	2	1	no	—
6	C₂×C₁₆×C₂₈₃	C₂²	1	1	yes	characteristic
7	C₃₂×C₂₈₃	C₄	1	2	yes	complemented
8	#17985376	—	4	1	no	—
9	C₄⋊Dic₂₈₃	—	4	1	no	—
10	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
11	C₁₆×C₂₈₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₈₃	Q₈	1	1	yes	characteristic
13	C₂×Dic₂₈₃	—	8	1	no	—
14	C₂₈₃⋊C₈	—	8	1	no	—
15	C₂×C₄×C₂₈₃	D₈	1	1	yes	characteristic
16	C₈×C₂₈₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₈₃	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₈₃	SD₃₂	1	1	yes	characteristic
19	C₄×C₂₈₃	#107	1	1	yes	characteristic
20	C₄×C₂₈₃	SD₃₂	1	1	yes	characteristic
21	Dic₂₈₃	—	16	1	no	—
22	C₂×C₂₈₃	—	2	1	no	—
23	C₂×C₂₈₃	#367	1	1	yes	characteristic
24	C₂₈₃	#1426	1	1	yes	characteristic, complemented, Sylow
25	#1426	—	283	1	no	maximal, Sylow
26	M₆₄	D₂₈₃	1	1	yes	characteristic
27	#368	—	283	1	no	—
28	#367	—	283	1	no	—
29	C₂×C₁₆	C₂×D₂₈₃	1	1	yes	characteristic
30	#108	—	566	1	no	—
31	#107	—	566	1	no	—
32	C₃₂	Dic₂₈₃	1	2	yes	complemented
33	M₁₆	—	1132	1	no	—
34	C₂×C₈	D₁₁₃₂	1	1	yes	characteristic
35	C₄⋊C₄	—	1132	1	no	—
36	C₁₆	C₂×Dic₂₈₃	1	1	yes	characteristic
37	C₁₆	Dic₅₆₆	1	1	yes	characteristic
38	C₂×C₄	—	2264	1	no	—
39	C₂×C₄	D₂₂₆₄	1	1	yes	characteristic
40	C₈	—	2264	1	no	—
41	C₈	C₄⋊Dic₂₈₃	1	1	yes	characteristic
42	C₈	Dic₁₁₃₂	1	1	yes	characteristic
43	C₂²	#22583555	1	1	yes	characteristic
44	C₄	—	4528	1	no	—
45	C₄	#22583544	1	1	yes	characteristic
46	C₄	#22583555	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#31826293	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#31826293
commutator	C₁₆×C₂₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₈₃
Fitting	M₆₄×C₂₈₃	C₂
socle	C₂×C₂₈₃	#367
prime radical	C₂²×C₂₈₃	SD₃₂
cosocle	C₂×C₁₆×C₂₈₃	C₂²
hypercenter	M₆₄	D₂₈₃
hypocenter	C₂₈₃	#1426
LCS	G ▷ C₁₆×C₂₈₃ ▷ C₈×C₂₈₃ ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₃₂×C₂₈₃	C₄	semidirect
24. C₂₈₃	#1426	semidirect
32. C₃₂	Dic₂₈₃	semidirect

Maximal subgroups

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

subgroup	index
#31826295	2
#31826293	2
M₆₄×C₂₈₃	2
#1426	283