Subgroups — #49119462

Order 36224.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₈₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#31826291	C₂	1	1	yes	maximal, characteristic
3	#366×C₂₈₃	C₂	1	1	yes	maximal, characteristic
4	#22583544	—	2	1	no	—
5	C₂₈₃⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₂₈₃	C₂²	1	1	yes	characteristic
7	#107×C₂₈₃	—	2	1	no	—
8	C₄⋊Dic₂₈₃	—	4	1	no	—
9	C₂×C₈×C₂₈₃	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₂₈₃	—	4	1	no	—
11	C₁₆×C₂₈₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₈₃	Q₈	1	1	yes	characteristic
13	C₂×Dic₂₈₃	—	8	1	no	—
14	C₂×C₄×C₂₈₃	—	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	D₁₆	1	1	yes	characteristic
19	C₄×C₂₈₃	—	16	1	no	—
20	C₄×C₂₈₃	#107	1	1	yes	characteristic
21	C₄×C₂₈₃	Q₃₂	1	1	yes	characteristic
22	Dic₂₈₃	—	16	1	no	—
23	C₂×C₂₈₃	#366	1	1	yes	characteristic
24	C₂×C₂₈₃	SD₆₄	1	1	yes	characteristic
25	C₂×C₂₈₃	SD₆₄	1	1	yes	characteristic
26	C₂₈₃	#1424	1	1	yes	characteristic, complemented, Sylow
27	#1424	—	283	1	no	maximal, Sylow
28	C₂×C₃₂	—	283	1	no	—
29	#366	—	283	1	no	—
30	#366	D₂₈₃	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₂₈₃	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	566	1	no	—
34	C₃₂	—	283	2	no	—
35	C₂×C₈	C₂²⋊D₂₈₃	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	1132	1	no	—
38	C₁₆	C₄×D₂₈₃	1	1	yes	characteristic
39	C₁₆	Dic₅₆₆	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	2264	1	no	—
42	C₂×C₄	#17985377	1	1	yes	characteristic
43	C₈	Dic₂₈₃⋊C₄	1	1	yes	characteristic
44	C₈	#17985382	1	1	yes	characteristic
45	C₂²	#22583551	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	4528	1	no	—
48	C₄	#22583543	1	1	yes	characteristic
49	C₄	#22583556	1	1	yes	characteristic
50	C₂	#31826290	1	1	yes	characteristic
51	C₂	#31826302	1	1	yes	characteristic
52	C₂	#31826303	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22583551
commutator	C₁₆×C₂₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₈₃
Fitting	#366×C₂₈₃	C₂
socle, prime radical	C₂²×C₂₈₃	D₁₆
cosocle	C₂×C₁₆×C₂₈₃	C₂²
hypercenter	#366	D₂₈₃
hypocenter	C₂₈₃	#1424
LCS	G ▷ C₁₆×C₂₈₃ ▷ C₈×C₂₈₃ ▷ C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₂₈₃⋊C₃₂	C₄	semidirect
26. C₂₈₃	#1424	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₈₃⋊C₃₂	2
#31826291	2
#366×C₂₈₃	2
#1424	283