Subgroups — #49120879

Order 36224.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31826870	C₂	1	4	yes	maximal
2	#31826845	C₂	1	2	yes	maximal
3	C₈²×C₂₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₃₂	—	2	4	no	—
5	#22583610	C₂²	1	4	yes	—
6	#22583544	—	2	8	no	—
7	C₄×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₂₈₃	C₂²	1	2	yes	—
9	C₂×Dic₅₆₆	—	2	4	no	—
10	Dic₁₁₃₂	—	4	8	no	—
11	C₄⋊Dic₂₈₃	—	2	8	no	—
12	C₂×C₈×C₂₈₃	D₄	1	2	yes	—
13	C₂×C₈×C₂₈₃	D₄	1	4	yes	—
14	C₄²×C₂₈₃	C₂³	1	1	yes	characteristic
15	Dic₅₆₆	—	4	8	no	—
16	C₂×Dic₂₈₃	—	4	4	no	—
17	C₂×C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₈₃	C₂×D₄	1	2	yes	—
19	C₈×C₂₈₃	D₈	1	4	yes	—
20	C₈×C₂₈₃	Q₁₆	1	8	yes	complemented
21	C₂²×C₂₈₃	#127	1	1	yes	characteristic
22	C₄×C₂₈₃	C₂×D₈	1	2	yes	—
23	C₄×C₂₈₃	C₂×Q₁₆	1	4	yes	—
24	Dic₂₈₃	—	8	4	no	—
25	C₂×C₂₈₃	#493	1	1	yes	characteristic
26	C₂×C₂₈₃	#494	1	2	yes	—
27	C₂₈₃	#1713	1	1	yes	characteristic, complemented, Sylow
28	#1713	—	283	1	no	maximal, Sylow
29	#500	—	283	4	no	—
30	#494	—	283	2	no	—
31	C₈²	D₂₈₃	1	1	yes	characteristic
32	C₂×Q₁₆	—	566	4	no	—
33	C₄⋊Q₈	—	283	4	no	—
34	#107	—	566	8	no	—
35	C₄×C₈	C₂×D₂₈₃	1	1	yes	characteristic
36	C₄×C₈	C₂×D₂₈₃	1	2	yes	—
37	C₂×Q₈	—	566	4	no	—
38	Q₁₆	—	1132	8	no	—
39	C₂×C₈	D₁₁₃₂	1	2	yes	—
40	C₂×C₈	D₁₁₃₂	1	4	yes	—
41	C₄⋊C₄	—	566	8	no	—
42	C₄²	C₂²×D₂₈₃	1	1	yes	characteristic
43	Q₈	—	1132	8	no	—
44	C₂×C₄	—	1132	4	no	—
45	C₂×C₄	C₂×D₁₁₃₂	1	1	yes	characteristic
46	C₂×C₄	C₂×D₁₁₃₂	1	2	yes	—
47	C₈	D₂₂₆₄	1	4	yes	—
48	C₈	Dic₁₁₃₂	1	8	yes	complemented
49	C₂²	#22583607	1	1	yes	characteristic
50	C₄	—	2264	4	no	—
51	C₄	C₂×D₂₂₆₄	1	2	yes	—
52	C₄	C₂×Dic₁₁₃₂	1	4	yes	—
53	C₂	#31826842	1	1	yes	characteristic
54	C₂	#31826845	1	2	yes	—

	subgroup	G/H
center	C₂²	#22583607
commutator, cosocle	C₄²×C₂₈₃	C₂³
Frattini	C₄²	C₂²×D₂₈₃
Fitting	C₈²×C₂₈₃	C₂
socle, prime radical	C₂²×C₂₈₃	#127
hypercenter	C₈²	D₂₈₃
hypocenter	C₂₈₃	#1713
LCS	G ▷ C₄²×C₂₈₃ ▷ C₂²×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₂₈₃	Q₁₆	semidirect
27. C₂₈₃	#1713	semidirect
48. C₈	Dic₁₁₃₂	semidirect

Maximal subgroups

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

subgroup	index
#31826870	2
#31826845	2
C₈²×C₂₈₃	2
#1713	283