Subgroups — #20298425

Order 7232.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268622	C₂	1	1	yes	maximal, characteristic
2	#16813556	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₁₃	—	2	1	no	—
5	#14268622	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₁₃	—	2	1	no	—
8	C₂×C₄×C₁₁₃	—	4	1	no	—
9	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
10	C₂×Dic₁₁₃	—	4	1	no	—
11	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₁₃	Q₈	1	1	yes	characteristic
13	C₂²×C₁₁₃	D₈	1	1	yes	characteristic
14	C₄×C₁₁₃	—	8	1	no	—
15	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₁₃	Q₁₆	1	1	yes	characteristic
17	Dic₁₁₃	—	8	1	no	—
18	C₂×C₁₁₃	#107	1	1	yes	characteristic
19	C₂×C₁₁₃	SD₃₂	1	1	yes	characteristic
20	C₂×C₁₁₃	SD₃₂	1	1	yes	characteristic
21	C₁₁₃	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	113	1	no	maximal, Sylow
23	C₂×C₁₆	—	113	1	no	—
24	#107	—	113	1	no	—
25	#107	D₁₁₃	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	226	1	no	—
29	C₁₆	—	113	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	452	1	no	—
32	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
33	C₈	Dic₂₂₆	1	1	yes	characteristic
34	C₈	C₄×D₁₁₃	1	1	yes	characteristic
35	C₂²	#14268632	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	904	1	no	—
38	C₄	#14268626	1	1	yes	characteristic
39	C₄	#14268637	1	1	yes	characteristic
40	C₂	#16813555	1	1	yes	characteristic
41	C₂	#16813565	1	1	yes	characteristic
42	C₂	#16813566	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14268632
commutator	C₈×C₁₁₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₁₃
Fitting	#107×C₁₁₃	C₂
socle	C₂²×C₁₁₃	D₈
hypercenter	#107	D₁₁₃
hypocenter	C₁₁₃	#367
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. #14268622	C₄	semidirect
21. C₁₁₃	#367	semidirect