Subgroups — #20299000

Order 7232.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813614	C₂	1	2	yes	maximal
2	#16813556	C₂	1	2	yes	maximal
3	#16813554	C₂	1	2	yes	maximal
4	C₄×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊Dic₁₁₃	C₂²	1	4	yes	—
6	#14268626	—	2	4	no	—
7	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₁₃	D₄	1	2	yes	—
11	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
12	C₂×Dic₁₁₃	—	2	4	no	—
13	C₈×C₁₁₃	Q₈	1	2	yes	—
14	C₈×C₁₁₃	Q₈	1	2	yes	—
15	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
16	C₄×C₁₁₃	—	2	2	no	—
17	C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
18	C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
19	Dic₁₁₃	—	4	4	no	—
20	C₂×C₁₁₃	C₄⋊Q₈	1	1	yes	characteristic
21	C₂×C₁₁₃	#135	1	2	yes	—
22	C₁₁₃	#499	1	1	yes	characteristic, complemented, Sylow
23	#499	—	113	1	no	maximal, Sylow
24	#125	—	113	2	no	—
25	#107	—	113	2	no	—
26	#106	—	113	2	no	—
27	C₄×C₈	D₁₁₃	1	1	yes	characteristic
28	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
29	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
30	C₄⋊C₄	—	113	4	no	—
31	C₄⋊C₄	—	226	4	no	—
32	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
33	C₂×C₄	—	226	4	no	—
34	C₂×C₄	D₄₅₂	1	2	yes	—
35	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
36	C₈	Dic₂₂₆	1	2	yes	—
37	C₈	Dic₂₂₆	1	2	yes	—
38	C₂²	C₂×D₄₅₂	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	452	4	no	—
41	C₄	C₂×Dic₂₂₆	1	1	yes	characteristic
42	C₄	C₂×Dic₂₂₆	1	1	yes	characteristic
43	C₂	#16813622	1	1	yes	characteristic
44	C₂	#16813644	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₅₂
commutator	C₂×C₄×C₁₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₄×C₈×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	C₄×C₈	D₁₁₃
hypocenter	C₁₁₃	#499
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
22. C₁₁₃	#499	semidirect