Subgroups — #20299027

Order 7232.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813641	C₂	1	2	yes	maximal, complemented
2	Dic₉₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813566	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14268646	—	2	2	no	—
7	Dic₄₅₂	C₂²	1	2	yes	—
8	#14268635	—	2	2	no	—
9	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
10	#14268622	C₂²	1	1	yes	characteristic
11	D₈×C₁₁₃	C₂²	1	2	yes	—
12	C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
13	D₄×C₁₁₃	—	2	2	no	—
14	C₂²⋊D₁₁₃	—	4	2	no	—
15	C₂×Dic₁₁₃	—	4	2	no	—
16	C₄×D₁₁₃	D₄	1	1	yes	characteristic
17	Dic₂₂₆	—	2	2	no	—
18	C₈×C₁₁₃	C₂³	1	1	yes	characteristic
19	#11744751	D₄	1	1	yes	characteristic
20	C₂²×C₁₁₃	—	4	2	no	—
21	C₂×D₁₁₃	D₈	1	1	yes	characteristic
22	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
23	Dic₁₁₃	—	4	2	no	—
24	Dic₁₁₃	D₈	1	1	yes	characteristic
25	C₂×C₁₁₃	—	8	2	no	—
26	C₂×C₁₁₃	C₂×D₈	1	1	yes	characteristic
27	D₁₁₃	—	2	1	no	—
28	C₁₁₃	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	113	1	no	maximal, Sylow
30	#135	—	113	2	no	—
31	Q₃₂	—	113	1	no	—
32	SD₃₂	—	113	2	no	—
33	D₁₆	D₁₁₃	1	1	yes	characteristic, complemented
34	C₂×C₁₆	—	113	1	no	—
35	#41	—	226	2	no	—
36	Q₁₆	—	113	2	no	—
37	SD₁₆	—	226	2	no	—
38	D₈	C₂×D₁₁₃	1	2	yes	—
39	C₂×C₈	—	113	1	no	—
40	C₁₆	—	113	1	no	—
41	C₁₆	C₂×D₁₁₃	1	1	yes	characteristic
42	Q₈	—	226	2	no	—
43	D₄	—	2	2	no	—
44	D₄	—	452	2	no	—
45	C₂×C₄	—	113	1	no	—
46	C₂×C₄	—	452	2	no	—
47	C₈	—	113	1	no	—
48	C₈	C₂²×D₁₁₃	1	1	yes	characteristic
49	C₂²	—	4	2	no	—
50	C₂²	—	113	1	no	—
51	C₄	—	113	1	no	—
52	C₄	—	452	2	no	—
53	C₄	D₄×D₁₁₃	1	1	yes	characteristic
54	C₂	—	8	2	no	—
55	C₂	—	226	1	no	—
56	C₂	D₈×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₁₃
commutator	C₈×C₁₁₃	C₂³
Frattini	C₈	C₂²×D₁₁₃
Fitting	D₁₆×C₁₁₃	C₂
socle	C₂×C₁₁₃	C₂×D₈
hypercenter	D₁₆	D₁₁₃
hypocenter	C₁₁₃	#508
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #16813641	C₂	semidirect
2. Dic₉₀₄	C₂	semidirect
3. #16813566	C₂	semidirect
4. C₁₆×D₁₁₃	C₂	semidirect
5. D₁₆×C₁₁₃	C₂	semidirect
28. C₁₁₃	#508	semidirect
33. D₁₆	D₁₁₃	semidirect