Subgroups — #20299515

Order 7232.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813697	C₂	1	1	yes	maximal, characteristic, complemented
2	#16813690	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813645	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#90673	—	2	1	no	—
5	#14268650	—	2	1	no	—
6	#14268648	—	2	1	no	—
7	#14268634	—	2	1	no	—
8	D₉₀₄	C₄	1	1	yes	characteristic, complemented
9	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
11	C₂×#90673	—	4	1	no	—
12	Q₈×C₁₁₃	—	2	1	no	—
13	D₄₅₂	—	2	1	no	—
14	D₄₅₂	—	4	1	no	—
15	C₄×D₁₁₃	—	4	1	no	—
16	C₄×D₁₁₃	D₄	1	1	yes	characteristic
17	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	#11744751	D₄	1	1	yes	characteristic
19	C₂×D₁₁₃	—	4	1	no	—
20	C₂×D₁₁₃	D₈	1	1	yes	characteristic
21	#90673	—	8	1	no	—
22	C₄×C₁₁₃	—	4	1	no	—
23	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₁₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₁₁₃	#102	1	1	yes	characteristic
26	D₁₁₃	—	2	1	no	—
27	D₁₁₃	—	8	1	no	—
28	C₁₁₃	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	113	1	no	maximal, Sylow
30	#135	—	113	1	no	—
31	M₃₂	—	113	1	no	—
32	#106	—	113	1	no	—
33	#41	—	226	1	no	—
34	Q₁₆	#90673	1	1	yes	characteristic, complemented
35	SD₁₆	—	226	1	no	—
36	D₈	—	113	1	no	—
37	C₂×C₈	—	113	1	no	—
38	C₄⋊C₄	—	226	1	no	—
39	C₁₆	—	226	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	452	1	no	—
42	D₄	—	226	1	no	—
43	C₂×C₄	—	113	1	no	—
44	C₂×C₄	—	452	1	no	—
45	C₂×C₄	—	452	1	no	—
46	C₈	—	113	1	no	—
47	C₈	C₂×#90673	1	1	yes	characteristic
48	C₂²	—	113	1	no	—
49	C₂²	—	452	1	no	—
50	C₄	—	4	1	no	—
51	C₄	—	113	1	no	—
52	C₄	—	904	1	no	—
53	C₄	C₂²⋊#90673	1	1	yes	characteristic
54	C₂	—	904	1	no	—
55	C₂	—	226	1	no	—
56	C₂	#16813684	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16813684
commutator	C₈×C₁₁₃	C₂×C₄
Frattini	C₈	C₂×#90673
Fitting	Q₁₆×C₁₁₃	C₄
socle	C₂×C₁₁₃	#102
hypercenter	Q₁₆	#90673
hypocenter	C₁₁₃	#360
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #16813697	C₂	semidirect
2. #16813690	C₂	semidirect
8. D₉₀₄	C₄	semidirect
10. Q₁₆×C₁₁₃	C₄	semidirect
28. C₁₁₃	#360	semidirect
34. Q₁₆	#90673	semidirect