Subgroups — #20272916

Order 6784.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133123	C₂	1	1	yes	maximal, characteristic
2	#16810449	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#366	C₂	1	1	yes	maximal, characteristic
4	#13133151	—	2	1	no	—
5	#13133123	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
7	#107×C₅₃	—	2	1	no	—
8	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
9	C₄⋊C₄×C₅₃	—	4	1	no	—
10	C₄⋊Dic₅₃	—	4	1	no	—
11	C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₅₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₅₃	—	8	1	no	—
14	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
15	C₂×Dic₅₃	—	8	1	no	—
16	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₅₃	Q₁₆	1	1	yes	characteristic
18	C₂²×C₅₃	D₁₆	1	1	yes	characteristic
19	C₄×C₅₃	—	16	1	no	—
20	C₄×C₅₃	#107	1	1	yes	characteristic
21	C₄×C₅₃	Q₃₂	1	1	yes	characteristic
22	Dic₅₃	—	16	1	no	—
23	#1424	—	53	1	no	maximal, Sylow
24	C₂×C₅₃	#366	1	1	yes	characteristic
25	C₂×C₅₃	SD₆₄	1	1	yes	characteristic
26	C₂×C₅₃	SD₆₄	1	1	yes	characteristic
27	C₂×C₃₂	—	53	1	no	—
28	#366	—	53	1	no	—
29	#366	D₅₃	1	1	yes	characteristic
30	C₅₃	#1424	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	106	1	no	—
34	C₃₂	—	53	2	no	—
35	C₂×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	212	1	no	—
38	C₁₆	Dic₁₀₆	1	1	yes	characteristic
39	C₁₆	C₄×D₅₃	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	424	1	no	—
42	C₂×C₄	#11719922	1	1	yes	characteristic
43	C₈	#11719919	1	1	yes	characteristic
44	C₈	#11719925	1	1	yes	characteristic
45	C₂²	#13133158	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	848	1	no	—
48	C₄	#13133150	1	1	yes	characteristic
49	C₄	#13133163	1	1	yes	characteristic
50	C₂	#16810448	1	1	yes	characteristic
51	C₂	#16810460	1	1	yes	characteristic
52	C₂	#16810461	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13133158
commutator	C₁₆×C₅₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₅₃
Fitting	C₅₃×#366	C₂
socle	C₂²×C₅₃	D₁₆
hypercenter	#366	D₅₃
hypocenter	C₅₃	#1424
LCS	G ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. #13133123	C₄	semidirect
30. C₅₃	#1424	semidirect