Subgroups — #20272915

Order 6784.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16810449	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic
3	#13133151	—	2	2	no	—
4	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
5	C₃₂×C₅₃	C₄	1	2	yes	complemented
6	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
7	C₄⋊Dic₅₃	—	4	2	no	—
8	C₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₅₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
11	C₂×Dic₅₃	—	8	2	no	—
12	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₅₃	Q₁₆	1	1	yes	characteristic
14	C₂²×C₅₃	D₁₆	1	1	yes	characteristic
15	C₄×C₅₃	#107	1	1	yes	characteristic
16	C₄×C₅₃	Q₃₂	1	1	yes	characteristic
17	Dic₅₃	—	16	2	no	—
18	#1423	—	53	1	no	maximal, Sylow
19	C₂×C₅₃	#366	1	1	yes	characteristic
20	C₂×C₅₃	D₃₂	1	1	yes	characteristic
21	C₂×C₅₃	Q₆₄	1	1	yes	characteristic
22	C₂×C₃₂	D₅₃	1	1	yes	characteristic
23	#366	—	53	2	no	—
24	C₅₃	#1423	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
26	#107	—	106	2	no	—
27	C₃₂	Dic₅₃	1	2	yes	complemented
28	C₂×C₈	D₂₁₂	1	1	yes	characteristic
29	C₄⋊C₄	—	212	2	no	—
30	C₁₆	Dic₁₀₆	1	1	yes	characteristic
31	C₁₆	C₂×Dic₅₃	1	1	yes	characteristic
32	C₂×C₄	—	424	2	no	—
33	C₂×C₄	D₄₂₄	1	1	yes	characteristic
34	C₈	Dic₂₁₂	1	1	yes	characteristic
35	C₈	C₄⋊Dic₅₃	1	1	yes	characteristic
36	C₂²	D₈₄₈	1	1	yes	characteristic
37	C₄	—	848	2	no	—
38	C₄	#13133151	1	1	yes	characteristic
39	C₄	Dic₄₂₄	1	1	yes	characteristic
40	C₂	#16810449	1	1	yes	characteristic
41	C₂	D₁₆₉₆	1	1	yes	characteristic
42	C₂	Dic₈₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈₄₈
commutator	C₁₆×C₅₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₅₃
Fitting	C₂×C₃₂×C₅₃	C₂
socle	C₂²×C₅₃	D₁₆
hypercenter	C₂×C₃₂	D₅₃
hypocenter	C₅₃	#1423
LCS	G ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₅₃	C₄	semidirect
24. C₅₃	#1423	semidirect
27. C₃₂	Dic₅₃	semidirect