Subgroups — #20274869

Order 6784.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#88322	C₂	1	6	yes	maximal
2	C₅₃×#376	C₂	1	1	yes	maximal, characteristic
3	C₂²×#88322	C₂²	1	4	yes	—
4	C₄⋊#88322	—	2	12	no	—
5	C₂×C₄²×C₅₃	C₂²	1	3	yes	—
6	#95×C₅₃	C₄	1	4	yes	—
7	C₂²×C₄×C₅₃	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
9	C₄²×C₅₃	D₄	1	6	yes	—
10	C₄²×C₅₃	Q₈	1	6	yes	—
11	C₂×#88322	—	2	12	no	—
12	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅₃	—	2	12	no	—
14	C₂×C₄×C₅₃	C₄⋊C₄	1	12	yes	—
15	C₂×C₄×C₅₃	C₂×D₄	1	3	yes	—
16	C₂×C₄×C₅₃	C₂×Q₈	1	3	yes	—
17	#88322	—	4	4	no	—
18	C₂²×C₅₃	C₂×C₄⋊C₄	1	3	yes	—
19	C₂²×C₅₃	#131	1	4	yes	—
20	C₄×C₅₃	—	2	12	no	—
21	C₄×C₅₃	#127	1	1	yes	characteristic
22	C₄×C₅₃	C₄⋊Q₈	1	3	yes	—
23	#1843	—	53	1	no	maximal, Sylow
24	C₂×C₅₃	#384	1	1	yes	characteristic
25	C₂×C₅₃	#424	1	6	yes	—
26	C₂×C₄⋊C₈	—	53	6	no	—
27	#376	D₅₃	1	1	yes	characteristic
28	C₅₃	#1843	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₈	—	53	4	no	—
30	C₂×C₄²	C₂×D₅₃	1	3	yes	—
31	C₄⋊C₈	—	106	12	no	—
32	#95	Dic₅₃	1	4	yes	—
33	C₂²×C₄	C₂×Dic₅₃	1	6	yes	—
34	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
35	C₂×C₈	—	106	12	no	—
36	C₄²	Dic₁₀₆	1	6	yes	—
37	C₄²	D₂₁₂	1	6	yes	—
38	C₂³	C₂²×Dic₅₃	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₅₃	1	12	yes	—
41	C₂×C₄	C₂×Dic₁₀₆	1	3	yes	—
42	C₂×C₄	C₂×D₂₁₂	1	3	yes	—
43	C₈	—	212	4	no	—
44	C₂²	C₂×C₄⋊Dic₅₃	1	3	yes	—
45	C₂²	#13133224	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#13133214	1	1	yes	characteristic
48	C₄	#13133217	1	3	yes	—
49	C₂	#16810493	1	1	yes	characteristic
50	C₂	#16810650	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₃
commutator, socle	C₂³×C₅₃	C₂²×C₄
Fitting	C₅₃×#376	C₂
hypercenter	#376	D₅₃
hypocenter	C₅₃	#1843
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
28. C₅₃	#1843	semidirect