Subgroups — #20272754

Order 6784.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16810444	C₂	1	2	yes	maximal
2	C₅₃×#494	C₂	1	1	yes	maximal, characteristic
3	#13133157	—	2	2	no	—
4	C₂×Q₁₆×C₅₃	—	2	2	no	—
5	C₄⋊Q₈×C₅₃	C₄	1	2	yes	—
6	C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₅₃	—	2	2	no	—
8	Q₁₆×C₅₃	—	4	2	no	—
9	Q₁₆×C₅₃	—	4	2	no	—
10	C₂×C₈×C₅₃	D₄	1	2	yes	—
11	C₄⋊C₄×C₅₃	—	4	2	no	—
12	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
13	#11719908	—	4	2	no	—
14	Q₈×C₅₃	—	4	4	no	—
15	C₂×C₄×C₅₃	—	2	1	no	—
16	C₂×C₄×C₅₃	—	4	2	no	—
17	C₂×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
18	C₈×C₅₃	D₈	1	2	yes	—
19	C₈×C₅₃	SD₁₆	1	2	yes	—
20	C₂²×C₅₃	#100	1	1	yes	characteristic
21	C₄×C₅₃	—	2	2	no	—
22	C₄×C₅₃	—	8	2	no	—
23	C₄×C₅₃	#102	1	2	yes	—
24	#1358	—	53	1	no	maximal, Sylow
25	C₂×C₅₃	—	2	1	no	—
26	C₂×C₅₃	#331	1	1	yes	characteristic
27	#494	D₅₃	1	1	yes	characteristic
28	#364	—	53	2	no	—
29	C₅₃	#1358	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₁₆	—	2	2	no	—
31	C₄⋊Q₈	Dic₅₃	1	2	yes	—
32	M₃₂	—	106	2	no	—
33	C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
34	C₂×Q₈	—	2	2	no	—
35	Q₁₆	—	4	2	no	—
36	Q₁₆	—	4	2	no	—
37	C₂×C₈	C₂²⋊D₅₃	1	2	yes	—
38	C₄⋊C₄	—	4	2	no	—
39	C₄²	C₂×Dic₅₃	1	1	yes	characteristic
40	C₁₆	—	212	2	no	—
41	Q₈	—	4	4	no	—
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	C₂²⋊Dic₅₃	1	1	yes	characteristic
45	C₈	#11719922	1	2	yes	—
46	C₈	#11719923	1	2	yes	—
47	C₂²	#13133134	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	8	2	no	—
50	C₄	#13133138	1	2	yes	—
51	C₂	—	2	1	no	—
52	C₂	#16810367	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16810367
commutator	C₄²×C₅₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₅₃
Fitting	C₅₃×#494	C₂
socle	C₂×C₅₃	#331
hypercenter	#494	D₅₃
hypocenter	C₅₃	#1358
LCS	G ▷ C₄²×C₅₃ ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
29. C₅₃	#1358	semidirect