Subgroups — #21422231

Order 7552.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837236	C₂	1	1	yes	maximal, characteristic
2	#16837177	C₂	1	1	yes	maximal, characteristic
3	C₅₉×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₅₉	C₄	1	1	yes	characteristic
6	C₅₉⋊C₃₂	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
8	C₃₂×C₅₉	C₄	1	2	yes	complemented
9	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₅₉	C₈	1	1	yes	characteristic
11	C₂×C₅₉⋊C₈	C₈	1	1	yes	characteristic
12	C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
14	C₅₉⋊C₁₆	C₈	1	2	yes	—
15	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₅₉	—	2	1	no	—
17	C₈×C₅₉	C₄²	1	1	yes	characteristic
18	C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
19	C₅₉⋊C₈	—	2	1	no	—
20	C₂²×C₅₉	M₃₂	1	1	yes	characteristic
21	C₄×C₅₉	C₄×C₈	1	1	yes	characteristic
22	C₄×C₅₉	M₃₂	1	1	yes	characteristic
23	Dic₅₉	—	4	1	no	—
24	#1398	—	59	1	no	maximal, Sylow
25	C₂×C₅₉	—	2	1	no	—
26	C₂×C₅₉	#346	1	1	yes	characteristic
27	M₆₄	—	59	1	no	—
28	M₆₄	D₅₉	1	1	yes	characteristic
29	#346	—	59	1	no	—
30	C₅₉	#1398	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	—	59	1	no	—
32	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
33	C₄×C₈	—	59	1	no	—
34	C₃₂	—	59	2	no	—
35	C₃₂	Dic₅₉	1	2	yes	complemented
36	C₂×C₈	—	59	1	no	—
37	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
38	C₄²	—	59	1	no	—
39	C₁₆	—	59	2	no	—
40	C₁₆	C₄×D₅₉	1	1	yes	characteristic
41	C₁₆	C₂×Dic₅₉	1	1	yes	characteristic
42	C₂×C₄	—	118	1	no	—
43	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
44	C₈	—	118	1	no	—
45	C₈	C₈×D₅₉	1	1	yes	characteristic
46	C₈	C₄×Dic₅₉	1	1	yes	characteristic
47	C₂²	#14273666	1	1	yes	characteristic
48	C₄	—	236	1	no	—
49	C₄	C₈×Dic₅₉	1	1	yes	characteristic
50	C₄	#14273666	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#16837177	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₅₉
commutator	C₄×C₅₉	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₅₉
Fitting	C₅₉×M₆₄	C₂
socle	C₂×C₅₉	#346
hypercenter	M₆₄	D₅₉
hypocenter	C₅₉	#1398
LCS	G ▷ C₄×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
6. C₅₉⋊C₃₂	C₄	semidirect
8. C₃₂×C₅₉	C₄	semidirect
30. C₅₉	#1398	semidirect
35. C₃₂	Dic₅₉	semidirect