Subgroups — #21422157

Order 7552.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837223	C₂	1	1	yes	maximal, characteristic
2	#16837223	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#499	C₂	1	1	yes	maximal, characteristic
4	#14273667	—	2	1	no	—
5	#14273667	—	2	1	no	—
6	#125×C₅₉	C₄	1	2	yes	—
7	#107×C₅₉	—	2	1	no	—
8	#106×C₅₉	—	2	1	no	—
9	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
12	C₄⋊C₄×C₅₉	—	2	2	no	—
13	C₄⋊C₄×C₅₉	—	4	2	no	—
14	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₅₉⋊C₁₆	—	4	1	no	—
16	C₅₉⋊C₁₆	—	4	1	no	—
17	C₂×C₄×C₅₉	—	2	1	no	—
18	C₂×C₄×C₅₉	—	4	2	no	—
19	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
21	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
22	C₈×C₅₉	Q₁₆	1	1	yes	characteristic
23	C₈×C₅₉	Q₁₆	1	1	yes	characteristic
24	C₂²×C₅₉	#100	1	1	yes	characteristic
25	C₄×C₅₉	—	4	1	no	—
26	C₄×C₅₉	—	8	2	no	—
27	C₄×C₅₉	#103	1	1	yes	characteristic
28	C₄×C₅₉	#103	1	1	yes	characteristic
29	#1366	—	59	1	no	maximal, Sylow
30	C₂×C₅₉	—	2	1	no	—
31	C₂×C₅₉	#333	1	1	yes	characteristic
32	#499	D₅₉	1	1	yes	characteristic
33	#364	—	59	1	no	—
34	#364	—	59	1	no	—
35	C₅₉	#1366	1	1	yes	characteristic, complemented, Sylow
36	#125	Dic₅₉	1	2	yes	—
37	M₃₂	—	118	1	no	—
38	M₃₂	—	118	1	no	—
39	#107	—	2	1	no	—
40	#106	—	2	1	no	—
41	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
42	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
44	C₄⋊C₄	—	2	2	no	—
45	C₄⋊C₄	—	4	2	no	—
46	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
47	C₁₆	—	236	1	no	—
48	C₁₆	—	236	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	4	2	no	—
51	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
52	C₈	#11745671	1	1	yes	characteristic
53	C₈	#11745671	1	1	yes	characteristic
54	C₈	#11745672	1	1	yes	characteristic
55	C₈	#11745672	1	1	yes	characteristic
56	C₂²	#14273644	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	2	no	—
59	C₄	#14273651	1	1	yes	characteristic
60	C₄	#14273651	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#16837151	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837151
commutator	C₄²×C₅₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₅₉×#499	C₂
socle	C₂×C₅₉	#333
hypercenter	#499	D₅₉
hypocenter	C₅₉	#1366
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
35. C₅₉	#1366	semidirect