Subgroups — #28475412

Order 15104.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21422160	C₂	1	2	yes	maximal
2	C₅₉×#1710	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₅₉⋊C₁₆)	—	2	2	no	—
4	C₅₉×#500	C₄	1	2	yes	—
5	C₅₉×#487	—	2	2	no	—
6	C₈²×C₅₉	C₂²	1	1	yes	characteristic
7	C₂×C₅₉⋊C₁₆	—	4	2	no	—
8	C₄⋊Q₈×C₅₉	—	2	2	no	—
9	#107×C₅₉	—	4	2	no	—
10	#103×C₅₉	—	4	2	no	—
11	#103×C₅₉	—	4	2	no	—
12	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
13	C₄×C₈×C₅₉	D₄	1	2	yes	—
14	C₂×Q₈×C₅₉	—	4	2	no	—
15	C₂×C₈×C₅₉	—	2	1	no	—
16	C₂×C₈×C₅₉	D₈	1	2	yes	—
17	C₂×C₈×C₅₉	SD₁₆	1	2	yes	—
18	C₄⋊C₄×C₅₉	—	4	2	no	—
19	C₄⋊C₄×C₅₉	—	4	2	no	—
20	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₅₉⋊C₁₆	—	8	2	no	—
22	Q₈×C₅₉	—	8	2	no	—
23	Q₈×C₅₉	—	8	2	no	—
24	C₂×C₄×C₅₉	—	8	2	no	—
25	C₂×C₄×C₅₉	#100	1	1	yes	characteristic
26	C₂×C₄×C₅₉	#102	1	2	yes	—
27	C₈×C₅₉	—	2	2	no	—
28	C₈×C₅₉	—	2	2	no	—
29	C₈×C₅₉	—	2	2	no	—
30	#7093	—	59	1	no	maximal, Sylow
31	C₂²×C₅₉	#331	1	1	yes	characteristic
32	C₄×C₅₉	—	2	1	no	—
33	C₄×C₅₉	—	16	2	no	—
34	C₄×C₅₉	#359	1	2	yes	—
35	C₄×C₅₉	#360	1	2	yes	—
36	#1710	D₅₉	1	1	yes	characteristic
37	#1367	—	59	2	no	—
38	C₂×C₅₉	#1358	1	1	yes	characteristic
39	C₂×C₅₉	#1360	1	2	yes	—
40	#500	Dic₅₉	1	2	yes	—
41	#487	—	2	2	no	—
42	C₄⋊C₁₆	—	118	2	no	—
43	C₈²	C₂×D₅₉	1	1	yes	characteristic
44	C₅₉	#7093	1	1	yes	characteristic, complemented, Sylow
45	C₄⋊Q₈	—	2	2	no	—
46	C₂×C₁₆	—	236	2	no	—
47	#107	—	4	2	no	—
48	#103	—	4	2	no	—
49	#103	—	4	2	no	—
50	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
51	C₄×C₈	C₂²⋊D₅₉	1	2	yes	—
52	C₂×Q₈	—	4	2	no	—
53	C₂×C₈	—	2	1	no	—
54	C₂×C₈	#11745669	1	2	yes	—
55	C₂×C₈	#11745670	1	2	yes	—
56	C₄⋊C₄	—	4	2	no	—
57	C₄⋊C₄	—	4	2	no	—
58	C₄²	C₂²⋊Dic₅₉	1	1	yes	characteristic
59	C₁₆	—	472	2	no	—
60	Q₈	—	8	2	no	—
61	Q₈	—	8	2	no	—
62	C₂×C₄	—	8	2	no	—
63	C₂×C₄	#14273644	1	1	yes	characteristic
64	C₂×C₄	#14273648	1	2	yes	—
65	C₈	—	2	2	no	—
66	C₈	—	2	2	no	—
67	C₈	—	2	2	no	—
68	C₂²	#16837146	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	16	2	no	—
71	C₄	#16837209	1	2	yes	—
72	C₄	#16837212	1	2	yes	—
73	C₂	#21422135	1	1	yes	characteristic
74	C₂	#21422139	1	2	yes	—

	subgroup	G/H
center	C₂²	#16837146
commutator	C₄×C₈×C₅₉	C₂×C₄
Frattini	C₈²	C₂×D₅₉
Fitting	C₅₉×#1710	C₂
socle, prime radical	C₂²×C₅₉	#331
cosocle	C₈²×C₅₉	C₂²
hypercenter	#1710	D₅₉
hypocenter	C₅₉	#7093
LCS	G ▷ C₄×C₈×C₅₉ ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1710

Complements

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

N	H ≅ G/N	type
44. C₅₉	#7093	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21422160	2
C₅₉×#1710	2
#7093	59