Subgroups — #28476352

Order 15104.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21422294	C₂	1	1	yes	maximal, characteristic
2	#21422172	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2253	C₂	1	1	yes	maximal, characteristic
4	#16837236	—	2	1	no	—
5	#16837223	—	2	1	no	—
6	C₅₉×#499	—	2	1	no	—
7	C₅₉×#367	C₄	1	2	yes	—
8	C₅₉×#366	—	2	1	no	—
9	C₄×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
10	#14273667	—	4	1	no	—
11	C₅₉⋊C₃₂	—	4	1	no	—
12	#125×C₅₉	—	4	1	no	—
13	C₂×C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₅₉	D₄	1	1	yes	characteristic
15	#107×C₅₉	—	2	2	no	—
16	#106×C₅₉	—	4	1	no	—
17	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	D₈	1	1	yes	characteristic
20	C₄⋊C₄×C₅₉	—	4	2	no	—
21	C₄⋊C₄×C₅₉	—	8	2	no	—
22	C₄²×C₅₉	SD₁₆	1	1	yes	characteristic
23	C₁₆×C₅₉	—	2	1	no	—
24	C₁₆×C₅₉	SD₁₆	1	1	yes	characteristic
25	C₁₆×C₅₉	Q₁₆	1	1	yes	characteristic
26	C₅₉⋊C₁₆	—	8	1	no	—
27	C₂×C₄×C₅₉	—	2	1	no	—
28	C₂×C₄×C₅₉	—	8	2	no	—
29	C₂×C₄×C₅₉	#102	1	1	yes	characteristic
30	C₈×C₅₉	#101	1	1	yes	characteristic
31	C₈×C₅₉	#103	1	1	yes	characteristic
32	C₈×C₅₉	SD₃₂	1	1	yes	characteristic
33	C₈×C₅₉	Q₃₂	1	1	yes	characteristic
34	#7454	—	59	1	no	maximal, Sylow
35	C₂²×C₅₉	#361	1	1	yes	characteristic
36	C₄×C₅₉	—	4	1	no	—
37	C₄×C₅₉	—	16	2	no	—
38	C₄×C₅₉	#332	1	1	yes	characteristic
39	C₄×C₅₉	#358	1	1	yes	characteristic
40	#2253	D₅₉	1	1	yes	characteristic
41	#1422	—	59	1	no	—
42	#1373	—	59	1	no	—
43	C₂×C₅₉	—	2	1	no	—
44	C₂×C₅₉	#1365	1	1	yes	characteristic
45	#499	—	2	1	no	—
46	M₆₄	—	118	1	no	—
47	#367	Dic₅₉	1	2	yes	—
48	#366	—	2	1	no	—
49	#364	—	118	1	no	—
50	C₄×C₁₆	C₂×D₅₉	1	1	yes	characteristic
51	C₅₉	#7454	1	1	yes	characteristic, complemented, Sylow
52	#125	—	4	1	no	—
53	M₃₂	—	236	1	no	—
54	C₂×C₁₆	C₂×Dic₅₉	1	1	yes	characteristic
55	C₂×C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
56	#107	—	2	2	no	—
57	#106	—	4	1	no	—
58	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
59	C₃₂	—	236	1	no	—
60	C₂×C₈	#11745669	1	1	yes	characteristic
61	C₂×C₈	C₂²⋊Dic₅₉	1	1	yes	characteristic
62	C₄⋊C₄	—	4	2	no	—
63	C₄⋊C₄	—	8	2	no	—
64	C₄²	#11745670	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	472	1	no	—
67	C₁₆	#11745671	1	1	yes	characteristic
68	C₁₆	#11745672	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	8	2	no	—
71	C₂×C₄	#14273648	1	1	yes	characteristic
72	C₈	#14273646	1	1	yes	characteristic
73	C₈	#14273651	1	1	yes	characteristic
74	C₈	#14273670	1	1	yes	characteristic
75	C₈	#14273673	1	1	yes	characteristic
76	C₂²	#16837215	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	16	2	no	—
79	C₄	#16837148	1	1	yes	characteristic
80	C₄	#16837206	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#21422154	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21422154
commutator	C₂×C₁₆×C₅₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₅₉
Fitting	C₅₉×#2253	C₂
socle	C₂×C₅₉	#1365
prime radical	C₂²×C₅₉	#361
cosocle	C₄×C₁₆×C₅₉	C₂²
hypercenter	#2253	D₅₉
hypocenter	C₅₉	#7454
LCS	G ▷ C₂×C₁₆×C₅₉ ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2253

Complements

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

N	H ≅ G/N	type
51. C₅₉	#7454	semidirect

Maximal subgroups

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

subgroup	index
#21422294	2
#21422172	2
C₅₉×#2253	2
#7454	59