Subgroups — #21422148

Order 7552.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#16837153	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#499	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
6	#125×C₅₉	—	2	1	no	—
7	#107×C₅₉	C₄	1	1	yes	characteristic
8	#107×C₅₉	C₄	1	1	yes	characteristic
9	#106×C₅₉	—	2	1	no	—
10	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
13	C₄⋊C₄×C₅₉	—	2	1	no	—
14	C₄⋊C₄×C₅₉	—	2	1	no	—
15	C₄⋊C₄×C₅₉	—	4	1	no	—
16	C₄⋊C₄×C₅₉	—	4	1	no	—
17	C₄²×C₅₉	D₄	1	1	yes	characteristic
18	C₂×C₅₉⋊C₈	—	4	1	no	—
19	C₅₉⋊C₁₆	—	4	1	no	—
20	C₂×C₄×C₅₉	—	4	1	no	—
21	C₂×C₄×C₅₉	—	4	1	no	—
22	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
24	C₂×C₄×C₅₉	SD₁₆	1	1	yes	characteristic
25	C₈×C₅₉	—	2	1	no	—
26	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
27	C₈×C₅₉	Q₁₆	1	1	yes	characteristic
28	C₅₉⋊C₈	—	8	1	no	—
29	C₂²×C₅₉	#102	1	1	yes	characteristic
30	C₄×C₅₉	—	2	1	no	—
31	C₄×C₅₉	—	2	1	no	—
32	C₄×C₅₉	—	8	1	no	—
33	C₄×C₅₉	—	8	1	no	—
34	C₄×C₅₉	#101	1	1	yes	characteristic
35	C₄×C₅₉	#103	1	1	yes	characteristic
36	#1363	—	59	1	no	maximal, Sylow
37	C₂×C₅₉	#332	1	1	yes	characteristic
38	C₂×C₅₉	#359	1	1	yes	characteristic
39	C₂×C₅₉	#360	1	1	yes	characteristic
40	#499	D₅₉	1	1	yes	characteristic
41	C₄⋊C₁₆	—	59	1	no	—
42	#334	—	59	1	no	—
43	C₅₉	#1363	1	1	yes	characteristic, complemented, Sylow
44	#125	—	2	1	no	—
45	C₂×C₁₆	—	118	1	no	—
46	#107	Dic₅₉	1	1	yes	characteristic
47	#107	Dic₅₉	1	1	yes	characteristic
48	#106	—	2	1	no	—
49	C₄⋊C₈	—	118	1	no	—
50	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
51	C₂×C₈	—	236	1	no	—
52	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	—	4	1	no	—
57	C₄⋊C₄	—	4	1	no	—
58	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
59	C₁₆	—	236	1	no	—
60	C₂×C₄	—	4	1	no	—
61	C₂×C₄	—	4	1	no	—
62	C₂×C₄	#11745669	1	1	yes	characteristic
63	C₂×C₄	#11745670	1	1	yes	characteristic
64	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	472	1	no	—
67	C₈	#11745671	1	1	yes	characteristic
68	C₈	#11745672	1	1	yes	characteristic
69	C₂²	#14273648	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	2	1	no	—
72	C₄	—	8	1	no	—
73	C₄	—	8	1	no	—
74	C₄	#14273646	1	1	yes	characteristic
75	C₄	#14273651	1	1	yes	characteristic
76	C₂	#16837148	1	1	yes	characteristic
77	C₂	#16837209	1	1	yes	characteristic
78	C₂	#16837212	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14273648
commutator	C₂×C₈×C₅₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₅₉×#499	C₂
socle	C₂²×C₅₉	#102
hypercenter	#499	D₅₉
hypocenter	C₅₉	#1363
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
43. C₅₉	#1363	semidirect