Subgroups — #21422152

Order 7552.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837807	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#335	C₂	1	1	yes	maximal, characteristic
4	#14273727	—	2	1	no	—
5	C₂×C₅₉⋊C₁₆	—	2	1	no	—
6	#14273661	—	2	1	no	—
7	#14273661	C₄	1	2	yes	—
8	C₄⋊C₈×C₅₉	—	2	1	no	—
9	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₁₈	—	4	1	no	—
11	C₂×C₈×C₅₉	—	4	1	no	—
12	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
14	C₄²×C₅₉	D₄	1	1	yes	characteristic
15	C₄⋊Dic₅₉	—	2	2	no	—
16	C₄⋊Dic₅₉	—	4	1	no	—
17	C₅₉⋊C₁₆	—	4	1	no	—
18	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₅₉	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₅₉	—	4	2	no	—
22	Dic₁₁₈	—	8	1	no	—
23	Dic₁₁₈	—	8	1	no	—
24	C₈×C₅₉	—	2	1	no	—
25	C₈×C₅₉	—	8	1	no	—
26	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
27	C₈×C₅₉	Q₁₆	1	1	yes	characteristic
28	C₂²×C₅₉	#102	1	1	yes	characteristic
29	C₄×C₅₉	—	2	1	no	—
30	C₄×C₅₉	#101	1	1	yes	characteristic
31	C₄×C₅₉	#103	1	1	yes	characteristic
32	C₄×C₅₉	D₁₆	1	1	yes	characteristic
33	C₄×C₅₉	SD₃₂	1	1	yes	characteristic
34	Dic₅₉	—	8	2	no	—
35	#1364	—	59	1	no	maximal, Sylow
36	C₂×C₅₉	#332	1	1	yes	characteristic
37	C₂×C₅₉	#357	1	1	yes	characteristic
38	C₂×C₅₉	#362	1	1	yes	characteristic
39	#500	—	59	1	no	—
40	C₄⋊C₁₆	—	59	1	no	—
41	#335	D₅₉	1	1	yes	characteristic
42	C₅₉	#1364	1	1	yes	characteristic, complemented, Sylow
43	C₄⋊Q₈	—	118	1	no	—
44	C₂×C₁₆	—	118	1	no	—
45	#107	—	59	2	no	—
46	#107	—	118	1	no	—
47	C₄⋊C₈	—	2	1	no	—
48	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
49	C₂×Q₈	—	236	1	no	—
50	C₂×C₈	—	4	1	no	—
51	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
52	C₂×C₈	D₂₃₆	1	1	yes	characteristic
53	C₄⋊C₄	—	118	2	no	—
54	C₄⋊C₄	—	236	1	no	—
55	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
56	C₁₆	—	236	1	no	—
57	Q₈	—	472	1	no	—
58	Q₈	—	472	1	no	—
59	C₂×C₄	—	236	2	no	—
60	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
61	C₂×C₄	#11745669	1	1	yes	characteristic
62	C₂×C₄	#11745671	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	8	1	no	—
65	C₈	#11745660	1	1	yes	characteristic
66	C₈	Dic₂₃₆	1	1	yes	characteristic
67	C₂²	#14273647	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	472	2	no	—
70	C₄	#14273645	1	1	yes	characteristic
71	C₄	#14273652	1	1	yes	characteristic
72	C₄	#14273668	1	1	yes	characteristic
73	C₄	#14273670	1	1	yes	characteristic
74	C₂	#16837149	1	1	yes	characteristic
75	C₂	#16837202	1	1	yes	characteristic
76	C₂	#16837217	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14273647
commutator	C₂×C₈×C₅₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₅₉×#335	C₂
socle	C₂²×C₅₉	#102
hypercenter	#335	D₅₉
hypocenter	C₅₉	#1364
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
42. C₅₉	#1364	semidirect