Subgroups — #21422084

Order 7552.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837184	C₂	1	1	yes	maximal, characteristic
2	#16837159	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#470	C₂	1	1	yes	maximal, characteristic
4	#14273686	—	2	1	no	—
5	#14273667	—	2	1	no	—
6	C₂×Q₁₆×C₅₉	C₄	1	1	yes	characteristic, complemented
7	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
8	C₂²⋊Q₈×C₅₉	—	2	1	no	—
9	#106×C₅₉	C₄	1	1	yes	characteristic, complemented
10	#103×C₅₉	—	2	1	no	—
11	C₂×Q₈×C₅₉	—	2	1	no	—
12	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
13	Q₁₆×C₅₉	—	4	1	no	—
14	M₁₆×C₅₉	—	4	1	no	—
15	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₅₉	—	2	1	no	—
18	C₄⋊C₄×C₅₉	—	4	1	no	—
19	C₂²⋊C₄×C₅₉	—	4	1	no	—
20	C₂²⋊Dic₅₉	—	4	1	no	—
21	C₄⋊Dic₅₉	—	4	1	no	—
22	C₄×Dic₅₉	—	2	2	no	—
23	C₅₉⋊C₁₆	—	4	1	no	—
24	C₂³×C₅₉	D₈	1	1	yes	characteristic
25	Q₈×C₅₉	—	4	1	no	—
26	Q₈×C₅₉	—	4	1	no	—
27	C₂×C₄×C₅₉	—	2	1	no	—
28	C₂×C₄×C₅₉	—	2	1	no	—
29	C₂×C₄×C₅₉	—	4	1	no	—
30	C₂×C₄×C₅₉	—	4	1	no	—
31	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₅₉	SD₁₆	1	1	yes	characteristic
33	C₂×Dic₅₉	—	4	2	no	—
34	C₈×C₅₉	—	2	1	no	—
35	C₈×C₅₉	—	2	1	no	—
36	C₂²×C₅₉	—	2	1	no	—
37	C₂²×C₅₉	—	4	1	no	—
38	C₂²×C₅₉	#102	1	1	yes	characteristic
39	C₄×C₅₉	—	2	1	no	—
40	C₄×C₅₉	—	8	1	no	—
41	C₄×C₅₉	—	8	1	no	—
42	C₄×C₅₉	#99	1	1	yes	characteristic
43	C₄×C₅₉	#104	1	1	yes	characteristic
44	Dic₅₉	—	8	2	no	—
45	#1340	—	59	1	no	maximal, Sylow
46	C₂×C₅₉	—	2	1	no	—
47	C₂×C₅₉	—	4	1	no	—
48	C₂×C₅₉	#327	1	1	yes	characteristic
49	#470	D₅₉	1	1	yes	characteristic
50	#349	—	59	1	no	—
51	H(3,ℤ/4)	—	59	1	no	—
52	C₅₉	#1340	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	Dic₅₉	1	1	yes	characteristic, complemented
54	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
55	C₂²⋊Q₈	—	2	1	no	—
56	#117	—	118	1	no	—
57	M₃₂	—	118	1	no	—
58	#106	Dic₅₉	1	1	yes	characteristic, complemented
59	#103	—	2	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
62	Q₁₆	—	4	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄⋊C₄	—	236	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	236	1	no	—
71	C₄²	—	118	2	no	—
72	C₁₆	—	236	1	no	—
73	C₂³	#11745669	1	1	yes	characteristic
74	Q₈	—	4	1	no	—
75	Q₈	—	4	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	—	236	2	no	—
81	C₂×C₄	#11745670	1	1	yes	characteristic
82	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#14273648	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	8	1	no	—
90	C₄	—	8	1	no	—
91	C₄	—	472	2	no	—
92	C₄	#14273642	1	1	yes	characteristic
93	C₄	#14273654	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#16837136	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837136
commutator	C₂×C₈×C₅₉	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₅₉
Fitting	C₅₉×#470	C₂
socle	C₂×C₅₉	#327
hypercenter	#470	D₅₉
hypocenter	C₅₉	#1340
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

Complements

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

N	H ≅ G/N	type
6. C₂×Q₁₆×C₅₉	C₄	semidirect
9. #106×C₅₉	C₄	semidirect
52. C₅₉	#1340	semidirect
53. C₂×Q₁₆	Dic₅₉	semidirect
58. #106	Dic₅₉	semidirect