Subgroups — #21421971

Order 7552.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837426	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11745664	—	2	2	no	—
4	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
5	C₄⋊(C₅₉⋊C₈)	C₄	1	4	yes	—
6	C₂²×C₈×C₅₉	C₄	1	2	yes	—
7	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₅₉	—	2	2	no	—
9	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₅₉	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₅₉	—	2	2	no	—
13	C₂×C₈×C₅₉	—	4	2	no	—
14	C₄²×C₅₉	C₂×C₄	1	2	yes	—
15	C₄²×C₅₉	D₄	1	2	yes	—
16	#11745664	—	4	2	no	—
17	#11745664	—	4	2	no	—
18	C₂×C₅₉⋊C₈	—	2	4	no	—
19	C₂³×C₅₉	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₅₉	—	2	1	no	—
21	C₂×C₄×C₅₉	—	2	1	no	—
22	C₂×C₄×C₅₉	—	4	1	no	—
23	C₂×C₄×C₅₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
25	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
28	C₂×C₄×C₅₉	SD₁₆	1	2	yes	—
29	C₂×C₄×C₅₉	Q₁₆	1	1	yes	characteristic
30	C₈×C₅₉	—	4	2	no	—
31	C₅₉⋊C₈	—	4	4	no	—
32	C₂²×C₅₉	—	2	1	no	—
33	C₂²×C₅₉	—	2	1	no	—
34	C₂²×C₅₉	#95	1	1	yes	characteristic
35	C₂²×C₅₉	#106	1	1	yes	characteristic
36	C₂²×C₅₉	#107	1	1	yes	characteristic
37	C₄×C₅₉	—	2	2	no	—
38	C₄×C₅₉	—	2	1	no	—
39	C₄×C₅₉	#100	1	1	yes	characteristic
40	C₄×C₅₉	#101	1	1	yes	characteristic
41	C₄×C₅₉	#102	1	2	yes	—
42	C₄×C₅₉	#103	1	2	yes	—
43	#1292	—	59	1	no	maximal, Sylow
44	C₂×C₅₉	—	2	1	no	—
45	C₂×C₅₉	—	2	1	no	—
46	C₂×C₅₉	#338	1	1	yes	characteristic
47	C₂×C₅₉	#340	1	1	yes	characteristic
48	C₂×C₅₉	#343	1	1	yes	characteristic
49	#423	—	59	2	no	—
50	C₂×C₄⋊C₈	D₅₉	1	1	yes	characteristic
51	C₅₉	#1292	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₁₆	—	118	2	no	—
53	C₂²×C₈	Dic₅₉	1	2	yes	—
54	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
55	C₄⋊C₈	—	2	2	no	—
56	C₄⋊C₈	—	59	4	no	—
57	C₄⋊C₈	—	118	2	no	—
58	C₂²×C₄	Dic₁₁₈	1	1	yes	characteristic
59	C₂²×C₄	D₂₃₆	1	1	yes	characteristic
60	C₂²×C₄	C₂×Dic₅₉	1	1	yes	characteristic
61	M₁₆	—	236	2	no	—
62	M₁₆	—	236	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	4	2	no	—
65	C₂×C₈	—	118	4	no	—
66	C₄²	C₄×D₅₉	1	2	yes	—
67	C₄²	C₂²⋊D₅₉	1	2	yes	—
68	C₂³	C₄⋊Dic₅₉	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	#11745660	1	2	yes	—
73	C₂×C₄	D₄₇₂	1	1	yes	characteristic
74	C₂×C₄	Dic₂₃₆	1	1	yes	characteristic
75	C₂×C₄	C₄×Dic₅₉	1	1	yes	characteristic
76	C₂×C₄	Dic₅₉⋊C₄	1	2	yes	—
77	C₂×C₄	(C₂×D₅₉)⋊C₄	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
79	C₈	—	4	2	no	—
80	C₈	—	236	4	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₅₉⋊#95	1	1	yes	characteristic
84	C₂²	#14273659	1	1	yes	characteristic
85	C₂²	#14273661	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#14273644	1	1	yes	characteristic
89	C₄	#14273646	1	1	yes	characteristic
90	C₄	#14273649	1	2	yes	—
91	C₄	#14273652	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	C₅₉⋊#338	1	1	yes	characteristic
95	C₂	#16837165	1	1	yes	characteristic
96	C₂	#16837171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₅₉⋊#95
commutator	C₂×C₄×C₅₉	C₄²
Frattini	C₂×C₄²	C₂×D₅₉
Fitting	C₂×C₄⋊C₈×C₅₉	C₂
socle	C₂²×C₅₉	#95
hypercenter	C₂×C₄⋊C₈	D₅₉
hypocenter	C₅₉	#1292
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
51. C₅₉	#1292	semidirect