Subgroups — #21426391

Order 7552.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837818	C₂	1	1	yes	maximal, characteristic
2	#16837235	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₅₉	C₂	1	2	yes	maximal, complemented
5	C₅₉×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#14273733	C₄	1	1	yes	characteristic
7	#14273667	C₄	1	1	yes	characteristic
8	#14273666	C₄	1	2	yes	—
9	C₁₆×D₅₉	C₂²	1	2	yes	—
10	C₅₉⋊C₃₂	C₂²	1	1	yes	characteristic
11	C₅₉⋊C₃₂	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	C₃₂×C₅₉	C₂²	1	2	yes	—
14	#11745685	C₈	1	1	yes	characteristic
15	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
16	#11745664	C₈	1	1	yes	characteristic
17	#11745659	C₈	1	2	yes	—
18	C₈×D₅₉	C₂×C₄	1	2	yes	—
19	C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₅₉	C₂³	1	1	yes	characteristic
21	C₅₉⋊C₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₅₉	C₁₆	1	2	yes	—
24	D₂₃₆	C₁₆	1	1	yes	characteristic
25	C₄×D₅₉	C₂×C₈	1	2	yes	—
26	Dic₁₁₈	C₁₆	1	1	yes	characteristic
27	C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
28	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
29	C₅₉⋊C₈	C₂×C₈	1	2	yes	—
30	C₂²×C₅₉	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₅₉	C₂×C₁₆	1	2	yes	—
32	C₄×C₅₉	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
34	Dic₅₉	C₂×C₁₆	1	2	yes	—
35	#2258	—	59	1	no	maximal, Sylow
36	C₂×C₅₉	—	2	1	no	—
37	C₂×C₅₉	C₂²×C₁₆	1	1	yes	characteristic
38	D₅₉	—	2	2	no	—
39	#504	—	59	1	no	—
40	M₆₄	—	59	2	no	—
41	M₆₄	D₅₉	1	1	yes	characteristic, complemented
42	C₂×C₃₂	—	59	1	no	—
43	C₂×C₃₂	—	59	2	no	—
44	C₅₉	#2258	1	1	yes	characteristic, complemented, Sylow
45	#131	—	59	1	no	—
46	M₃₂	—	59	1	no	—
47	M₃₂	—	59	2	no	—
48	C₂×C₁₆	—	59	2	no	—
49	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
50	C₃₂	—	59	1	no	—
51	C₃₂	—	59	1	no	—
52	C₃₂	C₂×D₅₉	1	2	yes	—
53	#41	—	59	1	no	—
54	M₁₆	—	59	1	no	—
55	M₁₆	—	59	2	no	—
56	C₂×C₈	—	59	2	no	—
57	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
58	C₁₆	—	59	2	no	—
59	C₁₆	C₄×D₅₉	1	1	yes	characteristic
60	C₁₆	C₂²×D₅₉	1	1	yes	characteristic
61	Q₈	—	59	1	no	—
62	D₄	—	59	2	no	—
63	D₄	—	59	1	no	—
64	C₂×C₄	—	59	2	no	—
65	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
66	C₈	—	59	2	no	—
67	C₈	C₈×D₅₉	1	1	yes	characteristic
68	C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
69	C₂²	—	59	2	no	—
70	C₂²	C₁₆×D₅₉	1	1	yes	characteristic
71	C₄	—	59	2	no	—
72	C₄	C₁₆×D₅₉	1	1	yes	characteristic
73	C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	118	2	no	—
76	C₂	C₂×C₁₆×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₅₉
commutator, socle	C₂×C₅₉	C₂²×C₁₆
Fitting	C₅₉×M₆₄	C₂
hypercenter	M₆₄	D₅₉
hypocenter	C₅₉	#2258
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #16837235	C₂	semidirect
3. C₂×C₅₉⋊C₃₂	C₂	semidirect
4. C₃₂×D₅₉	C₂	semidirect
5. C₅₉×M₆₄	C₂	semidirect
41. M₆₄	D₅₉	semidirect
44. C₅₉	#2258	semidirect