Subgroups — #16837836

Order 3776.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14273746	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#14273672	C₂	1	1	yes	maximal, characteristic, complemented
4	#14273671	C₂	1	1	yes	maximal, characteristic, complemented
5	#14273668	C₂	1	1	yes	maximal, characteristic, complemented
6	#14273666	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#11745687	—	2	1	no	—
9	D₄×D₅₉	—	2	1	no	—
10	D₈×C₅₉	C₂²	1	1	yes	characteristic
11	D₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
12	#11745670	—	2	1	no	—
13	#11745669	—	2	1	no	—
14	Dic₂₃₆	C₂²	1	1	yes	characteristic, complemented
15	D₄₇₂	C₂²	1	1	yes	characteristic
16	C₈×D₅₉	C₂²	1	1	yes	characteristic
17	C₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
18	C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₅₉	—	4	1	no	—
20	D₄×C₅₉	—	2	1	no	—
21	D₄×C₅₉	—	2	1	no	—
22	C₂²⋊D₅₉	—	4	1	no	—
23	C₂²⋊D₅₉	—	4	1	no	—
24	C₂×Dic₅₉	—	4	1	no	—
25	D₂₃₆	—	2	1	no	—
26	C₄×D₅₉	D₄	1	1	yes	characteristic
27	Dic₁₁₈	—	2	1	no	—
28	C₈×C₅₉	C₂³	1	1	yes	characteristic
29	C₅₉⋊C₈	D₄	1	1	yes	characteristic
30	C₂²×C₅₉	—	4	1	no	—
31	C₂²×C₅₉	—	4	1	no	—
32	C₂×D₅₉	—	4	1	no	—
33	C₂×D₅₉	—	8	2	no	—
34	C₂×D₅₉	D₈	1	1	yes	characteristic
35	C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
36	Dic₅₉	—	4	1	no	—
37	Dic₅₉	D₈	1	1	yes	characteristic
38	C₂×C₅₉	—	8	1	no	—
39	C₂×C₅₉	—	8	1	no	—
40	C₂×C₅₉	C₂×D₈	1	1	yes	characteristic
41	D₅₉	—	2	1	no	—
42	D₅₉	—	8	1	no	—
43	#509	—	59	1	no	maximal, Sylow
44	C₅₉	#509	1	1	yes	characteristic, complemented, Sylow
45	#135	—	59	1	no	—
46	C₂×D₈	—	59	1	no	—
47	SD₃₂	—	59	1	no	—
48	SD₃₂	—	59	1	no	—
49	D₁₆	—	59	1	no	—
50	D₁₆	D₅₉	1	1	yes	characteristic, complemented
51	M₃₂	—	59	1	no	—
52	#41	—	118	1	no	—
53	C₂×D₄	—	118	1	no	—
54	Q₁₆	—	59	1	no	—
55	SD₁₆	—	118	1	no	—
56	D₈	—	59	1	no	—
57	D₈	—	118	1	no	—
58	D₈	C₂×D₅₉	1	1	yes	characteristic
59	D₈	C₂×D₅₉	1	1	yes	characteristic, complemented
60	C₂×C₈	—	59	1	no	—
61	C₁₆	—	59	1	no	—
62	C₁₆	C₂×D₅₉	1	1	yes	characteristic, complemented
63	C₂³	—	236	1	no	—
64	Q₈	—	118	1	no	—
65	D₄	—	2	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	118	1	no	—
68	D₄	—	236	1	no	—
69	D₄	—	236	1	no	—
70	C₂×C₄	—	59	1	no	—
71	C₂×C₄	—	236	1	no	—
72	C₈	—	59	1	no	—
73	C₈	C₂²×D₅₉	1	1	yes	characteristic
74	C₂²	—	4	1	no	—
75	C₂²	—	4	1	no	—
76	C₂²	—	59	1	no	—
77	C₂²	—	472	2	no	—
78	C₂²	—	236	1	no	—
79	C₄	—	59	1	no	—
80	C₄	—	236	1	no	—
81	C₄	D₄×D₅₉	1	1	yes	characteristic
82	C₂	—	8	1	no	—
83	C₂	—	8	1	no	—
84	C₂	—	118	1	no	—
85	C₂	—	472	1	no	—
86	C₂	D₈×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₅₉
commutator, cosocle	C₈×C₅₉	C₂³
Frattini	C₈	C₂²×D₅₉
Fitting	D₁₆×C₅₉	C₂
socle	C₂×C₅₉	C₂×D₈
hypercenter	D₁₆	D₅₉
hypocenter	C₅₉	#509
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #14273746	C₂	semidirect
2. D₈×D₅₉	C₂	semidirect
3. #14273672	C₂	semidirect
4. #14273671	C₂	semidirect
5. #14273668	C₂	semidirect
6. #14273666	C₂	semidirect
7. D₁₆×C₅₉	C₂	semidirect
11. D₈×C₅₉	C₂²	semidirect
14. Dic₂₃₆	C₂²	semidirect
17. C₁₆×C₅₉	C₂²	semidirect
18. C₅₉⋊C₁₆	C₂²	semidirect
44. C₅₉	#509	semidirect
50. D₁₆	D₅₉	semidirect
59. D₈	C₂×D₅₉	semidirect
62. C₁₆	C₂×D₅₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14273746	2
D₈×D₅₉	2
#14273672	2
#14273671	2
#14273668	2
#14273666	2
D₁₆×C₅₉	2
#509	59