Subgroups — #16837745

Order 3776.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14273707	C₂	1	1	yes	maximal, characteristic
2	#14273685	C₂	1	1	yes	maximal, characteristic
3	#14273658	C₂	1	1	yes	maximal, characteristic, complemented
4	#14273652	C₂	1	1	yes	maximal, characteristic, complemented
5	#14273650	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₅₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#107×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₅₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₁₈	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
13	(C₂×D₅₉)⋊C₄	—	2	1	no	—
14	(C₂×D₅₉)⋊C₄	—	2	1	no	—
15	C₄⋊Dic₅₉	—	2	1	no	—
16	C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
17	C₄×Dic₅₉	—	2	1	no	—
18	C₂×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₅₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₅₉	—	2	1	no	—
21	C₂×C₄×C₅₉	—	2	1	no	—
22	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₅₉	—	2	1	no	—
24	C₂×Dic₅₉	—	2	1	no	—
25	C₂×Dic₅₉	D₄	1	1	yes	characteristic
26	C₄×D₅₉	—	2	1	no	—
27	C₄×D₅₉	—	2	1	no	—
28	Dic₁₁₈	—	2	1	no	—
29	Dic₁₁₈	—	2	1	no	—
30	C₈×C₅₉	—	2	1	no	—
31	C₅₉⋊C₈	—	2	1	no	—
32	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
33	C₂×D₅₉	—	2	1	no	—
34	C₂×D₅₉	—	2	1	no	—
35	C₂×D₅₉	—	2	1	no	—
36	C₄×C₅₉	—	4	1	no	—
37	C₄×C₅₉	—	4	1	no	—
38	C₄×C₅₉	#41	1	1	yes	characteristic
39	C₄×C₅₉	#41	1	1	yes	characteristic
40	Dic₅₉	—	2	1	no	—
41	Dic₅₉	—	4	1	no	—
42	Dic₅₉	—	4	1	no	—
43	C₂×C₅₉	#123	1	1	yes	characteristic
44	C₂×C₅₉	#135	1	1	yes	characteristic
45	C₂×C₅₉	#137	1	1	yes	characteristic
46	D₅₉	—	4	1	no	—
47	#485	—	59	1	no	maximal, Sylow
48	C₅₉	#485	1	1	yes	characteristic, complemented, Sylow
49	C₂²⋊Q₈	—	59	1	no	—
50	#117	—	59	1	no	—
51	#107	D₅₉	1	1	yes	characteristic, complemented
52	#106	—	59	1	no	—
53	#103	—	59	1	no	—
54	#103	—	59	1	no	—
55	C₂²⋊C₈	—	59	1	no	—
56	C₂×Q₈	—	59	1	no	—
57	C₂²×C₄	—	59	1	no	—
58	C₂×C₈	—	59	1	no	—
59	C₂×C₈	C₂×D₅₉	1	1	yes	characteristic
60	C₄⋊C₄	—	59	1	no	—
61	C₄⋊C₄	—	118	1	no	—
62	C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
64	C₂²⋊C₄	—	118	1	no	—
65	C₂²⋊C₄	—	118	1	no	—
66	C₄²	—	118	1	no	—
67	C₂³	—	59	1	no	—
68	Q₈	—	118	1	no	—
69	Q₈	—	118	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	59	1	no	—
73	C₂×C₄	—	118	1	no	—
74	C₂×C₄	—	118	1	no	—
75	C₂×C₄	—	118	1	no	—
76	C₂×C₄	—	118	1	no	—
77	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	118	1	no	—
80	C₂²	—	118	1	no	—
81	C₂²	—	118	1	no	—
82	C₂²	—	118	1	no	—
83	C₂²	D₄×D₅₉	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	118	1	no	—
87	C₄	—	236	1	no	—
88	C₄	—	236	1	no	—
89	C₄	#11745685	1	1	yes	characteristic
90	C₄	#11745689	1	1	yes	characteristic
91	C₂	—	236	1	no	—
92	C₂	#14273712	1	1	yes	characteristic
93	C₂	#14273746	1	1	yes	characteristic
94	C₂	#14273759	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅₉
commutator, cosocle	C₂×C₄×C₅₉	C₂³
Frattini	C₂×C₄	C₂²×D₅₉
Fitting	#107×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₄
prime radical	C₂²×D₅₉	D₄
hypercenter	#107	D₅₉
hypocenter	C₅₉	#485
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. #14273658	C₂	semidirect
4. #14273652	C₂	semidirect
5. #14273650	C₂	semidirect
7. #107×C₅₉	C₂	semidirect
48. C₅₉	#485	semidirect
51. #107	D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#14273707	2
#14273685	2
#14273658	2
#14273652	2
#14273650	2
(C₂×D₅₉)⋊C₈	2
#107×C₅₉	2
#485	59