Subgroups — #16837810

Order 3776.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14273726	C₂	1	1	yes	maximal, characteristic
2	#14273718	C₂	1	1	yes	maximal, characteristic
3	#14273660	C₂	1	1	yes	maximal, characteristic
4	#14273659	C₂	1	1	yes	maximal, characteristic
5	#14273658	C₂	1	1	yes	maximal, characteristic
6	#14273637	C₂	1	1	yes	maximal, characteristic
7	#107×C₅₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₁₈	—	2	1	no	—
9	C₂×C₈×C₅₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₅₉	—	2	1	no	—
13	C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
15	Dic₅₉⋊C₄	—	2	1	no	—
16	Dic₅₉⋊C₄	—	2	1	no	—
17	C₄×Dic₅₉	C₂²	1	1	yes	characteristic
18	C₂×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅₉	—	2	1	no	—
20	C₂×C₄×C₅₉	—	2	1	no	—
21	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₅₉	—	2	1	no	—
23	C₂×Dic₅₉	—	2	1	no	—
24	C₂×Dic₅₉	D₄	1	1	yes	characteristic
25	C₂×Dic₅₉	D₄	1	1	yes	characteristic
26	Dic₁₁₈	—	4	2	no	—
27	C₈×C₅₉	Q₈	1	2	yes	complemented
28	C₅₉⋊C₈	Q₈	1	2	yes	complemented
29	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₅₉	—	4	1	no	—
31	C₄×C₅₉	—	4	1	no	—
32	C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
34	Dic₅₉	—	2	1	no	—
35	Dic₅₉	—	2	1	no	—
36	Dic₅₉	—	4	1	no	—
37	Dic₅₉	—	4	1	no	—
38	C₂×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₅₉	#137	1	1	yes	characteristic
41	#501	—	59	1	no	maximal, Sylow
42	C₅₉	#501	1	1	yes	characteristic, complemented, Sylow
43	C₄⋊Q₈	—	59	1	no	—
44	#125	—	59	1	no	—
45	#107	—	59	1	no	—
46	#107	D₅₉	1	1	yes	characteristic
47	#106	—	59	1	no	—
48	#106	—	59	1	no	—
49	#97	—	59	1	no	—
50	C₂×Q₈	—	118	1	no	—
51	C₂×C₈	—	59	1	no	—
52	C₂×C₈	C₂×D₅₉	1	1	yes	characteristic
53	C₄⋊C₄	—	59	1	no	—
54	C₄⋊C₄	—	59	1	no	—
55	C₄⋊C₄	—	118	1	no	—
56	C₄⋊C₄	—	118	1	no	—
57	C₄⋊C₄	—	118	1	no	—
58	C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
60	C₄²	—	59	1	no	—
61	Q₈	—	236	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	59	1	no	—
65	C₂×C₄	—	59	1	no	—
66	C₂×C₄	—	118	1	no	—
67	C₂×C₄	—	118	1	no	—
68	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
69	C₈	—	59	2	no	—
70	C₈	Dic₁₁₈	1	2	yes	complemented
71	C₂²	D₄×D₅₉	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	118	1	no	—
75	C₄	—	118	1	no	—
76	C₄	—	236	1	no	—
77	C₄	—	236	1	no	—
78	C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
79	C₄	Q₈×D₅₉	1	1	yes	characteristic
80	C₂	#14273726	1	1	yes	characteristic
81	C₂	#14273751	1	1	yes	characteristic
82	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, prime radical	C₂²×C₅₉	C₂×D₄
hypercenter	#107	D₅₉
hypocenter	C₅₉	#501
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
27. C₈×C₅₉	Q₈	semidirect
28. C₅₉⋊C₈	Q₈	semidirect
42. C₅₉	#501	semidirect
70. C₈	Dic₁₁₈	semidirect

Maximal subgroups

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

subgroup	index
#14273726	2
#14273718	2
#14273660	2
#14273659	2
#14273658	2
#14273637	2
#107×C₅₉	2
#501	59