Subgroups — #16837494

Order 3776.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745672	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₅₉	C₂	1	1	yes	maximal, characteristic
3	#14273692	C₂	1	1	yes	maximal, characteristic
4	#14273660	C₂	1	1	yes	maximal, characteristic
5	#14273652	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₅₉	C₂	1	1	yes	maximal, characteristic
7	#103×C₅₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₅₉	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	#11745672	C₄	1	4	yes	complemented
13	C₄⋊Dic₅₉	—	2	1	no	—
14	C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
15	Dic₅₉⋊C₄	—	2	1	no	—
16	C₄×Dic₅₉	—	2	1	no	—
17	C₄×Dic₅₉	—	2	1	no	—
18	C₄×Dic₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
20	Q₈×C₅₉	—	2	1	no	—
21	Q₈×C₅₉	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₅₉	—	2	1	no	—
23	C₂×C₄×C₅₉	—	2	1	no	—
24	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
25	C₂×Dic₅₉	—	2	1	no	—
26	C₂×Dic₅₉	—	2	1	no	—
27	C₂×Dic₅₉	D₄	1	1	yes	characteristic
28	C₂×Dic₅₉	D₄	1	1	yes	characteristic
29	Dic₁₁₈	—	2	1	no	—
30	Dic₁₁₈	C₂×C₄	1	2	yes	—
31	C₈×C₅₉	—	2	1	no	—
32	C₅₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₅₉	—	2	2	no	—
35	C₄×C₅₉	—	4	1	no	—
36	C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₅₉	#41	1	1	yes	characteristic
38	Dic₅₉	—	2	2	no	—
39	Dic₅₉	—	2	1	no	—
40	Dic₅₉	—	4	1	no	—
41	Dic₅₉	Q₁₆	1	2	yes	complemented
42	C₂×C₅₉	C₄×D₄	1	1	yes	characteristic
43	C₂×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
44	C₂×C₅₉	#135	1	1	yes	characteristic
45	C₄×Q₁₆	—	59	1	no	maximal, Sylow
46	C₅₉	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₂×Q₁₆	—	59	1	no	—
48	C₄×Q₈	—	59	1	no	—
49	C₄×Q₈	—	59	1	no	—
50	#107	—	59	1	no	—
51	#103	—	59	1	no	—
52	#103	D₅₉	1	1	yes	characteristic
53	C₄×C₈	—	59	1	no	—
54	C₂×Q₈	—	59	1	no	—
55	C₂×Q₈	C₂×D₅₉	1	1	yes	characteristic
56	Q₁₆	—	59	4	no	—
57	C₂×C₈	—	59	1	no	—
58	C₂×C₈	C₂×D₅₉	1	1	yes	characteristic
59	C₄⋊C₄	—	59	1	no	—
60	C₄⋊C₄	—	118	1	no	—
61	C₄⋊C₄	—	118	1	no	—
62	C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
63	C₄²	—	59	1	no	—
64	C₄²	—	118	1	no	—
65	C₄²	—	118	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	59	2	no	—
68	Q₈	—	118	1	no	—
69	Q₈	C₄×D₅₉	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	59	1	no	—
73	C₂×C₄	—	59	1	no	—
74	C₂×C₄	—	118	1	no	—
75	C₂×C₄	—	118	1	no	—
76	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	59	2	no	—
79	C₂²	D₄×D₅₉	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	4	1	no	—
82	C₄	—	59	2	no	—
83	C₄	—	118	2	no	—
84	C₄	—	118	1	no	—
85	C₄	—	236	1	no	—
86	C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
87	C₄	#11745687	1	1	yes	characteristic
88	C₂	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
89	C₂	Q₁₆×D₅₉	1	1	yes	characteristic
90	C₂	#14273748	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅₉
commutator	C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₉
Fitting	#103×C₅₉	C₂
socle, prime radical	C₂²×C₅₉	C₂×D₄
cosocle	C₂×C₄×C₅₉	C₂³
hypercenter	#103	D₅₉
hypocenter	C₅₉	C₄×Q₁₆
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
12. #11745672	C₄	semidirect
41. Dic₅₉	Q₁₆	semidirect
46. C₅₉	C₄×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745672	2
Q₈×Dic₅₉	2
#14273692	2
#14273660	2
#14273652	2
C₈×Dic₅₉	2
#103×C₅₉	2
C₄×Q₁₆	59