Group #21423944 — subgroups

Subgroups — #21423944

Order 7552.

316 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₉⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₅₉	C₂	1	2	yes	maximal
3	C₄²×Dic₅₉	C₂	1	1	yes	maximal, characteristic
4	#16837157	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₅₉	C₄	1	2	yes	—
8	C₂×C₄×Dic₅₉	C₄	1	2	yes	—
9	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
11	Dic₅₉⋊C₈	C₄	1	8	yes	complemented
12	C₈×Dic₅₉	—	2	4	no	—
13	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₅₉	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₅₉	—	2	2	no	—
21	C₂×C₈×C₅₉	—	2	2	no	—
22	C₂×C₈×C₅₉	C₂×C₄	1	4	yes	—
23	C₄²×C₅₉	—	2	2	no	—
24	C₄×Dic₅₉	—	2	4	no	—
25	C₄×Dic₅₉	C₈	1	8	yes	complemented
26	C₄×Dic₅₉	C₂×C₄	1	4	yes	—
27	C₄×Dic₅₉	D₄	1	2	yes	—
28	C₄×Dic₅₉	Q₈	1	2	yes	—
29	C₂×C₅₉⋊C₈	—	2	2	no	—
30	C₂×C₅₉⋊C₈	—	2	2	no	—
31	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
32	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₅₉	—	2	2	no	—
34	C₂×C₄×C₅₉	—	2	2	no	—
35	C₂×C₄×C₅₉	C₂×C₈	1	4	yes	—
36	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₅₉	#41	1	2	yes	—
40	C₂×Dic₅₉	—	2	2	no	—
41	C₂×Dic₅₉	C₄²	1	2	yes	—
42	C₂×Dic₅₉	C₄²	1	2	yes	—
43	C₂×Dic₅₉	C₄⋊C₄	1	4	yes	—
44	C₂×Dic₅₉	C₂×C₈	1	4	yes	—
45	C₂×Dic₅₉	C₂×C₈	1	4	yes	—
46	C₂×Dic₅₉	M₁₆	1	4	yes	—
47	C₈×C₅₉	—	2	4	no	—
48	C₅₉⋊C₈	—	2	4	no	—
49	C₂²×C₅₉	C₂×C₄²	1	1	yes	characteristic
50	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₅₉	#117	1	1	yes	characteristic
52	C₂²×C₅₉	C₂²×C₈	1	2	yes	—
53	C₂²×C₅₉	C₂×M₁₆	1	2	yes	—
54	C₄×C₅₉	—	2	4	no	—
55	C₄×C₅₉	C₄×D₄	1	2	yes	—
56	C₄×C₅₉	C₄×Q₈	1	2	yes	—
57	Dic₅₉	—	2	2	no	—
58	Dic₅₉	C₄×C₈	1	4	yes	complemented
59	Dic₅₉	C₄⋊C₈	1	8	yes	complemented
60	C₄×C₄⋊C₈	—	59	1	no	maximal, Sylow
61	C₂×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₅₉	C₂×C₄×C₈	1	1	yes	characteristic
63	C₂×C₅₉	C₄×M₁₆	1	1	yes	characteristic
64	C₂×C₅₉	C₂×C₄⋊C₈	1	2	yes	—
65	C₂×C₅₉	#431	1	2	yes	—
66	C₂×C₄⋊C₈	—	59	2	no	—
67	C₂×C₄×C₈	—	59	2	no	—
68	C₄³	—	59	1	no	—
69	#336	—	59	1	no	—
70	#336	D₅₉	1	1	yes	characteristic
71	C₅₉	C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₈	—	59	2	no	—
73	C₂²×C₈	C₂×D₅₉	1	2	yes	—
74	C₂×C₄²	—	59	2	no	—
75	C₂×C₄²	—	59	1	no	—
76	C₂×C₄²	—	59	1	no	—
77	C₂×C₄²	—	59	2	no	—
78	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
79	C₄⋊C₈	—	59	8	no	—
80	C₄×C₈	—	118	4	no	—
81	C₂²×C₄	—	59	1	no	—
82	C₂²×C₄	—	59	2	no	—
83	C₂²×C₄	—	59	1	no	—
84	C₂²×C₄	C₄×D₅₉	1	2	yes	—
85	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	59	4	no	—
89	C₂×C₈	—	118	2	no	—
90	C₂×C₈	—	118	2	no	—
91	C₂×C₈	C₄×D₅₉	1	4	yes	—
92	C₄²	—	2	2	no	—
93	C₄²	—	59	8	no	—
94	C₄²	—	59	4	no	—
95	C₄²	—	59	2	no	—
96	C₄²	—	59	2	no	—
97	C₄²	—	118	4	no	—
98	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	59	2	no	—
102	C₂×C₄	—	59	4	no	—
103	C₂×C₄	—	59	4	no	—
104	C₂×C₄	—	59	4	no	—
105	C₂×C₄	—	59	4	no	—
106	C₂×C₄	—	59	2	no	—
107	C₂×C₄	—	118	2	no	—
108	C₂×C₄	C₈×D₅₉	1	4	yes	—
109	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
110	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
111	C₂×C₄	#11745687	1	2	yes	—
112	C₂×C₄	Q₈×D₅₉	1	1	yes	characteristic
113	C₈	—	2	4	no	—
114	C₈	—	118	4	no	—
115	C₂²	C₄²×D₅₉	1	1	yes	characteristic
116	C₂²	C₄⋊C₄×D₅₉	1	1	yes	characteristic
117	C₂²	#14273683	1	1	yes	characteristic
118	C₂²	C₂×C₈×D₅₉	1	2	yes	—
119	C₂²	M₁₆×D₅₉	1	2	yes	—
120	C₄	—	2	4	no	—
121	C₄	—	59	8	no	—
122	C₄	—	59	4	no	—
123	C₄	—	118	2	no	—
124	C₄	(C₂²⋊D₅₉)⋊C₄	1	2	yes	—
125	C₄	#14273692	1	2	yes	—
126	C₂	#16837253	1	1	yes	characteristic
127	C₂	C₄×C₈×D₅₉	1	1	yes	characteristic
128	C₂	#16837354	1	1	yes	characteristic
129	C₂	C₄⋊C₈×D₅₉	1	2	yes	—
130	C₂	#16837452	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₉⋊C₈

C₂

yes

maximal

C₂×C₈×Dic₅₉

C₂

yes

maximal

C₄²×Dic₅₉

C₂

yes

maximal, characteristic

#16837157

C₂

yes

maximal, characteristic

C₅₉×#336

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₅₉

C₄

yes

—

C₂×C₄×Dic₅₉

C₄

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

Dic₅₉⋊C₈

C₄

yes

complemented

C₈×Dic₅₉

—

C₂²×C₈×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₄²×C₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

C₈

yes

complemented

C₄×Dic₅₉

C₂×C₄

yes

—

C₄×Dic₅₉

D₄

yes

—

C₄×Dic₅₉

Q₈

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂³×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₈

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

C₄²

yes

—

C₂×Dic₅₉

C₄²

yes

—

C₂×Dic₅₉

C₄⋊C₄

yes

—

C₂×Dic₅₉

C₂×C₈

yes

—

C₂×Dic₅₉

C₂×C₈

yes

—

C₂×Dic₅₉

M₁₆

yes

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

C₂×C₄²

yes

characteristic

C₂²×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₅₉

#117

yes

characteristic

C₂²×C₅₉

C₂²×C₈

yes

—

C₂²×C₅₉

C₂×M₁₆

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₄×D₄

yes

—

C₄×C₅₉

C₄×Q₈

yes

—

Dic₅₉

—

Dic₅₉

C₄×C₈

yes

complemented

Dic₅₉

C₄⋊C₈

yes

complemented

C₄×C₄⋊C₈

—

maximal, Sylow

C₂×C₅₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₅₉

C₂×C₄×C₈

yes

characteristic

C₂×C₅₉

C₄×M₁₆

yes

characteristic

C₂×C₅₉

C₂×C₄⋊C₈

yes

—

C₂×C₅₉

#431

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

—

C₄³

—

#336

—

#336

D₅₉

yes

characteristic

C₅₉

C₄×C₄⋊C₈

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₄⋊C₈

—

C₄×C₈

—

118

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

C₄×D₅₉

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

118

—

C₂³

C₂×C₄×D₅₉

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

118

—

108

C₂×C₄

C₈×D₅₉

yes

—

109

C₂×C₄

C₂×C₄×D₅₉

yes

—

110

C₂×C₄

D₄×D₅₉

yes

characteristic

111

C₂×C₄

#11745687

yes

—

112

C₂×C₄

Q₈×D₅₉

yes

characteristic

113

C₈

—

114

C₈

—

118

—

115

C₂²

C₄²×D₅₉

yes

characteristic

116

C₂²

C₄⋊C₄×D₅₉

yes

characteristic

117

C₂²

#14273683

yes

characteristic

118

C₂²

C₂×C₈×D₅₉

yes

—

119

C₂²

M₁₆×D₅₉

yes

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

118

—

124

C₄

(C₂²⋊D₅₉)⋊C₄

yes

—

125

C₄

#14273692

yes

—

126

C₂

#16837253

yes

characteristic

127

C₂

C₄×C₈×D₅₉

yes

characteristic

128

C₂

#16837354

yes

characteristic

129

C₂

C₄⋊C₈×D₅₉

yes

—

130

C₂

#16837452

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₉
commutator	C₂×C₅₉	C₂×C₄×C₈
Fitting	C₅₉×#336	C₂
socle	C₂³×C₅₉	C₂²×C₄
hypercenter	#336	D₅₉
hypocenter	C₅₉	C₄×C₄⋊C₈
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₅₉

commutator

C₂×C₅₉

C₂×C₄×C₈

Fitting

C₅₉×#336

C₂

socle

C₂³×C₅₉

C₂²×C₄

hypercenter

#336

D₅₉

hypocenter

C₅₉

C₄×C₄⋊C₈

LCS

G ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
11. Dic₅₉⋊C₈	C₄	semidirect
25. C₄×Dic₅₉	C₈	semidirect
58. Dic₅₉	C₄×C₈	semidirect
59. Dic₅₉	C₄⋊C₈	semidirect
71. C₅₉	C₄×C₄⋊C₈	semidirect

H ≅ G/N

type

11. Dic₅₉⋊C₈

C₄

semidirect

25. C₄×Dic₅₉

C₈

semidirect

58. Dic₅₉

C₄×C₈

semidirect

59. Dic₅₉

C₄⋊C₈

semidirect

71. C₅₉

C₄×C₄⋊C₈

semidirect

Subgroups — #21423944

Conjugacy classes of subgroups

Complements