Group #13091258 — subgroups

Subgroups — #10624815⋊C₂ #13091258

Order 1458.

170 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 24 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	#10624815	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#4169⋊C₃	—	3	1	no	maximal
3	#4169⋊C₃	—	3	1	no	maximal
4	#4169⋊C₃	—	3	1	no	maximal
5	C₃×#4169	—	3	1	no	maximal
6	(3₋¹⁺²⋊C₉)⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
7	#6891	D₃	1	1	yes	characteristic
8	#6891	D₃	1	1	yes	characteristic
9	#6891	D₃	1	1	yes	characteristic
10	C₃×C₃²⋊C₉	D₃	1	1	yes	characteristic
11	3₋¹⁺²⋊C₉	—	2	1	no	—
12	3₋¹⁺²⋊C₉	—	2	1	no	—
13	3₋¹⁺²⋊C₉	—	2	1	no	—
14	3₋¹⁺²⋊C₉	—	2	1	no	—
15	3₋¹⁺²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
16	C₃²×C₃⋊D₃	—	9	1	no	—
17	C₃⋊AGL(1,ℤ/9)	—	3	1	no	—
18	C₃⋊AGL(1,ℤ/9)	—	3	1	no	—
19	C₃⋊AGL(1,ℤ/9)	—	3	1	no	—
20	C₃×C₃⋊D₉	—	3	1	no	—
21	#4169	—	3	1	no	—
22	#4169	—	3	1	no	—
23	#4169	—	3	1	no	—
24	#4169	—	3	1	no	—
25	#4169	—	3	1	no	—
26	#4169	—	3	1	no	—
27	#4169	—	3	1	no	—
28	#4169	—	3	1	no	—
29	#4169	—	3	1	no	—
30	#4169	—	3	1	no	—
31	#4169	—	3	1	no	—
32	#4169	—	3	1	no	—
33	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
34	C₃×3₋¹⁺²	—	2	1	no	—
35	C₃×3₋¹⁺²	—	3	1	no	—
36	C₃×3₋¹⁺²	—	3	1	no	—
37	C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
38	C₃²×C₉	—	2	1	no	—
39	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
40	C₃²⋊C₉	—	2	1	no	—
41	C₃²⋊C₉	—	2	1	no	—
42	C₃²⋊C₉	—	3	1	no	—
43	C₃²⋊C₉	—	3	1	no	—
44	C₃²⋊C₉	—	3	1	no	—
45	C₃²⋊C₉	—	3	1	no	—
46	C₃²⋊C₉	—	3	1	no	—
47	C₃²⋊C₉	—	3	1	no	—
48	C₃²⋊C₉	—	3	1	no	—
49	C₃²⋊C₉	—	3	1	no	—
50	C₃²⋊C₉	—	3	1	no	—
51	C₃²⋊C₉	—	3	1	no	—
52	C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
53	C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
54	C₃×C₃⋊D₃	—	9	1	no	—
55	C₃×C₃⋊D₃	—	9	1	no	—
56	C₃×C₃⋊D₃	—	9	1	no	—
57	C₃×C₃⋊D₃	—	9	1	no	—
58	C₃²×D₃	—	27	1	no	—
59	C₃²×D₃	—	27	1	no	—
60	C₃²×D₃	—	27	1	no	—
61	C₃²×D₃	—	27	1	no	—
62	C₃⋊D₉	—	3	1	no	—
63	C₃⋊D₉	—	3	1	no	—
64	C₃⋊D₉	—	3	1	no	—
65	C₃⋊D₉	—	3	1	no	—
66	AGL(1,ℤ/9)	—	27	1	no	—
67	AGL(1,ℤ/9)	—	27	1	no	—
68	AGL(1,ℤ/9)	—	27	1	no	—
69	C₃×D₉	—	27	1	no	—
70	C₃³	—	3	1	no	—
71	C₃³	—	6	1	no	—
72	C₃³	—	9	1	no	—
73	C₃³	—	9	1	no	—
74	C₃³	—	9	1	no	—
75	C₃³	#272	1	1	yes	characteristic
76	C₃³	#272	1	1	yes	characteristic
77	C₃³	#272	1	1	yes	characteristic
78	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
79	3₋¹⁺²	—	3	1	no	—
80	3₋¹⁺²	—	6	1	no	—
81	3₋¹⁺²	—	6	2	no	—
82	3₋¹⁺²	—	6	1	no	—
83	3₋¹⁺²	—	9	1	no	—
84	3₋¹⁺²	—	9	1	no	—
85	3₋¹⁺²	—	18	1	no	—
86	3₋¹⁺²	—	18	1	no	—
87	C₃×C₉	—	3	1	no	—
88	C₃×C₉	—	3	1	no	—
89	C₃×C₉	—	3	1	no	—
90	C₃×C₉	—	3	1	no	—
91	C₃×C₉	—	6	1	no	—
92	C₃×C₉	—	6	1	no	—
93	C₃×C₉	—	6	1	no	—
94	C₃×C₉	—	6	1	no	—
95	C₃×C₉	—	9	1	no	—
96	C₃×C₉	—	18	1	no	—
97	C₂×C₃²	—	81	1	no	—
98	C₃⋊D₃	—	9	1	no	—
99	C₃×D₃	—	27	1	no	—
100	C₃×D₃	—	27	1	no	—
101	C₃×D₃	—	27	1	no	—
102	C₃×D₃	—	27	1	no	—
103	C₃×D₃	—	27	1	no	—
104	C₃×D₃	—	27	1	no	—
105	C₃×D₃	—	27	1	no	—
106	C₃×D₃	—	27	1	no	—
107	C₃×D₃	—	27	1	no	—
108	C₃×D₃	—	27	1	no	—
109	C₃×D₃	—	27	1	no	—
110	C₃×D₃	—	27	1	no	—
111	C₃×D₃	—	27	1	no	—
112	C₃×D₃	—	27	1	no	—
113	C₃×D₃	—	27	1	no	—
114	C₃×D₃	—	27	1	no	—
115	D₉	—	27	1	no	—
116	D₉	—	27	1	no	—
117	D₉	—	27	1	no	—
118	D₉	—	27	1	no	—
119	C₃²	—	2	1	no	—
120	C₃²	—	3	1	no	—
121	C₃²	—	3	1	no	—
122	C₃²	—	3	1	no	—
123	C₃²	—	3	1	no	—
124	C₃²	—	3	1	no	—
125	C₃²	—	3	1	no	—
126	C₃²	—	3	1	no	—
127	C₃²	—	3	1	no	—
128	C₃²	—	3	1	no	—
129	C₃²	—	3	1	no	—
130	C₃²	—	3	1	no	—
131	C₃²	—	3	1	no	—
132	C₃²	—	3	1	no	—
133	C₃²	—	3	1	no	—
134	C₃²	—	3	1	no	—
135	C₃²	—	9	1	no	—
136	C₃²	—	18	1	no	—
137	C₃²	—	18	3	no	—
138	C₃²	C₃×#272	1	1	yes	characteristic
139	C₃²	#4207	1	1	yes	characteristic
140	C₉	—	9	1	no	—
141	C₉	—	9	1	no	—
142	C₉	—	9	1	no	—
143	C₉	—	9	1	no	—
144	C₉	—	18	1	no	—
145	C₉	—	18	1	no	—
146	C₉	—	18	1	no	—
147	C₉	—	18	1	no	—
148	C₂×C₃	—	81	1	no	—
149	C₂×C₃	—	81	1	no	—
150	C₂×C₃	—	81	1	no	—
151	C₂×C₃	—	81	1	no	—
152	D₃	—	27	1	no	—
153	D₃	—	27	1	no	—
154	D₃	—	27	1	no	—
155	D₃	—	27	1	no	—
156	C₃	—	3	1	no	—
157	C₃	—	6	1	no	—
158	C₃	—	9	1	no	—
159	C₃	—	9	1	no	—
160	C₃	—	9	1	no	—
161	C₃	#92304	1	1	yes	characteristic
162	C₃	#4183⋊C₃	1	1	yes	characteristic
163	C₃	#4184⋊C₃	1	1	yes	characteristic
164	C₃	#6912⋊C₂	1	1	yes	characteristic
165	C₂	—	81	1	no	Sylow

subgroup

G/H

class size

multiplicity

normal?

properties

#10624815

C₂

yes

maximal, characteristic, complemented, Sylow

—

—

—

—

(3₋¹⁺²⋊C₉)⋊C₂

C₃

yes

maximal, characteristic, complemented

#6891

D₃

yes

characteristic

#6891

D₃

yes

characteristic

#6891

D₃

yes

characteristic

C₃×C₃²⋊C₉

D₃

yes

characteristic

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

C₂×C₃

yes

characteristic, complemented

C₃²×C₃⋊D₃

—

C₃⋊AGL(1,ℤ/9)

—

C₃⋊AGL(1,ℤ/9)

—

C₃⋊AGL(1,ℤ/9)

—

C₃×C₃⋊D₉

—

—

—

—

—

—

—

—

—

—

—

—

—

C₃⁴

C₃⋊D₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃×D₃

yes

characteristic

C₃²×C₉

—

C₃²×C₉

C₃×D₃

yes

characteristic

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃×D₃

yes

characteristic

C₃²⋊C₉

C₃×D₃

yes

characteristic

C₃×C₃⋊D₃

—

C₃×C₃⋊D₃

—

C₃×C₃⋊D₃

—

C₃×C₃⋊D₃

—

C₃²×D₃

—

C₃²×D₃

—

C₃²×D₃

—

C₃²×D₃

—

C₃⋊D₉

—

C₃⋊D₉

—

C₃⋊D₉

—

C₃⋊D₉

—

AGL(1,ℤ/9)

—

AGL(1,ℤ/9)

—

AGL(1,ℤ/9)

—

C₃×D₉

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

yes

C₃³

yes

C₃³

yes

C₃³

C₃×C₃⋊D₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₂×C₃²

—

C₃⋊D₃

—

C₃×D₃

—

100

C₃×D₃

—

101

C₃×D₃

—

102

C₃×D₃

—

103

C₃×D₃

—

104

C₃×D₃

—

105

C₃×D₃

—

106

C₃×D₃

—

107

C₃×D₃

—

108

C₃×D₃

—

109

C₃×D₃

—

110

C₃×D₃

—

111

C₃×D₃

—

112

C₃×D₃

—

113

C₃×D₃

—

114

C₃×D₃

—

115

D₉

—

116

D₉

—

117

D₉

—

118

D₉

—

119

C₃²

—

120

C₃²

—

121

C₃²

—

122

C₃²

—

123

C₃²

—

124

C₃²

—

125

C₃²

—

126

C₃²

—

127

C₃²

—

128

C₃²

—

129

C₃²

—

130

C₃²

—

131

C₃²

—

132

C₃²

—

133

C₃²

—

134

C₃²

—

135

C₃²

—

136

C₃²

—

137

C₃²

—

138

C₃²

C₃×#272

yes

characteristic

139

C₃²

#4207

yes

characteristic

140

C₉

—

141

C₉

—

142

C₉

—

143

C₉

—

144

C₉

—

145

C₉

—

146

C₉

—

147

C₉

—

148

C₂×C₃

—

149

C₂×C₃

—

150

C₂×C₃

—

151

C₂×C₃

—

152

D₃

—

153

D₃

—

154

D₃

—

155

D₃

—

156

C₃

—

157

C₃

—

158

C₃

—

159

C₃

—

160

C₃

—

161

C₃

#92304

yes

characteristic

162

C₃

#4183⋊C₃

yes

characteristic

163

C₃

#4184⋊C₃

yes

characteristic

164

C₃

#6912⋊C₂

yes

characteristic

165

C₂

—

Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	3₋¹⁺²⋊C₉	C₂×C₃
Frattini	C₃³	C₃×C₃⋊D₃
Fitting	#10624815	C₂
socle	C₃²	C₃×#272
LCS	G ▷ 3₋¹⁺²⋊C₉
UCS	C₁

subgroup

G/H

center, hypercenter

C₁

commutator, cosocle, hypocenter

3₋¹⁺²⋊C₉

C₂×C₃

Frattini

C₃³

C₃×C₃⋊D₃

C₂

C₃²

G ▷ 3₋¹⁺²⋊C₉

C₁

N	H ≅ G/N	type
1. #10624815	C₂	semidirect
6. (3₋¹⁺²⋊C₉)⋊C₂	C₃	semidirect
15. 3₋¹⁺²⋊C₉	C₂×C₃	semidirect

H ≅ G/N

type

1. #10624815

C₂

semidirect

6. (3₋¹⁺²⋊C₉)⋊C₂

C₃

semidirect

15. 3₋¹⁺²⋊C₉

C₂×C₃

semidirect

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

subgroup	index
#10624815	2
#4169⋊C₃	3
C₃×#4169	3
(3₋¹⁺²⋊C₉)⋊C₂	3

subgroup

index

#10624815

#4169⋊C₃

C₃×#4169

(3₋¹⁺²⋊C₉)⋊C₂

Subgroups — #10624815⋊C₂ #13091258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624815⋊C2 #13091258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624815⋊C₂ #13091258