Group #13091266 — subgroups

Subgroups — #10624824⋊C₂ #13091266

Order 1458.

221 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 221 conjugacy classes of subgroups — too many to draw. Only its 25 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	#10624824	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊AGL(1,ℤ/9)	—	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	C₃²×3₋¹⁺²	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⋊AGL(1,ℤ/9)	—	3	1	no	—
21	C₃⋊AGL(1,ℤ/9)	—	3	1	no	—
22	C₃×C₃⋊D₉	—	3	1	no	—
23	C₃×C₃⋊D₉	—	3	1	no	—
24	C₃×AGL(1,ℤ/9)	—	9	3	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	#4169	—	3	1	no	—
34	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
35	C₃×3₋¹⁺²	—	2	1	no	—
36	C₃×3₋¹⁺²	—	3	3	no	—
37	C₃×3₋¹⁺²	—	3	1	no	—
38	C₃×3₋¹⁺²	—	3	1	no	—
39	C₃×3₋¹⁺²	—	3	1	no	—
40	C₃×3₋¹⁺²	—	3	1	no	—
41	C₃×3₋¹⁺²	—	6	3	no	—
42	C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
43	C₃²×C₉	—	2	1	no	—
44	C₃²×C₉	—	3	1	no	—
45	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
46	C₃²⋊C₉	—	2	1	no	—
47	C₃²⋊C₉	—	2	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	—	3	1	no	—
53	C₃²⋊C₉	—	3	1	no	—
54	C₃²⋊C₉	—	3	1	no	—
55	C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
56	C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
57	C₃×C₃⋊D₃	—	9	1	no	—
58	C₃×C₃⋊D₃	—	9	1	no	—
59	C₃×C₃⋊D₃	—	9	1	no	—
60	C₃×C₃⋊D₃	—	9	1	no	—
61	C₃²×D₃	—	27	1	no	—
62	C₃²×D₃	—	27	1	no	—
63	C₃²×D₃	—	27	1	no	—
64	C₃²×D₃	—	27	1	no	—
65	C₃⋊D₉	—	3	1	no	—
66	C₃⋊D₉	—	3	1	no	—
67	C₃⋊D₉	—	3	1	no	—
68	C₃⋊D₉	—	3	1	no	—
69	AGL(1,ℤ/9)	—	9	3	no	—
70	AGL(1,ℤ/9)	—	9	3	no	—
71	AGL(1,ℤ/9)	—	9	3	no	—
72	AGL(1,ℤ/9)	—	27	1	no	—
73	AGL(1,ℤ/9)	—	27	1	no	—
74	C₃×D₉	—	9	3	no	—
75	C₃×D₉	—	27	1	no	—
76	C₃³	—	3	1	no	—
77	C₃³	—	3	1	no	—
78	C₃³	—	6	1	no	—
79	C₃³	—	6	1	no	—
80	C₃³	—	9	1	no	—
81	C₃³	—	9	1	no	—
82	C₃³	#272	1	1	yes	characteristic
83	C₃³	#272	1	1	yes	characteristic
84	C₃³	#272	1	1	yes	characteristic
85	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
86	3₋¹⁺²	—	3	3	no	—
87	3₋¹⁺²	—	3	3	no	—
88	3₋¹⁺²	—	3	3	no	—
89	3₋¹⁺²	—	3	1	no	—
90	3₋¹⁺²	—	6	3	no	—
91	3₋¹⁺²	—	6	3	no	—
92	3₋¹⁺²	—	6	3	no	—
93	3₋¹⁺²	—	6	1	no	—
94	3₋¹⁺²	—	6	2	no	—
95	3₋¹⁺²	—	6	1	no	—
96	3₋¹⁺²	—	9	1	no	—
97	3₋¹⁺²	—	18	1	no	—
98	C₃×C₉	—	3	1	no	—
99	C₃×C₉	—	3	3	no	—
100	C₃×C₉	—	3	1	no	—
101	C₃×C₉	—	3	1	no	—
102	C₃×C₉	—	3	1	no	—
103	C₃×C₉	—	6	1	no	—
104	C₃×C₉	—	6	3	no	—
105	C₃×C₉	—	6	1	no	—
106	C₃×C₉	—	6	1	no	—
107	C₃×C₉	—	6	1	no	—
108	C₃×C₉	—	9	1	no	—
109	C₃×C₉	—	18	1	no	—
110	C₂×C₃²	—	81	1	no	—
111	C₃⋊D₃	—	9	1	no	—
112	C₃×D₃	—	27	1	no	—
113	C₃×D₃	—	27	1	no	—
114	C₃×D₃	—	27	1	no	—
115	C₃×D₃	—	27	1	no	—
116	C₃×D₃	—	27	1	no	—
117	C₃×D₃	—	27	1	no	—
118	C₃×D₃	—	27	1	no	—
119	C₃×D₃	—	27	1	no	—
120	C₃×D₃	—	27	1	no	—
121	C₃×D₃	—	27	1	no	—
122	C₃×D₃	—	27	1	no	—
123	C₃×D₃	—	27	1	no	—
124	C₃×D₃	—	27	1	no	—
125	C₃×D₃	—	27	1	no	—
126	C₃×D₃	—	27	1	no	—
127	C₃×D₃	—	27	1	no	—
128	D₉	—	9	3	no	—
129	D₉	—	27	1	no	—
130	D₉	—	27	1	no	—
131	D₉	—	27	1	no	—
132	C₃²	—	2	1	no	—
133	C₃²	—	2	1	no	—
134	C₃²	—	3	1	no	—
135	C₃²	—	3	1	no	—
136	C₃²	—	3	1	no	—
137	C₃²	—	3	1	no	—
138	C₃²	—	3	1	no	—
139	C₃²	—	3	1	no	—
140	C₃²	—	3	1	no	—
141	C₃²	—	3	1	no	—
142	C₃²	—	3	1	no	—
143	C₃²	—	3	1	no	—
144	C₃²	—	3	1	no	—
145	C₃²	—	3	1	no	—
146	C₃²	—	3	1	no	—
147	C₃²	—	3	1	no	—
148	C₃²	—	9	1	no	—
149	C₃²	—	18	1	no	—
150	C₃²	—	18	1	no	—
151	C₃²	—	18	2	no	—
152	C₃²	#4183	1	1	yes	characteristic
153	C₃²	C₃×#272	1	1	yes	characteristic
154	C₃²	#4207	1	1	yes	characteristic
155	C₉	—	3	3	no	—
156	C₉	—	6	3	no	—
157	C₉	—	9	1	no	—
158	C₉	—	9	1	no	—
159	C₉	—	9	1	no	—
160	C₉	—	18	1	no	—
161	C₉	—	18	1	no	—
162	C₉	—	18	1	no	—
163	C₂×C₃	—	81	1	no	—
164	C₂×C₃	—	81	1	no	—
165	C₂×C₃	—	81	1	no	—
166	C₂×C₃	—	81	1	no	—
167	D₃	—	27	1	no	—
168	D₃	—	27	1	no	—
169	D₃	—	27	1	no	—
170	D₃	—	27	1	no	—
171	C₃	—	3	1	no	—
172	C₃	—	3	1	no	—
173	C₃	—	6	1	no	—
174	C₃	—	6	1	no	—
175	C₃	—	9	1	no	—
176	C₃	—	9	1	no	—
177	C₃	#92304	1	1	yes	characteristic
178	C₃	C₃×#4183	1	1	yes	characteristic
179	C₃	#4184⋊C₃	1	1	yes	characteristic
180	C₃	#6912⋊C₂	1	1	yes	characteristic
181	C₂	—	81	1	no	Sylow

subgroup

G/H

class size

multiplicity

normal?

properties

#10624824

C₂

yes

maximal, characteristic, complemented, Sylow

—

—

—

—

(3₋¹⁺²⋊C₉)⋊C₂

C₃

yes

maximal, characteristic, complemented

C₃²×3₋¹⁺²

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×C₃⋊D₉

—

C₃×C₃⋊D₉

—

—

—

—

—

—

—

—

—

—

—

C₃⁴

C₃⋊D₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃×D₃

yes

characteristic

C₃²×C₉

—

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

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

—

—

—

—

—

—

C₃×D₉

—

C₃×D₉

—

C₃³

—

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

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

100

C₃×C₉

—

101

C₃×C₉

—

102

C₃×C₉

—

103

C₃×C₉

—

104

C₃×C₉

—

105

C₃×C₉

—

106

C₃×C₉

—

107

C₃×C₉

—

108

C₃×C₉

—

109

C₃×C₉

—

110

C₂×C₃²

—

111

C₃⋊D₃

—

112

C₃×D₃

—

113

C₃×D₃

—

114

C₃×D₃

—

115

C₃×D₃

—

116

C₃×D₃

—

117

C₃×D₃

—

118

C₃×D₃

—

119

C₃×D₃

—

120

C₃×D₃

—

121

C₃×D₃

—

122

C₃×D₃

—

123

C₃×D₃

—

124

C₃×D₃

—

125

C₃×D₃

—

126

C₃×D₃

—

127

C₃×D₃

—

128

D₉

—

129

D₉

—

130

D₉

—

131

D₉

—

132

C₃²

—

133

C₃²

—

134

C₃²

—

135

C₃²

—

136

C₃²

—

137

C₃²

—

138

C₃²

—

139

C₃²

—

140

C₃²

—

141

C₃²

—

142

C₃²

—

143

C₃²

—

144

C₃²

—

145

C₃²

—

146

C₃²

—

147

C₃²

—

148

C₃²

—

149

C₃²

—

150

C₃²

—

151

C₃²

—

152

C₃²

#4183

yes

characteristic

153

C₃²

C₃×#272

yes

characteristic

154

C₃²

#4207

yes

characteristic

155

C₉

—

156

C₉

—

157

C₉

—

158

C₉

—

159

C₉

—

160

C₉

—

161

C₉

—

162

C₉

—

163

C₂×C₃

—

164

C₂×C₃

—

165

C₂×C₃

—

166

C₂×C₃

—

167

D₃

—

168

D₃

—

169

D₃

—

170

D₃

—

171

C₃

—

172

C₃

—

173

C₃

—

174

C₃

—

175

C₃

—

176

C₃

—

177

C₃

#92304

yes

characteristic

178

C₃

C₃×#4183

yes

characteristic

179

C₃

#4184⋊C₃

yes

characteristic

180

C₃

#6912⋊C₂

yes

characteristic

181

C₂

—

Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	3₋¹⁺²⋊C₉	C₂×C₃
Frattini	C₃³	C₃×C₃⋊D₃
Fitting	#10624824	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. #10624824	C₂	semidirect
6. (3₋¹⁺²⋊C₉)⋊C₂	C₃	semidirect
15. 3₋¹⁺²⋊C₉	C₂×C₃	semidirect

H ≅ G/N

type

1. #10624824

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
#10624824	2
C₃×C₃⋊AGL(1,ℤ/9)	3
#4169⋊C₃	3
C₃×#4169	3
(3₋¹⁺²⋊C₉)⋊C₂	3

subgroup

index

(3₋¹⁺²⋊C₉)⋊C₂

Subgroups — #10624824⋊C₂ #13091266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624824⋊C2 #13091266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624824⋊C₂ #13091266