Group #14518175 — subgroups

Subgroups — D₃×(C₂²⋊C₉)⋊C₉ #14518175

Order 1944.

287 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 287 conjugacy classes of subgroups — too many to draw. Only its 63 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	C₃×(C₂²⋊C₉)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×D₃×C₂²⋊C₉	C₃	1	2	yes	maximal
4	C₃×D₃×C₂²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₂×(C₂²⋊C₉)⋊C₉	—	3	1	no	maximal
6	D₃×C₉⋊C₉	—	4	1	no	maximal
7	C₂²×C₃²×C₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃×D₃×C₉	—	3	1	no	—
9	C₂×C₃×D₃×C₉	—	3	1	no	—
10	C₃²×C₂²⋊C₉	C₂×C₃	1	1	yes	characteristic
11	C₃²×C₂²⋊C₉	C₂×C₃	1	2	yes	—
12	(C₂²⋊C₉)⋊C₉	—	2	1	no	—
13	(C₂²⋊C₉)⋊C₉	—	2	2	no	—
14	(C₂²⋊C₉)⋊C₉	—	2	1	no	—
15	(C₂²⋊C₉)⋊C₉	D₃	1	1	yes	characteristic, direct product factor
16	C₃×C₉⋊C₉	—	4	1	no	Sylow
17	C₂²×C₃²×D₃	C₃²	1	1	yes	characteristic
18	C₂³×C₃×C₉	—	3	1	no	—
19	C₂²×D₃×C₉	—	3	1	no	—
20	C₂×C₃×C₂²⋊C₉	—	3	1	no	—
21	C₂×C₃×C₂²⋊C₉	—	3	2	no	—
22	D₃×C₂²⋊C₉	—	3	2	no	—
23	D₃×C₂²⋊C₉	C₉	1	3	yes	complemented
24	C₂×C₃²×C₉	—	3	1	no	—
25	C₃×D₃×C₉	—	3	1	no	—
26	C₃×D₃×C₉	—	4	1	no	—
27	C₃×D₃×C₉	—	4	2	no	—
28	C₃×D₃×C₉	A₄	1	1	yes	characteristic
29	C₂×C₉⋊C₉	—	12	1	no	—
30	C₂²×C₃³	C₂×C₃²	1	1	yes	characteristic
31	C₂×C₃²×D₃	—	3	1	no	—
32	C₂×C₃²×D₃	—	3	1	no	—
33	C₂²×C₃×C₉	—	2	1	no	—
34	C₂²×C₃×C₉	—	3	1	no	—
35	C₂²×C₃×C₉	—	6	1	no	—
36	C₂²×C₃×C₉	—	9	1	no	—
37	C₂²×C₃×C₉	—	9	1	no	—
38	C₂²×C₃×C₉	C₃×D₃	1	1	yes	characteristic
39	C₂×D₃×C₉	—	3	3	no	—
40	C₂×D₃×C₉	—	3	3	no	—
41	C₃×C₂²⋊C₉	—	2	1	no	—
42	C₃×C₂²⋊C₉	—	2	3	no	—
43	C₃×C₂²⋊C₉	—	2	2	no	—
44	C₃×C₂²⋊C₉	—	3	2	no	—
45	C₃×C₂²⋊C₉	—	6	2	no	—
46	C₃×C₂²⋊C₉	C₂×C₉	1	3	yes	complemented
47	C₃×C₂²⋊C₉	C₃×D₃	1	2	yes	—
48	C₃×C₂²⋊C₉	C₃×D₃	1	1	yes	characteristic
49	C₃²×C₉	—	4	1	no	—
50	C₃²×C₉	—	4	2	no	—
51	C₃²×C₉	C₂×A₄	1	1	yes	characteristic
52	C₉⋊C₉	—	4	1	no	—
53	C₉⋊C₉	—	8	1	no	—
54	C₉⋊C₉	—	8	2	no	—
55	C₉⋊C₉	—	8	1	no	—
56	C₂³×C₃²	—	3	1	no	—
57	C₂²×C₃×D₃	C₃×C₉	1	1	yes	characteristic
58	C₂²×C₃×D₃	3₋¹⁺²	1	2	yes	—
59	C₂²×C₃×D₃	3₋¹⁺²	1	1	yes	characteristic
60	C₂³×C₉	—	9	1	no	—
61	C₂×C₂²⋊C₉	—	3	3	no	—
62	C₂×C₂²⋊C₉	—	9	2	no	—
63	C₂×C₃³	—	3	1	no	—
64	C₃²×D₃	—	3	1	no	—
65	C₃²×D₃	C₃×A₄	1	1	yes	characteristic
66	C₂×C₃×C₉	—	3	1	no	—
67	C₂×C₃×C₉	—	3	3	no	—
68	C₂×C₃×C₉	—	3	1	no	—
69	C₂×C₃×C₉	—	6	3	no	—
70	C₂×C₃×C₉	—	6	1	no	—
71	C₂×C₃×C₉	—	9	1	no	—
72	C₂×C₃×C₉	—	12	1	no	—
73	C₂×C₃×C₉	—	12	2	no	—
74	D₃×C₉	—	3	3	no	—
75	D₃×C₉	—	3	1	no	—
76	D₃×C₉	—	4	3	no	—
77	D₃×C₉	—	12	2	no	—
78	C₂²×C₃²	—	2	1	no	—
79	C₂²×C₃²	—	2	2	no	—
80	C₂²×C₃²	—	2	1	no	—
81	C₂²×C₃²	—	9	1	no	—
82	C₂²×C₃²	—	9	1	no	—
83	C₂²×C₃²	C₂×C₃×C₉	1	1	yes	characteristic
84	C₂²×C₃²	C₂×3₋¹⁺²	1	2	yes	—
85	C₂²×C₃²	C₂×3₋¹⁺²	1	1	yes	characteristic
86	C₂²×C₃²	C₃²×D₃	1	1	yes	characteristic
87	C₂×C₃×D₃	—	3	1	no	—
88	C₂×C₃×D₃	—	3	2	no	—
89	C₂×C₃×D₃	—	3	1	no	—
90	C₂×C₃×D₃	—	3	1	no	—
91	C₂×C₃×D₃	—	3	1	no	—
92	C₂×C₃×D₃	—	3	2	no	—
93	C₂²×C₉	—	3	1	no	—
94	C₂²×C₉	—	6	1	no	—
95	C₂²×C₉	—	9	3	no	—
96	C₂²×C₉	—	9	3	no	—
97	C₂²⋊C₉	—	2	3	no	—
98	C₂²⋊C₉	—	3	2	no	—
99	C₂²⋊C₉	—	6	2	no	—
100	C₂²⋊C₉	D₃×C₉	1	3	yes	complemented
101	C₃³	C₂×C₃×A₄	1	1	yes	characteristic
102	C₃×C₉	—	2	1	no	—
103	C₃×C₉	—	3	1	no	—
104	C₃×C₉	—	4	1	no	—
105	C₃×C₉	—	4	3	no	—
106	C₃×C₉	—	4	2	no	—
107	C₃×C₉	—	6	1	no	—
108	C₃×C₉	—	8	3	no	—
109	C₃×C₉	—	8	1	no	—
110	C₃×C₉	—	8	2	no	—
111	C₃×C₉	—	12	2	no	—
112	C₃×C₉	—	24	2	no	—
113	C₃×C₉	D₃×A₄	1	1	yes	characteristic
114	C₂³×C₃	—	3	1	no	—
115	C₂³×C₃	—	3	2	no	—
116	C₂³×C₃	—	3	1	no	—
117	C₂²×D₃	C₉⋊C₉	1	1	yes	characteristic, complemented
118	C₂×C₃²	—	3	1	no	—
119	C₂×C₃²	—	3	1	no	—
120	C₂×C₃²	—	3	1	no	—
121	C₂×C₃²	—	3	2	no	—
122	C₂×C₃²	—	3	1	no	—
123	C₂×C₃²	—	6	1	no	—
124	C₂×C₃²	—	6	1	no	—
125	C₂×C₃²	—	6	2	no	—
126	C₂×C₃²	—	9	1	no	—
127	C₃×D₃	—	3	1	no	—
128	C₃×D₃	—	3	2	no	—
129	C₃×D₃	—	3	1	no	—
130	C₃×D₃	C₉×A₄	1	1	yes	characteristic
131	C₃×D₃	C₉⋊A₄	1	2	yes	—
132	C₃×D₃	#1094	1	1	yes	characteristic
133	C₂×C₉	—	3	3	no	—
134	C₂×C₉	—	6	3	no	—
135	C₂×C₉	—	9	1	no	—
136	C₂×C₉	—	9	3	no	—
137	C₂×C₉	—	12	3	no	—
138	C₂×C₉	—	36	2	no	—
139	C₂²×C₃	—	2	1	no	—
140	C₂²×C₃	—	2	1	no	—
141	C₂²×C₃	—	2	2	no	—
142	C₂²×C₃	—	9	1	no	—
143	C₂²×C₃	—	9	1	no	—
144	C₂²×C₃	—	9	2	no	—
145	C₂²×C₃	—	9	1	no	—
146	C₂²×C₃	—	9	1	no	—
147	C₂²×C₃	—	9	2	no	—
148	C₂²×C₃	C₂×C₉⋊C₉	1	1	yes	characteristic, complemented
149	C₂²×C₃	C₃×D₃×C₉	1	1	yes	characteristic
150	C₂²×C₃	D₃×3₋¹⁺²	1	2	yes	—
151	C₂²×C₃	D₃×3₋¹⁺²	1	1	yes	characteristic
152	C₂×D₃	—	3	1	no	—
153	C₂×D₃	—	3	1	no	—
154	C₃²	—	2	1	no	—
155	C₃²	—	2	2	no	—
156	C₃²	—	2	1	no	—
157	C₃²	C₂×C₉×A₄	1	1	yes	characteristic
158	C₃²	C₂×C₉⋊A₄	1	2	yes	—
159	C₃²	C₂×#1094	1	1	yes	characteristic
160	C₃²	C₃×D₃×A₄	1	1	yes	characteristic
161	C₉	—	3	1	no	—
162	C₉	—	4	3	no	—
163	C₉	—	6	1	no	—
164	C₉	—	8	3	no	—
165	C₉	—	12	2	no	—
166	C₉	—	24	2	no	—
167	C₂³	—	3	1	no	Sylow
168	C₂×C₃	—	3	1	no	—
169	C₂×C₃	—	3	1	no	—
170	C₂×C₃	—	3	1	no	—
171	C₂×C₃	—	3	2	no	—
172	C₂×C₃	—	3	2	no	—
173	C₂×C₃	—	3	1	no	—
174	C₂×C₃	—	3	1	no	—
175	C₂×C₃	—	6	1	no	—
176	C₂×C₃	—	6	2	no	—
177	C₂×C₃	—	6	1	no	—
178	C₂×C₃	—	9	1	no	—
179	C₂×C₃	—	9	2	no	—
180	C₂×C₃	—	9	1	no	—
181	D₃	—	3	1	no	—
182	D₃	(C₂²⋊C₉)⋊C₉	1	1	yes	characteristic, direct product factor
183	C₂²	—	9	1	no	—
184	C₂²	—	9	1	no	—
185	C₂²	D₃×C₉⋊C₉	1	1	yes	characteristic, complemented
186	C₃	—	2	1	no	—
187	C₃	—	2	2	no	—
188	C₃	—	2	1	no	—
189	C₃	C₂×(C₂²⋊C₉)⋊C₉	1	1	yes	characteristic, complemented
190	C₃	D₃×C₉×A₄	1	1	yes	characteristic
191	C₃	D₃×C₉⋊A₄	1	2	yes	—
192	C₃	D₃×#1094	1	1	yes	characteristic
193	C₂	—	3	1	no	—
194	C₂	—	3	1	no	—
195	C₂	—	9	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×(C₂²⋊C₉)⋊C₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₃×D₃×C₉

C₃

yes

maximal, characteristic

C₃×D₃×C₂²⋊C₉

C₃

yes

maximal

C₃×D₃×C₂²⋊C₉

C₃

yes

maximal, characteristic

C₂×(C₂²⋊C₉)⋊C₉

—

maximal

D₃×C₉⋊C₉

—

maximal

C₂²×C₃²×C₉

C₂×C₃

yes

characteristic

C₂×C₃×D₃×C₉

—

C₂×C₃×D₃×C₉

—

C₃²×C₂²⋊C₉

C₂×C₃

yes

characteristic

C₃²×C₂²⋊C₉

C₂×C₃

yes

—

(C₂²⋊C₉)⋊C₉

—

(C₂²⋊C₉)⋊C₉

—

(C₂²⋊C₉)⋊C₉

—

(C₂²⋊C₉)⋊C₉

D₃

yes

characteristic, direct product factor

C₃×C₉⋊C₉

—

Sylow

C₂²×C₃²×D₃

C₃²

yes

characteristic

C₂³×C₃×C₉

—

C₂²×D₃×C₉

—

C₂×C₃×C₂²⋊C₉

—

C₂×C₃×C₂²⋊C₉

—

D₃×C₂²⋊C₉

—

D₃×C₂²⋊C₉

C₉

yes

complemented

C₂×C₃²×C₉

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃×D₃×C₉

A₄

yes

characteristic

C₂×C₉⋊C₉

—

C₂²×C₃³

C₂×C₃²

yes

characteristic

C₂×C₃²×D₃

—

C₂×C₃²×D₃

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

C₃×D₃

yes

characteristic

C₂×D₃×C₉

—

C₂×D₃×C₉

—

C₃×C₂²⋊C₉

—

C₃×C₂²⋊C₉

—

C₃×C₂²⋊C₉

—

C₃×C₂²⋊C₉

—

C₃×C₂²⋊C₉

—

C₃×C₂²⋊C₉

C₂×C₉

yes

complemented

C₃×C₂²⋊C₉

C₃×D₃

yes

—

C₃×C₂²⋊C₉

C₃×D₃

yes

characteristic

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₂×A₄

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₂³×C₃²

—

C₂²×C₃×D₃

C₃×C₉

yes

characteristic

C₂²×C₃×D₃

3₋¹⁺²

yes

—

C₂²×C₃×D₃

3₋¹⁺²

yes

characteristic

C₂³×C₉

—

C₂×C₂²⋊C₉

—

C₂×C₂²⋊C₉

—

C₂×C₃³

—

C₃²×D₃

—

C₃²×D₃

C₃×A₄

yes

characteristic

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

D₃×C₉

—

D₃×C₉

—

D₃×C₉

—

D₃×C₉

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

C₂×C₃×C₉

yes

characteristic

C₂²×C₃²

C₂×3₋¹⁺²

yes

—

C₂²×C₃²

C₂×3₋¹⁺²

yes

characteristic

C₂²×C₃²

C₃²×D₃

yes

characteristic

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²⋊C₉

—

C₂²⋊C₉

—

C₂²⋊C₉

—

100

C₂²⋊C₉

D₃×C₉

yes

complemented

101

C₃³

C₂×C₃×A₄

yes

characteristic

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

C₃×C₉

—

111

C₃×C₉

—

112

C₃×C₉

—

113

C₃×C₉

D₃×A₄

yes

characteristic

114

C₂³×C₃

—

115

C₂³×C₃

—

116

C₂³×C₃

—

117

C₂²×D₃

C₉⋊C₉

yes

characteristic, complemented

118

C₂×C₃²

—

119

C₂×C₃²

—

120

C₂×C₃²

—

121

C₂×C₃²

—

122

C₂×C₃²

—

123

C₂×C₃²

—

124

C₂×C₃²

—

125

C₂×C₃²

—

126

C₂×C₃²

—

127

C₃×D₃

—

128

C₃×D₃

—

129

C₃×D₃

—

130

C₃×D₃

C₉×A₄

yes

characteristic

131

C₃×D₃

C₉⋊A₄

yes

—

132

C₃×D₃

#1094

yes

characteristic

133

C₂×C₉

—

134

C₂×C₉

—

135

C₂×C₉

—

136

C₂×C₉

—

137

C₂×C₉

—

138

C₂×C₉

—

139

C₂²×C₃

—

140

C₂²×C₃

—

141

C₂²×C₃

—

142

C₂²×C₃

—

143

C₂²×C₃

—

144

C₂²×C₃

—

145

C₂²×C₃

—

146

C₂²×C₃

—

147

C₂²×C₃

—

148

C₂²×C₃

C₂×C₉⋊C₉

yes

characteristic, complemented

149

C₂²×C₃

C₃×D₃×C₉

yes

characteristic

150

C₂²×C₃

D₃×3₋¹⁺²

yes

—

151

C₂²×C₃

D₃×3₋¹⁺²

yes

characteristic

152

C₂×D₃

—

153

C₂×D₃

—

154

C₃²

—

155

C₃²

—

156

C₃²

—

157

C₃²

C₂×C₉×A₄

yes

characteristic

158

C₃²

C₂×C₉⋊A₄

yes

—

159

C₃²

C₂×#1094

yes

characteristic

160

C₃²

C₃×D₃×A₄

yes

characteristic

161

C₉

—

162

C₉

—

163

C₉

—

164

C₉

—

165

C₉

—

166

C₉

—

167

C₂³

—

Sylow

168

C₂×C₃

—

169

C₂×C₃

—

170

C₂×C₃

—

171

C₂×C₃

—

172

C₂×C₃

—

173

C₂×C₃

—

174

C₂×C₃

—

175

C₂×C₃

—

176

C₂×C₃

—

177

C₂×C₃

—

178

C₂×C₃

—

179

C₂×C₃

—

180

C₂×C₃

—

181

D₃

—

182

D₃

(C₂²⋊C₉)⋊C₉

yes

characteristic, direct product factor

183

C₂²

—

184

C₂²

—

185

C₂²

D₃×C₉⋊C₉

yes

characteristic, complemented

186

C₃

—

187

C₃

—

188

C₃

—

189

C₃

C₂×(C₂²⋊C₉)⋊C₉

yes

characteristic, complemented

190

C₃

D₃×C₉×A₄

yes

characteristic

191

C₃

D₃×C₉⋊A₄

yes

—

192

C₃

D₃×#1094

yes

characteristic

193

C₂

—

194

C₂

—

195

C₂

—

	subgroup	G/H
center, Frattini	C₃²	C₃×D₃×A₄
commutator	C₂²×C₃²	C₂×C₃×C₉
Fitting	C₂²×C₃²×C₉	C₂×C₃
socle, cosocle	C₂²×C₃³	C₂×C₃²
prime radical	C₂²×C₃²×D₃	C₃²
hypercenter	C₃×C₉	D₃×A₄
hypocenter	C₂²×C₃	C₂×C₉⋊C₉
LCS	G ▷ C₂²×C₃² ▷ C₂²×C₃
UCS	C₁ ◁ C₃² ◁ C₃×C₉

subgroup

G/H

center, Frattini

C₃²

C₃×D₃×A₄

commutator

C₂²×C₃²

C₂×C₃×C₉

Fitting

C₂²×C₃²×C₉

C₂×C₃

socle, cosocle

C₂²×C₃³

C₂×C₃²

prime radical

C₂²×C₃²×D₃

C₃²

hypercenter

C₃×C₉

D₃×A₄

hypocenter

C₂²×C₃

C₂×C₉⋊C₉

LCS

G ▷ C₂²×C₃² ▷ C₂²×C₃

UCS

C₁ ◁ C₃² ◁ C₃×C₉

N	H ≅ G/N	type
1. C₃×(C₂²⋊C₉)⋊C₉	C₂	semidirect
15. (C₂²⋊C₉)⋊C₉	D₃	direct (N × H)
23. D₃×C₂²⋊C₉	C₉	semidirect
46. C₃×C₂²⋊C₉	C₂×C₉	semidirect
100. C₂²⋊C₉	D₃×C₉	semidirect
117. C₂²×D₃	C₉⋊C₉	semidirect
148. C₂²×C₃	C₂×C₉⋊C₉	semidirect
182. D₃	(C₂²⋊C₉)⋊C₉	direct (N × H)
185. C₂²	D₃×C₉⋊C₉	semidirect
189. C₃	C₂×(C₂²⋊C₉)⋊C₉	semidirect

H ≅ G/N

type

1. C₃×(C₂²⋊C₉)⋊C₉

C₂

semidirect

15. (C₂²⋊C₉)⋊C₉

D₃

direct (N × H)

23. D₃×C₂²⋊C₉

C₉

semidirect

46. C₃×C₂²⋊C₉

C₂×C₉

semidirect

100. C₂²⋊C₉

D₃×C₉

semidirect

117. C₂²×D₃

C₉⋊C₉

semidirect

148. C₂²×C₃

C₂×C₉⋊C₉

semidirect

182. D₃

(C₂²⋊C₉)⋊C₉

direct (N × H)

185. C₂²

D₃×C₉⋊C₉

semidirect

189. C₃

C₂×(C₂²⋊C₉)⋊C₉

semidirect

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

subgroup	index
C₃×(C₂²⋊C₉)⋊C₉	2
C₂²×C₃×D₃×C₉	3
C₃×D₃×C₂²⋊C₉	3
C₂×(C₂²⋊C₉)⋊C₉	3
D₃×C₉⋊C₉	4

subgroup

index

C₃×(C₂²⋊C₉)⋊C₉

C₂²×C₃×D₃×C₉

C₃×D₃×C₂²⋊C₉

C₂×(C₂²⋊C₉)⋊C₉

D₃×C₉⋊C₉

Subgroups — D₃×(C₂²⋊C₉)⋊C₉ #14518175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×(C22⋊C9)⋊C9 #14518175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×(C₂²⋊C₉)⋊C₉ #14518175