Group #19135930 — subgroups

Subgroups — #19135930

Order 5504.

250 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 91 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×#13063258	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063256	C₂	1	1	yes	maximal, characteristic
3	#14582797	C₂	1	1	yes	maximal, characteristic
4	#14582661	C₂	1	1	yes	maximal, characteristic
5	#14582661	C₂	1	1	yes	maximal, characteristic
6	#14582654	C₂	1	1	yes	maximal, characteristic
7	C₂×#125×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₄₃⋊C₄	—	2	1	no	—
13	#13063258	—	2	2	no	—
14	#13063256	—	2	2	no	—
15	C₄₃⋊#95	—	2	1	no	—
16	#125×C₄₃	—	2	2	no	—
17	#125×C₄₃	—	2	2	no	—
18	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
19	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
20	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	—	2	1	no	—
24	C₂²×C₄×C₄₃	—	2	1	no	—
25	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²×Dic₄₃	—	2	1	no	—
29	C₂²×Dic₄₃	—	2	1	no	—
30	C₄⋊C₄×C₄₃	—	2	4	no	—
31	C₄⋊C₄×C₄₃	—	2	4	no	—
32	C₄⋊C₄×C₄₃	—	2	1	no	—
33	C₄⋊C₄×C₄₃	—	2	1	no	—
34	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
35	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
36	C₄²×C₄₃	—	2	1	no	—
37	C₄²×C₄₃	—	2	1	no	—
38	C₄⋊Dic₄₃	—	2	1	no	—
39	C₄⋊Dic₄₃	—	2	1	no	—
40	C₄⋊Dic₄₃	—	2	1	no	—
41	C₄⋊Dic₄₃	Q₈	1	2	yes	—
42	Dic₄₃⋊C₄	—	4	2	no	—
43	C₂×C₄₃⋊C₈	—	2	1	no	—
44	C₂×C₄₃⋊C₈	—	2	1	no	—
45	C₂×C₄₃⋊C₈	—	2	1	no	—
46	C₂×C₄₃⋊C₈	—	2	1	no	—
47	C₂×C₄₃⋊C₈	Q₈	1	2	yes	—
48	C₂×C₄₃⋊C₈	Q₈	1	2	yes	—
49	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₄₃	—	2	1	no	—
51	C₂×C₄×C₄₃	—	2	1	no	—
52	C₂×C₄×C₄₃	—	2	2	no	—
53	C₂×C₄×C₄₃	—	2	2	no	—
54	C₂×C₄×C₄₃	—	2	1	no	—
55	C₂×C₄×C₄₃	—	2	1	no	—
56	C₂×C₄×C₄₃	—	2	1	no	—
57	C₂×C₄×C₄₃	—	2	1	no	—
58	C₂×C₄×C₄₃	—	4	1	no	—
59	C₂×C₄×C₄₃	—	4	1	no	—
60	C₂×C₄×C₄₃	—	4	1	no	—
61	C₂×C₄×C₄₃	—	4	1	no	—
62	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
67	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
68	C₂×Dic₄₃	—	2	2	no	—
69	C₂×Dic₄₃	—	4	1	no	—
70	C₂×Dic₄₃	—	4	1	no	—
71	C₂×Dic₄₃	—	4	1	no	—
72	C₂×Dic₄₃	—	4	1	no	—
73	C₂×Dic₄₃	—	4	1	no	—
74	C₄₃⋊C₈	—	2	2	no	—
75	C₄₃⋊C₈	—	2	2	no	—
76	C₂²×C₄₃	#120	1	1	yes	characteristic
77	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
78	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
79	C₂²×C₄₃	#135	1	1	yes	characteristic
80	C₂²×C₄₃	#135	1	1	yes	characteristic
81	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
82	C₂²×C₄₃	#137	1	1	yes	characteristic
83	C₄×C₄₃	—	4	1	no	—
84	C₄×C₄₃	—	4	2	no	—
85	C₄×C₄₃	—	4	1	no	—
86	C₄×C₄₃	—	4	2	no	—
87	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
88	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
89	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
90	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
91	Dic₄₃	—	4	2	no	—
92	Dic₄₃	—	8	1	no	—
93	#2059	—	43	1	no	maximal, Sylow
94	C₂×C₄₃	#395	1	1	yes	characteristic
95	C₂×C₄₃	#449	1	1	yes	characteristic
96	C₂×C₄₃	#452	1	1	yes	characteristic
97	C₂×C₄₃	#478	1	1	yes	characteristic
98	C₂×C₄₃	#479	1	1	yes	characteristic
99	C₂×C₄₃	#499	1	1	yes	characteristic
100	C₂×C₄₃	#501	1	1	yes	characteristic
101	C₂×#125	D₄₃	1	1	yes	characteristic
102	C₂×#107	—	43	1	no	—
103	C₂×#106	—	43	1	no	—
104	#389	—	43	1	no	—
105	#340	—	43	1	no	—
106	#340	—	43	1	no	—
107	#336	—	43	1	no	—
108	C₄₃	#2059	1	1	yes	characteristic, complemented, Sylow
109	C₂²×C₈	—	43	1	no	—
110	C₂²×C₈	—	43	1	no	—
111	#125	—	2	2	no	—
112	#125	—	2	2	no	—
113	C₂×C₄⋊C₄	—	2	1	no	—
114	C₂×C₄⋊C₄	—	2	1	no	—
115	C₂×C₄⋊C₄	—	43	1	no	—
116	C₂×C₄⋊C₄	—	43	1	no	—
117	C₂×C₄⋊C₄	—	86	1	no	—
118	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
119	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
120	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
121	#107	—	86	2	no	—
122	#106	—	86	2	no	—
123	#95	—	86	1	no	—
124	C₂²×C₄	—	2	1	no	—
125	C₂²×C₄	—	2	1	no	—
126	C₂²×C₄	—	86	1	no	—
127	C₂²×C₄	—	86	1	no	—
128	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
129	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
130	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
131	C₂×C₈	—	43	2	no	—
132	C₂×C₈	—	43	2	no	—
133	C₂×C₈	—	86	1	no	—
134	C₂×C₈	—	86	1	no	—
135	C₂×C₈	—	86	1	no	—
136	C₂×C₈	—	86	1	no	—
137	C₄⋊C₄	—	2	4	no	—
138	C₄⋊C₄	—	2	4	no	—
139	C₄⋊C₄	—	2	1	no	—
140	C₄⋊C₄	—	2	1	no	—
141	C₄⋊C₄	—	43	2	no	—
142	C₄⋊C₄	—	86	1	no	—
143	C₄⋊C₄	—	86	1	no	—
144	C₄⋊C₄	—	86	1	no	—
145	C₄⋊C₄	—	172	2	no	—
146	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
147	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
148	C₄²	—	2	1	no	—
149	C₄²	—	2	1	no	—
150	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	4	1	no	—
160	C₂×C₄	—	4	1	no	—
161	C₂×C₄	—	4	1	no	—
162	C₂×C₄	—	4	1	no	—
163	C₂×C₄	—	86	2	no	—
164	C₂×C₄	—	172	1	no	—
165	C₂×C₄	—	172	1	no	—
166	C₂×C₄	—	172	1	no	—
167	C₂×C₄	—	172	1	no	—
168	C₂×C₄	—	172	1	no	—
169	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
170	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
171	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
172	C₂×C₄	#10621902	1	1	yes	characteristic
173	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
174	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
175	C₈	—	86	2	no	—
176	C₈	—	86	2	no	—
177	C₂²	#13063294	1	1	yes	characteristic
178	C₂²	#13063301	1	1	yes	characteristic
179	C₂²	#13063323	1	1	yes	characteristic
180	C₂²	#13063345	1	1	yes	characteristic
181	C₂²	#13063345	1	1	yes	characteristic
182	C₂²	#13063350	1	1	yes	characteristic
183	C₂²	#13063355	1	1	yes	characteristic
184	C₄	—	4	1	no	—
185	C₄	—	4	2	no	—
186	C₄	—	4	1	no	—
187	C₄	—	4	2	no	—
188	C₄	—	344	1	no	—
189	C₄	—	172	2	no	—
190	C₄	#13063301	1	1	yes	characteristic
191	C₄	#13063301	1	1	yes	characteristic
192	C₄	#13063323	1	1	yes	characteristic
193	C₄	#13063323	1	1	yes	characteristic
194	C₂	#14582818	1	1	yes	characteristic
195	C₂	#14583044	1	1	yes	characteristic
196	C₂	#14583061	1	1	yes	characteristic
197	C₂	#14583196	1	1	yes	characteristic
198	C₂	#14583203	1	1	yes	characteristic
199	C₂	#14583298	1	1	yes	characteristic
200	C₂	#14583309	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063258

C₂

yes

maximal, characteristic

C₂×#13063256

C₂

yes

maximal, characteristic

#14582797

C₂

yes

maximal, characteristic

#14582661

C₂

yes

maximal, characteristic

#14582661

C₂

yes

maximal, characteristic

#14582654

C₂

yes

maximal, characteristic

C₂×#125×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

—

#13063258

—

#13063256

—

C₄₃⋊#95

—

#125×C₄₃

—

#125×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

Q₈

yes

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

Q₈

yes

—

C₂×C₄₃⋊C₈

Q₈

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

C₄⋊Q₈

yes

characteristic

C₄×C₄₃

C₄⋊Q₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

100

C₂×C₄₃

#501

yes

characteristic

101

C₂×#125

D₄₃

yes

characteristic

102

C₂×#107

—

103

C₂×#106

—

104

#389

—

105

#340

—

106

#340

—

107

#336

—

108

C₄₃

#2059

yes

characteristic, complemented, Sylow

109

C₂²×C₈

—

110

C₂²×C₈

—

111

#125

—

112

#125

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

119

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

120

C₂×C₄²

C₂×D₄₃

yes

characteristic

121

#107

—

122

#106

—

123

#95

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

129

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

130

C₂²×C₄

C₂²×D₄₃

yes

characteristic

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

172

—

146

C₄⋊C₄

C₂²⋊D₄₃

yes

—

147

C₄⋊C₄

C₂²⋊D₄₃

yes

—

148

C₄²

—

149

C₄²

—

150

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

172

—

165

C₂×C₄

—

172

—

166

C₂×C₄

—

172

—

167

C₂×C₄

—

172

—

168

C₂×C₄

—

172

—

169

C₂×C₄

Q₈×D₄₃

yes

characteristic

170

C₂×C₄

Q₈×D₄₃

yes

characteristic

171

C₂×C₄

Q₈×D₄₃

yes

characteristic

172

C₂×C₄

#10621902

yes

characteristic

173

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

174

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

175

C₈

—

176

C₈

—

177

C₂²

#13063294

yes

characteristic

178

C₂²

#13063301

yes

characteristic

179

C₂²

#13063323

yes

characteristic

180

C₂²

#13063345

yes

characteristic

181

C₂²

#13063345

yes

characteristic

182

C₂²

#13063350

yes

characteristic

183

C₂²

#13063355

yes

characteristic

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

344

—

189

C₄

—

172

—

190

C₄

#13063301

yes

characteristic

191

C₄

#13063301

yes

characteristic

192

C₄

#13063323

yes

characteristic

193

C₄

#13063323

yes

characteristic

194

C₂

#14582818

yes

characteristic

195

C₂

#14583044

yes

characteristic

196

C₂

#14583061

yes

characteristic

197

C₂

#14583196

yes

characteristic

198

C₂

#14583203

yes

characteristic

199

C₂

#14583298

yes

characteristic

200

C₂

#14583309

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#125×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#125	D₄₃
hypocenter	C₄₃	#2059
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#125×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
108. C₄₃	#2059	semidirect

H ≅ G/N

type

108. C₄₃

#2059

semidirect

Subgroups — #19135930

Conjugacy classes of subgroups

Complements