Group #19135826 — subgroups

Subgroups — #19135826

Order 5504.

402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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×#13063246	C₂	1	2	yes	maximal, complemented
2	C₂×#13063246	C₂	1	2	yes	maximal, complemented
3	#14582797	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582654	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#127×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₃⋊C₄	—	2	1	no	—
10	#13063246	—	2	4	no	—
11	#13063246	—	2	4	no	—
12	C₄₃⋊#95	—	2	1	no	—
13	C₂²×D₄×C₄₃	—	2	1	no	—
14	C₂²×D₄×C₄₃	—	2	1	no	—
15	C₂²×D₄×C₄₃	C₂²	1	2	yes	—
16	#127×C₄₃	—	2	4	no	—
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄₃	—	2	2	no	—
19	C₂×D₄×C₄₃	—	2	4	no	—
20	C₂×D₄×C₄₃	—	2	4	no	—
21	C₂×D₄×C₄₃	—	2	2	no	—
22	C₂×D₄×C₄₃	—	2	2	no	—
23	C₂×D₄×C₄₃	—	2	2	no	—
24	C₂×D₄×C₄₃	—	2	2	no	—
25	C₂×D₄×C₄₃	—	2	2	no	—
26	C₂×D₄×C₄₃	—	4	2	no	—
27	C₂×D₄×C₄₃	—	4	2	no	—
28	C₂×D₄×C₄₃	—	4	2	no	—
29	C₂×D₄×C₄₃	—	4	2	no	—
30	C₂×D₄×C₄₃	D₄	1	4	yes	—
31	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
34	C₂²×Dic₄₃	—	2	1	no	—
35	C₂²×Dic₄₃	—	2	1	no	—
36	C₄²×C₄₃	—	2	2	no	—
37	C₄⋊Dic₄₃	—	2	1	no	—
38	C₄⋊Dic₄₃	—	2	2	no	—
39	C₄⋊Dic₄₃	D₄	1	2	yes	complemented
40	Dic₄₃⋊C₄	—	4	2	no	—
41	C₂×C₄₃⋊C₈	—	2	2	no	—
42	C₂×C₄₃⋊C₈	—	2	2	no	—
43	C₂×C₄₃⋊C₈	—	2	2	no	—
44	C₂³×C₄₃	—	2	4	no	—
45	C₂³×C₄₃	—	4	2	no	—
46	C₂³×C₄₃	—	4	2	no	—
47	C₂³×C₄₃	—	4	2	no	—
48	C₂³×C₄₃	—	4	2	no	—
49	C₂³×C₄₃	—	4	2	no	—
50	C₂³×C₄₃	—	4	2	no	—
51	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
52	D₄×C₄₃	—	2	4	no	—
53	D₄×C₄₃	—	2	4	no	—
54	D₄×C₄₃	—	4	8	no	—
55	D₄×C₄₃	—	4	8	no	—
56	D₄×C₄₃	—	4	2	no	—
57	D₄×C₄₃	—	4	2	no	—
58	C₂×C₄×C₄₃	—	2	1	no	—
59	C₂×C₄×C₄₃	—	2	1	no	—
60	C₂×C₄×C₄₃	—	2	1	no	—
61	C₂×C₄×C₄₃	—	2	1	no	—
62	C₂×C₄×C₄₃	D₈	1	2	yes	—
63	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
64	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₄₃	#41	1	2	yes	—
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	—	4	2	no	—
75	C₂²×C₄₃	—	4	4	no	—
76	C₂²×C₄₃	—	4	4	no	—
77	C₂²×C₄₃	—	4	4	no	—
78	C₂²×C₄₃	—	8	2	no	—
79	C₂²×C₄₃	—	8	2	no	—
80	C₂²×C₄₃	—	8	2	no	—
81	C₂²×C₄₃	—	8	2	no	—
82	C₂²×C₄₃	#120	1	1	yes	characteristic
83	C₂²×C₄₃	#121	1	1	yes	characteristic
84	C₂²×C₄₃	#124	1	1	yes	characteristic
85	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
86	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
87	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₄×C₄₃	—	2	2	no	—
90	C₄×C₄₃	—	2	2	no	—
91	C₄×C₄₃	#121	1	2	yes	—
92	C₄×C₄₃	#123	1	2	yes	—
93	Dic₄₃	—	4	2	no	—
94	Dic₄₃	—	8	1	no	—
95	#2041	—	43	1	no	maximal, Sylow
96	C₂×C₄₃	—	8	4	no	—
97	C₂×C₄₃	#394	1	1	yes	characteristic
98	C₂×C₄₃	#447	1	1	yes	characteristic
99	C₂×C₄₃	#450	1	1	yes	characteristic
100	C₂×C₄₃	#459	1	1	yes	characteristic
101	C₂×C₄₃	#460	1	1	yes	characteristic
102	C₂×C₄₃	#486	1	1	yes	characteristic
103	C₂×C₄₃	#490	1	1	yes	characteristic
104	C₂×#127	D₄₃	1	1	yes	characteristic
105	C₂×#102	—	43	2	no	—
106	C₂×#102	—	43	2	no	—
107	#389	—	43	1	no	—
108	#336	—	43	1	no	—
109	C₄₃	#2041	1	1	yes	characteristic, complemented, Sylow
110	C₂²×D₄	—	2	1	no	—
111	C₂²×D₄	—	2	1	no	—
112	C₂²×D₄	C₂×D₄₃	1	2	yes	—
113	C₂²×C₈	—	43	2	no	—
114	#127	—	2	4	no	—
115	C₂×C₄⋊C₄	—	43	1	no	—
116	C₂×C₄⋊C₄	—	43	1	no	—
117	C₂×C₄⋊C₄	—	86	1	no	—
118	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
119	#102	—	86	4	no	—
120	#102	—	86	4	no	—
121	#95	—	86	1	no	—
122	C₂⁴	—	2	2	no	—
123	C₂×D₄	—	2	4	no	—
124	C₂×D₄	—	2	4	no	—
125	C₂×D₄	—	2	2	no	—
126	C₂×D₄	—	2	2	no	—
127	C₂×D₄	—	2	2	no	—
128	C₂×D₄	—	2	2	no	—
129	C₂×D₄	—	2	2	no	—
130	C₂×D₄	—	4	2	no	—
131	C₂×D₄	—	4	2	no	—
132	C₂×D₄	—	4	2	no	—
133	C₂×D₄	—	4	2	no	—
134	C₂×D₄	C₂²⋊D₄₃	1	4	yes	—
135	C₂²×C₄	—	86	1	no	—
136	C₂²×C₄	—	86	1	no	—
137	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
138	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
139	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
140	C₂×C₈	—	86	2	no	—
141	C₂×C₈	—	86	2	no	—
142	C₂×C₈	—	86	2	no	—
143	C₄⋊C₄	—	43	2	no	—
144	C₄⋊C₄	—	86	1	no	—
145	C₄⋊C₄	—	86	2	no	—
146	C₄⋊C₄	—	172	2	no	—
147	C₄²	—	2	2	no	—
148	C₂³	—	2	4	no	—
149	C₂³	—	4	2	no	—
150	C₂³	—	4	2	no	—
151	C₂³	—	4	2	no	—
152	C₂³	—	4	2	no	—
153	C₂³	—	4	2	no	—
154	C₂³	—	4	2	no	—
155	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
156	D₄	—	2	4	no	—
157	D₄	—	2	4	no	—
158	D₄	—	4	8	no	—
159	D₄	—	4	8	no	—
160	D₄	—	4	2	no	—
161	D₄	—	4	2	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	86	2	no	—
167	C₂×C₄	—	172	1	no	—
168	C₂×C₄	—	172	1	no	—
169	C₂×C₄	—	172	1	no	—
170	C₂×C₄	—	172	1	no	—
171	C₂×C₄	—	172	1	no	—
172	C₂×C₄	#10621882	1	2	yes	—
173	C₂×C₄	#10621883	1	2	yes	—
174	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
175	C₂×C₄	#10621900	1	2	yes	—
176	C₂×C₄	#10621900	1	1	yes	characteristic
177	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
178	C₈	—	172	2	no	—
179	C₂²	—	4	4	no	—
180	C₂²	—	4	4	no	—
181	C₂²	—	4	4	no	—
182	C₂²	—	8	2	no	—
183	C₂²	—	8	2	no	—
184	C₂²	—	8	2	no	—
185	C₂²	—	8	2	no	—
186	C₂²	#13063294	1	1	yes	characteristic
187	C₂²	#13063296	1	1	yes	characteristic
188	C₂²	#13063312	1	1	yes	characteristic
189	C₂²	C₂×#10621882	1	1	yes	characteristic
190	C₂²	C₂×#10621883	1	1	yes	characteristic
191	C₂²	#13063351	1	1	yes	characteristic
192	C₂²	#13063351	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	2	2	no	—
195	C₄	—	344	1	no	—
196	C₄	—	172	2	no	—
197	C₄	#13063297	1	2	yes	—
198	C₄	#13063306	1	2	yes	—
199	C₂	—	8	4	no	—
200	C₂	#14582813	1	1	yes	characteristic
201	C₂	#14583033	1	1	yes	characteristic
202	C₂	#14583050	1	1	yes	characteristic
203	C₂	#14583091	1	1	yes	characteristic
204	C₂	#14583096	1	1	yes	characteristic
205	C₂	#14583245	1	1	yes	characteristic
206	C₂	#14583263	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063246

C₂

yes

maximal, complemented

C₂×#13063246

C₂

yes

maximal, complemented

#14582797

C₂

yes

maximal, characteristic, complemented

#14582654

C₂

yes

maximal, characteristic, complemented

C₂×#127×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

—

#13063246

—

#13063246

—

C₄₃⋊#95

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

C₂²

yes

—

#127×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

complemented

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂²×C₄₃

C₂×SD₁₆

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

Dic₄₃

—

#2041

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

100

C₂×C₄₃

#459

yes

characteristic

101

C₂×C₄₃

#460

yes

characteristic

102

C₂×C₄₃

#486

yes

characteristic

103

C₂×C₄₃

#490

yes

characteristic

104

C₂×#127

D₄₃

yes

characteristic

105

C₂×#102

—

106

C₂×#102

—

107

#389

—

108

#336

—

109

C₄₃

#2041

yes

characteristic, complemented, Sylow

110

C₂²×D₄

—

111

C₂²×D₄

—

112

C₂²×D₄

C₂×D₄₃

yes

—

113

C₂²×C₈

—

114

#127

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄²

C₂×D₄₃

yes

characteristic

119

#102

—

120

#102

—

121

#95

—

122

C₂⁴

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

C₂²⋊D₄₃

yes

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

138

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

139

C₂²×C₄

C₂²×D₄₃

yes

characteristic

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

172

—

147

C₄²

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

—

155

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

156

D₄

—

157

D₄

—

158

D₄

—

159

D₄

—

160

D₄

—

161

D₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

172

—

168

C₂×C₄

—

172

—

169

C₂×C₄

—

172

—

170

C₂×C₄

—

172

—

171

C₂×C₄

—

172

—

172

C₂×C₄

#10621882

yes

—

173

C₂×C₄

#10621883

yes

—

174

C₂×C₄

D₄×D₄₃

yes

characteristic

175

C₂×C₄

#10621900

yes

—

176

C₂×C₄

#10621900

yes

characteristic

177

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

178

C₈

—

172

—

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

#13063294

yes

characteristic

187

C₂²

#13063296

yes

characteristic

188

C₂²

#13063312

yes

characteristic

189

C₂²

C₂×#10621882

yes

characteristic

190

C₂²

C₂×#10621883

yes

characteristic

191

C₂²

#13063351

yes

characteristic

192

C₂²

#13063351

yes

characteristic

193

C₄

—

194

C₄

—

195

C₄

—

344

—

196

C₄

—

172

—

197

C₄

#13063297

yes

—

198

C₄

#13063306

yes

—

199

C₂

—

200

C₂

#14582813

yes

characteristic

201

C₂

#14583033

yes

characteristic

202

C₂

#14583050

yes

characteristic

203

C₂

#14583091

yes

characteristic

204

C₂

#14583096

yes

characteristic

205

C₂

#14583245

yes

characteristic

206

C₂

#14583263

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#127×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#127	D₄₃
hypocenter	C₄₃	#2041
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#127×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×#13063246	C₂	semidirect
2. C₂×#13063246	C₂	semidirect
3. #14582797	C₂	semidirect
4. #14582654	C₂	semidirect
39. C₄⋊Dic₄₃	D₄	semidirect
109. C₄₃	#2041	semidirect

H ≅ G/N

type

1. C₂×#13063246

C₂

semidirect

2. C₂×#13063246

C₂

semidirect

3. #14582797

C₂

semidirect

4. #14582654

C₂

semidirect

39. C₄⋊Dic₄₃

D₄

semidirect

109. C₄₃

#2041

semidirect

Subgroups — #19135826

Conjugacy classes of subgroups

Complements