Group #18081923 — subgroups

Subgroups — #18081923

Order 4864.

400 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14563766	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562199	C₂	1	2	yes	maximal, complemented
3	#14562195	C₂	1	2	yes	maximal
4	#14561918	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3131	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	#11926410	C₂²	1	2	yes	—
8	#11926307	—	2	2	no	—
9	#11926281	—	2	4	no	—
10	#11926278	—	2	4	no	—
11	#11926265	—	2	1	no	—
12	C₈×C₁₉⋊C₈	—	2	1	no	—
13	C₁₉×#533	C₂²	1	1	yes	characteristic
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₁₉×#488	—	2	1	no	—
16	C₁₉×#488	—	2	1	no	—
17	C₁₉×#487	C₄	1	2	yes	complemented
18	C₁₉×#486	C₄	1	2	yes	complemented
19	C₁₉×#416	—	2	2	no	—
20	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×#41×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
24	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
25	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
26	C₁₉×#125	—	2	1	no	—
27	C₁₉×#124	—	2	1	no	—
28	C₁₉×C₂²⋊Q₈	—	2	2	no	—
29	C₁₉×#121	—	2	2	no	—
30	C₄×Q₈×C₁₉	—	2	2	no	—
31	C₄×D₄×C₁₉	—	2	2	no	—
32	C₁₉×#117	—	2	1	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₉	—	2	2	no	—
35	C₁₉×#103	—	2	2	no	—
36	C₁₉×#103	—	2	2	no	—
37	C₁₉×#102	—	2	2	no	—
38	C₁₉×#102	—	2	2	no	—
39	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
42	C₁₉⋊#95	—	2	2	no	—
43	C₁₉⋊#95	—	2	2	no	—
44	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
45	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
46	C₄×C₁₉⋊C₈	—	2	2	no	—
47	#41×C₁₉	—	4	4	no	—
48	C₂×Q₈×C₁₉	—	2	1	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×D₄×C₁₉	—	2	1	no	—
51	C₂×D₄×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	2	4	no	—
58	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	4	2	no	—
64	C₂²⋊C₄×C₁₉	—	4	1	no	—
65	C₂²⋊C₄×C₁₉	—	4	2	no	—
66	C₄²×C₁₉	—	4	1	no	—
67	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	#41	1	2	yes	—
70	C₄⋊Dic₁₉	—	4	4	no	—
71	C₂×C₁₉⋊C₈	—	2	4	no	—
72	#9757	—	19	1	no	maximal, Sylow
73	C₂³×C₁₉	—	4	1	no	—
74	C₂³×C₁₉	#127	1	1	yes	characteristic
75	Q₈×C₁₉	—	4	2	no	—
76	Q₈×C₁₉	—	8	2	no	—
77	D₄×C₁₉	—	4	2	no	—
78	D₄×C₁₉	—	8	2	no	—
79	D₄×C₁₉	—	8	2	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	1	no	—
83	C₂×C₄×C₁₉	—	8	2	no	—
84	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₁₉	#121	1	2	yes	—
87	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#135	1	4	yes	—
89	C₂×Dic₁₉	—	8	4	no	—
90	C₂×Dic₁₉	—	8	2	no	—
91	C₈×C₁₉	—	2	2	no	—
92	C₈×C₁₉	—	2	2	no	—
93	C₁₉⋊C₈	—	4	4	no	—
94	#3131	D₁₉	1	1	yes	characteristic
95	#1835	—	19	1	no	—
96	#1518	—	19	2	no	—
97	#1517	—	19	2	no	—
98	#1450	—	19	1	no	—
99	C₂²×C₁₉	—	2	2	no	—
100	C₂²×C₁₉	—	8	1	no	—
101	C₂²×C₁₉	—	8	2	no	—
102	C₂²×C₁₉	#390	1	1	yes	characteristic
103	C₂²×C₁₉	#495	1	2	yes	—
104	C₄×C₁₉	—	2	2	no	—
105	C₄×C₁₉	—	2	2	no	—
106	C₄×C₁₉	—	8	1	no	—
107	C₄×C₁₉	—	8	2	no	—
108	C₄×C₁₉	#416	1	2	yes	—
109	C₄×C₁₉	#488	1	2	yes	—
110	Dic₁₉	—	16	2	no	—
111	#533	C₂×D₁₉	1	1	yes	characteristic
112	#532	C₂×D₁₉	1	1	yes	characteristic
113	#488	—	2	1	no	—
114	#488	—	2	1	no	—
115	#487	Dic₁₉	1	2	yes	complemented
116	#486	Dic₁₉	1	2	yes	complemented
117	#431	—	19	2	no	—
118	#416	—	2	2	no	—
119	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
120	#382	—	19	2	no	—
121	#340	—	38	2	no	—
122	#328	—	38	4	no	—
123	#327	—	38	4	no	—
124	#322	—	38	1	no	—
125	C₈²	—	38	1	no	—
126	C₂×C₁₉	—	2	2	no	—
127	C₂×C₁₉	—	16	1	no	—
128	C₂×C₁₉	#1958	1	1	yes	characteristic
129	C₂×C₁₉	#1976	1	2	yes	—
130	C₂×#41	—	2	1	no	—
131	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
132	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
133	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
134	#127	C₂×Dic₁₉	1	1	yes	characteristic
135	#125	—	2	1	no	—
136	#124	—	2	1	no	—
137	C₂²⋊Q₈	—	2	2	no	—
138	#121	—	2	2	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	#117	—	2	1	no	—
142	C₂×C₄⋊C₄	—	38	2	no	—
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	38	2	no	—
145	#103	—	2	2	no	—
146	#103	—	2	2	no	—
147	#102	—	2	2	no	—
148	#102	—	2	2	no	—
149	C₂²⋊C₈	—	19	4	no	—
150	C₄×C₈	—	38	2	no	—
151	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
152	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
153	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
154	#95	—	38	2	no	—
155	#95	—	38	2	no	—
156	C₁₉	#9757	1	1	yes	characteristic, complemented, Sylow
157	#41	—	4	4	no	—
158	C₂×Q₈	—	2	2	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×D₄	—	2	2	no	—
161	C₂×D₄	—	2	1	no	—
162	C₂×D₄	—	4	1	no	—
163	C₂²×C₄	—	4	1	no	—
164	C₂²×C₄	—	76	2	no	—
165	C₂²×C₄	D₄×D₁₉	1	2	yes	—
166	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
167	C₂×C₈	—	2	4	no	—
168	C₂×C₈	—	38	4	no	—
169	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
170	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	76	4	no	—
176	C₂²⋊C₄	—	4	1	no	—
177	C₂²⋊C₄	—	4	2	no	—
178	C₄²	—	4	1	no	—
179	C₄²	#64543	1	2	yes	—
180	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
181	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
182	C₂³	—	4	1	no	—
183	C₂³	#10597386	1	1	yes	characteristic
184	Q₈	—	4	2	no	—
185	Q₈	—	8	2	no	—
186	D₄	—	4	2	no	—
187	D₄	—	8	2	no	—
188	D₄	—	8	2	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	8	2	no	—
193	C₂×C₄	—	152	4	no	—
194	C₂×C₄	—	152	2	no	—
195	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
196	C₂×C₄	#10597382	1	1	yes	characteristic
197	C₂×C₄	#10597384	1	2	yes	—
198	C₂×C₄	#10597396	1	4	yes	—
199	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
200	C₈	—	2	2	no	—
201	C₈	—	2	2	no	—
202	C₈	—	76	4	no	—
203	C₂²	—	2	2	no	—
204	C₂²	—	8	1	no	—
205	C₂²	—	8	2	no	—
206	C₂²	#11926447	1	1	yes	characteristic
207	C₂²	#11926926	1	2	yes	—
208	C₄	—	2	2	no	—
209	C₄	—	2	2	no	—
210	C₄	—	8	1	no	—
211	C₄	—	8	2	no	—
212	C₄	—	304	2	no	—
213	C₄	#11926540	1	2	yes	—
214	C₄	#11926898	1	2	yes	—
215	C₂	—	2	2	no	—
216	C₂	—	16	1	no	—
217	C₂	#14564447	1	1	yes	characteristic
218	C₂	#14564534	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563766

C₂

yes

maximal, characteristic, complemented

#14562199

C₂

yes

maximal, complemented

#14562195

C₂

yes

maximal

#14561918

C₂

yes

maximal, characteristic, complemented

C₁₉×#3131

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

#11926410

C₂²

yes

—

—

—

—

—

C₈×C₁₉⋊C₈

—

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#488

—

C₁₉×#488

—

C₁₉×#487

C₄

yes

complemented

C₁₉×#486

C₄

yes

complemented

C₁₉×#416

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#125

—

C₁₉×#124

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#102

—

C₁₉×#102

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

#9757

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#127

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#3131

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

#390

yes

characteristic

103

C₂²×C₁₉

#495

yes

—

104

C₄×C₁₉

—

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

#416

yes

—

109

C₄×C₁₉

#488

yes

—

110

Dic₁₉

—

111

#533

C₂×D₁₉

yes

characteristic

112

#532

C₂×D₁₉

yes

characteristic

113

#488

—

114

#488

—

115

#487

Dic₁₉

yes

complemented

116

#486

Dic₁₉

yes

complemented

117

#431

—

118

#416

—

119

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

120

#382

—

121

#340

—

122

#328

—

123

#327

—

124

#322

—

125

C₈²

—

126

C₂×C₁₉

—

127

C₂×C₁₉

—

128

C₂×C₁₉

#1958

yes

characteristic

129

C₂×C₁₉

#1976

yes

—

130

C₂×#41

—

131

C₂²×C₈

C₂²⋊D₁₉

yes

—

132

C₄⋊Q₈

C₂×Dic₁₉

yes

characteristic

133

C₄⋊Q₈

C₂×Dic₁₉

yes

—

134

#127

C₂×Dic₁₉

yes

characteristic

135

#125

—

136

#124

—

137

C₂²⋊Q₈

—

138

#121

—

139

C₄×Q₈

—

140

C₄×D₄

—

141

#117

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

C₄⋊C₈

—

145

#103

—

146

#103

—

147

#102

—

148

#102

—

149

C₂²⋊C₈

—

150

C₄×C₈

—

151

C₄×C₈

C₂×Dic₁₉

yes

—

152

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

153

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

154

#95

—

155

#95

—

156

C₁₉

#9757

yes

characteristic, complemented, Sylow

157

#41

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×D₄

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

D₄×D₁₉

yes

—

166

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

C₂²⋊Dic₁₉

yes

—

170

C₂×C₈

C₂²⋊Dic₁₉

yes

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₂²⋊C₄

—

177

C₂²⋊C₄

—

178

C₄²

—

179

C₄²

#64543

yes

—

180

C₄²

C₂²×Dic₁₉

yes

characteristic

181

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

182

C₂³

—

183

C₂³

#10597386

yes

characteristic

184

Q₈

—

185

Q₈

—

186

D₄

—

187

D₄

—

188

D₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

152

—

194

C₂×C₄

—

152

—

195

C₂×C₄

D₄×Dic₁₉

yes

—

196

C₂×C₄

#10597382

yes

characteristic

197

C₂×C₄

#10597384

yes

—

198

C₂×C₄

#10597396

yes

—

199

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

200

C₈

—

201

C₈

—

202

C₈

—

203

C₂²

—

204

C₂²

—

205

C₂²

—

206

C₂²

#11926447

yes

characteristic

207

C₂²

#11926926

yes

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

212

C₄

—

304

—

213

C₄

#11926540

yes

—

214

C₄

#11926898

yes

—

215

C₂

—

216

C₂

—

217

C₂

#14564447

yes

characteristic

218

C₂

#14564534

yes

—

	subgroup	G/H
center	C₂²	#11926447
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3131	C₂
socle	C₂²×C₁₉	#390
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3131	D₁₉
hypocenter	C₁₉	#9757
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3131

subgroup

G/H

center

C₂²

#11926447

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3131

C₂

socle

C₂²×C₁₉

#390

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3131

N	H ≅ G/N	type
1. #14563766	C₂	semidirect
2. #14562199	C₂	semidirect
4. #14561918	C₂	semidirect
17. C₁₉×#487	C₄	semidirect
18. C₁₉×#486	C₄	semidirect
115. #487	Dic₁₉	semidirect
116. #486	Dic₁₉	semidirect
156. C₁₉	#9757	semidirect

H ≅ G/N

type

1. #14563766

C₂

semidirect

2. #14562199

C₂

semidirect

4. #14561918

C₂

semidirect

17. C₁₉×#487

C₄

semidirect

18. C₁₉×#486

C₄

semidirect

115. #487

Dic₁₉

semidirect

116. #486

Dic₁₉

semidirect

156. C₁₉

#9757

semidirect

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

subgroup	index
#14563766	2
#14562199	2
#14562195	2
#14561918	2
C₁₉×#3131	2
#9757	19

subgroup

index

C₁₉×#3131

Subgroups — #18081923

Conjugacy classes of subgroups

Complements

Maximal subgroups