Group #18085379 — subgroups

Subgroups — #18085379

Order 4864.

554 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11926894	C₂	1	2	yes	maximal
2	#14564597	C₂	1	2	yes	maximal
3	#14564437	C₂	1	1	yes	maximal, characteristic
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#498	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	#11926894	—	2	4	no	—
8	#11926894	—	2	4	no	—
9	C₂×#10597273	—	2	2	no	—
10	C₂×#10597292	—	2	4	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
12	#11926414	C₂²	1	1	yes	characteristic
13	#11926306	—	2	4	no	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₁₉×#498	—	2	4	no	—
16	C₂×C₁₉×#106	—	2	2	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	—	2	2	no	—
19	C₂²×Dic₃₈	—	2	1	no	—
20	C₂²×C₈×C₁₉	D₄	1	2	yes	—
21	C₁₉×C₄⋊Q₈	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	D₄	1	4	yes	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	2	no	—
31	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
32	#10597315	—	2	2	no	—
33	#10597315	—	2	1	no	—
34	#10597315	D₄	1	2	yes	—
35	C₁₉×#106	—	2	8	no	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	#10597292	—	2	16	no	—
38	#10597273	—	4	4	no	—
39	C₄×C₁₉⋊C₈	—	2	2	no	—
40	C₄×C₁₉⋊C₈	—	2	2	no	—
41	C₂×Q₈×C₁₉	—	2	4	no	—
42	C₂×Q₈×C₁₉	—	4	2	no	—
43	C₂×Q₈×C₁₉	—	4	4	no	—
44	C₂×Q₈×C₁₉	—	4	4	no	—
45	C₂²×C₄×C₁₉	—	4	2	no	—
46	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×Dic₁₉	—	4	1	no	—
49	C₂²×Dic₁₉	—	4	1	no	—
50	C₂×Dic₃₈	—	2	2	no	—
51	C₂×Dic₃₈	—	4	2	no	—
52	C₂×Dic₃₈	—	4	2	no	—
53	C₂×Dic₃₈	—	4	1	no	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
57	C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₁₉	C₂×D₄	1	2	yes	—
63	C₄²×C₁₉	#41	1	1	yes	characteristic
64	C₄⋊Dic₁₉	—	2	4	no	—
65	C₄⋊Dic₁₉	—	4	2	no	—
66	C₄⋊Dic₁₉	—	4	2	no	—
67	C₄⋊Dic₁₉	—	4	4	no	—
68	C₂×C₁₉⋊C₈	—	2	4	no	—
69	C₂×C₁₉⋊C₈	—	2	4	no	—
70	C₂×C₁₉⋊C₈	—	2	4	no	—
71	#10317	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	#127	1	1	yes	characteristic
73	Q₈×C₁₉	—	4	8	no	—
74	Q₈×C₁₉	—	8	4	no	—
75	C₂×C₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	8	2	no	—
77	C₂×C₄×C₁₉	—	8	2	no	—
78	C₂×C₄×C₁₉	#120	1	2	yes	—
79	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
80	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
81	C₂×C₄×C₁₉	#121	1	2	yes	—
82	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
83	C₂×C₄×C₁₉	#135	1	4	yes	—
84	C₂×C₄×C₁₉	#137	1	2	yes	—
85	C₂×C₄×C₁₉	#137	1	4	yes	—
86	C₂×Dic₁₉	—	4	2	no	—
87	C₂×Dic₁₉	—	8	1	no	—
88	C₂×Dic₁₉	—	8	1	no	—
89	C₂×Dic₁₉	—	8	1	no	—
90	C₂×Dic₁₉	—	8	2	no	—
91	Dic₃₈	—	4	4	no	—
92	Dic₃₈	—	8	2	no	—
93	C₈×C₁₉	—	2	4	no	—
94	C₁₉⋊C₈	—	4	4	no	—
95	C₂×#498	D₁₉	1	1	yes	characteristic
96	C₂×#487	—	19	2	no	—
97	#1990	—	19	2	no	—
98	#1956	—	19	1	no	—
99	#1273	—	19	1	no	—
100	C₂²×C₁₉	#392	1	1	yes	characteristic
101	C₂²×C₁₉	#492	1	1	yes	characteristic
102	C₂²×C₁₉	#495	1	2	yes	—
103	C₂²×C₁₉	#497	1	2	yes	—
104	C₂²×C₁₉	#497	1	1	yes	characteristic
105	C₄×C₁₉	—	8	4	no	—
106	C₄×C₁₉	#448	1	2	yes	—
107	C₄×C₁₉	#452	1	4	yes	—
108	C₄×C₁₉	#461	1	2	yes	—
109	C₄×C₁₉	#464	1	4	yes	—
110	Dic₁₉	—	8	2	no	—
111	Dic₁₉	—	16	1	no	—
112	C₂×C₄⋊Q₈	—	19	1	no	—
113	C₂×C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
114	#498	—	2	4	no	—
115	#487	—	38	4	no	—
116	#487	—	38	4	no	—
117	C₂×#106	—	2	2	no	—
118	C₂×#103	—	38	4	no	—
119	C₂×#103	—	38	2	no	—
120	C₂×C₄×C₈	—	19	2	no	—
121	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
122	#384	—	19	1	no	—
123	#340	—	38	4	no	—
124	C₂×C₁₉	#1708	1	1	yes	characteristic
125	C₂×C₁₉	#1716	1	1	yes	characteristic
126	C₂×C₁₉	#1718	1	2	yes	—
127	C₂×C₁₉	#2013	1	1	yes	characteristic
128	C₂×C₁₉	#2015	1	2	yes	—
129	C₂²×Q₈	—	2	2	no	—
130	C₂²×Q₈	—	38	1	no	—
131	C₂²×C₈	—	19	4	no	—
132	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
133	C₄⋊Q₈	—	2	2	no	—
134	C₄⋊Q₈	—	2	2	no	—
135	C₄⋊Q₈	—	2	2	no	—
136	C₄⋊Q₈	—	19	2	no	—
137	C₄⋊Q₈	—	38	1	no	—
138	C₄⋊Q₈	—	38	2	no	—
139	C₄⋊Q₈	C₂²⋊D₁₉	1	4	yes	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	38	2	no	—
143	C₂×C₄⋊C₄	—	38	2	no	—
144	C₂×C₄⋊C₄	—	38	1	no	—
145	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
146	#106	—	2	8	no	—
147	#103	—	38	16	no	—
148	#103	—	76	4	no	—
149	C₄×C₈	—	2	2	no	—
150	C₄×C₈	—	38	2	no	—
151	C₄×C₈	—	38	2	no	—
152	C₁₉	#10317	1	1	yes	characteristic, complemented, Sylow
153	C₂×Q₈	—	2	4	no	—
154	C₂×Q₈	—	4	2	no	—
155	C₂×Q₈	—	4	4	no	—
156	C₂×Q₈	—	4	4	no	—
157	C₂×Q₈	—	38	2	no	—
158	C₂×Q₈	—	76	1	no	—
159	C₂×Q₈	—	76	2	no	—
160	C₂×Q₈	—	76	2	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	76	1	no	—
163	C₂²×C₄	—	76	1	no	—
164	C₂²×C₄	D₄×D₁₉	1	2	yes	—
165	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	38	4	no	—
169	C₂×C₈	—	38	4	no	—
170	C₂×C₈	—	38	4	no	—
171	C₂×C₈	#64527	1	4	yes	—
172	C₄⋊C₄	—	2	4	no	—
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	38	4	no	—
177	C₄⋊C₄	—	76	2	no	—
178	C₄⋊C₄	—	76	2	no	—
179	C₄⋊C₄	—	76	4	no	—
180	C₄²	D₄×D₁₉	1	1	yes	characteristic
181	C₄²	#64543	1	1	yes	characteristic
182	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
183	C₂³	#10597386	1	1	yes	characteristic
184	Q₈	—	4	8	no	—
185	Q₈	—	8	4	no	—
186	Q₈	—	76	4	no	—
187	Q₈	—	152	2	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	2	no	—
191	C₂×C₄	—	76	2	no	—
192	C₂×C₄	—	152	1	no	—
193	C₂×C₄	—	152	2	no	—
194	C₂×C₄	—	152	1	no	—
195	C₂×C₄	—	152	1	no	—
196	C₂×C₄	#10597361	1	4	yes	—
197	C₂×C₄	#10597362	1	4	yes	—
198	C₂×C₄	#10597383	1	2	yes	—
199	C₂×C₄	#10597384	1	1	yes	characteristic
200	C₂×C₄	#10597385	1	2	yes	—
201	C₂×C₄	C₂×#64527	1	2	yes	—
202	C₂×C₄	#10597388	1	2	yes	—
203	C₂×C₄	#10597399	1	1	yes	characteristic
204	C₈	—	2	4	no	—
205	C₈	—	76	4	no	—
206	C₂²	#11926452	1	1	yes	characteristic
207	C₂²	#11926918	1	1	yes	characteristic
208	C₂²	#11926925	1	2	yes	—
209	C₂²	#11926935	1	2	yes	—
210	C₂²	#11926936	1	1	yes	characteristic
211	C₄	—	8	4	no	—
212	C₄	—	304	1	no	—
213	C₄	—	152	2	no	—
214	C₄	#11926683	1	2	yes	—
215	C₄	#11926703	1	4	yes	—
216	C₄	#11926746	1	2	yes	—
217	C₄	#11926764	1	4	yes	—
218	C₂	#14563237	1	1	yes	characteristic
219	C₂	#14563269	1	1	yes	characteristic
220	C₂	#14563279	1	2	yes	—
221	C₂	#14564718	1	1	yes	characteristic
222	C₂	#14564727	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926894

C₂

yes

maximal

#14564597

C₂

yes

maximal

#14564437

C₂

yes

maximal, characteristic

C₁₉⋊#1273

C₂

yes

maximal, characteristic

C₂×C₁₉×#498

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

—

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

characteristic

#11926306

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#498

—

C₂×C₁₉×#106

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

#10597315

—

#10597315

—

#10597315

D₄

yes

—

C₁₉×#106

—

C₄×C₈×C₁₉

—

#10597292

—

#10597273

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₂×#498

D₁₉

yes

—

—

—

—

100

C₂²×C₁₉

#392

yes

characteristic

101

C₂²×C₁₉

#492

yes

characteristic

102

C₂²×C₁₉

#495

yes

—

103

C₂²×C₁₉

#497

yes

—

104

C₂²×C₁₉

#497

yes

characteristic

105

C₄×C₁₉

—

106

C₄×C₁₉

#448

yes

—

107

C₄×C₁₉

#452

yes

—

108

C₄×C₁₉

#461

yes

—

109

C₄×C₁₉

#464

yes

—

110

Dic₁₉

—

111

Dic₁₉

—

112

C₂×C₄⋊Q₈

—

113

C₂×C₄⋊Q₈

C₂×D₁₉

yes

—

114

#498

—

115

#487

—

116

#487

—

117

C₂×#106

—

118

C₂×#103

—

119

C₂×#103

—

120

C₂×C₄×C₈

—

121

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

122

#384

—

123

#340

—

124

C₂×C₁₉

#1708

yes

characteristic

125

C₂×C₁₉

#1716

yes

characteristic

126

C₂×C₁₉

#1718

yes

—

127

C₂×C₁₉

#2013

yes

characteristic

128

C₂×C₁₉

#2015

yes

—

129

C₂²×Q₈

—

130

C₂²×Q₈

—

131

C₂²×C₈

—

132

C₂²×C₈

C₂²⋊D₁₉

yes

—

133

C₄⋊Q₈

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄²

C₂²×D₁₉

yes

characteristic

146

#106

—

147

#103

—

148

#103

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₁₉

#10317

yes

characteristic, complemented, Sylow

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

D₄×D₁₉

yes

—

165

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

#64527

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄²

D₄×D₁₉

yes

characteristic

181

C₄²

#64543

yes

characteristic

182

C₄²

C₂×C₂²⋊D₁₉

yes

—

183

C₂³

#10597386

yes

characteristic

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

152

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

152

—

193

C₂×C₄

—

152

—

194

C₂×C₄

—

152

—

195

C₂×C₄

—

152

—

196

C₂×C₄

#10597361

yes

—

197

C₂×C₄

#10597362

yes

—

198

C₂×C₄

#10597383

yes

—

199

C₂×C₄

#10597384

yes

characteristic

200

C₂×C₄

#10597385

yes

—

201

C₂×C₄

C₂×#64527

yes

—

202

C₂×C₄

#10597388

yes

—

203

C₂×C₄

#10597399

yes

characteristic

204

C₈

—

205

C₈

—

206

C₂²

#11926452

yes

characteristic

207

C₂²

#11926918

yes

characteristic

208

C₂²

#11926925

yes

—

209

C₂²

#11926935

yes

—

210

C₂²

#11926936

yes

characteristic

211

C₄

—

212

C₄

—

304

—

213

C₄

—

152

—

214

C₄

#11926683

yes

—

215

C₄

#11926703

yes

—

216

C₄

#11926746

yes

—

217

C₄

#11926764

yes

—

218

C₂

#14563237

yes

characteristic

219

C₂

#14563269

yes

characteristic

220

C₂

#14563279

yes

—

221

C₂

#14564718

yes

characteristic

222

C₂

#14564727

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#498	C₂
socle, prime radical	C₂³×C₁₉	#127
hypercenter	C₂×#498	D₁₉
hypocenter	C₁₉	#10317
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#498

subgroup

G/H

center

C₂³

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#498

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#498

N	H ≅ G/N	type
152. C₁₉	#10317	semidirect

H ≅ G/N

type

152. C₁₉

#10317

semidirect

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

subgroup	index
C₂×#11926894	2
#14564597	2
#14564437	2
C₁₉⋊#1273	2
C₂×C₁₉×#498	2
#10317	19

subgroup

index

C₂×#11926894

#14564597

#14564437

C₁₉⋊#1273

C₂×C₁₉×#498

#10317

Subgroups — #18085379

Conjugacy classes of subgroups

Complements

Maximal subgroups