Group #18082344 — subgroups

Subgroups — #18082344

Order 4864.

494 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11926949	C₂	1	1	yes	maximal, characteristic
2	#14564595	C₂	1	2	yes	maximal
3	#14564436	C₂	1	2	yes	maximal
4	C₂×#11926266	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	2	yes	—
7	#11926949	—	2	2	no	—
8	#11926949	C₄	1	4	yes	complemented
9	C₂×#10597275	—	2	2	no	—
10	C₂×#10597267	—	2	4	no	—
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926306	—	2	4	no	—
14	#11926266	—	2	2	no	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#384	C₂²	1	2	yes	—
17	C₁₉×#340	—	2	2	no	—
18	C₂²×Dic₃₈	—	2	2	no	—
19	C₂²×C₈×C₁₉	D₄	1	2	yes	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
27	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
28	#10597315	—	2	2	no	—
29	#10597315	—	2	2	no	—
30	#10597315	—	2	2	no	—
31	#10597315	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₉	D₄	1	2	yes	—
34	#10597275	—	2	8	no	—
35	#10597267	—	4	8	no	—
36	C₄×C₁₉⋊C₈	—	2	1	no	—
37	C₄×C₁₉⋊C₈	—	2	1	no	—
38	C₄×C₁₉⋊C₈	—	2	1	no	—
39	C₄×C₁₉⋊C₈	—	2	1	no	—
40	C₂²×C₄×C₁₉	—	4	2	no	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×Dic₁₉	—	4	2	no	—
45	C₂×Dic₃₈	—	2	4	no	—
46	C₂×Dic₃₈	—	4	4	no	—
47	C₂×Dic₃₈	—	4	4	no	—
48	C₂×Dic₃₈	—	4	2	no	—
49	C₂×C₈×C₁₉	—	2	4	no	—
50	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
51	C₄⋊C₄×C₁₉	—	4	4	no	—
52	C₄⋊C₄×C₁₉	—	4	4	no	—
53	C₄⋊C₄×C₁₉	—	4	4	no	—
54	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₄²×C₁₉	#41	1	1	yes	characteristic
57	C₄²×C₁₉	#41	1	1	yes	characteristic
58	C₄⋊Dic₁₉	—	2	4	no	—
59	C₄⋊Dic₁₉	—	2	4	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₄⋊Dic₁₉	—	4	2	no	—
62	C₂×C₁₉⋊C₈	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	2	2	no	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	C₂×C₁₉⋊C₈	—	2	4	no	—
66	C₂×C₁₉⋊C₈	D₈	1	4	yes	—
67	#9831	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	#127	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	8	2	no	—
70	C₂×C₄×C₁₉	—	8	2	no	—
71	C₂×C₄×C₁₉	—	8	2	no	—
72	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
79	C₂×C₄×C₁₉	#135	1	2	yes	—
80	C₂×C₄×C₁₉	#137	1	4	yes	—
81	C₂×C₄×C₁₉	#137	1	4	yes	—
82	C₂×Dic₁₉	—	4	4	no	—
83	C₂×Dic₁₉	—	8	2	no	—
84	C₂×Dic₁₉	—	8	2	no	—
85	Dic₃₈	—	4	8	no	—
86	Dic₃₈	—	8	4	no	—
87	C₈×C₁₉	—	2	4	no	—
88	C₁₉⋊C₈	—	2	4	no	—
89	C₁₉⋊C₈	—	4	2	no	—
90	C₂×#500	—	19	1	no	—
91	#1990	—	19	2	no	—
92	#1956	—	19	2	no	—
93	#1834	D₁₉	1	1	yes	characteristic
94	C₂×#322	—	19	1	no	—
95	C₂²×C₁₉	#390	1	1	yes	characteristic
96	C₂²×C₁₉	#493	1	1	yes	characteristic
97	C₂²×C₁₉	#495	1	1	yes	characteristic
98	C₂²×C₁₉	#497	1	2	yes	—
99	C₂²×C₁₉	#497	1	2	yes	—
100	C₄×C₁₉	—	16	2	no	—
101	C₄×C₁₉	#419	1	2	yes	—
102	C₄×C₁₉	C₄×D₈	1	2	yes	—
103	C₄×C₁₉	#441	1	2	yes	—
104	C₄×C₁₉	#466	1	2	yes	—
105	C₄×C₁₉	#470	1	2	yes	—
106	C₄×C₁₉	#491	1	2	yes	—
107	Dic₁₉	—	8	4	no	—
108	C₂×C₄⋊Q₈	—	19	2	no	—
109	#500	—	19	4	no	—
110	#500	—	38	2	no	—
111	C₂×#107	—	38	2	no	—
112	C₂×#103	—	38	4	no	—
113	C₂×C₄×C₈	—	19	1	no	—
114	C₂×C₄×C₈	—	19	1	no	—
115	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
116	#384	C₂×D₁₉	1	2	yes	—
117	#340	—	2	2	no	—
118	#340	—	38	4	no	—
119	#322	—	38	2	no	—
120	C₂×C₁₉	#1718	1	2	yes	—
121	C₂×C₁₉	#1722	1	2	yes	—
122	C₂×C₁₉	#1960	1	1	yes	characteristic
123	C₂×C₁₉	#1970	1	1	yes	characteristic
124	C₂×C₁₉	#1971	1	1	yes	characteristic
125	C₂²×Q₈	—	38	2	no	—
126	C₂²×C₈	—	19	2	no	—
127	C₂²×C₈	—	19	2	no	—
128	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
129	C₄⋊Q₈	—	19	4	no	—
130	C₄⋊Q₈	—	38	2	no	—
131	C₄⋊Q₈	—	38	2	no	—
132	C₄⋊Q₈	—	38	2	no	—
133	C₂×C₄⋊C₄	—	2	2	no	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄⋊C₄	—	38	2	no	—
137	C₂×C₄⋊C₄	—	38	2	no	—
138	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
139	#107	—	38	8	no	—
140	#103	—	76	8	no	—
141	C₄×C₈	—	38	1	no	—
142	C₄×C₈	—	38	1	no	—
143	C₄×C₈	—	38	1	no	—
144	C₄×C₈	—	38	1	no	—
145	C₄×C₈	C₄×D₁₉	1	2	yes	—
146	C₄×C₈	D₇₆	1	2	yes	—
147	C₁₉	#9831	1	1	yes	characteristic, complemented, Sylow
148	C₂×Q₈	—	38	4	no	—
149	C₂×Q₈	—	76	2	no	—
150	C₂×Q₈	—	76	4	no	—
151	C₂×Q₈	—	76	4	no	—
152	C₂²×C₄	—	4	2	no	—
153	C₂²×C₄	—	76	2	no	—
154	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
155	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
156	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	—	19	4	no	—
159	C₂×C₈	—	38	2	no	—
160	C₂×C₈	—	38	2	no	—
161	C₂×C₈	—	38	2	no	—
162	C₂×C₈	—	38	4	no	—
163	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
164	C₄⋊C₄	—	4	4	no	—
165	C₄⋊C₄	—	4	4	no	—
166	C₄⋊C₄	—	4	4	no	—
167	C₄⋊C₄	—	38	4	no	—
168	C₄⋊C₄	—	38	4	no	—
169	C₄⋊C₄	—	76	2	no	—
170	C₄⋊C₄	—	76	2	no	—
171	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
172	C₄²	C₂×D₇₆	1	1	yes	characteristic
173	C₄²	#64545	1	1	yes	characteristic
174	C₄²	#64545	1	1	yes	characteristic
175	C₂³	#10597386	1	1	yes	characteristic
176	Q₈	—	76	8	no	—
177	Q₈	—	152	4	no	—
178	C₂×C₄	—	8	2	no	—
179	C₂×C₄	—	8	2	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	76	4	no	—
182	C₂×C₄	—	152	2	no	—
183	C₂×C₄	—	152	2	no	—
184	C₂×C₄	#10597339	1	1	yes	characteristic
185	C₂×C₄	#10597339	1	1	yes	characteristic
186	C₂×C₄	#10597341	1	1	yes	characteristic
187	C₂×C₄	#10597341	1	1	yes	characteristic
188	C₂×C₄	D₈×D₁₉	1	2	yes	—
189	C₂×C₄	#10597361	1	4	yes	—
190	C₂×C₄	#10597365	1	2	yes	—
191	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
192	C₂×C₄	#10597393	1	1	yes	characteristic
193	C₂×C₄	#10597397	1	4	yes	—
194	C₈	—	2	4	no	—
195	C₈	—	38	4	no	—
196	C₈	—	76	2	no	—
197	C₂²	#11926445	1	1	yes	characteristic
198	C₂²	#11926919	1	1	yes	characteristic
199	C₂²	#11926929	1	1	yes	characteristic
200	C₂²	#11926935	1	2	yes	—
201	C₂²	#11926939	1	2	yes	—
202	C₄	—	16	2	no	—
203	C₄	—	152	4	no	—
204	C₄	#11926552	1	2	yes	—
205	C₄	#11926626	1	2	yes	—
206	C₄	#11926650	1	2	yes	—
207	C₄	#11926781	1	2	yes	—
208	C₄	#11926803	1	2	yes	—
209	C₄	#11926914	1	2	yes	—
210	C₂	#14563284	1	2	yes	—
211	C₂	#14563308	1	2	yes	—
212	C₂	#14564454	1	1	yes	characteristic
213	C₂	#14564499	1	1	yes	characteristic
214	C₂	#14564504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926949

C₂

yes

maximal, characteristic

#14564595

C₂

yes

maximal

#14564436

C₂

yes

maximal

C₂×#11926266

C₂

yes

maximal, characteristic

C₁₉×#1834

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

#11926949

—

#11926949

C₄

yes

complemented

C₂×#10597275

—

C₂×#10597267

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

#11926306

—

#11926266

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₁₉×#340

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂²×C₁₉⋊C₈

D₄

yes

—

—

—

—

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#10597275

—

#10597267

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₈

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

C₂×#322

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

—

100

C₄×C₁₉

—

101

C₄×C₁₉

#419

yes

—

102

C₄×C₁₉

C₄×D₈

yes

—

103

C₄×C₁₉

#441

yes

—

104

C₄×C₁₉

#466

yes

—

105

C₄×C₁₉

#470

yes

—

106

C₄×C₁₉

#491

yes

—

107

Dic₁₉

—

108

C₂×C₄⋊Q₈

—

109

#500

—

110

#500

—

111

C₂×#107

—

112

C₂×#103

—

113

C₂×C₄×C₈

—

114

C₂×C₄×C₈

—

115

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

116

#384

C₂×D₁₉

yes

—

117

#340

—

118

#340

—

119

#322

—

120

C₂×C₁₉

#1718

yes

—

121

C₂×C₁₉

#1722

yes

—

122

C₂×C₁₉

#1960

yes

characteristic

123

C₂×C₁₉

#1970

yes

characteristic

124

C₂×C₁₉

#1971

yes

characteristic

125

C₂²×Q₈

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₂²×C₈

C₂²⋊D₁₉

yes

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄²

C₂²×D₁₉

yes

characteristic

139

#107

—

140

#103

—

141

C₄×C₈

—

142

C₄×C₈

—

143

C₄×C₈

—

144

C₄×C₈

—

145

C₄×C₈

C₄×D₁₉

yes

—

146

C₄×C₈

D₇₆

yes

—

147

C₁₉

#9831

yes

characteristic, complemented, Sylow

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

D₄×D₁₉

yes

characteristic

155

C₂²×C₄

D₄×D₁₉

yes

characteristic

156

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄²

C₂×C₄×D₁₉

yes

characteristic

172

C₄²

C₂×D₇₆

yes

characteristic

173

C₄²

#64545

yes

characteristic

174

C₄²

#64545

yes

characteristic

175

C₂³

#10597386

yes

characteristic

176

Q₈

—

177

Q₈

—

152

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

152

—

183

C₂×C₄

—

152

—

184

C₂×C₄

#10597339

yes

characteristic

185

C₂×C₄

#10597339

yes

characteristic

186

C₂×C₄

#10597341

yes

characteristic

187

C₂×C₄

#10597341

yes

characteristic

188

C₂×C₄

D₈×D₁₉

yes

—

189

C₂×C₄

#10597361

yes

—

190

C₂×C₄

#10597365

yes

—

191

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

192

C₂×C₄

#10597393

yes

characteristic

193

C₂×C₄

#10597397

yes

—

194

C₈

—

195

C₈

—

196

C₈

—

197

C₂²

#11926445

yes

characteristic

198

C₂²

#11926919

yes

characteristic

199

C₂²

#11926929

yes

characteristic

200

C₂²

#11926935

yes

—

201

C₂²

#11926939

yes

—

202

C₄

—

203

C₄

—

152

—

204

C₄

#11926552

yes

—

205

C₄

#11926626

yes

—

206

C₄

#11926650

yes

—

207

C₄

#11926781

yes

—

208

C₄

#11926803

yes

—

209

C₄

#11926914

yes

—

210

C₂

#14563284

yes

—

211

C₂

#14563308

yes

—

212

C₂

#14564454

yes

characteristic

213

C₂

#14564499

yes

characteristic

214

C₂

#14564504

yes

characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1834	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1834	D₁₉
hypocenter	C₁₉	#9831
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1834

C₂

socle, prime radical

C₂³×C₁₉

#127

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
8. #11926949	C₄	semidirect
147. C₁₉	#9831	semidirect

H ≅ G/N

type

8. #11926949

C₄

semidirect

147. C₁₉

#9831

semidirect

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

subgroup	index
C₂×#11926949	2
#14564595	2
#14564436	2
C₂×#11926266	2
C₁₉×#1834	2
#9831	19

subgroup

index

C₁₉×#1834

Subgroups — #18082344

Conjugacy classes of subgroups

Complements

Maximal subgroups