Group #18073552 — subgroups

Subgroups — #18073552

Order 4864.

436 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 143 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	#14562297	C₂	1	1	yes	maximal, characteristic
2	#14562227	C₂	1	1	yes	maximal, characteristic
3	#14561924	C₂	1	2	yes	maximal, complemented
4	#14561524	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₄×#64520	C₂²	1	2	yes	—
8	#11926293	C₄	1	2	yes	—
9	#11926288	C₄	1	2	yes	—
10	#11926284	C₄	1	4	yes	—
11	#11926266	—	2	2	no	—
12	#11926265	—	2	2	no	—
13	C₂×C₁₉×#131	C₄	1	2	yes	—
14	C₁₉×#532	C₂²	1	1	yes	characteristic
15	C₁₉×#436	—	2	2	no	—
16	C₈×D₄×C₁₉	—	2	2	no	—
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₁₉×#408	C₄	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
21	C₁₉×#131	—	4	4	no	—
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
28	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
29	C₁₉×#124	C₂×C₄	1	2	yes	—
30	C₁₉×#121	—	2	2	no	—
31	C₄×D₄×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×#64520	—	2	2	no	—
34	C₁₉×C₄⋊C₈	—	2	2	no	—
35	C₁₉×C₂²⋊C₈	—	2	4	no	—
36	C₄×C₈×C₁₉	D₄	1	2	yes	—
37	C₄×C₈×C₁₉	D₄	1	2	yes	—
38	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	4	yes	—
40	#10597260	C₂×C₄	1	4	yes	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₄×C₁₉⋊C₈	—	2	2	no	—
43	#41×C₁₉	—	4	2	no	—
44	#41×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	C₄²	1	2	yes	—
46	C₂×D₄×C₁₉	—	2	2	no	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	C₄²	1	2	yes	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	#41	1	2	yes	—
52	M₁₆×C₁₉	—	4	4	no	—
53	M₁₆×C₁₉	—	4	2	no	—
54	C₂×C₈×C₁₉	—	2	2	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	4	1	no	—
57	C₂×C₈×C₁₉	—	4	4	no	—
58	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	2	yes	—
66	#64520	—	4	4	no	—
67	C₂×C₁₉⋊C₈	—	2	4	no	—
68	C₂×C₁₉⋊C₈	—	2	4	no	—
69	#8243	—	19	1	no	maximal, Sylow
70	C₂³×C₁₉	—	2	2	no	—
71	C₂³×C₁₉	#117	1	1	yes	characteristic
72	Q₈×C₁₉	—	4	2	no	—
73	D₄×C₁₉	—	4	2	no	—
74	D₄×C₁₉	—	4	4	no	—
75	D₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	—	2	1	no	—
78	C₂×C₄×C₁₉	—	2	4	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
86	C₈×C₁₉	—	2	1	no	—
87	C₈×C₁₉	—	2	2	no	—
88	C₈×C₁₉	—	4	2	no	—
89	C₈×C₁₉	#100	1	2	yes	—
90	C₁₉⋊C₈	—	4	4	no	—
91	C₁₉⋊C₈	—	4	4	no	—
92	#2931	D₁₉	1	1	yes	characteristic
93	#1543	—	19	1	no	—
94	#1525	—	19	1	no	—
95	#1451	—	19	2	no	—
96	#1299	—	19	2	no	—
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	—	2	2	no	—
99	C₂²×C₁₉	—	4	2	no	—
100	C₂²×C₁₉	—	4	4	no	—
101	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
102	C₄×C₁₉	—	2	1	no	—
103	C₄×C₁₉	—	2	2	no	—
104	C₄×C₁₉	—	4	2	no	—
105	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
106	C₄×C₁₉	#413	1	1	yes	characteristic
107	C₄×C₁₉	#444	1	4	yes	—
108	C₂×#131	Dic₁₉	1	2	yes	—
109	#532	C₂×D₁₉	1	1	yes	characteristic
110	#436	—	2	2	no	—
111	C₈×D₄	—	2	2	no	—
112	#431	—	19	2	no	—
113	#423	C₂×D₁₉	1	1	yes	characteristic
114	#408	Dic₁₉	1	2	yes	—
115	C₄×M₁₆	—	19	2	no	—
116	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
117	#333	—	19	2	no	—
118	#331	—	19	2	no	—
119	#329	—	19	4	no	—
120	#322	—	38	2	no	—
121	#322	—	38	2	no	—
122	C₂×C₁₉	—	4	1	no	—
123	C₂×C₁₉	—	8	2	no	—
124	C₂×C₁₉	C₄×#100	1	1	yes	characteristic
125	C₂×C₁₉	#1765	1	2	yes	—
126	C₂×#41	C₂×Dic₁₉	1	2	yes	—
127	#131	—	4	4	no	—
128	C₂×M₁₆	—	2	2	no	—
129	C₂×M₁₆	—	38	2	no	—
130	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
131	C₂²×C₈	—	2	2	no	—
132	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
133	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
134	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
135	#127	C₄×D₁₉	1	1	yes	characteristic
136	#124	C₄×D₁₉	1	2	yes	—
137	#121	—	2	2	no	—
138	C₄×D₄	—	2	2	no	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	C₄⋊C₈	—	2	2	no	—
141	C₄⋊C₈	—	19	4	no	—
142	C₂²⋊C₈	—	2	4	no	—
143	C₂²⋊C₈	—	38	2	no	—
144	#97	—	19	4	no	—
145	C₄×C₈	—	38	2	no	—
146	C₄×C₈	—	38	2	no	—
147	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
148	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
149	C₁₉	#8243	1	1	yes	characteristic, complemented, Sylow
150	#41	—	4	2	no	—
151	#41	—	4	2	no	—
152	C₂×Q₈	C₄×Dic₁₉	1	2	yes	—
153	C₂×D₄	—	2	2	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	C₄×Dic₁₉	1	2	yes	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	#64541	1	2	yes	—
158	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
159	M₁₆	—	4	4	no	—
160	M₁₆	—	4	2	no	—
161	M₁₆	—	76	4	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	4	1	no	—
165	C₂×C₈	—	4	4	no	—
166	C₂×C₈	—	38	4	no	—
167	C₂×C₈	—	38	4	no	—
168	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
169	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
170	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
171	C₄⋊C₄	—	2	2	no	—
172	C₂²⋊C₄	—	2	4	no	—
173	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
174	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
175	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
176	C₂³	—	2	2	no	—
177	C₂³	#10597372	1	1	yes	characteristic
178	Q₈	—	4	2	no	—
179	D₄	—	4	2	no	—
180	D₄	—	4	4	no	—
181	D₄	—	4	4	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
189	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
190	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
191	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
192	C₈	—	2	2	no	—
193	C₈	—	2	1	no	—
194	C₈	—	4	2	no	—
195	C₈	—	76	4	no	—
196	C₈	—	76	4	no	—
197	C₈	#10597290	1	2	yes	—
198	C₂²	—	2	1	no	—
199	C₂²	—	2	2	no	—
200	C₂²	—	4	2	no	—
201	C₂²	—	4	4	no	—
202	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
203	C₄	—	2	1	no	—
204	C₄	—	2	2	no	—
205	C₄	—	4	2	no	—
206	C₄	C₂×#10597290	1	1	yes	characteristic
207	C₄	#11926528	1	1	yes	characteristic
208	C₄	#11926664	1	4	yes	—
209	C₂	—	4	1	no	—
210	C₂	—	8	2	no	—
211	C₂	C₄×#10597290	1	1	yes	characteristic
212	C₂	#14563477	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14562297

C₂

yes

maximal, characteristic

#14562227

C₂

yes

maximal, characteristic

#14561924

C₂

yes

maximal, complemented

#14561524

C₂

yes

maximal, complemented

C₁₉×#2931

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₄×#64520

C₂²

yes

—

#11926293

C₄

yes

—

#11926288

C₄

yes

—

#11926284

C₄

yes

—

#11926266

—

#11926265

—

C₂×C₁₉×#131

C₄

yes

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#436

—

C₈×D₄×C₁₉

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#408

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

C₂×C₄

yes

—

C₁₉×#131

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

C₂×C₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂×C₄

yes

—

#10597260

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₄²

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄²

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8243

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#117

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#100

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2931

D₁₉

yes

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₄×C₁₉

—

105

C₄×C₁₉

C₂×#100

yes

characteristic

106

C₄×C₁₉

#413

yes

characteristic

107

C₄×C₁₉

#444

yes

—

108

C₂×#131

Dic₁₉

yes

—

109

#532

C₂×D₁₉

yes

characteristic

110

#436

—

111

C₈×D₄

—

112

#431

—

113

#423

C₂×D₁₉

yes

characteristic

114

#408

Dic₁₉

yes

—

115

C₄×M₁₆

—

116

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

117

#333

—

118

#331

—

119

#329

—

120

#322

—

121

#322

—

122

C₂×C₁₉

—

123

C₂×C₁₉

—

124

C₂×C₁₉

C₄×#100

yes

characteristic

125

C₂×C₁₉

#1765

yes

—

126

C₂×#41

C₂×Dic₁₉

yes

—

127

#131

—

128

C₂×M₁₆

—

129

C₂×M₁₆

—

130

C₂×M₁₆

C₂×Dic₁₉

yes

—

131

C₂²×C₈

—

132

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

133

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

134

C₄⋊Q₈

C₄×D₁₉

yes

characteristic

135

#127

C₄×D₁₉

yes

characteristic

136

#124

C₄×D₁₉

yes

—

137

#121

—

138

C₄×D₄

—

139

C₂×C₄²

C₂²×D₁₉

yes

characteristic

140

C₄⋊C₈

—

141

C₄⋊C₈

—

142

C₂²⋊C₈

—

143

C₂²⋊C₈

—

144

#97

—

145

C₄×C₈

—

146

C₄×C₈

—

147

C₄×C₈

C₂²⋊D₁₉

yes

—

148

C₄×C₈

C₂²⋊D₁₉

yes

—

149

C₁₉

#8243

yes

characteristic, complemented, Sylow

150

#41

—

151

#41

—

152

C₂×Q₈

C₄×Dic₁₉

yes

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

C₄×Dic₁₉

yes

—

156

C₂²×C₄

—

157

C₂²×C₄

#64541

yes

—

158

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

159

M₁₆

—

160

M₁₆

—

161

M₁₆

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

C₂²⋊Dic₁₉

yes

—

169

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

170

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

171

C₄⋊C₄

—

172

C₂²⋊C₄

—

173

C₄²

C₂×C₄×D₁₉

yes

characteristic

174

C₄²

C₂×C₄×D₁₉

yes

characteristic

175

C₄²

C₂×C₂²⋊D₁₉

yes

—

176

C₂³

—

177

C₂³

#10597372

yes

characteristic

178

Q₈

—

179

D₄

—

180

D₄

—

181

D₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

189

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

190

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

191

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

192

C₈

—

193

C₈

—

194

C₈

—

195

C₈

—

196

C₈

—

197

C₈

#10597290

yes

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

C₄×C₂²⋊Dic₁₉

yes

characteristic

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

C₂×#10597290

yes

characteristic

207

C₄

#11926528

yes

characteristic

208

C₄

#11926664

yes

—

209

C₂

—

210

C₂

—

211

C₂

C₄×#10597290

yes

characteristic

212

C₂

#14563477

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2931	C₂
socle	C₂²×C₁₉	C₄×C₂²⋊C₄
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2931	D₁₉
hypocenter	C₁₉	#8243
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2931

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2931

C₂

socle

C₂²×C₁₉

C₄×C₂²⋊C₄

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2931

N	H ≅ G/N	type
3. #14561924	C₂	semidirect
4. #14561524	C₂	semidirect
149. C₁₉	#8243	semidirect

H ≅ G/N

type

3. #14561924

C₂

semidirect

4. #14561524

C₂

semidirect

149. C₁₉

#8243

semidirect

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

subgroup	index
#14562297	2
#14562227	2
#14561924	2
#14561524	2
C₁₉×#2931	2
#8243	19

subgroup

index

C₁₉×#2931

Subgroups — #18073552

Conjugacy classes of subgroups

Complements

Maximal subgroups