Group #18076182 — subgroups

Subgroups — #18076182

Order 4864.

310 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 123 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	#14563323	C₂	1	1	yes	maximal, characteristic
2	#14562381	C₂	1	2	yes	maximal
3	#14561480	C₂	1	1	yes	maximal, characteristic
4	#14561463	C₂	1	2	yes	maximal
5	C₁₉×#1281	C₂	1	1	yes	maximal, characteristic
6	#11926597	C₂²	1	2	yes	—
7	C₂×#10597272	C₄	1	1	yes	characteristic
8	C₂×#10597272	C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₉	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₉	C₄	1	1	yes	characteristic
12	#11926390	C₂²	1	1	yes	characteristic
13	#11926296	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	C₁₉×#431	C₂²	1	2	yes	—
16	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₁₉×C₄⋊C₈	—	2	2	no	—
25	C₁₉×C₂²⋊C₈	—	2	2	no	—
26	C₁₉×#97	—	2	2	no	—
27	C₄×C₈×C₁₉	—	2	2	no	—
28	C₁₉⋊#95	—	2	2	no	—
29	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
30	#10597272	—	2	2	no	—
31	#10597272	—	2	2	no	—
32	C₈×Dic₁₉	—	2	2	no	—
33	C₈×Dic₁₉	C₈	1	4	yes	complemented
34	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
35	C₄×C₁₉⋊C₈	—	2	2	no	—
36	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
37	C₄×C₁₉⋊C₈	D₄	1	1	yes	characteristic
38	C₄×C₁₉⋊C₈	Q₈	1	1	yes	characteristic
39	C₄×C₁₉⋊C₈	Q₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	#41	1	2	yes	—
42	C₂²×Dic₁₉	—	2	1	no	—
43	C₂²×Dic₁₉	—	2	1	no	—
44	C₂×C₈×C₁₉	—	2	1	no	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	—	2	1	no	—
47	C₂×C₈×C₁₉	—	2	1	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
50	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
51	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
53	C₄²×C₁₉	#41	1	2	yes	—
54	C₄×Dic₁₉	—	2	1	no	—
55	C₄×Dic₁₉	—	2	1	no	—
56	C₄×Dic₁₉	C₂×C₈	1	2	yes	—
57	C₄×Dic₁₉	M₁₆	1	2	yes	—
58	C₂×C₁₉⋊C₈	—	2	1	no	—
59	C₂×C₁₉⋊C₈	—	2	1	no	—
60	C₂×C₁₉⋊C₈	—	4	2	no	—
61	C₂×C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₁₉⋊C₈	C₂×C₈	1	2	yes	—
66	C₂×C₁₉⋊C₈	M₁₆	1	2	yes	—
67	#8780	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	#117	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
72	C₂×C₄×C₁₉	#124	1	2	yes	—
73	C₂×C₄×C₁₉	#125	1	2	yes	—
74	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
78	C₂×Dic₁₉	—	2	2	no	—
79	C₂×Dic₁₉	—	2	2	no	—
80	C₂×Dic₁₉	—	4	2	no	—
81	C₂×Dic₁₉	—	4	2	no	—
82	C₈×C₁₉	—	2	2	no	—
83	C₈×C₁₉	—	2	2	no	—
84	C₈×C₁₉	—	8	2	no	—
85	C₁₉⋊C₈	—	2	1	no	—
86	C₁₉⋊C₈	—	2	1	no	—
87	C₁₉⋊C₈	—	8	2	no	—
88	C₁₉⋊C₈	C₄⋊C₈	1	2	yes	—
89	C₁₉⋊C₈	C₄⋊C₈	1	2	yes	—
90	#1726	—	19	1	no	—
91	#1564	—	19	2	no	—
92	#1281	—	19	1	no	—
93	#1281	D₁₉	1	1	yes	characteristic
94	#1274	—	19	2	no	—
95	C₂²×C₁₉	—	2	2	no	—
96	C₂²×C₁₉	#382	1	1	yes	characteristic
97	C₂²×C₁₉	#431	1	1	yes	characteristic
98	C₂²×C₁₉	#432	1	1	yes	characteristic
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	2	2	no	—
101	C₄×C₁₉	C₂×C₄⋊C₈	1	1	yes	characteristic
102	C₄×C₁₉	#423	1	1	yes	characteristic
103	C₄×C₁₉	#431	1	1	yes	characteristic
104	C₄×C₁₉	#432	1	1	yes	characteristic
105	Dic₁₉	—	4	2	no	—
106	Dic₁₉	—	4	2	no	—
107	#431	—	19	2	no	—
108	#431	C₂×D₁₉	1	2	yes	—
109	C₂×#97	—	19	1	no	—
110	C₂×#97	—	19	1	no	—
111	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
112	C₂×C₄×C₈	—	19	1	no	—
113	C₂×C₄×C₈	—	19	1	no	—
114	C₂×C₄×C₈	—	19	1	no	—
115	#376	—	19	1	no	—
116	#335	—	38	2	no	—
117	#334	—	38	2	no	—
118	C₂×C₁₉	—	2	1	no	—
119	C₂×C₁₉	—	2	1	no	—
120	C₂×C₁₉	#1831	1	1	yes	characteristic
121	C₂×C₁₉	#1833	1	2	yes	—
122	C₂²×C₈	—	19	1	no	—
123	C₂²×C₈	—	19	1	no	—
124	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
125	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
126	C₂×C₄²	—	19	1	no	—
127	C₂×C₄²	—	19	1	no	—
128	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
129	C₄⋊C₈	—	2	2	no	—
130	C₄⋊C₈	—	38	2	no	—
131	C₂²⋊C₈	—	2	2	no	—
132	C₂²⋊C₈	—	38	2	no	—
133	#97	—	2	2	no	—
134	#97	—	38	2	no	—
135	#97	—	38	2	no	—
136	C₄×C₈	—	2	2	no	—
137	C₄×C₈	—	19	4	no	—
138	C₄×C₈	—	19	1	no	—
139	C₄×C₈	—	19	1	no	—
140	C₄×C₈	—	19	1	no	—
141	C₄×C₈	—	19	1	no	—
142	C₄×C₈	—	38	2	no	—
143	C₄×C₈	—	38	2	no	—
144	#95	—	38	2	no	—
145	C₁₉	#8780	1	1	yes	characteristic, complemented, Sylow
146	C₂²×C₄	—	38	1	no	—
147	C₂²×C₄	—	38	1	no	—
148	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
149	C₂²×C₄	#64541	1	2	yes	—
150	C₂×C₈	—	2	1	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	2	1	no	—
153	C₂×C₈	—	2	1	no	—
154	C₂×C₈	—	4	2	no	—
155	C₂×C₈	—	19	1	no	—
156	C₂×C₈	—	19	1	no	—
157	C₂×C₈	—	19	2	no	—
158	C₂×C₈	—	19	2	no	—
159	C₂×C₈	—	19	1	no	—
160	C₂×C₈	—	19	1	no	—
161	C₂×C₈	—	38	1	no	—
162	C₂×C₈	—	38	1	no	—
163	C₂×C₈	—	76	2	no	—
164	C₂×C₈	C₈×D₁₉	1	2	yes	—
165	C₂×C₈	#64515	1	2	yes	—
166	C₄²	—	19	2	no	—
167	C₄²	—	19	2	no	—
168	C₄²	—	38	1	no	—
169	C₄²	—	38	1	no	—
170	C₄²	D₄×D₁₉	1	1	yes	characteristic
171	C₄²	#64543	1	2	yes	—
172	C₄²	Q₈×D₁₉	1	1	yes	characteristic
173	C₂³	#10597318	1	1	yes	characteristic
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	—	38	2	no	—
176	C₂×C₄	—	38	2	no	—
177	C₂×C₄	—	76	2	no	—
178	C₂×C₄	—	76	2	no	—
179	C₂×C₄	#10597323	1	1	yes	characteristic
180	C₂×C₄	#10597331	1	2	yes	—
181	C₂×C₄	#10597335	1	2	yes	—
182	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
183	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
184	C₂×C₄	C₂×#64515	1	1	yes	characteristic
185	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
186	C₂×C₄	M₁₆×D₁₉	1	1	yes	characteristic
187	C₈	—	2	2	no	—
188	C₈	—	2	2	no	—
189	C₈	—	8	2	no	—
190	C₈	—	19	2	no	—
191	C₈	—	19	2	no	—
192	C₈	—	38	1	no	—
193	C₈	—	38	1	no	—
194	C₈	—	152	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	#11926408	1	1	yes	characteristic
197	C₂²	#11926595	1	1	yes	characteristic
198	C₂²	#11926599	1	1	yes	characteristic
199	C₄	—	2	2	no	—
200	C₄	—	2	2	no	—
201	C₄	—	76	2	no	—
202	C₄	—	76	2	no	—
203	C₄	C₄⋊C₈×D₁₉	1	1	yes	characteristic
204	C₄	#11926566	1	1	yes	characteristic
205	C₄	#11926594	1	1	yes	characteristic
206	C₄	#11926598	1	1	yes	characteristic
207	C₂	—	2	1	no	—
208	C₂	—	2	1	no	—
209	C₂	#14563750	1	1	yes	characteristic
210	C₂	#14563756	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563323

C₂

yes

maximal, characteristic

#14562381

C₂

yes

maximal

#14561480

C₂

yes

maximal, characteristic

#14561463

C₂

yes

maximal

C₁₉×#1281

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

—

C₂×#10597272

C₄

yes

characteristic

C₂×#10597272

C₄

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×Dic₁₉

C₄

yes

characteristic

C₂×C₈×Dic₁₉

C₄

yes

characteristic

#11926390

C₂²

yes

characteristic

#11926296

—

#11926294

—

C₁₉×#431

C₂²

yes

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597272

—

#10597272

—

C₈×Dic₁₉

—

C₈×Dic₁₉

C₈

yes

complemented

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

D₄

yes

characteristic

C₄×C₁₉⋊C₈

Q₈

yes

characteristic

C₄×C₁₉⋊C₈

Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂×C₈

yes

—

C₄×Dic₁₉

M₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₈

yes

—

C₂×C₁₉⋊C₈

M₁₆

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#125

yes

—

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₄⋊C₈

yes

—

C₁₉⋊C₈

C₄⋊C₈

yes

—

—

—

—

D₁₉

yes

characteristic

#1274

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

C₂×C₄⋊C₈

yes

characteristic

102

C₄×C₁₉

#423

yes

characteristic

103

C₄×C₁₉

#431

yes

characteristic

104

C₄×C₁₉

#432

yes

characteristic

105

Dic₁₉

—

106

Dic₁₉

—

107

#431

—

108

#431

C₂×D₁₉

yes

—

109

C₂×#97

—

110

C₂×#97

—

111

C₂×#97

C₂×D₁₉

yes

characteristic

112

C₂×C₄×C₈

—

113

C₂×C₄×C₈

—

114

C₂×C₄×C₈

—

115

#376

—

116

#335

—

117

#334

—

118

C₂×C₁₉

—

119

C₂×C₁₉

—

120

C₂×C₁₉

#1831

yes

characteristic

121

C₂×C₁₉

#1833

yes

—

122

C₂²×C₈

—

123

C₂²×C₈

—

124

C₂²×C₈

C₄×D₁₉

yes

characteristic

125

C₂²×C₈

C₄×D₁₉

yes

characteristic

126

C₂×C₄²

—

127

C₂×C₄²

—

128

C₂×C₄²

C₂²×D₁₉

yes

characteristic

129

C₄⋊C₈

—

130

C₄⋊C₈

—

131

C₂²⋊C₈

—

132

C₂²⋊C₈

—

133

#97

—

134

#97

—

135

#97

—

136

C₄×C₈

—

137

C₄×C₈

—

138

C₄×C₈

—

139

C₄×C₈

—

140

C₄×C₈

—

141

C₄×C₈

—

142

C₄×C₈

—

143

C₄×C₈

—

144

#95

—

145

C₁₉

#8780

yes

characteristic, complemented, Sylow

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

149

C₂²×C₄

#64541

yes

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

C₈×D₁₉

yes

—

165

C₂×C₈

#64515

yes

—

166

C₄²

—

167

C₄²

—

168

C₄²

—

169

C₄²

—

170

C₄²

D₄×D₁₉

yes

characteristic

171

C₄²

#64543

yes

—

172

C₄²

Q₈×D₁₉

yes

characteristic

173

C₂³

#10597318

yes

characteristic

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

#10597323

yes

characteristic

180

C₂×C₄

#10597331

yes

—

181

C₂×C₄

#10597335

yes

—

182

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

183

C₂×C₄

C₂×C₈×D₁₉

yes

characteristic

184

C₂×C₄

C₂×#64515

yes

characteristic

185

C₂×C₄

M₁₆×D₁₉

yes

characteristic

186

C₂×C₄

M₁₆×D₁₉

yes

characteristic

187

C₈

—

188

C₈

—

189

C₈

—

190

C₈

—

191

C₈

—

192

C₈

—

193

C₈

—

194

C₈

—

152

—

195

C₂²

—

196

C₂²

#11926408

yes

characteristic

197

C₂²

#11926595

yes

characteristic

198

C₂²

#11926599

yes

characteristic

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

C₄⋊C₈×D₁₉

yes

characteristic

204

C₄

#11926566

yes

characteristic

205

C₄

#11926594

yes

characteristic

206

C₄

#11926598

yes

characteristic

207

C₂

—

208

C₂

—

209

C₂

#14563750

yes

characteristic

210

C₂

#14563756

yes

—

	subgroup	G/H
center	C₂×C₄	#10597323
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1281	C₂
socle	C₂²×C₁₉	#382
prime radical	C₂³×C₁₉	#117
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1281	D₁₉
hypocenter	C₁₉	#8780
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂×C₄

#10597323

commutator

C₂×C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1281

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
33. C₈×Dic₁₉	C₈	semidirect
145. C₁₉	#8780	semidirect

H ≅ G/N

type

33. C₈×Dic₁₉

C₈

semidirect

145. C₁₉

#8780

semidirect

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

subgroup	index
#14563323	2
#14562381	2
#14561480	2
#14561463	2
C₁₉×#1281	2
#8780	19

subgroup

index

C₁₉×#1281

Subgroups — #18076182

Conjugacy classes of subgroups

Complements

Maximal subgroups