Group #14564355 — subgroups

Subgroups — #14564355

Order 2432.

248 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 105 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×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597272	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₁₉⋊C₄	C₂	1	1	yes	maximal, characteristic
5	#11926299	C₂	1	1	yes	maximal, characteristic
6	#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₄	C₄	1	1	yes	characteristic
12	C₂×Dic₁₉⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	—	2	2	no	—
18	C₁₉⋊#95	C₄	1	1	yes	characteristic
19	C₁₉⋊#95	C₄	1	1	yes	characteristic
20	#10597272	—	2	2	no	—
21	Dic₁₉⋊C₈	—	2	2	no	—
22	Dic₁₉⋊C₈	—	2	2	no	—
23	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	—	2	1	no	—
32	C₂×C₈×C₁₉	—	2	1	no	—
33	C₂×C₈×C₁₉	—	2	1	no	—
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	D₄	1	2	yes	—
36	C₄²×C₁₉	—	2	1	no	—
37	C₄²×C₁₉	—	2	1	no	—
38	Dic₁₉⋊C₄	—	2	2	no	—
39	Dic₁₉⋊C₄	—	2	2	no	—
40	C₄×Dic₁₉	—	2	1	no	—
41	C₄×Dic₁₉	—	2	1	no	—
42	C₄×Dic₁₉	D₄	1	2	yes	—
43	C₄×Dic₁₉	Q₈	1	2	yes	—
44	C₂×C₁₉⋊C₈	—	2	1	no	—
45	C₂×C₁₉⋊C₈	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	C₂×C₁₉⋊C₈	—	2	1	no	—
49	C₂×C₁₉⋊C₈	Q₈	1	2	yes	—
50	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	M₁₆	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
63	C₂×Dic₁₉	—	2	1	no	—
64	C₂×Dic₁₉	—	2	1	no	—
65	C₂×Dic₁₉	—	2	1	no	—
66	C₂×Dic₁₉	—	2	1	no	—
67	C₂×Dic₁₉	—	2	1	no	—
68	C₂×Dic₁₉	—	2	1	no	—
69	C₂×Dic₁₉	—	2	1	no	—
70	C₂×Dic₁₉	—	2	1	no	—
71	C₂×Dic₁₉	—	2	1	no	—
72	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
73	C₂×Dic₁₉	C₄⋊C₄	1	2	yes	—
74	C₂×Dic₁₉	M₁₆	1	2	yes	—
75	C₈×C₁₉	—	2	2	no	—
76	C₈×C₁₉	—	4	1	no	—
77	C₁₉⋊C₈	—	2	2	no	—
78	C₁₉⋊C₈	—	4	1	no	—
79	#1940	—	19	1	no	maximal, Sylow
80	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
82	C₂²×C₁₉	C₄×Q₈	1	1	yes	characteristic
83	C₂²×C₁₉	C₂×M₁₆	1	1	yes	characteristic
84	C₂²×C₁₉	C₂×M₁₆	1	1	yes	characteristic
85	C₂²×C₁₉	#131	1	1	yes	characteristic
86	C₂²×C₁₉	#131	1	1	yes	characteristic
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	4	1	no	—
89	C₄×C₁₉	#121	1	1	yes	characteristic
90	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
91	C₄×C₁₉	#125	1	1	yes	characteristic
92	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
93	Dic₁₉	—	2	2	no	—
94	Dic₁₉	—	2	2	no	—
95	Dic₁₉	—	2	2	no	—
96	Dic₁₉	—	4	1	no	—
97	C₂×C₄⋊C₈	—	19	1	no	—
98	C₂×C₄⋊C₈	—	19	1	no	—
99	C₂×C₄⋊C₈	D₁₉	1	1	yes	characteristic
100	C₂×#97	—	19	1	no	—
101	C₄×C₄⋊C₄	—	19	1	no	—
102	#336	—	19	1	no	—
103	#336	—	19	1	no	—
104	C₂×C₁₉	#389	1	1	yes	characteristic
105	C₂×C₁₉	#423	1	1	yes	characteristic
106	C₂×C₁₉	#424	1	1	yes	characteristic
107	C₂×C₁₉	#435	1	1	yes	characteristic
108	C₂×C₁₉	#435	1	1	yes	characteristic
109	C₂×C₁₉	#446	1	1	yes	characteristic
110	C₂×C₁₉	#446	1	1	yes	characteristic
111	C₂²×C₈	—	19	1	no	—
112	C₂²×C₈	—	19	1	no	—
113	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
114	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
115	C₂×C₄⋊C₄	—	19	1	no	—
116	C₂×C₄⋊C₄	—	19	1	no	—
117	C₂×C₄²	—	19	1	no	—
118	C₂×C₄²	—	19	1	no	—
119	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
120	C₄⋊C₈	—	2	2	no	—
121	C₄⋊C₈	—	38	2	no	—
122	C₄⋊C₈	—	38	2	no	—
123	#97	—	38	2	no	—
124	#95	—	19	1	no	—
125	#95	—	19	1	no	—
126	C₁₉	#1940	1	1	yes	characteristic, complemented, Sylow
127	C₂²×C₄	—	19	1	no	—
128	C₂²×C₄	—	19	1	no	—
129	C₂²×C₄	—	19	1	no	—
130	C₂²×C₄	—	19	1	no	—
131	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
132	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
133	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	2	1	no	—
137	C₂×C₈	—	2	1	no	—
138	C₂×C₈	—	2	1	no	—
139	C₂×C₈	—	19	2	no	—
140	C₂×C₈	—	38	1	no	—
141	C₂×C₈	—	38	1	no	—
142	C₂×C₈	—	38	1	no	—
143	C₂×C₈	—	38	1	no	—
144	C₂×C₈	—	38	1	no	—
145	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
146	C₄⋊C₄	—	38	2	no	—
147	C₄⋊C₄	—	38	2	no	—
148	C₄²	—	2	1	no	—
149	C₄²	—	2	1	no	—
150	C₄²	—	19	2	no	—
151	C₄²	—	19	2	no	—
152	C₄²	—	38	1	no	—
153	C₄²	—	38	1	no	—
154	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	19	2	no	—
161	C₂×C₄	—	19	2	no	—
162	C₂×C₄	—	19	2	no	—
163	C₂×C₄	—	38	1	no	—
164	C₂×C₄	—	38	1	no	—
165	C₂×C₄	—	38	1	no	—
166	C₂×C₄	—	38	1	no	—
167	C₂×C₄	—	38	1	no	—
168	C₂×C₄	—	38	1	no	—
169	C₂×C₄	—	38	1	no	—
170	C₂×C₄	—	38	1	no	—
171	C₂×C₄	—	38	1	no	—
172	C₂×C₄	#64515	1	2	yes	—
173	C₂×C₄	#64541	1	1	yes	characteristic
174	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
175	C₂×C₄	#64543	1	1	yes	characteristic
176	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
177	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
178	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
179	C₈	—	2	2	no	—
180	C₈	—	4	1	no	—
181	C₈	—	38	2	no	—
182	C₈	—	76	1	no	—
183	C₂²	#10597333	1	1	yes	characteristic
184	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
185	C₂²	C₂×#64515	1	1	yes	characteristic
186	C₂²	#10597347	1	1	yes	characteristic
187	C₂²	M₁₆×D₁₉	1	1	yes	characteristic
188	C₂²	#10597353	1	1	yes	characteristic
189	C₂²	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
190	C₄	—	2	2	no	—
191	C₄	—	4	1	no	—
192	C₄	—	38	2	no	—
193	C₄	—	38	2	no	—
194	C₄	—	38	2	no	—
195	C₄	—	76	1	no	—
196	C₄	#10597335	1	1	yes	characteristic
197	C₄	#10597342	1	1	yes	characteristic
198	C₄	#10597385	1	1	yes	characteristic
199	C₄	#10597390	1	1	yes	characteristic
200	C₂	#11926439	1	1	yes	characteristic
201	C₂	#11926566	1	1	yes	characteristic
202	C₂	#11926569	1	1	yes	characteristic
203	C₂	#11926613	1	1	yes	characteristic
204	C₂	#11926615	1	1	yes	characteristic
205	C₂	#11926671	1	1	yes	characteristic
206	C₂	#11926673	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597272

C₂

yes

maximal, characteristic

C₄×Dic₁₉⋊C₄

C₂

yes

maximal, characteristic

#11926299

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

C₄

yes

characteristic

C₂×Dic₁₉⋊C₄

C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉⋊#95

C₄

yes

characteristic

C₁₉⋊#95

C₄

yes

characteristic

#10597272

—

Dic₁₉⋊C₈

—

Dic₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₂×Dic₁₉

M₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1940

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₂²×C₁₉

C₄×Q₈

yes

characteristic

C₂²×C₁₉

C₂×M₁₆

yes

characteristic

C₂²×C₁₉

C₂×M₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#125

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₁₉

yes

characteristic

100

C₂×#97

—

101

C₄×C₄⋊C₄

—

102

#336

—

103

#336

—

104

C₂×C₁₉

#389

yes

characteristic

105

C₂×C₁₉

#423

yes

characteristic

106

C₂×C₁₉

#424

yes

characteristic

107

C₂×C₁₉

#435

yes

characteristic

108

C₂×C₁₉

#435

yes

characteristic

109

C₂×C₁₉

#446

yes

characteristic

110

C₂×C₁₉

#446

yes

characteristic

111

C₂²×C₈

—

112

C₂²×C₈

—

113

C₂²×C₈

C₂×D₁₉

yes

characteristic

114

C₂²×C₈

C₂×D₁₉

yes

characteristic

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

—

117

C₂×C₄²

—

118

C₂×C₄²

—

119

C₂×C₄²

C₂×D₁₉

yes

characteristic

120

C₄⋊C₈

—

121

C₄⋊C₈

—

122

C₄⋊C₈

—

123

#97

—

124

#95

—

125

#95

—

126

C₁₉

#1940

yes

characteristic, complemented, Sylow

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

C₄×D₁₉

yes

characteristic

132

C₂²×C₄

C₄×D₁₉

yes

characteristic

133

C₂²×C₄

C₂²×D₁₉

yes

characteristic

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

C₂²⋊D₁₉

yes

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄²

—

149

C₄²

—

150

C₄²

—

151

C₄²

—

152

C₄²

—

153

C₄²

—

154

C₂³

C₂×C₄×D₁₉

yes

characteristic

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

#64515

yes

—

173

C₂×C₄

#64541

yes

characteristic

174

C₂×C₄

D₄×D₁₉

yes

characteristic

175

C₂×C₄

#64543

yes

characteristic

176

C₂×C₄

Q₈×D₁₉

yes

characteristic

177

C₂×C₄

Q₈×D₁₉

yes

characteristic

178

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₂²

#10597333

yes

characteristic

184

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

185

C₂²

C₂×#64515

yes

characteristic

186

C₂²

#10597347

yes

characteristic

187

C₂²

M₁₆×D₁₉

yes

characteristic

188

C₂²

#10597353

yes

characteristic

189

C₂²

C₄×C₂²⋊D₁₉

yes

characteristic

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

#10597335

yes

characteristic

197

C₄

#10597342

yes

characteristic

198

C₄

#10597385

yes

characteristic

199

C₄

#10597390

yes

characteristic

200

C₂

#11926439

yes

characteristic

201

C₂

#11926566

yes

characteristic

202

C₂

#11926569

yes

characteristic

203

C₂

#11926613

yes

characteristic

204

C₂

#11926615

yes

characteristic

205

C₂

#11926671

yes

characteristic

206

C₂

#11926673

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator, socle, prime radical	C₂³×C₁₉	C₂²×C₄
Fitting	C₂×C₁₉×C₄⋊C₈	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₄⋊C₈	D₁₉
hypocenter	C₁₉	#1940
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator, socle, prime radical

C₂³×C₁₉

C₂²×C₄

Fitting

C₂×C₁₉×C₄⋊C₈

C₂

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₄⋊C₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
126. C₁₉	#1940	semidirect

H ≅ G/N

type

126. C₁₉

#1940

semidirect

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

subgroup	index
C₂×Dic₁₉⋊C₈	2
C₂×#10597272	2
C₄×Dic₁₉⋊C₄	2
#11926299	2
#11926298	2
C₂×C₁₉×C₄⋊C₈	2
#1940	19

subgroup

index

C₂×Dic₁₉⋊C₈

C₄×Dic₁₉⋊C₄

C₂×C₁₉×C₄⋊C₈

Subgroups — #14564355

Conjugacy classes of subgroups

Complements

Maximal subgroups