Group #14564084 — subgroups

Subgroups — #14564084

Order 2432.

358 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10597372	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597294	C₂	1	2	yes	maximal, complemented
3	#11926508	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926303	C₂	1	2	yes	maximal, complemented
5	C₁₉×#525	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#123	—	2	1	no	—
9	C₁₉×C₂²⋊Q₈	C₄	1	2	yes	complemented
10	C₁₉×#121	C₄	1	2	yes	complemented
11	C₁₉×#120	—	2	1	no	—
12	C₄×D₄×C₁₉	—	2	2	no	—
13	C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
15	#10597372	—	2	4	no	—
16	C₂×C₄⋊Dic₁₉	—	2	1	no	—
17	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
18	C₂×#64520	C₂²	1	2	yes	—
19	#10597294	—	2	4	no	—
20	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
21	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
22	#41×C₁₉	—	2	2	no	—
23	#41×C₁₉	—	2	2	no	—
24	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×D₄×C₁₉	—	2	2	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	—	2	2	no	—
29	C₂²×C₄×C₁₉	—	2	2	no	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	D₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₉	—	2	2	no	—
36	C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
38	C₂²⋊C₄×C₁₉	—	2	2	no	—
39	C₂²⋊C₄×C₁₉	—	2	1	no	—
40	C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₄²×C₁₉	—	2	1	no	—
42	C₂²⋊Dic₁₉	—	2	4	no	—
43	C₄⋊Dic₁₉	—	2	4	no	—
44	C₄×Dic₁₉	—	2	2	no	—
45	C₄×Dic₁₉	D₄	1	4	yes	complemented
46	#64520	—	2	2	no	—
47	#64520	—	2	2	no	—
48	C₂×C₁₉⋊C₈	—	2	2	no	—
49	C₂³×C₁₉	—	2	1	no	—
50	C₂³×C₁₉	—	2	1	no	—
51	C₂³×C₁₉	—	2	1	no	—
52	C₂³×C₁₉	—	4	2	no	—
53	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
55	Q₈×C₁₉	—	2	2	no	—
56	D₄×C₁₉	—	2	2	no	—
57	D₄×C₁₉	—	4	4	no	—
58	D₄×C₁₉	—	4	1	no	—
59	D₄×C₁₉	—	4	1	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	4	no	—
63	C₂×C₄×C₁₉	—	2	4	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#41	1	2	yes	—
72	C₂×Dic₁₉	—	2	4	no	—
73	C₂×Dic₁₉	—	4	4	no	—
74	C₁₉⋊C₈	—	4	2	no	—
75	#1897	—	19	1	no	maximal, Sylow
76	C₂²×C₁₉	—	2	2	no	—
77	C₂²×C₁₉	—	2	2	no	—
78	C₂²×C₁₉	—	2	2	no	—
79	C₂²×C₁₉	—	2	2	no	—
80	C₂²×C₁₉	—	4	2	no	—
81	C₂²×C₁₉	—	4	2	no	—
82	C₂²×C₁₉	—	4	1	no	—
83	C₂²×C₁₉	—	4	2	no	—
84	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₁₉	#120	1	1	yes	characteristic
86	C₂²×C₁₉	#123	1	1	yes	characteristic
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	4	1	no	—
89	C₄×C₁₉	—	4	2	no	—
90	C₄×C₁₉	C₄×D₄	1	2	yes	—
91	C₄×C₁₉	#121	1	2	yes	—
92	Dic₁₉	—	4	4	no	—
93	#525	D₁₉	1	1	yes	characteristic
94	C₂×#117	—	19	1	no	—
95	C₂×#104	—	19	2	no	—
96	#407	—	19	1	no	—
97	#339	—	19	2	no	—
98	C₂×C₁₉	—	2	1	no	—
99	C₂×C₁₉	—	2	1	no	—
100	C₂×C₁₉	—	4	2	no	—
101	C₂×C₁₉	—	8	1	no	—
102	C₂×C₁₉	#386	1	1	yes	characteristic
103	C₂×C₁₉	#421	1	2	yes	—
104	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
105	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
106	C₂×M₁₆	—	19	2	no	—
107	#123	—	2	1	no	—
108	C₂²⋊Q₈	Dic₁₉	1	2	yes	complemented
109	#121	Dic₁₉	1	2	yes	complemented
110	#120	—	2	1	no	—
111	C₄×D₄	—	2	2	no	—
112	#117	—	38	4	no	—
113	#117	C₂×D₁₉	1	1	yes	characteristic
114	C₂×C₄⋊C₄	—	38	1	no	—
115	C₂×C₂²⋊C₄	—	38	1	no	—
116	C₂×C₄²	—	19	2	no	—
117	#104	—	38	4	no	—
118	C₂²⋊C₈	—	38	2	no	—
119	C₁₉	#1897	1	1	yes	characteristic, complemented, Sylow
120	C₂⁴	C₂²⋊D₁₉	1	1	yes	characteristic
121	#41	—	2	2	no	—
122	#41	—	2	2	no	—
123	C₂×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
124	C₂×D₄	—	2	2	no	—
125	C₂×D₄	—	2	1	no	—
126	C₂×D₄	C₂×Dic₁₉	1	1	yes	characteristic
127	C₂²×C₄	—	2	2	no	—
128	C₂²×C₄	—	2	2	no	—
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	38	2	no	—
131	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
132	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
133	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
134	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
135	M₁₆	—	38	2	no	—
136	M₁₆	—	38	2	no	—
137	C₂×C₈	—	38	2	no	—
138	C₄⋊C₄	—	2	2	no	—
139	C₄⋊C₄	—	38	4	no	—
140	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
141	C₂²⋊C₄	—	2	2	no	—
142	C₂²⋊C₄	—	2	1	no	—
143	C₂²⋊C₄	—	2	2	no	—
144	C₂²⋊C₄	—	38	4	no	—
145	C₄²	—	2	1	no	—
146	C₄²	—	19	4	no	—
147	C₄²	—	38	2	no	—
148	C₂³	—	2	1	no	—
149	C₂³	—	2	1	no	—
150	C₂³	—	2	1	no	—
151	C₂³	—	4	2	no	—
152	C₂³	C₂²⋊Dic₁₉	1	2	yes	—
153	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
154	Q₈	—	2	2	no	—
155	D₄	—	2	2	no	—
156	D₄	—	4	4	no	—
157	D₄	—	4	1	no	—
158	D₄	—	4	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	4	2	no	—
166	C₂×C₄	—	38	4	no	—
167	C₂×C₄	—	76	4	no	—
168	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
169	C₂×C₄	D₄×D₁₉	1	2	yes	—
170	C₂×C₄	#64543	1	2	yes	—
171	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
172	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
173	C₈	—	76	2	no	—
174	C₂²	—	2	2	no	—
175	C₂²	—	2	2	no	—
176	C₂²	—	2	2	no	—
177	C₂²	—	2	2	no	—
178	C₂²	—	4	2	no	—
179	C₂²	—	4	2	no	—
180	C₂²	—	4	2	no	—
181	C₂²	—	4	1	no	—
182	C₂²	#10597381	1	1	yes	characteristic
183	C₂²	#10597383	1	1	yes	characteristic
184	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
185	C₄	—	2	2	no	—
186	C₄	—	4	2	no	—
187	C₄	—	4	1	no	—
188	C₄	—	76	4	no	—
189	C₄	D₄×Dic₁₉	1	2	yes	—
190	C₄	#10597385	1	2	yes	—
191	C₂	—	2	1	no	—
192	C₂	—	2	1	no	—
193	C₂	—	4	2	no	—
194	C₂	—	8	1	no	—
195	C₂	#11926424	1	1	yes	characteristic
196	C₂	#11926561	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597372

C₂

yes

maximal, characteristic, complemented

C₂×#10597294

C₂

yes

maximal, complemented

#11926508

C₂

yes

maximal, characteristic, complemented

#11926303

C₂

yes

maximal, complemented

C₁₉×#525

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

C₄

yes

complemented

C₁₉×#121

C₄

yes

complemented

C₁₉×#120

—

C₄×D₄×C₁₉

—

C₁₉×#117

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

#10597372

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

—

#10597294

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

D₄

yes

characteristic

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

complemented

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×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×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1897

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

#525

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

100

C₂×C₁₉

—

101

C₂×C₁₉

—

102

C₂×C₁₉

#386

yes

characteristic

103

C₂×C₁₉

#421

yes

—

104

C₂×#41

C₂×D₁₉

yes

characteristic

105

C₂³×C₄

C₂×D₁₉

yes

characteristic

106

C₂×M₁₆

—

107

#123

—

108

C₂²⋊Q₈

Dic₁₉

yes

complemented

109

#121

Dic₁₉

yes

complemented

110

#120

—

111

C₄×D₄

—

112

#117

—

113

#117

C₂×D₁₉

yes

characteristic

114

C₂×C₄⋊C₄

—

115

C₂×C₂²⋊C₄

—

116

C₂×C₄²

—

117

#104

—

118

C₂²⋊C₈

—

119

C₁₉

#1897

yes

characteristic, complemented, Sylow

120

C₂⁴

C₂²⋊D₁₉

yes

characteristic

121

#41

—

122

#41

—

123

C₂×Q₈

C₂×Dic₁₉

yes

characteristic

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

C₂×Dic₁₉

yes

characteristic

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

C₂×Dic₁₉

yes

—

132

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

133

C₂²×C₄

C₂²⋊D₁₉

yes

—

134

C₂²×C₄

C₂²×D₁₉

yes

characteristic

135

M₁₆

—

136

M₁₆

—

137

C₂×C₈

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

C₂×Dic₁₉

yes

—

141

C₂²⋊C₄

—

142

C₂²⋊C₄

—

143

C₂²⋊C₄

—

144

C₂²⋊C₄

—

145

C₄²

—

146

C₄²

—

147

C₄²

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

C₂²⋊Dic₁₉

yes

—

153

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

154

Q₈

—

155

D₄

—

156

D₄

—

157

D₄

—

158

D₄

—

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

C₂²⋊Dic₁₉

yes

—

169

C₂×C₄

D₄×D₁₉

yes

—

170

C₂×C₄

#64543

yes

—

171

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

172

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

173

C₈

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

—

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

#10597381

yes

characteristic

183

C₂²

#10597383

yes

characteristic

184

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

D₄×Dic₁₉

yes

—

190

C₄

#10597385

yes

—

191

C₂

—

192

C₂

—

193

C₂

—

194

C₂

—

195

C₂

#11926424

yes

characteristic

196

C₂

#11926561

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#525	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#525	D₁₉
hypocenter	C₁₉	#1897
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #525

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting, prime radical

C₁₉×#525

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #525

N	H ≅ G/N	type
1. C₂×#10597372	C₂	semidirect
2. C₂×#10597294	C₂	semidirect
3. #11926508	C₂	semidirect
4. #11926303	C₂	semidirect
9. C₁₉×C₂²⋊Q₈	C₄	semidirect
10. C₁₉×#121	C₄	semidirect
45. C₄×Dic₁₉	D₄	semidirect
108. C₂²⋊Q₈	Dic₁₉	semidirect
109. #121	Dic₁₉	semidirect
119. C₁₉	#1897	semidirect

H ≅ G/N

type

1. C₂×#10597372

C₂

semidirect

2. C₂×#10597294

C₂

semidirect

3. #11926508

C₂

semidirect

4. #11926303

C₂

semidirect

9. C₁₉×C₂²⋊Q₈

C₄

semidirect

10. C₁₉×#121

C₄

semidirect

45. C₄×Dic₁₉

D₄

semidirect

108. C₂²⋊Q₈

Dic₁₉

semidirect

109. #121

Dic₁₉

semidirect

119. C₁₉

#1897

semidirect

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

subgroup	index
C₂×#10597372	2
C₂×#10597294	2
#11926508	2
#11926303	2
C₁₉×#525	2
#1897	19

subgroup

index

C₁₉×#525

Subgroups — #14564084

Conjugacy classes of subgroups

Complements

Maximal subgroups