Group #14564222 — subgroups

Subgroups — #14564222

Order 2432.

230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 99 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	#11926443	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926307	C₂	1	1	yes	maximal, characteristic
4	#11926306	C₂	1	1	yes	maximal, characteristic
5	#11926306	C₂	1	1	yes	maximal, characteristic
6	#11926298	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	—	2	1	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	—	2	1	no	—
15	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₁₉×#106	C₄	1	4	yes	complemented
18	C₁₉⋊#95	—	2	1	no	—
19	C₁₉⋊#95	—	2	1	no	—
20	C₂²×C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	—	2	1	no	—
24	C₂²×Dic₁₉	—	2	1	no	—
25	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
26	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	—	2	1	no	—
36	C₄⋊Dic₁₉	—	2	1	no	—
37	C₄⋊Dic₁₉	—	4	2	no	—
38	C₄⋊Dic₁₉	Q₈	1	2	yes	—
39	C₄×Dic₁₉	—	2	1	no	—
40	C₄×Dic₁₉	—	2	1	no	—
41	C₄×Dic₁₉	—	4	2	no	—
42	C₂×C₁₉⋊C₈	—	2	1	no	—
43	C₂×C₁₉⋊C₈	—	2	1	no	—
44	C₂×C₁₉⋊C₈	—	2	1	no	—
45	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂×Dic₁₉	—	2	1	no	—
59	C₂×Dic₁₉	—	2	1	no	—
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	2	1	no	—
62	C₂×Dic₁₉	—	2	1	no	—
63	C₂×Dic₁₉	—	2	1	no	—
64	C₂×Dic₁₉	—	4	1	no	—
65	C₂×Dic₁₉	—	4	1	no	—
66	C₂×Dic₁₉	—	4	1	no	—
67	C₂×Dic₁₉	—	4	1	no	—
68	C₂×Dic₁₉	—	4	1	no	—
69	C₂×Dic₁₉	SD₁₆	1	2	yes	—
70	C₈×C₁₉	—	2	2	no	—
71	C₁₉⋊C₈	—	4	1	no	—
72	#1920	—	19	1	no	maximal, Sylow
73	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
74	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
75	C₂²×C₁₉	#123	1	1	yes	characteristic
76	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
77	C₂²×C₁₉	#135	1	1	yes	characteristic
78	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
79	C₂²×C₁₉	#137	1	1	yes	characteristic
80	C₄×C₁₉	—	4	2	no	—
81	C₄×C₁₉	—	4	2	no	—
82	C₄×C₁₉	#117	1	1	yes	characteristic
83	C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
84	C₄×C₁₉	#125	1	1	yes	characteristic
85	C₄×C₁₉	#126	1	1	yes	characteristic
86	Dic₁₉	—	2	2	no	—
87	Dic₁₉	—	4	2	no	—
88	Dic₁₉	—	4	1	no	—
89	Dic₁₉	—	8	1	no	—
90	C₂×#106	D₁₉	1	1	yes	characteristic
91	#389	—	19	1	no	—
92	C₄×C₄⋊C₄	—	19	1	no	—
93	#340	—	19	1	no	—
94	#340	—	19	1	no	—
95	#340	—	19	1	no	—
96	#336	—	19	1	no	—
97	C₂×C₁₉	#387	1	1	yes	characteristic
98	C₂×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
99	C₂×C₁₉	#440	1	1	yes	characteristic
100	C₂×C₁₉	#476	1	1	yes	characteristic
101	C₂×C₁₉	#479	1	1	yes	characteristic
102	C₂×C₁₉	#482	1	1	yes	characteristic
103	C₂×C₁₉	#483	1	1	yes	characteristic
104	C₂²×C₈	—	19	1	no	—
105	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
106	C₂×C₄⋊C₄	—	19	1	no	—
107	C₂×C₄⋊C₄	—	19	1	no	—
108	C₂×C₄⋊C₄	—	38	1	no	—
109	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
110	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
111	C₂×C₄²	—	19	1	no	—
112	C₂×C₄²	—	38	1	no	—
113	#106	Dic₁₉	1	4	yes	complemented
114	#95	—	38	1	no	—
115	#95	—	38	1	no	—
116	C₁₉	#1920	1	1	yes	characteristic, complemented, Sylow
117	C₂²×C₄	—	2	1	no	—
118	C₂²×C₄	—	2	1	no	—
119	C₂²×C₄	—	19	1	no	—
120	C₂²×C₄	—	19	1	no	—
121	C₂²×C₄	—	38	1	no	—
122	C₂²×C₄	—	38	1	no	—
123	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
124	C₂×C₈	—	2	1	no	—
125	C₂×C₈	—	2	1	no	—
126	C₂×C₈	—	38	1	no	—
127	C₂×C₈	—	38	1	no	—
128	C₂×C₈	—	38	1	no	—
129	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
130	C₄⋊C₄	—	2	1	no	—
131	C₄⋊C₄	—	2	1	no	—
132	C₄⋊C₄	—	19	2	no	—
133	C₄⋊C₄	—	38	1	no	—
134	C₄⋊C₄	—	38	1	no	—
135	C₄⋊C₄	—	38	1	no	—
136	C₄⋊C₄	—	76	2	no	—
137	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
138	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
139	C₄²	—	38	1	no	—
140	C₄²	—	38	1	no	—
141	C₄²	—	76	2	no	—
142	C₂³	D₄×D₁₉	1	1	yes	characteristic
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	4	1	no	—
146	C₂×C₄	—	4	1	no	—
147	C₂×C₄	—	4	1	no	—
148	C₂×C₄	—	4	1	no	—
149	C₂×C₄	—	19	2	no	—
150	C₂×C₄	—	38	1	no	—
151	C₂×C₄	—	38	1	no	—
152	C₂×C₄	—	38	1	no	—
153	C₂×C₄	—	38	2	no	—
154	C₂×C₄	—	38	1	no	—
155	C₂×C₄	—	38	1	no	—
156	C₂×C₄	—	76	1	no	—
157	C₂×C₄	—	76	1	no	—
158	C₂×C₄	—	76	1	no	—
159	C₂×C₄	—	76	1	no	—
160	C₂×C₄	—	76	1	no	—
161	C₂×C₄	#64541	1	1	yes	characteristic
162	C₂×C₄	#64541	1	1	yes	characteristic
163	C₂×C₄	#64543	1	1	yes	characteristic
164	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
165	C₂×C₄	#64545	1	1	yes	characteristic
166	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
167	C₈	—	2	2	no	—
168	C₈	—	76	1	no	—
169	C₂²	#10597340	1	1	yes	characteristic
170	C₂²	#10597342	1	1	yes	characteristic
171	C₂²	SD₁₆×D₁₉	1	1	yes	characteristic
172	C₂²	#10597360	1	1	yes	characteristic
173	C₂²	#10597361	1	1	yes	characteristic
174	C₂²	#10597362	1	1	yes	characteristic
175	C₂²	D₄×Dic₁₉	1	1	yes	characteristic
176	C₄	—	4	2	no	—
177	C₄	—	4	2	no	—
178	C₄	—	38	2	no	—
179	C₄	—	76	2	no	—
180	C₄	—	76	1	no	—
181	C₄	—	152	1	no	—
182	C₄	#10597335	1	1	yes	characteristic
183	C₄	#10597344	1	1	yes	characteristic
184	C₄	#10597372	1	1	yes	characteristic
185	C₄	Q₈×Dic₁₉	1	1	yes	characteristic
186	C₂	#11926430	1	1	yes	characteristic
187	C₂	SD₁₆×Dic₁₉	1	1	yes	characteristic
188	C₂	#11926645	1	1	yes	characteristic
189	C₂	#11926833	1	1	yes	characteristic
190	C₂	#11926854	1	1	yes	characteristic
191	C₂	#11926870	1	1	yes	characteristic
192	C₂	#11926876	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926443

C₂

yes

maximal, characteristic

C₄⋊C₄×Dic₁₉

C₂

yes

maximal, characteristic

#11926307

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, characteristic

#11926298

C₂

yes

maximal, characteristic

C₂×C₁₉×#106

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#106

C₄

yes

complemented

C₁₉⋊#95

—

C₁₉⋊#95

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

Q₈

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

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

—

C₂×Dic₁₉

—

C₂×Dic₁₉

SD₁₆

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1920

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#123

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₄×Q₈

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#106

D₁₉

yes

characteristic

#389

—

C₄×C₄⋊C₄

—

—

—

—

—

C₂×C₁₉

#387

yes

characteristic

C₂×C₁₉

C₄×SD₁₆

yes

characteristic

C₂×C₁₉

#440

yes

characteristic

100

C₂×C₁₉

#476

yes

characteristic

101

C₂×C₁₉

#479

yes

characteristic

102

C₂×C₁₉

#482

yes

characteristic

103

C₂×C₁₉

#483

yes

characteristic

104

C₂²×C₈

—

105

C₂²×C₈

C₂×D₁₉

yes

characteristic

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

110

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

111

C₂×C₄²

—

112

C₂×C₄²

—

113

#106

Dic₁₉

yes

complemented

114

#95

—

115

#95

—

116

C₁₉

#1920

yes

characteristic, complemented, Sylow

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

C₂²×D₁₉

yes

characteristic

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

C₂×Dic₁₉

yes

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

C₂×Dic₁₉

yes

—

138

C₄⋊C₄

C₂×Dic₁₉

yes

—

139

C₄²

—

140

C₄²

—

141

C₄²

—

142

C₂³

D₄×D₁₉

yes

characteristic

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

#64541

yes

characteristic

162

C₂×C₄

#64541

yes

characteristic

163

C₂×C₄

#64543

yes

characteristic

164

C₂×C₄

Q₈×D₁₉

yes

characteristic

165

C₂×C₄

#64545

yes

characteristic

166

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

167

C₈

—

168

C₈

—

169

C₂²

#10597340

yes

characteristic

170

C₂²

#10597342

yes

characteristic

171

C₂²

SD₁₆×D₁₉

yes

characteristic

172

C₂²

#10597360

yes

characteristic

173

C₂²

#10597361

yes

characteristic

174

C₂²

#10597362

yes

characteristic

175

C₂²

D₄×Dic₁₉

yes

characteristic

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

152

—

182

C₄

#10597335

yes

characteristic

183

C₄

#10597344

yes

characteristic

184

C₄

#10597372

yes

characteristic

185

C₄

Q₈×Dic₁₉

yes

characteristic

186

C₂

#11926430

yes

characteristic

187

C₂

SD₁₆×Dic₁₉

yes

characteristic

188

C₂

#11926645

yes

characteristic

189

C₂

#11926833

yes

characteristic

190

C₂

#11926854

yes

characteristic

191

C₂

#11926870

yes

characteristic

192

C₂

#11926876

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	#1920
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#106

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
17. C₁₉×#106	C₄	semidirect
113. #106	Dic₁₉	semidirect
116. C₁₉	#1920	semidirect

H ≅ G/N

type

17. C₁₉×#106

C₄

semidirect

113. #106

Dic₁₉

semidirect

116. C₁₉

#1920

semidirect

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

subgroup	index
#11926443	2
C₄⋊C₄×Dic₁₉	2
#11926307	2
#11926306	2
#11926298	2
C₂×C₁₉×#106	2
#1920	19

subgroup

index

C₄⋊C₄×Dic₁₉

C₂×C₁₉×#106

Subgroups — #14564222

Conjugacy classes of subgroups

Complements

Maximal subgroups