Group #14564568 — subgroups

Subgroups — #14564568

Order 2432.

344 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 113 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×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597292	C₂	1	2	yes	maximal, complemented
3	C₂×#10597289	C₂	1	2	yes	maximal
4	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#124	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#124	—	2	2	no	—
9	C₁₉×#124	C₄	1	4	yes	complemented
10	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
11	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×C₄×Dic₁₉	—	2	1	no	—
15	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
16	#10597292	—	2	4	no	—
17	#10597289	—	2	4	no	—
18	C₁₉⋊#95	—	2	1	no	—
19	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
20	C₂⁴×C₁₉	—	2	1	no	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	—	2	2	no	—
24	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×D₄×C₁₉	—	2	2	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	—	2	2	no	—
28	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×Dic₁₉	—	2	2	no	—
34	C₂²⋊C₄×C₁₉	—	2	4	no	—
35	C₂²⋊C₄×C₁₉	—	2	4	no	—
36	C₄²×C₁₉	C₂×C₄	1	2	yes	—
37	C₄²×C₁₉	D₄	1	2	yes	—
38	C₄⋊Dic₁₉	—	2	2	no	—
39	C₄⋊Dic₁₉	D₄	1	4	yes	—
40	C₄×Dic₁₉	—	4	2	no	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂×C₁₉⋊C₈	—	2	2	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂³×C₁₉	—	2	2	no	—
45	C₂³×C₁₉	—	4	2	no	—
46	C₂³×C₁₉	—	4	2	no	—
47	C₂³×C₁₉	—	4	1	no	—
48	C₂³×C₁₉	—	4	1	no	—
49	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
50	Q₈×C₁₉	—	2	4	no	—
51	Q₈×C₁₉	—	4	1	no	—
52	Q₈×C₁₉	—	4	1	no	—
53	D₄×C₁₉	—	2	4	no	—
54	D₄×C₁₉	—	4	1	no	—
55	D₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	4	2	no	—
61	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
62	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
63	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
65	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	#41	1	2	yes	—
67	C₂×Dic₁₉	—	2	4	no	—
68	C₂×Dic₁₉	—	4	2	no	—
69	C₂×Dic₁₉	—	4	2	no	—
70	C₁₉⋊C₈	—	4	2	no	—
71	#1983	—	19	1	no	maximal, Sylow
72	C₂²×C₁₉	—	4	2	no	—
73	C₂²×C₁₉	—	4	2	no	—
74	C₂²×C₁₉	—	4	2	no	—
75	C₂²×C₁₉	—	8	2	no	—
76	C₂²×C₁₉	—	8	2	no	—
77	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₁₉	#121	1	2	yes	—
79	C₂²×C₁₉	#135	1	2	yes	—
80	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
81	C₂²×C₁₉	#137	1	1	yes	characteristic
82	C₄×C₁₉	—	2	2	no	—
83	C₄×C₁₉	—	2	2	no	—
84	C₄×C₁₉	—	4	2	no	—
85	C₄×C₁₉	C₄×D₄	1	2	yes	—
86	C₄×C₁₉	#124	1	1	yes	characteristic
87	C₄×C₁₉	#127	1	1	yes	characteristic
88	Dic₁₉	—	4	4	no	—
89	C₂×#124	D₁₉	1	1	yes	characteristic
90	C₂×C₄⋊C₈	—	19	1	no	—
91	C₂×#103	—	19	2	no	—
92	C₂×#102	—	19	2	no	—
93	C₄×C₄⋊C₄	—	19	1	no	—
94	C₂×C₁₉	—	8	2	no	—
95	C₂×C₁₉	#390	1	1	yes	characteristic
96	C₂×C₁₉	#416	1	1	yes	characteristic
97	C₂×C₁₉	#417	1	1	yes	characteristic
98	C₂×C₁₉	#463	1	2	yes	—
99	C₂×C₁₉	#464	1	2	yes	—
100	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
101	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
102	C₂²×C₈	—	19	2	no	—
103	#124	—	2	2	no	—
104	#124	Dic₁₉	1	4	yes	complemented
105	C₂×C₄⋊C₄	—	19	2	no	—
106	C₂×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₄²	—	38	1	no	—
109	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
110	C₄⋊C₈	—	38	2	no	—
111	#103	—	38	4	no	—
112	#102	—	38	4	no	—
113	#95	—	38	1	no	—
114	C₁₉	#1983	1	1	yes	characteristic, complemented, Sylow
115	C₂⁴	—	2	1	no	—
116	C₂×Q₈	—	2	1	no	—
117	C₂×Q₈	—	2	2	no	—
118	C₂×Q₈	—	2	2	no	—
119	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
120	C₂×D₄	—	2	2	no	—
121	C₂×D₄	—	2	2	no	—
122	C₂×D₄	—	2	1	no	—
123	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
124	C₂²×C₄	—	2	1	no	—
125	C₂²×C₄	—	38	2	no	—
126	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
127	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
128	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
129	C₂×C₈	—	38	2	no	—
130	C₂×C₈	—	38	2	no	—
131	C₂×C₈	—	38	2	no	—
132	C₄⋊C₄	—	19	4	no	—
133	C₄⋊C₄	—	38	2	no	—
134	C₂²⋊C₄	—	2	4	no	—
135	C₂²⋊C₄	—	2	4	no	—
136	C₄²	—	76	2	no	—
137	C₄²	C₂×Dic₁₉	1	2	yes	—
138	C₄²	C₂²⋊D₁₉	1	2	yes	—
139	C₂³	—	2	2	no	—
140	C₂³	—	4	2	no	—
141	C₂³	—	4	1	no	—
142	C₂³	—	4	2	no	—
143	C₂³	—	4	1	no	—
144	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
145	Q₈	—	2	4	no	—
146	Q₈	—	4	1	no	—
147	Q₈	—	4	1	no	—
148	D₄	—	2	4	no	—
149	D₄	—	4	1	no	—
150	D₄	—	4	1	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	4	2	no	—
156	C₂×C₄	—	38	4	no	—
157	C₂×C₄	—	76	2	no	—
158	C₂×C₄	—	76	2	no	—
159	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
160	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
161	C₂×C₄	D₄×D₁₉	1	2	yes	—
162	C₂×C₄	#64543	1	2	yes	—
163	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
164	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
165	C₈	—	76	2	no	—
166	C₂²	—	4	2	no	—
167	C₂²	—	4	2	no	—
168	C₂²	—	4	2	no	—
169	C₂²	—	8	2	no	—
170	C₂²	—	8	2	no	—
171	C₂²	#10597384	1	2	yes	—
172	C₂²	#10597395	1	1	yes	characteristic
173	C₂²	#10597396	1	2	yes	—
174	C₂²	#10597397	1	1	yes	characteristic
175	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
176	C₄	—	2	2	no	—
177	C₄	—	2	2	no	—
178	C₄	—	4	2	no	—
179	C₄	—	76	4	no	—
180	C₄	D₄×Dic₁₉	1	2	yes	—
181	C₄	#10597382	1	1	yes	characteristic
182	C₄	#10597386	1	1	yes	characteristic
183	C₂	—	8	2	no	—
184	C₂	#11926447	1	1	yes	characteristic
185	C₂	#11926540	1	1	yes	characteristic
186	C₂	#11926545	1	1	yes	characteristic
187	C₂	#11926756	1	2	yes	—
188	C₂	#11926763	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic, complemented

C₂×#10597292

C₂

yes

maximal, complemented

C₂×#10597289

C₂

yes

maximal

C₄×C₄⋊Dic₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#124

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#124

—

C₁₉×#124

C₄

yes

complemented

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597292

—

#10597289

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

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

C₂²⋊C₄

yes

—

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

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1983

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

#135

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×#124

D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₂×#103

—

C₂×#102

—

C₄×C₄⋊C₄

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#464

yes

—

100

C₂²×Q₈

C₂×D₁₉

yes

characteristic

101

C₂²×D₄

C₂×D₁₉

yes

characteristic

102

C₂²×C₈

—

103

#124

—

104

#124

Dic₁₉

yes

complemented

105

C₂×C₄⋊C₄

—

106

C₂×C₂²⋊C₄

—

107

C₂×C₂²⋊C₄

—

108

C₂×C₄²

—

109

C₂×C₄²

C₂×D₁₉

yes

characteristic

110

C₄⋊C₈

—

111

#103

—

112

#102

—

113

#95

—

114

C₁₉

#1983

yes

characteristic, complemented, Sylow

115

C₂⁴

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

C₂×Dic₁₉

yes

—

120

C₂×D₄

—

121

C₂×D₄

—

122

C₂×D₄

—

123

C₂×D₄

C₂×Dic₁₉

yes

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

127

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

128

C₂²×C₄

C₂²×D₁₉

yes

characteristic

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₂²⋊C₄

—

135

C₂²⋊C₄

—

136

C₄²

—

137

C₄²

C₂×Dic₁₉

yes

—

138

C₄²

C₂²⋊D₁₉

yes

—

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

—

143

C₂³

—

144

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

145

Q₈

—

146

Q₈

—

147

Q₈

—

148

D₄

—

149

D₄

—

150

D₄

—

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

C₂²⋊Dic₁₉

yes

—

160

C₂×C₄

C₂²⋊Dic₁₉

yes

—

161

C₂×C₄

D₄×D₁₉

yes

—

162

C₂×C₄

#64543

yes

—

163

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

164

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

165

C₈

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

#10597384

yes

—

172

C₂²

#10597395

yes

characteristic

173

C₂²

#10597396

yes

—

174

C₂²

#10597397

yes

characteristic

175

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

D₄×Dic₁₉

yes

—

181

C₄

#10597382

yes

characteristic

182

C₄

#10597386

yes

characteristic

183

C₂

—

184

C₂

#11926447

yes

characteristic

185

C₂

#11926540

yes

characteristic

186

C₂

#11926545

yes

characteristic

187

C₂

#11926756

yes

—

188

C₂

#11926763

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#124	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#124	D₁₉
hypocenter	C₁₉	#1983
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#124

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

N	H ≅ G/N	type
1. C₂×C₄⋊(C₁₉⋊C₈)	C₂	semidirect
2. C₂×#10597292	C₂	semidirect
4. C₄×C₄⋊Dic₁₉	C₂	semidirect
9. C₁₉×#124	C₄	semidirect
104. #124	Dic₁₉	semidirect
114. C₁₉	#1983	semidirect

H ≅ G/N

type

1. C₂×C₄⋊(C₁₉⋊C₈)

C₂

semidirect

2. C₂×#10597292

C₂

semidirect

4. C₄×C₄⋊Dic₁₉

C₂

semidirect

9. C₁₉×#124

C₄

semidirect

104. #124

Dic₁₉

semidirect

114. C₁₉

#1983

semidirect

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

subgroup	index
C₂×C₄⋊(C₁₉⋊C₈)	2
C₂×#10597292	2
C₂×#10597289	2
C₄×C₄⋊Dic₁₉	2
C₂×C₁₉×#124	2
#1983	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₂×#10597292

C₂×#10597289

C₄×C₄⋊Dic₁₉

C₂×C₁₉×#124

#1983

Subgroups — #14564568

Conjugacy classes of subgroups

Complements

Maximal subgroups