Group #14574089 — subgroups

Subgroups — #14574089

Order 2432.

552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10597361	C₂	1	4	yes	maximal, complemented
2	#11927092	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926935	C₂	1	4	yes	maximal, complemented
5	#11926924	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926923	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#64515	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₈×D₁₉	C₂²	1	2	yes	—
11	C₂×#64543	C₂²	1	2	yes	—
12	C₂×SD₁₆×C₁₉	C₂²	1	4	yes	—
13	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₉×#127	C₂²	1	1	yes	characteristic
15	#10597390	C₂²	1	2	yes	—
16	C₂×#64528	C₂²	1	4	yes	—
17	#10597384	—	2	2	no	—
18	#10597382	C₂²	1	2	yes	—
19	D₄×Dic₁₉	—	2	2	no	—
20	C₂×#64526	C₂²	1	4	yes	—
21	#10597361	—	2	16	no	—
22	C₂×Dic₇₆	C₂²	1	4	yes	—
23	C₂×#64515	C₂²	1	2	yes	—
24	C₄⋊C₄×D₁₉	—	2	2	no	—
25	#10597334	—	2	2	no	—
26	C₄²×D₁₉	C₂²	1	1	yes	characteristic
27	#10597315	C₂²	1	1	yes	characteristic
28	#10597315	C₂²	1	1	yes	characteristic
29	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	#10597272	C₂²	1	2	yes	—
31	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
33	C₂×D₄×C₁₉	—	2	2	no	—
34	C₂×D₄×C₁₉	C₂³	1	2	yes	—
35	C₂×C₂²⋊D₁₉	—	2	2	no	—
36	C₂²×Dic₁₉	—	2	2	no	—
37	Q₈×D₁₉	—	2	8	no	—
38	#64543	—	2	8	no	—
39	C₂×C₄×D₁₉	—	2	2	no	—
40	C₂×C₄×D₁₉	D₄	1	2	yes	—
41	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
42	C₂×Dic₃₈	—	2	2	no	—
43	C₂×Dic₃₈	C₂³	1	2	yes	—
44	C₂×Dic₃₈	C₂³	1	2	yes	—
45	SD₁₆×C₁₉	—	2	8	no	—
46	C₂×C₈×C₁₉	C₂³	1	2	yes	—
47	C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²⋊Dic₁₉	—	2	4	no	—
50	#64528	—	2	8	no	—
51	#64526	—	2	8	no	—
52	C₄⋊Dic₁₉	—	2	2	no	—
53	C₄⋊Dic₁₉	—	2	2	no	—
54	Dic₁₉⋊C₄	—	2	4	no	—
55	C₄×Dic₁₉	D₄	1	2	yes	—
56	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
57	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
58	Dic₇₆	—	2	8	no	—
59	#64515	D₄	1	8	yes	complemented
60	C₂³×C₁₉	—	2	2	no	—
61	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
62	Q₈×C₁₉	—	2	4	no	—
63	D₄×C₁₉	—	2	4	no	—
64	D₄×C₁₉	—	4	4	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
68	C₂²⋊D₁₉	—	4	4	no	—
69	C₂×Dic₁₉	—	2	2	no	—
70	C₂×Dic₁₉	—	2	2	no	—
71	C₂×Dic₁₉	—	4	4	no	—
72	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
73	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
74	C₄×D₁₉	—	2	4	no	—
75	C₄×D₁₉	—	4	4	no	—
76	C₄×D₁₉	C₂×D₄	1	4	yes	—
77	Dic₃₈	—	2	4	no	—
78	Dic₃₈	—	2	4	no	—
79	Dic₃₈	—	4	4	no	—
80	C₈×C₁₉	C₂×D₄	1	4	yes	—
81	C₁₉⋊C₈	C₂×D₄	1	4	yes	—
82	#3152	—	19	1	no	maximal, Sylow
83	C₂²×C₁₉	—	4	2	no	—
84	C₂²×C₁₉	—	4	4	no	—
85	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
86	C₂×D₁₉	—	2	2	no	—
87	C₂×D₁₉	#127	1	2	yes	—
88	C₄×C₁₉	—	4	2	no	—
89	C₄×C₁₉	#137	1	4	yes	complemented
90	C₄×C₁₉	C₂²×D₄	1	2	yes	—
91	Dic₁₉	—	2	2	no	—
92	Dic₁₉	—	4	2	no	—
93	Dic₁₉	—	4	2	no	—
94	Dic₁₉	#127	1	2	yes	—
95	C₂×#137	—	19	4	no	—
96	#532	—	19	1	no	—
97	C₂×C₄⋊Q₈	—	19	1	no	—
98	#497	—	19	4	no	—
99	#494	—	19	1	no	—
100	#494	—	19	1	no	—
101	#492	—	19	1	no	—
102	#492	D₁₉	1	1	yes	characteristic, complemented
103	C₄×M₁₆	—	19	1	no	—
104	C₂×C₁₉	—	8	2	no	—
105	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
106	C₂×C₁₉	C₂×#137	1	2	yes	—
107	D₁₉	—	2	2	no	—
108	C₂×#41	—	19	2	no	—
109	C₂²×Q₈	—	19	2	no	—
110	#137	—	38	16	no	—
111	C₂×Q₁₆	—	19	4	no	—
112	C₂×Q₁₆	—	19	4	no	—
113	C₂×SD₁₆	—	19	4	no	—
114	C₂×SD₁₆	C₂×D₁₉	1	4	yes	—
115	C₂×M₁₆	—	19	2	no	—
116	C₄⋊Q₈	—	19	2	no	—
117	C₄⋊Q₈	—	19	1	no	—
118	C₄⋊Q₈	—	19	1	no	—
119	C₄⋊Q₈	—	38	2	no	—
120	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
121	#127	C₂×D₁₉	1	1	yes	characteristic
122	#124	—	19	2	no	—
123	#121	—	38	2	no	—
124	C₄×D₄	—	38	2	no	—
125	C₂×C₄⋊C₄	—	38	2	no	—
126	C₂×C₄²	—	19	1	no	—
127	#97	—	19	2	no	—
128	C₄×C₈	—	19	1	no	—
129	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
130	C₁₉	#3152	1	1	yes	characteristic, complemented, Sylow
131	#41	—	38	8	no	—
132	C₂×Q₈	—	19	2	no	—
133	C₂×Q₈	—	19	2	no	—
134	C₂×Q₈	—	38	2	no	—
135	C₂×Q₈	—	38	8	no	—
136	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
137	C₂×D₄	—	2	2	no	—
138	C₂×D₄	—	38	2	no	—
139	C₂×D₄	C₂²×D₁₉	1	2	yes	—
140	C₂²×C₄	—	19	1	no	—
141	C₂²×C₄	—	19	2	no	—
142	C₂²×C₄	—	38	2	no	—
143	C₂²×C₄	—	38	2	no	—
144	Q₁₆	—	38	8	no	—
145	Q₁₆	—	38	8	no	—
146	SD₁₆	—	2	8	no	—
147	SD₁₆	—	38	8	no	—
148	M₁₆	—	19	8	no	—
149	C₂×C₈	—	19	2	no	—
150	C₂×C₈	C₂²×D₁₉	1	2	yes	—
151	C₄⋊C₄	—	2	2	no	—
152	C₄⋊C₄	—	38	4	no	—
153	C₄⋊C₄	—	38	2	no	—
154	C₄⋊C₄	—	38	2	no	—
155	C₂²⋊C₄	—	38	4	no	—
156	C₄²	—	19	2	no	—
157	C₄²	—	19	1	no	—
158	C₄²	C₂²×D₁₉	1	1	yes	characteristic
159	C₂³	—	2	2	no	—
160	C₂³	—	19	1	no	—
161	Q₈	—	2	4	no	—
162	Q₈	—	38	4	no	—
163	Q₈	—	38	4	no	—
164	Q₈	—	76	4	no	—
165	D₄	—	2	4	no	—
166	D₄	—	4	4	no	—
167	D₄	—	76	4	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	19	1	no	—
170	C₂×C₄	—	19	4	no	—
171	C₂×C₄	—	19	2	no	—
172	C₂×C₄	—	38	4	no	—
173	C₂×C₄	—	38	2	no	—
174	C₂×C₄	—	38	2	no	—
175	C₂×C₄	—	76	4	no	—
176	C₂×C₄	—	76	4	no	—
177	C₂×C₄	D₄×D₁₉	1	2	yes	—
178	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
179	C₈	—	19	4	no	—
180	C₈	D₄×D₁₉	1	4	yes	—
181	C₂²	—	4	4	no	—
182	C₂²	—	4	2	no	—
183	C₂²	—	19	2	no	—
184	C₂²	—	38	2	no	—
185	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
186	C₄	—	4	2	no	—
187	C₄	—	19	2	no	—
188	C₄	—	38	2	no	—
189	C₄	—	76	2	no	—
190	C₄	—	76	2	no	—
191	C₄	#10597361	1	4	yes	complemented
192	C₄	C₂×D₄×D₁₉	1	2	yes	—
193	C₂	—	8	2	no	—
194	C₂	—	38	2	no	—
195	C₂	#127×D₁₉	1	1	yes	characteristic
196	C₂	C₂×#10597361	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597361

C₂

yes

maximal, complemented

#11927092

C₂

yes

maximal, characteristic

C₄⋊Q₈×D₁₉

C₂

yes

maximal, characteristic, complemented

#11926935

C₂

yes

maximal, complemented

#11926924

C₂

yes

maximal, characteristic, complemented

#11926923

C₂

yes

maximal, characteristic, complemented

#11926916

C₂

yes

maximal, characteristic, complemented

C₄×#64515

C₂

yes

maximal, characteristic, complemented

C₁₉×#492

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

C₂²

yes

—

C₂×#64543

C₂²

yes

—

C₂×SD₁₆×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

characteristic

#10597390

C₂²

yes

—

C₂×#64528

C₂²

yes

—

#10597384

—

#10597382

C₂²

yes

—

D₄×Dic₁₉

—

C₂×#64526

C₂²

yes

—

#10597361

—

C₂×Dic₇₆

C₂²

yes

—

C₂×#64515

C₂²

yes

—

C₄⋊C₄×D₁₉

—

#10597334

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597272

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

C₂³

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

Q₈×D₁₉

—

#64543

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

—

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₂×Dic₃₈

C₂³

yes

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

#64528

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

Dic₇₆

—

#64515

D₄

yes

complemented

C₂³×C₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

C₂×D₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

—

C₁₉⋊C₈

C₂×D₄

yes

—

#3152

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

#127

yes

—

C₄×C₁₉

—

C₄×C₁₉

#137

yes

complemented

C₄×C₁₉

C₂²×D₄

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#127

yes

—

C₂×#137

—

#532

—

C₂×C₄⋊Q₈

—

#497

—

#494

—

100

#494

—

101

#492

—

102

#492

D₁₉

yes

characteristic, complemented

103

C₄×M₁₆

—

104

C₂×C₁₉

—

105

C₂×C₁₉

C₂×#127

yes

characteristic

106

C₂×C₁₉

C₂×#137

yes

—

107

D₁₉

—

108

C₂×#41

—

109

C₂²×Q₈

—

110

#137

—

111

C₂×Q₁₆

—

112

C₂×Q₁₆

—

113

C₂×SD₁₆

—

114

C₂×SD₁₆

C₂×D₁₉

yes

—

115

C₂×M₁₆

—

116

C₄⋊Q₈

—

117

C₄⋊Q₈

—

118

C₄⋊Q₈

—

119

C₄⋊Q₈

—

120

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

121

#127

C₂×D₁₉

yes

characteristic

122

#124

—

123

#121

—

124

C₄×D₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄²

—

127

#97

—

128

C₄×C₈

—

129

C₄×C₈

C₂×D₁₉

yes

characteristic

130

C₁₉

#3152

yes

characteristic, complemented, Sylow

131

#41

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

C₂²×D₁₉

yes

—

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂×D₄

C₂²×D₁₉

yes

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

Q₁₆

—

145

Q₁₆

—

146

SD₁₆

—

147

SD₁₆

—

148

M₁₆

—

149

C₂×C₈

—

150

C₂×C₈

C₂²×D₁₉

yes

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₂²⋊C₄

—

156

C₄²

—

157

C₄²

—

158

C₄²

C₂²×D₁₉

yes

characteristic

159

C₂³

—

160

C₂³

—

161

Q₈

—

162

Q₈

—

163

Q₈

—

164

Q₈

—

165

D₄

—

166

D₄

—

167

D₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

D₄×D₁₉

yes

—

178

C₂×C₄

C₂³×D₁₉

yes

characteristic

179

C₈

—

180

C₈

D₄×D₁₉

yes

—

181

C₂²

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

C₂×D₄×D₁₉

yes

characteristic

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

#10597361

yes

complemented

192

C₄

C₂×D₄×D₁₉

yes

—

193

C₂

—

194

C₂

—

195

C₂

#127×D₁₉

yes

characteristic

196

C₂

C₂×#10597361

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#492	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#11927092	C₂
hypercenter	#492	D₁₉
hypocenter	C₁₉	#3152
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#492

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
1. C₂×#10597361	C₂	semidirect
3. C₄⋊Q₈×D₁₉	C₂	semidirect
4. #11926935	C₂	semidirect
5. #11926924	C₂	semidirect
6. #11926923	C₂	semidirect
7. #11926916	C₂	semidirect
8. C₄×#64515	C₂	semidirect
9. C₁₉×#492	C₂	semidirect
59. #64515	D₄	semidirect
89. C₄×C₁₉	#137	semidirect
102. #492	D₁₉	semidirect
130. C₁₉	#3152	semidirect
191. C₄	#10597361	semidirect

H ≅ G/N

type

1. C₂×#10597361

C₂

semidirect

3. C₄⋊Q₈×D₁₉

C₂

semidirect

4. #11926935

C₂

semidirect

5. #11926924

C₂

semidirect

6. #11926923

C₂

semidirect

7. #11926916

C₂

semidirect

8. C₄×#64515

C₂

semidirect

9. C₁₉×#492

C₂

semidirect

59. #64515

D₄

semidirect

89. C₄×C₁₉

#137

semidirect

102. #492

D₁₉

semidirect

130. C₁₉

#3152

semidirect

191. C₄

#10597361

semidirect

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

subgroup	index
C₂×#10597361	2
#11927092	2
C₄⋊Q₈×D₁₉	2
#11926935	2
#11926924	2
#11926923	2
#11926916	2
C₄×#64515	2
C₁₉×#492	2
#3152	19

subgroup

index

C₄⋊Q₈×D₁₉

C₁₉×#492

Subgroups — #14574089

Conjugacy classes of subgroups

Complements

Maximal subgroups