Group #14564549 — subgroups

Subgroups — #14564549

Order 2432.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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	C₂²×#64528	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597279	C₂	1	1	yes	maximal, characteristic
3	#11926552	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597293	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597281	C₂	1	1	yes	maximal, characteristic
6	#11926500	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#419	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×#64528	—	2	1	no	—
13	C₂×#64528	—	2	1	no	—
14	C₂×#64528	—	2	2	no	—
15	C₂×#64528	C₄	1	4	yes	complemented
16	C₂×#64520	C₂²	1	1	yes	characteristic
17	C₂×#64520	C₂²	1	1	yes	characteristic
18	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₉×#103	—	2	2	no	—
20	#10597293	—	2	2	no	—
21	#10597281	—	2	2	no	—
22	#10597279	—	2	2	no	—
23	#10597267	—	2	2	no	—
24	#10597260	—	2	1	no	—
25	C₄×C₁₉⋊C₈	—	2	1	no	—
26	C₂×Q₈×C₁₉	—	2	1	no	—
27	C₂×Q₈×C₁₉	—	2	1	no	—
28	C₂×Q₈×C₁₉	—	2	1	no	—
29	C₂×Q₈×C₁₉	—	2	1	no	—
30	C₂×Q₈×C₁₉	—	2	1	no	—
31	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₉	—	2	1	no	—
35	C₂×Dic₃₈	—	2	1	no	—
36	C₂×Dic₃₈	—	2	1	no	—
37	C₂×Dic₃₈	—	2	1	no	—
38	C₂×Dic₃₈	—	2	1	no	—
39	C₂×Dic₃₈	—	2	1	no	—
40	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
41	M₁₆×C₁₉	—	2	1	no	—
42	M₁₆×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	—	2	1	no	—
44	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
45	C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₄²×C₁₉	—	2	1	no	—
47	#64528	—	2	4	no	—
48	#64528	—	2	4	no	—
49	#64520	—	2	1	no	—
50	#64520	—	2	1	no	—
51	#64520	—	2	1	no	—
52	#64520	D₄	1	2	yes	—
53	C₂×C₁₉⋊C₈	—	2	1	no	—
54	C₂×C₁₉⋊C₈	—	2	1	no	—
55	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
56	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
58	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
59	C₂³×C₁₉	#41	1	1	yes	characteristic
60	Q₈×C₁₉	—	2	2	no	—
61	Q₈×C₁₉	—	2	2	no	—
62	Q₈×C₁₉	—	4	1	no	—
63	Q₈×C₁₉	—	4	1	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	4	1	no	—
67	C₂×C₄×C₁₉	—	4	1	no	—
68	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
74	C₂×Dic₁₉	—	2	2	no	—
75	C₂×Dic₁₉	—	4	1	no	—
76	C₂×Dic₁₉	—	4	1	no	—
77	Dic₃₈	—	2	2	no	—
78	Dic₃₈	—	2	2	no	—
79	Dic₃₈	—	4	1	no	—
80	Dic₃₈	—	4	1	no	—
81	C₈×C₁₉	—	4	1	no	—
82	C₁₉⋊C₈	—	2	2	no	—
83	C₁₉⋊C₈	—	4	1	no	—
84	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
85	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
86	#1979	—	19	1	no	maximal, Sylow
87	C₂²×C₁₉	—	2	2	no	—
88	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
89	C₂²×C₁₉	#121	1	1	yes	characteristic
90	C₂²×C₁₉	#124	1	1	yes	characteristic
91	C₄×C₁₉	—	4	2	no	—
92	C₄×C₁₉	—	4	2	no	—
93	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
95	C₄×C₁₉	#121	1	1	yes	characteristic
96	C₄×C₁₉	#127	1	1	yes	characteristic
97	Dic₁₉	—	4	2	no	—
98	C₂²×Q₁₆	—	19	1	no	—
99	C₂×#108	—	19	1	no	—
100	#419	—	19	1	no	—
101	#419	D₁₉	1	1	yes	characteristic
102	C₂×#101	—	19	1	no	—
103	C₂×#101	—	19	1	no	—
104	#405	—	19	1	no	—
105	C₂×C₁₉	—	2	1	no	—
106	C₂×C₁₉	—	2	1	no	—
107	C₂×C₁₉	#390	1	1	yes	characteristic
108	C₂×C₁₉	#473	1	2	yes	—
109	C₂²×Q₈	—	19	1	no	—
110	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
111	C₂×Q₁₆	—	19	4	no	—
112	C₂×Q₁₆	—	38	1	no	—
113	C₂×Q₁₆	—	38	1	no	—
114	C₂×Q₁₆	—	38	2	no	—
115	C₂×M₁₆	—	19	1	no	—
116	C₂×M₁₆	—	19	1	no	—
117	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
118	C₂²×C₈	—	19	1	no	—
119	#117	C₂×D₁₉	1	1	yes	characteristic
120	#108	—	38	2	no	—
121	#103	—	2	2	no	—
122	#103	—	38	2	no	—
123	#101	—	38	2	no	—
124	#101	—	38	2	no	—
125	#97	—	38	1	no	—
126	C₄×C₈	—	38	1	no	—
127	C₁₉	#1979	1	1	yes	characteristic, complemented, Sylow
128	C₂×Q₈	—	2	1	no	—
129	C₂×Q₈	—	2	1	no	—
130	C₂×Q₈	—	2	1	no	—
131	C₂×Q₈	—	2	1	no	—
132	C₂×Q₈	—	2	1	no	—
133	C₂×Q₈	—	19	2	no	—
134	C₂×Q₈	—	38	1	no	—
135	C₂×Q₈	—	38	1	no	—
136	C₂×Q₈	—	38	1	no	—
137	C₂×Q₈	—	38	1	no	—
138	C₂×Q₈	—	38	1	no	—
139	C₂×Q₈	C₄×D₁₉	1	2	yes	—
140	C₂²×C₄	—	2	1	no	—
141	C₂²×C₄	—	38	1	no	—
142	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
143	Q₁₆	—	38	4	no	—
144	Q₁₆	—	38	4	no	—
145	M₁₆	—	2	1	no	—
146	M₁₆	—	2	1	no	—
147	M₁₆	—	19	2	no	—
148	M₁₆	—	38	1	no	—
149	M₁₆	—	38	1	no	—
150	M₁₆	—	38	1	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	19	2	no	—
153	C₂×C₈	—	19	1	no	—
154	C₂×C₈	—	19	1	no	—
155	C₂×C₈	—	19	2	no	—
156	C₂×C₈	—	38	1	no	—
157	C₂×C₈	—	38	1	no	—
158	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
159	C₂²⋊C₄	—	2	1	no	—
160	C₄²	—	2	1	no	—
161	C₂³	#64543	1	1	yes	characteristic
162	Q₈	—	2	2	no	—
163	Q₈	—	2	2	no	—
164	Q₈	—	4	1	no	—
165	Q₈	—	4	1	no	—
166	Q₈	—	38	2	no	—
167	Q₈	—	38	2	no	—
168	Q₈	—	76	1	no	—
169	Q₈	—	76	1	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	4	1	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	—	38	2	no	—
175	C₂×C₄	—	76	1	no	—
176	C₂×C₄	—	76	1	no	—
177	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
178	C₂×C₄	#64541	1	1	yes	characteristic
179	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
180	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
181	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
182	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
183	C₈	—	4	1	no	—
184	C₈	—	19	2	no	—
185	C₈	—	19	2	no	—
186	C₈	—	38	2	no	—
187	C₈	—	76	1	no	—
188	C₂²	—	2	2	no	—
189	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
190	C₂²	#10597331	1	1	yes	characteristic
191	C₂²	#10597385	1	1	yes	characteristic
192	C₄	—	4	2	no	—
193	C₄	—	4	2	no	—
194	C₄	—	76	2	no	—
195	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
196	C₄	#10597330	1	1	yes	characteristic
197	C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
198	C₄	#10597386	1	1	yes	characteristic
199	C₂	—	2	1	no	—
200	C₂	—	2	1	no	—
201	C₂	#11926444	1	1	yes	characteristic
202	C₂	#11926817	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64528

C₂

yes

maximal, characteristic

C₂×#10597279

C₂

yes

maximal, characteristic

#11926552

C₂

yes

maximal, characteristic

C₂×#10597293

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal, characteristic

#11926500

C₂

yes

maximal, characteristic

C₁₉×#419

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

—

—

C₄

yes

complemented

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#103

—

—

—

—

—

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

—

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

#41

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

#1979

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂²×Q₁₆

—

C₂×#108

—

100

#419

—

101

#419

D₁₉

yes

characteristic

102

C₂×#101

—

103

C₂×#101

—

104

#405

—

105

C₂×C₁₉

—

106

C₂×C₁₉

—

107

C₂×C₁₉

#390

yes

characteristic

108

C₂×C₁₉

#473

yes

—

109

C₂²×Q₈

—

110

C₂²×Q₈

C₂×D₁₉

yes

characteristic

111

C₂×Q₁₆

—

112

C₂×Q₁₆

—

113

C₂×Q₁₆

—

114

C₂×Q₁₆

—

115

C₂×M₁₆

—

116

C₂×M₁₆

—

117

C₂×M₁₆

C₂×D₁₉

yes

characteristic

118

C₂²×C₈

—

119

#117

C₂×D₁₉

yes

characteristic

120

#108

—

121

#103

—

122

#103

—

123

#101

—

124

#101

—

125

#97

—

126

C₄×C₈

—

127

C₁₉

#1979

yes

characteristic, complemented, Sylow

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

C₄×D₁₉

yes

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

C₂²×D₁₉

yes

characteristic

143

Q₁₆

—

144

Q₁₆

—

145

M₁₆

—

146

M₁₆

—

147

M₁₆

—

148

M₁₆

—

149

M₁₆

—

150

M₁₆

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₄⋊C₄

C₂²⋊D₁₉

yes

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₂³

#64543

yes

characteristic

162

Q₈

—

163

Q₈

—

164

Q₈

—

165

Q₈

—

166

Q₈

—

167

Q₈

—

168

Q₈

—

169

Q₈

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

178

C₂×C₄

#64541

yes

characteristic

179

C₂×C₄

D₄×D₁₉

yes

characteristic

180

C₂×C₄

D₄×D₁₉

yes

characteristic

181

C₂×C₄

D₄×D₁₉

yes

characteristic

182

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

183

C₈

—

184

C₈

—

185

C₈

—

186

C₈

—

187

C₈

—

188

C₂²

—

189

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

190

C₂²

#10597331

yes

characteristic

191

C₂²

#10597385

yes

characteristic

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

196

C₄

#10597330

yes

characteristic

197

C₄

C₄×C₂²⋊D₁₉

yes

characteristic

198

C₄

#10597386

yes

characteristic

199

C₂

—

200

C₂

—

201

C₂

#11926444

yes

characteristic

202

C₂

#11926817

yes

—

	subgroup	G/H
center	C₂²	#10597385
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#419	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂³×C₁₉	#41
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#419	D₁₉
hypocenter	C₁₉	#1979
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #419

subgroup

G/H

center

C₂²

#10597385

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#419

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #419

N	H ≅ G/N	type
15. C₂×#64528	C₄	semidirect
127. C₁₉	#1979	semidirect

H ≅ G/N

type

15. C₂×#64528

C₄

semidirect

127. C₁₉

#1979

semidirect

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

subgroup	index
C₂²×#64528	2
C₂×#10597279	2
#11926552	2
C₂×#10597293	2
C₂×#10597281	2
#11926500	2
C₁₉×#419	2
#1979	19

subgroup

index

C₂²×#64528

C₁₉×#419

Subgroups — #14564549

Conjugacy classes of subgroups

Complements

Maximal subgroups