Group #14564677 — subgroups

Subgroups — #14564677

Order 2432.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10597395	C₂	1	2	yes	maximal, complemented
2	C₂×#10597294	C₂	1	2	yes	maximal, complemented
3	#11926445	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926313	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#41×C₁₉	C₂²	1	2	yes	—
7	C₂²×D₇₆	C₂²	1	1	yes	characteristic
8	C₁₉×C₂²⋊Q₈	—	2	2	no	—
9	C₁₉×#121	—	2	2	no	—
10	C₁₉×#121	—	2	2	no	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	#10597395	—	2	4	no	—
13	#10597395	—	2	4	no	—
14	C₂×#64527	—	2	2	no	—
15	C₂×#64525	—	2	2	no	—
16	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
17	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×#64520	C₂²	1	2	yes	—
19	#10597294	—	2	4	no	—
20	C₂³×D₁₉	—	2	1	no	—
21	#41×C₁₉	—	2	2	no	—
22	#41×C₁₉	—	2	2	no	—
23	#41×C₁₉	—	2	2	no	—
24	#41×C₁₉	—	2	2	no	—
25	C₂×Q₈×C₁₉	D₄	1	2	yes	—
26	C₂×D₄×C₁₉	—	2	2	no	—
27	C₂×D₄×C₁₉	—	2	2	no	—
28	C₂×D₄×C₁₉	D₄	1	2	yes	—
29	C₂²×C₄×C₁₉	—	2	2	no	—
30	C₂²×C₄×C₁₉	D₄	1	2	yes	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂×D₇₆	—	2	2	no	—
34	C₂×D₇₆	—	2	2	no	—
35	C₂×D₇₆	—	2	1	no	—
36	C₂×D₇₆	D₄	1	2	yes	complemented
37	C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂²⋊C₄×C₁₉	—	2	4	no	—
40	#64527	—	2	8	no	—
41	#64525	—	2	8	no	—
42	(C₂×D₁₉)⋊C₄	—	4	4	no	—
43	C₄×Dic₁₉	—	2	2	no	—
44	#64520	—	2	2	no	—
45	#64520	D₄	1	4	yes	complemented
46	C₂×C₁₉⋊C₈	—	2	2	no	—
47	C₂³×C₁₉	—	2	2	no	—
48	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×D₁₉	—	2	2	no	—
50	C₂²×D₁₉	—	4	2	no	—
51	C₂²×D₁₉	—	4	2	no	—
52	C₂²×D₁₉	—	4	1	no	—
53	C₂²×D₁₉	—	4	1	no	—
54	Q₈×C₁₉	—	2	2	no	—
55	Q₈×C₁₉	—	2	2	no	—
56	D₄×C₁₉	—	2	2	no	—
57	D₄×C₁₉	—	2	2	no	—
58	D₄×C₁₉	—	4	2	no	—
59	D₄×C₁₉	—	4	2	no	—
60	D₄×C₁₉	—	8	2	no	—
61	C₂×C₄×C₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	4	2	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
70	C₂×Dic₁₉	—	2	2	no	—
71	C₂×Dic₁₉	—	4	1	no	—
72	C₂×Dic₁₉	—	4	1	no	—
73	D₇₆	—	2	4	no	—
74	D₇₆	—	4	2	no	—
75	C₁₉⋊C₈	—	2	4	no	—
76	#2006	—	19	1	no	maximal, Sylow
77	C₂²×C₁₉	—	2	1	no	—
78	C₂²×C₁₉	—	2	1	no	—
79	C₂²×C₁₉	—	4	2	no	—
80	C₂²×C₁₉	—	4	2	no	—
81	C₂²×C₁₉	—	4	2	no	—
82	C₂²×C₁₉	#120	1	1	yes	characteristic
83	C₂²×C₁₉	#121	1	1	yes	characteristic
84	C₂²×C₁₉	#127	1	1	yes	characteristic
85	C₂×D₁₉	—	4	4	no	—
86	C₂×D₁₉	—	4	2	no	—
87	C₂×D₁₉	—	8	2	no	—
88	C₂×D₁₉	—	8	1	no	—
89	C₂×D₁₉	—	8	1	no	—
90	C₄×C₁₉	—	4	2	no	—
91	C₄×C₁₉	—	4	2	no	—
92	C₄×C₁₉	#120	1	2	yes	—
93	C₄×C₁₉	#121	1	2	yes	—
94	Dic₁₉	—	4	2	no	—
95	C₂×AGL(1,ℤ/8)	—	19	2	no	—
96	#537	D₁₉	1	1	yes	characteristic, complemented
97	C₂×#104	—	19	2	no	—
98	#390	—	19	1	no	—
99	#343	—	19	1	no	—
100	C₂×C₁₉	—	2	1	no	—
101	C₂×C₁₉	—	2	1	no	—
102	C₂×C₁₉	—	8	2	no	—
103	C₂×C₁₉	#392	1	1	yes	characteristic
104	C₂×C₁₉	#453	1	1	yes	characteristic
105	C₂×C₁₉	#454	1	1	yes	characteristic
106	D₁₉	—	8	2	no	—
107	C₂×#41	C₂×D₁₉	1	2	yes	—
108	C₂²×D₄	—	19	1	no	—
109	AGL(1,ℤ/8)	—	38	4	no	—
110	AGL(1,ℤ/8)	—	38	4	no	—
111	C₂×SD₁₆	—	38	2	no	—
112	C₂×D₈	—	38	2	no	—
113	C₂×M₁₆	—	19	2	no	—
114	C₂²⋊Q₈	—	2	2	no	—
115	#121	—	2	2	no	—
116	#121	—	2	2	no	—
117	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
118	C₂×C₂²⋊C₄	—	38	2	no	—
119	C₂×C₄²	—	19	1	no	—
120	#104	—	38	4	no	—
121	C₁₉	#2006	1	1	yes	characteristic, complemented, Sylow
122	C₂⁴	—	38	1	no	—
123	#41	—	2	2	no	—
124	#41	—	2	2	no	—
125	#41	—	2	2	no	—
126	#41	—	2	2	no	—
127	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
128	C₂×D₄	—	2	2	no	—
129	C₂×D₄	—	2	2	no	—
130	C₂×D₄	—	19	2	no	—
131	C₂×D₄	—	38	2	no	—
132	C₂×D₄	—	38	1	no	—
133	C₂×D₄	—	38	2	no	—
134	C₂×D₄	C₂²⋊D₁₉	1	2	yes	—
135	C₂²×C₄	—	2	2	no	—
136	C₂²×C₄	—	38	1	no	—
137	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
138	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
139	SD₁₆	—	38	8	no	—
140	D₈	—	38	8	no	—
141	M₁₆	—	19	4	no	—
142	M₁₆	—	38	2	no	—
143	C₂×C₈	—	38	2	no	—
144	C₄⋊C₄	—	2	2	no	—
145	C₄⋊C₄	—	2	2	no	—
146	C₂²⋊C₄	—	2	4	no	—
147	C₂²⋊C₄	—	76	4	no	—
148	C₄²	—	38	2	no	—
149	C₂³	—	2	2	no	—
150	C₂³	—	38	2	no	—
151	C₂³	—	76	2	no	—
152	C₂³	—	76	2	no	—
153	C₂³	—	76	1	no	—
154	C₂³	—	76	1	no	—
155	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
156	Q₈	—	2	2	no	—
157	Q₈	—	2	2	no	—
158	D₄	—	2	2	no	—
159	D₄	—	2	2	no	—
160	D₄	—	4	2	no	—
161	D₄	—	4	2	no	—
162	D₄	—	8	2	no	—
163	D₄	—	38	4	no	—
164	D₄	—	76	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	4	2	no	—
168	C₂×C₄	—	4	2	no	—
169	C₂×C₄	—	4	2	no	—
170	C₂×C₄	—	38	2	no	—
171	C₂×C₄	—	76	1	no	—
172	C₂×C₄	—	76	1	no	—
173	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
174	C₂×C₄	D₄×D₁₉	1	2	yes	—
175	C₂×C₄	#64543	1	1	yes	characteristic
176	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
177	C₈	—	38	4	no	—
178	C₂²	—	2	1	no	—
179	C₂²	—	2	1	no	—
180	C₂²	—	4	2	no	—
181	C₂²	—	4	2	no	—
182	C₂²	—	4	2	no	—
183	C₂²	—	76	4	no	—
184	C₂²	—	76	2	no	—
185	C₂²	—	152	2	no	—
186	C₂²	—	152	1	no	—
187	C₂²	—	152	1	no	—
188	C₂²	#10597384	1	1	yes	characteristic
189	C₂²	#10597386	1	1	yes	characteristic
190	C₂²	#10597399	1	1	yes	characteristic
191	C₄	—	4	2	no	—
192	C₄	—	4	2	no	—
193	C₄	—	76	2	no	—
194	C₄	#10597383	1	2	yes	—
195	C₄	#10597385	1	2	yes	—
196	C₂	—	2	1	no	—
197	C₂	—	2	1	no	—
198	C₂	—	8	2	no	—
199	C₂	—	152	2	no	—
200	C₂	#11926452	1	1	yes	characteristic
201	C₂	#11926712	1	1	yes	characteristic
202	C₂	#11926717	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597395

C₂

yes

maximal, complemented

C₂×#10597294

C₂

yes

maximal, complemented

#11926445

C₂

yes

maximal, characteristic, complemented

#11926313

C₂

yes

maximal, characteristic, complemented

C₁₉×#537

C₂

yes

maximal, characteristic, complemented

C₂×#41×C₁₉

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₁₉×#121

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

—

—

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

#10597294

—

C₂³×D₁₉

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

complemented

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

#64527

—

#64525

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

—

#64520

—

#64520

D₄

yes

complemented

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×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×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₁₉⋊C₈

—

#2006

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

C₂×AGL(1,ℤ/8)

—

#537

D₁₉

yes

characteristic, complemented

C₂×#104

—

#390

—

#343

—

100

C₂×C₁₉

—

101

C₂×C₁₉

—

102

C₂×C₁₉

—

103

C₂×C₁₉

#392

yes

characteristic

104

C₂×C₁₉

#453

yes

characteristic

105

C₂×C₁₉

#454

yes

characteristic

106

D₁₉

—

107

C₂×#41

C₂×D₁₉

yes

—

108

C₂²×D₄

—

109

AGL(1,ℤ/8)

—

110

AGL(1,ℤ/8)

—

111

C₂×SD₁₆

—

112

C₂×D₈

—

113

C₂×M₁₆

—

114

C₂²⋊Q₈

—

115

#121

—

116

#121

—

117

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

118

C₂×C₂²⋊C₄

—

119

C₂×C₄²

—

120

#104

—

121

C₁₉

#2006

yes

characteristic, complemented, Sylow

122

C₂⁴

—

123

#41

—

124

#41

—

125

#41

—

126

#41

—

127

C₂×Q₈

C₂²⋊D₁₉

yes

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

—

131

C₂×D₄

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

C₂²⋊D₁₉

yes

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₂²⋊D₁₉

yes

—

138

C₂²×C₄

C₂²×D₁₉

yes

characteristic

139

SD₁₆

—

140

D₈

—

141

M₁₆

—

142

M₁₆

—

143

C₂×C₈

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₂²⋊C₄

—

147

C₂²⋊C₄

—

148

C₄²

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

154

C₂³

—

155

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

156

Q₈

—

157

Q₈

—

158

D₄

—

159

D₄

—

160

D₄

—

161

D₄

—

162

D₄

—

163

D₄

—

164

D₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

D₄×D₁₉

yes

characteristic

174

C₂×C₄

D₄×D₁₉

yes

—

175

C₂×C₄

#64543

yes

characteristic

176

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

177

C₈

—

178

C₂²

—

179

C₂²

—

180

C₂²

—

181

C₂²

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

185

C₂²

—

152

—

186

C₂²

—

152

—

187

C₂²

—

152

—

188

C₂²

#10597384

yes

characteristic

189

C₂²

#10597386

yes

characteristic

190

C₂²

#10597399

yes

characteristic

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

#10597383

yes

—

195

C₄

#10597385

yes

—

196

C₂

—

197

C₂

—

198

C₂

—

199

C₂

—

152

—

200

C₂

#11926452

yes

characteristic

201

C₂

#11926712

yes

characteristic

202

C₂

#11926717

yes

characteristic

	subgroup	G/H
center	C₂²	#10597399
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#537	C₂
socle	C₂²×C₁₉	#120
hypercenter	#537	D₁₉
hypocenter	C₁₉	#2006
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #537

subgroup

G/H

center

C₂²

#10597399

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#537

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #537

N	H ≅ G/N	type
1. C₂×#10597395	C₂	semidirect
2. C₂×#10597294	C₂	semidirect
3. #11926445	C₂	semidirect
4. #11926313	C₂	semidirect
5. C₁₉×#537	C₂	semidirect
36. C₂×D₇₆	D₄	semidirect
45. #64520	D₄	semidirect
96. #537	D₁₉	semidirect
121. C₁₉	#2006	semidirect

H ≅ G/N

type

1. C₂×#10597395

C₂

semidirect

2. C₂×#10597294

C₂

semidirect

3. #11926445

C₂

semidirect

4. #11926313

C₂

semidirect

5. C₁₉×#537

C₂

semidirect

36. C₂×D₇₆

D₄

semidirect

45. #64520

D₄

semidirect

96. #537

D₁₉

semidirect

121. C₁₉

#2006

semidirect

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

subgroup	index
C₂×#10597395	2
C₂×#10597294	2
#11926445	2
#11926313	2
C₁₉×#537	2
#2006	19

subgroup

index

C₁₉×#537

Subgroups — #14564677

Conjugacy classes of subgroups

Complements

Maximal subgroups