Group #14564898 — subgroups

Subgroups — #14564898

Order 2432.

276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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×#64516	C₂	1	1	yes	maximal, characteristic
2	#11926552	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926548	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597281	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597280	C₂	1	1	yes	maximal, characteristic
6	#11926309	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₇₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×#64520	C₂²	1	1	yes	characteristic
14	C₂×#64520	C₂²	1	1	yes	characteristic
15	C₂×#64516	—	2	2	no	—
16	C₂×#64516	—	2	2	no	—
17	C₂×#64516	—	2	2	no	—
18	C₁₉×C₄⋊C₈	—	2	2	no	—
19	#10597281	—	2	2	no	—
20	#10597280	—	2	2	no	—
21	#10597267	—	2	2	no	—
22	#10597266	—	2	2	no	—
23	C₂³×D₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	—	2	1	no	—
26	C₂×D₇₆	—	2	1	no	—
27	C₂×D₇₆	—	2	1	no	—
28	C₂×D₇₆	—	2	1	no	—
29	C₂×D₇₆	—	2	1	no	—
30	C₂×D₇₆	—	2	1	no	—
31	C₂×D₇₆	D₄	1	2	yes	—
32	C₂×Dic₃₈	—	2	1	no	—
33	C₂×Dic₃₈	—	2	1	no	—
34	C₂×Dic₃₈	—	2	1	no	—
35	C₂×Dic₃₈	—	2	1	no	—
36	C₂×Dic₃₈	—	2	1	no	—
37	C₂×Dic₃₈	D₄	1	2	yes	—
38	M₁₆×C₁₉	—	2	1	no	—
39	M₁₆×C₁₉	—	2	1	no	—
40	C₂×C₈×C₁₉	—	2	1	no	—
41	C₂×C₈×C₁₉	—	2	1	no	—
42	C₂×C₈×C₁₉	—	2	1	no	—
43	C₂×C₈×C₁₉	D₄	1	2	yes	—
44	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
45	C₂²⋊C₄×C₁₉	—	2	1	no	—
46	C₄²×C₁₉	—	2	1	no	—
47	#64520	—	2	1	no	—
48	#64520	—	2	1	no	—
49	#64520	—	2	1	no	—
50	#64520	—	2	1	no	—
51	C₂×C₁₉⋊C₈	—	2	1	no	—
52	C₂×C₁₉⋊C₈	—	2	1	no	—
53	#64516	—	2	8	no	—
54	C₂³×C₁₉	#41	1	1	yes	characteristic
55	C₂²×D₁₉	—	2	2	no	—
56	C₂²×D₁₉	—	4	1	no	—
57	C₂²×D₁₉	—	4	1	no	—
58	C₂²×D₁₉	—	8	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
65	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	4	1	no	—
68	C₂×Dic₁₉	—	4	1	no	—
69	D₇₆	—	2	2	no	—
70	D₇₆	—	2	2	no	—
71	D₇₆	—	4	1	no	—
72	D₇₆	—	4	1	no	—
73	Dic₃₈	—	2	2	no	—
74	Dic₃₈	—	2	2	no	—
75	Dic₃₈	—	4	1	no	—
76	Dic₃₈	—	4	1	no	—
77	C₈×C₁₉	—	2	2	no	—
78	C₈×C₁₉	—	4	1	no	—
79	C₁₉⋊C₈	—	4	1	no	—
80	C₁₉⋊C₈	—	4	1	no	—
81	#2046	—	19	1	no	maximal, Sylow
82	C₂²×C₁₉	—	2	2	no	—
83	C₂²×C₁₉	#121	1	1	yes	characteristic
84	C₂²×C₁₉	#123	1	1	yes	characteristic
85	C₂²×C₁₉	#123	1	1	yes	characteristic
86	C₂×D₁₉	—	4	2	no	—
87	C₂×D₁₉	—	8	2	no	—
88	C₂×D₁₉	—	8	2	no	—
89	C₂×D₁₉	—	8	2	no	—
90	C₄×C₁₉	—	4	2	no	—
91	C₄×C₁₉	#120	1	1	yes	characteristic
92	C₄×C₁₉	#121	1	1	yes	characteristic
93	C₄×C₁₉	#121	1	1	yes	characteristic
94	C₄×C₁₉	#124	1	1	yes	characteristic
95	Dic₁₉	—	4	2	no	—
96	C₂²×SD₁₆	—	19	1	no	—
97	#424	D₁₉	1	1	yes	characteristic, complemented
98	#419	—	19	1	no	—
99	#418	—	19	1	no	—
100	C₂×#101	—	19	1	no	—
101	C₂×#100	—	19	1	no	—
102	#341	—	19	1	no	—
103	C₂×C₁₉	—	2	1	no	—
104	C₂×C₁₉	—	2	1	no	—
105	C₂×C₁₉	#394	1	1	yes	characteristic
106	C₂×C₁₉	#471	1	2	yes	—
107	D₁₉	—	8	2	no	—
108	C₂²×Q₈	—	19	1	no	—
109	C₂²×D₄	—	19	1	no	—
110	C₂×SD₁₆	—	38	2	no	—
111	C₂×SD₁₆	—	38	2	no	—
112	C₂×SD₁₆	—	38	2	no	—
113	C₂×M₁₆	—	19	1	no	—
114	C₂×M₁₆	—	19	1	no	—
115	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
116	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
117	#117	C₂×D₁₉	1	1	yes	characteristic
118	C₄⋊C₈	—	2	2	no	—
119	#103	—	38	2	no	—
120	#102	—	38	2	no	—
121	#101	—	38	2	no	—
122	#100	—	38	2	no	—
123	C₁₉	#2046	1	1	yes	characteristic, complemented, Sylow
124	C₂⁴	—	38	1	no	—
125	C₂×Q₈	—	19	2	no	—
126	C₂×Q₈	—	38	1	no	—
127	C₂×Q₈	—	38	1	no	—
128	C₂×Q₈	—	38	1	no	—
129	C₂×Q₈	—	38	1	no	—
130	C₂×Q₈	—	38	1	no	—
131	C₂×D₄	—	19	2	no	—
132	C₂×D₄	—	38	1	no	—
133	C₂×D₄	—	38	1	no	—
134	C₂×D₄	—	38	1	no	—
135	C₂×D₄	—	38	1	no	—
136	C₂×D₄	—	38	1	no	—
137	C₂²×C₄	—	38	1	no	—
138	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
139	SD₁₆	—	38	8	no	—
140	M₁₆	—	2	1	no	—
141	M₁₆	—	2	1	no	—
142	M₁₆	—	38	1	no	—
143	M₁₆	—	38	1	no	—
144	M₁₆	—	38	1	no	—
145	M₁₆	—	38	1	no	—
146	C₂×C₈	—	2	1	no	—
147	C₂×C₈	—	2	1	no	—
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	38	1	no	—
150	C₂×C₈	—	38	1	no	—
151	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
152	C₄⋊C₄	D₇₆	1	2	yes	—
153	C₂²⋊C₄	—	2	1	no	—
154	C₄²	—	2	1	no	—
155	C₂³	—	38	2	no	—
156	C₂³	—	76	1	no	—
157	C₂³	—	76	1	no	—
158	C₂³	—	152	2	no	—
159	C₂³	#64541	1	1	yes	characteristic
160	Q₈	—	38	2	no	—
161	Q₈	—	38	2	no	—
162	Q₈	—	76	1	no	—
163	Q₈	—	76	1	no	—
164	D₄	—	38	2	no	—
165	D₄	—	38	2	no	—
166	D₄	—	76	1	no	—
167	D₄	—	76	1	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	38	2	no	—
170	C₂×C₄	—	76	1	no	—
171	C₂×C₄	—	76	1	no	—
172	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
173	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
174	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
175	C₂×C₄	#64545	1	1	yes	characteristic
176	C₂×C₄	#64545	1	1	yes	characteristic
177	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
178	C₈	—	2	2	no	—
179	C₈	—	4	1	no	—
180	C₈	—	76	1	no	—
181	C₈	—	76	1	no	—
182	C₂²	—	2	2	no	—
183	C₂²	—	76	2	no	—
184	C₂²	—	152	2	no	—
185	C₂²	—	152	2	no	—
186	C₂²	—	152	2	no	—
187	C₂²	#10597340	1	1	yes	characteristic
188	C₂²	#10597340	1	1	yes	characteristic
189	C₂²	#10597376	1	1	yes	characteristic
190	C₄	—	4	2	no	—
191	C₄	—	76	2	no	—
192	C₄	#10597341	1	1	yes	characteristic
193	C₄	#10597341	1	1	yes	characteristic
194	C₄	#10597383	1	1	yes	characteristic
195	C₄	#10597393	1	1	yes	characteristic
196	C₂	—	2	1	no	—
197	C₂	—	2	1	no	—
198	C₂	—	152	2	no	—
199	C₂	#11926461	1	1	yes	characteristic
200	C₂	#11926807	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64516

C₂

yes

maximal, characteristic

#11926552

C₂

yes

maximal, characteristic, complemented

#11926548

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal, characteristic, complemented

C₂×#10597280

C₂

yes

maximal, characteristic

#11926309

C₂

yes

maximal, characteristic, complemented

C₁₉×#424

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

—

—

C₁₉×C₄⋊C₈

—

—

—

—

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#64516

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

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

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2046

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂²×SD₁₆

—

#424

D₁₉

yes

characteristic, complemented

#419

—

#418

—

100

C₂×#101

—

101

C₂×#100

—

102

#341

—

103

C₂×C₁₉

—

104

C₂×C₁₉

—

105

C₂×C₁₉

#394

yes

characteristic

106

C₂×C₁₉

#471

yes

—

107

D₁₉

—

108

C₂²×Q₈

—

109

C₂²×D₄

—

110

C₂×SD₁₆

—

111

C₂×SD₁₆

—

112

C₂×SD₁₆

—

113

C₂×M₁₆

—

114

C₂×M₁₆

—

115

C₂×M₁₆

C₂×D₁₉

yes

characteristic

116

C₂²×C₈

C₂×D₁₉

yes

characteristic

117

#117

C₂×D₁₉

yes

characteristic

118

C₄⋊C₈

—

119

#103

—

120

#102

—

121

#101

—

122

#100

—

123

C₁₉

#2046

yes

characteristic, complemented, Sylow

124

C₂⁴

—

125

C₂×Q₈

—

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×D₄

—

132

C₂×D₄

—

133

C₂×D₄

—

134

C₂×D₄

—

135

C₂×D₄

—

136

C₂×D₄

—

137

C₂²×C₄

—

138

C₂²×C₄

C₂²×D₁₉

yes

characteristic

139

SD₁₆

—

140

M₁₆

—

141

M₁₆

—

142

M₁₆

—

143

M₁₆

—

144

M₁₆

—

145

M₁₆

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

C₂²⋊D₁₉

yes

—

152

C₄⋊C₄

D₇₆

yes

—

153

C₂²⋊C₄

—

154

C₄²

—

155

C₂³

—

156

C₂³

—

157

C₂³

—

158

C₂³

—

152

—

159

C₂³

#64541

yes

characteristic

160

Q₈

—

161

Q₈

—

162

Q₈

—

163

Q₈

—

164

D₄

—

165

D₄

—

166

D₄

—

167

D₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

C₂×D₇₆

yes

characteristic

173

C₂×C₄

D₄×D₁₉

yes

characteristic

174

C₂×C₄

D₄×D₁₉

yes

characteristic

175

C₂×C₄

#64545

yes

characteristic

176

C₂×C₄

#64545

yes

characteristic

177

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

182

C₂²

—

183

C₂²

—

184

C₂²

—

152

—

185

C₂²

—

152

—

186

C₂²

—

152

—

187

C₂²

#10597340

yes

characteristic

188

C₂²

#10597340

yes

characteristic

189

C₂²

#10597376

yes

characteristic

190

C₄

—

191

C₄

—

192

C₄

#10597341

yes

characteristic

193

C₄

#10597341

yes

characteristic

194

C₄

#10597383

yes

characteristic

195

C₄

#10597393

yes

characteristic

196

C₂

—

197

C₂

—

198

C₂

—

152

—

199

C₂

#11926461

yes

characteristic

200

C₂

#11926807

yes

—

	subgroup	G/H
center	C₂²	#10597376
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#424	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂²×D₇₆	C₂²
hypercenter	#424	D₁₉
hypocenter	C₁₉	#2046
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#10597376

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#424

C₂

socle

C₂²×C₁₉

#121

prime radical

C₂²×D₇₆

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
2. #11926552	C₂	semidirect
4. C₂×#10597281	C₂	semidirect
6. #11926309	C₂	semidirect
7. C₁₉×#424	C₂	semidirect
97. #424	D₁₉	semidirect
123. C₁₉	#2046	semidirect

H ≅ G/N

type

2. #11926552

C₂

semidirect

4. C₂×#10597281

C₂

semidirect

6. #11926309

C₂

semidirect

7. C₁₉×#424

C₂

semidirect

97. #424

D₁₉

semidirect

123. C₁₉

#2046

semidirect

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

subgroup	index
C₂²×#64516	2
#11926552	2
#11926548	2
C₂×#10597281	2
C₂×#10597280	2
#11926309	2
C₁₉×#424	2
#2046	19

subgroup

index

C₂²×#64516

C₁₉×#424

Subgroups — #14564898

Conjugacy classes of subgroups

Complements

Maximal subgroups