Group #14564705 — subgroups

Subgroups — #14564705

Order 2432.

510 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 97 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×#64525	C₂	1	2	yes	maximal, complemented
2	C₂×#10597320	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597266	C₂	1	2	yes	maximal, complemented
4	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×D₇₆	—	2	2	no	—
8	C₂²×D₇₆	C₂²	1	2	yes	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×#64525	—	2	4	no	—
13	C₂×#64525	—	2	4	no	—
14	C₂×#64525	—	2	4	no	—
15	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
16	#10597320	—	2	4	no	—
17	#10597266	—	2	4	no	—
18	C₂⁴×C₁₉	—	2	1	no	—
19	C₂³×D₁₉	—	2	2	no	—
20	C₂×D₄×C₁₉	—	2	2	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	D₄	1	2	yes	complemented
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	D₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×D₇₆	—	2	2	no	—
28	C₂×D₇₆	—	2	2	no	—
29	C₂×D₇₆	—	2	2	no	—
30	C₂×D₇₆	—	2	2	no	—
31	C₂×D₇₆	—	2	8	no	—
32	C₂×D₇₆	—	2	2	no	—
33	C₂×D₇₆	—	4	4	no	—
34	C₂×D₇₆	—	4	4	no	—
35	C₂×D₇₆	D₄	1	4	yes	—
36	C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂²⋊C₄×C₁₉	—	4	4	no	—
38	C₄²×C₁₉	—	2	2	no	—
39	#64525	—	2	16	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂×C₁₉⋊C₈	D₄	1	4	yes	complemented
43	C₂³×C₁₉	—	2	2	no	—
44	C₂³×C₁₉	—	4	1	no	—
45	C₂³×C₁₉	—	4	1	no	—
46	C₂³×C₁₉	—	4	2	no	—
47	C₂³×C₁₉	—	4	2	no	—
48	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×D₁₉	—	2	4	no	—
50	C₂²×D₁₉	—	4	2	no	—
51	C₂²×D₁₉	—	4	2	no	—
52	C₂²×D₁₉	—	4	4	no	—
53	C₂²×D₁₉	—	4	4	no	—
54	D₄×C₁₉	—	2	4	no	—
55	D₄×C₁₉	—	4	2	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	4	1	no	—
59	C₂×C₄×C₁₉	—	4	2	no	—
60	C₂×C₄×C₁₉	D₈	1	4	yes	complemented
61	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
64	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
65	D₇₆	—	2	4	no	—
66	D₇₆	—	2	4	no	—
67	D₇₆	—	4	16	no	—
68	D₇₆	—	4	2	no	—
69	D₇₆	—	4	2	no	—
70	C₁₉⋊C₈	—	2	4	no	—
71	#2011	—	19	1	no	maximal, Sylow
72	C₂²×C₁₉	—	4	2	no	—
73	C₂²×C₁₉	—	4	4	no	—
74	C₂²×C₁₉	—	8	2	no	—
75	C₂²×C₁₉	—	8	1	no	—
76	C₂²×C₁₉	—	8	1	no	—
77	C₂²×C₁₉	#120	1	1	yes	characteristic
78	C₂²×C₁₉	#121	1	1	yes	characteristic
79	C₂²×C₁₉	#127	1	1	yes	characteristic
80	C₂²×C₁₉	C₂×D₈	1	2	yes	—
81	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
82	C₂×D₁₉	—	4	4	no	—
83	C₂×D₁₉	—	4	8	no	—
84	C₂×D₁₉	—	8	4	no	—
85	C₂×D₁₉	—	8	2	no	—
86	C₂×D₁₉	—	8	2	no	—
87	C₄×C₁₉	—	2	4	no	—
88	C₄×C₁₉	—	8	1	no	—
89	C₄×C₁₉	#120	1	2	yes	—
90	C₄×C₁₉	#121	1	2	yes	—
91	C₂²×D₈	—	19	2	no	—
92	C₂×#127	—	19	1	no	—
93	C₂×#102	—	19	2	no	—
94	#390	D₁₉	1	1	yes	characteristic, complemented
95	#336	—	19	1	no	—
96	C₂×C₁₉	—	8	2	no	—
97	C₂×C₁₉	#392	1	1	yes	characteristic
98	C₂×C₁₉	#447	1	2	yes	—
99	C₂×C₁₉	#459	1	2	yes	—
100	C₂×C₁₉	#493	1	1	yes	characteristic
101	C₂×C₁₉	#496	1	1	yes	characteristic
102	D₁₉	—	8	4	no	—
103	C₂²×D₄	—	19	2	no	—
104	C₂²×D₄	—	38	2	no	—
105	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
106	C₂×D₈	—	38	4	no	—
107	C₂×D₈	—	38	4	no	—
108	C₂×D₈	—	38	4	no	—
109	C₂²×C₈	—	19	2	no	—
110	#127	—	38	4	no	—
111	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
112	C₂×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
114	#102	—	38	4	no	—
115	C₁₉	#2011	1	1	yes	characteristic, complemented, Sylow
116	C₂⁴	—	2	1	no	—
117	C₂⁴	—	38	2	no	—
118	C₂×D₄	—	2	1	no	—
119	C₂×D₄	—	2	2	no	—
120	C₂×D₄	—	2	2	no	—
121	C₂×D₄	—	19	4	no	—
122	C₂×D₄	—	38	8	no	—
123	C₂×D₄	—	38	2	no	—
124	C₂×D₄	—	38	2	no	—
125	C₂×D₄	—	38	2	no	—
126	C₂×D₄	—	38	2	no	—
127	C₂×D₄	—	38	2	no	—
128	C₂×D₄	—	76	4	no	—
129	C₂×D₄	—	76	4	no	—
130	C₂×D₄	D₇₆	1	2	yes	complemented
131	C₂²×C₄	—	2	1	no	—
132	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
133	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
134	D₈	—	38	16	no	—
135	C₂×C₈	—	19	4	no	—
136	C₂×C₈	—	38	2	no	—
137	C₂×C₈	—	38	2	no	—
138	C₄⋊C₄	—	2	2	no	—
139	C₂²⋊C₄	—	4	4	no	—
140	C₄²	—	2	2	no	—
141	C₂³	—	2	2	no	—
142	C₂³	—	4	2	no	—
143	C₂³	—	4	1	no	—
144	C₂³	—	4	1	no	—
145	C₂³	—	4	2	no	—
146	C₂³	—	38	4	no	—
147	C₂³	—	76	2	no	—
148	C₂³	—	76	4	no	—
149	C₂³	—	76	2	no	—
150	C₂³	—	76	4	no	—
151	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
152	D₄	—	2	4	no	—
153	D₄	—	4	2	no	—
154	D₄	—	38	4	no	—
155	D₄	—	38	4	no	—
156	D₄	—	76	16	no	—
157	D₄	—	76	2	no	—
158	D₄	—	76	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	4	1	no	—
163	C₂×C₄	#64525	1	4	yes	complemented
164	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
165	C₂×C₄	#64541	1	1	yes	characteristic
166	C₂×C₄	D₄×D₁₉	1	2	yes	—
167	C₂×C₄	D₄×D₁₉	1	2	yes	—
168	C₈	—	38	4	no	—
169	C₂²	—	4	2	no	—
170	C₂²	—	4	4	no	—
171	C₂²	—	8	1	no	—
172	C₂²	—	8	2	no	—
173	C₂²	—	8	1	no	—
174	C₂²	—	76	8	no	—
175	C₂²	—	76	4	no	—
176	C₂²	—	152	2	no	—
177	C₂²	—	152	2	no	—
178	C₂²	—	152	4	no	—
179	C₂²	#10597376	1	1	yes	characteristic
180	C₂²	C₂×#64525	1	2	yes	—
181	C₂²	#10597383	1	1	yes	characteristic
182	C₂²	#10597386	1	1	yes	characteristic
183	C₂²	#10597395	1	2	yes	—
184	C₄	—	2	4	no	—
185	C₄	—	8	1	no	—
186	C₄	#10597328	1	2	yes	—
187	C₄	#10597330	1	2	yes	—
188	C₂	—	8	2	no	—
189	C₂	—	152	4	no	—
190	C₂	#11926453	1	1	yes	characteristic
191	C₂	#11926677	1	2	yes	—
192	C₂	#11926739	1	2	yes	—
193	C₂	#11926920	1	1	yes	characteristic
194	C₂	#11926934	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64525

C₂

yes

maximal, complemented

C₂×#10597320

C₂

yes

maximal, characteristic, complemented

C₂×#10597266

C₂

yes

maximal, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#390

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

—

C₂²×D₇₆

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

—

—

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597320

—

#10597266

—

C₂⁴×C₁₉

—

C₂³×D₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

#64525

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

complemented

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

complemented

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

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₁₉⋊C₈

—

#2011

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×D₈

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

C₄×C₁₉

#121

yes

—

C₂²×D₈

—

C₂×#127

—

C₂×#102

—

#390

D₁₉

yes

characteristic, complemented

#336

—

C₂×C₁₉

—

C₂×C₁₉

#392

yes

characteristic

C₂×C₁₉

#447

yes

—

C₂×C₁₉

#459

yes

—

100

C₂×C₁₉

#493

yes

characteristic

101

C₂×C₁₉

#496

yes

characteristic

102

D₁₉

—

103

C₂²×D₄

—

104

C₂²×D₄

—

105

C₂²×D₄

C₂×D₁₉

yes

characteristic

106

C₂×D₈

—

107

C₂×D₈

—

108

C₂×D₈

—

109

C₂²×C₈

—

110

#127

—

111

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

112

C₂×C₂²⋊C₄

—

113

C₂×C₄²

C₂×D₁₉

yes

characteristic

114

#102

—

115

C₁₉

#2011

yes

characteristic, complemented, Sylow

116

C₂⁴

—

117

C₂⁴

—

118

C₂×D₄

—

119

C₂×D₄

—

120

C₂×D₄

—

121

C₂×D₄

—

122

C₂×D₄

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

—

130

C₂×D₄

D₇₆

yes

complemented

131

C₂²×C₄

—

132

C₂²×C₄

C₂²⋊D₁₉

yes

—

133

C₂²×C₄

C₂²×D₁₉

yes

characteristic

134

D₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₄⋊C₄

—

139

C₂²⋊C₄

—

140

C₄²

—

141

C₂³

—

142

C₂³

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

152

D₄

—

153

D₄

—

154

D₄

—

155

D₄

—

156

D₄

—

157

D₄

—

158

D₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

#64525

yes

complemented

164

C₂×C₄

C₂×D₇₆

yes

characteristic

165

C₂×C₄

#64541

yes

characteristic

166

C₂×C₄

D₄×D₁₉

yes

—

167

C₂×C₄

D₄×D₁₉

yes

—

168

C₈

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

152

—

177

C₂²

—

152

—

178

C₂²

—

152

—

179

C₂²

#10597376

yes

characteristic

180

C₂²

C₂×#64525

yes

—

181

C₂²

#10597383

yes

characteristic

182

C₂²

#10597386

yes

characteristic

183

C₂²

#10597395

yes

—

184

C₄

—

185

C₄

—

186

C₄

#10597328

yes

—

187

C₄

#10597330

yes

—

188

C₂

—

189

C₂

—

152

—

190

C₂

#11926453

yes

characteristic

191

C₂

#11926677

yes

—

192

C₂

#11926739

yes

—

193

C₂

#11926920

yes

characteristic

194

C₂

#11926934

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#390	C₂
socle	C₂³×C₁₉	C₂×D₄
hypercenter	#390	D₁₉
hypocenter	C₁₉	#2011
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#390

C₂

socle

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

N	H ≅ G/N	type
1. C₂²×#64525	C₂	semidirect
2. C₂×#10597320	C₂	semidirect
3. C₂×#10597266	C₂	semidirect
4. #11926299	C₂	semidirect
5. C₁₉×#390	C₂	semidirect
23. C₂×D₄×C₁₉	D₄	semidirect
42. C₂×C₁₉⋊C₈	D₄	semidirect
60. C₂×C₄×C₁₉	D₈	semidirect
94. #390	D₁₉	semidirect
115. C₁₉	#2011	semidirect
130. C₂×D₄	D₇₆	semidirect
163. C₂×C₄	#64525	semidirect

H ≅ G/N

type

1. C₂²×#64525

C₂

semidirect

2. C₂×#10597320

C₂

semidirect

3. C₂×#10597266

C₂

semidirect

4. #11926299

C₂

semidirect

5. C₁₉×#390

C₂

semidirect

23. C₂×D₄×C₁₉

D₄

semidirect

42. C₂×C₁₉⋊C₈

D₄

semidirect

60. C₂×C₄×C₁₉

D₈

semidirect

94. #390

D₁₉

semidirect

115. C₁₉

#2011

semidirect

130. C₂×D₄

D₇₆

semidirect

163. C₂×C₄

#64525

semidirect

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

subgroup	index
C₂²×#64525	2
C₂×#10597320	2
C₂×#10597266	2
#11926299	2
C₁₉×#390	2
#2011	19

subgroup

index

C₂²×#64525

C₁₉×#390

Subgroups — #14564705

Conjugacy classes of subgroups

Complements

Maximal subgroups