Group #14564771 — subgroups

Subgroups — #14564771

Order 2432.

326 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10597315	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597289	C₂	1	2	yes	maximal
3	#11926306	C₂	1	2	yes	maximal, complemented
4	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	—	2	1	no	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	—	2	1	no	—
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	#10597315	—	2	4	no	—
16	#10597289	—	2	4	no	—
17	C₂⁴×C₁₉	—	2	1	no	—
18	C₂×D₄×C₁₉	—	2	2	no	—
19	C₂×D₄×C₁₉	—	2	2	no	—
20	C₂×D₄×C₁₉	—	2	1	no	—
21	C₂×D₄×C₁₉	Q₈	1	2	yes	complemented
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	2	no	—
27	C₂×Dic₃₈	—	2	4	no	—
28	C₂×Dic₃₈	—	4	2	no	—
29	C₂×Dic₃₈	—	4	2	no	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂²⋊C₄×C₁₉	—	4	2	no	—
32	C₂²⋊C₄×C₁₉	—	4	2	no	—
33	C₄²×C₁₉	—	2	2	no	—
34	C₄⋊Dic₁₉	—	2	4	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₄⋊Dic₁₉	D₄	1	4	yes	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂³×C₁₉	—	2	2	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	—	4	1	no	—
44	C₂³×C₁₉	—	4	1	no	—
45	C₂³×C₁₉	—	4	1	no	—
46	C₂³×C₁₉	—	4	1	no	—
47	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
48	D₄×C₁₉	—	2	4	no	—
49	D₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	D₈	1	2	yes	—
58	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂×C₄×C₁₉	#41	1	2	yes	—
63	C₂×Dic₁₉	—	2	4	no	—
64	C₂×Dic₁₉	—	4	2	no	—
65	C₂×Dic₁₉	—	4	2	no	—
66	Dic₃₈	—	4	8	no	—
67	C₁₉⋊C₈	—	4	2	no	—
68	#2023	—	19	1	no	maximal, Sylow
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	—	4	2	no	—
71	C₂²×C₁₉	—	4	2	no	—
72	C₂²×C₁₉	—	8	1	no	—
73	C₂²×C₁₉	—	8	1	no	—
74	C₂²×C₁₉	—	8	1	no	—
75	C₂²×C₁₉	—	8	1	no	—
76	C₂²×C₁₉	#120	1	1	yes	characteristic
77	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
78	C₂²×C₁₉	#124	1	1	yes	characteristic
79	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
80	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
81	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
82	C₂²×C₁₉	#137	1	1	yes	characteristic
83	C₄×C₁₉	—	2	2	no	—
84	C₄×C₁₉	—	2	2	no	—
85	C₄×C₁₉	—	8	1	no	—
86	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
87	C₄×C₁₉	#124	1	2	yes	—
88	Dic₁₉	—	4	4	no	—
89	C₂×C₄⋊Q₈	—	19	1	no	—
90	C₂×#102	—	19	2	no	—
91	#390	D₁₉	1	1	yes	characteristic
92	#340	—	19	2	no	—
93	#336	—	19	1	no	—
94	C₂×C₁₉	—	8	2	no	—
95	C₂×C₁₉	#393	1	1	yes	characteristic
96	C₂×C₁₉	#447	1	1	yes	characteristic
97	C₂×C₁₉	#448	1	1	yes	characteristic
98	C₂×C₁₉	#474	1	1	yes	characteristic
99	C₂×C₁₉	#476	1	1	yes	characteristic
100	C₂×C₁₉	#486	1	1	yes	characteristic
101	C₂×C₁₉	#489	1	1	yes	characteristic
102	C₂²×Q₈	—	38	1	no	—
103	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
104	C₂²×C₈	—	19	2	no	—
105	C₄⋊Q₈	—	38	4	no	—
106	C₂×C₄⋊C₄	—	19	2	no	—
107	C₂×C₄⋊C₄	—	38	1	no	—
108	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
109	C₂×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
112	#102	—	38	4	no	—
113	C₁₉	#2023	1	1	yes	characteristic, complemented, Sylow
114	C₂⁴	—	2	1	no	—
115	C₂×Q₈	—	38	4	no	—
116	C₂×Q₈	—	76	2	no	—
117	C₂×Q₈	—	76	2	no	—
118	C₂×D₄	—	2	1	no	—
119	C₂×D₄	—	2	2	no	—
120	C₂×D₄	—	2	2	no	—
121	C₂×D₄	Dic₃₈	1	2	yes	complemented
122	C₂²×C₄	—	2	1	no	—
123	C₂²×C₄	—	38	2	no	—
124	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
125	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
126	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
127	C₂×C₈	—	38	2	no	—
128	C₂×C₈	—	38	2	no	—
129	C₂×C₈	—	38	2	no	—
130	C₄⋊C₄	—	2	2	no	—
131	C₄⋊C₄	—	19	4	no	—
132	C₄⋊C₄	—	38	4	no	—
133	C₄⋊C₄	—	38	2	no	—
134	C₂²⋊C₄	—	4	2	no	—
135	C₂²⋊C₄	—	4	2	no	—
136	C₄²	—	2	2	no	—
137	C₂³	—	2	2	no	—
138	C₂³	—	4	1	no	—
139	C₂³	—	4	1	no	—
140	C₂³	—	4	1	no	—
141	C₂³	—	4	1	no	—
142	C₂³	—	4	1	no	—
143	C₂³	—	4	1	no	—
144	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
145	Q₈	—	76	8	no	—
146	D₄	—	2	4	no	—
147	D₄	—	4	2	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	4	1	no	—
153	C₂×C₄	—	4	1	no	—
154	C₂×C₄	—	4	1	no	—
155	C₂×C₄	—	38	4	no	—
156	C₂×C₄	—	76	2	no	—
157	C₂×C₄	—	76	2	no	—
158	C₂×C₄	#64525	1	2	yes	—
159	C₂×C₄	#64526	1	2	yes	—
160	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
161	C₂×C₄	#64541	1	1	yes	characteristic
162	C₂×C₄	D₄×D₁₉	1	2	yes	—
163	C₂×C₄	#64543	1	2	yes	—
164	C₈	—	76	2	no	—
165	C₂²	—	4	2	no	—
166	C₂²	—	4	2	no	—
167	C₂²	—	4	2	no	—
168	C₂²	—	8	1	no	—
169	C₂²	—	8	1	no	—
170	C₂²	—	8	1	no	—
171	C₂²	—	8	1	no	—
172	C₂²	#10597370	1	1	yes	characteristic
173	C₂²	C₂×#64525	1	1	yes	characteristic
174	C₂²	C₂×#64526	1	1	yes	characteristic
175	C₂²	#10597382	1	1	yes	characteristic
176	C₂²	#10597383	1	1	yes	characteristic
177	C₂²	#10597395	1	1	yes	characteristic
178	C₂²	#10597397	1	1	yes	characteristic
179	C₄	—	2	2	no	—
180	C₄	—	2	2	no	—
181	C₄	—	8	1	no	—
182	C₄	—	76	4	no	—
183	C₄	#10597324	1	2	yes	—
184	C₄	#10597331	1	2	yes	—
185	C₂	—	8	2	no	—
186	C₂	#11926456	1	1	yes	characteristic
187	C₂	#11926677	1	1	yes	characteristic
188	C₂	#11926682	1	1	yes	characteristic
189	C₂	#11926824	1	1	yes	characteristic
190	C₂	#11926834	1	1	yes	characteristic
191	C₂	#11926890	1	1	yes	characteristic
192	C₂	#11926903	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic, complemented

C₂×#10597289

C₂

yes

maximal

#11926306

C₂

yes

maximal, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#390

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597315

—

#10597289

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

Q₈

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

#2023

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#124

yes

characteristic

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#124

yes

—

Dic₁₉

—

C₂×C₄⋊Q₈

—

C₂×#102

—

#390

D₁₉

yes

characteristic

#340

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

100

C₂×C₁₉

#486

yes

characteristic

101

C₂×C₁₉

#489

yes

characteristic

102

C₂²×Q₈

—

103

C₂²×D₄

C₂×D₁₉

yes

characteristic

104

C₂²×C₈

—

105

C₄⋊Q₈

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

—

108

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

109

C₂×C₂²⋊C₄

—

110

C₂×C₂²⋊C₄

—

111

C₂×C₄²

C₂×D₁₉

yes

characteristic

112

#102

—

113

C₁₉

#2023

yes

characteristic, complemented, Sylow

114

C₂⁴

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×D₄

—

119

C₂×D₄

—

120

C₂×D₄

—

121

C₂×D₄

Dic₃₈

yes

complemented

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

125

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

126

C₂²×C₄

C₂²×D₁₉

yes

characteristic

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₂²⋊C₄

—

135

C₂²⋊C₄

—

136

C₄²

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

—

143

C₂³

—

144

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

145

Q₈

—

146

D₄

—

147

D₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

#64525

yes

—

159

C₂×C₄

#64526

yes

—

160

C₂×C₄

C₂×Dic₃₈

yes

characteristic

161

C₂×C₄

#64541

yes

characteristic

162

C₂×C₄

D₄×D₁₉

yes

—

163

C₂×C₄

#64543

yes

—

164

C₈

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

#10597370

yes

characteristic

173

C₂²

C₂×#64525

yes

characteristic

174

C₂²

C₂×#64526

yes

characteristic

175

C₂²

#10597382

yes

characteristic

176

C₂²

#10597383

yes

characteristic

177

C₂²

#10597395

yes

characteristic

178

C₂²

#10597397

yes

characteristic

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

#10597324

yes

—

184

C₄

#10597331

yes

—

185

C₂

—

186

C₂

#11926456

yes

characteristic

187

C₂

#11926677

yes

characteristic

188

C₂

#11926682

yes

characteristic

189

C₂

#11926824

yes

characteristic

190

C₂

#11926834

yes

characteristic

191

C₂

#11926890

yes

characteristic

192

C₂

#11926903

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
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#390	D₁₉
hypocenter	C₁₉	#2023
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

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

N	H ≅ G/N	type
1. C₂×#10597315	C₂	semidirect
3. #11926306	C₂	semidirect
4. #11926299	C₂	semidirect
21. C₂×D₄×C₁₉	Q₈	semidirect
113. C₁₉	#2023	semidirect
121. C₂×D₄	Dic₃₈	semidirect

H ≅ G/N

type

1. C₂×#10597315

C₂

semidirect

3. #11926306

C₂

semidirect

4. #11926299

C₂

semidirect

21. C₂×D₄×C₁₉

Q₈

semidirect

113. C₁₉

#2023

semidirect

121. C₂×D₄

Dic₃₈

semidirect

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

subgroup	index
C₂×#10597315	2
C₂×#10597289	2
#11926306	2
#11926299	2
C₁₉×#390	2
#2023	19

subgroup

index

C₁₉×#390

Subgroups — #14564771

Conjugacy classes of subgroups

Complements

Maximal subgroups