Group #14573122 — subgroups

Subgroups — #14573122

Order 2432.

480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597397	C₂	1	2	yes	maximal
2	C₂×#10597315	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926754	C₂	1	4	yes	maximal, complemented
4	#11926749	C₂	1	4	yes	maximal, complemented
5	#11926568	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926552	C₂	1	2	yes	maximal, complemented
7	C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	2	yes	—
10	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
11	C₄×D₄×C₁₉	—	2	2	no	—
12	C₄×D₄×C₁₉	C₂²	1	2	yes	—
13	C₁₉×#117	—	2	1	no	—
14	C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	—	2	1	no	—
16	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	#10597397	—	2	8	no	—
18	C₂×#64528	C₂²	1	4	yes	—
19	C₂×#64526	C₂²	1	4	yes	—
20	C₂×C₄⋊Dic₁₉	—	2	2	no	—
21	C₂×#64520	C₂²	1	2	yes	—
22	#10597315	—	2	1	no	—
23	#10597315	—	2	1	no	—
24	#10597315	C₂²	1	4	yes	—
25	#10597267	C₂²	1	8	yes	—
26	C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
27	#41×C₁₉	—	2	2	no	—
28	#41×C₁₉	D₄	1	4	yes	—
29	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×D₄×C₁₉	—	2	1	no	—
31	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	—	2	1	no	—
33	C₂²×C₄×C₁₉	—	2	2	no	—
34	C₂²×C₄×C₁₉	D₄	1	2	yes	—
35	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×Dic₁₉	—	2	2	no	—
37	C₂×Dic₃₈	—	2	4	no	—
38	C₂×Dic₃₈	—	2	4	no	—
39	C₂×Dic₃₈	—	2	2	no	—
40	C₂×Dic₃₈	C₂³	1	4	yes	—
41	C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
43	C₂²⋊C₄×C₁₉	—	2	1	no	—
44	C₂²⋊C₄×C₁₉	—	2	2	no	—
45	C₄²×C₁₉	—	2	1	no	—
46	C₄²×C₁₉	—	2	2	no	—
47	C₄²×C₁₉	D₄	1	1	yes	characteristic
48	C₄²×C₁₉	D₄	1	1	yes	characteristic
49	C₄²×C₁₉	C₂³	1	2	yes	—
50	#64528	—	2	8	no	—
51	#64526	—	2	8	no	—
52	C₄⋊Dic₁₉	—	2	4	no	—
53	C₄⋊Dic₁₉	—	2	4	no	—
54	#64520	—	2	4	no	—
55	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
56	C₂³×C₁₉	—	2	1	no	—
57	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
58	Q₈×C₁₉	—	2	1	no	—
59	Q₈×C₁₉	C₂×D₄	1	2	yes	—
60	D₄×C₁₉	—	2	4	no	—
61	D₄×C₁₉	—	2	1	no	—
62	D₄×C₁₉	C₂×D₄	1	2	yes	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	4	no	—
65	C₂×C₄×C₁₉	—	2	4	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	4	4	no	—
68	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
72	C₂×C₄×C₁₉	#41	1	2	yes	—
73	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
74	C₂×Dic₁₉	—	2	4	no	—
75	C₂×Dic₁₉	—	4	4	no	—
76	Dic₃₈	—	2	4	no	—
77	Dic₃₈	—	2	4	no	—
78	Dic₃₈	—	4	4	no	—
79	C₁₉⋊C₈	—	2	4	no	—
80	#3039	—	19	1	no	maximal, Sylow
81	C₂²×C₁₉	—	2	2	no	—
82	C₂²×C₁₉	—	2	2	no	—
83	C₂²×C₁₉	—	4	2	no	—
84	C₂²×C₁₉	#121	1	2	yes	—
85	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	4	2	no	—
89	C₄×C₁₉	#121	1	2	yes	—
90	C₄×C₁₉	#137	1	4	yes	complemented
91	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
92	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
93	Dic₁₉	—	4	4	no	—
94	C₂×#137	—	19	2	no	—
95	C₂×C₄⋊Q₈	—	19	1	no	—
96	C₄×#41	D₁₉	1	1	yes	characteristic
97	#462	—	19	4	no	—
98	#461	—	19	4	no	—
99	#423	—	19	1	no	—
100	#419	—	19	2	no	—
101	C₂×C₁₉	—	2	2	no	—
102	C₂×C₁₉	—	4	2	no	—
103	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
104	C₂×C₁₉	C₂×#137	1	2	yes	—
105	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
106	C₂²×Q₈	—	19	2	no	—
107	#137	—	38	8	no	—
108	C₂×Q₁₆	—	19	4	no	—
109	C₂×SD₁₆	—	19	4	no	—
110	C₂×M₁₆	—	19	2	no	—
111	C₄⋊Q₈	—	19	4	no	—
112	C₄⋊Q₈	—	38	1	no	—
113	C₄⋊Q₈	—	38	1	no	—
114	C₄×Q₈	C₂×D₁₉	1	2	yes	—
115	C₄×D₄	—	2	2	no	—
116	C₄×D₄	C₂×D₁₉	1	2	yes	—
117	#117	—	2	1	no	—
118	#117	C₂×D₁₉	1	1	yes	characteristic
119	C₂×C₄⋊C₄	—	38	2	no	—
120	C₂×C₄²	—	2	1	no	—
121	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
122	C₄⋊C₈	—	19	4	no	—
123	#103	—	19	8	no	—
124	C₁₉	#3039	1	1	yes	characteristic, complemented, Sylow
125	#41	—	2	2	no	—
126	#41	D₇₆	1	4	yes	—
127	C₂×Q₈	—	19	4	no	—
128	C₂×Q₈	—	38	2	no	—
129	C₂×Q₈	—	38	4	no	—
130	C₂×Q₈	—	38	4	no	—
131	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
132	C₂×D₄	—	2	1	no	—
133	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
134	C₂²×C₄	—	2	1	no	—
135	C₂²×C₄	—	2	2	no	—
136	C₂²×C₄	—	38	2	no	—
137	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
138	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
139	Q₁₆	—	38	8	no	—
140	SD₁₆	—	38	8	no	—
141	M₁₆	—	38	4	no	—
142	C₂×C₈	—	19	4	no	—
143	C₄⋊C₄	—	2	2	no	—
144	C₄⋊C₄	—	38	4	no	—
145	C₄⋊C₄	—	38	4	no	—
146	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
147	C₂²⋊C₄	—	2	1	no	—
148	C₂²⋊C₄	—	2	2	no	—
149	C₄²	—	2	1	no	—
150	C₄²	—	2	2	no	—
151	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
152	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
153	C₄²	C₂²×D₁₉	1	2	yes	—
154	C₂³	—	2	1	no	—
155	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
156	Q₈	—	2	1	no	—
157	Q₈	—	38	4	no	—
158	Q₈	—	38	4	no	—
159	Q₈	—	76	4	no	—
160	Q₈	C₂×D₇₆	1	2	yes	—
161	D₄	—	2	4	no	—
162	D₄	—	2	1	no	—
163	D₄	C₂×D₇₆	1	2	yes	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	38	4	no	—
170	C₂×C₄	—	76	4	no	—
171	C₂×C₄	C₂×D₇₆	1	2	yes	—
172	C₂×C₄	#64541	1	2	yes	—
173	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
174	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
175	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
176	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
177	C₈	—	38	4	no	—
178	C₂²	—	2	2	no	—
179	C₂²	—	2	2	no	—
180	C₂²	—	4	2	no	—
181	C₂²	#10597376	1	2	yes	—
182	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
183	C₄	—	2	2	no	—
184	C₄	—	2	2	no	—
185	C₄	—	4	2	no	—
186	C₄	—	76	4	no	—
187	C₄	#10597376	1	2	yes	—
188	C₄	#10597397	1	4	yes	complemented
189	C₄	C₂²×D₇₆	1	1	yes	characteristic
190	C₄	C₂×#64541	1	1	yes	characteristic
191	C₂	—	2	2	no	—
192	C₂	—	4	2	no	—
193	C₂	C₂×#10597376	1	1	yes	characteristic
194	C₂	C₂×#10597397	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597397

C₂

yes

maximal

C₂×#10597315

C₂

yes

maximal, characteristic, complemented

#11926754

C₂

yes

maximal, complemented

#11926749

C₂

yes

maximal, complemented

#11926568

C₂

yes

maximal, characteristic, complemented

#11926552

C₂

yes

maximal, complemented

C₄×#41×C₁₉

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

C₂²

yes

—

C₁₉×#117

—

C₁₉×#117

C₂²

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597397

—

C₂×#64528

C₂²

yes

—

C₂×#64526

C₂²

yes

—

C₂×C₄⋊Dic₁₉

—

C₂×#64520

C₂²

yes

—

#10597315

—

#10597315

—

#10597315

C₂²

yes

—

#10597267

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

D₄

yes

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

—

#64528

—

#64526

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

C₂×D₄

yes

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

#3039

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#137

yes

complemented

C₄×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

C₂×#137

—

C₂×C₄⋊Q₈

—

C₄×#41

D₁₉

yes

—

—

—

100

#419

—

101

C₂×C₁₉

—

102

C₂×C₁₉

—

103

C₂×C₁₉

C₂×#121

yes

characteristic

104

C₂×C₁₉

C₂×#137

yes

—

105

C₂×#41

C₂×D₁₉

yes

characteristic

106

C₂²×Q₈

—

107

#137

—

108

C₂×Q₁₆

—

109

C₂×SD₁₆

—

110

C₂×M₁₆

—

111

C₄⋊Q₈

—

112

C₄⋊Q₈

—

113

C₄⋊Q₈

—

114

C₄×Q₈

C₂×D₁₉

yes

—

115

C₄×D₄

—

116

C₄×D₄

C₂×D₁₉

yes

—

117

#117

—

118

#117

C₂×D₁₉

yes

characteristic

119

C₂×C₄⋊C₄

—

120

C₂×C₄²

—

121

C₂×C₄²

C₂×D₁₉

yes

characteristic

122

C₄⋊C₈

—

123

#103

—

124

C₁₉

#3039

yes

characteristic, complemented, Sylow

125

#41

—

126

#41

D₇₆

yes

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

C₂²×D₁₉

yes

characteristic

132

C₂×D₄

—

133

C₂×D₄

C₂²×D₁₉

yes

characteristic

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₂²⋊D₁₉

yes

—

138

C₂²×C₄

C₂²×D₁₉

yes

characteristic

139

Q₁₆

—

140

SD₁₆

—

141

M₁₆

—

142

C₂×C₈

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

C₂²×D₁₉

yes

—

147

C₂²⋊C₄

—

148

C₂²⋊C₄

—

149

C₄²

—

150

C₄²

—

151

C₄²

C₂²⋊D₁₉

yes

characteristic

152

C₄²

C₂²⋊D₁₉

yes

characteristic

153

C₄²

C₂²×D₁₉

yes

—

154

C₂³

—

155

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

156

Q₈

—

157

Q₈

—

158

Q₈

—

159

Q₈

—

160

Q₈

C₂×D₇₆

yes

—

161

D₄

—

162

D₄

—

163

D₄

C₂×D₇₆

yes

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

C₂×D₇₆

yes

—

172

C₂×C₄

#64541

yes

—

173

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

174

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

175

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

176

C₂×C₄

C₂³×D₁₉

yes

characteristic

177

C₈

—

178

C₂²

—

179

C₂²

—

180

C₂²

—

181

C₂²

#10597376

yes

—

182

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

183

C₄

—

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

#10597376

yes

—

188

C₄

#10597397

yes

complemented

189

C₄

C₂²×D₇₆

yes

characteristic

190

C₄

C₂×#64541

yes

characteristic

191

C₂

—

192

C₂

—

193

C₂

C₂×#10597376

yes

characteristic

194

C₂

C₂×#10597397

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₄×#41×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#41×C₁₉	C₂²
hypercenter	C₄×#41	D₁₉
hypocenter	C₁₉	#3039
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#41

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₄×#41×C₁₉

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂×#41×C₁₉

C₂²

hypercenter

C₄×#41

D₁₉

hypocenter

C₁₉

#3039

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#41

N	H ≅ G/N	type
2. C₂×#10597315	C₂	semidirect
3. #11926754	C₂	semidirect
4. #11926749	C₂	semidirect
5. #11926568	C₂	semidirect
6. #11926552	C₂	semidirect
90. C₄×C₁₉	#137	semidirect
124. C₁₉	#3039	semidirect
188. C₄	#10597397	semidirect

H ≅ G/N

type

2. C₂×#10597315

C₂

semidirect

3. #11926754

C₂

semidirect

4. #11926749

C₂

semidirect

5. #11926568

C₂

semidirect

6. #11926552

C₂

semidirect

90. C₄×C₁₉

#137

semidirect

124. C₁₉

#3039

semidirect

188. C₄

#10597397

semidirect

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

subgroup	index
C₂×#10597397	2
C₂×#10597315	2
#11926754	2
#11926749	2
#11926568	2
#11926552	2
C₄×#41×C₁₉	2
#3039	19

subgroup

index

C₄×#41×C₁₉

Subgroups — #14573122

Conjugacy classes of subgroups

Complements

Maximal subgroups