Group #14573415 — subgroups

Subgroups — C₂×#11926854 #14573415

Order 2432.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597336	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597333	C₂	1	1	yes	maximal, characteristic
3	#11926854	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10597264	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597273	C₂	1	1	yes	maximal, characteristic
7	C₂×#10597267	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	—	2	1	no	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₉⋊C₄	—	2	1	no	—
16	C₂×Dic₁₉⋊C₄	—	2	1	no	—
17	C₂×C₄×Dic₁₉	—	2	1	no	—
18	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#10597336	—	2	2	no	—
21	#10597336	C₂²	1	4	yes	—
22	#10597333	—	2	2	no	—
23	#10597333	C₂²	1	4	yes	—
24	C₁₉×#106	C₂²	1	4	yes	—
25	#10597273	C₂²	1	4	yes	—
26	Dic₁₉⋊C₈	C₂²	1	4	yes	—
27	#10597267	C₂²	1	4	yes	—
28	#10597264	C₂²	1	4	yes	—
29	C₂²×C₄×C₁₉	—	2	1	no	—
30	C₂²×C₄×C₁₉	—	2	1	no	—
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	1	no	—
33	C₂²×Dic₁₉	—	2	1	no	—
34	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
35	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
36	C₂×Dic₃₈	—	2	1	no	—
37	C₂×Dic₃₈	—	2	2	no	—
38	C₂×Dic₃₈	Q₈	1	4	yes	—
39	C₂×Dic₃₈	C₂³	1	2	yes	—
40	C₂×C₈×C₁₉	—	2	2	no	—
41	C₂×C₈×C₁₉	C₂³	1	2	yes	—
42	C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
45	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
46	C₄⋊Dic₁₉	—	2	1	no	—
47	C₄⋊Dic₁₉	—	2	4	no	—
48	C₄⋊Dic₁₉	C₂³	1	2	yes	—
49	Dic₁₉⋊C₄	—	2	4	no	—
50	Dic₁₉⋊C₄	—	2	4	no	—
51	C₄×Dic₁₉	—	2	4	no	—
52	C₄×Dic₁₉	D₄	1	2	yes	—
53	C₄×Dic₁₉	C₂³	1	2	yes	—
54	C₂×C₁₉⋊C₈	—	2	2	no	—
55	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
56	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	4	2	no	—
60	C₂×C₄×C₁₉	—	4	2	no	—
61	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
63	C₂×C₄×C₁₉	#41	1	2	yes	—
64	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
65	C₂×Dic₁₉	—	2	4	no	—
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	2	2	no	—
69	C₂×Dic₁₉	—	2	2	no	—
70	C₂×Dic₁₉	—	4	2	no	—
71	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
72	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
73	Dic₃₈	—	2	4	no	—
74	Dic₃₈	—	2	2	no	—
75	Dic₃₈	C₂×Q₈	1	4	yes	—
76	C₈×C₁₉	—	2	2	no	—
77	C₁₉⋊C₈	—	2	2	no	—
78	C₂×#479	—	19	1	no	maximal, Sylow
79	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
80	C₂²×C₁₉	#135	1	2	yes	—
81	C₂²×C₁₉	#137	1	2	yes	—
82	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
83	C₄×C₁₉	—	4	2	no	—
84	C₄×C₁₉	—	4	2	no	—
85	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
86	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
87	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
88	Dic₁₉	—	2	4	no	—
89	Dic₁₉	—	2	2	no	—
90	Dic₁₉	—	2	2	no	—
91	Dic₁₉	—	4	2	no	—
92	C₂×#125	—	19	1	no	—
93	C₂×C₄×Q₈	—	19	1	no	—
94	#479	—	19	8	no	—
95	C₂×#107	—	19	1	no	—
96	C₂×#106	D₁₉	1	1	yes	characteristic
97	C₂×C₄⋊C₈	—	19	1	no	—
98	C₂×#103	—	19	1	no	—
99	C₂×#103	—	19	1	no	—
100	C₂×C₁₉	#479	1	4	yes	complemented
101	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
103	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
104	C₂²×Q₈	—	19	1	no	—
105	C₂²×C₈	—	19	1	no	—
106	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
107	#125	—	19	4	no	—
108	#125	—	38	2	no	—
109	C₄×Q₈	—	19	4	no	—
110	C₄×Q₈	—	38	2	no	—
111	C₂×C₄⋊C₄	—	19	1	no	—
112	C₂×C₄⋊C₄	—	38	1	no	—
113	C₂×C₄⋊C₄	—	38	1	no	—
114	C₂×C₄⋊C₄	—	38	1	no	—
115	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
116	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
117	C₂×C₄²	—	19	1	no	—
118	C₂×C₄²	—	38	1	no	—
119	#107	—	19	4	no	—
120	#106	C₂×D₁₉	1	4	yes	—
121	C₄⋊C₈	—	19	4	no	—
122	#103	—	19	4	no	—
123	#103	—	19	4	no	—
124	C₁₉	C₂×#479	1	1	yes	characteristic, complemented, Sylow
125	C₂×Q₈	—	19	4	no	—
126	C₂×Q₈	—	19	2	no	—
127	C₂×Q₈	—	38	2	no	—
128	C₂×Q₈	—	38	1	no	—
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	2	1	no	—
131	C₂²×C₄	—	19	1	no	—
132	C₂²×C₄	—	19	1	no	—
133	C₂²×C₄	—	38	1	no	—
134	C₂²×C₄	—	38	1	no	—
135	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	19	2	no	—
138	C₂×C₈	—	38	2	no	—
139	C₂×C₈	C₂²×D₁₉	1	2	yes	—
140	C₄⋊C₄	—	2	1	no	—
141	C₄⋊C₄	—	2	1	no	—
142	C₄⋊C₄	—	19	2	no	—
143	C₄⋊C₄	—	38	4	no	—
144	C₄⋊C₄	—	38	4	no	—
145	C₄⋊C₄	—	38	4	no	—
146	C₄⋊C₄	—	38	1	no	—
147	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
148	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
149	C₄²	—	19	2	no	—
150	C₄²	—	19	2	no	—
151	C₄²	—	38	4	no	—
152	C₂³	D₄×D₁₉	1	1	yes	characteristic
153	Q₈	—	19	4	no	—
154	Q₈	—	38	2	no	—
155	Q₈	—	38	4	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	4	2	no	—
159	C₂×C₄	—	4	2	no	—
160	C₂×C₄	—	19	2	no	—
161	C₂×C₄	—	19	2	no	—
162	C₂×C₄	—	38	2	no	—
163	C₂×C₄	—	38	4	no	—
164	C₂×C₄	—	38	2	no	—
165	C₂×C₄	—	38	2	no	—
166	C₂×C₄	—	38	2	no	—
167	C₂×C₄	—	76	2	no	—
168	C₂×C₄	#64541	1	2	yes	—
169	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
170	C₂×C₄	Q₈×D₁₉	1	2	yes	—
171	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
172	C₈	—	2	2	no	—
173	C₈	—	38	2	no	—
174	C₂²	#10597342	1	2	yes	—
175	C₂²	#10597361	1	2	yes	—
176	C₂²	#10597362	1	2	yes	—
177	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
178	C₄	—	4	2	no	—
179	C₄	—	4	2	no	—
180	C₄	—	38	4	no	—
181	C₄	—	38	2	no	—
182	C₄	—	38	2	no	—
183	C₄	—	76	2	no	—
184	C₄	#10597342	1	2	yes	—
185	C₄	C₂×#64541	1	1	yes	characteristic
186	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
187	C₂	#11926854	1	4	yes	direct product factor
188	C₂	C₂×#10597342	1	1	yes	characteristic
189	C₂	C₂×#10597362	1	1	yes	characteristic
190	C₂	C₂×#10597361	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597336

C₂

yes

maximal, characteristic

C₂×#10597333

C₂

yes

maximal, characteristic

#11926854

C₂

yes

maximal, direct product factor

C₂×#10597264

C₂

yes

maximal, characteristic

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal, characteristic

C₂×C₁₉×#106

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597336

—

#10597336

C₂²

yes

—

#10597333

—

#10597333

C₂²

yes

—

C₁₉×#106

C₂²

yes

—

#10597273

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597267

C₂²

yes

—

#10597264

C₂²

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

—

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

C₂×Q₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₂×#479

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

#135

yes

—

C₂²×C₁₉

#137

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

C₂²×Q₈

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#125

—

C₂×C₄×Q₈

—

#479

—

C₂×#107

—

C₂×#106

D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₂×#103

—

C₂×#103

—

100

C₂×C₁₉

#479

yes

complemented

101

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

102

C₂×C₁₉

C₂×#135

yes

characteristic

103

C₂×C₁₉

C₂×#137

yes

characteristic

104

C₂²×Q₈

—

105

C₂²×C₈

—

106

C₂²×C₈

C₂×D₁₉

yes

characteristic

107

#125

—

108

#125

—

109

C₄×Q₈

—

110

C₄×Q₈

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

116

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

117

C₂×C₄²

—

118

C₂×C₄²

—

119

#107

—

120

#106

C₂×D₁₉

yes

—

121

C₄⋊C₈

—

122

#103

—

123

#103

—

124

C₁₉

C₂×#479

yes

characteristic, complemented, Sylow

125

C₂×Q₈

—

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

C₂²×D₁₉

yes

characteristic

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

C₂²×D₁₉

yes

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

C₂²×D₁₉

yes

—

148

C₄⋊C₄

C₂²×D₁₉

yes

—

149

C₄²

—

150

C₄²

—

151

C₄²

—

152

C₂³

D₄×D₁₉

yes

characteristic

153

Q₈

—

154

Q₈

—

155

Q₈

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

#64541

yes

—

169

C₂×C₄

D₄×D₁₉

yes

characteristic

170

C₂×C₄

Q₈×D₁₉

yes

—

171

C₂×C₄

C₂³×D₁₉

yes

characteristic

172

C₈

—

173

C₈

—

174

C₂²

#10597342

yes

—

175

C₂²

#10597361

yes

—

176

C₂²

#10597362

yes

—

177

C₂²

C₂×D₄×D₁₉

yes

characteristic

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

—

184

C₄

#10597342

yes

—

185

C₄

C₂×#64541

yes

characteristic

186

C₄

C₂×Q₈×D₁₉

yes

characteristic

187

C₂

#11926854

yes

direct product factor

188

C₂

C₂×#10597342

yes

characteristic

189

C₂

C₂×#10597362

yes

characteristic

190

C₂

C₂×#10597361

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	C₂×#479
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#106

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
3. #11926854	C₂	direct (N × H)
100. C₂×C₁₉	#479	semidirect
124. C₁₉	C₂×#479	semidirect
187. C₂	#11926854	direct (N × H)

H ≅ G/N

type

3. #11926854

C₂

direct (N × H)

100. C₂×C₁₉

#479

semidirect

124. C₁₉

C₂×#479

semidirect

187. C₂

#11926854

direct (N × H)

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

subgroup	index
C₂×#10597336	2
C₂×#10597333	2
#11926854	2
C₂×#10597264	2
C₂×Dic₁₉⋊C₈	2
C₂×#10597273	2
C₂×#10597267	2
C₂×C₁₉×#106	2
C₂×#479	19

subgroup

index

C₂×Dic₁₉⋊C₈

C₂×C₁₉×#106

Subgroups — C₂×#11926854 #14573415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926854 #14573415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926854 #14573415