Group #18073457 — subgroups

Subgroups — C₄×#11926286 #18073457

Order 4864.

532 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 175 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	C₄×#10597260	C₂	1	2	yes	maximal
2	C₂×#11926286	C₂	1	2	yes	maximal
3	#14561516	C₂	1	2	yes	maximal
4	C₄×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597260	—	2	2	no	—
6	C₂×#10597260	C₂²	1	4	yes	—
7	C₂×C₄×C₁₉⋊C₈	—	2	2	no	—
8	#11926286	C₄	1	8	yes	direct product factor
9	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
10	C₁₉×#389	C₄	1	2	yes	—
11	C₁₉×#387	—	2	2	no	—
12	C₁₉×#382	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
14	C₄×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
15	C₄³×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#125	—	2	2	no	—
17	C₁₉×#125	C₂×C₄	1	4	yes	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂²×C₁₉⋊C₈	—	2	4	no	—
29	C₁₉×#95	—	2	2	no	—
30	C₁₉×#95	—	2	2	no	—
31	C₁₉×#95	—	2	2	no	—
32	#10597260	—	2	8	no	—
33	#10597260	—	2	4	no	—
34	#10597260	C₂×C₄	1	8	yes	—
35	C₄×C₁₉⋊C₈	—	2	8	no	—
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₄⋊C₄×C₁₉	—	2	2	no	—
44	C₄⋊C₄×C₁₉	—	2	8	no	—
45	C₄⋊C₄×C₁₉	—	4	2	no	—
46	C₄⋊C₄×C₁₉	—	4	4	no	—
47	C₄⋊C₄×C₁₉	C₄²	1	4	yes	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	—	2	4	no	—
50	C₄²×C₁₉	—	2	4	no	—
51	C₄²×C₁₉	—	4	1	no	—
52	C₄²×C₁₉	—	4	4	no	—
53	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
54	C₄²×C₁₉	#41	1	2	yes	—
55	C₂×C₁₉⋊C₈	—	2	8	no	—
56	C₂×C₁₉⋊C₈	—	2	8	no	—
57	C₂×C₁₉⋊C₈	—	2	8	no	—
58	C₄×#330	—	19	1	no	maximal, Sylow
59	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	4	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	—	4	2	no	—
71	C₂×C₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	—	4	2	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	#101	1	2	yes	—
75	C₂×C₄×C₁₉	#104	1	4	yes	—
76	C₂×C₄×C₁₉	#104	1	4	yes	—
77	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
80	C₁₉⋊C₈	—	2	16	no	—
81	C₄×#125	D₁₉	1	1	yes	characteristic
82	C₄×#97	—	19	2	no	—
83	C₂×#330	—	19	2	no	—
84	#1295	—	19	2	no	—
85	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
87	C₂²×C₁₉	#413	1	1	yes	characteristic
88	C₂²×C₁₉	C₂×#104	1	2	yes	—
89	C₂²×C₁₉	C₂×#104	1	2	yes	—
90	C₄×C₁₉	—	2	1	no	—
91	C₄×C₁₉	—	2	1	no	—
92	C₄×C₁₉	—	2	4	no	—
93	C₄×C₁₉	—	2	4	no	—
94	C₄×C₁₉	—	4	4	no	—
95	C₄×C₁₉	—	4	1	no	—
96	C₄×C₁₉	—	8	2	no	—
97	C₄×C₁₉	#330	1	4	yes	complemented
98	C₂×#125	C₂×D₁₉	1	1	yes	characteristic
99	C₂×#97	—	19	4	no	—
100	C₂×#97	—	38	2	no	—
101	C₂×C₄×C₈	—	38	2	no	—
102	#389	Dic₁₉	1	2	yes	—
103	#387	—	2	2	no	—
104	#382	C₂×D₁₉	1	1	yes	characteristic
105	C₄×C₄⋊C₄	—	2	2	no	—
106	C₄×C₄⋊C₄	Dic₁₉	1	2	yes	—
107	C₄³	C₂×D₁₉	1	1	yes	characteristic
108	#330	—	19	8	no	—
109	C₂×C₁₉	C₂×#330	1	1	yes	characteristic
110	C₂×C₁₉	#1524	1	2	yes	—
111	C₂×C₁₉	#1526	1	1	yes	characteristic
112	C₂×C₁₉	C₄×#101	1	1	yes	characteristic
113	C₂×C₁₉	C₄×#104	1	2	yes	—
114	C₂²×C₈	—	38	4	no	—
115	#125	—	2	2	no	—
116	#125	C₄×D₁₉	1	4	yes	—
117	C₂×C₄⋊C₄	—	2	2	no	—
118	C₂×C₄⋊C₄	—	2	2	no	—
119	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
120	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
121	C₂×C₄²	—	2	2	no	—
122	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
123	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
124	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
125	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
126	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
127	#97	—	19	8	no	—
128	#97	—	38	8	no	—
129	#97	—	38	4	no	—
130	C₄×C₈	—	38	8	no	—
131	#95	—	2	2	no	—
132	#95	—	2	2	no	—
133	#95	—	2	2	no	—
134	C₁₉	C₄×#330	1	1	yes	characteristic, complemented, Sylow
135	C₂²×C₄	—	2	2	no	—
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
138	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
139	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
140	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
141	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
142	C₂×C₈	—	38	8	no	—
143	C₂×C₈	—	38	8	no	—
144	C₂×C₈	—	38	8	no	—
145	C₄⋊C₄	—	2	2	no	—
146	C₄⋊C₄	—	2	8	no	—
147	C₄⋊C₄	—	4	2	no	—
148	C₄⋊C₄	—	4	4	no	—
149	C₄⋊C₄	C₄×Dic₁₉	1	4	yes	—
150	C₄²	—	2	2	no	—
151	C₄²	—	2	4	no	—
152	C₄²	—	2	4	no	—
153	C₄²	—	4	1	no	—
154	C₄²	—	4	4	no	—
155	C₄²	C₂×C₄×D₁₉	1	2	yes	—
156	C₄²	#64541	1	2	yes	—
157	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	4	2	no	—
168	C₂×C₄	—	4	2	no	—
169	C₂×C₄	—	4	2	no	—
170	C₂×C₄	—	4	2	no	—
171	C₂×C₄	—	4	2	no	—
172	C₂×C₄	#10597293	1	2	yes	—
173	C₂×C₄	#10597294	1	4	yes	—
174	C₂×C₄	#10597294	1	4	yes	—
175	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
176	C₂×C₄	#10597372	1	1	yes	characteristic
177	C₂×C₄	C₄×C₂²⋊D₁₉	1	4	yes	—
178	C₈	—	38	16	no	—
179	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
180	C₂²	C₂×#10597293	1	1	yes	characteristic
181	C₂²	#11926528	1	1	yes	characteristic
182	C₂²	C₂×#10597294	1	2	yes	—
183	C₂²	C₂×#10597294	1	2	yes	—
184	C₄	—	2	1	no	—
185	C₄	—	2	1	no	—
186	C₄	—	2	4	no	—
187	C₄	—	2	4	no	—
188	C₄	—	4	4	no	—
189	C₄	—	4	1	no	—
190	C₄	—	8	2	no	—
191	C₄	#11926286	1	4	yes	direct product factor
192	C₂	C₂×#11926286	1	1	yes	characteristic
193	C₂	#14562223	1	2	yes	—
194	C₂	#14562230	1	1	yes	characteristic
195	C₂	C₄×#10597293	1	1	yes	characteristic
196	C₂	C₄×#10597294	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597260

C₂

yes

maximal

C₂×#11926286

C₂

yes

maximal

#14561516

C₂

yes

maximal

C₄×C₁₉×#125

C₂

yes

maximal, characteristic

C₂×#10597260

—

C₂×#10597260

C₂²

yes

—

C₂×C₄×C₁₉⋊C₈

—

#11926286

C₄

yes

direct product factor

C₂×C₁₉×#125

C₂²

yes

characteristic

C₁₉×#389

C₄

yes

—

C₁₉×#387

—

C₁₉×#382

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₄×C₄⋊C₄×C₁₉

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#125

—

C₁₉×#125

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

#10597260

—

#10597260

—

#10597260

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₄²

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₄×#330

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#101

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₉

#117

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₁₉⋊C₈

—

C₄×#125

D₁₉

yes

characteristic

C₄×#97

—

C₂×#330

—

#1295

—

C₂²×C₁₉

C₄×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×#104

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#330

yes

complemented

C₂×#125

C₂×D₁₉

yes

characteristic

C₂×#97

—

100

C₂×#97

—

101

C₂×C₄×C₈

—

102

#389

Dic₁₉

yes

—

103

#387

—

104

#382

C₂×D₁₉

yes

characteristic

105

C₄×C₄⋊C₄

—

106

C₄×C₄⋊C₄

Dic₁₉

yes

—

107

C₄³

C₂×D₁₉

yes

characteristic

108

#330

—

109

C₂×C₁₉

C₂×#330

yes

characteristic

110

C₂×C₁₉

#1524

yes

—

111

C₂×C₁₉

#1526

yes

characteristic

112

C₂×C₁₉

C₄×#101

yes

characteristic

113

C₂×C₁₉

C₄×#104

yes

—

114

C₂²×C₈

—

115

#125

—

116

#125

C₄×D₁₉

yes

—

117

C₂×C₄⋊C₄

—

118

C₂×C₄⋊C₄

—

119

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

120

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

121

C₂×C₄²

—

122

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

123

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

124

C₂×C₄²

C₂²⋊D₁₉

yes

—

125

C₂×C₄²

C₂²⋊D₁₉

yes

—

126

C₂×C₄²

C₂²×D₁₉

yes

characteristic

127

#97

—

128

#97

—

129

#97

—

130

C₄×C₈

—

131

#95

—

132

#95

—

133

#95

—

134

C₁₉

C₄×#330

yes

characteristic, complemented, Sylow

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

138

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

139

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

140

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

141

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄⋊C₄

—

149

C₄⋊C₄

C₄×Dic₁₉

yes

—

150

C₄²

—

151

C₄²

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₄²

C₂×C₄×D₁₉

yes

—

156

C₄²

#64541

yes

—

157

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

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

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

#10597293

yes

—

173

C₂×C₄

#10597294

yes

—

174

C₂×C₄

#10597294

yes

—

175

C₂×C₄

C₂×C₄×Dic₁₉

yes

characteristic

176

C₂×C₄

#10597372

yes

characteristic

177

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

178

C₈

—

179

C₂²

C₄×C₂²⋊Dic₁₉

yes

characteristic

180

C₂²

C₂×#10597293

yes

characteristic

181

C₂²

#11926528

yes

characteristic

182

C₂²

C₂×#10597294

yes

—

183

C₂²

C₂×#10597294

yes

—

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

#11926286

yes

direct product factor

192

C₂

C₂×#11926286

yes

characteristic

193

C₂

#14562223

yes

—

194

C₂

#14562230

yes

characteristic

195

C₂

C₄×#10597293

yes

characteristic

196

C₂

C₄×#10597294

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#125	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#125	D₁₉
hypocenter	C₁₉	C₄×#330
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#125

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₁₉

commutator

C₂×C₄×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#125

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#125

N	H ≅ G/N	type
8. #11926286	C₄	direct (N × H)
97. C₄×C₁₉	#330	semidirect
134. C₁₉	C₄×#330	semidirect
191. C₄	#11926286	direct (N × H)

H ≅ G/N

type

8. #11926286

C₄

direct (N × H)

97. C₄×C₁₉

#330

semidirect

134. C₁₉

C₄×#330

semidirect

191. C₄

#11926286

direct (N × H)

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

subgroup	index
C₄×#10597260	2
C₂×#11926286	2
#14561516	2
C₄×C₁₉×#125	2
C₄×#330	19

subgroup

index

C₄×C₁₉×#125

Subgroups — C₄×#11926286 #18073457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#11926286 #18073457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11926286 #18073457