Group #18069135 — subgroups

Subgroups — #18069135

Order 4864.

304 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14563752	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1767	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
5	C₂×C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
6	C₂×#10597260	C₄	1	2	yes	—
7	#11926299	—	2	1	no	—
8	#11926299	—	2	1	no	—
9	#11926299	—	2	1	no	—
10	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
11	C₂×C₁₉×#97	C₄	1	2	yes	—
12	C₄³×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#336	—	2	1	no	—
14	C₂²×C₈×C₁₉	—	2	2	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
22	C₂²×C₁₉⋊C₈	—	2	2	no	—
23	C₂²×C₁₉⋊C₈	—	2	2	no	—
24	C₁₉×C₄⋊C₈	—	2	4	no	—
25	C₁₉×#97	—	4	2	no	—
26	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
27	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
28	#10597260	—	4	2	no	—
29	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	—	2	4	no	—
37	C₂×C₈×C₁₉	—	4	2	no	—
38	C₂×C₈×C₁₉	—	4	2	no	—
39	C₄²×C₁₉	—	2	1	no	—
40	C₄²×C₁₉	—	2	1	no	—
41	C₄²×C₁₉	—	2	1	no	—
42	C₄²×C₁₉	—	2	1	no	—
43	C₄²×C₁₉	—	2	1	no	—
44	C₄²×C₁₉	—	2	1	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	—	2	2	no	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	4	1	no	—
49	C₂×C₁₉⋊C₈	—	2	4	no	—
50	C₂×C₁₉⋊C₈	—	4	2	no	—
51	C₂×C₁₉⋊C₈	—	4	2	no	—
52	C₂×C₁₉⋊C₈	—	4	2	no	—
53	C₂×C₁₉⋊C₈	—	4	2	no	—
54	C₂×C₁₉⋊C₈	—	4	2	no	—
55	#7042	—	19	1	no	maximal, Sylow
56	C₂³×C₁₉	#95	1	1	yes	characteristic
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	1	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#101	1	1	yes	characteristic
78	C₂×C₄×C₁₉	#104	1	2	yes	—
79	C₂×C₄×C₁₉	#104	1	2	yes	—
80	C₂×C₄×C₁₉	#108	1	2	yes	—
81	C₈×C₁₉	—	4	4	no	—
82	C₁₉⋊C₈	—	4	4	no	—
83	C₁₉⋊C₈	—	8	2	no	—
84	#1831	—	19	1	no	—
85	#1767	—	19	1	no	—
86	#1767	D₁₉	1	1	yes	characteristic
87	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
88	C₂²×C₁₉	#339	1	1	yes	characteristic
89	C₂²×C₁₉	#339	1	1	yes	characteristic
90	C₂²×C₁₉	#341	1	1	yes	characteristic
91	C₂²×C₁₉	#343	1	1	yes	characteristic
92	C₂²×C₁₉	#343	1	1	yes	characteristic
93	C₂²×C₁₉	#343	1	1	yes	characteristic
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	2	1	no	—
96	C₄×C₁₉	—	2	1	no	—
97	C₄×C₁₉	—	2	1	no	—
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	—	4	1	no	—
100	C₄×C₁₉	—	4	1	no	—
101	C₄×C₁₉	—	4	1	no	—
102	C₄×C₁₉	#329	1	2	yes	—
103	C₄×C₁₉	#330	1	2	yes	—
104	C₂×C₄⋊C₈	—	2	1	no	—
105	C₂×C₄⋊C₈	—	19	2	no	—
106	C₂×C₄⋊C₈	—	38	1	no	—
107	C₂×#97	—	19	2	no	—
108	C₂×#97	Dic₁₉	1	2	yes	—
109	C₄³	C₂×D₁₉	1	1	yes	characteristic
110	#336	—	2	1	no	—
111	#336	—	38	1	no	—
112	#336	—	38	1	no	—
113	#336	—	38	1	no	—
114	C₂×C₁₉	#1285	1	1	yes	characteristic
115	C₂×C₁₉	#1285	1	1	yes	characteristic
116	C₂×C₁₉	#1290	1	1	yes	characteristic
117	C₂×C₁₉	#1295	1	1	yes	characteristic
118	C₂×C₁₉	#1299	1	1	yes	characteristic
119	C₂×C₁₉	#1299	1	1	yes	characteristic
120	C₂×C₁₉	#1309	1	1	yes	characteristic
121	C₂²×C₈	—	2	2	no	—
122	C₂²×C₈	—	38	2	no	—
123	C₂²×C₈	—	38	2	no	—
124	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
125	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
126	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
127	C₂×C₄²	D₇₆	1	1	yes	characteristic
128	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
129	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
130	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
131	C₄⋊C₈	—	2	4	no	—
132	C₄⋊C₈	—	38	4	no	—
133	C₄⋊C₈	—	76	2	no	—
134	#97	—	4	2	no	—
135	#97	—	76	2	no	—
136	C₁₉	#7042	1	1	yes	characteristic, complemented, Sylow
137	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
138	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
139	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
140	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
141	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
142	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
143	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
144	C₂×C₈	—	2	4	no	—
145	C₂×C₈	—	4	2	no	—
146	C₂×C₈	—	4	2	no	—
147	C₂×C₈	—	38	4	no	—
148	C₂×C₈	—	76	2	no	—
149	C₂×C₈	—	76	2	no	—
150	C₂×C₈	—	76	2	no	—
151	C₂×C₈	—	76	2	no	—
152	C₂×C₈	—	76	2	no	—
153	C₄²	—	2	2	no	—
154	C₄²	—	2	2	no	—
155	C₄²	—	2	1	no	—
156	C₄²	—	2	1	no	—
157	C₄²	—	2	1	no	—
158	C₄²	—	2	1	no	—
159	C₄²	—	2	2	no	—
160	C₄²	—	2	1	no	—
161	C₄²	—	2	1	no	—
162	C₄²	—	4	1	no	—
163	C₂³	C₁₉⋊#95	1	1	yes	characteristic
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	#10597262	1	2	yes	—
180	C₂×C₄	#10597279	1	2	yes	—
181	C₂×C₄	#10597280	1	1	yes	characteristic
182	C₂×C₄	#10597280	1	1	yes	characteristic
183	C₂×C₄	#10597281	1	1	yes	characteristic
184	C₂×C₄	#10597281	1	1	yes	characteristic
185	C₂×C₄	#10597282	1	2	yes	—
186	C₂×C₄	#10597290	1	1	yes	characteristic
187	C₂×C₄	#10597293	1	1	yes	characteristic
188	C₈	—	4	4	no	—
189	C₈	—	76	4	no	—
190	C₈	—	152	2	no	—
191	C₂²	#11926300	1	1	yes	characteristic
192	C₂²	#11926304	1	1	yes	characteristic
193	C₂²	#11926305	1	1	yes	characteristic
194	C₂²	#11926308	1	1	yes	characteristic
195	C₂²	#11926312	1	1	yes	characteristic
196	C₂²	#11926312	1	1	yes	characteristic
197	C₂²	#11926313	1	1	yes	characteristic
198	C₄	—	2	1	no	—
199	C₄	—	2	1	no	—
200	C₄	—	2	1	no	—
201	C₄	—	2	1	no	—
202	C₄	—	2	2	no	—
203	C₄	—	4	1	no	—
204	C₄	—	4	1	no	—
205	C₄	—	4	1	no	—
206	C₄	#11926283	1	2	yes	—
207	C₄	#11926285	1	2	yes	—
208	C₂	#14561490	1	1	yes	characteristic
209	C₂	#14561491	1	1	yes	characteristic
210	C₂	#14561504	1	1	yes	characteristic
211	C₂	#14561517	1	1	yes	characteristic
212	C₂	#14561524	1	1	yes	characteristic
213	C₂	#14561525	1	1	yes	characteristic
214	C₂	C₁₉⋊#1309	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563752

C₂

yes

maximal, characteristic

#14563488

C₂

yes

maximal, characteristic

C₁₉×#1767

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×C₄⋊(C₁₉⋊C₈)

C₄

yes

—

C₂×#10597260

C₄

yes

—

#11926299

—

#11926299

—

#11926299

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×#97

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

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

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

#108

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1831

—

#1767

—

#1767

D₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

#329

yes

—

103

C₄×C₁₉

#330

yes

—

104

C₂×C₄⋊C₈

—

105

C₂×C₄⋊C₈

—

106

C₂×C₄⋊C₈

—

107

C₂×#97

—

108

C₂×#97

Dic₁₉

yes

—

109

C₄³

C₂×D₁₉

yes

characteristic

110

#336

—

111

#336

—

112

#336

—

113

#336

—

114

C₂×C₁₉

#1285

yes

characteristic

115

C₂×C₁₉

#1285

yes

characteristic

116

C₂×C₁₉

#1290

yes

characteristic

117

C₂×C₁₉

#1295

yes

characteristic

118

C₂×C₁₉

#1299

yes

characteristic

119

C₂×C₁₉

#1299

yes

characteristic

120

C₂×C₁₉

#1309

yes

characteristic

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂²×C₈

—

124

C₂×C₄²

Dic₃₈

yes

characteristic

125

C₂×C₄²

C₄×D₁₉

yes

characteristic

126

C₂×C₄²

C₄×D₁₉

yes

characteristic

127

C₂×C₄²

D₇₆

yes

characteristic

128

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

129

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

130

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

131

C₄⋊C₈

—

132

C₄⋊C₈

—

133

C₄⋊C₈

—

134

#97

—

135

#97

—

136

C₁₉

#7042

yes

characteristic, complemented, Sylow

137

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

138

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

139

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

140

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

141

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

142

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

143

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

156

C₄²

—

157

C₄²

—

158

C₄²

—

159

C₄²

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₂³

C₁₉⋊#95

yes

characteristic

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

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

#10597262

yes

—

180

C₂×C₄

#10597279

yes

—

181

C₂×C₄

#10597280

yes

characteristic

182

C₂×C₄

#10597280

yes

characteristic

183

C₂×C₄

#10597281

yes

characteristic

184

C₂×C₄

#10597281

yes

characteristic

185

C₂×C₄

#10597282

yes

—

186

C₂×C₄

#10597290

yes

characteristic

187

C₂×C₄

#10597293

yes

characteristic

188

C₈

—

189

C₈

—

190

C₈

—

152

—

191

C₂²

#11926300

yes

characteristic

192

C₂²

#11926304

yes

characteristic

193

C₂²

#11926305

yes

characteristic

194

C₂²

#11926308

yes

characteristic

195

C₂²

#11926312

yes

characteristic

196

C₂²

#11926312

yes

characteristic

197

C₂²

#11926313

yes

characteristic

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

#11926283

yes

—

207

C₄

#11926285

yes

—

208

C₂

#14561490

yes

characteristic

209

C₂

#14561491

yes

characteristic

210

C₂

#14561504

yes

characteristic

211

C₂

#14561517

yes

characteristic

212

C₂

#14561524

yes

characteristic

213

C₂

#14561525

yes

characteristic

214

C₂

C₁₉⋊#1309

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1767	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1767	D₁₉
hypocenter	C₁₉	#7042
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₄³

C₂×D₁₉

Fitting

C₁₉×#1767

C₂

socle, prime radical

C₂³×C₁₉

#95

cosocle

C₄³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

N	H ≅ G/N	type
136. C₁₉	#7042	semidirect

H ≅ G/N

type

136. C₁₉

#7042

semidirect

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

subgroup	index
#14563752	2
#14563488	2
C₁₉×#1767	2
#7042	19

subgroup

index

#14563752

#14563488

C₁₉×#1767

#7042

Subgroups — #18069135

Conjugacy classes of subgroups

Complements

Maximal subgroups