Group #18080057 — subgroups

Subgroups — #18080057

Order 4864.

488 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14572706	C₂	1	1	yes	maximal, characteristic
2	#14562352	C₂	1	2	yes	maximal, complemented
3	#14562270	C₂	1	1	yes	maximal, characteristic
4	#14561507	C₂	1	2	yes	maximal, complemented
5	C₁₉×#3152	C₂	1	1	yes	maximal, characteristic
6	#11926616	—	2	4	no	—
7	#11926601	C₂²	1	2	yes	—
8	#11926601	C₂²	1	2	yes	—
9	#11926511	—	2	2	no	—
10	#11926290	—	2	4	no	—
11	#11926284	—	2	2	no	—
12	C₂×C₁₉×#137	—	2	2	no	—
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₁₉×#497	—	2	2	no	—
16	C₁₉×#494	C₄	1	2	yes	—
17	C₁₉×#492	C₄	1	2	yes	—
18	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×#41×C₁₉	D₄	1	2	yes	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₁₉×#137	—	4	4	no	—
22	C₁₉×#137	—	4	4	no	—
23	C₂×Q₁₆×C₁₉	—	2	4	no	—
24	C₂×SD₁₆×C₁₉	—	2	4	no	—
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₁₉×C₄⋊Q₈	—	2	2	no	—
27	C₁₉×C₄⋊Q₈	—	2	1	no	—
28	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
30	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
31	C₁₉×#124	D₄	1	2	yes	—
32	C₁₉×#121	—	2	2	no	—
33	C₄×D₄×C₁₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×#64520	—	2	2	no	—
37	C₂²×C₁₉⋊C₈	—	2	2	no	—
38	C₁₉×#97	—	2	1	no	—
39	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
41	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
45	#10597260	—	2	2	no	—
46	#10597260	—	2	2	no	—
47	#41×C₁₉	—	4	2	no	—
48	#41×C₁₉	—	4	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂×Q₈×C₁₉	—	4	2	no	—
52	C₂×Q₈×C₁₉	—	4	1	no	—
53	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	4	1	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	2	yes	—
61	Q₁₆×C₁₉	—	4	8	no	—
62	SD₁₆×C₁₉	—	4	8	no	—
63	M₁₆×C₁₉	—	2	4	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	2	yes	—
71	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
72	#64520	—	8	2	no	—
73	C₂×C₁₉⋊C₈	—	2	4	no	—
74	C₂×C₁₉⋊C₈	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	8	2	no	—
76	#9421	—	19	1	no	maximal, Sylow
77	C₂³×C₁₉	—	2	2	no	—
78	C₂³×C₁₉	#123	1	1	yes	characteristic
79	Q₈×C₁₉	—	4	2	no	—
80	Q₈×C₁₉	—	4	4	no	—
81	Q₈×C₁₉	—	8	2	no	—
82	D₄×C₁₉	—	4	2	no	—
83	D₄×C₁₉	—	8	2	no	—
84	D₄×C₁₉	—	8	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	8	1	no	—
92	C₂×C₄×C₁₉	—	8	1	no	—
93	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
95	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	2	yes	—
97	C₈×C₁₉	—	2	4	no	—
98	C₁₉⋊C₈	—	4	4	no	—
99	C₁₉⋊C₈	—	8	2	no	—
100	#3152	D₁₉	1	1	yes	characteristic
101	#2980	—	19	1	no	—
102	#1556	—	19	2	no	—
103	#1536	—	19	1	no	—
104	#1291	—	19	2	no	—
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	—	2	2	no	—
107	C₂²×C₁₉	—	4	2	no	—
108	C₂²×C₁₉	—	4	4	no	—
109	C₂²×C₁₉	#386	1	1	yes	characteristic
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	—	4	2	no	—
114	C₄×C₁₉	—	8	2	no	—
115	C₄×C₁₉	#453	1	2	yes	—
116	C₂×#137	—	2	2	no	—
117	#532	C₂×D₁₉	1	1	yes	characteristic
118	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
119	#497	—	2	2	no	—
120	#494	Dic₁₉	1	2	yes	—
121	#492	Dic₁₉	1	2	yes	—
122	#435	—	38	4	no	—
123	#432	—	19	2	no	—
124	#432	—	19	2	no	—
125	#408	—	38	2	no	—
126	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
127	#332	—	38	4	no	—
128	#329	—	38	2	no	—
129	C₂×C₁₉	—	4	1	no	—
130	C₂×C₁₉	—	8	2	no	—
131	C₂×C₁₉	#1887	1	1	yes	characteristic
132	C₂×C₁₉	#1902	1	2	yes	—
133	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
134	C₂²×Q₈	—	2	1	no	—
135	#137	—	4	4	no	—
136	#137	—	4	4	no	—
137	C₂×Q₁₆	—	2	4	no	—
138	C₂×SD₁₆	—	2	4	no	—
139	C₂×M₁₆	—	2	1	no	—
140	C₂×M₁₆	—	38	2	no	—
141	C₂²×C₈	—	38	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	1	no	—
144	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
145	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
146	#127	C₂×Dic₁₉	1	1	yes	characteristic
147	#124	C₂²⋊D₁₉	1	2	yes	—
148	#121	—	2	2	no	—
149	C₄×D₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
152	C₄⋊C₈	—	19	4	no	—
153	C₄⋊C₈	—	38	2	no	—
154	C₂²⋊C₈	—	38	4	no	—
155	C₂²⋊C₈	—	38	2	no	—
156	C₂²⋊C₈	—	38	2	no	—
157	#97	—	2	1	no	—
158	#97	—	38	2	no	—
159	#97	—	38	2	no	—
160	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
161	C₁₉	#9421	1	1	yes	characteristic, complemented, Sylow
162	#41	—	4	2	no	—
163	#41	—	4	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	—	4	1	no	—
168	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
169	C₂×D₄	—	2	2	no	—
170	C₂×D₄	—	2	2	no	—
171	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	4	1	no	—
174	C₂²×C₄	#64543	1	2	yes	—
175	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
176	Q₁₆	—	4	8	no	—
177	SD₁₆	—	4	8	no	—
178	M₁₆	—	2	4	no	—
179	M₁₆	—	152	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	38	4	no	—
182	C₂×C₈	—	76	2	no	—
183	C₂×C₈	—	152	2	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₂²⋊C₄	—	2	4	no	—
188	C₄²	D₄×D₁₉	1	2	yes	—
189	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
190	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
191	C₂³	—	2	2	no	—
192	C₂³	#10597381	1	1	yes	characteristic
193	Q₈	—	4	2	no	—
194	Q₈	—	4	4	no	—
195	Q₈	—	8	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	2	no	—
198	D₄	—	8	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	8	1	no	—
206	C₂×C₄	—	8	1	no	—
207	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
208	C₂×C₄	#10597383	1	1	yes	characteristic
209	C₂×C₄	#10597385	1	2	yes	—
210	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
211	C₈	—	2	4	no	—
212	C₈	—	76	4	no	—
213	C₈	—	152	2	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	2	1	no	—
216	C₂²	—	4	4	no	—
217	C₂²	—	4	2	no	—
218	C₂²	#11926424	1	1	yes	characteristic
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	2	1	no	—
222	C₄	—	4	2	no	—
223	C₄	—	8	2	no	—
224	C₄	#11926711	1	2	yes	—
225	C₂	—	4	1	no	—
226	C₂	—	8	2	no	—
227	C₂	#14564034	1	1	yes	characteristic
228	C₂	#14564110	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572706

C₂

yes

maximal, characteristic

#14562352

C₂

yes

maximal, complemented

#14562270

C₂

yes

maximal, characteristic

#14561507

C₂

yes

maximal, complemented

C₁₉×#3152

C₂

yes

maximal, characteristic

#11926616

—

#11926601

C₂²

yes

—

#11926601

C₂²

yes

—

#11926511

—

#11926290

—

#11926284

—

C₂×C₁₉×#137

—

C₁₉×#532

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#497

—

C₁₉×#494

C₄

yes

—

C₁₉×#492

C₄

yes

—

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

—

C₂²×Q₈×C₁₉

—

C₁₉×#137

—

C₁₉×#137

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

D₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64520

—

C₂²×C₁₉⋊C₈

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

#10597260

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9421

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

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

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

100

#3152

D₁₉

yes

characteristic

101

#2980

—

102

#1556

—

103

#1536

—

104

#1291

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

#386

yes

characteristic

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#453

yes

—

116

C₂×#137

—

117

#532

C₂×D₁₉

yes

characteristic

118

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

119

#497

—

120

#494

Dic₁₉

yes

—

121

#492

Dic₁₉

yes

—

122

#435

—

123

#432

—

124

#432

—

125

#408

—

126

C₄×M₁₆

C₂×D₁₉

yes

characteristic

127

#332

—

128

#329

—

129

C₂×C₁₉

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#1887

yes

characteristic

132

C₂×C₁₉

#1902

yes

—

133

C₂×#41

C₂²⋊D₁₉

yes

—

134

C₂²×Q₈

—

135

#137

—

136

#137

—

137

C₂×Q₁₆

—

138

C₂×SD₁₆

—

139

C₂×M₁₆

—

140

C₂×M₁₆

—

141

C₂²×C₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

C₂×Dic₁₉

yes

—

145

C₄⋊Q₈

C₂×Dic₁₉

yes

characteristic

146

#127

C₂×Dic₁₉

yes

characteristic

147

#124

C₂²⋊D₁₉

yes

—

148

#121

—

149

C₄×D₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄²

C₂²×D₁₉

yes

characteristic

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

C₂²⋊C₈

—

155

C₂²⋊C₈

—

156

C₂²⋊C₈

—

157

#97

—

158

#97

—

159

#97

—

160

C₄×C₈

C₂×Dic₁₉

yes

—

161

C₁₉

#9421

yes

characteristic, complemented, Sylow

162

#41

—

163

#41

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

C₂²⋊Dic₁₉

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

#64543

yes

—

175

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

176

Q₁₆

—

177

SD₁₆

—

178

M₁₆

—

179

M₁₆

—

152

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

152

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₄²

D₄×D₁₉

yes

—

189

C₄²

C₂²×Dic₁₉

yes

characteristic

190

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

191

C₂³

—

192

C₂³

#10597381

yes

characteristic

193

Q₈

—

194

Q₈

—

195

Q₈

—

196

D₄

—

197

D₄

—

198

D₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

D₄×Dic₁₉

yes

—

208

C₂×C₄

#10597383

yes

characteristic

209

C₂×C₄

#10597385

yes

—

210

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

211

C₈

—

212

C₈

—

213

C₈

—

152

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#11926424

yes

characteristic

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

#11926711

yes

—

225

C₂

—

226

C₂

—

227

C₂

#14564034

yes

characteristic

228

C₂

#14564110

yes

—

	subgroup	G/H
center	C₂²	#11926424
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3152	C₂
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3152	D₁₉
hypocenter	C₁₉	#9421
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

subgroup

G/H

center

C₂²

#11926424

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3152

C₂

socle

C₂²×C₁₉

#386

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

N	H ≅ G/N	type
2. #14562352	C₂	semidirect
4. #14561507	C₂	semidirect
161. C₁₉	#9421	semidirect

H ≅ G/N

type

2. #14562352

C₂

semidirect

4. #14561507

C₂

semidirect

161. C₁₉

#9421

semidirect

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

subgroup	index
#14572706	2
#14562352	2
#14562270	2
#14561507	2
C₁₉×#3152	2
#9421	19

subgroup

index

C₁₉×#3152

Subgroups — #18080057

Conjugacy classes of subgroups

Complements

Maximal subgroups