Group #18085377 — subgroups

Subgroups — #18085377

Order 4864.

586 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 159 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×#11926942	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926940	C₂	1	2	yes	maximal
3	#14564436	C₂	1	2	yes	maximal
4	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	2	yes	—
7	#11926942	—	2	4	no	—
8	#11926940	—	2	4	no	—
9	#11926940	—	2	4	no	—
10	C₂×#10597274	—	2	2	no	—
11	C₂×#10597265	—	2	4	no	—
12	C₂×#10597267	—	2	4	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#103	—	2	2	no	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#384	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₁₉	—	2	1	no	—
19	C₂²×Dic₃₈	—	2	2	no	—
20	C₂²×C₈×C₁₉	D₄	1	2	yes	—
21	C₁₉×C₄⋊Q₈	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	—	2	1	no	—
23	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
31	#10597315	—	2	2	no	—
32	#10597315	—	2	2	no	—
33	#10597315	—	2	2	no	—
34	#10597315	D₄	1	4	yes	—
35	C₁₉×#103	—	4	4	no	—
36	C₄×C₈×C₁₉	—	2	2	no	—
37	#10597274	—	2	8	no	—
38	#10597267	—	4	8	no	—
39	#10597265	—	2	16	no	—
40	C₄×C₁₉⋊C₈	—	2	2	no	—
41	C₄×C₁₉⋊C₈	—	2	2	no	—
42	C₂×Q₈×C₁₉	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	4	1	no	—
44	C₂×Q₈×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	4	2	no	—
46	C₂²×C₄×C₁₉	—	4	1	no	—
47	C₂²×C₄×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	4	2	no	—
51	C₂×Dic₃₈	—	2	4	no	—
52	C₂×Dic₃₈	—	4	4	no	—
53	C₂×Dic₃₈	—	4	4	no	—
54	C₂×Dic₃₈	—	4	2	no	—
55	C₂×C₈×C₁₉	—	2	2	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	SD₁₆	1	4	yes	—
58	C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₄⋊C₄×C₁₉	—	4	4	no	—
61	C₄⋊C₄×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₁₉	C₂×D₄	1	2	yes	—
64	C₄²×C₁₉	#41	1	1	yes	characteristic
65	C₄⋊Dic₁₉	—	2	4	no	—
66	C₄⋊Dic₁₉	—	2	4	no	—
67	C₄⋊Dic₁₉	—	4	2	no	—
68	C₄⋊Dic₁₉	—	4	2	no	—
69	C₂×C₁₉⋊C₈	—	2	4	no	—
70	C₂×C₁₉⋊C₈	—	2	4	no	—
71	C₂×C₁₉⋊C₈	SD₁₆	1	8	yes	—
72	#10316	—	19	1	no	maximal, Sylow
73	C₂³×C₁₉	#127	1	1	yes	characteristic
74	Q₈×C₁₉	—	4	4	no	—
75	Q₈×C₁₉	—	8	2	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	8	1	no	—
78	C₂×C₄×C₁₉	—	8	1	no	—
79	C₂×C₄×C₁₉	—	8	2	no	—
80	C₂×C₄×C₁₉	—	8	1	no	—
81	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#120	1	2	yes	—
83	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
84	C₂×C₄×C₁₉	#121	1	2	yes	—
85	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
86	C₂×C₄×C₁₉	C₂×SD₁₆	1	4	yes	—
87	C₂×C₄×C₁₉	#137	1	2	yes	—
88	C₂×C₄×C₁₉	#137	1	4	yes	—
89	C₂×Dic₁₉	—	4	4	no	—
90	C₂×Dic₁₉	—	8	2	no	—
91	C₂×Dic₁₉	—	8	2	no	—
92	Dic₃₈	—	4	8	no	—
93	Dic₃₈	—	8	4	no	—
94	C₈×C₁₉	—	2	4	no	—
95	C₁₉⋊C₈	—	2	8	no	—
96	C₂×#498	—	19	1	no	—
97	C₂×#498	—	19	2	no	—
98	#1956	—	19	2	no	—
99	#1956	D₁₉	1	1	yes	characteristic
100	#1273	—	19	1	no	—
101	C₂²×C₁₉	#392	1	1	yes	characteristic
102	C₂²×C₁₉	#492	1	2	yes	—
103	C₂²×C₁₉	#492	1	1	yes	characteristic
104	C₂²×C₁₉	#497	1	2	yes	—
105	C₂²×C₁₉	#497	1	1	yes	characteristic
106	C₄×C₁₉	—	8	2	no	—
107	C₄×C₁₉	—	16	1	no	—
108	C₄×C₁₉	#448	1	2	yes	—
109	C₄×C₁₉	#448	1	4	yes	—
110	C₄×C₁₉	#461	1	4	yes	—
111	C₄×C₁₉	#461	1	2	yes	—
112	Dic₁₉	—	8	4	no	—
113	C₂×C₄⋊Q₈	—	19	2	no	—
114	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
115	#498	—	38	4	no	—
116	#498	—	38	4	no	—
117	#498	—	38	4	no	—
118	C₂×#106	—	38	4	no	—
119	C₂×#106	—	38	2	no	—
120	C₂×#103	—	2	2	no	—
121	C₂×#103	—	38	4	no	—
122	C₂×C₄×C₈	—	19	2	no	—
123	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
124	#384	C₂×D₁₉	1	1	yes	characteristic
125	C₂×C₁₉	#1705	1	1	yes	characteristic
126	C₂×C₁₉	#1716	1	1	yes	characteristic
127	C₂×C₁₉	#1716	1	2	yes	—
128	C₂×C₁₉	#2013	1	1	yes	characteristic
129	C₂×C₁₉	#2013	1	2	yes	—
130	C₂²×Q₈	—	2	1	no	—
131	C₂²×Q₈	—	38	2	no	—
132	C₂²×C₈	—	19	4	no	—
133	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
134	C₄⋊Q₈	—	2	1	no	—
135	C₄⋊Q₈	—	2	2	no	—
136	C₄⋊Q₈	—	19	4	no	—
137	C₄⋊Q₈	—	38	2	no	—
138	C₄⋊Q₈	—	38	2	no	—
139	C₄⋊Q₈	—	38	2	no	—
140	C₄⋊Q₈	D₇₆	1	2	yes	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄⋊C₄	—	38	2	no	—
145	C₂×C₄⋊C₄	—	38	2	no	—
146	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
147	#106	—	38	16	no	—
148	#106	—	38	8	no	—
149	#103	—	4	4	no	—
150	#103	—	76	8	no	—
151	C₄×C₈	—	2	2	no	—
152	C₄×C₈	—	38	2	no	—
153	C₄×C₈	—	38	2	no	—
154	C₁₉	#10316	1	1	yes	characteristic, complemented, Sylow
155	C₂×Q₈	—	2	2	no	—
156	C₂×Q₈	—	4	1	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	—	38	4	no	—
160	C₂×Q₈	—	76	2	no	—
161	C₂×Q₈	—	76	4	no	—
162	C₂×Q₈	—	76	4	no	—
163	C₂²×C₄	—	4	1	no	—
164	C₂²×C₄	—	4	1	no	—
165	C₂²×C₄	—	76	2	no	—
166	C₂²×C₄	D₄×D₁₉	1	2	yes	—
167	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	19	8	no	—
171	C₂×C₈	—	38	4	no	—
172	C₂×C₈	—	38	4	no	—
173	C₂×C₈	#64526	1	4	yes	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	4	no	—
178	C₄⋊C₄	—	38	4	no	—
179	C₄⋊C₄	—	38	4	no	—
180	C₄⋊C₄	—	76	2	no	—
181	C₄⋊C₄	—	76	2	no	—
182	C₄²	C₂×D₇₆	1	1	yes	characteristic
183	C₄²	#64541	1	1	yes	characteristic
184	C₄²	D₄×D₁₉	1	2	yes	—
185	C₂³	#10597386	1	1	yes	characteristic
186	Q₈	—	4	4	no	—
187	Q₈	—	8	2	no	—
188	Q₈	—	76	8	no	—
189	Q₈	—	152	4	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	8	1	no	—
192	C₂×C₄	—	8	1	no	—
193	C₂×C₄	—	8	2	no	—
194	C₂×C₄	—	8	1	no	—
195	C₂×C₄	—	76	4	no	—
196	C₂×C₄	—	152	2	no	—
197	C₂×C₄	—	152	2	no	—
198	C₂×C₄	#10597328	1	2	yes	—
199	C₂×C₄	#10597330	1	2	yes	—
200	C₂×C₄	SD₁₆×D₁₉	1	4	yes	—
201	C₂×C₄	#10597364	1	4	yes	—
202	C₂×C₄	#10597376	1	1	yes	characteristic
203	C₂×C₄	C₂×#64526	1	2	yes	—
204	C₂×C₄	#10597383	1	1	yes	characteristic
205	C₂×C₄	#10597397	1	2	yes	—
206	C₈	—	2	4	no	—
207	C₈	—	38	8	no	—
208	C₂²	#11926453	1	1	yes	characteristic
209	C₂²	#11926915	1	2	yes	—
210	C₂²	#11926916	1	1	yes	characteristic
211	C₂²	#11926937	1	2	yes	—
212	C₂²	#11926939	1	1	yes	characteristic
213	C₄	—	8	2	no	—
214	C₄	—	16	1	no	—
215	C₄	—	152	4	no	—
216	C₄	#11926682	1	2	yes	—
217	C₄	#11926684	1	4	yes	—
218	C₄	#11926748	1	4	yes	—
219	C₄	#11926749	1	2	yes	—
220	C₂	#14563221	1	1	yes	characteristic
221	C₂	#14563266	1	1	yes	characteristic
222	C₂	#14563270	1	2	yes	—
223	C₂	#14564717	1	1	yes	characteristic
224	C₂	#14564719	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926942

C₂

yes

maximal, characteristic

C₂×#11926940

C₂

yes

maximal

#14564436

C₂

yes

maximal

C₁₉⋊#1273

C₂

yes

maximal, characteristic

C₁₉×#1956

C₂

yes

maximal, characteristic

C₂×#10597315

C₂²

yes

—

—

—

—

—

—

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

—

—

—

D₄

yes

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

#10597274

—

#10597267

—

#10597265

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

SD₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

SD₁₆

yes

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

100

#1273

—

101

C₂²×C₁₉

#392

yes

characteristic

102

C₂²×C₁₉

#492

yes

—

103

C₂²×C₁₉

#492

yes

characteristic

104

C₂²×C₁₉

#497

yes

—

105

C₂²×C₁₉

#497

yes

characteristic

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

#448

yes

—

109

C₄×C₁₉

#448

yes

—

110

C₄×C₁₉

#461

yes

—

111

C₄×C₁₉

#461

yes

—

112

Dic₁₉

—

113

C₂×C₄⋊Q₈

—

114

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

115

#498

—

116

#498

—

117

#498

—

118

C₂×#106

—

119

C₂×#106

—

120

C₂×#103

—

121

C₂×#103

—

122

C₂×C₄×C₈

—

123

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

124

#384

C₂×D₁₉

yes

characteristic

125

C₂×C₁₉

#1705

yes

characteristic

126

C₂×C₁₉

#1716

yes

characteristic

127

C₂×C₁₉

#1716

yes

—

128

C₂×C₁₉

#2013

yes

characteristic

129

C₂×C₁₉

#2013

yes

—

130

C₂²×Q₈

—

131

C₂²×Q₈

—

132

C₂²×C₈

—

133

C₂²×C₈

C₂²⋊D₁₉

yes

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

D₇₆

yes

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄²

C₂²×D₁₉

yes

characteristic

147

#106

—

148

#106

—

149

#103

—

150

#103

—

151

C₄×C₈

—

152

C₄×C₈

—

153

C₄×C₈

—

154

C₁₉

#10316

yes

characteristic, complemented, Sylow

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

D₄×D₁₉

yes

—

167

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

#64526

yes

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄²

C₂×D₇₆

yes

characteristic

183

C₄²

#64541

yes

characteristic

184

C₄²

D₄×D₁₉

yes

—

185

C₂³

#10597386

yes

characteristic

186

Q₈

—

187

Q₈

—

188

Q₈

—

189

Q₈

—

152

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

152

—

197

C₂×C₄

—

152

—

198

C₂×C₄

#10597328

yes

—

199

C₂×C₄

#10597330

yes

—

200

C₂×C₄

SD₁₆×D₁₉

yes

—

201

C₂×C₄

#10597364

yes

—

202

C₂×C₄

#10597376

yes

characteristic

203

C₂×C₄

C₂×#64526

yes

—

204

C₂×C₄

#10597383

yes

characteristic

205

C₂×C₄

#10597397

yes

—

206

C₈

—

207

C₈

—

208

C₂²

#11926453

yes

characteristic

209

C₂²

#11926915

yes

—

210

C₂²

#11926916

yes

characteristic

211

C₂²

#11926937

yes

—

212

C₂²

#11926939

yes

characteristic

213

C₄

—

214

C₄

—

215

C₄

—

152

—

216

C₄

#11926682

yes

—

217

C₄

#11926684

yes

—

218

C₄

#11926748

yes

—

219

C₄

#11926749

yes

—

220

C₂

#14563221

yes

characteristic

221

C₂

#14563266

yes

characteristic

222

C₂

#14563270

yes

—

223

C₂

#14564717

yes

characteristic

224

C₂

#14564719

yes

—

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1956	C₂
socle, prime radical	C₂³×C₁₉	#127
hypercenter	#1956	D₁₉
hypocenter	C₁₉	#10316
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1956

C₂

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
154. C₁₉	#10316	semidirect

H ≅ G/N

type

154. C₁₉

#10316

semidirect

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

subgroup	index
C₂×#11926942	2
C₂×#11926940	2
#14564436	2
C₁₉⋊#1273	2
C₁₉×#1956	2
#10316	19

subgroup

index

C₂×#11926942

C₂×#11926940

#14564436

C₁₉⋊#1273

C₁₉×#1956

#10316

Subgroups — #18085377

Conjugacy classes of subgroups

Complements

Maximal subgroups