Group #18082366 — subgroups

Subgroups — #18082366

Order 4864.

526 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11926924	C₂	1	1	yes	maximal, characteristic
2	#14564595	C₂	1	2	yes	maximal
3	#14564595	C₂	1	2	yes	maximal
4	C₂×#11926266	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1834	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₇₆	—	2	2	no	—
7	C₂×#10597315	C₂²	1	2	yes	—
8	#11926924	—	2	2	no	—
9	#11926924	C₄	1	4	yes	complemented
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	#11926306	—	2	4	no	—
13	#11926306	—	2	4	no	—
14	#11926266	—	2	2	no	—
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₁₉×#384	C₂²	1	2	yes	—
17	C₁₉×#340	—	2	2	no	—
18	C₂²×Dic₃₈	—	2	2	no	—
19	C₂²×C₈×C₁₉	D₄	1	2	yes	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	—	2	2	no	—
25	C₂×C₄⋊Dic₁₉	—	2	2	no	—
26	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
27	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
28	C₂×Dic₇₆	—	2	8	no	—
29	C₂×Dic₇₆	—	4	8	no	—
30	#10597315	—	2	2	no	—
31	#10597315	—	2	2	no	—
32	#10597315	—	2	2	no	—
33	#10597315	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₉	D₄	1	2	yes	—
36	C₄×C₁₉⋊C₈	—	2	1	no	—
37	C₄×C₁₉⋊C₈	—	2	1	no	—
38	C₄×C₁₉⋊C₈	—	2	1	no	—
39	C₄×C₁₉⋊C₈	—	2	1	no	—
40	C₂²×C₄×C₁₉	—	4	2	no	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂²×Dic₁₉	—	4	2	no	—
45	C₂×Dic₃₈	—	2	4	no	—
46	C₂×Dic₃₈	—	4	8	no	—
47	C₂×Dic₃₈	—	4	2	no	—
48	C₂×C₈×C₁₉	—	2	4	no	—
49	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
50	C₄⋊C₄×C₁₉	—	4	4	no	—
51	C₄⋊C₄×C₁₉	—	4	4	no	—
52	C₄⋊C₄×C₁₉	—	4	4	no	—
53	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₄²×C₁₉	#41	1	1	yes	characteristic
56	C₄²×C₁₉	#41	1	1	yes	characteristic
57	C₄⋊Dic₁₉	—	2	4	no	—
58	C₄⋊Dic₁₉	—	2	4	no	—
59	C₄⋊Dic₁₉	—	4	2	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	C₂×C₁₉⋊C₈	—	2	2	no	—
62	C₂×C₁₉⋊C₈	—	2	2	no	—
63	C₂×C₁₉⋊C₈	—	2	2	no	—
64	C₂×C₁₉⋊C₈	—	2	4	no	—
65	C₂×C₁₉⋊C₈	Q₁₆	1	4	yes	complemented
66	Dic₇₆	—	4	16	no	—
67	#9835	—	19	1	no	maximal, Sylow
68	C₂³×C₁₉	#127	1	1	yes	characteristic
69	C₂×C₄×C₁₉	—	8	2	no	—
70	C₂×C₄×C₁₉	—	8	2	no	—
71	C₂×C₄×C₁₉	—	8	2	no	—
72	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
77	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
79	C₂×C₄×C₁₉	#135	1	2	yes	—
80	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
81	C₂×C₄×C₁₉	#137	1	4	yes	—
82	C₂×Dic₁₉	—	4	4	no	—
83	C₂×Dic₁₉	—	8	4	no	—
84	Dic₃₈	—	4	8	no	—
85	Dic₃₈	—	8	4	no	—
86	C₈×C₁₉	—	2	4	no	—
87	C₁₉⋊C₈	—	2	4	no	—
88	C₁₉⋊C₈	—	4	2	no	—
89	C₂×#494	—	19	1	no	—
90	#1990	—	19	2	no	—
91	#1990	—	19	2	no	—
92	#1834	D₁₉	1	1	yes	characteristic
93	C₂×#322	—	19	1	no	—
94	C₂²×C₁₉	#390	1	1	yes	characteristic
95	C₂²×C₁₉	#494	1	1	yes	characteristic
96	C₂²×C₁₉	#495	1	1	yes	characteristic
97	C₂²×C₁₉	#496	1	2	yes	—
98	C₂²×C₁₉	#497	1	2	yes	—
99	C₄×C₁₉	—	16	2	no	—
100	C₄×C₁₉	#418	1	2	yes	—
101	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
102	C₄×C₁₉	#441	1	2	yes	—
103	C₄×C₁₉	#467	1	2	yes	—
104	C₄×C₁₉	#470	1	2	yes	—
105	C₄×C₁₉	#490	1	2	yes	—
106	Dic₁₉	—	8	4	no	—
107	C₂²×Q₁₆	—	38	2	no	—
108	C₂×C₄⋊Q₈	—	19	2	no	—
109	#494	—	19	4	no	—
110	#494	—	38	2	no	—
111	C₂×C₄×C₈	—	19	1	no	—
112	C₂×C₄×C₈	—	19	1	no	—
113	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
114	#384	C₂×D₁₉	1	2	yes	—
115	#340	—	2	2	no	—
116	#340	—	38	4	no	—
117	#340	—	38	4	no	—
118	#322	—	38	2	no	—
119	C₂×C₁₉	#1720	1	2	yes	—
120	C₂×C₁₉	#1723	1	2	yes	—
121	C₂×C₁₉	#1961	1	1	yes	characteristic
122	C₂×C₁₉	#1969	1	1	yes	characteristic
123	C₂×C₁₉	#1971	1	1	yes	characteristic
124	C₂²×Q₈	—	38	2	no	—
125	C₂×Q₁₆	—	38	8	no	—
126	C₂×Q₁₆	—	76	8	no	—
127	C₂²×C₈	—	19	2	no	—
128	C₂²×C₈	—	19	2	no	—
129	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
130	C₄⋊Q₈	—	19	4	no	—
131	C₄⋊Q₈	—	38	2	no	—
132	C₄⋊Q₈	—	38	2	no	—
133	C₄⋊Q₈	—	38	2	no	—
134	C₂×C₄⋊C₄	—	2	2	no	—
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	38	2	no	—
138	C₂×C₄⋊C₄	—	38	2	no	—
139	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	C₄×C₈	—	38	1	no	—
141	C₄×C₈	—	38	1	no	—
142	C₄×C₈	—	38	1	no	—
143	C₄×C₈	—	38	1	no	—
144	C₄×C₈	C₄×D₁₉	1	2	yes	—
145	C₄×C₈	D₇₆	1	2	yes	—
146	C₁₉	#9835	1	1	yes	characteristic, complemented, Sylow
147	C₂×Q₈	—	38	4	no	—
148	C₂×Q₈	—	76	2	no	—
149	C₂×Q₈	—	76	8	no	—
150	C₂²×C₄	—	4	2	no	—
151	C₂²×C₄	—	76	2	no	—
152	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
153	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
154	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
155	Q₁₆	—	76	16	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	19	4	no	—
158	C₂×C₈	—	38	2	no	—
159	C₂×C₈	—	38	2	no	—
160	C₂×C₈	—	38	2	no	—
161	C₂×C₈	—	38	4	no	—
162	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
163	C₄⋊C₄	—	4	4	no	—
164	C₄⋊C₄	—	4	4	no	—
165	C₄⋊C₄	—	4	4	no	—
166	C₄⋊C₄	—	38	4	no	—
167	C₄⋊C₄	—	38	4	no	—
168	C₄⋊C₄	—	76	2	no	—
169	C₄⋊C₄	—	76	2	no	—
170	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
171	C₄²	C₂×D₇₆	1	1	yes	characteristic
172	C₄²	#64545	1	1	yes	characteristic
173	C₄²	#64545	1	1	yes	characteristic
174	C₂³	#10597386	1	1	yes	characteristic
175	Q₈	—	76	8	no	—
176	Q₈	—	152	4	no	—
177	C₂×C₄	—	8	2	no	—
178	C₂×C₄	—	8	2	no	—
179	C₂×C₄	—	8	2	no	—
180	C₂×C₄	—	76	4	no	—
181	C₂×C₄	—	152	4	no	—
182	C₂×C₄	#10597339	1	1	yes	characteristic
183	C₂×C₄	#10597339	1	1	yes	characteristic
184	C₂×C₄	#10597341	1	1	yes	characteristic
185	C₂×C₄	#10597341	1	1	yes	characteristic
186	C₂×C₄	#10597358	1	2	yes	—
187	C₂×C₄	#10597361	1	4	yes	—
188	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
189	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
190	C₂×C₄	#10597393	1	1	yes	characteristic
191	C₂×C₄	#10597395	1	4	yes	—
192	C₈	—	2	4	no	—
193	C₈	—	38	4	no	—
194	C₈	—	76	2	no	—
195	C₂²	#11926445	1	1	yes	characteristic
196	C₂²	#11926922	1	1	yes	characteristic
197	C₂²	#11926927	1	1	yes	characteristic
198	C₂²	#11926934	1	2	yes	—
199	C₂²	#11926935	1	2	yes	—
200	C₄	—	16	2	no	—
201	C₄	—	152	4	no	—
202	C₄	#11926548	1	2	yes	—
203	C₄	#11926638	1	2	yes	—
204	C₄	#11926650	1	2	yes	—
205	C₄	#11926786	1	2	yes	—
206	C₄	#11926803	1	2	yes	—
207	C₄	#11926910	1	2	yes	—
208	C₂	#14563294	1	2	yes	—
209	C₂	#14563314	1	2	yes	—
210	C₂	#14564458	1	1	yes	characteristic
211	C₂	#14564494	1	1	yes	characteristic
212	C₂	#14564504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926924

C₂

yes

maximal, characteristic

#14564595

C₂

yes

maximal

#14564595

C₂

yes

maximal

C₂×#11926266

C₂

yes

maximal, characteristic

C₁₉×#1834

C₂

yes

maximal, characteristic

C₂²×Dic₇₆

—

C₂×#10597315

C₂²

yes

—

#11926924

—

#11926924

C₄

yes

complemented

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₁₉×#340

—

C₂²×Dic₃₈

—

C₂²×C₈×C₁₉

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

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

—

—

—

C₂×C₄

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

Q₁₆

yes

complemented

Dic₇₆

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

D₁₉

yes

characteristic

C₂×#322

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

—

100

C₄×C₁₉

#418

yes

—

101

C₄×C₁₉

C₄×Q₁₆

yes

—

102

C₄×C₁₉

#441

yes

—

103

C₄×C₁₉

#467

yes

—

104

C₄×C₁₉

#470

yes

—

105

C₄×C₁₉

#490

yes

—

106

Dic₁₉

—

107

C₂²×Q₁₆

—

108

C₂×C₄⋊Q₈

—

109

#494

—

110

#494

—

111

C₂×C₄×C₈

—

112

C₂×C₄×C₈

—

113

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

114

#384

C₂×D₁₉

yes

—

115

#340

—

116

#340

—

117

#340

—

118

#322

—

119

C₂×C₁₉

#1720

yes

—

120

C₂×C₁₉

#1723

yes

—

121

C₂×C₁₉

#1961

yes

characteristic

122

C₂×C₁₉

#1969

yes

characteristic

123

C₂×C₁₉

#1971

yes

characteristic

124

C₂²×Q₈

—

125

C₂×Q₁₆

—

126

C₂×Q₁₆

—

127

C₂²×C₈

—

128

C₂²×C₈

—

129

C₂²×C₈

C₂²⋊D₁₉

yes

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄²

C₂²×D₁₉

yes

characteristic

140

C₄×C₈

—

141

C₄×C₈

—

142

C₄×C₈

—

143

C₄×C₈

—

144

C₄×C₈

C₄×D₁₉

yes

—

145

C₄×C₈

D₇₆

yes

—

146

C₁₉

#9835

yes

characteristic, complemented, Sylow

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

D₄×D₁₉

yes

characteristic

153

C₂²×C₄

D₄×D₁₉

yes

characteristic

154

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

155

Q₁₆

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄²

C₂×C₄×D₁₉

yes

characteristic

171

C₄²

C₂×D₇₆

yes

characteristic

172

C₄²

#64545

yes

characteristic

173

C₄²

#64545

yes

characteristic

174

C₂³

#10597386

yes

characteristic

175

Q₈

—

176

Q₈

—

152

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

152

—

182

C₂×C₄

#10597339

yes

characteristic

183

C₂×C₄

#10597339

yes

characteristic

184

C₂×C₄

#10597341

yes

characteristic

185

C₂×C₄

#10597341

yes

characteristic

186

C₂×C₄

#10597358

yes

—

187

C₂×C₄

#10597361

yes

—

188

C₂×C₄

Q₁₆×D₁₉

yes

—

189

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

190

C₂×C₄

#10597393

yes

characteristic

191

C₂×C₄

#10597395

yes

—

192

C₈

—

193

C₈

—

194

C₈

—

195

C₂²

#11926445

yes

characteristic

196

C₂²

#11926922

yes

characteristic

197

C₂²

#11926927

yes

characteristic

198

C₂²

#11926934

yes

—

199

C₂²

#11926935

yes

—

200

C₄

—

201

C₄

—

152

—

202

C₄

#11926548

yes

—

203

C₄

#11926638

yes

—

204

C₄

#11926650

yes

—

205

C₄

#11926786

yes

—

206

C₄

#11926803

yes

—

207

C₄

#11926910

yes

—

208

C₂

#14563294

yes

—

209

C₂

#14563314

yes

—

210

C₂

#14564458

yes

characteristic

211

C₂

#14564494

yes

characteristic

212

C₂

#14564504

yes

characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1834	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1834	D₁₉
hypocenter	C₁₉	#9835
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1834

C₂

socle, prime radical

C₂³×C₁₉

#127

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1834

N	H ≅ G/N	type
9. #11926924	C₄	semidirect
65. C₂×C₁₉⋊C₈	Q₁₆	semidirect
146. C₁₉	#9835	semidirect

H ≅ G/N

type

9. #11926924

C₄

semidirect

65. C₂×C₁₉⋊C₈

Q₁₆

semidirect

146. C₁₉

#9835

semidirect

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

subgroup	index
C₂×#11926924	2
#14564595	2
C₂×#11926266	2
C₁₉×#1834	2
#9835	19

subgroup

index

C₁₉×#1834

Subgroups — #18082366

Conjugacy classes of subgroups

Complements

Maximal subgroups