Group #18069147 — subgroups

Subgroups — C₁₉⋊#7047 #18069147

Order 4864.

608 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14563545	C₂	1	2	yes	maximal
2	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	4	yes	—
6	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
8	C₂×C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
9	C₂⁵×C₁₉	Q₈	1	1	yes	characteristic
10	C₂³×C₄×C₁₉	—	4	4	no	—
11	C₂³×C₄×C₁₉	—	4	2	no	—
12	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
13	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	2	yes	—
16	C₂²×C₈×C₁₉	—	2	2	no	—
17	C₂²×C₁₉⋊C₈	—	2	4	no	—
18	C₁₉×C₂²⋊C₈	—	4	4	no	—
19	C₁₉×C₂²⋊C₈	—	4	2	no	—
20	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
21	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
22	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
23	C₂⁴×C₁₉	—	2	2	no	—
24	C₂⁴×C₁₉	—	2	4	no	—
25	C₂⁴×C₁₉	—	4	2	no	—
26	C₂⁴×C₁₉	—	4	1	no	—
27	C₂⁴×C₁₉	—	4	1	no	—
28	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
29	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	—	2	4	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	4	no	—
33	C₂²×C₄×C₁₉	—	2	4	no	—
34	C₂²×C₄×C₁₉	—	2	4	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	—	4	2	no	—
37	C₂²×C₄×C₁₉	—	4	2	no	—
38	C₂²×C₄×C₁₉	—	4	1	no	—
39	C₂²×C₄×C₁₉	—	4	2	no	—
40	C₂²×C₄×C₁₉	—	4	16	no	—
41	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
43	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₉	—	4	4	no	—
45	C₂×C₈×C₁₉	—	4	2	no	—
46	C₂×C₁₉⋊C₈	—	4	4	no	—
47	C₂×C₁₉⋊C₈	—	4	4	no	—
48	C₂×C₁₉⋊C₈	—	4	4	no	—
49	#7047	—	19	1	no	maximal, Sylow
50	C₂³×C₁₉	—	2	2	no	—
51	C₂³×C₁₉	—	2	1	no	—
52	C₂³×C₁₉	—	2	2	no	—
53	C₂³×C₁₉	—	2	2	no	—
54	C₂³×C₁₉	—	2	2	no	—
55	C₂³×C₁₉	—	2	2	no	—
56	C₂³×C₁₉	—	2	2	no	—
57	C₂³×C₁₉	—	2	2	no	—
58	C₂³×C₁₉	—	2	2	no	—
59	C₂³×C₁₉	—	2	1	no	—
60	C₂³×C₁₉	—	4	4	no	—
61	C₂³×C₁₉	—	4	8	no	—
62	C₂³×C₁₉	—	4	8	no	—
63	C₂³×C₁₉	—	4	4	no	—
64	C₂³×C₁₉	—	4	4	no	—
65	C₂³×C₁₉	#95	1	1	yes	characteristic
66	C₂³×C₁₉	#108	1	2	yes	—
67	C₂³×C₁₉	#108	1	4	yes	—
68	C₂×C₄×C₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	4	4	no	—
74	C₂×C₄×C₁₉	—	4	8	no	—
75	C₂×C₄×C₁₉	—	4	8	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	#99	1	4	yes	—
78	C₂×C₄×C₁₉	#99	1	2	yes	—
79	C₈×C₁₉	—	8	2	no	—
80	C₁₉⋊C₈	—	8	4	no	—
81	#1779	—	19	2	no	—
82	#1779	D₁₉	1	1	yes	characteristic
83	C₂²×C₁₉	—	2	4	no	—
84	C₂²×C₁₉	—	2	2	no	—
85	C₂²×C₁₉	—	2	4	no	—
86	C₂²×C₁₉	—	2	4	no	—
87	C₂²×C₁₉	—	2	4	no	—
88	C₂²×C₁₉	—	4	16	no	—
89	C₂²×C₁₉	—	4	2	no	—
90	C₂²×C₁₉	—	4	2	no	—
91	C₂²×C₁₉	—	4	2	no	—
92	C₂²×C₁₉	—	4	1	no	—
93	C₂²×C₁₉	—	4	2	no	—
94	C₂²×C₁₉	—	4	2	no	—
95	C₂²×C₁₉	—	4	1	no	—
96	C₂²×C₁₉	#338	1	1	yes	characteristic
97	C₂²×C₁₉	#341	1	2	yes	—
98	C₂²×C₁₉	#341	1	1	yes	characteristic
99	C₂²×C₁₉	#342	1	2	yes	—
100	C₂²×C₁₉	#342	1	1	yes	characteristic
101	C₄×C₁₉	—	2	4	no	—
102	C₄×C₁₉	—	2	2	no	—
103	C₄×C₁₉	—	4	1	no	—
104	C₂⁴×C₄	C₂×D₁₉	1	1	yes	characteristic
105	C₂×C₂²⋊C₈	—	2	2	no	—
106	C₂×C₂²⋊C₈	—	19	4	no	—
107	C₂×C₂²⋊C₈	—	38	2	no	—
108	C₂×C₂²⋊C₈	—	38	2	no	—
109	C₂×C₂²⋊C₈	Dic₁₉	1	2	yes	—
110	C₂×C₁₉	—	4	4	no	—
111	C₂×C₁₉	—	4	2	no	—
112	C₂×C₁₉	#1293	1	2	yes	—
113	C₂×C₁₉	#1293	1	1	yes	characteristic
114	C₂×C₁₉	#1298	1	1	yes	characteristic
115	C₂×C₁₉	#1298	1	2	yes	—
116	C₂×C₁₉	#1304	1	1	yes	characteristic
117	C₂⁵	Dic₃₈	1	1	yes	characteristic
118	C₂³×C₄	—	4	4	no	—
119	C₂³×C₄	—	4	2	no	—
120	C₂³×C₄	C₄×D₁₉	1	2	yes	—
121	C₂³×C₄	D₇₆	1	1	yes	characteristic
122	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
123	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
124	C₂²×C₈	—	2	2	no	—
125	C₂²×C₈	—	38	4	no	—
126	C₂²⋊C₈	—	4	4	no	—
127	C₂²⋊C₈	—	4	2	no	—
128	C₂²⋊C₈	—	76	4	no	—
129	C₂²⋊C₈	—	76	4	no	—
130	C₂²⋊C₈	—	76	4	no	—
131	C₁₉	#7047	1	1	yes	characteristic, complemented, Sylow
132	C₂⁴	—	2	2	no	—
133	C₂⁴	—	2	4	no	—
134	C₂⁴	—	4	2	no	—
135	C₂⁴	—	4	1	no	—
136	C₂⁴	—	4	1	no	—
137	C₂⁴	Dic₁₉⋊C₄	1	2	yes	—
138	C₂⁴	C₄⋊Dic₁₉	1	1	yes	characteristic
139	C₂²×C₄	—	2	4	no	—
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	2	4	no	—
144	C₂²×C₄	—	4	2	no	—
145	C₂²×C₄	—	4	2	no	—
146	C₂²×C₄	—	4	1	no	—
147	C₂²×C₄	—	4	2	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	4	16	no	—
150	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
151	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
152	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
153	C₂×C₈	—	4	4	no	—
154	C₂×C₈	—	4	2	no	—
155	C₂×C₈	—	76	4	no	—
156	C₂×C₈	—	76	4	no	—
157	C₂×C₈	—	76	4	no	—
158	C₂³	—	2	2	no	—
159	C₂³	—	2	1	no	—
160	C₂³	—	2	2	no	—
161	C₂³	—	2	2	no	—
162	C₂³	—	2	2	no	—
163	C₂³	—	2	2	no	—
164	C₂³	—	2	2	no	—
165	C₂³	—	2	2	no	—
166	C₂³	—	2	2	no	—
167	C₂³	—	2	1	no	—
168	C₂³	—	4	4	no	—
169	C₂³	—	4	8	no	—
170	C₂³	—	4	8	no	—
171	C₂³	—	4	4	no	—
172	C₂³	—	4	4	no	—
173	C₂³	#10597276	1	2	yes	—
174	C₂³	#10597279	1	4	yes	—
175	C₂³	C₁₉⋊#95	1	1	yes	characteristic
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	4	8	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	8	no	—
185	C₂×C₄	#10597263	1	4	yes	—
186	C₂×C₄	#10597291	1	2	yes	—
187	C₈	—	8	2	no	—
188	C₈	—	152	4	no	—
189	C₂²	—	2	4	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	4	no	—
192	C₂²	—	2	4	no	—
193	C₂²	—	2	4	no	—
194	C₂²	—	4	16	no	—
195	C₂²	—	4	2	no	—
196	C₂²	—	4	1	no	—
197	C₂²	—	4	2	no	—
198	C₂²	—	4	2	no	—
199	C₂²	—	4	2	no	—
200	C₂²	—	4	1	no	—
201	C₂²	—	4	2	no	—
202	C₂²	C₁₉⋊#338	1	1	yes	characteristic
203	C₂²	#11926308	1	2	yes	—
204	C₂²	#11926309	1	1	yes	characteristic
205	C₂²	#11926310	1	2	yes	—
206	C₂²	#11926311	1	1	yes	characteristic
207	C₄	—	2	2	no	—
208	C₄	—	2	4	no	—
209	C₄	—	4	1	no	—
210	C₂	—	4	4	no	—
211	C₂	—	4	2	no	—
212	C₂	#14561511	1	2	yes	—
213	C₂	#14561512	1	1	yes	characteristic
214	C₂	#14561522	1	1	yes	characteristic
215	C₂	#14561523	1	2	yes	—
216	C₂	C₁₉⋊#1304	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563545

C₂

yes

maximal

C₁₉×#1779

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₂⁴×C₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×C₂²⋊C₈

C₄

yes

—

C₂⁵×C₁₉

Q₈

yes

characteristic

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₁₉⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₄⋊C₄

yes

—

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7047

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂³×C₁₉

#108

yes

—

C₂³×C₁₉

#108

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

#99

yes

—

C₂×C₄×C₁₉

#99

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1779

—

#1779

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#338

yes

characteristic

C₂²×C₁₉

#341

yes

—

C₂²×C₁₉

#341

yes

characteristic

C₂²×C₁₉

#342

yes

—

100

C₂²×C₁₉

#342

yes

characteristic

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₂⁴×C₄

C₂×D₁₉

yes

characteristic

105

C₂×C₂²⋊C₈

—

106

C₂×C₂²⋊C₈

—

107

C₂×C₂²⋊C₈

—

108

C₂×C₂²⋊C₈

—

109

C₂×C₂²⋊C₈

Dic₁₉

yes

—

110

C₂×C₁₉

—

111

C₂×C₁₉

—

112

C₂×C₁₉

#1293

yes

—

113

C₂×C₁₉

#1293

yes

characteristic

114

C₂×C₁₉

#1298

yes

characteristic

115

C₂×C₁₉

#1298

yes

—

116

C₂×C₁₉

#1304

yes

characteristic

117

C₂⁵

Dic₃₈

yes

characteristic

118

C₂³×C₄

—

119

C₂³×C₄

—

120

C₂³×C₄

C₄×D₁₉

yes

—

121

C₂³×C₄

D₇₆

yes

characteristic

122

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

123

C₂³×C₄

C₂²⋊D₁₉

yes

—

124

C₂²×C₈

—

125

C₂²×C₈

—

126

C₂²⋊C₈

—

127

C₂²⋊C₈

—

128

C₂²⋊C₈

—

129

C₂²⋊C₈

—

130

C₂²⋊C₈

—

131

C₁₉

#7047

yes

characteristic, complemented, Sylow

132

C₂⁴

—

133

C₂⁴

—

134

C₂⁴

—

135

C₂⁴

—

136

C₂⁴

—

137

C₂⁴

Dic₁₉⋊C₄

yes

—

138

C₂⁴

C₄⋊Dic₁₉

yes

characteristic

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

151

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

152

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

—

164

C₂³

—

165

C₂³

—

166

C₂³

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

—

173

C₂³

#10597276

yes

—

174

C₂³

#10597279

yes

—

175

C₂³

C₁₉⋊#95

yes

characteristic

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

#10597263

yes

—

186

C₂×C₄

#10597291

yes

—

187

C₈

—

188

C₈

—

152

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

C₁₉⋊#338

yes

characteristic

203

C₂²

#11926308

yes

—

204

C₂²

#11926309

yes

characteristic

205

C₂²

#11926310

yes

—

206

C₂²

#11926311

yes

characteristic

207

C₄

—

208

C₄

—

209

C₄

—

210

C₂

—

211

C₂

—

212

C₂

#14561511

yes

—

213

C₂

#14561512

yes

characteristic

214

C₂

#14561522

yes

characteristic

215

C₂

#14561523

yes

—

216

C₂

C₁₉⋊#1304

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂⁴×C₄	C₂×D₁₉
Fitting	C₁₉×#1779	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁵×C₁₉	Q₈
cosocle	C₂⁴×C₄×C₁₉	C₂²
hypercenter	#1779	D₁₉
hypocenter	C₁₉	#7047
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ #1779

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂⁴×C₄

C₂×D₁₉

Fitting

C₁₉×#1779

C₂

socle

C₂³×C₁₉

#95

prime radical

C₂⁵×C₁₉

Q₈

cosocle

C₂⁴×C₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ #1779

N	H ≅ G/N	type
131. C₁₉	#7047	semidirect

H ≅ G/N

type

131. C₁₉

#7047

semidirect

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

subgroup	index
#14563545	2
C₁₉×#1779	2
#7047	19

subgroup

index

#14563545

C₁₉×#1779

#7047

Subgroups — C₁₉⋊#7047 #18069147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19⋊#7047 #18069147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊#7047 #18069147