Group #18069148 — subgroups

Subgroups — C₁₉⋊#7048 #18069148

Order 4864.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14563384	C₂	1	1	yes	maximal, characteristic
2	#14563384	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1745	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597260	—	2	1	no	—
5	C₂×#10597260	—	2	1	no	—
6	#11926299	—	2	1	no	—
7	#11926299	—	2	1	no	—
8	#11926299	C₄	1	2	yes	—
9	#11926299	C₄	1	2	yes	—
10	C₂×C₁₉×#97	—	2	1	no	—
11	C₄³×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#336	—	2	1	no	—
13	C₁₉×#336	C₄	1	2	yes	—
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×#97	—	2	4	no	—
25	#10597260	—	2	4	no	—
26	#10597260	—	2	4	no	—
27	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	—	2	4	no	—
35	C₂×C₈×C₁₉	—	4	2	no	—
36	C₂×C₈×C₁₉	—	4	2	no	—
37	C₄²×C₁₉	—	2	2	no	—
38	C₄²×C₁₉	—	2	2	no	—
39	C₄²×C₁₉	—	2	2	no	—
40	C₄²×C₁₉	—	4	1	no	—
41	C₄²×C₁₉	—	4	1	no	—
42	C₄²×C₁₉	—	4	1	no	—
43	C₄²×C₁₉	—	4	1	no	—
44	C₂×C₁₉⋊C₈	—	2	4	no	—
45	C₂×C₁₉⋊C₈	—	2	4	no	—
46	C₂×C₁₉⋊C₈	—	4	2	no	—
47	C₂×C₁₉⋊C₈	—	4	2	no	—
48	C₂×C₁₉⋊C₈	—	4	2	no	—
49	C₂×C₁₉⋊C₈	—	4	2	no	—
50	#7048	—	19	1	no	maximal, Sylow
51	C₂³×C₁₉	#95	1	1	yes	characteristic
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	—	2	1	no	—
54	C₂×C₄×C₁₉	—	2	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
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	#104	1	2	yes	—
71	C₂×C₄×C₁₉	#104	1	2	yes	—
72	C₂×C₄×C₁₉	#104	1	2	yes	—
73	C₈×C₁₉	—	4	4	no	—
74	C₁₉⋊C₈	—	4	4	no	—
75	C₁₉⋊C₈	—	4	4	no	—
76	#1745	—	19	1	no	—
77	#1745	—	19	1	no	—
78	#1745	D₁₉	1	1	yes	characteristic
79	C₂²×C₁₉	#338	1	1	yes	characteristic
80	C₂²×C₁₉	#339	1	1	yes	characteristic
81	C₂²×C₁₉	#339	1	1	yes	characteristic
82	C₂²×C₁₉	#339	1	1	yes	characteristic
83	C₂²×C₁₉	#344	1	1	yes	characteristic
84	C₂²×C₁₉	#344	1	1	yes	characteristic
85	C₂²×C₁₉	#344	1	1	yes	characteristic
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	4	1	no	—
90	C₄×C₁₉	—	4	1	no	—
91	C₄×C₁₉	—	4	1	no	—
92	C₄×C₁₉	—	4	1	no	—
93	C₂×#97	—	2	1	no	—
94	C₂×#97	—	38	1	no	—
95	C₂×#97	—	38	1	no	—
96	C₄³	C₂×D₁₉	1	1	yes	characteristic
97	#336	—	2	1	no	—
98	#336	—	19	2	no	—
99	#336	—	19	2	no	—
100	#336	—	38	1	no	—
101	#336	—	38	1	no	—
102	#336	Dic₁₉	1	2	yes	—
103	C₂×C₁₉	#1291	1	1	yes	characteristic
104	C₂×C₁₉	#1291	1	1	yes	characteristic
105	C₂×C₁₉	#1291	1	1	yes	characteristic
106	C₂×C₁₉	#1300	1	1	yes	characteristic
107	C₂×C₁₉	#1300	1	1	yes	characteristic
108	C₂×C₁₉	#1300	1	1	yes	characteristic
109	C₂×C₁₉	#1308	1	1	yes	characteristic
110	C₂²×C₈	—	2	2	no	—
111	C₂²×C₈	—	38	2	no	—
112	C₂²×C₈	—	38	2	no	—
113	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
114	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
115	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
116	C₂×C₄²	D₇₆	1	1	yes	characteristic
117	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
118	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
119	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
120	#97	—	2	4	no	—
121	#97	—	38	4	no	—
122	#97	—	38	4	no	—
123	C₁₉	#7048	1	1	yes	characteristic, complemented, Sylow
124	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
125	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
126	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
127	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
128	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
129	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
130	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
131	C₂×C₈	—	2	4	no	—
132	C₂×C₈	—	4	2	no	—
133	C₂×C₈	—	4	2	no	—
134	C₂×C₈	—	38	4	no	—
135	C₂×C₈	—	38	4	no	—
136	C₂×C₈	—	76	2	no	—
137	C₂×C₈	—	76	2	no	—
138	C₂×C₈	—	76	2	no	—
139	C₂×C₈	—	76	2	no	—
140	C₄²	—	2	2	no	—
141	C₄²	—	2	2	no	—
142	C₄²	—	2	2	no	—
143	C₄²	—	4	1	no	—
144	C₄²	—	4	1	no	—
145	C₄²	—	4	1	no	—
146	C₄²	—	4	1	no	—
147	C₂³	C₁₉⋊#95	1	1	yes	characteristic
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	1	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	#10597262	1	2	yes	—
167	C₂×C₄	#10597282	1	2	yes	—
168	C₂×C₄	#10597294	1	2	yes	—
169	C₈	—	4	4	no	—
170	C₈	—	76	4	no	—
171	C₈	—	76	4	no	—
172	C₂²	C₁₉⋊#338	1	1	yes	characteristic
173	C₂²	#11926303	1	1	yes	characteristic
174	C₂²	#11926304	1	1	yes	characteristic
175	C₂²	#11926305	1	1	yes	characteristic
176	C₂²	#11926314	1	1	yes	characteristic
177	C₂²	#11926315	1	1	yes	characteristic
178	C₂²	#11926316	1	1	yes	characteristic
179	C₄	—	2	2	no	—
180	C₄	—	2	2	no	—
181	C₄	—	2	2	no	—
182	C₄	—	4	1	no	—
183	C₄	—	4	1	no	—
184	C₄	—	4	1	no	—
185	C₄	—	4	1	no	—
186	C₂	#14561506	1	1	yes	characteristic
187	C₂	#14561507	1	1	yes	characteristic
188	C₂	#14561508	1	1	yes	characteristic
189	C₂	#14561527	1	1	yes	characteristic
190	C₂	#14561528	1	1	yes	characteristic
191	C₂	#14561529	1	1	yes	characteristic
192	C₂	C₁₉⋊#1308	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563384

C₂

yes

maximal, characteristic

#14563384

C₂

yes

maximal, characteristic

C₁₉×#1745

C₂

yes

maximal, characteristic

—

—

—

—

C₄

yes

—

#11926299

C₄

yes

—

C₂×C₁₉×#97

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

C₄

yes

—

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×#97

—

#10597260

—

#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

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1745

—

#1745

—

#1745

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

—

C₄×C₁₉

—

C₂×#97

—

C₂×#97

—

C₂×#97

—

C₄³

C₂×D₁₉

yes

—

—

—

100

#336

—

101

#336

—

102

#336

Dic₁₉

yes

—

103

C₂×C₁₉

#1291

yes

characteristic

104

C₂×C₁₉

#1291

yes

characteristic

105

C₂×C₁₉

#1291

yes

characteristic

106

C₂×C₁₉

#1300

yes

characteristic

107

C₂×C₁₉

#1300

yes

characteristic

108

C₂×C₁₉

#1300

yes

characteristic

109

C₂×C₁₉

#1308

yes

characteristic

110

C₂²×C₈

—

111

C₂²×C₈

—

112

C₂²×C₈

—

113

C₂×C₄²

Dic₃₈

yes

characteristic

114

C₂×C₄²

C₄×D₁₉

yes

characteristic

115

C₂×C₄²

C₄×D₁₉

yes

characteristic

116

C₂×C₄²

D₇₆

yes

characteristic

117

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

118

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

119

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

120

#97

—

121

#97

—

122

#97

—

123

C₁₉

#7048

yes

characteristic, complemented, Sylow

124

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

125

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

126

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

127

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

128

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

129

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

130

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₄²

—

141

C₄²

—

142

C₄²

—

143

C₄²

—

144

C₄²

—

145

C₄²

—

146

C₄²

—

147

C₂³

C₁₉⋊#95

yes

characteristic

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

#10597262

yes

—

167

C₂×C₄

#10597282

yes

—

168

C₂×C₄

#10597294

yes

—

169

C₈

—

170

C₈

—

171

C₈

—

172

C₂²

C₁₉⋊#338

yes

characteristic

173

C₂²

#11926303

yes

characteristic

174

C₂²

#11926304

yes

characteristic

175

C₂²

#11926305

yes

characteristic

176

C₂²

#11926314

yes

characteristic

177

C₂²

#11926315

yes

characteristic

178

C₂²

#11926316

yes

characteristic

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

—

184

C₄

—

185

C₄

—

186

C₂

#14561506

yes

characteristic

187

C₂

#14561507

yes

characteristic

188

C₂

#14561508

yes

characteristic

189

C₂

#14561527

yes

characteristic

190

C₂

#14561528

yes

characteristic

191

C₂

#14561529

yes

characteristic

192

C₂

C₁₉⋊#1308

yes

characteristic

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1745	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1745	D₁₉
hypocenter	C₁₉	#7048
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

subgroup

G/H

center

C₂³

C₁₉⋊#95

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₄³

C₂×D₁₉

Fitting

C₁₉×#1745

C₂

socle, prime radical

C₂³×C₁₉

#95

cosocle

C₄³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

N	H ≅ G/N	type
123. C₁₉	#7048	semidirect

H ≅ G/N

type

123. C₁₉

#7048

semidirect

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

subgroup	index
#14563384	2
C₁₉×#1745	2
#7048	19

subgroup

index

#14563384

C₁₉×#1745

#7048

Subgroups — C₁₉⋊#7048 #18069148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19⋊#7048 #18069148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊#7048 #18069148