Group #18086678 — subgroups

Subgroups — #18086678

Order 4864.

386 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 73 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	#14575016	C₂	1	1	yes	maximal, characteristic
2	#14563809	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562358	C₂	1	2	yes	maximal, complemented
4	#14562247	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1307	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	2	yes	—
7	#11926835	—	2	2	no	—
8	#11926797	—	2	2	no	—
9	#11926740	—	2	2	no	—
10	C₂×#10597279	—	2	2	no	—
11	#11926568	C₂²	1	1	yes	characteristic
12	C₂×#10597260	C₂²	1	1	yes	characteristic
13	#11926291	—	2	2	no	—
14	#11926287	—	2	2	no	—
15	#11926283	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₂×#64541	—	2	2	no	—
19	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	#10597376	—	2	2	no	—
22	#10597376	—	2	2	no	—
23	C₂×#64520	—	2	1	no	—
24	C₂²×C₁₉⋊C₈	—	2	1	no	—
25	C₂×D₁₅₂	—	2	2	no	—
26	#10597321	—	2	2	no	—
27	#10597320	D₄	1	2	yes	—
28	C₄×D₇₆	—	2	2	no	—
29	C₄×D₇₆	—	2	2	no	—
30	#10597315	D₄	1	2	yes	—
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₂²⋊C₈	—	2	2	no	—
34	C₁₉×#97	—	2	2	no	—
35	#10597279	—	4	4	no	—
36	#10597278	—	2	4	no	—
37	#10597274	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	#10597260	—	2	1	no	—
40	#10597260	D₄	1	2	yes	—
41	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	2	yes	—
43	C₂×C₂²⋊D₁₉	—	4	2	no	—
44	#64541	—	8	4	no	—
45	C₂×D₇₆	—	2	2	no	—
46	C₂×D₇₆	—	2	2	no	—
47	C₂×D₇₆	—	2	2	no	—
48	C₂×C₄×D₁₉	—	4	2	no	—
49	C₂×Dic₃₈	—	2	2	no	—
50	M₁₆×C₁₉	—	4	2	no	—
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₄²×C₁₉	C₂×D₄	1	2	yes	—
54	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₄²×C₁₉	#41	1	1	yes	characteristic
56	(C₂×D₁₉)⋊C₄	—	4	2	no	—
57	(C₂×D₁₉)⋊C₄	—	4	2	no	—
58	C₄⋊Dic₁₉	—	2	2	no	—
59	C₄⋊Dic₁₉	—	2	2	no	—
60	#64520	—	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	—	4	1	no	—
65	D₁₅₂	—	8	2	no	—
66	#10524	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	#124	1	1	yes	characteristic
68	C₂²×D₁₉	—	4	2	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#121	1	2	yes	—
74	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
75	C₂×C₄×C₁₉	#123	1	2	yes	—
76	C₂²⋊D₁₉	—	8	4	no	—
77	C₂×Dic₁₉	—	4	2	no	—
78	D₇₆	—	4	2	no	—
79	D₇₆	—	4	2	no	—
80	D₇₆	—	8	2	no	—
81	D₇₆	—	8	2	no	—
82	C₄×D₁₉	—	8	4	no	—
83	Dic₃₈	—	8	2	no	—
84	C₈×C₁₉	—	4	2	no	—
85	C₈×C₁₉	—	8	2	no	—
86	C₁₉⋊C₈	—	2	4	no	—
87	C₁₉⋊C₈	—	8	1	no	—
88	#3253	—	19	1	no	—
89	#1849	—	19	1	no	—
90	#1557	—	19	2	no	—
91	#1530	—	19	2	no	—
92	#1307	D₁₉	1	1	yes	characteristic, complemented
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	2	1	no	—
95	C₂²×C₁₉	#394	1	1	yes	characteristic
96	C₂×D₁₉	—	8	2	no	—
97	C₂×D₁₉	—	8	2	no	—
98	C₂×D₁₉	—	8	2	no	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	2	2	no	—
101	C₄×C₁₉	—	2	1	no	—
102	C₄×C₁₉	#453	1	1	yes	characteristic
103	C₄×C₁₉	#456	1	1	yes	characteristic
104	Dic₁₉	—	8	2	no	—
105	#532	—	19	2	no	—
106	#476	—	38	2	no	—
107	#469	—	38	2	no	—
108	#459	—	38	2	no	—
109	#432	C₂×D₁₉	1	2	yes	—
110	C₂×#108	—	38	2	no	—
111	#423	—	19	1	no	—
112	#423	C₂×D₁₉	1	1	yes	characteristic
113	C₂×#97	—	19	1	no	—
114	#332	—	38	2	no	—
115	#331	—	38	2	no	—
116	#329	—	38	4	no	—
117	C₂×C₁₉	—	4	1	no	—
118	C₂×C₁₉	#2039	1	1	yes	characteristic
119	C₂×C₁₉	#2048	1	2	yes	—
120	D₁₉	—	16	2	no	—
121	C₂×#41	—	38	2	no	—
122	C₂×D₈	—	38	2	no	—
123	C₂×M₁₆	—	38	1	no	—
124	C₂×M₁₆	D₇₆	1	2	yes	—
125	C₂²×C₈	—	38	1	no	—
126	C₄⋊Q₈	—	19	2	no	—
127	#127	—	19	2	no	—
128	#124	—	38	2	no	—
129	#121	—	38	2	no	—
130	#121	—	38	2	no	—
131	C₄×D₄	—	38	2	no	—
132	C₄×D₄	—	38	2	no	—
133	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
134	#108	—	76	4	no	—
135	#106	—	38	2	no	—
136	C₄⋊C₈	—	2	2	no	—
137	C₄⋊C₈	—	2	2	no	—
138	C₄⋊C₈	—	38	2	no	—
139	#102	—	38	4	no	—
140	C₂²⋊C₈	—	2	2	no	—
141	#97	—	2	2	no	—
142	#97	—	19	2	no	—
143	#97	—	38	1	no	—
144	C₁₉	#10524	1	1	yes	characteristic, complemented, Sylow
145	#41	—	152	4	no	—
146	C₂×Q₈	—	38	2	no	—
147	C₂×D₄	—	38	2	no	—
148	C₂×D₄	—	38	2	no	—
149	C₂×D₄	—	38	2	no	—
150	C₂×D₄	—	76	2	no	—
151	C₂²×C₄	—	76	2	no	—
152	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
153	C₂²×C₄	#64541	1	2	yes	—
154	D₈	—	152	2	no	—
155	M₁₆	—	4	2	no	—
156	M₁₆	—	76	2	no	—
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	4	2	no	—
159	C₂×C₈	—	38	2	no	—
160	C₂×C₈	—	38	2	no	—
161	C₂×C₈	—	38	2	no	—
162	C₂×C₈	—	76	1	no	—
163	C₄⋊C₄	—	38	2	no	—
164	C₄⋊C₄	—	38	2	no	—
165	C₂²⋊C₄	—	76	2	no	—
166	C₂²⋊C₄	—	76	2	no	—
167	C₄²	D₄×D₁₉	1	2	yes	—
168	C₄²	D₄×D₁₉	1	1	yes	characteristic
169	C₄²	#64545	1	1	yes	characteristic
170	C₂³	—	76	2	no	—
171	C₂³	#10597321	1	1	yes	characteristic
172	Q₈	—	152	2	no	—
173	D₄	—	76	2	no	—
174	D₄	—	76	2	no	—
175	D₄	—	152	2	no	—
176	D₄	—	152	2	no	—
177	D₄	—	152	4	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	76	2	no	—
182	C₂×C₄	—	152	4	no	—
183	C₂×C₄	#10597328	1	1	yes	characteristic
184	C₂×C₄	#10597330	1	2	yes	—
185	C₂×C₄	#10597340	1	2	yes	—
186	C₂×C₄	#10597341	1	1	yes	characteristic
187	C₈	—	4	2	no	—
188	C₈	—	8	2	no	—
189	C₈	—	38	4	no	—
190	C₈	—	152	1	no	—
191	C₂²	—	2	2	no	—
192	C₂²	—	2	1	no	—
193	C₂²	—	152	2	no	—
194	C₂²	—	152	2	no	—
195	C₂²	—	152	2	no	—
196	C₂²	#11926462	1	1	yes	characteristic
197	C₄	—	2	2	no	—
198	C₄	—	2	2	no	—
199	C₄	—	2	1	no	—
200	C₄	—	152	2	no	—
201	C₄	#11926714	1	1	yes	characteristic
202	C₄	#11926729	1	1	yes	characteristic
203	C₂	—	4	1	no	—
204	C₂	—	304	2	no	—
205	C₂	#14564860	1	1	yes	characteristic
206	C₂	#14564911	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14575016

C₂

yes

maximal, characteristic

#14563809

C₂

yes

maximal, characteristic, complemented

#14562358

C₂

yes

maximal, complemented

#14562247

C₂

yes

maximal, complemented

C₁₉×#1307

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

C₂×#10597260

C₂²

yes

—

—

—

C₁₉×#432

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₂×#64541

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂²×C₁₉⋊C₈

—

C₂×D₁₅₂

—

#10597321

—

#10597320

D₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

#10597279

—

#10597278

—

#10597274

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#394

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

#453

yes

characteristic

103

C₄×C₁₉

#456

yes

characteristic

104

Dic₁₉

—

105

#532

—

106

#476

—

107

#469

—

108

#459

—

109

#432

C₂×D₁₉

yes

—

110

C₂×#108

—

111

#423

—

112

#423

C₂×D₁₉

yes

characteristic

113

C₂×#97

—

114

#332

—

115

#331

—

116

#329

—

117

C₂×C₁₉

—

118

C₂×C₁₉

#2039

yes

characteristic

119

C₂×C₁₉

#2048

yes

—

120

D₁₉

—

121

C₂×#41

—

122

C₂×D₈

—

123

C₂×M₁₆

—

124

C₂×M₁₆

D₇₆

yes

—

125

C₂²×C₈

—

126

C₄⋊Q₈

—

127

#127

—

128

#124

—

129

#121

—

130

#121

—

131

C₄×D₄

—

132

C₄×D₄

—

133

C₂×C₄²

C₂²×D₁₉

yes

characteristic

134

#108

—

135

#106

—

136

C₄⋊C₈

—

137

C₄⋊C₈

—

138

C₄⋊C₈

—

139

#102

—

140

C₂²⋊C₈

—

141

#97

—

142

#97

—

143

#97

—

144

C₁₉

#10524

yes

characteristic, complemented, Sylow

145

#41

—

152

—

146

C₂×Q₈

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂²×C₄

—

152

C₂²×C₄

C₂×D₇₆

yes

characteristic

153

C₂²×C₄

#64541

yes

—

154

D₈

—

152

—

155

M₁₆

—

156

M₁₆

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₂²⋊C₄

—

166

C₂²⋊C₄

—

167

C₄²

D₄×D₁₉

yes

—

168

C₄²

D₄×D₁₉

yes

characteristic

169

C₄²

#64545

yes

characteristic

170

C₂³

—

171

C₂³

#10597321

yes

characteristic

172

Q₈

—

152

—

173

D₄

—

174

D₄

—

175

D₄

—

152

—

176

D₄

—

152

—

177

D₄

—

152

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

152

—

183

C₂×C₄

#10597328

yes

characteristic

184

C₂×C₄

#10597330

yes

—

185

C₂×C₄

#10597340

yes

—

186

C₂×C₄

#10597341

yes

characteristic

187

C₈

—

188

C₈

—

189

C₈

—

190

C₈

—

152

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

152

—

194

C₂²

—

152

—

195

C₂²

—

152

—

196

C₂²

#11926462

yes

characteristic

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

152

—

201

C₄

#11926714

yes

characteristic

202

C₄

#11926729

yes

characteristic

203

C₂

—

204

C₂

—

304

—

205

C₂

#14564860

yes

characteristic

206

C₂

#14564911

yes

—

	subgroup	G/H
center	C₂²	#11926462
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1307	C₂
socle	C₂²×C₁₉	#394
prime radical	#14575016	C₂
hypercenter	#1307	D₁₉
hypocenter	C₁₉	#10524
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1307

subgroup

G/H

center

C₂²

#11926462

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1307

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1307

N	H ≅ G/N	type
2. #14563809	C₂	semidirect
3. #14562358	C₂	semidirect
4. #14562247	C₂	semidirect
5. C₁₉×#1307	C₂	semidirect
92. #1307	D₁₉	semidirect
144. C₁₉	#10524	semidirect

H ≅ G/N

type

2. #14563809

C₂

semidirect

3. #14562358

C₂

semidirect

4. #14562247

C₂

semidirect

5. C₁₉×#1307

C₂

semidirect

92. #1307

D₁₉

semidirect

144. C₁₉

#10524

semidirect

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

subgroup	index
#14575016	2
#14563809	2
#14562358	2
#14562247	2
C₁₉×#1307	2
#10524	19

subgroup

index

C₁₉×#1307

Subgroups — #18086678

Conjugacy classes of subgroups

Complements

Maximal subgroups