Group #18085644 — subgroups

Subgroups — #18085644

Order 4864.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14564463	C₂	1	1	yes	maximal, characteristic
2	#14562194	C₂	1	2	yes	maximal
3	#14561493	C₂	1	2	yes	maximal, complemented
4	#14561468	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2864	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927094	C₂²	1	1	yes	characteristic
7	#11926597	C₂²	1	2	yes	—
8	#11926568	C₂²	1	1	yes	characteristic
9	C₂×#10597262	—	2	2	no	—
10	#11926277	—	2	4	no	—
11	C₁₉×#389	—	2	2	no	—
12	C₁₉×#387	—	2	4	no	—
13	C₁₉×#382	C₂²	1	2	yes	—
14	C₄³×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×#64541	—	2	1	no	—
16	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
17	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₄²×C₁₉	—	2	2	no	—
19	C₂×C₄²×C₁₉	D₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	#10597376	—	2	2	no	—
22	C₂×#64520	—	2	1	no	—
23	#10597321	—	2	1	no	—
24	#10597320	Q₈	1	1	yes	characteristic
25	C₄×D₇₆	—	2	2	no	—
26	#10597315	Q₈	1	1	yes	characteristic
27	C₁₉×#95	—	2	4	no	—
28	C₁₉×#95	—	2	2	no	—
29	C₁₉×#95	D₄	1	4	yes	—
30	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
31	#10597262	—	4	4	no	—
32	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
33	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
34	C₄×C₁₉⋊C₈	—	2	2	no	—
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	—	2	4	no	—
37	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₂²⋊D₁₉	—	4	1	no	—
40	#64541	—	4	2	no	—
41	#64541	—	4	2	no	—
42	C₂×D₇₆	—	2	1	no	—
43	C₂×D₇₆	—	2	2	no	—
44	C₂×C₄×D₁₉	—	4	1	no	—
45	C₂×Dic₃₈	—	2	1	no	—
46	C₄⋊C₄×C₁₉	—	4	8	no	—
47	C₄⋊C₄×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₄²×C₁₉	—	2	2	no	—
50	C₄²×C₁₉	—	2	2	no	—
51	C₄²×C₁₉	—	4	4	no	—
52	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
53	C₄²×C₁₉	#41	1	1	yes	characteristic
54	C₄²×C₁₉	#41	1	2	yes	—
55	(C₂×D₁₉)⋊C₄	—	4	2	no	—
56	C₄⋊Dic₁₉	—	2	2	no	—
57	#64520	—	4	2	no	—
58	C₂×C₁₉⋊C₈	—	4	2	no	—
59	C₂×C₁₉⋊C₈	—	4	1	no	—
60	#10366	—	19	1	no	maximal, Sylow
61	C₂³×C₁₉	#120	1	1	yes	characteristic
62	C₂²×D₁₉	—	4	1	no	—
63	C₂×C₄×C₁₉	—	2	4	no	—
64	C₂×C₄×C₁₉	—	4	2	no	—
65	C₂×C₄×C₁₉	—	4	2	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	—	4	8	no	—
68	C₂×C₄×C₁₉	—	4	4	no	—
69	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
70	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#124	1	2	yes	—
72	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#135	1	2	yes	—
74	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
75	C₂²⋊D₁₉	—	8	2	no	—
76	C₂×Dic₁₉	—	4	1	no	—
77	D₇₆	—	4	2	no	—
78	D₇₆	—	8	2	no	—
79	C₄×D₁₉	—	8	1	no	—
80	C₄×D₁₉	—	8	1	no	—
81	Dic₃₈	—	4	2	no	—
82	C₁₉⋊C₈	—	8	2	no	—
83	C₁₉⋊C₈	—	8	1	no	—
84	#2864	D₁₉	1	1	yes	characteristic, complemented
85	#1962	—	19	1	no	—
86	#1517	—	19	2	no	—
87	#1286	—	19	2	no	—
88	#1276	—	19	1	no	—
89	C₂²×C₁₉	—	2	2	no	—
90	C₂²×C₁₉	#393	1	1	yes	characteristic
91	C₂²×C₁₉	#449	1	2	yes	—
92	C₂×D₁₉	—	8	1	no	—
93	C₂×D₁₉	—	8	2	no	—
94	C₄×C₁₉	—	2	2	no	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	4	4	no	—
97	C₄×C₁₉	—	8	4	no	—
98	C₄×C₁₉	#478	1	2	yes	—
99	C₄×C₁₉	#488	1	1	yes	characteristic
100	C₄×C₁₉	#490	1	1	yes	characteristic
101	Dic₁₉	—	8	1	no	—
102	#532	—	19	1	no	—
103	#431	—	19	2	no	—
104	#423	—	19	1	no	—
105	C₂×#104	—	38	2	no	—
106	#389	—	2	2	no	—
107	#387	—	2	4	no	—
108	#382	C₂×D₁₉	1	2	yes	—
109	C₄³	C₂×D₁₉	1	1	yes	characteristic
110	#327	—	38	4	no	—
111	C₂×C₁₉	—	2	2	no	—
112	C₂×C₁₉	#2025	1	1	yes	characteristic
113	C₂×C₁₉	#2031	1	2	yes	—
114	D₁₉	—	16	1	no	—
115	C₂×#41	—	38	1	no	—
116	C₂×M₁₆	—	38	1	no	—
117	C₄⋊Q₈	—	19	1	no	—
118	#127	—	19	1	no	—
119	#124	—	38	1	no	—
120	#121	—	38	2	no	—
121	C₄×D₄	—	38	2	no	—
122	C₂×C₄⋊C₄	—	2	4	no	—
123	C₂×C₄⋊C₄	—	2	2	no	—
124	C₂×C₄²	—	2	2	no	—
125	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
126	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
127	C₄⋊C₈	—	38	2	no	—
128	C₄⋊C₈	—	38	2	no	—
129	#104	—	76	4	no	—
130	C₂²⋊C₈	—	38	2	no	—
131	C₄×C₈	—	38	2	no	—
132	#95	—	2	4	no	—
133	#95	—	2	2	no	—
134	#95	C₂²⋊D₁₉	1	4	yes	—
135	C₁₉	#10366	1	1	yes	characteristic, complemented, Sylow
136	#41	—	76	2	no	—
137	#41	—	76	2	no	—
138	C₂×Q₈	—	38	1	no	—
139	C₂×D₄	—	38	1	no	—
140	C₂×D₄	—	38	2	no	—
141	C₂×D₄	—	76	1	no	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	2	4	no	—
144	C₂²×C₄	—	76	1	no	—
145	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
146	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
147	M₁₆	—	76	2	no	—
148	C₂×C₈	—	76	2	no	—
149	C₂×C₈	—	76	1	no	—
150	C₄⋊C₄	—	4	8	no	—
151	C₄⋊C₄	—	4	2	no	—
152	C₄⋊C₄	—	4	2	no	—
153	C₄⋊C₄	—	38	2	no	—
154	C₂²⋊C₄	—	76	2	no	—
155	C₄²	—	2	2	no	—
156	C₄²	—	2	2	no	—
157	C₄²	—	4	4	no	—
158	C₄²	Q₈×D₁₉	1	1	yes	characteristic
159	C₄²	#64545	1	1	yes	characteristic
160	C₄²	#64545	1	2	yes	—
161	C₂³	—	76	1	no	—
162	C₂³	#10597399	1	1	yes	characteristic
163	Q₈	—	76	2	no	—
164	D₄	—	76	2	no	—
165	D₄	—	152	2	no	—
166	D₄	—	152	2	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	4	2	no	—
169	C₂×C₄	—	4	2	no	—
170	C₂×C₄	—	4	2	no	—
171	C₂×C₄	—	4	8	no	—
172	C₂×C₄	—	4	4	no	—
173	C₂×C₄	—	76	1	no	—
174	C₂×C₄	—	152	1	no	—
175	C₂×C₄	—	152	1	no	—
176	C₂×C₄	#10597392	1	2	yes	—
177	C₂×C₄	#10597392	1	1	yes	characteristic
178	C₂×C₄	#10597393	1	2	yes	—
179	C₂×C₄	#10597393	1	1	yes	characteristic
180	C₂×C₄	#10597395	1	2	yes	—
181	C₂×C₄	#10597396	1	2	yes	—
182	C₈	—	152	2	no	—
183	C₈	—	152	1	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	152	1	no	—
186	C₂²	—	152	2	no	—
187	C₂²	#11926455	1	1	yes	characteristic
188	C₂²	#11926689	1	2	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	2	2	no	—
191	C₄	—	4	4	no	—
192	C₄	—	8	4	no	—
193	C₄	—	152	1	no	—
194	C₄	#11926841	1	2	yes	—
195	C₄	#11926901	1	1	yes	characteristic
196	C₄	#11926910	1	1	yes	characteristic
197	C₂	—	2	2	no	—
198	C₂	—	304	1	no	—
199	C₂	#14564778	1	1	yes	characteristic
200	C₂	#14564804	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564463

C₂

yes

maximal, characteristic

#14562194

C₂

yes

maximal

#14561493

C₂

yes

maximal, complemented

#14561468

C₂

yes

maximal, characteristic, complemented

C₁₉×#2864

C₂

yes

maximal, characteristic, complemented

#11927094

C₂²

yes

characteristic

#11926597

C₂²

yes

—

#11926568

C₂²

yes

characteristic

C₂×#10597262

—

#11926277

—

C₁₉×#389

—

C₁₉×#387

—

C₁₉×#382

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂×#64541

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

Q₈

yes

characteristic

C₄×D₇₆

—

#10597315

Q₈

yes

characteristic

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

D₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

#10597262

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2864

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂²×C₁₉

—

C₂²×C₁₉

#393

yes

characteristic

C₂²×C₁₉

#449

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#478

yes

—

C₄×C₁₉

#488

yes

characteristic

100

C₄×C₁₉

#490

yes

characteristic

101

Dic₁₉

—

102

#532

—

103

#431

—

104

#423

—

105

C₂×#104

—

106

#389

—

107

#387

—

108

#382

C₂×D₁₉

yes

—

109

C₄³

C₂×D₁₉

yes

characteristic

110

#327

—

111

C₂×C₁₉

—

112

C₂×C₁₉

#2025

yes

characteristic

113

C₂×C₁₉

#2031

yes

—

114

D₁₉

—

115

C₂×#41

—

116

C₂×M₁₆

—

117

C₄⋊Q₈

—

118

#127

—

119

#124

—

120

#121

—

121

C₄×D₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄²

—

125

C₂×C₄²

C₂²⋊D₁₉

yes

—

126

C₂×C₄²

C₂²×D₁₉

yes

characteristic

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

#104

—

130

C₂²⋊C₈

—

131

C₄×C₈

—

132

#95

—

133

#95

—

134

#95

C₂²⋊D₁₉

yes

—

135

C₁₉

#10366

yes

characteristic, complemented, Sylow

136

#41

—

137

#41

—

138

C₂×Q₈

—

139

C₂×D₄

—

140

C₂×D₄

—

141

C₂×D₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

146

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

147

M₁₆

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₂²⋊C₄

—

155

C₄²

—

156

C₄²

—

157

C₄²

—

158

C₄²

Q₈×D₁₉

yes

characteristic

159

C₄²

#64545

yes

characteristic

160

C₄²

#64545

yes

—

161

C₂³

—

162

C₂³

#10597399

yes

characteristic

163

Q₈

—

164

D₄

—

165

D₄

—

152

—

166

D₄

—

152

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

152

—

175

C₂×C₄

—

152

—

176

C₂×C₄

#10597392

yes

—

177

C₂×C₄

#10597392

yes

characteristic

178

C₂×C₄

#10597393

yes

—

179

C₂×C₄

#10597393

yes

characteristic

180

C₂×C₄

#10597395

yes

—

181

C₂×C₄

#10597396

yes

—

182

C₈

—

152

—

183

C₈

—

152

—

184

C₂²

—

185

C₂²

—

152

—

186

C₂²

—

152

—

187

C₂²

#11926455

yes

characteristic

188

C₂²

#11926689

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

152

—

194

C₄

#11926841

yes

—

195

C₄

#11926901

yes

characteristic

196

C₄

#11926910

yes

characteristic

197

C₂

—

198

C₂

—

304

—

199

C₂

#14564778

yes

characteristic

200

C₂

#14564804

yes

—

	subgroup	G/H
center	C₂²	#11926455
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2864	C₂
socle	C₂²×C₁₉	#393
prime radical	#11927094	C₂²
hypercenter	#2864	D₁₉
hypocenter	C₁₉	#10366
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2864

subgroup

G/H

center

C₂²

#11926455

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2864

C₂

C₂²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2864

N	H ≅ G/N	type
3. #14561493	C₂	semidirect
4. #14561468	C₂	semidirect
5. C₁₉×#2864	C₂	semidirect
84. #2864	D₁₉	semidirect
135. C₁₉	#10366	semidirect

H ≅ G/N

type

3. #14561493

C₂

semidirect

4. #14561468

C₂

semidirect

5. C₁₉×#2864

C₂

semidirect

84. #2864

D₁₉

semidirect

135. C₁₉

#10366

semidirect

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

subgroup	index
#14564463	2
#14562194	2
#14561493	2
#14561468	2
C₁₉×#2864	2
#10366	19

subgroup

index

C₁₉×#2864

Subgroups — #18085644

Conjugacy classes of subgroups

Complements

Maximal subgroups