Group #18070813 — subgroups

Subgroups — #18070813

Order 4864.

468 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 127 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	2	yes	maximal
2	#14561461	C₂	1	4	yes	maximal
3	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597260	—	2	2	no	—
5	#11926299	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	—
7	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₉	C₄	1	2	yes	—
9	C₁₉×#391	C₂²	1	2	yes	—
10	C₁₉×#389	—	2	2	no	—
11	C₁₉×#384	C₄	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
13	C₄³×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
15	C₁₉×C₄⋊Q₈	—	2	4	no	—
16	C₄×Q₈×C₁₉	—	4	4	no	—
17	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₉	—	2	2	no	—
22	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	D₄	1	2	yes	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×C₁₉⋊C₈	—	2	4	no	—
28	C₁₉×#95	—	2	4	no	—
29	#10597260	—	2	8	no	—
30	C₂×Q₈×C₁₉	—	2	2	no	—
31	C₂×Q₈×C₁₉	—	4	2	no	—
32	C₂×Q₈×C₁₉	—	4	2	no	—
33	C₂×Q₈×C₁₉	M₁₆	1	4	yes	—
34	C₂²×C₄×C₁₉	—	2	2	no	—
35	C₂²×C₄×C₁₉	—	2	2	no	—
36	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
41	C₄⋊C₄×C₁₉	—	2	8	no	—
42	C₄⋊C₄×C₁₉	—	4	2	no	—
43	C₄⋊C₄×C₁₉	—	4	4	no	—
44	C₄⋊C₄×C₁₉	—	4	4	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	—	2	4	no	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	4	no	—
49	C₄²×C₁₉	—	4	1	no	—
50	C₄²×C₁₉	—	4	4	no	—
51	C₂×C₁₉⋊C₈	—	2	8	no	—
52	C₂×C₁₉⋊C₈	—	4	4	no	—
53	C₂×C₁₉⋊C₈	—	4	4	no	—
54	#7639	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	Q₈×C₁₉	—	4	4	no	—
57	Q₈×C₁₉	—	4	4	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	4	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	4	2	no	—
69	C₂×C₄×C₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	—	4	2	no	—
71	C₂×C₄×C₁₉	—	4	4	no	—
72	C₂×C₄×C₁₉	#100	1	2	yes	—
73	C₂×C₄×C₁₉	#104	1	4	yes	—
74	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
75	C₂×C₄×C₁₉	#137	1	4	yes	—
76	C₁₉⋊C₈	—	4	8	no	—
77	C₄×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
78	#1745	—	19	2	no	—
79	#1272	—	19	4	no	—
80	C₂²×C₁₉	#407	1	1	yes	characteristic
81	C₂²×C₁₉	#410	1	1	yes	characteristic
82	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
83	C₂²×C₁₉	#419	1	2	yes	—
84	C₂²×C₁₉	C₂×#104	1	2	yes	—
85	C₄×C₁₉	—	2	2	no	—
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	4	no	—
88	C₄×C₁₉	—	2	4	no	—
89	C₄×C₁₉	—	4	4	no	—
90	C₄×C₁₉	—	4	1	no	—
91	C₄×C₁₉	—	8	2	no	—
92	C₂×C₄⋊Q₈	Dic₁₉	1	1	yes	characteristic
93	C₂×C₄×Q₈	Dic₁₉	1	2	yes	—
94	C₂×#97	—	38	2	no	—
95	#391	C₂×D₁₉	1	2	yes	—
96	#389	—	2	2	no	—
97	#384	Dic₁₉	1	1	yes	characteristic
98	C₄×C₄⋊C₄	—	2	2	no	—
99	C₄³	C₂×D₁₉	1	1	yes	characteristic
100	#336	—	19	4	no	—
101	#336	—	38	2	no	—
102	C₂×C₁₉	#1466	1	1	yes	characteristic
103	C₂×C₁₉	#1491	1	2	yes	—
104	C₂×C₁₉	#1506	1	2	yes	—
105	C₂×C₁₉	#1525	1	1	yes	characteristic
106	C₂×C₁₉	#1558	1	1	yes	characteristic
107	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
108	C₂²×C₈	—	38	4	no	—
109	C₄⋊Q₈	—	2	4	no	—
110	C₄×Q₈	—	4	4	no	—
111	C₂×C₄⋊C₄	—	2	2	no	—
112	C₂×C₄⋊C₄	—	2	2	no	—
113	C₂×C₄⋊C₄	—	2	2	no	—
114	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
115	C₂×C₄²	—	2	2	no	—
116	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
117	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
118	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
119	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
120	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
121	#97	—	38	8	no	—
122	#95	—	2	4	no	—
123	C₁₉	#7639	1	1	yes	characteristic, complemented, Sylow
124	C₂×Q₈	—	2	2	no	—
125	C₂×Q₈	—	4	2	no	—
126	C₂×Q₈	—	4	2	no	—
127	C₂×Q₈	#64520	1	4	yes	—
128	C₂²×C₄	—	2	2	no	—
129	C₂²×C₄	—	2	2	no	—
130	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
131	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
132	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
133	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
134	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
135	C₂×C₈	—	38	8	no	—
136	C₂×C₈	—	76	4	no	—
137	C₂×C₈	—	76	4	no	—
138	C₄⋊C₄	—	2	8	no	—
139	C₄⋊C₄	—	4	2	no	—
140	C₄⋊C₄	—	4	4	no	—
141	C₄⋊C₄	—	4	4	no	—
142	C₄²	—	2	4	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	2	4	no	—
145	C₄²	—	2	2	no	—
146	C₄²	—	4	1	no	—
147	C₄²	—	4	4	no	—
148	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
149	Q₈	—	4	4	no	—
150	Q₈	—	4	4	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	4	2	no	—
163	C₂×C₄	—	4	4	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	#10597290	1	2	yes	—
166	C₂×C₄	#10597294	1	4	yes	—
167	C₂×C₄	C₂×#64520	1	2	yes	—
168	C₂×C₄	#10597388	1	4	yes	—
169	C₈	—	76	8	no	—
170	C₂²	#11926508	1	1	yes	characteristic
171	C₂²	#11926518	1	1	yes	characteristic
172	C₂²	C₂×#10597290	1	1	yes	characteristic
173	C₂²	#11926553	1	2	yes	—
174	C₂²	C₂×#10597294	1	2	yes	—
175	C₄	—	2	4	no	—
176	C₄	—	2	2	no	—
177	C₄	—	2	4	no	—
178	C₄	—	2	2	no	—
179	C₄	—	4	1	no	—
180	C₄	—	4	4	no	—
181	C₄	—	8	2	no	—
182	C₂	#14561976	1	1	yes	characteristic
183	C₂	#14562082	1	2	yes	—
184	C₂	#14562147	1	2	yes	—
185	C₂	#14562227	1	1	yes	characteristic
186	C₂	#14562361	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563384

C₂

yes

maximal

#14561461

C₂

yes

maximal

C₄×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×#10597260

—

#11926299

—

#11926299

C₂²

yes

—

C₂×C₁₉×C₄⋊Q₈

C₄

yes

characteristic

C₂×C₄×Q₈×C₁₉

C₄

yes

—

C₁₉×#391

C₂²

yes

—

C₁₉×#389

—

C₁₉×#384

C₄

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

#10597260

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7639

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×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

#100

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₁₉⋊C₈

—

C₄×C₄⋊Q₈

D₁₉

yes

characteristic

#1745

—

#1272

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×#104

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×C₄⋊Q₈

Dic₁₉

yes

characteristic

C₂×C₄×Q₈

Dic₁₉

yes

—

C₂×#97

—

#391

C₂×D₁₉

yes

—

#389

—

#384

Dic₁₉

yes

characteristic

C₄×C₄⋊C₄

—

C₄³

C₂×D₁₉

yes

characteristic

100

#336

—

101

#336

—

102

C₂×C₁₉

#1466

yes

characteristic

103

C₂×C₁₉

#1491

yes

—

104

C₂×C₁₉

#1506

yes

—

105

C₂×C₁₉

#1525

yes

characteristic

106

C₂×C₁₉

#1558

yes

characteristic

107

C₂²×Q₈

C₂×Dic₁₉

yes

—

108

C₂²×C₈

—

109

C₄⋊Q₈

—

110

C₄×Q₈

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

115

C₂×C₄²

—

116

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

117

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

118

C₂×C₄²

C₂²⋊D₁₉

yes

—

119

C₂×C₄²

C₂²⋊D₁₉

yes

—

120

C₂×C₄²

C₂²×D₁₉

yes

characteristic

121

#97

—

122

#95

—

123

C₁₉

#7639

yes

characteristic, complemented, Sylow

124

C₂×Q₈

—

125

C₂×Q₈

—

126

C₂×Q₈

—

127

C₂×Q₈

#64520

yes

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

131

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

132

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

133

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

134

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄²

—

143

C₄²

—

144

C₄²

—

145

C₄²

—

146

C₄²

—

147

C₄²

—

148

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

149

Q₈

—

150

Q₈

—

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

#10597290

yes

—

166

C₂×C₄

#10597294

yes

—

167

C₂×C₄

C₂×#64520

yes

—

168

C₂×C₄

#10597388

yes

—

169

C₈

—

170

C₂²

#11926508

yes

characteristic

171

C₂²

#11926518

yes

characteristic

172

C₂²

C₂×#10597290

yes

characteristic

173

C₂²

#11926553

yes

—

174

C₂²

C₂×#10597294

yes

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

182

C₂

#14561976

yes

characteristic

183

C₂

#14562082

yes

—

184

C₂

#14562147

yes

—

185

C₂

#14562227

yes

characteristic

186

C₂

#14562361

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#7639
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

hypercenter

C₄×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

#7639

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
123. C₁₉	#7639	semidirect

H ≅ G/N

type

123. C₁₉

#7639

semidirect

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

subgroup	index
#14563384	2
#14561461	2
C₄×C₁₉×C₄⋊Q₈	2
#7639	19

subgroup

index

#14563384

#14561461

C₄×C₁₉×C₄⋊Q₈

#7639

Subgroups — #18070813

Conjugacy classes of subgroups

Complements

Maximal subgroups