Group #14571982 — subgroups

Subgroups — #14571982

Order 2432.

644 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 209 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	C₂×#10597392	C₂	1	2	yes	maximal
2	C₂×C₄²×D₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926451	C₂	1	2	yes	maximal, complemented
4	#11926440	C₂	1	4	yes	maximal, complemented
5	#11926414	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926401	C₂	1	4	yes	maximal
7	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
11	C₁₉×C₄⋊Q₈	—	2	4	no	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	#10597392	—	2	8	no	—
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
17	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
19	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
20	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
21	C₄²×D₁₉	—	2	4	no	—
22	C₁₉⋊#95	C₂²	1	8	yes	—
23	C₂³×D₁₉	C₂³	1	1	yes	characteristic
24	C₂×Q₈×C₁₉	—	2	4	no	—
25	C₂×Q₈×C₁₉	—	2	4	no	—
26	C₂×Q₈×C₁₉	—	2	4	no	—
27	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
30	C₂²×Dic₁₉	C₂³	1	4	yes	—
31	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	C₂³	1	2	yes	—
33	C₂×C₄×D₁₉	—	2	2	no	—
34	C₂×C₄×D₁₉	—	2	4	no	—
35	C₂×C₄×D₁₉	—	2	2	no	—
36	C₂×C₄×D₁₉	—	2	4	no	—
37	C₂×C₄×D₁₉	D₄	1	4	yes	—
38	C₂×C₄×D₁₉	Q₈	1	8	yes	complemented
39	C₄⋊C₄×C₁₉	—	2	8	no	—
40	C₄²×C₁₉	D₄	1	4	yes	—
41	(C₂×D₁₉)⋊C₄	—	2	8	no	—
42	C₄⋊Dic₁₉	—	2	4	no	—
43	C₄⋊Dic₁₉	—	2	8	no	—
44	Dic₁₉⋊C₄	—	2	8	no	—
45	C₄×Dic₁₉	—	2	2	no	—
46	C₄×Dic₁₉	—	2	4	no	—
47	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
48	C₂²×D₁₉	—	2	1	no	—
49	C₂²×D₁₉	—	2	1	no	—
50	C₂²×D₁₉	—	2	2	no	—
51	C₂²×D₁₉	C₂×D₄	1	2	yes	—
52	C₂²×D₁₉	C₂×Q₈	1	4	yes	—
53	Q₈×C₁₉	—	4	8	no	—
54	C₂×C₄×C₁₉	—	2	4	no	—
55	C₂×C₄×C₁₉	—	2	4	no	—
56	C₂×C₄×C₁₉	—	2	4	no	—
57	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
59	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
60	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
61	C₂×C₄×C₁₉	#41	1	2	yes	—
62	C₂×C₄×C₁₉	#41	1	4	yes	—
63	C₂×Dic₁₉	—	2	1	no	—
64	C₂×Dic₁₉	—	2	2	no	—
65	C₂×Dic₁₉	—	2	1	no	—
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	2	4	no	—
68	C₂×Dic₁₉	—	2	8	no	—
69	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
70	C₂×Dic₁₉	C₂×Q₈	1	4	yes	—
71	C₄×D₁₉	—	2	8	no	—
72	C₄×D₁₉	—	2	16	no	—
73	#2857	—	19	1	no	maximal, Sylow
74	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
75	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
76	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
77	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
78	C₂²×C₁₉	C₂×#41	1	2	yes	—
79	C₂×D₁₉	—	2	2	no	—
80	C₂×D₁₉	—	2	4	no	—
81	C₂×D₁₉	—	2	2	no	—
82	C₂×D₁₉	—	2	4	no	—
83	C₂×D₁₉	C₄⋊Q₈	1	4	yes	complemented
84	C₄×C₁₉	—	4	4	no	—
85	C₄×C₁₉	#121	1	4	yes	—
86	C₄×C₁₉	C₂²⋊Q₈	1	8	yes	complemented
87	Dic₁₉	—	2	2	no	—
88	Dic₁₉	—	2	4	no	—
89	Dic₁₉	—	4	4	no	—
90	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic, complemented
91	C₂×C₂²⋊Q₈	—	19	2	no	—
92	C₂²×C₄²	—	19	1	no	—
93	#391	—	19	2	no	—
94	#389	—	19	4	no	—
95	#384	—	19	1	no	—
96	#380	—	19	4	no	—
97	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
98	C₂×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
99	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
100	C₂×C₁₉	#532	1	1	yes	characteristic
101	C₂×C₁₉	#533	1	2	yes	—
102	D₁₉	—	2	4	no	—
103	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
104	C₂³×C₄	—	19	1	no	—
105	C₂³×C₄	—	19	2	no	—
106	C₄⋊Q₈	—	2	4	no	—
107	C₂²⋊Q₈	—	38	8	no	—
108	C₂×C₄⋊C₄	—	19	2	no	—
109	C₂×C₄⋊C₄	—	19	4	no	—
110	C₂×C₄⋊C₄	—	19	4	no	—
111	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
112	C₂×C₂²⋊C₄	—	19	4	no	—
113	C₂×C₄²	—	19	2	no	—
114	C₂×C₄²	—	19	1	no	—
115	C₂×C₄²	—	38	4	no	—
116	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
117	#95	—	19	8	no	—
118	C₁₉	#2857	1	1	yes	characteristic, complemented, Sylow
119	C₂⁴	—	19	1	no	—
120	C₂×Q₈	—	2	4	no	—
121	C₂×Q₈	—	2	4	no	—
122	C₂×Q₈	—	2	4	no	—
123	C₂²×C₄	—	19	2	no	—
124	C₂²×C₄	—	19	1	no	—
125	C₂²×C₄	—	19	4	no	—
126	C₂²×C₄	—	19	8	no	—
127	C₂²×C₄	—	19	4	no	—
128	C₂²×C₄	—	38	2	no	—
129	C₂²×C₄	—	38	4	no	—
130	C₂²×C₄	—	38	2	no	—
131	C₂²×C₄	—	38	4	no	—
132	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
133	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
134	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
135	C₄⋊C₄	—	2	8	no	—
136	C₄⋊C₄	—	38	8	no	—
137	C₄⋊C₄	—	38	4	no	—
138	C₄⋊C₄	—	38	8	no	—
139	C₂²⋊C₄	—	38	8	no	—
140	C₄²	—	38	2	no	—
141	C₄²	—	38	4	no	—
142	C₄²	C₂²⋊D₁₉	1	4	yes	—
143	C₂³	—	19	2	no	—
144	C₂³	—	19	4	no	—
145	C₂³	—	38	1	no	—
146	C₂³	—	38	2	no	—
147	C₂³	—	38	1	no	—
148	C₂³	C₂³×D₁₉	1	1	yes	characteristic
149	Q₈	—	4	8	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	4	no	—
153	C₂×C₄	—	19	2	no	—
154	C₂×C₄	—	19	4	no	—
155	C₂×C₄	—	38	1	no	—
156	C₂×C₄	—	38	2	no	—
157	C₂×C₄	—	38	1	no	—
158	C₂×C₄	—	38	2	no	—
159	C₂×C₄	—	38	8	no	—
160	C₂×C₄	—	38	16	no	—
161	C₂×C₄	—	38	4	no	—
162	C₂×C₄	—	38	8	no	—
163	C₂×C₄	D₄×D₁₉	1	2	yes	—
164	C₂×C₄	#64543	1	2	yes	—
165	C₂×C₄	Q₈×D₁₉	1	4	yes	—
166	C₂×C₄	#64545	1	4	yes	—
167	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
168	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
169	C₂²	—	19	4	no	—
170	C₂²	—	38	2	no	—
171	C₂²	—	38	4	no	—
172	C₂²	—	38	2	no	—
173	C₂²	—	38	4	no	—
174	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
175	C₂²	C₂×#64543	1	1	yes	characteristic
176	C₂²	C₂×Q₈×D₁₉	1	2	yes	—
177	C₂²	C₂×#64545	1	2	yes	—
178	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
179	C₄	—	4	4	no	—
180	C₄	—	38	2	no	—
181	C₄	—	38	4	no	—
182	C₄	—	76	4	no	—
183	C₄	#10597384	1	4	yes	—
184	C₄	#10597392	1	8	yes	complemented
185	C₂	—	38	4	no	—
186	C₂	C₂×#10597384	1	1	yes	characteristic
187	C₂	C₂×#10597392	1	2	yes	—
188	C₂	C₄⋊Q₈×D₁₉	1	1	yes	characteristic
189	C₂	#11927095	1	1	yes	characteristic
190	C₂	#11927099	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597392

C₂

yes

maximal

C₂×C₄²×D₁₉

C₂

yes

maximal, characteristic

#11926451

C₂

yes

maximal, complemented

#11926440

C₂

yes

maximal, complemented

#11926414

C₂

yes

maximal, characteristic, complemented

#11926401

C₂

yes

maximal

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×C₄×D₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597392

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₄²×D₁₉

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

—

C₂×C₄×D₁₉

Q₈

yes

complemented

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×D₄

yes

—

C₂²×D₁₉

C₂×Q₈

yes

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×Q₈

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

#2857

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

C₄⋊Q₈

yes

complemented

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

complemented

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

characteristic, complemented

C₂×C₂²⋊Q₈

—

C₂²×C₄²

—

—

—

—

—

C₂×C₁₉

C₂×#121

yes

characteristic

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

100

C₂×C₁₉

#532

yes

characteristic

101

C₂×C₁₉

#533

yes

—

102

D₁₉

—

103

C₂²×Q₈

C₂×D₁₉

yes

—

104

C₂³×C₄

—

105

C₂³×C₄

—

106

C₄⋊Q₈

—

107

C₂²⋊Q₈

—

108

C₂×C₄⋊C₄

—

109

C₂×C₄⋊C₄

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

112

C₂×C₂²⋊C₄

—

113

C₂×C₄²

—

114

C₂×C₄²

—

115

C₂×C₄²

—

116

C₂×C₄²

C₂×D₁₉

yes

characteristic

117

#95

—

118

C₁₉

#2857

yes

characteristic, complemented, Sylow

119

C₂⁴

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×Q₈

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

C₂²×D₁₉

yes

—

133

C₂²×C₄

C₂²×D₁₉

yes

characteristic

134

C₂²×C₄

C₂²×D₁₉

yes

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₂²⋊C₄

—

140

C₄²

—

141

C₄²

—

142

C₄²

C₂²⋊D₁₉

yes

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

—

148

C₂³

C₂³×D₁₉

yes

characteristic

149

Q₈

—

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

D₄×D₁₉

yes

—

164

C₂×C₄

#64543

yes

—

165

C₂×C₄

Q₈×D₁₉

yes

—

166

C₂×C₄

#64545

yes

—

167

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

168

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

C₂×D₄×D₁₉

yes

characteristic

175

C₂²

C₂×#64543

yes

characteristic

176

C₂²

C₂×Q₈×D₁₉

yes

—

177

C₂²

C₂×#64545

yes

—

178

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

#10597384

yes

—

184

C₄

#10597392

yes

complemented

185

C₂

—

186

C₂

C₂×#10597384

yes

characteristic

187

C₂

C₂×#10597392

yes

—

188

C₂

C₄⋊Q₈×D₁₉

yes

characteristic

189

C₂

#11927095

yes

characteristic

190

C₂

#11927099

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2857
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

prime radical

C₂³×D₁₉

C₂³

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
3. #11926451	C₂	semidirect
4. #11926440	C₂	semidirect
5. #11926414	C₂	semidirect
7. C₂×C₁₉×C₄⋊Q₈	C₂	semidirect
38. C₂×C₄×D₁₉	Q₈	semidirect
83. C₂×D₁₉	C₄⋊Q₈	semidirect
86. C₄×C₁₉	C₂²⋊Q₈	semidirect
90. C₂×C₄⋊Q₈	D₁₉	semidirect
118. C₁₉	#2857	semidirect
184. C₄	#10597392	semidirect

H ≅ G/N

type

3. #11926451

C₂

semidirect

4. #11926440

C₂

semidirect

5. #11926414

C₂

semidirect

7. C₂×C₁₉×C₄⋊Q₈

C₂

semidirect

38. C₂×C₄×D₁₉

Q₈

semidirect

83. C₂×D₁₉

C₄⋊Q₈

semidirect

86. C₄×C₁₉

C₂²⋊Q₈

semidirect

90. C₂×C₄⋊Q₈

D₁₉

semidirect

118. C₁₉

#2857

semidirect

184. C₄

#10597392

semidirect

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

subgroup	index
C₂×#10597392	2
C₂×C₄²×D₁₉	2
#11926451	2
#11926440	2
#11926414	2
#11926401	2
C₂×C₁₉×C₄⋊Q₈	2
#2857	19

subgroup

index

C₂×C₄²×D₁₉

C₂×C₁₉×C₄⋊Q₈

Subgroups — #14571982

Conjugacy classes of subgroups

Complements

Maximal subgroups