Group #20246614 — subgroups

Subgroups — C₂×#15689050 #20246614

Order 6016.

820 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 237 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	C₂²×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×(C₂×D₄₇)⋊C₄	C₂	1	2	yes	maximal
3	C₂²×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	#15689050	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇⋊#95	C₂	1	2	yes	maximal, complemented
6	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁴×D₄₇	C₂²	1	1	yes	characteristic
8	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂³×Dic₄₇	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₇	—	2	4	no	—
11	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
12	C₂×(C₂×D₄₇)⋊C₄	—	2	8	no	—
13	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
14	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	8	yes	—
15	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
16	C₄₇⋊#95	C₂²	1	8	yes	complemented
17	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
18	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
19	#95×C₄₇	C₂²	1	4	yes	complemented
20	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
21	C₂³×D₄₇	—	2	2	no	—
22	C₂³×D₄₇	—	2	2	no	—
23	C₂³×D₄₇	—	2	4	no	—
24	C₂³×D₄₇	—	2	4	no	—
25	C₂³×D₄₇	D₄	1	4	yes	—
26	C₂³×D₄₇	C₂³	1	2	yes	—
27	C₂²×C₄×C₄₇	—	2	4	no	—
28	C₂²×C₄×C₄₇	—	2	4	no	—
29	C₂²×C₄×C₄₇	—	2	4	no	—
30	C₂²×C₄×C₄₇	—	2	4	no	—
31	C₂²×C₄×C₄₇	D₄	1	4	yes	—
32	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
33	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
34	C₂²×Dic₄₇	—	2	4	no	—
35	C₂²×Dic₄₇	—	2	2	no	—
36	C₂²×Dic₄₇	—	2	4	no	—
37	C₂²×Dic₄₇	—	2	4	no	—
38	C₂²×Dic₄₇	—	2	4	no	—
39	C₂²×Dic₄₇	C₂³	1	2	yes	—
40	C₂²×Dic₄₇	C₂³	1	4	yes	—
41	(C₂×D₄₇)⋊C₄	—	2	16	no	—
42	(C₂×D₄₇)⋊C₄	—	2	8	no	—
43	C₄⋊Dic₄₇	—	2	8	no	—
44	C₂³×C₄₇	C₂×D₄	1	2	yes	—
45	C₂³×C₄₇	C₂×D₄	1	2	yes	—
46	C₂³×C₄₇	#41	1	4	yes	—
47	C₂³×C₄₇	#41	1	4	yes	—
48	C₂³×C₄₇	#41	1	2	yes	—
49	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
50	C₂²×D₄₇	—	2	8	no	—
51	C₂²×D₄₇	—	2	16	no	—
52	C₂²×D₄₇	—	2	2	no	—
53	C₂²×D₄₇	—	2	4	no	—
54	C₂²×D₄₇	—	2	4	no	—
55	C₂²×D₄₇	—	2	2	no	—
56	C₂²×D₄₇	—	4	4	no	—
57	C₂²×D₄₇	—	4	4	no	—
58	C₂²×D₄₇	—	4	8	no	—
59	C₂²×D₄₇	C₂×D₄	1	4	yes	—
60	C₂×C₄×C₄₇	—	2	8	no	—
61	C₂×C₄×C₄₇	—	2	4	no	—
62	C₂×C₄×C₄₇	—	2	4	no	—
63	C₂×C₄×C₄₇	—	2	4	no	—
64	C₂×C₄×C₄₇	—	2	4	no	—
65	C₂×C₄×C₄₇	—	4	8	no	—
66	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
67	C₂×Dic₄₇	—	2	4	no	—
68	C₂×Dic₄₇	—	2	4	no	—
69	C₂×Dic₄₇	—	2	2	no	—
70	C₂×Dic₄₇	—	2	4	no	—
71	C₂×Dic₄₇	—	2	4	no	—
72	C₂×Dic₄₇	—	4	8	no	—
73	C₂×Dic₄₇	—	4	4	no	—
74	C₂²×C₄₇	#121	1	4	yes	—
75	C₂²×C₄₇	#123	1	8	yes	—
76	C₂²×C₄₇	#123	1	4	yes	—
77	C₂²×C₄₇	#124	1	4	yes	—
78	C₂²×C₄₇	#126	1	8	yes	—
79	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
80	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
81	C₂²×C₄₇	C₂×#41	1	2	yes	—
82	C₂²×C₄₇	C₂×#41	1	2	yes	—
83	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
84	C₂×D₄₇	—	2	4	no	—
85	C₂×D₄₇	—	2	8	no	—
86	C₂×D₄₇	—	4	2	no	—
87	C₂×D₄₇	—	4	2	no	—
88	C₂×D₄₇	—	4	4	no	—
89	C₂×D₄₇	—	4	16	no	—
90	C₄×C₄₇	—	2	4	no	—
91	C₄×C₄₇	—	4	4	no	—
92	Dic₄₇	—	4	4	no	—
93	Dic₄₇	—	4	2	no	—
94	C₂×#397	—	47	1	no	maximal, Sylow
95	C₂×C₄₇	#397	1	8	yes	complemented
96	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
97	C₂×C₄₇	C₂×#123	1	2	yes	—
98	C₂×C₄₇	C₂×#123	1	1	yes	characteristic
99	C₂×C₄₇	C₂×#124	1	1	yes	characteristic
100	C₂×C₄₇	C₂×#126	1	2	yes	—
101	D₄₇	—	4	4	no	—
102	C₂²×C₄⋊C₄	—	47	1	no	—
103	C₂²×C₂²⋊C₄	—	47	2	no	—
104	C₂²×C₂²⋊C₄	—	47	1	no	—
105	#397	—	47	8	no	—
106	C₂×#95	—	47	2	no	—
107	C₂×#95	D₄₇	1	1	yes	characteristic, complemented
108	C₄₇	C₂×#397	1	1	yes	characteristic, complemented, Sylow
109	C₂⁵	—	47	1	no	—
110	C₂³×C₄	—	47	2	no	—
111	C₂³×C₄	—	47	1	no	—
112	C₂³×C₄	C₂×D₄₇	1	2	yes	—
113	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
114	C₂×C₄⋊C₄	—	47	4	no	—
115	C₂×C₄⋊C₄	—	94	4	no	—
116	C₂×C₂²⋊C₄	—	47	8	no	—
117	C₂×C₂²⋊C₄	—	47	4	no	—
118	C₂×C₂²⋊C₄	—	94	8	no	—
119	C₂×C₂²⋊C₄	—	94	4	no	—
120	#95	—	47	8	no	—
121	#95	C₂×D₄₇	1	4	yes	complemented
122	C₂⁴	—	47	4	no	—
123	C₂⁴	—	47	2	no	—
124	C₂⁴	—	94	2	no	—
125	C₂⁴	—	94	4	no	—
126	C₂⁴	—	94	4	no	—
127	C₂⁴	—	94	2	no	—
128	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
129	C₂²×C₄	—	2	4	no	—
130	C₂²×C₄	—	2	4	no	—
131	C₂²×C₄	—	2	4	no	—
132	C₂²×C₄	—	2	4	no	—
133	C₂²×C₄	—	47	2	no	—
134	C₂²×C₄	—	47	4	no	—
135	C₂²×C₄	—	94	2	no	—
136	C₂²×C₄	—	94	4	no	—
137	C₂²×C₄	—	94	4	no	—
138	C₂²×C₄	—	94	4	no	—
139	C₂²×C₄	—	94	4	no	—
140	C₂²×C₄	D₁₈₈	1	4	yes	—
141	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
142	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
143	C₄⋊C₄	—	94	8	no	—
144	C₂²⋊C₄	—	94	16	no	—
145	C₂²⋊C₄	—	94	8	no	—
146	C₂³	—	47	4	no	—
147	C₂³	—	94	8	no	—
148	C₂³	—	94	16	no	—
149	C₂³	—	94	2	no	—
150	C₂³	—	94	4	no	—
151	C₂³	—	94	4	no	—
152	C₂³	—	94	2	no	—
153	C₂³	—	188	4	no	—
154	C₂³	—	188	4	no	—
155	C₂³	—	188	8	no	—
156	C₂³	C₂×D₁₈₈	1	2	yes	—
157	C₂³	#10625350	1	4	yes	—
158	C₂³	D₄×D₄₇	1	2	yes	—
159	C₂³	#10625352	1	4	yes	—
160	C₂³	#10625354	1	2	yes	—
161	C₂³	C₂³×D₄₇	1	1	yes	characteristic
162	C₂×C₄	—	2	8	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	2	4	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	4	8	no	—
168	C₂×C₄	—	94	4	no	—
169	C₂×C₄	—	94	2	no	—
170	C₂×C₄	—	94	4	no	—
171	C₂×C₄	—	94	4	no	—
172	C₂×C₄	—	94	4	no	—
173	C₂×C₄	—	188	8	no	—
174	C₂×C₄	—	188	4	no	—
175	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
176	C₂²	—	94	4	no	—
177	C₂²	—	94	8	no	—
178	C₂²	—	188	16	no	—
179	C₂²	—	188	2	no	—
180	C₂²	—	188	2	no	—
181	C₂²	—	188	4	no	—
182	C₂²	#13093999	1	4	yes	—
183	C₂²	#13094006	1	8	yes	—
184	C₂²	#13094008	1	4	yes	—
185	C₂²	#13094012	1	4	yes	—
186	C₂²	#13094019	1	8	yes	—
187	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
188	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
189	C₂²	C₂×#10625352	1	2	yes	—
190	C₂²	C₂×#10625350	1	2	yes	—
191	C₂²	C₂×#10625354	1	1	yes	characteristic
192	C₄	—	2	4	no	—
193	C₄	—	4	4	no	—
194	C₄	—	188	4	no	—
195	C₄	—	188	2	no	—
196	C₂	—	188	4	no	—
197	C₂	#15689050	1	8	yes	direct product factor
198	C₂	C₂×#13093999	1	1	yes	characteristic
199	C₂	C₂×#13094006	1	2	yes	—
200	C₂	C₂×#13094008	1	1	yes	characteristic
201	C₂	C₂×#13094012	1	1	yes	characteristic
202	C₂	C₂×#13094019	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×(C₂×D₄₇)⋊C₄

C₂

yes

maximal

C₂²×(C₂×D₄₇)⋊C₄

C₂

yes

maximal, characteristic

#15689050

C₂

yes

maximal, direct product factor

C₂×C₄₇⋊#95

C₂

yes

maximal, complemented

C₂×#95×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

complemented

C₂×(C₂×D₄₇)⋊C₄

—

C₂×(C₂×D₄₇)⋊C₄

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

complemented

C₂³×C₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

complemented

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂³×D₄₇

—

C₂³×D₄₇

—

C₂³×D₄₇

—

C₂³×D₄₇

—

C₂³×D₄₇

D₄

yes

—

C₂³×D₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#124

yes

—

C₂²×C₄₇

#126

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

100

C₂×C₄₇

C₂×#126

yes

—

101

D₄₇

—

102

C₂²×C₄⋊C₄

—

103

C₂²×C₂²⋊C₄

—

104

C₂²×C₂²⋊C₄

—

105

#397

—

106

C₂×#95

—

107

C₂×#95

D₄₇

yes

characteristic, complemented

108

C₄₇

C₂×#397

yes

characteristic, complemented, Sylow

109

C₂⁵

—

110

C₂³×C₄

—

111

C₂³×C₄

—

112

C₂³×C₄

C₂×D₄₇

yes

—

113

C₂³×C₄

C₂×D₄₇

yes

characteristic

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₂²⋊C₄

—

117

C₂×C₂²⋊C₄

—

118

C₂×C₂²⋊C₄

—

119

C₂×C₂²⋊C₄

—

120

#95

—

121

#95

C₂×D₄₇

yes

complemented

122

C₂⁴

—

123

C₂⁴

—

124

C₂⁴

—

125

C₂⁴

—

126

C₂⁴

—

127

C₂⁴

—

128

C₂⁴

C₂²×D₄₇

yes

characteristic

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

D₁₈₈

yes

—

141

C₂²×C₄

C₂²×D₄₇

yes

—

142

C₂²×C₄

C₂²×D₄₇

yes

—

143

C₄⋊C₄

—

144

C₂²⋊C₄

—

145

C₂²⋊C₄

—

146

C₂³

—

147

C₂³

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

—

153

C₂³

—

188

—

154

C₂³

—

188

—

155

C₂³

—

188

—

156

C₂³

C₂×D₁₈₈

yes

—

157

C₂³

#10625350

yes

—

158

C₂³

D₄×D₄₇

yes

—

159

C₂³

#10625352

yes

—

160

C₂³

#10625354

yes

—

161

C₂³

C₂³×D₄₇

yes

characteristic

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

188

—

174

C₂×C₄

—

188

—

175

C₂×C₄

C₂×D₁₈₈

yes

—

176

C₂²

—

177

C₂²

—

178

C₂²

—

188

—

179

C₂²

—

188

—

180

C₂²

—

188

—

181

C₂²

—

188

—

182

C₂²

#13093999

yes

—

183

C₂²

#13094006

yes

—

184

C₂²

#13094008

yes

—

185

C₂²

#13094012

yes

—

186

C₂²

#13094019

yes

—

187

C₂²

C₂×D₄×D₄₇

yes

characteristic

188

C₂²

C₂²×D₁₈₈

yes

characteristic

189

C₂²

C₂×#10625352

yes

—

190

C₂²

C₂×#10625350

yes

—

191

C₂²

C₂×#10625354

yes

characteristic

192

C₄

—

193

C₄

—

194

C₄

—

188

—

195

C₄

—

188

—

196

C₂

—

188

—

197

C₂

#15689050

yes

direct product factor

198

C₂

C₂×#13093999

yes

characteristic

199

C₂

C₂×#13094006

yes

—

200

C₂

C₂×#13094008

yes

characteristic

201

C₂

C₂×#13094012

yes

characteristic

202

C₂

C₂×#13094019

yes

—

	subgroup	G/H
center	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂×#95×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	C₂×#397
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

subgroup

G/H

center

C₂⁴

C₂²×D₄₇

commutator

C₂³×C₄₇

C₂⁴

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂×#95×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂×#95

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂×#95

N	H ≅ G/N	type
1. C₂²×C₄⋊Dic₄₇	C₂	semidirect
4. #15689050	C₂	direct (N × H)
5. C₂×C₄₇⋊#95	C₂	semidirect
6. C₂×#95×C₄₇	C₂	semidirect
11. C₂×C₄⋊Dic₄₇	C₂²	semidirect
16. C₄₇⋊#95	C₂²	semidirect
19. #95×C₄₇	C₂²	semidirect
95. C₂×C₄₇	#397	semidirect
107. C₂×#95	D₄₇	semidirect
108. C₄₇	C₂×#397	semidirect
121. #95	C₂×D₄₇	semidirect
197. C₂	#15689050	direct (N × H)

H ≅ G/N

type

1. C₂²×C₄⋊Dic₄₇

C₂

semidirect

4. #15689050

C₂

direct (N × H)

5. C₂×C₄₇⋊#95

C₂

semidirect

6. C₂×#95×C₄₇

C₂

semidirect

11. C₂×C₄⋊Dic₄₇

C₂²

semidirect

16. C₄₇⋊#95

C₂²

semidirect

19. #95×C₄₇

C₂²

semidirect

95. C₂×C₄₇

#397

semidirect

107. C₂×#95

D₄₇

semidirect

108. C₄₇

C₂×#397

semidirect

121. #95

C₂×D₄₇

semidirect

197. C₂

#15689050

direct (N × H)

Subgroups — C₂×#15689050 #20246614

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689050 #20246614

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689050 #20246614