Group #20245785 — subgroups

Subgroups — #20245785

Order 6016.

568 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 197 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×C₄²×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#15688991	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688987	C₂	1	2	yes	maximal, complemented
4	#15688985	C₂	1	2	yes	maximal
5	#15688982	C₂	1	2	yes	maximal
6	#15688974	C₂	1	2	yes	maximal, complemented
7	#15688970	C₂	1	2	yes	maximal
8	#15688968	C₂	1	2	yes	maximal, complemented
9	C₄₇×#383	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
14	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
15	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
16	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
19	C₄²×D₄₇	C₄	1	8	yes	complemented
20	C₄₇⋊#95	C₂²	1	2	yes	—
21	C₄₇⋊#95	C₂²	1	4	yes	—
22	C₄₇⋊#95	C₂²	1	2	yes	—
23	C₄₇⋊#95	C₂²	1	2	yes	—
24	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	#95×C₄₇	C₂²	1	2	yes	—
26	#95×C₄₇	C₂²	1	2	yes	—
27	#95×C₄₇	C₂²	1	2	yes	—
28	C₂³×D₄₇	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
30	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
33	C₂²×Dic₄₇	C₂³	1	4	yes	—
34	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
35	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
36	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
37	C₂×C₄×D₄₇	—	2	4	no	—
38	C₂×C₄×D₄₇	—	2	4	no	—
39	C₂×C₄×D₄₇	—	2	4	no	—
40	C₂×C₄×D₄₇	C₂×C₄	1	4	yes	—
41	C₂×C₄×D₄₇	C₂×C₄	1	4	yes	—
42	C₂×C₄×D₄₇	C₂×C₄	1	4	yes	—
43	C₄²×C₄₇	C₂×C₄	1	4	yes	—
44	(C₂×D₄₇)⋊C₄	—	2	8	no	—
45	Dic₄₇⋊C₄	—	2	8	no	—
46	C₄×Dic₄₇	—	2	8	no	—
47	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
48	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
49	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
50	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
51	C₂²×D₄₇	—	2	2	no	—
52	C₂²×D₄₇	—	2	2	no	—
53	C₂²×D₄₇	C₂²×C₄	1	2	yes	—
54	C₂²×D₄₇	#41	1	4	yes	—
55	C₂×C₄×C₄₇	—	2	2	no	—
56	C₂×C₄×C₄₇	—	2	2	no	—
57	C₂×C₄×C₄₇	—	2	2	no	—
58	C₂×C₄×C₄₇	—	2	4	no	—
59	C₂×C₄×C₄₇	—	2	4	no	—
60	C₂×C₄×C₄₇	—	2	4	no	—
61	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
62	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
63	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
64	C₂×Dic₄₇	—	2	2	no	—
65	C₂×Dic₄₇	—	2	4	no	—
66	C₂×Dic₄₇	—	2	4	no	—
67	C₂×Dic₄₇	—	2	4	no	—
68	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
69	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
70	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
71	C₂×Dic₄₇	#41	1	4	yes	—
72	C₂×Dic₄₇	#41	1	4	yes	—
73	C₄×D₄₇	—	2	8	no	—
74	C₄×D₄₇	—	2	8	no	—
75	C₄×D₄₇	—	2	8	no	—
76	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
77	C₂²×C₄₇	C₂×#41	1	2	yes	—
78	C₂²×C₄₇	C₂×#41	1	2	yes	—
79	C₂²×C₄₇	C₂×#41	1	2	yes	—
80	C₂×D₄₇	—	2	2	no	—
81	C₂×D₄₇	—	2	2	no	—
82	C₂×D₄₇	—	2	8	no	—
83	C₂×D₄₇	#117	1	4	yes	—
84	C₄×C₄₇	—	2	2	no	—
85	C₄×C₄₇	—	2	2	no	—
86	C₄×C₄₇	—	2	2	no	—
87	C₄×C₄₇	—	4	4	no	—
88	Dic₄₇	—	2	2	no	—
89	Dic₄₇	—	4	4	no	—
90	Dic₄₇	#117	1	4	yes	—
91	Dic₄₇	#117	1	4	yes	—
92	#2283	—	47	1	no	maximal, Sylow
93	C₂×C₄₇	C₂×#117	1	1	yes	characteristic
94	C₂×C₄₇	C₂×#117	1	1	yes	characteristic
95	C₂×C₄₇	C₂×#117	1	1	yes	characteristic
96	C₂×C₄₇	#529	1	4	yes	—
97	D₄₇	—	2	4	no	—
98	C₂²×C₄²	—	47	1	no	—
99	#383	—	47	1	no	—
100	#383	D₄₇	1	1	yes	characteristic, complemented
101	#382	—	47	2	no	—
102	#381	—	47	2	no	—
103	#380	—	47	2	no	—
104	C₄×C₄⋊C₄	—	47	2	no	—
105	C₄×C₂²⋊C₄	—	47	2	no	—
106	#376	—	47	2	no	—
107	C₄₇	#2283	1	1	yes	characteristic, complemented, Sylow
108	C₂³×C₄	—	47	1	no	—
109	C₂³×C₄	—	47	1	no	—
110	C₂³×C₄	—	47	1	no	—
111	C₂×C₄⋊C₄	—	47	4	no	—
112	C₂×C₂²⋊C₄	—	47	4	no	—
113	C₂×C₄²	—	47	1	no	—
114	C₂×C₄²	—	47	1	no	—
115	C₂×C₄²	—	47	1	no	—
116	C₂×C₄²	—	47	8	no	—
117	C₂×C₄²	—	47	4	no	—
118	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
119	#95	—	47	2	no	—
120	#95	—	47	4	no	—
121	#95	—	47	2	no	—
122	#95	—	47	2	no	—
123	#95	C₂×D₄₇	1	2	yes	—
124	#95	C₂×D₄₇	1	2	yes	—
125	#95	C₂×D₄₇	1	2	yes	—
126	C₂⁴	—	47	1	no	—
127	C₂²×C₄	—	47	1	no	—
128	C₂²×C₄	—	47	1	no	—
129	C₂²×C₄	—	47	1	no	—
130	C₂²×C₄	—	47	4	no	—
131	C₂²×C₄	—	47	4	no	—
132	C₂²×C₄	—	47	4	no	—
133	C₂²×C₄	—	47	4	no	—
134	C₂²×C₄	—	94	4	no	—
135	C₂²×C₄	—	94	4	no	—
136	C₂²×C₄	—	94	4	no	—
137	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
138	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
139	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
140	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
141	C₄⋊C₄	—	94	8	no	—
142	C₂²⋊C₄	—	94	8	no	—
143	C₄²	—	47	4	no	—
144	C₄²	—	47	4	no	—
145	C₄²	—	47	4	no	—
146	C₄²	—	94	8	no	—
147	C₄²	C₄×D₄₇	1	4	yes	—
148	C₂³	—	47	2	no	—
149	C₂³	—	47	4	no	—
150	C₂³	—	94	2	no	—
151	C₂³	—	94	2	no	—
152	C₂³	C₂³×D₄₇	1	1	yes	characteristic
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	47	2	no	—
160	C₂×C₄	—	47	2	no	—
161	C₂×C₄	—	47	4	no	—
162	C₂×C₄	—	47	4	no	—
163	C₂×C₄	—	47	2	no	—
164	C₂×C₄	—	94	8	no	—
165	C₂×C₄	—	94	8	no	—
166	C₂×C₄	—	94	8	no	—
167	C₂×C₄	—	94	2	no	—
168	C₂×C₄	—	94	4	no	—
169	C₂×C₄	—	94	4	no	—
170	C₂×C₄	—	94	4	no	—
171	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
172	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
173	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
174	C₂²	—	47	4	no	—
175	C₂²	—	94	2	no	—
176	C₂²	—	94	2	no	—
177	C₂²	—	94	8	no	—
178	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
179	C₂²	#41×D₄₇	1	2	yes	—
180	C₂²	#41×D₄₇	1	2	yes	—
181	C₂²	#41×D₄₇	1	2	yes	—
182	C₄	—	2	2	no	—
183	C₄	—	2	2	no	—
184	C₄	—	2	2	no	—
185	C₄	—	4	4	no	—
186	C₄	—	47	4	no	—
187	C₄	—	47	4	no	—
188	C₄	—	94	2	no	—
189	C₄	—	188	4	no	—
190	C₂	—	94	4	no	—
191	C₂	#117×D₄₇	1	1	yes	characteristic
192	C₂	#117×D₄₇	1	1	yes	characteristic
193	C₂	#117×D₄₇	1	1	yes	characteristic
194	C₂	#15689656	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄²×D₄₇

C₂

yes

maximal, characteristic

#15688991

C₂

yes

maximal, characteristic, complemented

#15688987

C₂

yes

maximal, complemented

#15688985

C₂

yes

maximal

#15688982

C₂

yes

maximal

#15688974

C₂

yes

maximal, complemented

#15688970

C₂

yes

maximal

#15688968

C₂

yes

maximal, complemented

C₄₇×#383

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₄²×D₄₇

C₄

yes

complemented

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂³×D₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂²×C₄

yes

—

C₂²×D₄₇

#41

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

#41

yes

—

C₂×Dic₄₇

#41

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

#117

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

#117

yes

—

Dic₄₇

#117

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

C₂²×C₄²

—

#383

—

100

#383

D₄₇

yes

characteristic, complemented

101

#382

—

102

#381

—

103

#380

—

104

C₄×C₄⋊C₄

—

105

C₄×C₂²⋊C₄

—

106

#376

—

107

C₄₇

#2283

yes

characteristic, complemented, Sylow

108

C₂³×C₄

—

109

C₂³×C₄

—

110

C₂³×C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₂²⋊C₄

—

113

C₂×C₄²

—

114

C₂×C₄²

—

115

C₂×C₄²

—

116

C₂×C₄²

—

117

C₂×C₄²

—

118

C₂×C₄²

C₂×D₄₇

yes

characteristic

119

#95

—

120

#95

—

121

#95

—

122

#95

—

123

#95

C₂×D₄₇

yes

—

124

#95

C₂×D₄₇

yes

—

125

#95

C₂×D₄₇

yes

—

126

C₂⁴

—

127

C₂²×C₄

—

128

C₂²×C₄

—

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

C₂²×D₄₇

yes

—

138

C₂²×C₄

C₂²×D₄₇

yes

characteristic

139

C₂²×C₄

C₂²×D₄₇

yes

characteristic

140

C₂²×C₄

C₂²×D₄₇

yes

characteristic

141

C₄⋊C₄

—

142

C₂²⋊C₄

—

143

C₄²

—

144

C₄²

—

145

C₄²

—

146

C₄²

—

147

C₄²

C₄×D₄₇

yes

—

148

C₂³

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

C₂³×D₄₇

yes

characteristic

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

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

C₂×C₄×D₄₇

yes

—

172

C₂×C₄

C₂×C₄×D₄₇

yes

—

173

C₂×C₄

C₂×C₄×D₄₇

yes

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

C₂²×C₄×D₄₇

yes

characteristic

179

C₂²

#41×D₄₇

yes

—

180

C₂²

#41×D₄₇

yes

—

181

C₂²

#41×D₄₇

yes

—

182

C₄

—

183

C₄

—

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

—

188

—

190

C₂

—

191

C₂

#117×D₄₇

yes

characteristic

192

C₂

#117×D₄₇

yes

characteristic

193

C₂

#117×D₄₇

yes

characteristic

194

C₂

#15689656

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₄₇×#383	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	#383	D₄₇
hypocenter	C₄₇	#2283
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Fitting

C₄₇×#383

C₂

socle

C₂³×C₄₇

C₂⁴

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
2. #15688991	C₂	semidirect
3. #15688987	C₂	semidirect
6. #15688974	C₂	semidirect
8. #15688968	C₂	semidirect
9. C₄₇×#383	C₂	semidirect
19. C₄²×D₄₇	C₄	semidirect
100. #383	D₄₇	semidirect
107. C₄₇	#2283	semidirect

H ≅ G/N

type

2. #15688991

C₂

semidirect

3. #15688987

C₂

semidirect

6. #15688974

C₂

semidirect

8. #15688968

C₂

semidirect

9. C₄₇×#383

C₂

semidirect

19. C₄²×D₄₇

C₄

semidirect

100. #383

D₄₇

semidirect

107. C₄₇

#2283

semidirect

Subgroups — #20245785

Conjugacy classes of subgroups

Complements