Group #16950725 — subgroups

Subgroups — #16950725

Order 4352.

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

normal subgroups only

This group has 298 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	#14528470	C₂	1	1	yes	maximal, characteristic
2	#14526862	C₂	1	1	yes	maximal, characteristic
3	#14526861	C₂	1	2	yes	maximal
4	#14526861	C₂	1	2	yes	maximal
5	C₁₇×#1374	C₂	1	1	yes	maximal, characteristic
6	C₂²×#63214	C₂²	1	2	yes	—
7	C₂×#10587474	C₄	1	1	yes	characteristic
8	C₂×#10587486	C₄	1	1	yes	characteristic
9	C₂×#10587486	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
12	#11762655	C₄	1	1	yes	characteristic
13	C₂²×C₁₆×C₁₇	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
17	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
21	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₁₇	—	2	2	no	—
23	C₂×C₁₆×C₁₇	—	2	2	no	—
24	C₂×C₁₆×C₁₇	—	2	2	no	—
25	C₄×C₈×C₁₇	—	2	2	no	—
26	#10587502	C₈	1	2	yes	—
27	#10587502	C₈	1	2	yes	—
28	#10587486	—	2	2	no	—
29	#10587486	—	2	2	no	—
30	C₈×Dic₁₇	—	2	2	no	—
31	C₈×Dic₁₇	—	2	1	no	—
32	C₈×Dic₁₇	—	2	1	no	—
33	C₂×#63214	—	2	2	no	—
34	C₂×#63214	—	2	2	no	—
35	C₂×#63214	—	2	2	no	—
36	#10587474	—	2	2	no	—
37	C₂²×C₄×C₁₇	C₂×C₈	1	2	yes	—
38	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
39	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
40	C₂²×Dic₁₇	C₂×C₈	1	2	yes	—
41	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₁₇	—	2	1	no	—
43	C₂×C₈×C₁₇	—	2	1	no	—
44	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
45	C₂×C₈×C₁₇	#41	1	2	yes	—
46	C₂×C₈×C₁₇	#41	1	2	yes	—
47	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
48	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
49	C₄²×C₁₇	—	2	1	no	—
50	C₄²×C₁₇	—	2	1	no	—
51	C₄×Dic₁₇	—	2	1	no	—
52	C₄×Dic₁₇	—	2	1	no	—
53	C₄×Dic₁₇	—	2	1	no	—
54	C₄×Dic₁₇	—	2	1	no	—
55	C₂×#3622	—	2	1	no	—
56	C₂×#3622	—	2	1	no	—
57	C₂×#3622	—	2	1	no	—
58	C₂×#3622	—	2	1	no	—
59	C₂×#3622	M₁₆	1	2	yes	—
60	C₂×#3622	M₁₆	1	2	yes	—
61	C₁₆×C₁₇	—	4	2	no	—
62	#63214	—	4	2	no	—
63	#12895	—	17	1	no	maximal, Sylow
64	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
65	C₂×C₄×C₁₇	—	2	2	no	—
66	C₂×C₄×C₁₇	—	2	2	no	—
67	C₂×C₄×C₁₇	—	2	2	no	—
68	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
69	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
70	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
71	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
74	C₂×Dic₁₇	—	2	1	no	—
75	C₂×Dic₁₇	—	2	1	no	—
76	C₂×Dic₁₇	—	2	2	no	—
77	C₂×Dic₁₇	—	2	2	no	—
78	C₂×Dic₁₇	—	2	2	no	—
79	C₂×Dic₁₇	—	2	2	no	—
80	C₂×Dic₁₇	—	2	2	no	—
81	C₈×C₁₇	—	2	2	no	—
82	C₈×C₁₇	#126	1	2	yes	—
83	C₈×C₁₇	#126	1	2	yes	—
84	#3622	—	2	2	no	—
85	#3622	—	2	2	no	—
86	#1726	—	17	1	no	—
87	#1374	—	17	2	no	—
88	#1374	—	17	2	no	—
89	#1374	—	17	1	no	—
90	#1374	D₁₇	1	1	yes	characteristic
91	C₂²×C₁₇	#431	1	1	yes	characteristic
92	C₂²×C₁₇	#431	1	1	yes	characteristic
93	C₂²×C₁₇	#431	1	1	yes	characteristic
94	C₂²×C₁₇	#504	1	2	yes	—
95	C₂²×C₁₇	#504	1	2	yes	—
96	C₄×C₁₇	—	4	2	no	—
97	C₄×C₁₇	#383	1	1	yes	characteristic
98	C₄×C₁₇	#432	1	1	yes	characteristic
99	C₄×C₁₇	#432	1	1	yes	characteristic
100	C₄×C₁₇	#432	1	1	yes	characteristic
101	Dic₁₇	—	4	1	no	—
102	Dic₁₇	—	4	2	no	—
103	Dic₁₇	—	4	1	no	—
104	C₂²×C₁₆	—	17	2	no	—
105	C₂²×C₁₆	C₂×D₁₇	1	2	yes	—
106	C₂×#97	—	17	1	no	—
107	C₂×#97	—	17	1	no	—
108	C₂×#97	—	17	1	no	—
109	C₂×C₄×C₈	—	17	1	no	—
110	C₂×C₄×C₈	—	17	1	no	—
111	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
112	#376	—	17	1	no	—
113	C₂×C₁₇	#1839	1	1	yes	characteristic
114	C₂×C₁₇	#2164	1	2	yes	—
115	C₂×C₁₇	#2164	1	1	yes	characteristic
116	C₂×C₁₇	#2164	1	2	yes	—
117	C₂×C₁₇	#2164	1	1	yes	characteristic
118	C₂²×C₈	—	17	1	no	—
119	C₂²×C₈	—	17	1	no	—
120	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
121	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
122	C₂×C₄²	—	17	1	no	—
123	C₂×C₄²	—	17	1	no	—
124	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
125	C₂×C₁₆	—	2	2	no	—
126	C₂×C₁₆	—	2	2	no	—
127	C₂×C₁₆	—	2	2	no	—
128	C₂×C₁₆	—	34	2	no	—
129	C₂×C₁₆	—	34	2	no	—
130	C₂×C₁₆	—	34	2	no	—
131	#97	—	34	2	no	—
132	#97	—	34	2	no	—
133	#97	—	34	2	no	—
134	C₄×C₈	—	2	2	no	—
135	C₄×C₈	—	34	2	no	—
136	C₄×C₈	—	34	1	no	—
137	C₄×C₈	—	34	1	no	—
138	#95	—	17	2	no	—
139	#95	—	17	2	no	—
140	C₁₇	#12895	1	1	yes	characteristic, complemented, Sylow
141	C₂²×C₄	—	17	1	no	—
142	C₂²×C₄	—	17	2	no	—
143	C₂²×C₄	—	17	1	no	—
144	C₂²×C₄	C₈×D₁₇	1	2	yes	—
145	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
146	C₂×C₈	—	2	1	no	—
147	C₂×C₈	—	2	1	no	—
148	C₂×C₈	—	17	2	no	—
149	C₂×C₈	—	17	2	no	—
150	C₂×C₈	—	34	1	no	—
151	C₂×C₈	—	34	1	no	—
152	C₂×C₈	—	34	1	no	—
153	C₂×C₈	—	34	1	no	—
154	C₂×C₈	#63218	1	2	yes	—
155	C₂×C₈	#63252	1	2	yes	—
156	C₂×C₈	#63254	1	1	yes	characteristic
157	C₂×C₈	#63254	1	2	yes	—
158	C₂×C₈	#63256	1	1	yes	characteristic
159	C₄²	—	2	1	no	—
160	C₄²	—	2	1	no	—
161	C₄²	—	34	1	no	—
162	C₄²	—	34	1	no	—
163	C₄²	—	34	1	no	—
164	C₄²	—	34	1	no	—
165	C₁₆	—	4	2	no	—
166	C₁₆	—	68	2	no	—
167	C₂³	C₂×C₈×D₁₇	1	1	yes	characteristic
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	34	2	no	—
172	C₂×C₄	—	34	2	no	—
173	C₂×C₄	—	34	2	no	—
174	C₂×C₄	—	34	2	no	—
175	C₂×C₄	—	34	1	no	—
176	C₂×C₄	—	34	1	no	—
177	C₂×C₄	—	34	2	no	—
178	C₂×C₄	#10587558	1	1	yes	characteristic
179	C₂×C₄	#10587563	1	1	yes	characteristic
180	C₂×C₄	#10587578	1	1	yes	characteristic
181	C₂×C₄	C₂×#63218	1	1	yes	characteristic
182	C₂×C₄	M₁₆×D₁₇	1	1	yes	characteristic
183	C₂×C₄	M₁₆×D₁₇	1	1	yes	characteristic
184	C₈	—	2	2	no	—
185	C₈	—	34	2	no	—
186	C₈	—	34	2	no	—
187	C₈	#10587565	1	2	yes	—
188	C₈	#10587584	1	2	yes	—
189	C₂²	#11762859	1	1	yes	characteristic
190	C₂²	#11762860	1	1	yes	characteristic
191	C₂²	#11762861	1	1	yes	characteristic
192	C₂²	#11763225	1	2	yes	—
193	C₂²	#11763227	1	2	yes	—
194	C₄	—	4	2	no	—
195	C₄	—	68	1	no	—
196	C₄	—	68	2	no	—
197	C₄	—	68	1	no	—
198	C₄	#11762676	1	1	yes	characteristic
199	C₄	#11762863	1	1	yes	characteristic
200	C₄	#11762864	1	1	yes	characteristic
201	C₄	#11762865	1	1	yes	characteristic
202	C₂	#14528926	1	1	yes	characteristic
203	C₂	#14530588	1	2	yes	—
204	C₂	#14530589	1	1	yes	characteristic
205	C₂	#14530590	1	2	yes	—
206	C₂	#14530592	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14528470

C₂

yes

maximal, characteristic

#14526862

C₂

yes

maximal, characteristic

#14526861

C₂

yes

maximal

#14526861

C₂

yes

maximal

C₁₇×#1374

C₂

yes

maximal, characteristic

C₂²×#63214

C₂²

yes

—

C₂×#10587474

C₄

yes

characteristic

C₂×#10587486

C₄

yes

characteristic

C₂×#10587486

C₄

yes

characteristic

C₂×C₈×Dic₁₇

C₂²

yes

characteristic

C₂×C₈×Dic₁₇

C₂²

yes

characteristic

#11762655

C₄

yes

characteristic

C₂²×C₁₆×C₁₇

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄²×C₁₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂²×#3622

C₂×C₄

yes

characteristic

C₂²×#3622

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₇

—

C₂×C₁₆×C₁₇

—

C₂×C₁₆×C₁₇

—

C₄×C₈×C₁₇

—

#10587502

C₈

yes

—

#10587502

C₈

yes

—

#10587486

—

#10587486

—

C₈×Dic₁₇

—

C₈×Dic₁₇

—

C₈×Dic₁₇

—

—

—

—

—

C₂²×C₄×C₁₇

C₂×C₈

yes

—

C₂²×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂²×Dic₁₇

C₂×C₈

yes

characteristic

C₂²×Dic₁₇

C₂×C₈

yes

—

C₂²×Dic₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

#41

yes

—

C₂×C₈×C₁₇

#41

yes

—

C₂×C₈×C₁₇

yes

C₂×C₈×C₁₇

yes

C₄²×C₁₇

—

C₄²×C₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

—

—

—

—

M₁₆

yes

—

C₂×#3622

M₁₆

yes

—

C₁₆×C₁₇

—

#63214

—

#12895

—

maximal, Sylow

C₂³×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

—

C₈×C₁₇

#126

yes

—

C₈×C₁₇

#126

yes

—

—

—

—

—

—

—

D₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

—

C₂²×C₁₇

#504

yes

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

100

C₄×C₁₇

#432

yes

characteristic

101

Dic₁₇

—

102

Dic₁₇

—

103

Dic₁₇

—

104

C₂²×C₁₆

—

105

C₂²×C₁₆

C₂×D₁₇

yes

—

106

C₂×#97

—

107

C₂×#97

—

108

C₂×#97

—

109

C₂×C₄×C₈

—

110

C₂×C₄×C₈

—

111

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

112

#376

—

113

C₂×C₁₇

#1839

yes

characteristic

114

C₂×C₁₇

#2164

yes

—

115

C₂×C₁₇

#2164

yes

characteristic

116

C₂×C₁₇

#2164

yes

—

117

C₂×C₁₇

#2164

yes

characteristic

118

C₂²×C₈

—

119

C₂²×C₈

—

120

C₂²×C₈

C₄×D₁₇

yes

characteristic

121

C₂²×C₈

C₂²×D₁₇

yes

characteristic

122

C₂×C₄²

—

123

C₂×C₄²

—

124

C₂×C₄²

C₄×D₁₇

yes

characteristic

125

C₂×C₁₆

—

126

C₂×C₁₆

—

127

C₂×C₁₆

—

128

C₂×C₁₆

—

129

C₂×C₁₆

—

130

C₂×C₁₆

—

131

#97

—

132

#97

—

133

#97

—

134

C₄×C₈

—

135

C₄×C₈

—

136

C₄×C₈

—

137

C₄×C₈

—

138

#95

—

139

#95

—

140

C₁₇

#12895

yes

characteristic, complemented, Sylow

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

C₈×D₁₇

yes

—

145

C₂²×C₄

C₂×C₄×D₁₇

yes

characteristic

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

#63218

yes

—

155

C₂×C₈

#63252

yes

—

156

C₂×C₈

#63254

yes

characteristic

157

C₂×C₈

#63254

yes

—

158

C₂×C₈

#63256

yes

characteristic

159

C₄²

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₁₆

—

166

C₁₆

—

167

C₂³

C₂×C₈×D₁₇

yes

characteristic

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

#10587558

yes

characteristic

179

C₂×C₄

#10587563

yes

characteristic

180

C₂×C₄

#10587578

yes

characteristic

181

C₂×C₄

C₂×#63218

yes

characteristic

182

C₂×C₄

M₁₆×D₁₇

yes

characteristic

183

C₂×C₄

M₁₆×D₁₇

yes

characteristic

184

C₈

—

185

C₈

—

186

C₈

—

187

C₈

#10587565

yes

—

188

C₈

#10587584

yes

—

189

C₂²

#11762859

yes

characteristic

190

C₂²

#11762860

yes

characteristic

191

C₂²

#11762861

yes

characteristic

192

C₂²

#11763225

yes

—

193

C₂²

#11763227

yes

—

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

#11762676

yes

characteristic

199

C₄

#11762863

yes

characteristic

200

C₄

#11762864

yes

characteristic

201

C₄

#11762865

yes

characteristic

202

C₂

#14528926

yes

characteristic

203

C₂

#14530588

yes

—

204

C₂

#14530589

yes

characteristic

205

C₂

#14530590

yes

—

206

C₂

#14530592

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂²×C₈
Fitting	C₁₇×#1374	C₂
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1374	D₁₇
hypocenter	C₁₇	#12895
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈ ◁ #1374

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₁₇

commutator, socle, prime radical

C₂³×C₁₇

C₂²×C₈

Fitting

C₁₇×#1374

C₂

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂³×C₁₇ ▷ C₁₇

C₁ ◁ C₂²×C₈ ◁ #1374

N	H ≅ G/N	type
140. C₁₇	#12895	semidirect

H ≅ G/N

type

140. C₁₇

#12895

semidirect

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

subgroup	index
#14528470	2
#14526862	2
#14526861	2
C₁₇×#1374	2
#12895	17

subgroup

index

C₁₇×#1374

Subgroups — #16950725

Conjugacy classes of subgroups

Complements

Maximal subgroups