Group #17982665 — subgroups

Subgroups — #17982665

Order 4352.

290 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11763914	C₂	1	1	yes	maximal, characteristic
2	#14545976	C₂	1	2	yes	maximal
3	C₂×#11763904	C₂	1	1	yes	maximal, characteristic
4	#14545864	C₂	1	2	yes	maximal
5	#14544587	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587666	C₂²	1	2	yes	—
7	C₂×#10587665	C₂²	1	1	yes	characteristic
8	C₂×#10587665	C₂²	1	1	yes	characteristic
9	#11763914	—	2	2	no	—
10	#11763912	—	2	2	no	—
11	C₄⋊#63241	—	2	2	no	—
12	#11763904	—	2	2	no	—
13	C₂×#10587535	C₄	1	1	yes	characteristic
14	#11763774	C₂²	1	2	yes	—
15	C₂×C₈×#595	C₂²	1	1	yes	characteristic
16	#11763679	C₄	1	2	yes	—
17	#11762844	C₄	1	1	yes	characteristic
18	C₂×C₄×#595	C₂×C₄	1	1	yes	characteristic
19	C₂×#63243	C₂×C₄	1	2	yes	—
20	C₂×#63242	C₂³	1	1	yes	characteristic
21	C₂×#63241	—	2	1	no	—
22	C₂×#63241	—	2	2	no	—
23	C₂×#63241	D₄	1	1	yes	characteristic
24	C₂×#63241	D₄	1	1	yes	characteristic
25	#10587666	—	2	2	no	—
26	#10587666	—	2	2	no	—
27	#10587665	—	2	1	no	—
28	#10587665	—	2	1	no	—
29	#10587665	—	2	1	no	—
30	#10587665	Q₈	1	2	yes	—
31	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
32	#10587578	C₂×C₄	1	2	yes	—
33	#10587542	—	2	2	no	—
34	C₄×#3624	—	2	2	no	—
35	#10587535	—	2	2	no	—
36	C₈×#595	D₄	1	2	yes	—
37	C₈×#595	Q₈	1	2	yes	—
38	C₁₇×#106	C₈	1	1	yes	characteristic
39	#10587488	C₈	1	1	yes	characteristic
40	#10587478	C₈	1	2	yes	—
41	C₂²×#595	—	2	1	no	—
42	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×#3624	—	2	2	no	—
44	C₂×#3624	C₂×D₄	1	1	yes	characteristic
45	C₂×#3624	#41	1	1	yes	characteristic
46	C₄×#595	—	2	1	no	—
47	C₄×#595	C₄⋊C₄	1	2	yes	—
48	#63243	—	2	2	no	—
49	#63243	—	2	2	no	—
50	#63242	C₂×D₄	1	1	yes	characteristic
51	#63242	C₂×Q₈	1	1	yes	characteristic
52	#63242	C₂×Q₈	1	1	yes	characteristic
53	#63242	#41	1	1	yes	characteristic
54	#63241	—	2	1	no	—
55	#63241	—	2	1	no	—
56	#63241	—	2	2	no	—
57	#63241	—	4	2	no	—
58	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
59	C₄⋊C₄×C₁₇	C₂×C₈	1	2	yes	—
60	#63227	—	2	2	no	—
61	C₄⋊Dic₁₇	C₂×C₈	1	2	yes	—
62	C₄×Dic₁₇	—	2	2	no	—
63	C₂×#3622	C₂×C₈	1	1	yes	characteristic
64	C₈×D₁₇	C₄⋊C₄	1	2	yes	—
65	C₈×D₁₇	M₁₆	1	2	yes	—
66	#13162	—	17	1	no	maximal, Sylow
67	C₂²×D₁₇	#131	1	1	yes	characteristic
68	C₂×#595	—	2	2	no	—
69	C₂×#595	—	4	2	no	—
70	C₂×C₄×C₁₇	—	2	2	no	—
71	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
72	C₂×Dic₁₇	—	2	2	no	—
73	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
74	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
76	C₄×D₁₇	C₂×M₁₆	1	1	yes	characteristic
77	C₄×D₁₇	#131	1	1	yes	characteristic
78	#3624	—	4	2	no	—
79	#3624	#121	1	1	yes	characteristic
80	#3624	C₂²⋊Q₈	1	1	yes	characteristic
81	#3624	#125	1	1	yes	characteristic
82	#3624	C₄⋊Q₈	1	1	yes	characteristic
83	C₈×C₁₇	C₄⋊C₈	1	2	yes	—
84	#3622	C₄⋊C₈	1	2	yes	—
85	C₂×#364	—	17	1	no	—
86	#2151	—	17	2	no	—
87	C₂×#346	—	17	1	no	—
88	#1772	—	17	1	no	—
89	#1379	—	17	2	no	—
90	C₂²×C₁₇	C₈×D₄	1	1	yes	characteristic
91	C₂×D₁₇	—	2	2	no	—
92	C₂×D₁₇	#424	1	1	yes	characteristic
93	C₂×D₁₇	#446	1	1	yes	characteristic
94	#595	—	4	2	no	—
95	C₄×C₁₇	—	4	2	no	—
96	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
97	C₄×C₁₇	C₈×Q₈	1	1	yes	characteristic
98	Dic₁₇	—	4	2	no	—
99	Dic₁₇	#389	1	1	yes	characteristic
100	Dic₁₇	#436	1	1	yes	characteristic
101	C₂×M₃₂	—	17	2	no	—
102	C₂²×C₁₆	—	17	1	no	—
103	C₂²×C₁₆	—	17	1	no	—
104	C₂×#108	—	17	1	no	—
105	#427	—	17	1	no	—
106	#405	—	17	2	no	—
107	C₂×C₄×C₈	—	17	1	no	—
108	#364	—	34	2	no	—
109	C₄⋊C₁₆	—	34	2	no	—
110	C₄⋊C₁₆	—	34	2	no	—
111	#346	—	34	2	no	—
112	#339	—	17	2	no	—
113	C₂×C₁₇	#1939	1	1	yes	characteristic
114	C₂×C₁₇	#2171	1	2	yes	—
115	D₁₇	—	2	1	no	—
116	D₁₇	—	2	1	no	—
117	C₂×M₁₆	—	17	2	no	—
118	C₂²×C₈	—	17	1	no	—
119	C₂²×C₈	—	17	1	no	—
120	#117	—	17	2	no	—
121	C₂×C₄²	—	17	1	no	—
122	M₃₂	—	34	2	no	—
123	M₃₂	—	34	2	no	—
124	C₂×C₁₆	—	17	2	no	—
125	C₂×C₁₆	—	17	1	no	—
126	C₂×C₁₆	—	17	1	no	—
127	C₂×C₁₆	—	34	1	no	—
128	C₂×C₁₆	—	34	1	no	—
129	C₂×C₁₆	—	34	1	no	—
130	C₂×C₁₆	—	34	1	no	—
131	C₂×C₁₆	—	34	2	no	—
132	#108	—	34	2	no	—
133	#107	—	17	2	no	—
134	#106	—	17	1	no	—
135	#106	#3633	1	1	yes	characteristic
136	#97	—	34	2	no	—
137	C₄×C₈	—	17	2	no	—
138	C₄×C₈	—	17	2	no	—
139	C₄×C₈	—	34	2	no	—
140	C₁₇	#13162	1	1	yes	characteristic, complemented, Sylow
141	C₂²×C₄	—	17	1	no	—
142	C₂²×C₄	—	34	1	no	—
143	M₁₆	—	34	2	no	—
144	M₁₆	—	34	2	no	—
145	C₂×C₈	—	17	1	no	—
146	C₂×C₈	—	17	1	no	—
147	C₂×C₈	—	17	1	no	—
148	C₂×C₈	—	17	1	no	—
149	C₂×C₈	—	17	1	no	—
150	C₂×C₈	—	17	1	no	—
151	C₂×C₈	—	17	1	no	—
152	C₂×C₈	—	17	2	no	—
153	C₂×C₈	—	17	2	no	—
154	C₂×C₈	—	34	2	no	—
155	C₂×C₈	C₂×#3633	1	1	yes	characteristic
156	C₄⋊C₄	—	17	2	no	—
157	C₄⋊C₄	C₂×#3633	1	2	yes	—
158	C₂²⋊C₄	—	34	2	no	—
159	C₄²	—	17	2	no	—
160	C₄²	—	34	2	no	—
161	C₄²	—	34	1	no	—
162	C₁₆	—	34	1	no	—
163	C₁₆	—	34	1	no	—
164	C₁₆	—	34	2	no	—
165	C₁₆	—	68	2	no	—
166	C₂³	—	17	1	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	17	1	no	—
169	C₂×C₄	—	17	1	no	—
170	C₂×C₄	—	17	1	no	—
171	C₂×C₄	—	17	1	no	—
172	C₂×C₄	—	17	1	no	—
173	C₂×C₄	—	34	2	no	—
174	C₂×C₄	—	34	2	no	—
175	C₂×C₄	—	68	2	no	—
176	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
177	C₈	—	17	1	no	—
178	C₈	—	17	1	no	—
179	C₈	—	17	1	no	—
180	C₈	—	17	1	no	—
181	C₈	—	17	2	no	—
182	C₈	—	68	2	no	—
183	C₈	C₄⋊#3633	1	2	yes	—
184	C₂²	—	17	1	no	—
185	C₂²	—	17	1	no	—
186	C₂²	—	34	2	no	—
187	C₂²	D₄×#3633	1	1	yes	characteristic
188	C₄	—	4	2	no	—
189	C₄	—	17	1	no	—
190	C₄	—	17	1	no	—
191	C₄	—	68	2	no	—
192	C₄	—	68	2	no	—
193	C₄	C₂×C₄⋊#3633	1	1	yes	characteristic
194	C₄	Q₈×#3633	1	1	yes	characteristic
195	C₂	—	34	1	no	—
196	C₂	—	34	1	no	—
197	C₂	#14545933	1	1	yes	characteristic
198	C₂	#14546004	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763914

C₂

yes

maximal, characteristic

#14545976

C₂

yes

maximal

C₂×#11763904

C₂

yes

maximal, characteristic

#14545864

C₂

yes

maximal

#14544587

C₂

yes

maximal, characteristic

C₂×#10587666

C₂²

yes

—

C₂×#10587665

C₂²

yes

characteristic

C₂×#10587665

C₂²

yes

—

—

—

—

C₄

yes

characteristic

#11763774

C₂²

yes

—

C₂×C₈×#595

C₂²

yes

characteristic

#11763679

C₄

yes

—

#11762844

C₄

yes

characteristic

C₂×C₄×#595

C₂×C₄

yes

characteristic

C₂×#63243

C₂×C₄

yes

—

C₂×#63242

C₂³

yes

—

—

D₄

yes

characteristic

C₂×#63241

D₄

yes

—

—

—

—

—

Q₈

yes

—

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

#10587578

C₂×C₄

yes

—

—

—

—

D₄

yes

—

C₈×#595

Q₈

yes

—

C₁₇×#106

C₈

yes

characteristic

#10587488

C₈

yes

characteristic

#10587478

C₈

yes

—

C₂²×#595

—

C₂×C₄×D₁₇

C₂²×C₄

yes

characteristic

C₂×#3624

—

C₂×#3624

C₂×D₄

yes

yes

—

C₄⋊C₄

yes

—

#63243

—

#63243

—

#63242

C₂×D₄

yes

characteristic

#63242

C₂×Q₈

yes

characteristic

#63242

C₂×Q₈

yes

yes

—

—

—

—

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₄⋊C₄×C₁₇

C₂×C₈

yes

—

#63227

—

C₄⋊Dic₁₇

C₂×C₈

yes

—

C₄×Dic₁₇

—

C₂×#3622

C₂×C₈

yes

characteristic

C₈×D₁₇

C₄⋊C₄

yes

—

C₈×D₁₇

M₁₆

yes

—

—

C₂²×D₁₇

yes

—

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₄×D₄

yes

characteristic

C₄×D₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×D₁₇

C₄×Q₈

yes

characteristic

C₄×D₁₇

C₂×M₁₆

yes

C₄×D₁₇

yes

—

yes

C₂²⋊Q₈

yes

yes

C₄⋊Q₈

yes

characteristic

C₈×C₁₇

C₄⋊C₈

yes

—

#3622

C₄⋊C₈

yes

—

—

—

—

—

—

C₂²×C₁₇

C₈×D₄

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

yes

C₂×D₁₇

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₇

C₈×Q₈

yes

characteristic

Dic₁₇

—

Dic₁₇

#389

yes

characteristic

100

Dic₁₇

#436

yes

characteristic

101

C₂×M₃₂

—

102

C₂²×C₁₆

—

103

C₂²×C₁₆

—

104

C₂×#108

—

105

#427

—

106

#405

—

107

C₂×C₄×C₈

—

108

#364

—

109

C₄⋊C₁₆

—

110

C₄⋊C₁₆

—

111

#346

—

112

#339

—

113

C₂×C₁₇

#1939

yes

characteristic

114

C₂×C₁₇

#2171

yes

—

115

D₁₇

—

116

D₁₇

—

117

C₂×M₁₆

—

118

C₂²×C₈

—

119

C₂²×C₈

—

120

#117

—

121

C₂×C₄²

—

122

M₃₂

—

123

M₃₂

—

124

C₂×C₁₆

—

125

C₂×C₁₆

—

126

C₂×C₁₆

—

127

C₂×C₁₆

—

128

C₂×C₁₆

—

129

C₂×C₁₆

—

130

C₂×C₁₆

—

131

C₂×C₁₆

—

132

#108

—

133

#107

—

134

#106

—

135

yes

136

—

137

C₄×C₈

—

138

C₄×C₈

—

139

C₄×C₈

—

140

C₁₇

#13162

yes

characteristic, complemented, Sylow

141

C₂²×C₄

—

142

C₂²×C₄

—

143

M₁₆

—

144

M₁₆

—

145

C₂×C₈

—

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

—

155

C₂×C₈

C₂×#3633

yes

characteristic

156

C₄⋊C₄

—

157

C₄⋊C₄

C₂×#3633

yes

—

158

C₂²⋊C₄

—

159

C₄²

—

160

C₄²

—

161

C₄²

—

162

C₁₆

—

163

C₁₆

—

164

C₁₆

—

165

C₁₆

—

166

C₂³

—

167

C₂×C₄

—

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

C₂²×#3633

yes

characteristic

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₈

C₄⋊#3633

yes

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

D₄×#3633

yes

characteristic

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

C₂×C₄⋊#3633

yes

characteristic

194

C₄

Q₈×#3633

yes

characteristic

195

C₂

—

196

C₂

—

197

C₂

#14545933

yes

characteristic

198

C₂

#14546004

yes

—

	subgroup	G/H
center	C₂²	D₄×#3633
commutator	C₂×C₄×C₁₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×#3633
Fitting	C₁₇×#106	C₈
socle	C₂²×C₁₇	C₈×D₄
prime radical	C₂²×D₁₇	#131
cosocle	C₂×#63242	C₂³
hypercenter	#106	#3633
hypocenter	C₁₇	#13162
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#3633

commutator

C₂×C₄×C₁₇

C₂²×C₈

Frattini

C₂×C₄

C₂²×#3633

Fitting

C₁₇×#106

C₈

socle

C₂²×C₁₇

C₈×D₄

C₂²×D₁₇

C₂³

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
140. C₁₇	#13162	semidirect

H ≅ G/N

type

140. C₁₇

#13162

semidirect

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

subgroup	index
C₂×#11763914	2
#14545976	2
C₂×#11763904	2
#14545864	2
#14544587	2
#13162	17

subgroup

index

Subgroups — #17982665

Conjugacy classes of subgroups

Complements

Maximal subgroups