Group #17948597 — subgroups

Subgroups — #17948597

Order 4352.

282 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 98 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	C₄×#10587529	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587534	C₂	1	1	yes	maximal, characteristic
3	D₁₇×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587529	—	2	1	no	—
5	C₂×#10587534	C₄	1	2	yes	—
6	C₄×C₄⋊#595	—	2	1	no	—
7	#11763695	C₄	1	2	yes	complemented
8	C₄×#63216	—	2	1	no	—
9	#11763683	—	2	1	no	—
10	C₄⋊C₈×D₁₇	—	2	1	no	—
11	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
12	#11762562	C₄	1	1	yes	characteristic, complemented
13	#11762561	—	2	1	no	—
14	C₁₇×#335	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄⋊#595	—	2	2	no	—
16	C₂×C₄×#595	—	4	1	no	—
17	C₂×C₈×D₁₇	—	4	1	no	—
18	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
20	C₄²×D₁₇	D₄	1	1	yes	characteristic
21	(C₂×#595)⋊C₄	—	4	1	no	—
22	C₂×#63216	—	2	2	no	—
23	#10587534	—	2	2	no	—
24	#10587534	C₈	1	4	yes	complemented
25	#10587529	—	2	4	no	—
26	C₁₇×C₄⋊C₈	—	2	1	no	—
27	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
28	#10587485	—	4	1	no	—
29	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₇	Q₈	1	1	yes	characteristic
31	C₄⋊#3622	—	2	1	no	—
32	C₄×#3622	D₄	1	1	yes	characteristic
33	C₂²×#595	—	4	2	no	—
34	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
36	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
37	C₄⋊#595	—	2	4	no	—
38	C₄⋊#595	—	4	2	no	—
39	C₄×#595	—	8	1	no	—
40	C₄×#595	—	8	1	no	—
41	C₂×C₈×C₁₇	—	4	1	no	—
42	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
43	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
44	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
45	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
46	C₄×Dic₁₇	SD₁₆	1	1	yes	characteristic
47	C₄×Dic₁₇	Q₁₆	1	1	yes	characteristic
48	C₂×#3622	—	4	1	no	—
49	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
51	C₈×D₁₇	—	2	2	no	—
52	C₈×D₁₇	—	8	1	no	—
53	C₈×D₁₇	—	8	1	no	—
54	C₈×D₁₇	C₂×C₈	1	2	yes	—
55	C₈×D₁₇	M₁₆	1	2	yes	—
56	#63216	—	2	4	no	—
57	#7171	—	17	1	no	maximal, Sylow
58	C₂²×D₁₇	#102	1	1	yes	characteristic
59	C₂×#595	—	4	4	no	—
60	C₂×#595	—	8	2	no	—
61	C₂×#595	—	8	2	no	—
62	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
63	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
64	C₂×C₄×C₁₇	#103	1	1	yes	characteristic
65	C₂×Dic₁₇	#103	1	1	yes	characteristic
66	C₂×Dic₁₇	#106	1	1	yes	characteristic
67	C₂×Dic₁₇	#107	1	1	yes	characteristic
68	C₄×D₁₇	—	2	2	no	—
69	C₄×D₁₇	C₂²⋊C₈	1	2	yes	—
70	C₄×D₁₇	#104	1	2	yes	—
71	C₄×D₁₇	D₁₆	1	1	yes	characteristic
72	C₄×D₁₇	SD₃₂	1	1	yes	characteristic
73	C₄×D₁₇	SD₃₂	1	1	yes	characteristic
74	C₄×D₁₇	Q₃₂	1	1	yes	characteristic
75	C₈×C₁₇	—	2	1	no	—
76	C₈×C₁₇	—	8	1	no	—
77	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
78	C₈×C₁₇	#97	1	1	yes	characteristic
79	#3622	—	2	1	no	—
80	#3622	—	8	1	no	—
81	#3622	C₄⋊C₈	1	2	yes	—
82	C₂×C₄×C₁₆	—	17	1	no	—
83	C₄×#107	—	17	1	no	—
84	C₂×#335	—	17	1	no	—
85	C₂²×C₁₇	#340	1	1	yes	characteristic
86	C₂×D₁₇	D₄⋊C₈	1	2	yes	—
87	C₂×D₁₇	#357	1	1	yes	characteristic
88	C₂×D₁₇	#358	1	1	yes	characteristic
89	C₂×D₁₇	#359	1	2	yes	—
90	#595	—	8	4	no	—
91	C₄×C₁₇	—	2	1	no	—
92	C₄×C₁₇	#336	1	1	yes	characteristic
93	C₄×C₁₇	#339	1	1	yes	characteristic
94	C₄×C₁₇	#357	1	1	yes	characteristic
95	C₄×C₁₇	#358	1	1	yes	characteristic
96	Dic₁₇	—	2	1	no	—
97	Dic₁₇	Q₈⋊C₈	1	2	yes	—
98	Dic₁₇	#366	1	1	yes	characteristic
99	Dic₁₇	#367	1	1	yes	characteristic
100	C₂²×C₁₆	—	34	1	no	—
101	C₂×#107	—	17	2	no	—
102	C₂×C₄⋊C₈	—	34	1	no	—
103	C₂×C₄×C₈	—	17	1	no	—
104	C₄×C₄⋊C₄	—	34	1	no	—
105	C₄×C₁₆	—	17	2	no	—
106	C₄×C₁₆	—	34	1	no	—
107	#340	—	34	1	no	—
108	#335	—	17	1	no	—
109	#335	—	34	1	no	—
110	#335	#595	1	1	yes	characteristic, complemented
111	C₂×C₁₇	#1279	1	1	yes	characteristic
112	C₂×C₁₇	#1380	1	1	yes	characteristic
113	C₂×C₁₇	#1382	1	1	yes	characteristic
114	D₁₇	#1331	1	2	yes	—
115	D₁₇	#1332	1	2	yes	—
116	C₂²×C₈	—	17	1	no	—
117	C₂²×C₈	—	17	1	no	—
118	C₂²×C₈	—	68	1	no	—
119	C₂×C₄⋊C₄	—	34	2	no	—
120	C₂×C₄²	—	17	1	no	—
121	C₂×C₄²	—	68	1	no	—
122	C₂×C₁₆	—	34	2	no	—
123	C₂×C₁₆	—	34	4	no	—
124	#107	—	17	4	no	—
125	#107	—	34	2	no	—
126	C₄⋊C₈	—	2	1	no	—
127	C₄⋊C₈	—	34	1	no	—
128	C₄⋊C₈	—	68	1	no	—
129	C₄×C₈	—	17	1	no	—
130	C₄×C₈	—	17	1	no	—
131	C₄×C₈	—	17	1	no	—
132	C₄×C₈	C₂×#595	1	1	yes	characteristic
133	#95	—	68	1	no	—
134	C₁₇	#7171	1	1	yes	characteristic, complemented, Sylow
135	C₂²×C₄	—	17	1	no	—
136	C₂²×C₄	—	17	1	no	—
137	C₂²×C₄	—	17	1	no	—
138	C₂²×C₄	—	68	2	no	—
139	C₂×C₈	—	4	1	no	—
140	C₂×C₈	—	17	1	no	—
141	C₂×C₈	—	17	2	no	—
142	C₂×C₈	—	17	2	no	—
143	C₂×C₈	—	17	1	no	—
144	C₂×C₈	—	34	2	no	—
145	C₂×C₈	—	68	1	no	—
146	C₂×C₈	—	136	1	no	—
147	C₂×C₈	—	136	1	no	—
148	C₂×C₈	C₄×#595	1	1	yes	characteristic
149	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
150	C₄⋊C₄	—	34	4	no	—
151	C₄⋊C₄	—	68	2	no	—
152	C₄²	—	17	1	no	—
153	C₄²	—	17	1	no	—
154	C₄²	—	17	1	no	—
155	C₄²	—	136	1	no	—
156	C₄²	—	136	1	no	—
157	C₄²	C₂²⋊#595	1	1	yes	characteristic
158	C₁₆	—	34	4	no	—
159	C₂³	—	17	1	no	—
160	C₂×C₄	—	17	1	no	—
161	C₂×C₄	—	17	1	no	—
162	C₂×C₄	—	17	1	no	—
163	C₂×C₄	—	17	1	no	—
164	C₂×C₄	—	17	1	no	—
165	C₂×C₄	—	17	1	no	—
166	C₂×C₄	—	17	2	no	—
167	C₂×C₄	—	17	2	no	—
168	C₂×C₄	—	17	1	no	—
169	C₂×C₄	—	34	2	no	—
170	C₂×C₄	—	68	4	no	—
171	C₂×C₄	—	136	2	no	—
172	C₂×C₄	—	136	2	no	—
173	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
174	C₂×C₄	#10587547	1	1	yes	characteristic
175	C₂×C₄	#10587549	1	1	yes	characteristic
176	C₈	—	2	1	no	—
177	C₈	—	8	1	no	—
178	C₈	—	17	2	no	—
179	C₈	—	34	1	no	—
180	C₈	—	136	1	no	—
181	C₈	C₈×#595	1	1	yes	characteristic
182	C₈	#10587532	1	1	yes	characteristic
183	C₂²	—	17	2	no	—
184	C₂²	—	17	1	no	—
185	C₂²	—	17	1	no	—
186	C₂²	—	17	2	no	—
187	C₂²	#11763682	1	1	yes	characteristic
188	C₄	—	2	1	no	—
189	C₄	—	17	2	no	—
190	C₄	—	17	1	no	—
191	C₄	—	17	1	no	—
192	C₄	—	34	1	no	—
193	C₄	—	136	4	no	—
194	C₄	#11763674	1	1	yes	characteristic
195	C₄	#11763681	1	1	yes	characteristic
196	C₄	#11763721	1	1	yes	characteristic
197	C₄	#11763722	1	1	yes	characteristic
198	C₂	—	17	2	no	—
199	C₂	—	17	2	no	—
200	C₂	#14543618	1	1	yes	characteristic
201	C₂	#14543841	1	1	yes	characteristic
202	C₂	#14543847	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10587529

C₂

yes

maximal, characteristic

C₄×#10587534

C₂

yes

maximal, characteristic

D₁₇×#335

C₂

yes

maximal, characteristic

C₂×#10587529

—

C₂×#10587534

C₄

yes

—

C₄×C₄⋊#595

—

#11763695

C₄

yes

complemented

C₄×#63216

—

#11763683

—

C₄⋊C₈×D₁₇

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

#11762562

C₄

yes

characteristic, complemented

#11762561

—

C₁₇×#335

C₄

yes

characteristic, complemented

C₂×C₄⋊#595

—

C₂×C₄×#595

—

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×D₁₇

D₄

yes

characteristic

C₄²×D₁₇

D₄

yes

characteristic

(C₂×#595)⋊C₄

—

C₂×#63216

—

#10587534

—

#10587534

C₈

yes

complemented

#10587529

—

C₁₇×C₄⋊C₈

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

#10587485

—

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

Q₈

yes

characteristic

C₄⋊#3622

—

C₄×#3622

D₄

yes

characteristic

C₂²×#595

—

C₂×C₄×D₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₁₇

D₈

yes

characteristic

C₂×C₄×D₁₇

SD₁₆

yes

—

—

—

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄²

yes

characteristic

C₂×C₈×C₁₇

C₄⋊C₄

yes

characteristic

C₄²×C₁₇

C₂²⋊C₄

yes

characteristic

C₄×Dic₁₇

C₄⋊C₄

yes

characteristic

C₄×Dic₁₇

SD₁₆

yes

characteristic

C₄×Dic₁₇

Q₁₆

yes

characteristic

C₂×#3622

—

C₂×#3622

C₂²⋊C₄

yes

characteristic

C₂×#3622

C₄⋊C₄

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

C₂×C₈

yes

—

C₈×D₁₇

M₁₆

yes

—

—

—

C₂²×D₁₇

yes

—

—

—

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×Dic₁₇

yes

C₂×Dic₁₇

yes

C₂×Dic₁₇

yes

C₄×D₁₇

—

C₄×D₁₇

C₂²⋊C₈

yes

—

C₄×D₁₇

#104

yes

—

C₄×D₁₇

D₁₆

yes

characteristic

C₄×D₁₇

SD₃₂

yes

characteristic

C₄×D₁₇

SD₃₂

yes

characteristic

C₄×D₁₇

Q₃₂

yes

characteristic

C₈×C₁₇

—

C₈×C₁₇

—

C₈×C₁₇

C₄×C₈

yes

C₈×C₁₇

yes

—

—

C₄⋊C₈

yes

—

C₂×C₄×C₁₆

—

C₄×#107

—

C₂×#335

—

C₂²×C₁₇

#340

yes

characteristic

C₂×D₁₇

D₄⋊C₈

yes

—

C₂×D₁₇

yes

C₂×D₁₇

yes

C₂×D₁₇

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

Q₈⋊C₈

yes

—

Dic₁₇

yes

Dic₁₇

yes

100

C₂²×C₁₆

—

101

C₂×#107

—

102

C₂×C₄⋊C₈

—

103

C₂×C₄×C₈

—

104

C₄×C₄⋊C₄

—

105

C₄×C₁₆

—

106

C₄×C₁₆

—

107

#340

—

108

#335

—

109

#335

—

110

#335

#595

yes

characteristic, complemented

111

C₂×C₁₇

#1279

yes

characteristic

112

C₂×C₁₇

#1380

yes

characteristic

113

C₂×C₁₇

#1382

yes

characteristic

114

D₁₇

#1331

yes

—

115

D₁₇

#1332

yes

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

C₂²×C₈

—

119

C₂×C₄⋊C₄

—

120

C₂×C₄²

—

121

C₂×C₄²

—

122

C₂×C₁₆

—

123

C₂×C₁₆

—

124

#107

—

125

#107

—

126

C₄⋊C₈

—

127

C₄⋊C₈

—

128

C₄⋊C₈

—

129

C₄×C₈

—

130

C₄×C₈

—

131

C₄×C₈

—

132

C₄×C₈

C₂×#595

yes

characteristic

133

#95

—

134

C₁₇

#7171

yes

characteristic, complemented, Sylow

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

136

—

147

C₂×C₈

—

136

—

148

C₂×C₈

C₄×#595

yes

characteristic

149

C₂×C₈

C₄⋊#595

yes

characteristic

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

136

—

156

C₄²

—

136

—

157

C₄²

C₂²⋊#595

yes

characteristic

158

C₁₆

—

159

C₂³

—

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

—

136

—

172

C₂×C₄

—

136

—

173

C₂×C₄

(C₂×#595)⋊C₄

yes

characteristic

174

C₂×C₄

#10587547

yes

characteristic

175

C₂×C₄

#10587549

yes

characteristic

176

C₈

—

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

136

—

181

C₈

C₈×#595

yes

characteristic

182

C₈

#10587532

yes

characteristic

183

C₂²

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

#11763682

yes

characteristic

188

C₄

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

136

—

194

C₄

#11763674

yes

characteristic

195

C₄

#11763681

yes

characteristic

196

C₄

#11763721

yes

characteristic

197

C₄

#11763722

yes

characteristic

198

C₂

—

199

C₂

—

200

C₂

#14543618

yes

characteristic

201

C₂

#14543841

yes

characteristic

202

C₂

#14543847

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10587547
commutator	C₈×C₁₇	C₄×C₈
Frattini	C₄×C₈	C₂×#595
Fitting	C₁₇×#335	C₄
socle	C₂²×C₁₇	#340
prime radical	C₂²×D₁₇	#102
cosocle	C₄×C₈×D₁₇	C₂²
hypercenter	#335	#595
hypocenter	C₁₇	#7171
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

subgroup

G/H

center

C₂×C₄

#10587547

commutator

C₈×C₁₇

C₄×C₈

Frattini

C₄×C₈

C₂×#595

Fitting

C₁₇×#335

C₄

C₂²×C₁₇

C₂²×D₁₇

C₄×C₈×D₁₇

C₂²

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

N	H ≅ G/N	type
7. #11763695	C₄	semidirect
12. #11762562	C₄	semidirect
14. C₁₇×#335	C₄	semidirect
24. #10587534	C₈	semidirect
110. #335	#595	semidirect
134. C₁₇	#7171	semidirect

H ≅ G/N

type

7. #11763695

C₄

semidirect

12. #11762562

C₄

semidirect

14. C₁₇×#335

C₄

semidirect

24. #10587534

C₈

semidirect

110. #335

#595

semidirect

134. C₁₇

#7171

semidirect

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

subgroup	index
C₄×#10587529	2
C₄×#10587534	2
D₁₇×#335	2
#7171	17

subgroup

index

C₄×#10587529

C₄×#10587534

D₁₇×#335

#7171

Subgroups — #17948597

Conjugacy classes of subgroups

Complements

Maximal subgroups