Group #16927604 — subgroups

Subgroups — #16927604

Order 4352.

346 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 119 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	#14537718	C₂	1	1	yes	maximal, characteristic
2	#14528922	C₂	1	1	yes	maximal, characteristic
3	#14527472	C₂	1	2	yes	maximal
4	#14526659	C₂	1	2	yes	maximal
5	C₂×C₁₇×#335	C₂	1	1	yes	maximal, characteristic
6	#11763366	C₂²	1	1	yes	characteristic
7	#11762939	—	2	1	no	—
8	#11762939	C₄	1	2	yes	—
9	C₈×Dic₃₄	—	2	1	no	—
10	C₈×Dic₃₄	C₄	1	2	yes	—
11	#11762835	—	2	1	no	—
12	#11762833	C₂²	1	2	yes	—
13	#11762833	C₂²	1	1	yes	characteristic
14	#11762764	—	2	1	no	—
15	#11762574	—	2	1	no	—
16	#11762574	—	2	1	no	—
17	#11762557	—	2	2	no	—
18	#11762556	—	2	2	no	—
19	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
21	C₁₇×#335	—	2	1	no	—
22	C₁₇×#335	—	2	1	no	—
23	C₂²×C₈×C₁₇	—	2	2	no	—
24	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
27	#10587612	—	2	1	no	—
28	#10587610	—	2	1	no	—
29	#10587610	Q₈	1	2	yes	—
30	C₂×#63223	—	2	1	no	—
31	C₂×#63223	—	2	2	no	—
32	#10587556	—	2	1	no	—
33	#10587555	D₄	1	1	yes	characteristic
34	#10587555	D₄	1	1	yes	characteristic
35	C₄×Dic₃₄	—	2	1	no	—
36	C₄×Dic₃₄	C₂×C₄	1	2	yes	—
37	C₁₇×C₄⋊C₈	—	2	2	no	—
38	C₁₇×C₄⋊C₈	—	2	2	no	—
39	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
43	#10587486	—	2	2	no	—
44	#10587485	—	2	2	no	—
45	#10587485	—	2	2	no	—
46	C₈×Dic₁₇	—	2	2	no	—
47	C₄⋊#3622	—	2	1	no	—
48	C₄⋊#3622	—	2	2	no	—
49	C₄⋊#3622	—	2	2	no	—
50	C₄⋊#3622	C₂×C₄	1	2	yes	—
51	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
53	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
54	C₂×Dic₃₄	—	2	1	no	—
55	C₂×Dic₃₄	C₄⋊C₄	1	2	yes	—
56	C₂×C₈×C₁₇	—	2	2	no	—
57	C₂×C₈×C₁₇	—	2	2	no	—
58	C₂×C₈×C₁₇	—	4	2	no	—
59	C₂×C₈×C₁₇	—	8	2	no	—
60	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
65	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₁₇	#41	1	1	yes	characteristic
68	C₂²⋊Dic₁₇	—	2	2	no	—
69	C₄⋊Dic₁₇	—	2	1	no	—
70	C₄⋊Dic₁₇	—	2	1	no	—
71	C₄⋊Dic₁₇	—	2	1	no	—
72	C₄⋊Dic₁₇	C₄⋊C₄	1	2	yes	—
73	#63225	—	2	2	no	—
74	#63225	—	2	2	no	—
75	C₄×Dic₁₇	—	2	2	no	—
76	#63223	—	4	2	no	—
77	#63223	—	4	2	no	—
78	#63223	—	4	2	no	—
79	C₂×#3622	—	2	2	no	—
80	C₂×#3622	—	4	2	no	—
81	#8689	—	17	1	no	maximal, Sylow
82	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₇	—	2	1	no	—
84	C₂×C₄×C₁₇	—	2	1	no	—
85	C₂×C₄×C₁₇	—	4	1	no	—
86	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
89	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
91	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₁₇	#135	1	2	yes	—
93	C₂×C₄×C₁₇	#137	1	2	yes	—
94	C₂×Dic₁₇	—	2	2	no	—
95	C₂×Dic₁₇	—	2	2	no	—
96	Dic₃₄	—	4	1	no	—
97	Dic₃₄	—	4	1	no	—
98	Dic₃₄	—	4	2	no	—
99	C₈×C₁₇	—	2	1	no	—
100	C₈×C₁₇	—	2	1	no	—
101	C₈×C₁₇	—	2	1	no	—
102	C₈×C₁₇	—	2	1	no	—
103	C₈×C₁₇	—	8	2	no	—
104	#3622	—	4	2	no	—
105	#3622	—	8	2	no	—
106	#2960	—	17	1	no	—
107	#1837	—	17	1	no	—
108	C₂×#335	D₁₇	1	1	yes	characteristic
109	#1550	—	17	2	no	—
110	#1292	—	17	2	no	—
111	C₂²×C₁₇	—	2	1	no	—
112	C₂²×C₁₇	—	2	1	no	—
113	C₂²×C₁₇	#380	1	1	yes	characteristic
114	C₂²×C₁₇	#479	1	2	yes	—
115	C₄×C₁₇	—	2	1	no	—
116	C₄×C₁₇	—	2	1	no	—
117	C₄×C₁₇	—	2	1	no	—
118	C₄×C₁₇	#416	1	1	yes	characteristic
119	C₄×C₁₇	#419	1	1	yes	characteristic
120	C₄×C₁₇	#464	1	2	yes	—
121	C₄×C₁₇	#472	1	1	yes	characteristic
122	C₄×C₁₇	#473	1	1	yes	characteristic
123	Dic₁₇	—	4	2	no	—
124	Dic₁₇	—	4	2	no	—
125	#533	—	17	1	no	—
126	#446	—	17	2	no	—
127	#446	—	34	1	no	—
128	C₈×Q₈	—	17	2	no	—
129	C₈×Q₈	—	34	1	no	—
130	#424	—	34	1	no	—
131	#423	—	17	1	no	—
132	#423	—	17	2	no	—
133	C₂×C₄⋊C₈	C₂×D₁₇	1	2	yes	—
134	#405	—	34	1	no	—
135	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
136	#341	—	34	1	no	—
137	#341	—	34	1	no	—
138	#335	—	2	1	no	—
139	#335	—	2	1	no	—
140	#333	—	34	2	no	—
141	#332	—	34	2	no	—
142	C₂×C₁₇	—	2	2	no	—
143	C₂×C₁₇	#1805	1	1	yes	characteristic
144	C₂×C₁₇	#1813	1	1	yes	characteristic
145	C₂×C₁₇	#1816	1	1	yes	characteristic
146	C₂×M₁₆	—	34	1	no	—
147	C₂×M₁₆	—	34	2	no	—
148	C₂²×C₈	—	2	2	no	—
149	C₂²×C₈	D₆₈	1	1	yes	characteristic
150	C₂²×C₈	D₆₈	1	1	yes	characteristic
151	C₄⋊Q₈	—	17	1	no	—
152	C₄⋊Q₈	—	17	1	no	—
153	#125	—	34	1	no	—
154	C₂²⋊Q₈	—	17	2	no	—
155	C₂²⋊Q₈	—	34	1	no	—
156	C₄×Q₈	—	17	2	no	—
157	C₄×Q₈	—	34	1	no	—
158	#117	—	34	1	no	—
159	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	—	2	2	no	—
162	C₄⋊C₈	—	17	2	no	—
163	C₄⋊C₈	—	34	2	no	—
164	C₄⋊C₈	—	34	2	no	—
165	C₄⋊C₈	—	34	2	no	—
166	C₄⋊C₈	—	34	2	no	—
167	C₄⋊C₈	—	34	1	no	—
168	#97	—	34	2	no	—
169	C₄×C₈	—	34	2	no	—
170	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
171	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
172	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
173	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
174	C₁₇	#8689	1	1	yes	characteristic, complemented, Sylow
175	C₂×Q₈	—	17	2	no	—
176	C₂×Q₈	—	34	1	no	—
177	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
178	C₂²×C₄	#63254	1	1	yes	characteristic
179	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
180	M₁₆	—	68	2	no	—
181	M₁₆	—	68	2	no	—
182	M₁₆	—	68	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	8	2	no	—
187	C₂×C₈	—	34	2	no	—
188	C₂×C₈	—	68	2	no	—
189	C₂×C₈	#63227	1	1	yes	characteristic
190	C₂×C₈	#63227	1	1	yes	characteristic
191	C₂×C₈	#63227	1	1	yes	characteristic
192	C₂×C₈	#63227	1	1	yes	characteristic
193	C₄⋊C₄	—	17	2	no	—
194	C₄⋊C₄	—	34	2	no	—
195	C₄⋊C₄	—	34	1	no	—
196	C₄⋊C₄	—	34	1	no	—
197	C₄⋊C₄	—	34	1	no	—
198	C₄⋊C₄	—	34	2	no	—
199	C₂²⋊C₄	—	34	2	no	—
200	C₄²	—	34	2	no	—
201	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
202	C₄²	D₄×D₁₇	1	1	yes	characteristic
203	C₄²	#63256	1	1	yes	characteristic
204	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
205	C₂³	#10587583	1	1	yes	characteristic
206	Q₈	—	68	2	no	—
207	Q₈	—	68	1	no	—
208	Q₈	—	68	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	34	2	no	—
213	C₂×C₄	—	34	2	no	—
214	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
215	C₂×C₄	#10587578	1	1	yes	characteristic
216	C₂×C₄	#10587581	1	1	yes	characteristic
217	C₂×C₄	#10587590	1	2	yes	—
218	C₂×C₄	#10587595	1	2	yes	—
219	C₂×C₄	C₂×#63227	1	1	yes	characteristic
220	C₂×C₄	#10587624	1	1	yes	characteristic
221	C₂×C₄	#10587632	1	1	yes	characteristic
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	2	1	no	—
225	C₈	—	2	1	no	—
226	C₈	—	8	2	no	—
227	C₈	—	68	2	no	—
228	C₈	—	136	2	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	#11762666	1	1	yes	characteristic
232	C₂²	#11763117	1	2	yes	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	68	2	no	—
237	C₄	—	68	2	no	—
238	C₄	#11762806	1	1	yes	characteristic
239	C₄	#11762819	1	1	yes	characteristic
240	C₄	#11763032	1	2	yes	—
241	C₄	#11763076	1	1	yes	characteristic
242	C₄	#11763081	1	1	yes	characteristic
243	C₂	—	2	2	no	—
244	C₂	#14528800	1	1	yes	characteristic
245	C₂	#14528831	1	1	yes	characteristic
246	C₂	#14528849	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14537718

C₂

yes

maximal, characteristic

#14528922

C₂

yes

maximal, characteristic

#14527472

C₂

yes

maximal

#14526659

C₂

yes

maximal

C₂×C₁₇×#335

C₂

yes

maximal, characteristic

#11763366

C₂²

yes

characteristic

#11762939

—

#11762939

C₄

yes

—

C₈×Dic₃₄

—

C₈×Dic₃₄

C₄

yes

—

#11762835

—

#11762833

C₂²

yes

—

#11762833

C₂²

yes

—

—

—

—

—

C₂×C₁₇×C₄⋊C₈

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×#335

—

C₁₇×#335

—

C₂²×C₈×C₁₇

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂×C₄²×C₁₇

C₂³

yes

—

—

Q₈

yes

—

—

—

—

D₄

yes

characteristic

#10587555

D₄

yes

characteristic

C₄×Dic₃₄

—

C₄×Dic₃₄

C₂×C₄

yes

—

C₁₇×C₄⋊C₈

—

C₁₇×C₄⋊C₈

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

D₄

yes

characteristic

C₄×C₈×C₁₇

D₄

yes

—

—

—

C₈×Dic₁₇

—

—

—

—

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₇

#41

yes

characteristic

C₂×Dic₃₄

—

C₂×Dic₃₄

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂²⋊C₄

yes

characteristic

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄²×C₁₇

#41

yes

characteristic

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

C₄⋊C₄

yes

—

#63225

—

#63225

—

C₄×Dic₁₇

—

—

—

—

—

—

—

C₂³×C₁₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

#135

yes

—

C₂×C₄×C₁₇

#137

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

Dic₃₄

—

Dic₃₄

—

Dic₃₄

—

C₈×C₁₇

—

100

C₈×C₁₇

—

101

C₈×C₁₇

—

102

C₈×C₁₇

—

103

C₈×C₁₇

—

104

#3622

—

105

#3622

—

106

#2960

—

107

#1837

—

108

C₂×#335

D₁₇

yes

characteristic

109

#1550

—

110

#1292

—

111

C₂²×C₁₇

—

112

C₂²×C₁₇

—

113

C₂²×C₁₇

#380

yes

characteristic

114

C₂²×C₁₇

#479

yes

—

115

C₄×C₁₇

—

116

C₄×C₁₇

—

117

C₄×C₁₇

—

118

C₄×C₁₇

#416

yes

characteristic

119

C₄×C₁₇

#419

yes

characteristic

120

C₄×C₁₇

#464

yes

—

121

C₄×C₁₇

#472

yes

characteristic

122

C₄×C₁₇

#473

yes

characteristic

123

Dic₁₇

—

124

Dic₁₇

—

125

#533

—

126

#446

—

127

#446

—

128

C₈×Q₈

—

129

C₈×Q₈

—

130

#424

—

131

#423

—

132

#423

—

133

C₂×C₄⋊C₈

C₂×D₁₇

yes

—

134

#405

—

135

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

136

#341

—

137

#341

—

138

#335

—

139

#335

—

140

#333

—

141

#332

—

142

C₂×C₁₇

—

143

C₂×C₁₇

#1805

yes

characteristic

144

C₂×C₁₇

#1813

yes

characteristic

145

C₂×C₁₇

#1816

yes

characteristic

146

C₂×M₁₆

—

147

C₂×M₁₆

—

148

C₂²×C₈

—

149

C₂²×C₈

D₆₈

yes

characteristic

150

C₂²×C₈

D₆₈

yes

characteristic

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

#125

—

154

C₂²⋊Q₈

—

155

C₂²⋊Q₈

—

156

C₄×Q₈

—

157

C₄×Q₈

—

158

#117

—

159

C₂×C₄²

C₂²×D₁₇

yes

characteristic

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

#97

—

169

C₄×C₈

—

170

C₄×C₈

C₄×D₁₇

yes

characteristic

171

C₄×C₈

C₄×D₁₇

yes

characteristic

172

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

173

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

174

C₁₇

#8689

yes

characteristic, complemented, Sylow

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂²×C₄

C₂×D₆₈

yes

characteristic

178

C₂²×C₄

#63254

yes

characteristic

179

C₂²×C₄

Q₈×D₁₇

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

M₁₆

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

#63227

yes

characteristic

190

C₂×C₈

#63227

yes

characteristic

191

C₂×C₈

#63227

yes

characteristic

192

C₂×C₈

#63227

yes

characteristic

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₂²⋊C₄

—

200

C₄²

—

201

C₄²

C₂×C₄×D₁₇

yes

characteristic

202

C₄²

D₄×D₁₇

yes

characteristic

203

C₄²

#63256

yes

characteristic

204

C₄²

C₂×C₂²⋊D₁₇

yes

characteristic

205

C₂³

#10587583

yes

characteristic

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

C₄⋊C₄×D₁₇

yes

characteristic

215

C₂×C₄

#10587578

yes

characteristic

216

C₂×C₄

#10587581

yes

characteristic

217

C₂×C₄

#10587590

yes

—

218

C₂×C₄

#10587595

yes

—

219

C₂×C₄

C₂×#63227

yes

characteristic

220

C₂×C₄

#10587624

yes

characteristic

221

C₂×C₄

#10587632

yes

characteristic

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₈

—

227

C₈

—

228

C₈

—

136

—

229

C₂²

—

230

C₂²

—

231

C₂²

#11762666

yes

characteristic

232

C₂²

#11763117

yes

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

#11762806

yes

characteristic

239

C₄

#11762819

yes

characteristic

240

C₄

#11763032

yes

—

241

C₄

#11763076

yes

characteristic

242

C₄

#11763081

yes

characteristic

243

C₂

—

244

C₂

#14528800

yes

characteristic

245

C₂

#14528831

yes

characteristic

246

C₂

#14528849

yes

characteristic

	subgroup	G/H
center	C₂²	#11762666
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂×C₁₇×#335	C₂
socle	C₂²×C₁₇	#380
prime radical	C₂³×C₁₇	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂×#335	D₁₇
hypocenter	C₁₇	#8689
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#335

subgroup

G/H

center

C₂²

#11762666

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₂×C₁₇×#335

C₂

socle

C₂²×C₁₇

#380

prime radical

C₂³×C₁₇

C₂²⋊Q₈

cosocle

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#335

N	H ≅ G/N	type
174. C₁₇	#8689	semidirect

H ≅ G/N

type

174. C₁₇

#8689

semidirect

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

subgroup	index
#14537718	2
#14528922	2
#14527472	2
#14526659	2
C₂×C₁₇×#335	2
#8689	17

subgroup

index

C₂×C₁₇×#335

Subgroups — #16927604

Conjugacy classes of subgroups

Complements

Maximal subgroups