Group #16927554 — subgroups

Subgroups — #16927554

Order 4352.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14528915	C₂	1	1	yes	maximal, characteristic
3	#14527349	C₂	1	2	yes	maximal
4	#14526643	C₂	1	2	yes	maximal
5	C₁₇×#1564	C₂	1	1	yes	maximal, characteristic
6	#11763366	C₂²	1	1	yes	characteristic
7	#11762939	—	2	1	no	—
8	#11762939	C₄	1	2	yes	complemented
9	C₈×Dic₃₄	—	2	1	no	—
10	C₈×Dic₃₄	C₄	1	2	yes	complemented
11	#11762835	—	2	1	no	—
12	#11762833	C₂²	1	1	yes	characteristic
13	#11762764	—	2	1	no	—
14	#11762675	C₂²	1	2	yes	—
15	#11762572	—	2	1	no	—
16	#11762572	—	2	1	no	—
17	#11762547	—	2	4	no	—
18	C₁₇×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#335	—	2	1	no	—
21	C₁₇×#334	—	2	1	no	—
22	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
25	#10587612	—	2	1	no	—
26	C₂×C₄⋊Dic₁₇	—	2	2	no	—
27	#10587610	—	2	1	no	—
28	#10587610	D₄	1	2	yes	—
29	C₂×#63223	—	2	1	no	—
30	#10587556	—	2	1	no	—
31	#10587555	Q₈	1	1	yes	characteristic
32	#10587555	Q₈	1	1	yes	characteristic
33	C₄×Dic₃₄	—	2	1	no	—
34	C₄×Dic₃₄	C₂×C₄	1	2	yes	—
35	C₁₇×C₄⋊C₈	—	2	2	no	—
36	C₁₇×C₂²⋊C₈	—	2	2	no	—
37	C₄×C₈×C₁₇	—	2	2	no	—
38	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
42	#10587502	—	2	2	no	—
43	#10587502	—	2	2	no	—
44	#10587486	—	2	2	no	—
45	#10587485	—	2	2	no	—
46	#10587485	—	2	2	no	—
47	C₈×Dic₁₇	—	2	2	no	—
48	C₄⋊#3622	—	2	1	no	—
49	C₄⋊#3622	C₂×C₄	1	2	yes	—
50	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
53	C₂²×Dic₁₇	—	4	2	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
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	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
66	C₄²×C₁₇	#41	1	1	yes	characteristic
67	C₂²⋊Dic₁₇	—	2	2	no	—
68	C₄⋊Dic₁₇	—	2	1	no	—
69	C₄⋊Dic₁₇	—	2	1	no	—
70	C₄⋊Dic₁₇	—	2	1	no	—
71	C₄⋊Dic₁₇	—	4	2	no	—
72	C₄⋊Dic₁₇	—	4	2	no	—
73	C₄⋊Dic₁₇	C₄⋊C₄	1	2	yes	—
74	#63225	—	2	2	no	—
75	#63225	—	2	2	no	—
76	C₄×Dic₁₇	—	2	2	no	—
77	#63223	—	4	2	no	—
78	C₂×#3622	—	2	2	no	—
79	#8679	—	17	1	no	maximal, Sylow
80	C₂³×C₁₇	#121	1	1	yes	characteristic
81	C₂×C₄×C₁₇	—	4	1	no	—
82	C₂×C₄×C₁₇	—	4	1	no	—
83	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
86	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₇	#135	1	2	yes	—
90	C₂×C₄×C₁₇	#137	1	2	yes	—
91	C₂×Dic₁₇	—	2	2	no	—
92	C₂×Dic₁₇	—	2	2	no	—
93	C₂×Dic₁₇	—	8	2	no	—
94	C₂×Dic₁₇	—	8	2	no	—
95	C₂×Dic₁₇	—	8	2	no	—
96	Dic₃₄	—	4	2	no	—
97	Dic₃₄	—	4	2	no	—
98	C₈×C₁₇	—	2	1	no	—
99	C₈×C₁₇	—	2	1	no	—
100	C₈×C₁₇	—	2	1	no	—
101	C₈×C₁₇	—	2	1	no	—
102	C₈×C₁₇	—	8	2	no	—
103	#3622	—	4	2	no	—
104	#2960	—	17	1	no	—
105	#1835	—	17	1	no	—
106	#1564	D₁₇	1	1	yes	characteristic
107	#1518	—	17	2	no	—
108	#1286	—	17	2	no	—
109	C₂²×C₁₇	—	2	1	no	—
110	C₂²×C₁₇	—	2	1	no	—
111	C₂²×C₁₇	#380	1	1	yes	characteristic
112	C₂²×C₁₇	#464	1	2	yes	—
113	C₄×C₁₇	—	2	1	no	—
114	C₄×C₁₇	—	2	1	no	—
115	C₄×C₁₇	—	2	1	no	—
116	C₄×C₁₇	—	2	1	no	—
117	C₄×C₁₇	#416	1	1	yes	characteristic
118	C₄×C₁₇	#419	1	1	yes	characteristic
119	C₄×C₁₇	#479	1	2	yes	—
120	Dic₁₇	—	4	2	no	—
121	Dic₁₇	—	4	2	no	—
122	Dic₁₇	—	16	2	no	—
123	#533	—	17	1	no	—
124	#446	—	17	2	no	—
125	#446	—	34	1	no	—
126	C₈×Q₈	—	17	2	no	—
127	C₈×Q₈	—	34	1	no	—
128	#431	C₂×D₁₇	1	2	yes	—
129	#424	—	34	1	no	—
130	#423	—	17	1	no	—
131	#405	—	34	1	no	—
132	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
133	#382	—	17	2	no	—
134	#340	—	34	1	no	—
135	#340	—	34	1	no	—
136	#335	—	2	1	no	—
137	#334	—	2	1	no	—
138	#328	—	34	4	no	—
139	C₂×C₁₇	—	2	2	no	—
140	C₂×C₁₇	#1805	1	1	yes	characteristic
141	C₂×C₁₇	#1812	1	1	yes	characteristic
142	C₂×C₁₇	#1814	1	1	yes	characteristic
143	C₂×M₁₆	—	34	1	no	—
144	C₂²×C₈	D₆₈	1	1	yes	characteristic
145	C₂²×C₈	D₆₈	1	1	yes	characteristic
146	C₄⋊Q₈	—	17	1	no	—
147	C₄⋊Q₈	—	17	1	no	—
148	#125	—	34	1	no	—
149	C₂²⋊Q₈	—	17	2	no	—
150	C₂²⋊Q₈	—	34	1	no	—
151	C₄×Q₈	—	17	2	no	—
152	C₄×Q₈	—	34	1	no	—
153	#117	—	34	1	no	—
154	C₂×C₄⋊C₄	—	34	2	no	—
155	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	17	2	no	—
158	C₄⋊C₈	—	34	2	no	—
159	C₄⋊C₈	—	34	2	no	—
160	C₄⋊C₈	—	34	1	no	—
161	C₂²⋊C₈	—	2	2	no	—
162	#97	—	34	2	no	—
163	C₄×C₈	—	2	2	no	—
164	C₄×C₈	—	34	2	no	—
165	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
166	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
167	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
168	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
169	#95	—	34	2	no	—
170	#95	—	34	2	no	—
171	C₁₇	#8679	1	1	yes	characteristic, complemented, Sylow
172	C₂×Q₈	—	17	2	no	—
173	C₂×Q₈	—	34	1	no	—
174	C₂²×C₄	—	68	2	no	—
175	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
177	C₂²×C₄	#63256	1	1	yes	characteristic
178	M₁₆	—	68	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	34	2	no	—
183	C₂×C₈	#63227	1	1	yes	characteristic
184	C₂×C₈	#63227	1	1	yes	characteristic
185	C₂×C₈	#63227	1	1	yes	characteristic
186	C₂×C₈	#63227	1	1	yes	characteristic
187	C₄⋊C₄	—	17	2	no	—
188	C₄⋊C₄	—	34	2	no	—
189	C₄⋊C₄	—	34	1	no	—
190	C₄⋊C₄	—	34	1	no	—
191	C₄⋊C₄	—	34	2	no	—
192	C₄⋊C₄	—	34	1	no	—
193	C₄⋊C₄	—	68	2	no	—
194	C₄⋊C₄	—	68	2	no	—
195	C₂²⋊C₄	—	34	2	no	—
196	C₄²	—	34	2	no	—
197	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
198	C₄²	#63254	1	1	yes	characteristic
199	C₄²	Q₈×D₁₇	1	1	yes	characteristic
200	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
201	C₂³	#10587581	1	1	yes	characteristic
202	Q₈	—	68	2	no	—
203	Q₈	—	68	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	34	2	no	—
207	C₂×C₄	—	34	2	no	—
208	C₂×C₄	—	136	2	no	—
209	C₂×C₄	—	136	2	no	—
210	C₂×C₄	—	136	2	no	—
211	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
212	C₂×C₄	#10587578	1	1	yes	characteristic
213	C₂×C₄	#10587583	1	1	yes	characteristic
214	C₂×C₄	#10587590	1	2	yes	—
215	C₂×C₄	#10587595	1	2	yes	—
216	C₂×C₄	C₂×#63227	1	1	yes	characteristic
217	C₂×C₄	#10587624	1	1	yes	characteristic
218	C₂×C₄	#10587632	1	1	yes	characteristic
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	8	2	no	—
224	C₈	—	68	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#11762666	1	1	yes	characteristic
228	C₂²	#11763032	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	272	2	no	—
234	C₄	—	68	2	no	—
235	C₄	—	68	2	no	—
236	C₄	#11762806	1	1	yes	characteristic
237	C₄	#11762819	1	1	yes	characteristic
238	C₄	#11763117	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#14528800	1	1	yes	characteristic
241	C₂	#14528827	1	1	yes	characteristic
242	C₂	#14528839	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14537718

C₂

yes

maximal, characteristic

#14528915

C₂

yes

maximal, characteristic

#14527349

C₂

yes

maximal

#14526643

C₂

yes

maximal

C₁₇×#1564

C₂

yes

maximal, characteristic

#11763366

C₂²

yes

characteristic

#11762939

—

#11762939

C₄

yes

complemented

C₈×Dic₃₄

—

C₈×Dic₃₄

C₄

yes

complemented

#11762835

—

#11762833

C₂²

yes

characteristic

#11762764

—

#11762675

C₂²

yes

—

#11762572

—

#11762572

—

#11762547

—

C₁₇×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×#335

—

C₁₇×#334

—

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

D₄

yes

characteristic

C₂×C₄²×C₁₇

C₂³

yes

characteristic

#10587612

—

C₂×C₄⋊Dic₁₇

—

#10587610

—

#10587610

D₄

yes

—

C₂×#63223

—

#10587556

—

#10587555

Q₈

yes

characteristic

#10587555

Q₈

yes

characteristic

C₄×Dic₃₄

—

C₄×Dic₃₄

C₂×C₄

yes

—

C₁₇×C₄⋊C₈

—

C₁₇×C₂²⋊C₈

—

C₄×C₈×C₁₇

—

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

—

C₄⋊#3622

—

C₄⋊#3622

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

#41

yes

characteristic

C₂²×Dic₁₇

—

C₂×Dic₃₄

—

C₂×Dic₃₄

C₄⋊C₄

yes

—

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×Q₈

yes

characteristic

C₄²×C₁₇

#41

yes

characteristic

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

C₄⋊C₄

yes

—

#63225

—

#63225

—

C₄×Dic₁₇

—

—

—

—

C₂³×C₁₇

yes

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

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₇

#135

yes

—

C₂×C₄×C₁₇

#137

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

Dic₃₄

—

Dic₃₄

—

C₈×C₁₇

—

C₈×C₁₇

—

100

C₈×C₁₇

—

101

C₈×C₁₇

—

102

C₈×C₁₇

—

103

#3622

—

104

#2960

—

105

#1835

—

106

#1564

D₁₇

yes

characteristic

107

#1518

—

108

#1286

—

109

C₂²×C₁₇

—

110

C₂²×C₁₇

—

111

C₂²×C₁₇

#380

yes

characteristic

112

C₂²×C₁₇

#464

yes

—

113

C₄×C₁₇

—

114

C₄×C₁₇

—

115

C₄×C₁₇

—

116

C₄×C₁₇

—

117

C₄×C₁₇

#416

yes

characteristic

118

C₄×C₁₇

#419

yes

characteristic

119

C₄×C₁₇

#479

yes

—

120

Dic₁₇

—

121

Dic₁₇

—

122

Dic₁₇

—

123

#533

—

124

#446

—

125

#446

—

126

C₈×Q₈

—

127

C₈×Q₈

—

128

#431

C₂×D₁₇

yes

—

129

#424

—

130

#423

—

131

#405

—

132

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

133

#382

—

134

#340

—

135

#340

—

136

#335

—

137

#334

—

138

#328

—

139

C₂×C₁₇

—

140

C₂×C₁₇

#1805

yes

characteristic

141

C₂×C₁₇

#1812

yes

characteristic

142

C₂×C₁₇

#1814

yes

characteristic

143

C₂×M₁₆

—

144

C₂²×C₈

D₆₈

yes

characteristic

145

C₂²×C₈

D₆₈

yes

characteristic

146

C₄⋊Q₈

—

147

C₄⋊Q₈

—

148

#125

—

149

C₂²⋊Q₈

—

150

C₂²⋊Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

#117

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄²

C₂²×D₁₇

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₂²⋊C₈

—

162

#97

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

C₄×D₁₇

yes

characteristic

166

C₄×C₈

C₄×D₁₇

yes

characteristic

167

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

168

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

169

#95

—

170

#95

—

171

C₁₇

#8679

yes

characteristic, complemented, Sylow

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂×D₆₈

yes

characteristic

176

C₂²×C₄

D₄×D₁₇

yes

characteristic

177

C₂²×C₄

#63256

yes

characteristic

178

M₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

#63227

yes

characteristic

184

C₂×C₈

#63227

yes

characteristic

185

C₂×C₈

#63227

yes

characteristic

186

C₂×C₈

#63227

yes

characteristic

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₂²⋊C₄

—

196

C₄²

—

197

C₄²

C₂×C₄×D₁₇

yes

characteristic

198

C₄²

#63254

yes

characteristic

199

C₄²

Q₈×D₁₇

yes

characteristic

200

C₄²

C₂×C₂²⋊D₁₇

yes

characteristic

201

C₂³

#10587581

yes

characteristic

202

Q₈

—

203

Q₈

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

136

—

209

C₂×C₄

—

136

—

210

C₂×C₄

—

136

—

211

C₂×C₄

C₄⋊C₄×D₁₇

yes

characteristic

212

C₂×C₄

#10587578

yes

characteristic

213

C₂×C₄

#10587583

yes

characteristic

214

C₂×C₄

#10587590

yes

—

215

C₂×C₄

#10587595

yes

—

216

C₂×C₄

C₂×#63227

yes

characteristic

217

C₂×C₄

#10587624

yes

characteristic

218

C₂×C₄

#10587632

yes

characteristic

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₂²

—

226

C₂²

—

227

C₂²

#11762666

yes

characteristic

228

C₂²

#11763032

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

272

—

234

C₄

—

235

C₄

—

236

C₄

#11762806

yes

characteristic

237

C₄

#11762819

yes

characteristic

238

C₄

#11763117

yes

—

239

C₂

—

240

C₂

#14528800

yes

characteristic

241

C₂

#14528827

yes

characteristic

242

C₂

#14528839

yes

characteristic

	subgroup	G/H
center	C₂²	#11762666
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₁₇×#1564	C₂
socle	C₂²×C₁₇	#380
prime radical	C₂³×C₁₇	#121
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	#1564	D₁₇
hypocenter	C₁₇	#8679
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂²

#11762666

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₁₇×#1564

C₂

C₂²×C₁₇

C₂³×C₁₇

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
8. #11762939	C₄	semidirect
10. C₈×Dic₃₄	C₄	semidirect
171. C₁₇	#8679	semidirect

H ≅ G/N

type

8. #11762939

C₄

semidirect

10. C₈×Dic₃₄

C₄

semidirect

171. C₁₇

#8679

semidirect

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

subgroup	index
#14537718	2
#14528915	2
#14527349	2
#14526643	2
C₁₇×#1564	2
#8679	17

subgroup

index

C₁₇×#1564

Subgroups — #16927554

Conjugacy classes of subgroups

Complements

Maximal subgroups