Group #16945656 — subgroups

Subgroups — #16945656

Order 4352.

310 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 91 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	#14539368	C₂	1	1	yes	maximal, characteristic
2	#14530582	C₂	1	1	yes	maximal, characteristic
3	D₁₇×#335	C₂	1	1	yes	maximal, characteristic
4	#14526843	C₂	1	1	yes	maximal, characteristic, complemented
5	#14526841	C₂	1	1	yes	maximal, characteristic, complemented
6	#14526833	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1362	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763364	—	2	1	no	—
9	#11763214	C₂²	1	1	yes	characteristic
10	#11763159	—	2	1	no	—
11	#11763047	—	2	1	no	—
12	#11763047	C₄	1	2	yes	—
13	Q₁₆×Dic₁₇	—	2	1	no	—
14	Q₁₆×Dic₁₇	C₄	1	2	yes	—
15	C₄⋊C₈×D₁₇	—	2	1	no	—
16	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
17	C₄⋊#63214	C₂²	1	1	yes	characteristic
18	#11762588	—	2	1	no	—
19	C₁₆×Dic₁₇	—	2	1	no	—
20	#11762562	C₂²	1	1	yes	characteristic
21	#11762561	—	2	1	no	—
22	C₁₇×#494	C₂²	1	1	yes	characteristic
23	C₁₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₁₇×#335	C₂²	1	1	yes	characteristic
25	C₂×Q₁₆×C₁₇	—	2	1	no	—
26	C₂×Q₁₆×C₁₇	C₂×C₄	1	2	yes	—
27	C₁₇×C₄⋊Q₈	—	2	1	no	—
28	#10587632	—	2	2	no	—
29	Q₈×Dic₁₇	—	2	2	no	—
30	C₂×C₈×D₁₇	—	4	1	no	—
31	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
33	#10587583	—	4	1	no	—
34	#10587578	—	4	1	no	—
35	#10587576	—	4	1	no	—
36	#10587573	—	4	1	no	—
37	C₄²×D₁₇	D₄	1	1	yes	characteristic
38	#10587555	—	2	1	no	—
39	C₂×C₁₆×C₁₇	—	2	1	no	—
40	C₁₇×C₄⋊C₈	—	2	1	no	—
41	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
42	#10587506	—	2	2	no	—
43	#10587506	—	2	2	no	—
44	#10587489	—	2	1	no	—
45	#10587489	C₂×C₄	1	2	yes	—
46	#10587485	—	4	1	no	—
47	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
48	C₈×Dic₁₇	D₄	1	1	yes	characteristic
49	C₂×#63214	—	2	1	no	—
50	C₄⋊#3622	—	2	1	no	—
51	C₄×#3622	D₄	1	1	yes	characteristic
52	C₂×Q₈×C₁₇	—	2	2	no	—
53	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
55	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
56	C₂×Dic₃₄	—	4	1	no	—
57	Q₁₆×C₁₇	—	4	2	no	—
58	Q₁₆×C₁₇	—	4	1	no	—
59	Q₁₆×C₁₇	—	4	1	no	—
60	C₂×C₈×C₁₇	—	4	1	no	—
61	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
63	C₄⋊C₄×C₁₇	—	4	1	no	—
64	C₄⋊C₄×C₁₇	—	4	1	no	—
65	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
66	#63227	—	4	2	no	—
67	C₄⋊Dic₁₇	—	2	2	no	—
68	C₄⋊Dic₁₇	—	4	1	no	—
69	C₄⋊Dic₁₇	—	4	2	no	—
70	#63225	—	4	2	no	—
71	C₄×Dic₁₇	—	4	2	no	—
72	C₄×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₄×Dic₁₇	D₈	1	1	yes	characteristic
74	C₄×Dic₁₇	SD₁₆	1	1	yes	characteristic
75	C₂×#3622	—	4	1	no	—
76	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
78	C₈×D₁₇	—	2	1	no	—
79	C₈×D₁₇	—	2	1	no	—
80	C₈×D₁₇	—	4	1	no	—
81	C₈×D₁₇	—	8	2	no	—
82	C₁₆×C₁₇	—	4	1	no	—
83	#63214	—	4	1	no	—
84	#11949	—	17	1	no	maximal, Sylow
85	C₂²×D₁₇	#102	1	1	yes	characteristic
86	Q₈×C₁₇	—	4	2	no	—
87	Q₈×C₁₇	—	4	2	no	—
88	C₂×C₄×C₁₇	—	4	2	no	—
89	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×Dic₁₇	—	4	2	no	—
93	C₂×Dic₁₇	#102	1	1	yes	characteristic
94	C₂×Dic₁₇	#102	1	1	yes	characteristic
95	C₂×Dic₁₇	#102	1	1	yes	characteristic
96	C₄×D₁₇	—	2	1	no	—
97	C₄×D₁₇	—	2	1	no	—
98	C₄×D₁₇	—	4	1	no	—
99	C₄×D₁₇	SD₃₂	1	2	yes	—
100	C₄×D₁₇	Q₃₂	1	2	yes	—
101	Dic₃₄	—	8	2	no	—
102	C₈×C₁₇	—	2	1	no	—
103	C₈×C₁₇	—	8	1	no	—
104	C₈×C₁₇	#135	1	1	yes	characteristic
105	C₈×C₁₇	#135	1	1	yes	characteristic
106	#3622	—	2	1	no	—
107	#3622	—	2	1	no	—
108	#3622	—	8	1	no	—
109	#3170	—	17	1	no	—
110	#2162	—	17	1	no	—
111	C₂×#335	—	17	1	no	—
112	#1365	—	17	1	no	—
113	#1365	—	17	1	no	—
114	#1362	—	17	1	no	—
115	#1362	D₁₇	1	1	yes	characteristic, complemented
116	C₂²×C₁₇	C₂×#102	1	1	yes	characteristic
117	C₂×D₁₇	—	2	1	no	—
118	C₂×D₁₇	—	2	1	no	—
119	C₂×D₁₇	#358	1	2	yes	—
120	C₄×C₁₇	—	2	1	no	—
121	C₄×C₁₇	—	8	2	no	—
122	C₄×C₁₇	#413	1	1	yes	characteristic
123	C₄×C₁₇	#416	1	1	yes	characteristic
124	C₄×C₁₇	C₂×SD₃₂	1	1	yes	characteristic
125	C₄×C₁₇	C₂×Q₃₂	1	1	yes	characteristic
126	Dic₁₇	—	2	1	no	—
127	Dic₁₇	—	2	1	no	—
128	Dic₁₇	—	8	2	no	—
129	Dic₁₇	#358	1	2	yes	—
130	#533	—	34	1	no	—
131	#500	—	17	1	no	—
132	#494	C₂×D₁₇	1	1	yes	characteristic
133	#487	—	34	1	no	—
134	#467	—	17	2	no	—
135	#467	—	34	1	no	—
136	C₄×Q₁₆	—	17	2	no	—
137	C₄×Q₁₆	—	34	1	no	—
138	C₂×C₄⋊C₈	—	34	1	no	—
139	C₂×C₄×C₈	—	17	1	no	—
140	C₄⋊C₁₆	—	17	1	no	—
141	C₄⋊C₁₆	C₂×D₁₇	1	1	yes	characteristic
142	C₂²⋊C₁₆	—	34	1	no	—
143	C₄×C₁₆	—	34	1	no	—
144	#335	—	17	1	no	—
145	#335	—	34	1	no	—
146	#335	C₂×D₁₇	1	1	yes	characteristic
147	C₂×C₁₇	#1540	1	1	yes	characteristic
148	C₂×C₁₇	C₂×#358	1	1	yes	characteristic
149	C₂×C₁₇	#2148	1	1	yes	characteristic
150	D₁₇	—	2	2	no	—
151	C₂×Q₁₆	—	2	1	no	—
152	C₂×Q₁₆	C₄×D₁₇	1	2	yes	—
153	C₂²×C₈	—	17	1	no	—
154	C₂²×C₈	—	17	1	no	—
155	C₂²×C₈	—	68	1	no	—
156	C₄⋊Q₈	—	2	1	no	—
157	C₄⋊Q₈	—	34	1	no	—
158	#125	—	68	1	no	—
159	C₂²⋊Q₈	—	34	2	no	—
160	C₂²⋊Q₈	—	68	1	no	—
161	C₄×Q₈	—	34	2	no	—
162	C₄×Q₈	—	68	1	no	—
163	#117	—	68	1	no	—
164	C₂×C₄²	—	17	1	no	—
165	C₂×C₁₆	—	2	1	no	—
166	C₂×C₁₆	—	34	1	no	—
167	#107	—	17	2	no	—
168	#107	—	34	1	no	—
169	C₄⋊C₈	—	2	1	no	—
170	C₄⋊C₈	—	34	1	no	—
171	C₄⋊C₈	—	68	1	no	—
172	#103	—	34	2	no	—
173	#103	—	34	2	no	—
174	C₄×C₈	—	17	1	no	—
175	C₄×C₈	—	17	1	no	—
176	C₄×C₈	—	17	1	no	—
177	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
178	C₁₇	#11949	1	1	yes	characteristic, complemented, Sylow
179	C₂×Q₈	—	2	2	no	—
180	C₂×Q₈	—	68	1	no	—
181	C₂²×C₄	—	17	1	no	—
182	C₂²×C₄	—	17	1	no	—
183	C₂²×C₄	—	17	1	no	—
184	Q₁₆	—	4	2	no	—
185	Q₁₆	—	4	1	no	—
186	Q₁₆	—	4	1	no	—
187	C₂×C₈	—	4	1	no	—
188	C₂×C₈	—	17	1	no	—
189	C₂×C₈	—	17	1	no	—
190	C₂×C₈	—	34	1	no	—
191	C₂×C₈	—	34	1	no	—
192	C₂×C₈	—	68	1	no	—
193	C₂×C₈	—	68	1	no	—
194	C₂×C₈	—	136	2	no	—
195	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
196	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
197	C₄⋊C₄	—	4	1	no	—
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	34	2	no	—
200	C₄⋊C₄	—	68	2	no	—
201	C₄⋊C₄	—	68	2	no	—
202	C₄⋊C₄	—	68	1	no	—
203	C₂²⋊C₄	—	68	2	no	—
204	C₄²	—	17	1	no	—
205	C₄²	—	17	1	no	—
206	C₄²	—	17	1	no	—
207	C₄²	—	68	2	no	—
208	C₄²	D₄×D₁₇	1	1	yes	characteristic
209	C₁₆	—	4	1	no	—
210	C₁₆	—	68	1	no	—
211	C₂³	—	17	1	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	4	2	no	—
214	Q₈	—	136	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	17	1	no	—
217	C₂×C₄	—	17	2	no	—
218	C₂×C₄	—	17	2	no	—
219	C₂×C₄	—	17	1	no	—
220	C₂×C₄	—	17	1	no	—
221	C₂×C₄	—	34	1	no	—
222	C₂×C₄	—	34	1	no	—
223	C₂×C₄	—	68	1	no	—
224	C₂×C₄	—	68	2	no	—
225	C₂×C₄	C₂²⋊C₄×D₁₇	1	1	yes	characteristic
226	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
227	C₂×C₄	SD₁₆×D₁₇	1	1	yes	characteristic
228	C₈	—	2	1	no	—
229	C₈	—	8	1	no	—
230	C₈	—	34	1	no	—
231	C₈	—	34	1	no	—
232	C₈	—	136	1	no	—
233	C₈	#10587598	1	1	yes	characteristic
234	C₈	#10587602	1	1	yes	characteristic
235	C₂²	—	17	2	no	—
236	C₂²	—	34	1	no	—
237	C₂²	—	34	1	no	—
238	C₂²	#102×D₁₇	1	1	yes	characteristic
239	C₄	—	2	1	no	—
240	C₄	—	8	2	no	—
241	C₄	—	17	2	no	—
242	C₄	—	34	1	no	—
243	C₄	—	34	1	no	—
244	C₄	—	136	2	no	—
245	C₄	#11762790	1	1	yes	characteristic
246	C₄	#11762802	1	1	yes	characteristic
247	C₄	SD₃₂×D₁₇	1	1	yes	characteristic
248	C₄	Q₃₂×D₁₇	1	1	yes	characteristic
249	C₂	—	34	2	no	—
250	C₂	#14527430	1	1	yes	characteristic
251	C₂	D₁₇×#358	1	1	yes	characteristic
252	C₂	#14530532	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14539368

C₂

yes

maximal, characteristic

#14530582

C₂

yes

maximal, characteristic

D₁₇×#335

C₂

yes

maximal, characteristic

#14526843

C₂

yes

maximal, characteristic, complemented

#14526841

C₂

yes

maximal, characteristic, complemented

#14526833

C₂

yes

maximal, characteristic, complemented

C₁₇×#1362

C₂

yes

maximal, characteristic, complemented

#11763364

—

#11763214

C₂²

yes

—

—

C₄

yes

—

Q₁₆×Dic₁₇

—

Q₁₆×Dic₁₇

C₄

yes

—

C₄⋊C₈×D₁₇

—

C₄×C₈×D₁₇

C₂²

yes

characteristic

C₄⋊#63214

C₂²

yes

characteristic

#11762588

—

C₁₆×Dic₁₇

—

#11762562

C₂²

yes

characteristic

#11762561

—

C₁₇×#494

C₂²

yes

characteristic

C₁₇×C₄⋊C₁₆

C₂²

yes

characteristic

C₁₇×#335

C₂²

yes

characteristic

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

C₂×C₄

yes

—

C₁₇×C₄⋊Q₈

—

#10587632

—

Q₈×Dic₁₇

—

C₂×C₈×D₁₇

—

C₂×C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×D₁₇

D₄

yes

—

—

—

—

C₄²×D₁₇

D₄

yes

characteristic

#10587555

—

C₂×C₁₆×C₁₇

—

C₁₇×C₄⋊C₈

—

C₄×C₈×C₁₇

C₂³

yes

—

—

—

C₂×C₄

yes

—

#10587485

—

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

D₄

yes

—

—

D₄

yes

characteristic

C₂×Q₈×C₁₇

—

C₂×C₄×D₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₁₇

D₈

yes

characteristic

C₂×C₄×D₁₇

SD₁₆

yes

characteristic

C₂×Dic₃₄

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

C₂×D₄

yes

characteristic

#63227

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

#63225

—

C₄×Dic₁₇

—

C₄×Dic₁₇

C₂²⋊C₄

yes

characteristic

C₄×Dic₁₇

D₈

yes

characteristic

C₄×Dic₁₇

SD₁₆

yes

characteristic

C₂×#3622

—

C₂×#3622

C₂²⋊C₄

yes

characteristic

C₂×#3622

C₂²⋊C₄

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

—

C₁₆×C₁₇

—

—

—

C₂²×D₁₇

yes

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

C₂×SD₁₆

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

yes

C₂×Dic₁₇

yes

C₂×Dic₁₇

yes

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

SD₃₂

yes

—

100

C₄×D₁₇

Q₃₂

yes

—

101

Dic₃₄

—

102

C₈×C₁₇

—

103

C₈×C₁₇

—

104

C₈×C₁₇

#135

yes

characteristic

105

C₈×C₁₇

#135

yes

characteristic

106

#3622

—

107

#3622

—

108

#3622

—

109

#3170

—

110

#2162

—

111

C₂×#335

—

112

#1365

—

113

#1365

—

114

#1362

—

115

#1362

D₁₇

yes

characteristic, complemented

116

C₂²×C₁₇

C₂×#102

yes

characteristic

117

C₂×D₁₇

—

118

C₂×D₁₇

—

119

C₂×D₁₇

#358

yes

—

120

C₄×C₁₇

—

121

C₄×C₁₇

—

122

C₄×C₁₇

#413

yes

characteristic

123

C₄×C₁₇

#416

yes

characteristic

124

C₄×C₁₇

C₂×SD₃₂

yes

characteristic

125

C₄×C₁₇

C₂×Q₃₂

yes

characteristic

126

Dic₁₇

—

127

Dic₁₇

—

128

Dic₁₇

—

129

Dic₁₇

#358

yes

—

130

#533

—

131

#500

—

132

#494

C₂×D₁₇

yes

characteristic

133

#487

—

134

#467

—

135

#467

—

136

C₄×Q₁₆

—

137

C₄×Q₁₆

—

138

C₂×C₄⋊C₈

—

139

C₂×C₄×C₈

—

140

C₄⋊C₁₆

—

141

C₄⋊C₁₆

C₂×D₁₇

yes

characteristic

142

C₂²⋊C₁₆

—

143

C₄×C₁₆

—

144

#335

—

145

#335

—

146

#335

C₂×D₁₇

yes

characteristic

147

C₂×C₁₇

#1540

yes

characteristic

148

C₂×C₁₇

C₂×#358

yes

characteristic

149

C₂×C₁₇

#2148

yes

characteristic

150

D₁₇

—

151

C₂×Q₁₆

—

152

C₂×Q₁₆

C₄×D₁₇

yes

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

#125

—

159

C₂²⋊Q₈

—

160

C₂²⋊Q₈

—

161

C₄×Q₈

—

162

C₄×Q₈

—

163

#117

—

164

C₂×C₄²

—

165

C₂×C₁₆

—

166

C₂×C₁₆

—

167

#107

—

168

#107

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

#103

—

173

#103

—

174

C₄×C₈

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₄×C₈

C₂²×D₁₇

yes

characteristic

178

C₁₇

#11949

yes

characteristic, complemented, Sylow

179

C₂×Q₈

—

180

C₂×Q₈

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

Q₁₆

—

185

Q₁₆

—

186

Q₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

136

—

195

C₂×C₈

C₂×C₄×D₁₇

yes

characteristic

196

C₂×C₈

D₄×D₁₇

yes

characteristic

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

D₄×D₁₇

yes

characteristic

209

C₁₆

—

210

C₁₆

—

211

C₂³

—

212

Q₈

—

213

Q₈

—

214

Q₈

—

136

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

C₂²⋊C₄×D₁₇

yes

characteristic

226

C₂×C₄

D₈×D₁₇

yes

characteristic

227

C₂×C₄

SD₁₆×D₁₇

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

136

—

233

C₈

#10587598

yes

characteristic

234

C₈

#10587602

yes

characteristic

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

#102×D₁₇

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

136

—

245

C₄

#11762790

yes

characteristic

246

C₄

#11762802

yes

characteristic

247

C₄

SD₃₂×D₁₇

yes

characteristic

248

C₄

Q₃₂×D₁₇

yes

characteristic

249

C₂

—

250

C₂

#14527430

yes

characteristic

251

C₂

D₁₇×#358

yes

characteristic

252

C₂

#14530532

yes

characteristic

	subgroup	G/H
center	C₂²	#102×D₁₇
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₁₇×#1362	C₂
socle	C₂²×C₁₇	C₂×#102
prime radical	C₂²×D₁₇	#102
cosocle	C₄×C₈×C₁₇	C₂³
hypercenter	#1362	D₁₇
hypocenter	C₁₇	#11949
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

subgroup

G/H

center

C₂²

#102×D₁₇

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₁₇

Fitting

C₁₇×#1362

C₂

C₂²×C₁₇

C₂²×D₁₇

C₄×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

N	H ≅ G/N	type
4. #14526843	C₂	semidirect
5. #14526841	C₂	semidirect
6. #14526833	C₂	semidirect
7. C₁₇×#1362	C₂	semidirect
115. #1362	D₁₇	semidirect
178. C₁₇	#11949	semidirect

H ≅ G/N

type

4. #14526843

C₂

semidirect

5. #14526841

C₂

semidirect

6. #14526833

C₂

semidirect

7. C₁₇×#1362

C₂

semidirect

115. #1362

D₁₇

semidirect

178. C₁₇

#11949

semidirect

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

subgroup	index
#14539368	2
#14530582	2
D₁₇×#335	2
#14526843	2
#14526841	2
#14526833	2
C₁₇×#1362	2
#11949	17

subgroup

index

D₁₇×#335

C₁₇×#1362

Subgroups — #16945656

Conjugacy classes of subgroups

Complements

Maximal subgroups