Group #16934219 — subgroups

Subgroups — #16934219

Order 4352.

498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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	#14539363	C₂	1	1	yes	maximal, characteristic
2	#14529612	C₂	1	2	yes	maximal, complemented
3	#14527543	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527236	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1744	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763359	C₂²	1	2	yes	—
7	#11763214	C₄	1	1	yes	characteristic, complemented
8	#11763186	C₄	1	1	yes	characteristic, complemented
9	#11763156	C₄	1	2	yes	complemented
10	#11763045	—	2	2	no	—
11	C₄×D₁₃₆	—	2	2	no	—
12	#11762833	C₂²	1	2	yes	—
13	C₂×#10587476	—	2	4	no	—
14	#11762562	—	2	2	no	—
15	#11762538	—	2	4	no	—
16	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
18	C₄³×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#336	—	2	2	no	—
20	C₂×#63252	—	2	2	no	—
21	C₂²×C₈×C₁₇	—	2	1	no	—
22	C₂²×C₈×C₁₇	D₄	1	2	yes	—
23	C₂×C₄²×C₁₇	—	2	1	no	—
24	C₂×C₄²×C₁₇	—	2	1	no	—
25	C₂×C₄²×C₁₇	D₄	1	2	yes	—
26	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
27	#10587616	—	2	2	no	—
28	#10587616	—	2	2	no	—
29	C₂×#63223	—	2	2	no	—
30	C₂×D₁₃₆	—	2	2	no	—
31	#10587561	—	2	2	no	—
32	#10587560	C₂×C₄	1	2	yes	—
33	C₄×D₆₈	—	2	2	no	—
34	C₄×D₆₈	—	2	2	no	—
35	#10587555	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₇	—	2	1	no	—
37	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₇	D₄	1	2	yes	—
40	C₄×C₈×C₁₇	D₄	1	2	yes	—
41	#10587492	—	2	4	no	—
42	#10587489	—	2	2	no	—
43	#10587476	—	4	8	no	—
44	C₄⋊#3622	—	2	2	no	—
45	C₄⋊#3622	—	2	2	no	—
46	C₂²×C₄×C₁₇	—	2	2	no	—
47	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
50	C₂×C₂²⋊D₁₇	—	4	2	no	—
51	#63252	—	4	4	no	—
52	#63252	—	4	4	no	—
53	C₂×D₆₈	—	2	2	no	—
54	C₂×D₆₈	—	2	2	no	—
55	C₂×D₆₈	—	2	2	no	—
56	C₂×C₄×D₁₇	—	4	2	no	—
57	C₂×Dic₃₄	—	2	2	no	—
58	C₂×C₈×C₁₇	—	2	2	no	—
59	C₂×C₈×C₁₇	—	4	2	no	—
60	C₂×C₈×C₁₇	—	4	2	no	—
61	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
63	C₄²×C₁₇	—	2	2	no	—
64	C₄²×C₁₇	—	4	2	no	—
65	C₄²×C₁₇	—	4	2	no	—
66	C₄²×C₁₇	D₈	1	4	yes	complemented
67	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₇	#41	1	1	yes	characteristic
71	#63227	—	4	2	no	—
72	#63227	—	4	2	no	—
73	C₄⋊Dic₁₇	—	2	2	no	—
74	C₄⋊Dic₁₇	—	2	2	no	—
75	#63223	—	4	4	no	—
76	C₂×#3622	—	4	2	no	—
77	D₁₃₆	—	4	4	no	—
78	#9847	—	17	1	no	maximal, Sylow
79	C₂³×C₁₇	#121	1	1	yes	characteristic
80	C₂²×D₁₇	—	4	2	no	—
81	C₂×C₄×C₁₇	—	2	2	no	—
82	C₂×C₄×C₁₇	—	2	2	no	—
83	C₂×C₄×C₁₇	—	2	4	no	—
84	C₂×C₄×C₁₇	—	4	2	no	—
85	C₂×C₄×C₁₇	—	4	2	no	—
86	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
89	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
90	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
91	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
92	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
93	C₂×C₄×C₁₇	#135	1	2	yes	—
94	C₂²⋊D₁₇	—	8	4	no	—
95	C₂×Dic₁₇	—	4	2	no	—
96	D₆₈	—	4	4	no	—
97	D₆₈	—	4	4	no	—
98	D₆₈	—	4	4	no	—
99	C₄×D₁₇	—	8	2	no	—
100	C₄×D₁₇	—	8	2	no	—
101	Dic₃₄	—	4	4	no	—
102	C₈×C₁₇	—	2	2	no	—
103	C₈×C₁₇	—	2	2	no	—
104	C₈×C₁₇	—	4	2	no	—
105	#3622	—	8	2	no	—
106	#3169	—	17	1	no	—
107	#1962	—	17	2	no	—
108	#1744	D₁₇	1	1	yes	characteristic, complemented
109	#1567	—	17	1	no	—
110	#1492	—	17	2	no	—
111	C₂²×C₁₇	—	2	1	no	—
112	C₂²×C₁₇	—	2	1	no	—
113	C₂²×C₁₇	#390	1	1	yes	characteristic
114	C₂²×C₁₇	#466	1	2	yes	—
115	C₂×D₁₇	—	8	2	no	—
116	C₂×D₁₇	—	8	2	no	—
117	C₂×D₁₇	—	8	2	no	—
118	C₄×C₁₇	—	2	1	no	—
119	C₄×C₁₇	—	2	1	no	—
120	C₄×C₁₇	—	4	4	no	—
121	C₄×C₁₇	#421	1	2	yes	—
122	C₄×C₁₇	C₄×D₈	1	2	yes	—
123	C₄×C₁₇	#444	1	2	yes	—
124	C₄×C₁₇	#493	1	1	yes	characteristic
125	C₄×C₁₇	#495	1	1	yes	characteristic
126	Dic₁₇	—	8	2	no	—
127	#532	—	17	2	no	—
128	#500	—	17	1	no	—
129	#493	—	17	1	no	—
130	#486	—	17	2	no	—
131	#466	—	34	2	no	—
132	C₄×D₈	—	34	2	no	—
133	#423	—	17	2	no	—
134	C₂×#104	—	34	4	no	—
135	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
136	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
137	C₄³	C₂×D₁₇	1	1	yes	characteristic
138	#336	—	2	2	no	—
139	#335	—	34	2	no	—
140	D₄⋊C₈	—	34	4	no	—
141	C₂×C₁₇	—	2	2	no	—
142	C₂×C₁₇	#1963	1	1	yes	characteristic
143	C₂×C₁₇	#1970	1	1	yes	characteristic
144	C₂×C₁₇	#1975	1	1	yes	characteristic
145	D₁₇	—	16	2	no	—
146	C₂×#41	—	34	2	no	—
147	C₂×D₈	—	34	2	no	—
148	C₂×M₁₆	—	34	2	no	—
149	C₂²×C₈	—	2	1	no	—
150	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
151	C₄⋊Q₈	—	17	2	no	—
152	#127	—	17	2	no	—
153	#124	—	34	2	no	—
154	#121	—	34	2	no	—
155	#121	—	34	2	no	—
156	C₄×D₄	—	34	2	no	—
157	C₄×D₄	—	34	2	no	—
158	C₂×C₄²	—	2	1	no	—
159	C₂×C₄²	—	2	1	no	—
160	C₂×C₄²	D₆₈	1	2	yes	—
161	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
162	#107	—	34	2	no	—
163	C₄⋊C₈	—	34	2	no	—
164	C₄⋊C₈	—	34	2	no	—
165	#104	—	68	8	no	—
166	#102	—	34	4	no	—
167	C₄×C₈	—	2	1	no	—
168	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
169	C₄×C₈	C₄×D₁₇	1	1	yes	characteristic
170	C₄×C₈	D₆₈	1	2	yes	—
171	C₄×C₈	D₆₈	1	2	yes	—
172	C₁₇	#9847	1	1	yes	characteristic, complemented, Sylow
173	#41	—	68	4	no	—
174	#41	—	68	4	no	—
175	C₂×Q₈	—	34	2	no	—
176	C₂×D₄	—	34	2	no	—
177	C₂×D₄	—	34	2	no	—
178	C₂×D₄	—	34	2	no	—
179	C₂×D₄	—	68	2	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	68	2	no	—
182	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
183	C₂²×C₄	#63252	1	1	yes	characteristic
184	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
185	D₈	—	68	4	no	—
186	M₁₆	—	68	4	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	68	2	no	—
191	C₂×C₈	#63227	1	2	yes	—
192	C₂×C₈	#63227	1	2	yes	—
193	C₄⋊C₄	—	34	2	no	—
194	C₄⋊C₄	—	34	2	no	—
195	C₂²⋊C₄	—	68	2	no	—
196	C₂²⋊C₄	—	68	2	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	4	2	no	—
199	C₄²	—	4	2	no	—
200	C₄²	D₁₃₆	1	4	yes	complemented
201	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
202	C₄²	C₂×D₆₈	1	1	yes	characteristic
203	C₄²	C₂×D₆₈	1	1	yes	characteristic
204	C₄²	#63252	1	1	yes	characteristic
205	C₂³	—	68	2	no	—
206	C₂³	#10587616	1	1	yes	characteristic
207	Q₈	—	68	4	no	—
208	D₄	—	68	4	no	—
209	D₄	—	68	4	no	—
210	D₄	—	68	4	no	—
211	D₄	—	136	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	68	2	no	—
218	C₂×C₄	—	136	2	no	—
219	C₂×C₄	—	136	2	no	—
220	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
221	C₂×C₄	C₄×D₆₈	1	1	yes	characteristic
222	C₂×C₄	#10587560	1	1	yes	characteristic
223	C₂×C₄	#10587561	1	1	yes	characteristic
224	C₂×C₄	C₂×D₁₃₆	1	2	yes	—
225	C₂×C₄	#10587590	1	2	yes	—
226	C₂×C₄	C₂×#63227	1	1	yes	characteristic
227	C₂×C₄	#10587616	1	1	yes	characteristic
228	C₈	—	2	2	no	—
229	C₈	—	2	2	no	—
230	C₈	—	4	2	no	—
231	C₈	—	136	2	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	136	2	no	—
235	C₂²	—	136	2	no	—
236	C₂²	—	136	2	no	—
237	C₂²	#11762711	1	1	yes	characteristic
238	C₂²	#11763045	1	2	yes	—
239	C₄	—	2	1	no	—
240	C₄	—	2	1	no	—
241	C₄	—	4	4	no	—
242	C₄	—	136	2	no	—
243	C₄	#11762827	1	2	yes	—
244	C₄	C₄×D₁₃₆	1	2	yes	—
245	C₄	#11762932	1	2	yes	—
246	C₄	#11763186	1	1	yes	characteristic
247	C₄	#11763193	1	1	yes	characteristic
248	C₂	—	2	2	no	—
249	C₂	—	272	2	no	—
250	C₂	#14529616	1	1	yes	characteristic
251	C₂	#14529650	1	1	yes	characteristic
252	C₂	#14529677	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14539363

C₂

yes

maximal, characteristic

#14529612

C₂

yes

maximal, complemented

#14527543

C₂

yes

maximal, characteristic, complemented

#14527236

C₂

yes

maximal, complemented

C₁₇×#1744

C₂

yes

maximal, characteristic, complemented

#11763359

C₂²

yes

—

#11763214

C₄

yes

characteristic, complemented

#11763186

C₄

yes

characteristic, complemented

#11763156

C₄

yes

complemented

#11763045

—

C₄×D₁₃₆

—

#11762833

C₂²

yes

—

C₂×#10587476

—

#11762562

—

#11762538

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₄³×C₁₇

C₂²

yes

characteristic

C₁₇×#336

—

C₂×#63252

—

C₂²×C₈×C₁₇

—

C₂²×C₈×C₁₇

D₄

yes

—

C₂×C₄²×C₁₇

—

C₂×C₄²×C₁₇

—

C₂×C₄²×C₁₇

D₄

yes

—

C₂×C₄²×C₁₇

C₂³

yes

—

—

—

C₂×D₁₃₆

—

#10587561

—

#10587560

C₂×C₄

yes

—

C₄×D₆₈

—

C₄×D₆₈

—

#10587555

C₂×C₄

yes

—

C₄×C₈×C₁₇

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

D₄

yes

—

—

—

—

—

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₇

#41

yes

characteristic

C₂×C₂²⋊D₁₇

—

#63252

—

#63252

—

C₂×D₆₈

—

C₂×D₆₈

—

C₂×D₆₈

—

C₂×C₄×D₁₇

—

C₂×Dic₃₄

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₄²×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

D₈

yes

complemented

C₄²×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄²×C₁₇

C₂×D₄

yes

C₄²×C₁₇

yes

—

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

#63223

—

C₂×#3622

—

D₁₃₆

—

—

C₂³×C₁₇

yes

C₂²×D₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₄×D₄

yes

characteristic

C₂×C₄×C₁₇

C₄×D₄

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₂×D₈

yes

—

C₂×C₄×C₁₇

#135

yes

—

C₂²⋊D₁₇

—

C₂×Dic₁₇

—

D₆₈

—

D₆₈

—

D₆₈

—

C₄×D₁₇

—

100

C₄×D₁₇

—

101

Dic₃₄

—

102

C₈×C₁₇

—

103

C₈×C₁₇

—

104

C₈×C₁₇

—

105

#3622

—

106

#3169

—

107

#1962

—

108

#1744

D₁₇

yes

characteristic, complemented

109

#1567

—

110

#1492

—

111

C₂²×C₁₇

—

112

C₂²×C₁₇

—

113

C₂²×C₁₇

#390

yes

characteristic

114

C₂²×C₁₇

#466

yes

—

115

C₂×D₁₇

—

116

C₂×D₁₇

—

117

C₂×D₁₇

—

118

C₄×C₁₇

—

119

C₄×C₁₇

—

120

C₄×C₁₇

—

121

C₄×C₁₇

#421

yes

—

122

C₄×C₁₇

C₄×D₈

yes

—

123

C₄×C₁₇

#444

yes

—

124

C₄×C₁₇

#493

yes

characteristic

125

C₄×C₁₇

#495

yes

characteristic

126

Dic₁₇

—

127

#532

—

128

#500

—

129

#493

—

130

#486

—

131

#466

—

132

C₄×D₈

—

133

#423

—

134

C₂×#104

—

135

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

136

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

137

C₄³

C₂×D₁₇

yes

characteristic

138

#336

—

139

#335

—

140

D₄⋊C₈

—

141

C₂×C₁₇

—

142

C₂×C₁₇

#1963

yes

characteristic

143

C₂×C₁₇

#1970

yes

characteristic

144

C₂×C₁₇

#1975

yes

characteristic

145

D₁₇

—

146

C₂×#41

—

147

C₂×D₈

—

148

C₂×M₁₆

—

149

C₂²×C₈

—

150

C₂²×C₈

C₂²⋊D₁₇

yes

—

151

C₄⋊Q₈

—

152

#127

—

153

#124

—

154

#121

—

155

#121

—

156

C₄×D₄

—

157

C₄×D₄

—

158

C₂×C₄²

—

159

C₂×C₄²

—

160

C₂×C₄²

D₆₈

yes

—

161

C₂×C₄²

C₂²×D₁₇

yes

characteristic

162

#107

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

#104

—

166

#102

—

167

C₄×C₈

—

168

C₄×C₈

C₄×D₁₇

yes

characteristic

169

C₄×C₈

C₄×D₁₇

yes

characteristic

170

C₄×C₈

D₆₈

yes

—

171

C₄×C₈

D₆₈

yes

—

172

C₁₇

#9847

yes

characteristic, complemented, Sylow

173

#41

—

174

#41

—

175

C₂×Q₈

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

C₂×D₆₈

yes

characteristic

183

C₂²×C₄

#63252

yes

characteristic

184

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

185

D₈

—

186

M₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

#63227

yes

—

192

C₂×C₈

#63227

yes

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₂²⋊C₄

—

196

C₂²⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

—

200

C₄²

D₁₃₆

yes

complemented

201

C₄²

C₂×C₄×D₁₇

yes

characteristic

202

C₄²

C₂×D₆₈

yes

characteristic

203

C₄²

C₂×D₆₈

yes

characteristic

204

C₄²

#63252

yes

characteristic

205

C₂³

—

206

C₂³

#10587616

yes

characteristic

207

Q₈

—

208

D₄

—

209

D₄

—

210

D₄

—

211

D₄

—

136

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

136

—

219

C₂×C₄

—

136

—

220

C₂×C₄

C₄×D₆₈

yes

characteristic

221

C₂×C₄

C₄×D₆₈

yes

characteristic

222

C₂×C₄

#10587560

yes

characteristic

223

C₂×C₄

#10587561

yes

characteristic

224

C₂×C₄

C₂×D₁₃₆

yes

—

225

C₂×C₄

#10587590

yes

—

226

C₂×C₄

C₂×#63227

yes

characteristic

227

C₂×C₄

#10587616

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

136

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

136

—

235

C₂²

—

136

—

236

C₂²

—

136

—

237

C₂²

#11762711

yes

characteristic

238

C₂²

#11763045

yes

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

136

—

243

C₄

#11762827

yes

—

244

C₄

C₄×D₁₃₆

yes

—

245

C₄

#11762932

yes

—

246

C₄

#11763186

yes

characteristic

247

C₄

#11763193

yes

characteristic

248

C₂

—

249

C₂

—

272

—

250

C₂

#14529616

yes

characteristic

251

C₂

#14529650

yes

characteristic

252

C₂

#14529677

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10587560
commutator	C₄²×C₁₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₁₇×#1744	C₂
socle	C₂²×C₁₇	#390
prime radical	#14539363	C₂
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	#1744	D₁₇
hypocenter	C₁₇	#9847
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center

C₂×C₄

#10587560

commutator

C₄²×C₁₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₁₇×#1744

C₂

C₂²×C₁₇

C₂

C₂×C₄²×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1744

N	H ≅ G/N	type
2. #14529612	C₂	semidirect
3. #14527543	C₂	semidirect
4. #14527236	C₂	semidirect
5. C₁₇×#1744	C₂	semidirect
7. #11763214	C₄	semidirect
8. #11763186	C₄	semidirect
9. #11763156	C₄	semidirect
66. C₄²×C₁₇	D₈	semidirect
108. #1744	D₁₇	semidirect
172. C₁₇	#9847	semidirect
200. C₄²	D₁₃₆	semidirect

H ≅ G/N

type

2. #14529612

C₂

semidirect

3. #14527543

C₂

semidirect

4. #14527236

C₂

semidirect

5. C₁₇×#1744

C₂

semidirect

7. #11763214

C₄

semidirect

8. #11763186

C₄

semidirect

9. #11763156

C₄

semidirect

66. C₄²×C₁₇

D₈

semidirect

108. #1744

D₁₇

semidirect

172. C₁₇

#9847

semidirect

200. C₄²

D₁₃₆

semidirect

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

subgroup	index
#14539363	2
#14529612	2
#14527543	2
#14527236	2
C₁₇×#1744	2
#9847	17

subgroup

index

C₁₇×#1744

Subgroups — #16934219

Conjugacy classes of subgroups

Complements

Maximal subgroups