Group #16951774 — subgroups

Subgroups — #16951774

Order 4352.

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

normal subgroups only

This group has 490 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	#14541887	C₂	1	1	yes	maximal, characteristic, complemented
2	#14530500	C₂	1	2	yes	maximal, complemented
3	#14528830	C₂	1	1	yes	maximal, characteristic, complemented
4	#14526885	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3058	C₂	1	1	yes	maximal, characteristic
6	#11763226	—	2	4	no	—
7	C₂×#10587483	—	2	2	no	—
8	C₂×#10587483	C₂²	1	2	yes	—
9	#11762847	C₂²	1	2	yes	—
10	#11762783	—	2	1	no	—
11	#11762610	—	2	4	no	—
12	#11762566	—	2	1	no	—
13	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
15	C₁₇×#535	—	2	1	no	—
16	C₁₇×#469	C₄	1	4	yes	complemented
17	C₁₇×#466	—	2	2	no	—
18	C₁₇×#427	C₂²	1	1	yes	characteristic
19	C₁₇×#418	—	2	1	no	—
20	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
21	C₂²×D₄×C₁₇	—	2	1	no	—
22	C₂×D₈×C₁₇	—	2	2	no	—
23	C₂×D₈×C₁₇	—	2	1	no	—
24	C₂×D₈×C₁₇	—	2	2	no	—
25	C₂×D₈×C₁₇	C₂×C₄	1	2	yes	—
26	C₁₇×#131	—	2	2	no	—
27	C₁₇×#131	—	2	2	no	—
28	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
29	C₂×M₁₆×C₁₇	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₇	D₄	1	2	yes	—
31	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
32	C₁₇×#127	—	4	1	no	—
33	C₁₇×#124	—	4	1	no	—
34	C₁₇×#121	—	2	4	no	—
35	C₁₇×#120	—	4	2	no	—
36	C₁₇×#117	—	2	1	no	—
37	#10587612	—	2	2	no	—
38	C₁₇×#107	—	2	1	no	—
39	C₁₇×#106	C₂×C₄	1	2	yes	—
40	C₁₇×#102	—	2	4	no	—
41	#10587505	—	4	2	no	—
42	#10587489	—	2	2	no	—
43	#10587488	—	2	2	no	—
44	#10587483	—	2	4	no	—
45	#10587483	—	2	2	no	—
46	#10587483	—	2	2	no	—
47	C₂×#63214	—	2	4	no	—
48	C₂×#63214	D₄	1	4	yes	complemented
49	C₂⁴×C₁₇	—	4	1	no	—
50	#41×C₁₇	—	2	2	no	—
51	#41×C₁₇	—	2	2	no	—
52	C₂×Q₈×C₁₇	SD₁₆	1	1	yes	characteristic
53	C₂×D₄×C₁₇	—	2	2	no	—
54	C₂×D₄×C₁₇	—	4	4	no	—
55	C₂×D₄×C₁₇	—	4	2	no	—
56	C₂×D₄×C₁₇	—	4	1	no	—
57	C₂×D₄×C₁₇	—	4	2	no	—
58	C₂×D₄×C₁₇	D₈	1	2	yes	—
59	C₂×D₄×C₁₇	SD₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₁₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
62	D₈×C₁₇	—	2	4	no	—
63	D₈×C₁₇	—	4	1	no	—
64	D₈×C₁₇	—	4	1	no	—
65	M₁₆×C₁₇	—	2	2	no	—
66	M₁₆×C₁₇	—	2	4	no	—
67	C₂×C₈×C₁₇	—	2	2	no	—
68	C₂×C₈×C₁₇	—	2	2	no	—
69	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₇	#41	1	2	yes	—
74	C₄⋊C₄×C₁₇	—	2	2	no	—
75	C₂²⋊C₄×C₁₇	—	4	1	no	—
76	C₂²⋊C₄×C₁₇	—	4	4	no	—
77	C₄²×C₁₇	—	4	1	no	—
78	C₂²⋊Dic₁₇	—	4	2	no	—
79	C₄⋊Dic₁₇	—	4	2	no	—
80	C₄×Dic₁₇	—	4	2	no	—
81	#63214	—	2	4	no	—
82	#13074	—	17	1	no	maximal, Sylow
83	C₂³×C₁₇	—	4	2	no	—
84	C₂³×C₁₇	—	8	2	no	—
85	C₂³×C₁₇	—	16	2	no	—
86	C₂³×C₁₇	#102	1	2	yes	—
87	C₂³×C₁₇	C₂×D₈	1	1	yes	characteristic
88	Q₈×C₁₇	—	2	2	no	—
89	D₄×C₁₇	—	2	4	no	—
90	D₄×C₁₇	—	2	2	no	—
91	D₄×C₁₇	—	4	2	no	—
92	D₄×C₁₇	—	4	2	no	—
93	D₄×C₁₇	—	8	2	no	—
94	D₄×C₁₇	—	16	4	no	—
95	C₂×C₄×C₁₇	—	2	2	no	—
96	C₂×C₄×C₁₇	—	2	2	no	—
97	C₂×C₄×C₁₇	—	4	2	no	—
98	C₂×C₄×C₁₇	#102	1	2	yes	—
99	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₁₇	#121	1	2	yes	—
101	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₇	#135	1	2	yes	—
103	C₂×Dic₁₇	—	8	2	no	—
104	C₈×C₁₇	—	2	2	no	—
105	C₈×C₁₇	C₄×D₄	1	2	yes	—
106	C₈×C₁₇	#120	1	1	yes	characteristic
107	C₈×C₁₇	#123	1	1	yes	characteristic
108	#3407	—	17	1	no	—
109	#3058	D₁₇	1	1	yes	characteristic
110	#2140	—	17	2	no	—
111	#1812	—	17	1	no	—
112	#1384	—	17	2	no	—
113	C₂²×C₁₇	—	2	2	no	—
114	C₂²×C₁₇	—	4	1	no	—
115	C₂²×C₁₇	—	4	2	no	—
116	C₂²×C₁₇	—	8	4	no	—
117	C₂²×C₁₇	—	8	2	no	—
118	C₂²×C₁₇	—	16	4	no	—
119	C₂²×C₁₇	C₂×#102	1	1	yes	characteristic
120	C₂²×C₁₇	#466	1	2	yes	—
121	C₄×C₁₇	—	2	2	no	—
122	C₄×C₁₇	—	8	2	no	—
123	C₄×C₁₇	#386	1	1	yes	characteristic
124	C₄×C₁₇	#416	1	1	yes	characteristic
125	C₄×C₁₇	#465	1	2	yes	—
126	Dic₁₇	—	16	2	no	—
127	C₂²×D₈	C₂×D₁₇	1	1	yes	characteristic
128	C₂×#131	C₂×D₁₇	1	1	yes	characteristic
129	#535	—	2	1	no	—
130	#504	—	34	4	no	—
131	C₂×M₃₂	—	17	2	no	—
132	C₂×M₃₂	—	34	2	no	—
133	#469	Dic₁₇	1	4	yes	complemented
134	#466	—	2	2	no	—
135	#427	—	17	2	no	—
136	#427	C₂×D₁₇	1	1	yes	characteristic
137	#418	—	2	1	no	—
138	#410	—	34	1	no	—
139	#357	—	34	4	no	—
140	H(3,ℤ/4)	—	34	1	no	—
141	C₂×C₁₇	—	2	2	no	—
142	C₂×C₁₇	—	2	1	no	—
143	C₂×C₁₇	—	4	2	no	—
144	C₂×C₁₇	—	16	2	no	—
145	C₂×C₁₇	#1893	1	1	yes	characteristic
146	C₂×#41	C₂²⋊D₁₇	1	1	yes	characteristic
147	C₂²×D₄	—	2	1	no	—
148	C₂×D₈	—	2	2	no	—
149	C₂×D₈	—	2	2	no	—
150	C₂×D₈	—	2	1	no	—
151	C₂×D₈	C₂×Dic₁₇	1	2	yes	—
152	#131	—	2	2	no	—
153	#131	—	2	2	no	—
154	C₂×M₁₆	C₂×Dic₁₇	1	2	yes	—
155	C₂×M₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
156	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
157	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
158	#127	—	4	1	no	—
159	#124	—	4	1	no	—
160	#121	—	2	4	no	—
161	#120	—	4	2	no	—
162	#117	—	2	1	no	—
163	#117	—	34	2	no	—
164	M₃₂	—	34	4	no	—
165	M₃₂	—	34	2	no	—
166	M₃₂	—	34	2	no	—
167	C₂×C₁₆	—	17	4	no	—
168	C₂×C₁₆	—	34	4	no	—
169	#107	—	2	1	no	—
170	#107	—	34	2	no	—
171	#106	—	34	2	no	—
172	#106	C₂×Dic₁₇	1	2	yes	—
173	#102	—	2	4	no	—
174	#99	—	68	2	no	—
175	C₁₇	#13074	1	1	yes	characteristic, complemented, Sylow
176	C₂⁴	—	4	1	no	—
177	#41	—	2	2	no	—
178	#41	—	2	2	no	—
179	C₂×Q₈	#63229	1	1	yes	characteristic
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	—	4	4	no	—
182	C₂×D₄	—	4	1	no	—
183	C₂×D₄	—	4	2	no	—
184	C₂×D₄	—	4	2	no	—
185	C₂×D₄	#63228	1	2	yes	—
186	C₂×D₄	#63229	1	1	yes	characteristic
187	C₂²×C₄	C₂²⋊Dic₁₇	1	2	yes	—
188	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
189	D₈	—	2	4	no	—
190	D₈	—	4	1	no	—
191	D₈	—	4	1	no	—
192	M₁₆	—	2	2	no	—
193	M₁₆	—	2	4	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
197	C₂×C₈	D₄×D₁₇	1	2	yes	—
198	C₂×C₈	#63254	1	2	yes	—
199	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	68	2	no	—
203	C₂²⋊C₄	—	4	1	no	—
204	C₂²⋊C₄	—	4	4	no	—
205	C₂²⋊C₄	—	68	2	no	—
206	C₄²	—	4	1	no	—
207	C₄²	—	68	2	no	—
208	C₁₆	—	34	4	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	8	2	no	—
211	C₂³	—	16	2	no	—
212	C₂³	#10587503	1	2	yes	—
213	C₂³	C₂×#63228	1	1	yes	characteristic
214	Q₈	—	2	2	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	2	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	8	2	no	—
220	D₄	—	16	4	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	136	2	no	—
225	C₂×C₄	#10587503	1	2	yes	—
226	C₂×C₄	C₂×#63229	1	1	yes	characteristic
227	C₂×C₄	#10587625	1	2	yes	—
228	C₂×C₄	#10587636	1	2	yes	—
229	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
230	C₈	—	2	2	no	—
231	C₈	D₄×Dic₁₇	1	2	yes	—
232	C₈	#10587621	1	1	yes	characteristic
233	C₈	#10587623	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	8	4	no	—
238	C₂²	—	8	2	no	—
239	C₂²	—	16	4	no	—
240	C₂²	C₂×#10587503	1	1	yes	characteristic
241	C₂²	#11763043	1	2	yes	—
242	C₄	—	2	2	no	—
243	C₄	—	8	2	no	—
244	C₄	—	272	2	no	—
245	C₄	#11762689	1	1	yes	characteristic
246	C₄	#11762805	1	1	yes	characteristic
247	C₄	#11763036	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	2	no	—
250	C₂	—	4	2	no	—
251	C₂	—	16	2	no	—
252	C₂	#14529213	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14541887

C₂

yes

maximal, characteristic, complemented

#14530500

C₂

yes

maximal, complemented

#14528830

C₂

yes

maximal, characteristic, complemented

#14526885

C₂

yes

maximal, complemented

C₁₇×#3058

C₂

yes

maximal, characteristic

#11763226

—

C₂×#10587483

—

C₂×#10587483

C₂²

yes

—

#11762847

C₂²

yes

—

#11762783

—

#11762610

—

#11762566

—

C₂²×D₈×C₁₇

C₂²

yes

characteristic

C₂×C₁₇×#131

C₂²

yes

characteristic

C₁₇×#535

—

C₁₇×#469

C₄

yes

complemented

C₁₇×#466

—

C₁₇×#427

C₂²

yes

characteristic

C₁₇×#418

—

C₂×#41×C₁₇

D₄

yes

characteristic

C₂²×D₄×C₁₇

—

C₂×D₈×C₁₇

—

C₂×D₈×C₁₇

—

C₂×D₈×C₁₇

—

C₂×D₈×C₁₇

C₂×C₄

yes

—

C₁₇×#131

—

C₁₇×#131

—

C₂×M₁₆×C₁₇

C₂×C₄

yes

—

C₂×M₁₆×C₁₇

D₄

yes

characteristic

C₂²×C₈×C₁₇

D₄

yes

—

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₁₇×#127

—

C₁₇×#124

—

C₁₇×#121

—

C₁₇×#120

—

C₁₇×#117

—

#10587612

—

C₁₇×#107

—

C₁₇×#106

C₂×C₄

yes

—

C₁₇×#102

—

—

—

—

—

—

—

—

D₄

yes

complemented

C₂⁴×C₁₇

—

#41×C₁₇

—

#41×C₁₇

—

C₂×Q₈×C₁₇

SD₁₆

yes

characteristic

C₂×D₄×C₁₇

—

C₂×D₄×C₁₇

—

C₂×D₄×C₁₇

—

C₂×D₄×C₁₇

—

C₂×D₄×C₁₇

—

C₂×D₄×C₁₇

D₈

yes

—

C₂×D₄×C₁₇

SD₁₆

yes

characteristic

C₂²×C₄×C₁₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

D₈×C₁₇

—

D₈×C₁₇

—

D₈×C₁₇

—

M₁₆×C₁₇

—

M₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂²⋊C₄

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

#41

yes

—

C₄⋊C₄×C₁₇

—

C₂²⋊C₄×C₁₇

—

C₂²⋊C₄×C₁₇

—

C₄²×C₁₇

—

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄×Dic₁₇

—

#63214

—

#13074

—

maximal, Sylow

C₂³×C₁₇

—

C₂³×C₁₇

—

C₂³×C₁₇

—

C₂³×C₁₇

#102

yes

—

C₂³×C₁₇

C₂×D₈

yes

characteristic

Q₈×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#102

yes

—

C₂×C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₁₇

#121

yes

—

101

C₂×C₄×C₁₇

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₁₇

#135

yes

—

103

C₂×Dic₁₇

—

104

C₈×C₁₇

—

105

C₈×C₁₇

C₄×D₄

yes

—

106

C₈×C₁₇

#120

yes

characteristic

107

C₈×C₁₇

#123

yes

characteristic

108

#3407

—

109

#3058

D₁₇

yes

characteristic

110

#2140

—

111

#1812

—

112

#1384

—

113

C₂²×C₁₇

—

114

C₂²×C₁₇

—

115

C₂²×C₁₇

—

116

C₂²×C₁₇

—

117

C₂²×C₁₇

—

118

C₂²×C₁₇

—

119

C₂²×C₁₇

C₂×#102

yes

characteristic

120

C₂²×C₁₇

#466

yes

—

121

C₄×C₁₇

—

122

C₄×C₁₇

—

123

C₄×C₁₇

#386

yes

characteristic

124

C₄×C₁₇

#416

yes

characteristic

125

C₄×C₁₇

#465

yes

—

126

Dic₁₇

—

127

C₂²×D₈

C₂×D₁₇

yes

characteristic

128

C₂×#131

C₂×D₁₇

yes

characteristic

129

#535

—

130

#504

—

131

C₂×M₃₂

—

132

C₂×M₃₂

—

133

#469

Dic₁₇

yes

complemented

134

#466

—

135

#427

—

136

#427

C₂×D₁₇

yes

characteristic

137

#418

—

138

#410

—

139

#357

—

140

H(3,ℤ/4)

—

141

C₂×C₁₇

—

142

C₂×C₁₇

—

143

C₂×C₁₇

—

144

C₂×C₁₇

—

145

C₂×C₁₇

#1893

yes

characteristic

146

C₂×#41

C₂²⋊D₁₇

yes

characteristic

147

C₂²×D₄

—

148

C₂×D₈

—

149

C₂×D₈

—

150

C₂×D₈

—

151

C₂×D₈

C₂×Dic₁₇

yes

—

152

#131

—

153

#131

—

154

C₂×M₁₆

C₂×Dic₁₇

yes

—

155

C₂×M₁₆

C₂²⋊D₁₇

yes

characteristic

156

C₂²×C₈

C₂²⋊D₁₇

yes

—

157

C₂²×C₈

C₂²×D₁₇

yes

characteristic

158

#127

—

159

#124

—

160

#121

—

161

#120

—

162

#117

—

163

#117

—

164

M₃₂

—

165

M₃₂

—

166

M₃₂

—

167

C₂×C₁₆

—

168

C₂×C₁₆

—

169

#107

—

170

#107

—

171

#106

—

172

#106

C₂×Dic₁₇

yes

—

173

#102

—

174

#99

—

175

C₁₇

#13074

yes

characteristic, complemented, Sylow

176

C₂⁴

—

177

#41

—

178

#41

—

179

C₂×Q₈

#63229

yes

characteristic

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

#63228

yes

—

186

C₂×D₄

#63229

yes

characteristic

187

C₂²×C₄

C₂²⋊Dic₁₇

yes

—

188

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

189

D₈

—

190

D₈

—

191

D₈

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

C₂²⋊Dic₁₇

yes

—

197

C₂×C₈

D₄×D₁₇

yes

—

198

C₂×C₈

#63254

yes

—

199

C₂×C₈

C₂²×Dic₁₇

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

206

C₄²

—

207

C₄²

—

208

C₁₆

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

#10587503

yes

—

213

C₂³

C₂×#63228

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

D₄

—

220

D₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

136

—

225

C₂×C₄

#10587503

yes

—

226

C₂×C₄

C₂×#63229

yes

characteristic

227

C₂×C₄

#10587625

yes

—

228

C₂×C₄

#10587636

yes

—

229

C₂×C₄

C₂×C₂²⋊Dic₁₇

yes

characteristic

230

C₈

—

231

C₈

D₄×Dic₁₇

yes

—

232

C₈

#10587621

yes

characteristic

233

C₈

#10587623

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

C₂×#10587503

yes

characteristic

241

C₂²

#11763043

yes

—

242

C₄

—

243

C₄

—

244

C₄

—

272

—

245

C₄

#11762689

yes

characteristic

246

C₄

#11762805

yes

characteristic

247

C₄

#11763036

yes

—

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

—

252

C₂

#14529213

yes

characteristic

	subgroup	G/H
center	C₂	#14529213
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting, prime radical	C₁₇×#3058	C₂
socle	C₂×C₁₇	#1893
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#3058	D₁₇
hypocenter	C₁₇	#13074
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3058

subgroup

G/H

center

C₂

#14529213

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting, prime radical

C₁₇×#3058

C₂

socle

C₂×C₁₇

#1893

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3058

N	H ≅ G/N	type
1. #14541887	C₂	semidirect
2. #14530500	C₂	semidirect
3. #14528830	C₂	semidirect
4. #14526885	C₂	semidirect
16. C₁₇×#469	C₄	semidirect
48. C₂×#63214	D₄	semidirect
133. #469	Dic₁₇	semidirect
175. C₁₇	#13074	semidirect

H ≅ G/N

type

1. #14541887

C₂

semidirect

2. #14530500

C₂

semidirect

3. #14528830

C₂

semidirect

4. #14526885

C₂

semidirect

16. C₁₇×#469

C₄

semidirect

48. C₂×#63214

D₄

semidirect

133. #469

Dic₁₇

semidirect

175. C₁₇

#13074

semidirect

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

subgroup	index
#14541887	2
#14530500	2
#14528830	2
#14526885	2
C₁₇×#3058	2
#13074	17

subgroup

index

C₁₇×#3058

Subgroups — #16951774

Conjugacy classes of subgroups

Complements

Maximal subgroups