Finite Group Databasebeta

← C17×#11511 #16869255

Subgroups — C17×#11511 #16869255

Order 4352.

490 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#382C211yesmaximal, characteristic
2C17×#1463C212yesmaximal
3C17×#1324C214yesmaximal, complemented
4C22×C4⋊C4×C17C411yescharacteristic
5C22×C4⋊C4×C17C2211yescharacteristic
6C22×C42×C17C411yescharacteristic
7C17×#407—22no—
8C17×#382—22no—
9C17×#382C412yes—
10C17×#382C2212yes—
11C2×C17×#95—22no—
12C17×#324—22no—
13C17×#324C2214yes—
14C23×C4×C17—21no—
15C23×C4×C17—21no—
16C23×C4×C17C2×C411yescharacteristic
17C23×C4×C17D412yes—
18C2×M16×C17—42no—
19C2×C4⋊C4×C17—21no—
20C2×C4⋊C4×C17—41no—
21C2×C4⋊C4×C17—41no—
22C2×C4⋊C4×C17—41no—
23C2×C4⋊C4×C17—41no—
24C2×C4⋊C4×C17C2×C412yes—
25C2×C4⋊C4×C17C2×C411yescharacteristic
26C2×C4⋊C4×C17D412yes—
27C2×C4⋊C4×C17C2311yescharacteristic
28C2×C42×C17—21no—
29C2×C42×C17—24no—
30C2×C42×C17C2×C412yes—
31C17×C22⋊C8—24no—
32C17×C22⋊C8—42no—
33C17×#95—24no—
34C17×#95—24no—
35C24×C17C22⋊C411yescharacteristic
36C22×C4×C17—21no—
37C22×C4×C17—21no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—24no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17—22no—
44C22×C4×C17—22no—
45C22×C4×C17—42no—
46C22×C4×C17—42no—
47C22×C4×C17—44no—
48C22×C4×C17—44no—
49C22×C4×C17—41no—
50C22×C4×C17—41no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C412yes—
53C22×C4×C17C22×C411yescharacteristic
54C22×C4×C17C2×D412yes—
55M16×C17—84no—
56C2×C8×C17—44no—
57C4⋊C4×C17—41no—
58C4⋊C4×C17—42no—
59C4⋊C4×C17—41no—
60C4⋊C4×C17—42no—
61C4⋊C4×C17—42no—
62C42×C17—24no—
63C42×C17—22no—
64C42×C17M1614yescomplemented
65#11511C1711yesmaximal, characteristic, direct product factor, Sylow
66C23×C17—22no—
67C23×C17—22no—
68C23×C17—21no—
69C23×C17—21no—
70C23×C17#9911yescharacteristic
71C23×C17#9911yescharacteristic
72C23×C17C2×C22⋊C411yescharacteristic
73C2×C4×C17—24no—
74C2×C4×C17—24no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—24no—
80C2×C4×C17—22no—
81C2×C4×C17—22no—
82C2×C4×C17—48no—
83C2×C4×C17—42no—
84C2×C4×C17—42no—
85C2×C4×C17—44no—
86C2×C4×C17—42no—
87C2×C4×C17—42no—
88C2×C4×C17—44no—
89C2×C4×C17—42no—
90C2×C4×C17—82no—
91C2×C4×C17—82no—
92C2×C4×C17—82no—
93C2×C4×C17#10112yes—
94C2×C4×C17C2×M1612yes—
95C8×C17—84no—
96C2×#382C2×C1711yescharacteristic
97#1463C2×C1712yes—
98#1324C2×C1714yescomplemented
99C22×C17—24no—
100C22×C17—24no—
101C22×C17—21no—
102C22×C17—21no—
103C22×C17—21no—
104C22×C17—21no—
105C22×C17—21no—
106C22×C17—21no—
107C22×C17#35412yes—
108C22×C17#35512yes—
109C22×C17#40711yescharacteristic
110C22×C17C2×#9911yescharacteristic
111C22×C17C2×#10111yescharacteristic
112C4×C17—22no—
113C4×C17—22no—
114C4×C17—44no—
115C4×C17—42no—
116C4×C17—42no—
117C4×C17—82no—
118C22×C4⋊C4C4×C1711yescharacteristic
119C22×C4⋊C4C22×C1711yescharacteristic
120C22×C42C4×C1711yescharacteristic
121#407—22no—
122#382—22no—
123#382C4×C1712yes—
124#382C22×C1712yes—
125C2×#95—22no—
126#324—22no—
127#324C22×C1714yes—
128C2×C17—21no—
129C2×C17—22no—
130C2×C17—22no—
131C2×C17—21no—
132C2×C17#146311yescharacteristic
133C2×C17C2×#35411yescharacteristic
134C2×C17C2×#35511yescharacteristic
135C23×C4—21no—
136C23×C4—21no—
137C23×C4C2×C4×C1711yescharacteristic
138C23×C4D4×C1712yes—
139C2×M16—42no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4C2×C4×C1712yes—
146C2×C4⋊C4C2×C4×C1711yescharacteristic
147C2×C4⋊C4D4×C1712yes—
148C2×C4⋊C4C23×C1711yescharacteristic
149C2×C42—21no—
150C2×C42—24no—
151C2×C42C2×C4×C1712yes—
152C22⋊C8—24no—
153C22⋊C8—42no—
154#95—24no—
155#95—24no—
156C17#1151111yescharacteristic, direct product factor, Sylow
157C24C22⋊C4×C1711yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—24no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—44no—
170C22×C4—44no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4C22⋊C4×C1711yescharacteristic
174C22×C4C22⋊C4×C1712yes—
175C22×C4C22×C4×C1711yescharacteristic
176C22×C4C2×D4×C1712yes—
177M16—84no—
178C2×C8—44no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C42—24no—
185C42—22no—
186C42M16×C1714yescomplemented
187C23—22no—
188C23—22no—
189C23—21no—
190C23—21no—
191C23C17×#9911yescharacteristic
192C23C17×#9911yescharacteristic
193C23C2×C22⋊C4×C1711yescharacteristic
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—48no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4C17×#10112yes—
215C2×C4C2×M16×C1712yes—
216C8—84no—
217C22—24no—
218C22—24no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22C17×#35412yes—
226C22C17×#35512yes—
227C22C17×#40711yescharacteristic
228C22C2×C17×#9911yescharacteristic
229C22C2×C17×#10111yescharacteristic
230C4—22no—
231C4—22no—
232C4—44no—
233C4—42no—
234C4—42no—
235C4—82no—
236C2—21no—
237C2—22no—
238C2—22no—
239C2—21no—
240C2C17×#146311yescharacteristic
241C2C2×C17×#35411yescharacteristic
242C2C2×C17×#35511yescharacteristic
subgroupG/H
center, socleC22×C17C2×#99
commutatorC22×C4C22×C4×C17
Frattini, cosocleC2×C4⋊C4C23×C17
prime radicalC24×C17C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C24×C17 ◁ C22×C4⋊C4×C17 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C17×#1324C2semidirect
64. C42×C17M16semidirect
65. #11511C17direct (N × H)
98. #1324C2×C17semidirect
156. C17#11511direct (N × H)
186. C42M16×C17semidirect

Maximal subgroups

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

subgroupindex
C2×C17×#3822
C17×#14632
C17×#13242
#1151117