Finite Group Databasebeta

← C17×#11505 #16869249

Subgroups — C17×#11505 #16869249

Order 4352.

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

normal subgroups only

This group has 814 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×#390C211yesmaximal, characteristic
2C17×#1463C212yesmaximal, complemented
3C17×#1318C214yesmaximal, complemented
4C23×D4×C17C411yescharacteristic
5C22×C4⋊C4×C17C2211yescharacteristic
6C22×C22⋊C4×C17—22no—
7C22×C42×C17C411yescharacteristic
8C17×#407—22no—
9C17×#390—22no—
10C17×#390C412yes—
11C17×#390C2212yes—
12C17×#324—22no—
13C17×#324C2214yescomplemented
14C25×C17—21no—
15C22×D4×C17—24no—
16C22×D4×C17—21no—
17C22×D4×C17—41no—
18C22×D4×C17—41no—
19C22×D4×C17—42no—
20C22×D4×C17C2×C412yes—
21C23×C4×C17—21no—
22C23×C4×C17C2×C411yescharacteristic
23C23×C4×C17D412yes—
24C2×M16×C17—42no—
25C2×C4⋊C4×C17—41no—
26C2×C4⋊C4×C17—41no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17D412yes—
29C2×C4⋊C4×C17C2311yescharacteristic
30C2×C22⋊C4×C17—24no—
31C2×C22⋊C4×C17—24no—
32C2×C22⋊C4×C17—48no—
33C2×C42×C17—21no—
34C2×C42×C17—42no—
35C2×C42×C17C2×C412yes—
36C17×C22⋊C8—24no—
37C17×C22⋊C8—42no—
38C24×C17—24no—
39C24×C17—22no—
40C24×C17—42no—
41C24×C17—44no—
42C24×C17—44no—
43C24×C17—41no—
44C24×C17—41no—
45C24×C17C22⋊C411yescharacteristic
46C2×D4×C17—24no—
47C2×D4×C17—22no—
48C2×D4×C17—42no—
49C2×D4×C17—42no—
50C2×D4×C17—48no—
51C2×D4×C17—48no—
52C2×D4×C17—42no—
53C2×D4×C17—42no—
54C2×D4×C17M1614yescomplemented
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—22no—
58C22×C4×C17—22no—
59C22×C4×C17—24no—
60C22×C4×C17—22no—
61C22×C4×C17—22no—
62C22×C4×C17—22no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17—44no—
66C22×C4×C17C22⋊C411yescharacteristic
67C22×C4×C17C22⋊C412yes—
68C22×C4×C17C22×C411yescharacteristic
69C22×C4×C17C2×D412yes—
70M16×C17—84no—
71C2×C8×C17—44no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—42no—
74C4⋊C4×C17—41no—
75C22⋊C4×C17—48no—
76C22⋊C4×C17—48no—
77C42×C17—42no—
78C42×C17—42no—
79#11505C1711yesmaximal, characteristic, direct product factor, Sylow
80C23×C17—22no—
81C23×C17—22no—
82C23×C17—21no—
83C23×C17—21no—
84C23×C17—24no—
85C23×C17—44no—
86C23×C17—44no—
87C23×C17—44no—
88C23×C17—416no—
89C23×C17—44no—
90C23×C17—42no—
91C23×C17—42no—
92C23×C17—88no—
93C23×C17—82no—
94C23×C17—82no—
95C23×C17—82no—
96C23×C17—82no—
97C23×C17#9911yescharacteristic
98C23×C17#9911yescharacteristic
99C23×C17C2×C22⋊C411yescharacteristic
100D4×C17—44no—
101D4×C17—48no—
102D4×C17—44no—
103C2×C4×C17—24no—
104C2×C4×C17—24no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—24no—
110C2×C4×C17—22no—
111C2×C4×C17—22no—
112C2×C4×C17—48no—
113C2×C4×C17—42no—
114C2×C4×C17—44no—
115C2×C4×C17—42no—
116C2×C4×C17—42no—
117C2×C4×C17—42no—
118C2×C4×C17—82no—
119C2×C4×C17#10012yes—
120C2×C4×C17C2×M1612yes—
121C8×C17—84no—
122C2×#390C2×C1711yescharacteristic
123#1463C2×C1712yescomplemented
124#1318C2×C1714yescomplemented
125C22×C17—24no—
126C22×C17—24no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17—48no—
134C22×C17—44no—
135C22×C17—84no—
136C22×C17—88no—
137C22×C17—88no—
138C22×C17—82no—
139C22×C17—82no—
140C22×C17#35312yes—
141C22×C17#35512yes—
142C22×C17#40711yescharacteristic
143C22×C17C2×#9911yescharacteristic
144C22×C17C2×#10011yescharacteristic
145C4×C17—22no—
146C4×C17—22no—
147C4×C17—44no—
148C4×C17—42no—
149C4×C17—42no—
150C23×D4C4×C1711yescharacteristic
151C22×C4⋊C4C22×C1711yescharacteristic
152C22×C22⋊C4—22no—
153C22×C42C4×C1711yescharacteristic
154#407—22no—
155#390—22no—
156#390C4×C1712yes—
157#390C22×C1712yes—
158#324—22no—
159#324C22×C1714yescomplemented
160C2×C17—21no—
161C2×C17—21no—
162C2×C17—22no—
163C2×C17—22no—
164C2×C17—84no—
165C2×C17#146211yescharacteristic
166C2×C17C2×#35311yescharacteristic
167C2×C17C2×#35511yescharacteristic
168C25—21no—
169C22×D4—24no—
170C22×D4—21no—
171C22×D4—41no—
172C22×D4—41no—
173C22×D4—42no—
174C22×D4C2×C4×C1712yes—
175C23×C4—21no—
176C23×C4C2×C4×C1711yescharacteristic
177C23×C4D4×C1712yes—
178C2×M16—42no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C2×C4×C1711yescharacteristic
182C2×C4⋊C4D4×C1712yes—
183C2×C4⋊C4C23×C1711yescharacteristic
184C2×C22⋊C4—24no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—48no—
187C2×C42—21no—
188C2×C42—42no—
189C2×C42C2×C4×C1712yes—
190C22⋊C8—24no—
191C22⋊C8—42no—
192C17#1150511yescharacteristic, direct product factor, Sylow
193C24—24no—
194C24—22no—
195C24—44no—
196C24—42no—
197C24—44no—
198C24—41no—
199C24—41no—
200C24C22⋊C4×C1711yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—48no—
206C2×D4—48no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4M16×C1714yescomplemented
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—44no—
221C22×C4C22⋊C4×C1711yescharacteristic
222C22×C4C22⋊C4×C1712yes—
223C22×C4C22×C4×C1711yescharacteristic
224C22×C4C2×D4×C1712yes—
225M16—84no—
226C2×C8—44no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—41no—
230C22⋊C4—48no—
231C22⋊C4—48no—
232C42—42no—
233C42—42no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—24no—
239C23—44no—
240C23—44no—
241C23—44no—
242C23—416no—
243C23—44no—
244C23—42no—
245C23—42no—
246C23—88no—
247C23—82no—
248C23—82no—
249C23—82no—
250C23—82no—
251C23C17×#9911yescharacteristic
252C23C17×#9911yescharacteristic
253C23C2×C22⋊C4×C1711yescharacteristic
254D4—44no—
255D4—44no—
256D4—48no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—48no—
267C2×C4—42no—
268C2×C4—44no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—82no—
273C2×C4C17×#10012yes—
274C2×C4C2×M16×C1712yes—
275C8—84no—
276C22—24no—
277C22—24no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—48no—
285C22—44no—
286C22—84no—
287C22—88no—
288C22—88no—
289C22—82no—
290C22—82no—
291C22C17×#35312yes—
292C22C17×#35512yes—
293C22C17×#40711yescharacteristic
294C22C2×C17×#9911yescharacteristic
295C22C2×C17×#10011yescharacteristic
296C4—22no—
297C4—22no—
298C4—44no—
299C4—42no—
300C4—42no—
301C2—21no—
302C2—21no—
303C2—22no—
304C2—22no—
305C2—84no—
306C2C17×#146211yescharacteristic
307C2C2×C17×#35311yescharacteristic
308C2C2×C17×#35511yescharacteristic
subgroupG/H
center, socleC22×C17C2×#99
commutatorC22×C4C22×C4×C17
Frattini, cosocleC2×C4⋊C4C23×C17
prime radicalC23×D4×C17C4
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
2. C17×#1463C2semidirect
3. C17×#1318C2semidirect
13. C17×#324C22semidirect
54. C2×D4×C17M16semidirect
79. #11505C17direct (N × H)
123. #1463C2×C17semidirect
124. #1318C2×C17semidirect
159. #324C22×C17semidirect
192. C17#11505direct (N × H)
209. C2×D4M16×C17semidirect

Maximal subgroups

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

subgroupindex
C2×C17×#3902
C17×#14632
C17×#13182
#1150517