Finite Group Databasebeta

← #17010631

Subgroups — #17010631

Order 4352.

982 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 179 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
1#14539164C211yesmaximal, characteristic, complemented
2#14538883C212yesmaximal, complemented
3#14528012C218yesmaximal, complemented
4#14527510C211yesmaximal, characteristic, complemented
5#14527227C212yesmaximal, complemented
6C2×C17×#555C211yesmaximal, characteristic
7#11763366C2211yescharacteristic
8#11763177—22no—
9#11763159C2214yescomplemented
10#11763144—22no—
11#11763089C2214yescomplemented
12#11763014C2214yescomplemented
13#11762960—22no—
14#11762909—24no—
15#11762866C2212yes—
16#11762818—22no—
17C4×#63223C2211yescharacteristic
18#11762558C2214yescomplemented
19D4⋊#3622C2218yescomplemented
20C17×#555—24no—
21C17×#555—22no—
22C17×#555C2214yes—
23C2×C17×C4⋊Q8C2211yescharacteristic
24C2×C17×#124—22no—
25C2×C17×#121—22no—
26C2×C4×D4×C17C2212yes—
27C2×C17×#117—22no—
28C22×Q8×C17D412yes—
29C22×D4×C17—22no—
30C22×D4×C17D412yes—
31C23×C4×C17—22no—
32C17×C4⋊Q8—22no—
33C17×C4⋊Q8D412yes—
34C17×C4⋊Q8C2312yes—
35C17×#124—28no—
36C17×#124—28no—
37C17×#121—28no—
38C17×#121—28no—
39C4×D4×C17—22no—
40C4×D4×C17—22no—
41C4×D4×C17D414yes—
42C4×D4×C17C2314yes—
43C17×#117—28no—
44C17×#117—28no—
45C2×C4⋊C4×C17—22no—
46C2×C4⋊C4×C17D412yes—
47C2×C22⋊C4×C17—24no—
48C2×C22⋊C4×C17—22no—
49C2×C42×C17—22no—
50C2×C42×C17C2311yescharacteristic
51C2×#63229—24no—
52#10587612—21no—
53#10587610—22no—
54C2×#63223—21no—
55#10587556—21no—
56#10587555C2312yes—
57C4×Dic34—22no—
58#10587506—28no—
59#10587503—24no—
60C22⋊#3622—22no—
61#10587481—24no—
62#10587478—24no—
63C4⋊#3622C2314yes—
64#10587474—21no—
65#10587474—22no—
66C4×#3622C2312yes—
67C24×C17—22no—
68C2×Q8×C17—22no—
69C2×Q8×C17—44no—
70C2×Q8×C17C2×D414yes—
71C2×D4×C17—28no—
72C2×D4×C17—22no—
73C2×D4×C17—44no—
74C2×D4×C17—84no—
75C2×D4×C17C2×D414yes—
76C22×C4×C17—22no—
77C22×C4×C17—22no—
78C22×C4×C17—24no—
79C22×C4×C17—24no—
80C22×C4×C17—48no—
81C22×C4×C17C2×D412yes—
82C22×C4×C17C2×D411yescharacteristic
83C2×Dic34—22no—
84C4⋊C4×C17—24no—
85C4⋊C4×C17—22no—
86C4⋊C4×C17—24no—
87C4⋊C4×C17C2×D414yes—
88C22⋊C4×C17—216no—
89C22⋊C4×C17—24no—
90C22⋊C4×C17—24no—
91C42×C17—28no—
92C42×C17C2×D412yes—
93C42×C17C2×D411yescharacteristic
94C42×C17C2411yescharacteristic
95C22⋊Dic17—41no—
96#63229—48no—
97C4⋊Dic17—22no—
98C4⋊Dic17—22no—
99#63225—42no—
100C4×Dic17—41no—
101#63223—42no—
102C2×#3622—22no—
103C2×#3622—24no—
104#18552—171nomaximal, Sylow
105C23×C17—24no—
106C23×C17—44no—
107C23×C17—44no—
108C23×C17—44no—
109C23×C17#12011yescharacteristic
110Q8×C17—44no—
111Q8×C17—82no—
112D4×C17—24no—
113D4×C17—24no—
114D4×C17—44no—
115D4×C17—88no—
116C2×C4×C17—22no—
117C2×C4×C17—24no—
118C2×C4×C17—24no—
119C2×C4×C17—24no—
120C2×C4×C17—48no—
121C2×C4×C17—44no—
122C2×C4×C17—44no—
123C2×C4×C17—48no—
124C2×C4×C17#12011yescharacteristic
125C2×C4×C17#12012yes—
126C2×C4×C17C22×D411yescharacteristic
127C2×C4×C17C22×D412yes—
128C2×Dic17—42no—
129Dic34—44no—
130#3622—42no—
131#3622—44no—
132C2×#555D1711yescharacteristic
133#3139—171no—
134#3110—172no—
135#1646—178no—
136#1558—171no—
137#1490—172no—
138C22×C17—22no—
139C22×C17—44no—
140C22×C17—44no—
141C22×C17—44no—
142C22×C17—88no—
143C22×C17#45512yes—
144C22×C17C2×#12011yescharacteristic
145C4×C17—22no—
146C4×C17—21no—
147C4×C17—21no—
148C4×C17—44no—
149C4×C17—44no—
150C4×C17#57514yes—
151Dic17—82no—
152#555—22no—
153#555—24no—
154#555C2×D1714yes—
155#533—171no—
156C2×C4⋊Q8C2×D1711yescharacteristic
157C2×#124—22no—
158C2×#121—22no—
159C2×C4×D4C2×D1712yes—
160C2×#117—22no—
161#491—342no—
162#487—174no—
163#484—342no—
164#474—174no—
165#461—174no—
166#450—342no—
167#440—344no—
168#432—172no—
169#419—342no—
170C4×M16—171no—
171#333—174no—
172D4⋊C8—178no—
173C2×C17—22no—
174C2×C17—84no—
175C2×C17#300512yes—
176C2×C17C2×#45511yescharacteristic
177C22×Q8C22⋊D1712yes—
178C22×D4—22no—
179C22×D4C22⋊D1712yes—
180C23×C4—22no—
181C2×SD16—344no—
182C2×M16—341no—
183C4⋊Q8—22no—
184C4⋊Q8—172no—
185C4⋊Q8C22⋊D1712yes—
186C4⋊Q8C22×D1712yes—
187#125—341no—
188#124—28no—
189#124—28no—
190C22⋊Q8—342no—
191#121—28no—
192#121—28no—
193C4×Q8—342no—
194C4×D4—22no—
195C4×D4—22no—
196C4×D4C22⋊D1714yes—
197C4×D4C22×D1714yes—
198#117—28no—
199#117—28no—
200#117—341no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4C22⋊D1712yes—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—22no—
205C2×C42—22no—
206C2×C42C22×D1711yescharacteristic
207#107—344no—
208C4⋊C8—174no—
209#103—348no—
210#103—344no—
211#102—344no—
212C22⋊C8—342no—
213#97—341no—
214#97—342no—
215C4×C8—172no—
216C17#1855211yescharacteristic, complemented, Sylow
217C24—22no—
218C2×Q8—22no—
219C2×Q8—44no—
220C2×Q8—342no—
221C2×Q8C2×C22⋊D1714yes—
222C2×D4—28no—
223C2×D4—22no—
224C2×D4—44no—
225C2×D4—84no—
226C2×D4C2×C22⋊D1714yes—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—48no—
232C22×C4C2×C22⋊D1712yes—
233C22×C4C2×C22⋊D1711yescharacteristic
234SD16—688no—
235M16—682no—
236C2×C8—342no—
237C2×C8—344no—
238C4⋊C4—24no—
239C4⋊C4—24no—
240C4⋊C4—22no—
241C4⋊C4—342no—
242C4⋊C4—342no—
243C4⋊C4—682no—
244C4⋊C4C2×C22⋊D1714yes—
245C22⋊C4—216no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C22⋊C4—681no—
249C42—28no—
250C42—681no—
251C42C2×C22⋊D1711yescharacteristic
252C42C2×C22⋊D1712yes—
253C42C23×D1711yescharacteristic
254C23—24no—
255C23—44no—
256C23—44no—
257C23—44no—
258C23#1058763911yescharacteristic
259Q8—44no—
260Q8—82no—
261Q8—684no—
262D4—24no—
263D4—24no—
264D4—44no—
265D4—88no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—682no—
275C2×C4#1058763911yescharacteristic
276C2×C4#1058763912yes—
277C2×C4C22×C22⋊D1711yescharacteristic
278C2×C4C22×C22⋊D1712yes—
279C8—682no—
280C8—684no—
281C22—22no—
282C22—44no—
283C22—44no—
284C22—44no—
285C22—88no—
286C22#1176298712yes—
287C22C2×#1058763911yescharacteristic
288C4—22no—
289C4—21no—
290C4—21no—
291C4—44no—
292C4—44no—
293C4—1362no—
294C4#1176360714yes—
295C2—22no—
296C2—84no—
297C2#1453802612yes—
298C2C2×#1176298711yescharacteristic
subgroupG/H
centerC22C2×#10587639
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
Fitting, prime radicalC2×C17×#555C2
socleC22×C17C2×#120
hypercenterC2×#555D17
hypocenterC17#18552
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #14539164C2semidirect
2. #14538883C2semidirect
3. #14528012C2semidirect
4. #14527510C2semidirect
5. #14527227C2semidirect
9. #11763159C22semidirect
11. #11763089C22semidirect
12. #11763014C22semidirect
18. #11762558C22semidirect
19. D4⋊#3622C22semidirect
216. C17#18552semidirect

Maximal subgroups

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

subgroupindex
#145391642
#145388832
#145280122
#145275102
#145272272
C2×C17×#5552
#1855217