Finite Group Databasebeta

← #16940532

Subgroups — #16940532

Order 4352.

974 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531137C211yesmaximal, characteristic
2C2×#11762576C212yesmaximal
3C2×#11762576C211yesmaximal, characteristic
4C2×#11762575C212yesmaximal
5C17×#2315C211yesmaximal, characteristic
6C22×C22⋊Dic17C2212yes—
7C22×C22⋊Dic17C2212yes—
8C22⋊C4×Dic17—24no—
9C4×C22⋊Dic17—22no—
10#11762576—22no—
11#11762576—24no—
12#11762575C418yescomplemented
13C22×C22⋊C4×C17C2211yescharacteristic
14C22×C22⋊C4×C17C2211yescharacteristic
15C22×C22⋊C4×C17C2211yescharacteristic
16C17×#385—22no—
17C17×#385C414yescomplemented
18C17×#380—22no—
19C25×C17C2311yescharacteristic
20C23×C4×C17—21no—
21C23×C4×C17C2×C412yes—
22C23×C4×C17D412yes—
23C23×Dic17—22no—
24C23×Dic17—22no—
25C2×C4⋊C4×C17—24no—
26C2×C22⋊C4×C17—21no—
27C2×C22⋊C4×C17—22no—
28C2×C22⋊C4×C17—22no—
29C2×C22⋊C4×C17—22no—
30C2×C22⋊C4×C17—22no—
31C2×C22⋊C4×C17—21no—
32C2×C22⋊C4×C17—21no—
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17C2×C412yes—
35C2×C22⋊C4×C17C2×C414yes—
36C2×C22⋊C4×C17C2×C412yes—
37C2×C22⋊C4×C17D412yes—
38C2×C22⋊Dic17—22no—
39C2×C22⋊Dic17—22no—
40C2×C22⋊Dic17—22no—
41C2×C22⋊Dic17—22no—
42C2×C22⋊Dic17—22no—
43C2×C22⋊Dic17—22no—
44C2×C22⋊Dic17—22no—
45C2×C22⋊Dic17—22no—
46C2×C22⋊Dic17C2×C414yes—
47C2×C22⋊Dic17C2×C414yes—
48C2×C22⋊Dic17D414yes—
49C2×C22⋊Dic17Q814yes—
50C2×C4×Dic17—24no—
51C17×#95—24no—
52#10587502—24no—
53C24×C17—82no—
54C24×C17C22×C412yes—
55C24×C17C22×C411yescharacteristic
56C24×C17C2×D412yes—
57C24×C17C2×D411yescharacteristic
58C24×C17C2×D411yescharacteristic
59C24×C17C2×Q812yes—
60C24×C17#4112yes—
61C24×C17#4112yes—
62C24×C17#4112yes—
63C22×C4×C17—22no—
64C22×C4×C17—22no—
65C22×C4×C17—24no—
66C22×C4×C17—22no—
67C22×C4×C17—22no—
68C22×C4×C17—24no—
69C22×C4×C17—82no—
70C22×C4×C17—82no—
71C22×C4×C17—82no—
72C22×C4×C17C22⋊C414yes—
73C22×Dic17—24no—
74C22×Dic17—24no—
75C22×Dic17—24no—
76C22×Dic17—24no—
77C22×Dic17—42no—
78C22×Dic17—42no—
79C22×Dic17—84no—
80C22×Dic17—84no—
81C4⋊C4×C17—84no—
82C22⋊C4×C17—22no—
83C22⋊C4×C17—24no—
84C22⋊C4×C17—24no—
85C22⋊C4×C17—24no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—42no—
88C22⋊C4×C17—41no—
89C22⋊C4×C17C4214yescomplemented
90C22⋊Dic17—24no—
91C22⋊Dic17—24no—
92C22⋊Dic17—24no—
93C22⋊Dic17—24no—
94C22⋊Dic17—24no—
95C22⋊Dic17—42no—
96C22⋊Dic17—42no—
97C22⋊Dic17C4⋊C418yescomplemented
98C4×Dic17—84no—
99#10915—171nomaximal, Sylow
100C23×C17—44no—
101C23×C17—44no—
102C23×C17—42no—
103C23×C17—42no—
104C23×C17—42no—
105C23×C17—82no—
106C23×C17—82no—
107C23×C17—82no—
108C23×C17—82no—
109C23×C17C2×C4211yescharacteristic
110C23×C17C2×C22⋊C411yescharacteristic
111C23×C17C2×C4⋊C412yes—
112C23×C17#11712yes—
113C23×C17#11711yescharacteristic
114C23×C17C4×D412yes—
115C23×C17C4×D412yes—
116C23×C17C4×D412yes—
117C23×C17C4×D412yes—
118C23×C17C4×Q812yes—
119C23×C17C4×Q812yes—
120C23×C17#12011yescharacteristic
121C23×C17#12112yes—
122C23×C17C22⋊Q812yes—
123C23×C17C22⋊Q812yes—
124C23×C17#12312yes—
125C23×C17#12311yescharacteristic
126C23×C17#12411yescharacteristic
127C23×C17#12512yes—
128C23×C17#12612yes—
129C23×C17C4⋊Q811yescharacteristic
130C2×C4×C17—24no—
131C2×C4×C17—24no—
132C2×C4×C17—44no—
133C2×C4×C17—44no—
134C2×C4×C17—44no—
135C2×C4×C17—44no—
136C2×C4×C17—42no—
137C2×C4×C17—82no—
138C2×C4×C17—84no—
139C2×C4×C17—84no—
140C2×Dic17—28no—
141C2×Dic17—48no—
142C2×Dic17—44no—
143C2×Dic17—84no—
144C2×Dic17—84no—
145C2×Dic17—84no—
146C2×Dic17—84no—
147C2×Dic17—84no—
148#2315D1711yescharacteristic
149#2273—171no—
150C2×#342—172no—
151C2×#342—172no—
152C2×#342—171no—
153C22×C17—22no—
154C22×C17—24no—
155C22×C17—22no—
156C22×C17—24no—
157C22×C17—22no—
158C22×C17—42no—
159C22×C17—42no—
160C22×C17—42no—
161C22×C17—42no—
162C22×C17—42no—
163C22×C17—41no—
164C22×C17—42no—
165C22×C17—41no—
166C22×C17—42no—
167C22×C17—42no—
168C22×C17—42no—
169C22×C17—42no—
170C22×C17—42no—
171C22×C17—41no—
172C22×C17—42no—
173C22×C17—41no—
174C22×C17C4×C22⋊C411yescharacteristic
175C22×C17C4×C4⋊C412yes—
176C22×C17#38512yes—
177C22×C17#38611yescharacteristic
178C22×C17#38712yes—
179C22×C17#38712yes—
180C22×C17#38812yes—
181C22×C17#38912yes—
182C22×C17#39111yescharacteristic
183C4×C17—44no—
184C4×C17—44no—
185C4×C17—82no—
186Dic17—48no—
187Dic17—84no—
188C22×C22⋊C4—172no—
189C22×C22⋊C4—172no—
190C22×C22⋊C4C2×D1711yescharacteristic
191C22×C22⋊C4C2×D1711yescharacteristic
192C22×C22⋊C4C2×D1711yescharacteristic
193#385—22no—
194#385Dic1714yescomplemented
195#380—22no—
196C4×C22⋊C4—344no—
197C4×C22⋊C4—342no—
198#342—178no—
199#342—344no—
200#342—342no—
201C2×C17—22no—
202C2×C17—22no—
203C2×C17—21no—
204C2×C17—22no—
205C2×C17—22no—
206C2×C17—22no—
207C2×C17—22no—
208C2×C17—21no—
209C2×C17#143611yescharacteristic
210C2×C17#191312yes—
211C25C22×D1711yescharacteristic
212C23×C4—21no—
213C23×C4—342no—
214C23×C4—342no—
215C23×C4C2×Dic1712yes—
216C23×C4C22⋊D1712yes—
217C2×C4⋊C4—24no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—174no—
227C2×C22⋊C4—174no—
228C2×C22⋊C4—174no—
229C2×C22⋊C4—174no—
230C2×C22⋊C4—342no—
231C2×C22⋊C4—342no—
232C2×C22⋊C4—342no—
233C2×C22⋊C4—342no—
234C2×C22⋊C4—342no—
235C2×C22⋊C4—342no—
236C2×C22⋊C4—342no—
237C2×C22⋊C4—342no—
238C2×C22⋊C4C4×D1714yes—
239C2×C22⋊C4C2×Dic1712yes—
240C2×C22⋊C4C2×Dic1712yes—
241C2×C22⋊C4C22⋊D1712yes—
242C2×C42—344no—
243#95—24no—
244#95—344no—
245C17#1091511yescharacteristic, complemented, Sylow
246C24—82no—
247C24C2×C4×D1712yes—
248C24#6325212yes—
249C24D4×D1712yes—
250C24#6325412yes—
251C24Q8×D1712yes—
252C24#6325612yes—
253C24C22×Dic1711yescharacteristic
254C24C2×C22⋊D1711yescharacteristic
255C24C2×C22⋊D1711yescharacteristic
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—82no—
263C22×C4—82no—
264C22×C4—82no—
265C22×C4—344no—
266C22×C4—344no—
267C22×C4—344no—
268C22×C4—344no—
269C22×C4—682no—
270C22×C4—682no—
271C22×C4—1364no—
272C22×C4—1364no—
273C22×C4C22⋊Dic1714yes—
274C4⋊C4—84no—
275C22⋊C4—22no—
276C22⋊C4—24no—
277C22⋊C4—24no—
278C22⋊C4—24no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—42no—
282C22⋊C4—178no—
283C22⋊C4—344no—
284C22⋊C4—344no—
285C22⋊C4—344no—
286C22⋊C4—344no—
287C22⋊C4—344no—
288C22⋊C4—682no—
289C22⋊C4—682no—
290C22⋊C4C4×Dic1714yescomplemented
291C42—1364no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—44no—
296C23—44no—
297C23—82no—
298C23—82no—
299C23—82no—
300C23—82no—
301C23#1058757312yes—
302C23#1058757512yes—
303C23C4⋊C4×D1712yes—
304C23#1058757812yes—
305C23#1058757912yes—
306C23#1058758012yes—
307C23#1058758212yes—
308C23#1058758412yes—
309C23C2×C4×Dic1711yescharacteristic
310C23#1058761211yescharacteristic
311C23C4×C22⋊D1712yes—
312C23C4×C22⋊D1712yes—
313C23D4×Dic1712yes—
314C23#1058762111yescharacteristic
315C23#1058762311yescharacteristic
316C23#1058762512yes—
317C23#1058763011yescharacteristic
318C23Q8×Dic1712yes—
319C23#1058763212yes—
320C23#1058763311yescharacteristic
321C23C2×C22⋊Dic1711yescharacteristic
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—44no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—42no—
329C2×C4—82no—
330C2×C4—84no—
331C2×C4—84no—
332C2×C4—348no—
333C2×C4—688no—
334C2×C4—684no—
335C2×C4—1364no—
336C2×C4—1364no—
337C2×C4—1364no—
338C2×C4—1364no—
339C2×C4—1364no—
340C22—22no—
341C22—22no—
342C22—24no—
343C22—22no—
344C22—24no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—42no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22C4×C22⋊Dic1711yescharacteristic
362C22C4⋊C4×Dic1712yes—
363C22#1176268012yes—
364C22#1176268911yescharacteristic
365C22#1176269012yes—
366C22#1176269512yes—
367C22#1176269912yes—
368C22#1176270412yes—
369C22#1176271611yescharacteristic
370C4—44no—
371C4—44no—
372C4—82no—
373C4—688no—
374C4—1364no—
375C2—21no—
376C2—22no—
377C2—22no—
378C2—22no—
379C2—22no—
380C2—22no—
381C2—21no—
382C2—22no—
383C2#1452701611yescharacteristic
384C2#1452932712yes—
subgroupG/H
centerC22#11762689
commutatorC23×C17C2×C42
FrattiniC25C22×D17
FittingC17×#2315C2
socleC22×C17#386
prime radical, cosocleC25×C17C23
hypercenter#2315D17
hypocenterC17#10915
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C25 ◁ #2315

Complements

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

NH ≅ G/Ntype
12. #11762575C4semidirect
17. C17×#385C4semidirect
89. C22⋊C4×C17C42semidirect
97. C22⋊Dic17C4⋊C4semidirect
194. #385Dic17semidirect
245. C17#10915semidirect
290. C22⋊C4C4×Dic17semidirect

Maximal subgroups

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

subgroupindex
#145311372
C2×#117625762
C2×#117625752
C17×#23152
#1091517