Finite Group Databasebeta

← #17191934

Subgroups — #17191934

Order 4352.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14541187C211yesmaximal, characteristic, complemented
2#14531060C211yesmaximal, characteristic, complemented
3#14530975C211yesmaximal, characteristic, complemented
4#14530972C211yesmaximal, characteristic, complemented
5#14530964C211yesmaximal, characteristic, complemented
6#14530962C211yesmaximal, characteristic, complemented
7#14530941C211yesmaximal, characteristic, complemented
8#14530938C211yesmaximal, characteristic, complemented
9#14530885C211yesmaximal, characteristic, complemented
10#14530885C211yesmaximal, characteristic, complemented
11C4×#10587497C211yesmaximal, characteristic, complemented
12#14530616C211yesmaximal, characteristic, complemented
13#14530573C211yesmaximal, characteristic, complemented
14#14530570C211yesmaximal, characteristic, complemented
15C17×#3339C211yesmaximal, characteristic, complemented
16#11763505—21no—
17C2×#10587497C2211yescharacteristic
18C2×#10587483C2211yescharacteristic
19C2×#10587483C2211yescharacteristic
20#11763211C2211yescharacteristic
21#11763134—21no—
22#11763128—21no—
23#11763110—21no—
24#11763045C2211yescharacteristic
25#11763045C2211yescharacteristic
26C4×D136C2211yescharacteristic
27#11762847C2211yescharacteristic
28C2×#10587489C2211yescharacteristic
29#11762636C2211yescharacteristic
30#11762636C2211yescharacteristic
31#11762636C2211yescharacteristic
32#11762636C2211yescharacteristic
33#11762634C2211yescharacteristic
34#11762634C2211yescharacteristic
35#11762634C2211yescharacteristic
36#11762634C2211yescharacteristic
37#11762634C2211yescharacteristic
38C4⋊#63214C2211yescharacteristic
39#11762610C2211yescharacteristic
40#11762610C2211yescharacteristic
41#11762610C2211yescharacteristic
42#11762609C2211yescharacteristic
43#11762609C2211yescharacteristic
44#11762609C2211yescharacteristic
45C22⋊#63214C2211yescharacteristic
46C22⋊#63214C2211yescharacteristic
47C4×#63214C2211yescharacteristic
48C17×#553—21no—
49C17×#499C2211yescharacteristic
50C17×#482—21no—
51C17×#481—21no—
52C17×#478—21no—
53C17×#466C2211yescharacteristic
54C17×#466C2211yescharacteristic
55C4×D8×C17C2211yescharacteristic
56C8×D4×C17C2211yescharacteristic
57C17×#427C2211yescharacteristic
58C2×C17×#107C2211yescharacteristic
59C2×D8×C17C2311yescharacteristic
60C22×C8×C17C2311yescharacteristic
61C22×C8×C17C2311yescharacteristic
62C17×#126—41no—
63C17×#125—21no—
64C17×#123—41no—
65C17×#121—21no—
66C17×#121—21no—
67C17×#121—41no—
68C4×D4×C17—21no—
69C4×D4×C17—41no—
70C4×D4×C17D411yescharacteristic
71C17×#117—21no—
72C2×C4⋊C4×C17—21no—
73#10587625—41no—
74#10587616—21no—
75#10587616—21no—
76#10587612—21no—
77C2×C4⋊Dic17—21no—
78C2×D136C2311yescharacteristic
79#10587584—41no—
80#10587569—41no—
81#10587567—41no—
82C4×D68—21no—
83#10587556—21no—
84C17×#107—21no—
85C17×#107C2311yescharacteristic
86C17×#107C2311yescharacteristic
87C17×#107C2311yescharacteristic
88C17×#106—21no—
89C17×#106—21no—
90C17×C4⋊C8D411yescharacteristic
91C17×#102—21no—
92C17×#102—21no—
93C17×#102—21no—
94C17×C22⋊C8D411yescharacteristic
95C17×C22⋊C8D411yescharacteristic
96C4×C8×C17C2311yescharacteristic
97#10587497—22no—
98#10587492—21no—
99#10587492—21no—
100#10587492—21no—
101#10587489—21no—
102#10587489C2311yescharacteristic
103#10587489C2311yescharacteristic
104#10587489C2311yescharacteristic
105#10587488—21no—
106#10587488—21no—
107#10587483—22no—
108#10587483—22no—
109C2×#63214C2311yescharacteristic
110C2×#63214C2311yescharacteristic
111C2×#63214C2311yescharacteristic
112C2×#63214C2311yescharacteristic
113C2×D4×C17—21no—
114C2×D4×C17—41no—
115C2×D4×C17—41no—
116C2×D4×C17D811yescharacteristic
117C22×C4×C17—41no—
118C22×C4×C17—41no—
119C22×C4×C17C2×D411yescharacteristic
120C22×C4×C17C2×D411yescharacteristic
121C2×C22⋊D17—41no—
122C2×C22⋊D17—41no—
123C22×Dic17—41no—
124C2×D68—21no—
125C2×C4×D17—41no—
126D8×C17—21no—
127D8×C17—21no—
128C2×C8×C17—21no—
129C2×C8×C17—21no—
130C2×C8×C17—21no—
131C2×C8×C17—21no—
132C2×C8×C17C2×D411yescharacteristic
133C2×C8×C17C2×D411yescharacteristic
134C2×C8×C17C2×D411yescharacteristic
135C2×C8×C17C2411yescharacteristic
136C4⋊C4×C17—21no—
137C4⋊C4×C17—21no—
138C4⋊C4×C17—21no—
139C4⋊C4×C17—41no—
140C4⋊C4×C17—41no—
141C4⋊C4×C17—41no—
142C4⋊C4×C17D811yescharacteristic
143C22⋊C4×C17—41no—
144C22⋊C4×C17—41no—
145C22⋊C4×C17—41no—
146C22⋊C4×C17—41no—
147C22⋊C4×C17D811yescharacteristic
148C22⋊C4×C17D811yescharacteristic
149C42×C17—41no—
150C42×C17C2×D411yescharacteristic
151C22⋊Dic17—41no—
152#63227—41no—
153#63227—41no—
154#63227—41no—
155C4⋊Dic17—21no—
156C4⋊Dic17—21no—
157C4⋊Dic17—21no—
158C4⋊Dic17—41no—
159#63225—41no—
160#63225—41no—
161C4×Dic17—41no—
162D136—21no—
163D136—21no—
164#63214—21no—
165#63214—21no—
166#63214—21no—
167#63214#4112yes—
168#33922—171nomaximal, Sylow
169C23×C17—41no—
170C23×C17C2×D811yescharacteristic
171C23×C17C2×D811yescharacteristic
172C22×D17—41no—
173D4×C17—41no—
174D4×C17—41no—
175D4×C17—41no—
176D4×C17—82no—
177D4×C17—161no—
178C2×C4×C17—21no—
179C2×C4×C17—21no—
180C2×C4×C17—21no—
181C2×C4×C17—21no—
182C2×C4×C17—41no—
183C2×C4×C17—41no—
184C2×C4×C17—41no—
185C2×C4×C17—161no—
186C2×C4×C17—161no—
187C2×C4×C17C2×D811yescharacteristic
188C2×C4×C17C2×D811yescharacteristic
189C2×C4×C17C2×D811yescharacteristic
190C2×C4×C17C2×D811yescharacteristic
191C2×C4×C17C22×D411yescharacteristic
192C22⋊D17—82no—
193C22⋊D17—161no—
194C2×Dic17—41no—
195C2×Dic17—41no—
196C2×Dic17—41no—
197C2×Dic17—161no—
198D68—41no—
199D68—41no—
200C4×D17—161no—
201C8×C17—21no—
202C8×C17—21no—
203C8×C17—21no—
204C8×C17C2×#4111yescharacteristic
205C8×C172−1+411yescharacteristic
206#3339—171no—
207#3339D1711yescharacteristic, complemented
208#2253—171no—
209#2234—171no—
210#2234—171no—
211#2232—171no—
212#2232—171no—
213#2228—171no—
214#2228—171no—
215#2218—171no—
216#2218—171no—
217C4×D16—171no—
218#2169—171no—
219#2159—171no—
220#2159—171no—
221C22×C17—21no—
222C22×C17—21no—
223C22×C17—21no—
224C22×C17—21no—
225C22×C17—21no—
226C22×C17—21no—
227C22×C17—81no—
228C22×C17—81no—
229C22×C17—81no—
230C22×C17C22×D811yescharacteristic
231C2×D17—81no—
232C2×D17—81no—
233C2×D17—81no—
234C4×C17—21no—
235C4×C17—21no—
236C4×C17—21no—
237C4×C17—21no—
238C4×C17—81no—
239C4×C17—81no—
240C4×C17—81no—
241C4×C17#54711yescharacteristic
242C4×C17#57811yescharacteristic
243Dic17—81no—
244Dic17—81no—
245Dic17—81no—
246#553—21no—
247#553—341no—
248C2×D16—171no—
249C2×M32—171no—
250C2×M32—171no—
251#499—171no—
252#499C2×D1711yescharacteristic
253#482—21no—
254#482—341no—
255#481—21no—
256#481—341no—
257#478—21no—
258#478—341no—
259#466—171no—
260#466—171no—
261#466C2×D1711yescharacteristic
262#466C2×D1711yescharacteristic
263C4×D8—171no—
264C4×D8C2×D1711yescharacteristic
265C8×D4C2×D1711yescharacteristic
266#427—171no—
267#427C2×D1711yescharacteristic
268C2×#107—171no—
269C2×#107C2×D1711yescharacteristic
270#367—171no—
271#367—171no—
272#367—171no—
273#367—171no—
274#366—171no—
275#366—171no—
276#366—171no—
277#366—171no—
278#366—171no—
279C4⋊C16—171no—
280#357—171no—
281#357—171no—
282#357—171no—
283#357—171no—
284#357—171no—
285#357—171no—
286C22⋊C16—171no—
287C22⋊C16—171no—
288C4×C16—171no—
289C2×C17—41no—
290C2×C17—41no—
291C2×C17—161no—
292C2×C17#333411yescharacteristic
293C2×C17#341411yescharacteristic
294C2×C17#341511yescharacteristic
295D17—161no—
296C2×D8—171no—
297C2×D8C22×D1711yescharacteristic
298C22×C8C22×D1711yescharacteristic
299C22×C8C22×D1711yescharacteristic
300#126—41no—
301#126—681no—
302#125—21no—
303#125—341no—
304#123—41no—
305#123—681no—
306#121—21no—
307#121—21no—
308#121—41no—
309#121—341no—
310#121—341no—
311#121—681no—
312C4×D4—21no—
313C4×D4—41no—
314C4×D4—341no—
315C4×D4—681no—
316C4×D4C22⋊D1711yescharacteristic
317#117—21no—
318#117—341no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—341no—
321D16—342no—
322M32—342no—
323M32—342no—
324C2×C16—171no—
325C2×C16—171no—
326C2×C16—171no—
327C2×C16—171no—
328#107—21no—
329#107—171no—
330#107—171no—
331#107—171no—
332#107—341no—
333#107C22×D1711yescharacteristic
334#107C22×D1711yescharacteristic
335#107C22×D1711yescharacteristic
336#106—21no—
337#106—21no—
338#106—341no—
339#106—341no—
340C4⋊C8C22⋊D1711yescharacteristic
341#102—21no—
342#102—21no—
343#102—21no—
344#102—341no—
345#102—341no—
346#102—341no—
347C22⋊C8C22⋊D1711yescharacteristic
348C22⋊C8C22⋊D1711yescharacteristic
349C4×C8C22×D1711yescharacteristic
350C17#3392211yescharacteristic, complemented, Sylow
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—341no—
355C2×D4—681no—
356C2×D4—681no—
357C2×D4#6322811yescharacteristic
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—681no—
361C22×C4—681no—
362C22×C4C2×C22⋊D1711yescharacteristic
363C22×C4C2×C22⋊D1711yescharacteristic
364D8—21no—
365D8—21no—
366D8—341no—
367D8—341no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×C22⋊D1711yescharacteristic
373C2×C8C2×C22⋊D1711yescharacteristic
374C2×C8C2×C22⋊D1711yescharacteristic
375C2×C8C23×D1711yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—341no—
383C4⋊C4—341no—
384C4⋊C4—341no—
385C4⋊C4—681no—
386C4⋊C4—681no—
387C4⋊C4—681no—
388C4⋊C4#6322811yescharacteristic
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—681no—
394C22⋊C4—681no—
395C22⋊C4—681no—
396C22⋊C4—681no—
397C22⋊C4#6322811yescharacteristic
398C22⋊C4#6322811yescharacteristic
399C42—41no—
400C42—681no—
401C42C2×C22⋊D1711yescharacteristic
402C16—172no—
403C16—341no—
404C16—341no—
405C16—341no—
406C23—41no—
407C23—681no—
408C23C2×#6322811yescharacteristic
409C23C2×#6322811yescharacteristic
410D4—41no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—161no—
415D4—2721no—
416D4—681no—
417D4—681no—
418D4—1362no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—2721no—
429C2×C4—2721no—
430C2×C4—681no—
431C2×C4—681no—
432C2×C4—681no—
433C2×C4C2×#6322811yescharacteristic
434C2×C4C2×#6322811yescharacteristic
435C2×C4C2×#6322811yescharacteristic
436C2×C4C2×#6322811yescharacteristic
437C2×C4C22×C22⋊D1711yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8#41×D1711yescharacteristic
442C8#1058769711yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—1361no—
453C22—1361no—
454C22—1361no—
455C22C22×#6322811yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—1361no—
464C4—1361no—
465C4—1361no—
466C4#1176345811yescharacteristic
467C4#1176362411yescharacteristic
468C2—41no—
469C2—41no—
470C2—161no—
471C2—2721no—
472C2#1454112711yescharacteristic
473C2#1454191811yescharacteristic
474C2#1454192311yescharacteristic
subgroupG/H
centerC22C22×#63228
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#3339C2
socleC22×C17C22×D8
hypercenter#3339D17
hypocenterC17#33922
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #14541187C2semidirect
2. #14531060C2semidirect
3. #14530975C2semidirect
4. #14530972C2semidirect
5. #14530964C2semidirect
6. #14530962C2semidirect
7. #14530941C2semidirect
8. #14530938C2semidirect
9. #14530885C2semidirect
10. #14530885C2semidirect
11. C4×#10587497C2semidirect
12. #14530616C2semidirect
13. #14530573C2semidirect
14. #14530570C2semidirect
15. C17×#3339C2semidirect
207. #3339D17semidirect
350. C17#33922semidirect

Maximal subgroups

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

subgroupindex
#145411872
#145310602
#145309752
#145309722
#145309642
#145309622
#145309412
#145309382
#145308852
C4×#105874972
#145306162
#145305732
#145305702
C17×#33392
#3392217