Finite Group Databasebeta

← #17191295

Subgroups — #17191295

Order 4352.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14541132C211yesmaximal, characteristic, complemented
2#14531020C211yesmaximal, characteristic, complemented
3#14530979C211yesmaximal, characteristic, complemented
4#14530967C211yesmaximal, characteristic, complemented
5#14530931C211yesmaximal, characteristic, complemented
6#14530885C211yesmaximal, characteristic, complemented
7#14530882C211yesmaximal, characteristic, complemented
8#14530836C211yesmaximal, characteristic, complemented
9#14530707C211yesmaximal, characteristic, complemented
10#14530696C211yesmaximal, characteristic, complemented
11#14530658C211yesmaximal, characteristic, complemented
12#14530610C211yesmaximal, characteristic, complemented
13#14530496C211yesmaximal, characteristic, complemented
14C2×#11762610C211yesmaximal, characteristic, complemented
15C17×#3280C211yesmaximal, characteristic, complemented
16#11763463—21no—
17C2×#10587499C2211yescharacteristic, complemented
18C2×#10587497C2211yescharacteristic
19C2×#10587497C2211yescharacteristic
20C2×#10587483C2211yescharacteristic, complemented
21C22×#63214C2211yescharacteristic
22#11763214C2211yescharacteristic, complemented
23#11763123—21no—
24#11763123—21no—
25#11763090—21no—
26#11763045C2211yescharacteristic
27#11763045C2211yescharacteristic, complemented
28C4×D136C2211yescharacteristic, complemented
29C2×#10587489C2211yescharacteristic
30C2×#10587489C2211yescharacteristic, complemented
31#11762636C2211yescharacteristic, complemented
32#11762636C2211yescharacteristic, complemented
33#11762636C2211yescharacteristic, complemented
34C4⋊#63214C2211yescharacteristic, complemented
35#11762613C2211yescharacteristic, complemented
36#11762613C2211yescharacteristic, complemented
37#11762613C2211yescharacteristic, complemented
38#11762610C2211yescharacteristic
39#11762610C2211yescharacteristic
40#11762610C2211yescharacteristic
41#11762610C2211yescharacteristic
42#11762610C2211yescharacteristic
43#11762610C2211yescharacteristic
44#11762609C2211yescharacteristic, complemented
45C22⋊#63214C2211yescharacteristic
46C22⋊#63214C2211yescharacteristic, complemented
47#11762585C2211yescharacteristic, complemented
48C2×C17×#135C2211yescharacteristic
49C22×D8×C17C2211yescharacteristic
50C17×#546—21no—
51C17×#495C2211yescharacteristic
52C17×#467C2211yescharacteristic
53C17×#466C2211yescharacteristic
54C17×#463—21no—
55C17×#450—21no—
56C17×#449—21no—
57C4×D8×C17C2211yescharacteristic
58C8×D4×C17C2211yescharacteristic
59C2×#41×C17—21no—
60C22×D4×C17—21no—
61C2×#63254—41no—
62C17×#135—22no—
63C17×#135—41no—
64C2×Q16×C17C2311yescharacteristic
65C2×SD16×C17—21no—
66C2×SD16×C17—21no—
67C2×D8×C17—22no—
68C2×D8×C17—21no—
69C2×D8×C17—41no—
70C2×D8×C17C2311yescharacteristic
71C2×D8×C17C2311yescharacteristic
72C22×C8×C17C2311yescharacteristic
73C22×C8×C17C2311yescharacteristic
74C17×#124—21no—
75C17×#123—41no—
76C17×C22⋊Q8—21no—
77C17×#121—21no—
78C17×#121—41no—
79C17×#120—41no—
80C4×D4×C17—21no—
81C4×D4×C17D411yescharacteristic
82C2×C22⋊C4×C17—41no—
83#10587616—21no—
84#10587616—21no—
85C2×C4⋊Dic17—21no—
86C2×C4⋊Dic17—21no—
87C2×D136C2311yescharacteristic
88#10587583—41no—
89#10587572—41no—
90#10587572—41no—
91C4×D68—21no—
92#10587555—21no—
93C17×#107C2311yescharacteristic
94C17×C4⋊C8D411yescharacteristic
95C17×#103—21no—
96C17×#102—21no—
97C17×#102—21no—
98C17×C22⋊C8D411yescharacteristic
99C17×C22⋊C8D411yescharacteristic
100C4×C8×C17C2311yescharacteristic
101#10587499—41no—
102#10587497—22no—
103#10587497—41no—
104#10587492—21no—
105#10587492—21no—
106#10587492—21no—
107#10587489—21no—
108#10587489—21no—
109#10587489—21no—
110#10587489C2311yescharacteristic
111#10587489C2311yescharacteristic
112#10587489C2311yescharacteristic
113#10587483—41no—
114C2×#63214—41no—
115C2×#63214C2311yescharacteristic
116C2×#63214C2311yescharacteristic
117C2×#63214C2311yescharacteristic
118C2×#63214C2311yescharacteristic
119C24×C17—41no—
120#41×C17—42no—
121#41×C17—81no—
122C2×Q8×C17—21no—
123C2×D4×C17—21no—
124C2×D4×C17—21no—
125C2×D4×C17—42no—
126C2×D4×C17—41no—
127C2×D4×C17—41no—
128C2×D4×C17—41no—
129C2×D4×C17—81no—
130C2×D4×C17D811yescharacteristic
131C22×C4×C17—41no—
132C22×C4×C17—41no—
133C22×C4×C17C2×D411yescharacteristic
134C22×C4×C17C2×D411yescharacteristic
135C2×C22⋊D17—41no—
136C2×C22⋊D17—41no—
137C22×Dic17—41no—
138C22×Dic17—41no—
139#63254—84no—
140C2×D68—21no—
141C2×C4×D17—41no—
142C2×Dic34—41no—
143Q16×C17—21no—
144Q16×C17—21no—
145SD16×C17—42no—
146SD16×C17—81no—
147D8×C17—21no—
148D8×C17—21no—
149D8×C17—21no—
150D8×C17—42no—
151D8×C17#4112yescomplemented
152C2×C8×C17—21no—
153C2×C8×C17—21no—
154C2×C8×C17—21no—
155C2×C8×C17—21no—
156C2×C8×C17C2×D411yescharacteristic
157C2×C8×C17C2×D411yescharacteristic
158C2×C8×C17C2×D411yescharacteristic
159C2×C8×C17C2411yescharacteristic
160C4⋊C4×C17—21no—
161C4⋊C4×C17—41no—
162C4⋊C4×C17D811yescharacteristic
163C22⋊C4×C17—41no—
164C22⋊C4×C17—41no—
165C22⋊C4×C17—41no—
166C22⋊C4×C17—41no—
167C22⋊C4×C17—41no—
168C22⋊C4×C17D811yescharacteristic
169C22⋊C4×C17D811yescharacteristic
170C42×C17C2×D411yescharacteristic
171#63227—41no—
172#63227—41no—
173#63227—41no—
174C4⋊Dic17—21no—
175C4⋊Dic17—21no—
176C4⋊Dic17—21no—
177C4⋊Dic17—41no—
178C4⋊Dic17—41no—
179C4⋊Dic17—41no—
180D136—21no—
181D136—21no—
182#63214—21no—
183#63214—21no—
184#63214—21no—
185#63214—21no—
186#33873—171nomaximal, Sylow
187C23×C17—41no—
188C23×C17—41no—
189C23×C17—82no—
190C23×C17—82no—
191C23×C17—161no—
192C23×C17C2×D811yescharacteristic
193C23×C17C2×D811yescharacteristic
194C22×D17—41no—
195Q8×C17—41no—
196Q8×C17—41no—
197D4×C17—22no—
198D4×C17—22no—
199D4×C17—41no—
200D4×C17—41no—
201D4×C17—41no—
202D4×C17—82no—
203D4×C17—82no—
204D4×C17—161no—
205C2×C4×C17—21no—
206C2×C4×C17—21no—
207C2×C4×C17—21no—
208C2×C4×C17—21no—
209C2×C4×C17—41no—
210C2×C4×C17—41no—
211C2×C4×C17—82no—
212C2×C4×C17—161no—
213C2×C4×C17C2×D811yescharacteristic
214C2×C4×C17C2×D811yescharacteristic
215C2×C4×C17C2×D811yescharacteristic
216C2×C4×C17C2×D811yescharacteristic
217C2×C4×C17C22×D411yescharacteristic
218C22⋊D17—82no—
219C22⋊D17—82no—
220C2×Dic17—41no—
221C2×Dic17—41no—
222C2×Dic17—41no—
223C2×Dic17—82no—
224C2×Dic17—82no—
225D68—41no—
226D68—41no—
227C4×D17—82no—
228Dic34—82no—
229C8×C17—21no—
230C8×C17—21no—
231C8×C17—21no—
232C8×C17C2×#4111yescharacteristic
233C8×C17H(5,𝔽2)11yescharacteristic
234#3334—171no—
235#3280D1711yescharacteristic, complemented
236#2243—171no—
237#2235—171no—
238#2233—171no—
239#2226—171no—
240#2218—171no—
241#2217—171no—
242#2210—171no—
243#2186—171no—
244#2184—171no—
245#2177—171no—
246#2168—171no—
247#2139—171no—
248C2×#357—171no—
249C22×C17—21no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17—42no—
255C22×C17—81no—
256C22×C17—81no—
257C22×C17—81no—
258C22×C17—81no—
259C22×C17—81no—
260C22×C17—164no—
261C22×C17#50912yes—
262C22×C17C22×D811yescharacteristic
263C2×D17—81no—
264C2×D17—81no—
265C2×D17—81no—
266C4×C17—21no—
267C4×C17—21no—
268C4×C17—21no—
269C4×C17—21no—
270C4×C17—81no—
271C4×C17—81no—
272C4×C17#54611yescharacteristic
273C4×C17#57711yescharacteristic
274Dic17—81no—
275Dic17—81no—
276Dic17—81no—
277C2×#135C2×D1711yescharacteristic
278C22×D8C2×D1711yescharacteristic
279#547—341no—
280#546—21no—
281C2×SD32—171no—
282C2×D16—171no—
283C2×D16—171no—
284C2×M32—171no—
285C22×C16—171no—
286#500—171no—
287#495C2×D1711yescharacteristic
288#480—341no—
289#480—341no—
290#474—341no—
291#467C2×D1711yescharacteristic
292#466—171no—
293#466—171no—
294#466C2×D1711yescharacteristic
295#463—21no—
296#450—21no—
297#449—21no—
298C4×D8—171no—
299C4×D8C2×D1711yescharacteristic
300C8×D4C2×D1711yescharacteristic
301C2×#107—171no—
302C2×#107—171no—
303#367—171no—
304#367—171no—
305#367—171no—
306C4⋊C16—171no—
307#358—171no—
308#358—171no—
309#358—171no—
310#357—171no—
311#357—171no—
312#357—171no—
313#357—171no—
314#357—171no—
315#357—171no—
316#357—171no—
317C22⋊C16—171no—
318C22⋊C16—171no—
319#346—171no—
320C2×C17—22no—
321C2×C17—41no—
322C2×C17—82no—
323C2×C17—161no—
324C2×C17#329411yescharacteristic
325C2×C17C2×#50911yescharacteristic
326C2×C17#341611yescharacteristic
327D17—161no—
328C2×#41—21no—
329C2×#41—681no—
330C22×D4—21no—
331#135—22no—
332#135—41no—
333C2×Q16C22×D1711yescharacteristic
334C2×SD16—21no—
335C2×SD16—21no—
336C2×D8—22no—
337C2×D8—21no—
338C2×D8—41no—
339C2×D8—171no—
340C2×D8C22×D1711yescharacteristic
341C2×D8C22×D1711yescharacteristic
342C22×C8C22×D1711yescharacteristic
343C22×C8C22×D1711yescharacteristic
344C4⋊Q8—341no—
345#124—21no—
346#123—41no—
347#123—681no—
348#123—681no—
349C22⋊Q8—21no—
350C22⋊Q8—681no—
351#121—21no—
352#121—41no—
353#121—341no—
354#121—341no—
355#120—41no—
356C4×D4—21no—
357C4×D4—341no—
358C4×D4C22⋊D1711yescharacteristic
359C2×C4⋊C4—341no—
360C2×C4⋊C4—341no—
361C2×C22⋊C4—41no—
362SD32—681no—
363D16—342no—
364D16—681no—
365M32—681no—
366C2×C16—171no—
367C2×C16—171no—
368C2×C16—171no—
369C2×C16—171no—
370C2×C16—681no—
371#107—171no—
372#107—171no—
373#107—171no—
374#107—341no—
375#107—341no—
376#107—341no—
377#107C22×D1711yescharacteristic
378C4⋊C8C22⋊D1711yescharacteristic
379#103—21no—
380#102—21no—
381#102—21no—
382#102—341no—
383#102—341no—
384#102—341no—
385C22⋊C8C22⋊D1711yescharacteristic
386C22⋊C8C22⋊D1711yescharacteristic
387C4×C8C22×D1711yescharacteristic
388C17#3387311yescharacteristic, complemented, Sylow
389C24—41no—
390#41—42no—
391#41—81no—
392#41—1364no—
393C2×Q8—21no—
394C2×Q8—681no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—81no—
402C2×D4—341no—
403C2×D4—681no—
404C2×D4—681no—
405C2×D4#6322811yescharacteristic
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—681no—
409C22×C4—681no—
410C22×C4—681no—
411C22×C4C2×C22⋊D1711yescharacteristic
412C22×C4C2×C22⋊D1711yescharacteristic
413Q16—21no—
414Q16—21no—
415SD16—42no—
416SD16—81no—
417D8—21no—
418D8—21no—
419D8—21no—
420D8—42no—
421D8—341no—
422D8—341no—
423D8#6325412yescomplemented
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8C2×C22⋊D1711yescharacteristic
429C2×C8C2×C22⋊D1711yescharacteristic
430C2×C8C2×C22⋊D1711yescharacteristic
431C2×C8C23×D1711yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—341no—
435C4⋊C4—341no—
436C4⋊C4—341no—
437C4⋊C4—681no—
438C4⋊C4—681no—
439C4⋊C4—681no—
440C4⋊C4#6322811yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—681no—
447C22⋊C4—681no—
448C22⋊C4—681no—
449C22⋊C4#6322811yescharacteristic
450C22⋊C4#6322811yescharacteristic
451C42C2×C22⋊D1711yescharacteristic
452C16—341no—
453C16—341no—
454C16—341no—
455C16—341no—
456C23—41no—
457C23—41no—
458C23—82no—
459C23—82no—
460C23—161no—
461C23—681no—
462C23C2×#6322811yescharacteristic
463C23C2×#6322811yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—1362no—
467D4—22no—
468D4—22no—
469D4—41no—
470D4—41no—
471D4—41no—
472D4—82no—
473D4—82no—
474D4—161no—
475D4—681no—
476D4—681no—
477D4—1362no—
478D4—1362no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—82no—
486C2×C4—161no—
487C2×C4—681no—
488C2×C4—681no—
489C2×C4—681no—
490C2×C4—1362no—
491C2×C4—1362no—
492C2×C4—1362no—
493C2×C4C2×#6322811yescharacteristic
494C2×C4C2×#6322811yescharacteristic
495C2×C4C2×#6322811yescharacteristic
496C2×C4C2×#6322811yescharacteristic
497C2×C4C22×C22⋊D1711yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8C2×#6325411yescharacteristic
502C8#1058769111yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—164no—
515C22—1361no—
516C22—1361no—
517C22—1361no—
518C22#1176324412yes—
519C22C22×#6322811yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—1361no—
527C4—1361no—
528C4—1361no—
529C4#1176345311yescharacteristic
530C4#1176362011yescharacteristic
531C2—22no—
532C2—41no—
533C2—82no—
534C2—161no—
535C2—2721no—
536C2#1454059711yescharacteristic
537C2C2×#1176324411yescharacteristic
538C2#1454193111yescharacteristic
subgroupG/H
centerC22C22×#63228
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC17×#3280C2
socleC22×C17C22×D8
hypercenter#3280D17
hypocenterC17#33873
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #14541132C2semidirect
2. #14531020C2semidirect
3. #14530979C2semidirect
4. #14530967C2semidirect
5. #14530931C2semidirect
6. #14530885C2semidirect
7. #14530882C2semidirect
8. #14530836C2semidirect
9. #14530707C2semidirect
10. #14530696C2semidirect
11. #14530658C2semidirect
12. #14530610C2semidirect
13. #14530496C2semidirect
14. C2×#11762610C2semidirect
15. C17×#3280C2semidirect
17. C2×#10587499C22semidirect
20. C2×#10587483C22semidirect
22. #11763214C22semidirect
27. #11763045C22semidirect
28. C4×D136C22semidirect
30. C2×#10587489C22semidirect
31. #11762636C22semidirect
32. #11762636C22semidirect
33. #11762636C22semidirect
34. C4⋊#63214C22semidirect
35. #11762613C22semidirect
36. #11762613C22semidirect
37. #11762613C22semidirect
44. #11762609C22semidirect
46. C22⋊#63214C22semidirect
47. #11762585C22semidirect
151. D8×C17#41semidirect
235. #3280D17semidirect
388. C17#33873semidirect
423. D8#63254semidirect

Maximal subgroups

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

subgroupindex
#145411322
#145310202
#145309792
#145309672
#145309312
#145308852
#145308822
#145308362
#145307072
#145306962
#145306582
#145306102
#145304962
C2×#117626102
C17×#32802
#3387317