Finite Group Databasebeta

← #35559512

Subgroups — #35559512

Order 21248.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918102C211yesmaximal, characteristic, complemented
2#24909671C211yesmaximal, characteristic, complemented
3#24909654C211yesmaximal, characteristic, complemented
4#24909610C211yesmaximal, characteristic, complemented
5#24909600C211yesmaximal, characteristic, complemented
6#24909518C211yesmaximal, characteristic, complemented
7#24909518C211yesmaximal, characteristic, complemented
8#24909392C211yesmaximal, characteristic, complemented
9#24909375C211yesmaximal, characteristic
10#24909337C211yesmaximal, characteristic, complemented
11#24909327C211yesmaximal, characteristic, complemented
12C4×#14581736C211yesmaximal, characteristic, complemented
13C4×#14581733C211yesmaximal, characteristic, complemented
14#24909270C211yesmaximal, characteristic, complemented
15C83×#2948C211yesmaximal, characteristic, complemented
16#19128322—21no—
17C2×#14581736C2211yescharacteristic
18C2×#14581736C2211yescharacteristic
19C2×#14581733C2211yescharacteristic
20C2×#14581733C2211yescharacteristic
21#19128106C2211yescharacteristic, complemented
22#19128085C2211yescharacteristic, complemented
23#19128061—21no—
24#19127947—21no—
25#19127942C2211yescharacteristic
26#19127937C2211yescharacteristic
27#19127803—21no—
28C4×Dic332C2211yescharacteristic, complemented
29C4×D664C2211yescharacteristic, complemented
30#19127528C2211yescharacteristic, complemented
31#19127528C2211yescharacteristic, complemented
32#19127526C2211yescharacteristic, complemented
33#19127526C2211yescharacteristic, complemented
34C4⋊(C83⋊C16)C2211yescharacteristic, complemented
35C4⋊(C83⋊C16)C2211yescharacteristic, complemented
36#19127504C2211yescharacteristic, complemented
37#19127504C2211yescharacteristic, complemented
38#19127502C2211yescharacteristic
39#19127502C2211yescharacteristic
40#19127502C2211yescharacteristic
41#19127502C2211yescharacteristic
42#19127501C2211yescharacteristic, complemented
43#19127501C2211yescharacteristic, complemented
44C22⋊(C83⋊C16)C2211yescharacteristic
45C22⋊(C83⋊C16)C2211yescharacteristic
46#19127477C2211yescharacteristic, complemented
47C4×C83⋊C16C2211yescharacteristic, complemented
48C22×D8×C83C2211yescharacteristic
49#518×C83—21no—
50#442×C83—21no—
51#442×C83—21no—
52C4×D8×C83C2211yescharacteristic
53C4×D8×C83C2211yescharacteristic
54C4×D8×C83C2211yescharacteristic
55C4×D8×C83C2211yescharacteristic
56#427×C83C2211yescharacteristic
57#418×C83—21no—
58#405×C83C2211yescharacteristic
59C2×Dic332C2311yescharacteristic
60C2×#13050579—21no—
61C2×D664C2311yescharacteristic
62#14581792—21no—
63#14581787—41no—
64#14581780—21no—
65#14581778—41no—
66#14581774—41no—
67#14581771—21no—
68#14581770—41no—
69#14581766—21no—
70C4×Dic166—21no—
71C4×D332—21no—
72#14581736—22no—
73#14581736—22no—
74#14581733—22no—
75#14581733—22no—
76C2×C83⋊C16C2311yescharacteristic
77C2×C83⋊C16C2311yescharacteristic
78C2×C83⋊C16C2311yescharacteristic
79C2×C83⋊C16C2311yescharacteristic
80#14581726—21no—
81#14581726C2311yescharacteristic
82#14581726C2311yescharacteristic
83#14581717—21no—
84#14581717—21no—
85#14581714—21no—
86#14581714—21no—
87C22×D4×C83—21no—
88C2×D8×C83—22no—
89C2×D8×C83—22no—
90C2×D8×C83—21no—
91C2×D8×C83C2311yescharacteristic
92C2×D8×C83C2311yescharacteristic
93C2×M16×C83D411yescharacteristic
94C22×C8×C83C2311yescharacteristic
95C4×D4×C83—21no—
96C4×D4×C83—21no—
97C4×D4×C83—21no—
98C4×D4×C83—21no—
99C4×D4×C83—41no—
100C4×D4×C83—41no—
101#117×C83—21no—
102#117×C83D411yescharacteristic
103C2×C22⋊C4×C83—41no—
104C2×C22⋊C4×C83—41no—
105#107×C83C2311yescharacteristic
106#107×C83C2311yescharacteristic
107#106×C83—21no—
108#102×C83—21no—
109#102×C83—21no—
110#102×C83—21no—
111#102×C83—21no—
112#97×C83D411yescharacteristic
113#97×C83D411yescharacteristic
114C4×C8×C83C2311yescharacteristic
115C4×C8×C83C2311yescharacteristic
116C2×Dic166—21no—
117C2×Dic166—41no—
118C2×D332—21no—
119C2×C22⋊D83—41no—
120C2×C4×D83—41no—
121Dic332—21no—
122Dic332—21no—
123#13050579—42no—
124D664—21no—
125D664—21no—
126C4⋊Dic83—21no—
127C4⋊Dic83—21no—
128C4⋊Dic83—41no—
129Dic83⋊C4—41no—
130Dic83⋊C4—41no—
131C22⋊Dic83—41no—
132(C2×D83)⋊C4—41no—
133(C2×D83)⋊C4—41no—
134(C2×D83)⋊C4—41no—
135(C2×D83)⋊C4—41no—
136C4×Dic83—41no—
137C83⋊C16—21no—
138C83⋊C16—21no—
139C83⋊C16—21no—
140C83⋊C16—21no—
141C24×C83—41no—
142C2×D4×C83—24no—
143C2×D4×C83—21no—
144C2×D4×C83—21no—
145C2×D4×C83—42no—
146C2×D4×C83—41no—
147C22×C4×C83—41no—
148C22×C4×C83—41no—
149C22×C4×C83—41no—
150C22×C4×C83—41no—
151C22×C4×C83C2×D411yescharacteristic
152D8×C83—24no—
153D8×C83—21no—
154D8×C83—21no—
155D8×C83#4112yes—
156D8×C83#4112yes—
157M16×C83—41no—
158C2×C8×C83—21no—
159C2×C8×C83—21no—
160C2×C8×C83C2×D411yescharacteristic
161C2×C8×C83C2×D411yescharacteristic
162C2×C8×C83C2×D411yescharacteristic
163C2×C8×C83C2411yescharacteristic
164C4⋊C4×C83—21no—
165C4⋊C4×C83—21no—
166C4⋊C4×C83D811yescharacteristic
167C4⋊C4×C83D811yescharacteristic
168C22⋊C4×C83—41no—
169C22⋊C4×C83—41no—
170C22⋊C4×C83—41no—
171C22⋊C4×C83—41no—
172C22⋊C4×C83—41no—
173C22⋊C4×C83D811yescharacteristic
174C22⋊C4×C83D811yescharacteristic
175C42×C83—41no—
176C42×C83C2×D411yescharacteristic
177C42×C83C2×D411yescharacteristic
178C23×C83—44no—
179C23×C83—41no—
180C23×C83—41no—
181C23×C83—161no—
182C23×C83—161no—
183C23×C83C2×D811yescharacteristic
184C22×D83—41no—
185D4×C83—22no—
186D4×C83—22no—
187D4×C83—44no—
188D4×C83—41no—
189D4×C83—41no—
190C2×C4×C83—21no—
191C2×C4×C83—21no—
192C2×C4×C83—41no—
193C2×C4×C83—41no—
194C2×C4×C83—161no—
195C2×C4×C83—161no—
196C2×C4×C83—161no—
197C2×C4×C83—161no—
198C2×C4×C83C2×D811yescharacteristic
199C2×C4×C83C2×D811yescharacteristic
200C2×C4×C83C2×D811yescharacteristic
201C2×C4×C83C2×D811yescharacteristic
202C2×C4×C83C2×D811yescharacteristic
203C2×C4×C83C22×D411yescharacteristic
204C22⋊D83—161no—
205C2×Dic83—41no—
206C2×Dic83—41no—
207C2×Dic83—41no—
208D332—41no—
209D332—41no—
210C4×D83—161no—
211Dic166—41no—
212Dic166—41no—
213Dic166—161no—
214C8×C83—21no—
215C8×C83—21no—
216C8×C83—21no—
217C8×C83C2×#4111yescharacteristic
218C8×C83C2×#4111yescharacteristic
219C22×C83—21no—
220C22×C83—21no—
221C22×C83—21no—
222C22×C83—42no—
223C22×C83—42no—
224C22×C83—81no—
225C22×C83—81no—
226C22×C83—81no—
227C22×C83—81no—
228C22×C83—164no—
229C22×C83C22×D811yescharacteristic
230C2×D83—81no—
231C2×D83—81no—
232C2×D83—81no—
233C4×C83—21no—
234C4×C83—21no—
235C4×C83—21no—
236C4×C83—21no—
237C4×C83—21no—
238C4×C83—81no—
239C4×C83—81no—
240C4×C83#52511yescharacteristic
241C4×C83#57511yescharacteristic
242Dic83—81no—
243Dic83—81no—
244Dic83—81no—
245#33678—831nomaximal, Sylow
246C2×C83—41no—
247C2×C83—82no—
248C2×C83—82no—
249C2×C83#310011yescharacteristic
250C2×C83#341511yescharacteristic
251C2×C83#341611yescharacteristic
252D83—161no—
253#3175—831no—
254#2948D8311yescharacteristic, complemented
255#2237—831no—
256#2234—831no—
257#2226—831no—
258#2224—831no—
259#2210—831no—
260#2210—831no—
261#2187—831no—
262#2184—831no—
263#2177—831no—
264#2175—831no—
265C4×SD32—831no—
266C4×D16—831no—
267#2164—831no—
268C83#3367811yescharacteristic, complemented, Sylow
269C22×D8C2×D8311yescharacteristic
270#542—1661no—
271#518—21no—
272C2×SD32—831no—
273C2×SD32—831no—
274C2×D16—831no—
275C2×D16—831no—
276#500—831no—
277#495—831no—
278#489—1661no—
279#468—1661no—
280#467—831no—
281#466—831no—
282#442—21no—
283#442—21no—
284#440—1661no—
285C4×Q16—831no—
286C4×D8—831no—
287C4×D8C2×D8311yescharacteristic
288C4×D8C2×D8311yescharacteristic
289C4×D8C2×D8311yescharacteristic
290C4×D8C2×D8311yescharacteristic
291#427C2×D8311yescharacteristic
292#418—21no—
293#405C2×D8311yescharacteristic
294#367—831no—
295#367—831no—
296#366—831no—
297#366—831no—
298C4⋊C16—831no—
299C4⋊C16—831no—
300#358—831no—
301#358—831no—
302#357—831no—
303#357—831no—
304#357—831no—
305#357—831no—
306#357—831no—
307#357—831no—
308C22⋊C16—831no—
309C22⋊C16—831no—
310#346—831no—
311C4×C16—831no—
312C22×D4—21no—
313C2×Q16—831no—
314C2×SD16—1661no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—21no—
318C2×D8—831no—
319C2×D8C22×D8311yescharacteristic
320C2×D8C22×D8311yescharacteristic
321C2×M16C22⋊D8311yescharacteristic
322C22×C8C22×D8311yescharacteristic
323C4⋊Q8—1661no—
324#126—3321no—
325#124—3321no—
326#124—1661no—
327#123—3321no—
328C22⋊Q8—3321no—
329C22⋊Q8—1661no—
330#121—1661no—
331C4×Q8—1661no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—41no—
337C4×D4—41no—
338C4×D4—1661no—
339#117—21no—
340#117C22⋊D8311yescharacteristic
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343SD32—1662no—
344SD32—1662no—
345D16—1662no—
346D16—1662no—
347C2×C16—831no—
348C2×C16—831no—
349C2×C16—831no—
350C2×C16—831no—
351#107—831no—
352#107—831no—
353#107—1661no—
354#107C22×D8311yescharacteristic
355#107C22×D8311yescharacteristic
356#106—21no—
357#103—1661no—
358#103—1661no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—21no—
363#102—1661no—
364#102—1661no—
365#97C22⋊D8311yescharacteristic
366#97C22⋊D8311yescharacteristic
367C4×C8C22×D8311yescharacteristic
368C4×C8C22×D8311yescharacteristic
369C24—41no—
370C2×Q8—3321no—
371C2×Q8—1661no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—42no—
376C2×D4—41no—
377C2×D4—3321no—
378C2×D4—1661no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—3321no—
384C22×C4C2×C22⋊D8311yescharacteristic
385Q16—1661no—
386Q16—1661no—
387SD16—3322no—
388D8—24no—
389D8—21no—
390D8—21no—
391D8—1661no—
392D8—1661no—
393D8#1305059012yes—
394D8#1305059012yes—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×C22⋊D8311yescharacteristic
399C2×C8C2×C22⋊D8311yescharacteristic
400C2×C8C2×C22⋊D8311yescharacteristic
401C2×C8C23×D8311yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—3321no—
405C4⋊C4—3321no—
406C4⋊C4—3321no—
407C4⋊C4—1661no—
408C4⋊C4—1661no—
409C4⋊C4#1305057511yescharacteristic
410C4⋊C4#1305057511yescharacteristic
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—3321no—
417C22⋊C4—3321no—
418C22⋊C4—3321no—
419C22⋊C4—3321no—
420C22⋊C4—3321no—
421C22⋊C4#1305057511yescharacteristic
422C22⋊C4#1305057511yescharacteristic
423C42—41no—
424C42—3321no—
425C42C2×C22⋊D8311yescharacteristic
426C42C2×C22⋊D8311yescharacteristic
427C16—1661no—
428C16—1661no—
429C16—1661no—
430C16—1661no—
431C23—44no—
432C23—41no—
433C23—41no—
434C23—161no—
435C23—161no—
436C23—3321no—
437C23C2×#1305057511yescharacteristic
438Q8—13281no—
439Q8—3321no—
440Q8—3321no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—13281no—
447D4—3321no—
448D4—3321no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—161no—
457C2×C4—13281no—
458C2×C4—3321no—
459C2×C4—3321no—
460C2×C4—3321no—
461C2×C4C2×#1305057511yescharacteristic
462C2×C4C2×#1305057511yescharacteristic
463C2×C4C2×#1305057511yescharacteristic
464C2×C4C2×#1305057511yescharacteristic
465C2×C4C2×#1305057511yescharacteristic
466C2×C4C22×C22⋊D8311yescharacteristic
467C8—21no—
468C8—21no—
469C8—21no—
470C8C2×#1305059011yescharacteristic
471C8C2×#1305059011yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—164no—
482C22—6641no—
483C22—6641no—
484C22—6641no—
485C22C22×#1305057511yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—81no—
492C4—81no—
493C4—6641no—
494C4—6641no—
495C4—6641no—
496C4#1912821211yescharacteristic
497C4#1912849911yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—13281no—
502C2#2491746311yescharacteristic
503C2#2492060211yescharacteristic
504C2#2492061011yescharacteristic
subgroupG/H
centerC22C22×#13050575
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC83×#2948C2
socleC22×C83C22×D8
prime radical#24909375C2
hypercenter#2948D83
hypocenterC83#33678
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
1. #24918102C2semidirect
2. #24909671C2semidirect
3. #24909654C2semidirect
4. #24909610C2semidirect
5. #24909600C2semidirect
6. #24909518C2semidirect
7. #24909518C2semidirect
8. #24909392C2semidirect
10. #24909337C2semidirect
11. #24909327C2semidirect
12. C4×#14581736C2semidirect
13. C4×#14581733C2semidirect
14. #24909270C2semidirect
15. C83×#2948C2semidirect
21. #19128106C22semidirect
22. #19128085C22semidirect
28. C4×Dic332C22semidirect
29. C4×D664C22semidirect
30. #19127528C22semidirect
31. #19127528C22semidirect
32. #19127526C22semidirect
33. #19127526C22semidirect
34. C4⋊(C83⋊C16)C22semidirect
35. C4⋊(C83⋊C16)C22semidirect
36. #19127504C22semidirect
37. #19127504C22semidirect
42. #19127501C22semidirect
43. #19127501C22semidirect
46. #19127477C22semidirect
47. C4×C83⋊C16C22semidirect
254. #2948D83semidirect
268. C83#33678semidirect

Maximal subgroups

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

subgroupindex
#249181022
#249096712
#249096542
#249096102
#249096002
#249095182
#249093922
#249093752
#249093372
#249093272
C4×#145817362
C4×#145817332
#249092702
C83×#29482
#3367883