Finite Group Databasebeta

← C83×#19869 #35247693

Subgroups — C83×#19869 #35247693

Order 21248.

596 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3398C211yesmaximal, characteristic, complemented
2C83×#3392C211yesmaximal, characteristic
3C83×#3383C211yesmaximal, characteristic, complemented
4C83×#3304C211yesmaximal, characteristic
5C83×#1722C211yesmaximal, characteristic, complemented
6C83×#1686C211yesmaximal, characteristic, complemented
7C83×#1682C211yesmaximal, characteristic, complemented
8C83×#1673C211yesmaximal, characteristic, complemented
9C83×#1670C211yesmaximal, characteristic, complemented
10C83×#1650C211yesmaximal, characteristic, complemented
11C83×#1648C211yesmaximal, characteristic, complemented
12C83×#1642C211yesmaximal, characteristic
13C83×#1626C211yesmaximal, characteristic, complemented
14C83×#1584C211yesmaximal, characteristic, complemented
15C83×SD16⋊C8C211yesmaximal, characteristic, complemented
16#557×C83C2211yescharacteristic
17#557×C83C2211yescharacteristic
18#556×C83C2211yescharacteristic
19#550×C83C2211yescharacteristic
20#500×C83C2211yescharacteristic
21#500×C83C2211yescharacteristic
22#499×C83—21no—
23#497×C83—21no—
24#494×C83C2211yescharacteristic
25#492×C83—21no—
26#492×C83C2211yescharacteristic
27#486×C83C2211yescharacteristic
28#486×C83C2211yescharacteristic
29#482×C83—21no—
30#479×C83—21no—
31#479×C83—21no—
32#475×C83C2211yescharacteristic
33#475×C83C2211yescharacteristic
34#475×C83C2211yescharacteristic
35#465×C83—21no—
36#464×C83—21no—
37#462×C83—21no—
38#462×C83C2211yescharacteristic
39#461×C83—21no—
40#461×C83C2211yescharacteristic
41#461×C83C2211yescharacteristic
42#460×C83—21no—
43#460×C83C2211yescharacteristic
44#460×C83C2211yescharacteristic
45#452×C83—21no—
46#446×C83C2211yescharacteristic
47C8×Q8×C83C2211yescharacteristic
48C8×Q8×C83C2211yescharacteristic
49#441×C83—21no—
50C4×Q16×C83—21no—
51C4×Q16×C83C2211yescharacteristic
52C4×SD16×C83—21no—
53C4×SD16×C83C2211yescharacteristic
54C8×D4×C83C2211yescharacteristic
55#416×C83—21no—
56#335×C83C2211yescharacteristic
57#335×C83C2211yescharacteristic
58#332×C83C2211yescharacteristic
59#332×C83C2211yescharacteristic
60#332×C83C2211yescharacteristic
61#331×C83C2211yescharacteristic
62Q8⋊C8×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#41×C83—21no—
68C2×Q16×C83—21no—
69C2×Q16×C83—21no—
70C2×Q16×C83—21no—
71C2×Q16×C83D411yescharacteristic
72C2×SD16×C83—21no—
73C2×SD16×C83—21no—
74C2×SD16×C83—21no—
75C2×SD16×C83—21no—
76C2×SD16×C83—21no—
77C2×SD16×C83—21no—
78C2×SD16×C83D411yescharacteristic
79C22×C8×C83—21no—
80C4⋊Q8×C83—21no—
81C4⋊Q8×C83—21no—
82C4⋊Q8×C83C2311yescharacteristic
83C4⋊Q8×C83C2311yescharacteristic
84C4⋊Q8×C83C2311yescharacteristic
85#127×C83—21no—
86#127×C83C2311yescharacteristic
87#126×C83—41no—
88#125×C83—21no—
89#125×C83—21no—
90#125×C83—41no—
91#125×C83—41no—
92#124×C83—21no—
93C22⋊Q8×C83—21no—
94#121×C83—21no—
95#121×C83—41no—
96C4×Q8×C83—21no—
97C4×Q8×C83—21no—
98C4×Q8×C83—21no—
99C4×Q8×C83—21no—
100C4×Q8×C83—21no—
101C4×Q8×C83C2311yescharacteristic
102C4×Q8×C83C2311yescharacteristic
103C4×Q8×C83C2311yescharacteristic
104C4×D4×C83—21no—
105C4×D4×C83C2311yescharacteristic
106#117×C83—21no—
107#107×C83—21no—
108#107×C83—21no—
109#107×C83—41no—
110#107×C83D411yescharacteristic
111#106×C83—21no—
112#106×C83—21no—
113#106×C83—21no—
114#106×C83D411yescharacteristic
115C4⋊C8×C83—21no—
116C4⋊C8×C83—21no—
117C4⋊C8×C83—21no—
118C4⋊C8×C83C2311yescharacteristic
119C4⋊C8×C83C2311yescharacteristic
120C4⋊C8×C83C2311yescharacteristic
121C4⋊C8×C83C2311yescharacteristic
122#103×C83—21no—
123#103×C83—21no—
124#103×C83—21no—
125#103×C83—21no—
126#103×C83—21no—
127#103×C83—21no—
128#103×C83D411yescharacteristic
129#103×C83D411yescharacteristic
130#103×C83D411yescharacteristic
131#102×C83—21no—
132#102×C83—21no—
133#102×C83—21no—
134#102×C83—21no—
135#102×C83—41no—
136#102×C83D411yescharacteristic
137C22⋊C8×C83—21no—
138#97×C83—21no—
139C4×C8×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144#41×C83—42no—
145#41×C83—81no—
146C2×Q8×C83—21no—
147C2×Q8×C83—21no—
148C2×Q8×C83—21no—
149C2×Q8×C83C2×D411yescharacteristic
150C2×Q8×C83C2×D411yescharacteristic
151C2×Q8×C83C2×D411yescharacteristic
152C2×D4×C83—21no—
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—41no—
156C2×D4×C83—41no—
157C2×D4×C83C2×D411yescharacteristic
158C22×C4×C83—21no—
159C22×C4×C83—41no—
160Q16×C83—22no—
161Q16×C83—42no—
162Q16×C83—81no—
163Q16×C83—81no—
164SD16×C83—22no—
165SD16×C83—42no—
166SD16×C83—81no—
167SD16×C83—81no—
168SD16×C83—81no—
169SD16×C83—81no—
170SD16×C83—81no—
171C2×C8×C83—21no—
172C2×C8×C83—21no—
173C2×C8×C83—21no—
174C2×C8×C83—21no—
175C2×C8×C83—21no—
176C2×C8×C83—81no—
177C2×C8×C83C2×D411yescharacteristic
178C2×C8×C83C2×D411yescharacteristic
179C2×C8×C83C2×D411yescharacteristic
180C2×C8×C83C2×D411yescharacteristic
181C4⋊C4×C83—21no—
182C4⋊C4×C83—21no—
183C4⋊C4×C83—21no—
184C4⋊C4×C83—21no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—41no—
191C4⋊C4×C83—41no—
192C4⋊C4×C83—41no—
193C4⋊C4×C83—41no—
194C4⋊C4×C83—41no—
195C4⋊C4×C83—41no—
196C4⋊C4×C83—41no—
197C4⋊C4×C83C2×D411yescharacteristic
198C4⋊C4×C83C2×D411yescharacteristic
199C4⋊C4×C83C2×D411yescharacteristic
200C4⋊C4×C83C2×D411yescharacteristic
201C22⋊C4×C83—21no—
202C22⋊C4×C83—41no—
203C22⋊C4×C83—41no—
204C22⋊C4×C83—41no—
205C42×C83—21no—
206C42×C83—21no—
207C42×C83—21no—
208C42×C83—41no—
209C42×C83—41no—
210C42×C83—41no—
211C42×C83C2411yescharacteristic
212C23×C83—21no—
213C23×C83—41no—
214Q8×C83—21no—
215Q8×C83—21no—
216Q8×C83—21no—
217Q8×C83—21no—
218Q8×C83—21no—
219Q8×C83—41no—
220Q8×C83—41no—
221Q8×C83—41no—
222Q8×C83—41no—
223Q8×C83—41no—
224Q8×C83—41no—
225Q8×C83#13712yes—
226D4×C83—21no—
227D4×C83—21no—
228D4×C83—41no—
229D4×C83—41no—
230D4×C83—41no—
231D4×C83—41no—
232D4×C83—82no—
233D4×C83—81no—
234D4×C83—161no—
235C2×C4×C83—21no—
236C2×C4×C83—21no—
237C2×C4×C83—21no—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83—41no—
247C2×C4×C83—82no—
248C2×C4×C83C22×D411yescharacteristic
249C2×C4×C83C22×D411yescharacteristic
250C2×C4×C83H(5,𝔽2)11yescharacteristic
251C8×C83—21no—
252C8×C83—21no—
253C8×C83—21no—
254C8×C83—41no—
255C8×C83—41no—
256C8×C83—41no—
257C8×C83—41no—
258C8×C83—41no—
259C8×C83#13512yes—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83—81no—
264C22×C83—81no—
265C22×C83—81no—
266C22×C83D4211yescharacteristic
267C4×C83—22no—
268C4×C83—21no—
269C4×C83—41no—
270C4×C83—41no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83—41no—
274C4×C83—41no—
275C4×C83—81no—
276C4×C83—81no—
277C4×C83—81no—
278C4×C83C2×#13511yescharacteristic
279C4×C83C2×#13711yescharacteristic
280C4×C83#57611yescharacteristic
281C4×C83#57711yescharacteristic
282#19869C8311yesmaximal, characteristic, direct product factor, Sylow
283C2×C83—81no—
284C2×C83—161no—
285C2×C83#326611yescharacteristic
286C2×C83#328711yescharacteristic
287C2×C83#328911yescharacteristic
288#3398C2×C8311yescharacteristic, complemented
289#3392C2×C8311yescharacteristic
290#3383C2×C8311yescharacteristic, complemented
291#3304C2×C8311yescharacteristic
292#1722C2×C8311yescharacteristic, complemented
293#1686C2×C8311yescharacteristic, complemented
294#1682C2×C8311yescharacteristic, complemented
295#1673C2×C8311yescharacteristic, complemented
296#1670C2×C8311yescharacteristic, complemented
297#1650C2×C8311yescharacteristic, complemented
298#1648C2×C8311yescharacteristic, complemented
299#1642C2×C8311yescharacteristic
300#1626C2×C8311yescharacteristic, complemented
301#1584C2×C8311yescharacteristic, complemented
302SD16⋊C8C2×C8311yescharacteristic, complemented
303C83#1986911yescharacteristic, direct product factor, Sylow
304#557C22×C8311yescharacteristic
305#557C22×C8311yescharacteristic
306#556C22×C8311yescharacteristic
307#550C22×C8311yescharacteristic
308#500C22×C8311yescharacteristic
309#500C22×C8311yescharacteristic
310#499—21no—
311#497—21no—
312#494C22×C8311yescharacteristic
313#492—21no—
314#492C22×C8311yescharacteristic
315#486C22×C8311yescharacteristic
316#486C22×C8311yescharacteristic
317#482—21no—
318#479—21no—
319#479—21no—
320#475C22×C8311yescharacteristic
321#475C22×C8311yescharacteristic
322#475C22×C8311yescharacteristic
323#465—21no—
324#464—21no—
325#462—21no—
326#462C22×C8311yescharacteristic
327#461—21no—
328#461C22×C8311yescharacteristic
329#461C22×C8311yescharacteristic
330#460—21no—
331#460C22×C8311yescharacteristic
332#460C22×C8311yescharacteristic
333#452—21no—
334#446C22×C8311yescharacteristic
335C8×Q8C22×C8311yescharacteristic
336C8×Q8C22×C8311yescharacteristic
337#441—21no—
338C4×Q16—21no—
339C4×Q16C22×C8311yescharacteristic
340C4×SD16—21no—
341C4×SD16C22×C8311yescharacteristic
342C8×D4C22×C8311yescharacteristic
343#416—21no—
344#335C22×C8311yescharacteristic
345#335C22×C8311yescharacteristic
346#332C22×C8311yescharacteristic
347#332C22×C8311yescharacteristic
348#332C22×C8311yescharacteristic
349#331C22×C8311yescharacteristic
350Q8⋊C8C22×C8311yescharacteristic
351Q8⋊C8C22×C8311yescharacteristic
352Q8⋊C8C22×C8311yescharacteristic
353D4⋊C8C22×C8311yescharacteristic
354#322C22×C8311yescharacteristic
355C2×#41—21no—
356C2×Q16—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16D4×C8311yescharacteristic
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16D4×C8311yescharacteristic
367C22×C8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8C23×C8311yescharacteristic
371C4⋊Q8C23×C8311yescharacteristic
372C4⋊Q8C23×C8311yescharacteristic
373#127—21no—
374#127C23×C8311yescharacteristic
375#126—41no—
376#125—21no—
377#125—21no—
378#125—41no—
379#125—41no—
380#124—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—41no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C23×C8311yescharacteristic
390C4×Q8C23×C8311yescharacteristic
391C4×Q8C23×C8311yescharacteristic
392C4×D4—21no—
393C4×D4C23×C8311yescharacteristic
394#117—21no—
395#107—21no—
396#107—21no—
397#107—41no—
398#107D4×C8311yescharacteristic
399#106—21no—
400#106—21no—
401#106—21no—
402#106D4×C8311yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C8311yescharacteristic
407C4⋊C8C23×C8311yescharacteristic
408C4⋊C8C23×C8311yescharacteristic
409C4⋊C8C23×C8311yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103D4×C8311yescharacteristic
417#103D4×C8311yescharacteristic
418#103D4×C8311yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—41no—
424#102D4×C8311yescharacteristic
425C22⋊C8—21no—
426#97—21no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8C23×C8311yescharacteristic
430C4×C8C23×C8311yescharacteristic
431C4×C8C23×C8311yescharacteristic
432#41—42no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×D4×C8311yescharacteristic
438C2×Q8C2×D4×C8311yescharacteristic
439C2×Q8C2×D4×C8311yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4C2×D4×C8311yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448Q16—22no—
449Q16—42no—
450Q16—81no—
451Q16—81no—
452SD16—22no—
453SD16—42no—
454SD16—81no—
455SD16—81no—
456SD16—81no—
457SD16—81no—
458SD16—81no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—81no—
465C2×C8C2×D4×C8311yescharacteristic
466C2×C8C2×D4×C8311yescharacteristic
467C2×C8C2×D4×C8311yescharacteristic
468C2×C8C2×D4×C8311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4C2×D4×C8311yescharacteristic
486C4⋊C4C2×D4×C8311yescharacteristic
487C4⋊C4C2×D4×C8311yescharacteristic
488C4⋊C4C2×D4×C8311yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42C24×C8311yescharacteristic
500C23—21no—
501C23—41no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8#137×C8312yes—
514D4—21no—
515D4—21no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—82no—
521D4—81no—
522D4—161no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4C22×D4×C8311yescharacteristic
537C2×C4C22×D4×C8311yescharacteristic
538C2×C4H(5,𝔽2)×C8311yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8#135×C8312yes—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22D42×C8311yescharacteristic
555C4—21no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4C2×#135×C8311yescharacteristic
567C4C2×#137×C8311yescharacteristic
568C4#576×C8311yescharacteristic
569C4#577×C8311yescharacteristic
570C2—81no—
571C2—161no—
572C2C83×#326611yescharacteristic
573C2C83×#328711yescharacteristic
574C2C83×#328911yescharacteristic
subgroupG/H
center, socleC22×C83D42
commutator, Frattini, cosocleC42C24×C83
prime radical#550×C83C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3398C2semidirect
3. C83×#3383C2semidirect
5. C83×#1722C2semidirect
6. C83×#1686C2semidirect
7. C83×#1682C2semidirect
8. C83×#1673C2semidirect
9. C83×#1670C2semidirect
10. C83×#1650C2semidirect
11. C83×#1648C2semidirect
13. C83×#1626C2semidirect
14. C83×#1584C2semidirect
15. C83×SD16⋊C8C2semidirect
282. #19869C83direct (N × H)
288. #3398C2×C83semidirect
290. #3383C2×C83semidirect
292. #1722C2×C83semidirect
293. #1686C2×C83semidirect
294. #1682C2×C83semidirect
295. #1673C2×C83semidirect
296. #1670C2×C83semidirect
297. #1650C2×C83semidirect
298. #1648C2×C83semidirect
300. #1626C2×C83semidirect
301. #1584C2×C83semidirect
302. SD16⋊C8C2×C83semidirect
303. C83#19869direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#33982
C83×#33922
C83×#33832
C83×#33042
C83×#17222
C83×#16862
C83×#16822
C83×#16732
C83×#16702
C83×#16502
C83×#16482
C83×#16422
C83×#16262
C83×#15842
C83×SD16⋊C82
#1986983