Finite Group Databasebeta

← C83×#19784 #35247608

Subgroups — C83×#19784 #35247608

Order 21248.

622 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3358C211yesmaximal, characteristic, complemented
2C83×#3341C211yesmaximal, characteristic, complemented
3C83×#3329C211yesmaximal, characteristic, complemented
4C83×#3305C211yesmaximal, characteristic, complemented
5C83×#1719C211yesmaximal, characteristic, complemented
6C83×#1697C211yesmaximal, characteristic, complemented
7C83×#1683C211yesmaximal, characteristic, complemented
8C83×#1681C211yesmaximal, characteristic, complemented
9C83×#1676C211yesmaximal, characteristic, complemented
10C83×#1646C211yesmaximal, characteristic, complemented
11C83×#1637C211yesmaximal, characteristic, complemented
12C83×#1631C211yesmaximal, characteristic, complemented
13C83×#1624C211yesmaximal, characteristic, complemented
14C83×#1581C211yesmaximal, characteristic, complemented
15C83×SD16⋊C8C211yesmaximal, characteristic, complemented
16#555×C83C2211yescharacteristic
17#555×C83C2211yescharacteristic
18#550×C83C2211yescharacteristic
19D4×Q8×C83C2211yescharacteristic
20#500×C83C2211yescharacteristic
21#492×C83C2211yescharacteristic
22#487×C83C2211yescharacteristic
23#487×C83C2211yescharacteristic
24#486×C83—21no—
25#486×C83C2211yescharacteristic
26#486×C83C2211yescharacteristic
27#485×C83—21no—
28#482×C83—21no—
29#482×C83—21no—
30#482×C83—21no—
31#477×C83C2211yescharacteristic
32#477×C83C2211yescharacteristic
33#476×C83C2211yescharacteristic
34#476×C83C2211yescharacteristic
35#474×C83—21no—
36#474×C83C2211yescharacteristic
37#468×C83—21no—
38#466×C83—21no—
39#466×C83—21no—
40#461×C83C2211yescharacteristic
41#459×C83—21no—
42#459×C83C2211yescharacteristic
43#459×C83C2211yescharacteristic
44#449×C83—21no—
45#448×C83—21no—
46C8×Q8×C83C2211yescharacteristic
47C4×SD16×C83C2211yescharacteristic
48C4×D8×C83—21no—
49C4×D8×C83C2211yescharacteristic
50#436×C83C2211yescharacteristic
51C8×D4×C83C2211yescharacteristic
52C8×D4×C83C2211yescharacteristic
53#427×C83—21no—
54#419×C83—21no—
55#416×C83—21no—
56#335×C83C2211yescharacteristic
57#335×C83C2211yescharacteristic
58#333×C83C2211yescharacteristic
59#333×C83C2211yescharacteristic
60#332×C83C2211yescharacteristic
61#331×C83C2211yescharacteristic
62Q8⋊C8×C83C2211yescharacteristic
63D4⋊C8×C83C2211yescharacteristic
64D4⋊C8×C83C2211yescharacteristic
65D4⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#41×C83—21no—
68C22×Q8×C83—21no—
69C2×SD16×C83—21no—
70C2×SD16×C83—41no—
71C2×SD16×C83D411yescharacteristic
72C2×D8×C83—21no—
73C2×D8×C83—21no—
74C2×D8×C83D411yescharacteristic
75C2×M16×C83—21no—
76C22×C8×C83—21no—
77C22×C8×C83—21no—
78C4⋊Q8×C83—21no—
79C4⋊Q8×C83C2311yescharacteristic
80C4⋊Q8×C83C2311yescharacteristic
81C4⋊Q8×C83C2311yescharacteristic
82#127×C83—21no—
83#127×C83C2311yescharacteristic
84#124×C83—41no—
85#124×C83—41no—
86C22⋊Q8×C83—21no—
87C22⋊Q8×C83—41no—
88#121×C83—21no—
89#121×C83—21no—
90#121×C83—21no—
91#121×C83—21no—
92#121×C83—21no—
93#121×C83—41no—
94C4×Q8×C83C2311yescharacteristic
95C4×D4×C83—21no—
96C4×D4×C83—21no—
97C4×D4×C83C2311yescharacteristic
98C4×D4×C83C2311yescharacteristic
99C4×D4×C83C2311yescharacteristic
100#117×C83—21no—
101#117×C83—21no—
102#117×C83—21no—
103#117×C83—21no—
104#107×C83—21no—
105#107×C83—21no—
106#107×C83—21no—
107#107×C83—21no—
108#107×C83—21no—
109#107×C83D411yescharacteristic
110#106×C83—21no—
111#106×C83—21no—
112#106×C83D411yescharacteristic
113C4⋊C8×C83—21no—
114C4⋊C8×C83C2311yescharacteristic
115C4⋊C8×C83C2311yescharacteristic
116C4⋊C8×C83C2311yescharacteristic
117C4⋊C8×C83C2311yescharacteristic
118#103×C83—21no—
119#103×C83—21no—
120#103×C83—21no—
121#103×C83—21no—
122#103×C83—21no—
123#103×C83—41no—
124#103×C83D411yescharacteristic
125#102×C83—21no—
126#102×C83—21no—
127#102×C83—21no—
128#102×C83—21no—
129#102×C83—21no—
130#102×C83—21no—
131#102×C83—21no—
132#102×C83—21no—
133#102×C83—21no—
134#102×C83D411yescharacteristic
135#102×C83D411yescharacteristic
136#102×C83D411yescharacteristic
137C22⋊C8×C83—21no—
138C22⋊C8×C83—21no—
139C22⋊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×C83—41no—
150C2×Q8×C83—42no—
151C2×Q8×C83—81no—
152C2×Q8×C83C2×D411yescharacteristic
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—41no—
157C2×D4×C83—41no—
158C2×D4×C83—41no—
159C2×D4×C83—41no—
160C2×D4×C83C2×D411yescharacteristic
161C2×D4×C83C2×D411yescharacteristic
162C2×D4×C83C2×D411yescharacteristic
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—41no—
167C22×C4×C83—41no—
168SD16×C83—22no—
169SD16×C83—81no—
170SD16×C83—82no—
171D8×C83—41no—
172D8×C83—42no—
173D8×C83—81no—
174M16×C83—81no—
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—42no—
181C2×C8×C83—81no—
182C2×C8×C83C2×D411yescharacteristic
183C2×C8×C83C2×D411yescharacteristic
184C2×C8×C83C2×D411yescharacteristic
185C2×C8×C83C2×D411yescharacteristic
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—41no—
194C4⋊C4×C83C2×D411yescharacteristic
195C4⋊C4×C83C2×D411yescharacteristic
196C4⋊C4×C83C2×D411yescharacteristic
197C4⋊C4×C83C2×D411yescharacteristic
198C22⋊C4×C83—21no—
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—41no—
202C22⋊C4×C83—41no—
203C22⋊C4×C83—41no—
204C22⋊C4×C83—41no—
205C22⋊C4×C83—41no—
206C22⋊C4×C83—41no—
207C42×C83—21no—
208C42×C83—41no—
209C42×C83—41no—
210C42×C83C2411yescharacteristic
211C23×C83—21no—
212C23×C83—21no—
213C23×C83—21no—
214C23×C83—41no—
215Q8×C83—21no—
216Q8×C83—41no—
217Q8×C83—41no—
218Q8×C83—82no—
219Q8×C83—81no—
220Q8×C83—81no—
221Q8×C83#13512yes—
222D4×C83—21no—
223D4×C83—21no—
224D4×C83—21no—
225D4×C83—21no—
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—
235D4×C83—161no—
236D4×C83—161no—
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—41no—
248C2×C4×C83—41no—
249C2×C4×C83—41no—
250C2×C4×C83—41no—
251C2×C4×C83—82no—
252C2×C4×C83—82no—
253C2×C4×C83C22×D411yescharacteristic
254C2×C4×C83C22×D411yescharacteristic
255C2×C4×C83H(5,𝔽2)11yescharacteristic
256C8×C83—21no—
257C8×C83—21no—
258C8×C83—21no—
259C8×C83—21no—
260C8×C83—41no—
261C8×C83—41no—
262C8×C83—41no—
263C8×C83—41no—
264C8×C83—41no—
265C22×C83—41no—
266C22×C83—41no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83—41no—
270C22×C83—41no—
271C22×C83—41no—
272C22×C83—41no—
273C22×C83—41no—
274C22×C83—81no—
275C22×C83—81no—
276C22×C83—81no—
277C22×C83D4211yescharacteristic
278C4×C83—22no—
279C4×C83—21no—
280C4×C83—41no—
281C4×C83—41no—
282C4×C83—41no—
283C4×C83—41no—
284C4×C83—81no—
285C4×C83—81no—
286C4×C83—81no—
287C4×C83C2×#13511yescharacteristic
288C4×C83#57511yescharacteristic
289C4×C83#57611yescharacteristic
290C4×C83#57811yescharacteristic
291#19784C8311yesmaximal, characteristic, direct product factor, Sylow
292C2×C83—81no—
293C2×C83—81no—
294C2×C83—81no—
295C2×C83—161no—
296C2×C83#326911yescharacteristic
297C2×C83#328011yescharacteristic
298C2×C83#328811yescharacteristic
299#3358C2×C8311yescharacteristic, complemented
300#3341C2×C8311yescharacteristic, complemented
301#3329C2×C8311yescharacteristic, complemented
302#3305C2×C8311yescharacteristic, complemented
303#1719C2×C8311yescharacteristic, complemented
304#1697C2×C8311yescharacteristic, complemented
305#1683C2×C8311yescharacteristic, complemented
306#1681C2×C8311yescharacteristic, complemented
307#1676C2×C8311yescharacteristic, complemented
308#1646C2×C8311yescharacteristic, complemented
309#1637C2×C8311yescharacteristic, complemented
310#1631C2×C8311yescharacteristic, complemented
311#1624C2×C8311yescharacteristic, complemented
312#1581C2×C8311yescharacteristic, complemented
313SD16⋊C8C2×C8311yescharacteristic, complemented
314C83#1978411yescharacteristic, direct product factor, Sylow
315#555C22×C8311yescharacteristic
316#555C22×C8311yescharacteristic
317#550C22×C8311yescharacteristic
318D4×Q8C22×C8311yescharacteristic
319#500C22×C8311yescharacteristic
320#492C22×C8311yescharacteristic
321#487C22×C8311yescharacteristic
322#487C22×C8311yescharacteristic
323#486—21no—
324#486C22×C8311yescharacteristic
325#486C22×C8311yescharacteristic
326#485—21no—
327#482—21no—
328#482—21no—
329#482—21no—
330#477C22×C8311yescharacteristic
331#477C22×C8311yescharacteristic
332#476C22×C8311yescharacteristic
333#476C22×C8311yescharacteristic
334#474—21no—
335#474C22×C8311yescharacteristic
336#468—21no—
337#466—21no—
338#466—21no—
339#461C22×C8311yescharacteristic
340#459—21no—
341#459C22×C8311yescharacteristic
342#459C22×C8311yescharacteristic
343#449—21no—
344#448—21no—
345C8×Q8C22×C8311yescharacteristic
346C4×SD16C22×C8311yescharacteristic
347C4×D8—21no—
348C4×D8C22×C8311yescharacteristic
349#436C22×C8311yescharacteristic
350C8×D4C22×C8311yescharacteristic
351C8×D4C22×C8311yescharacteristic
352#427—21no—
353#419—21no—
354#416—21no—
355#335C22×C8311yescharacteristic
356#335C22×C8311yescharacteristic
357#333C22×C8311yescharacteristic
358#333C22×C8311yescharacteristic
359#332C22×C8311yescharacteristic
360#331C22×C8311yescharacteristic
361Q8⋊C8C22×C8311yescharacteristic
362D4⋊C8C22×C8311yescharacteristic
363D4⋊C8C22×C8311yescharacteristic
364D4⋊C8C22×C8311yescharacteristic
365#322C22×C8311yescharacteristic
366C2×#41—21no—
367C22×Q8—21no—
368C2×SD16—21no—
369C2×SD16—41no—
370C2×SD16D4×C8311yescharacteristic
371C2×D8—21no—
372C2×D8—21no—
373C2×D8D4×C8311yescharacteristic
374C2×M16—21no—
375C22×C8—21no—
376C22×C8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C8311yescharacteristic
379C4⋊Q8C23×C8311yescharacteristic
380C4⋊Q8C23×C8311yescharacteristic
381#127—21no—
382#127C23×C8311yescharacteristic
383#124—41no—
384#124—41no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387#121—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—41no—
393C4×Q8C23×C8311yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C8311yescharacteristic
397C4×D4C23×C8311yescharacteristic
398C4×D4C23×C8311yescharacteristic
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107D4×C8311yescharacteristic
409#106—21no—
410#106—21no—
411#106D4×C8311yescharacteristic
412C4⋊C8—21no—
413C4⋊C8C23×C8311yescharacteristic
414C4⋊C8C23×C8311yescharacteristic
415C4⋊C8C23×C8311yescharacteristic
416C4⋊C8C23×C8311yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—41no—
423#103D4×C8311yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102D4×C8311yescharacteristic
434#102D4×C8311yescharacteristic
435#102D4×C8311yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C4×C8—21no—
440C4×C8C23×C8311yescharacteristic
441C4×C8C23×C8311yescharacteristic
442C4×C8C23×C8311yescharacteristic
443#41—42no—
444#41—81no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—41no—
449C2×Q8—42no—
450C2×Q8—81no—
451C2×Q8C2×D4×C8311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C2×D4×C8311yescharacteristic
460C2×D4C2×D4×C8311yescharacteristic
461C2×D4C2×D4×C8311yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467SD16—22no—
468SD16—81no—
469SD16—82no—
470D8—41no—
471D8—42no—
472D8—81no—
473M16—81no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—81no—
481C2×C8C2×D4×C8311yescharacteristic
482C2×C8C2×D4×C8311yescharacteristic
483C2×C8C2×D4×C8311yescharacteristic
484C2×C8C2×D4×C8311yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C8311yescharacteristic
494C4⋊C4C2×D4×C8311yescharacteristic
495C4⋊C4C2×D4×C8311yescharacteristic
496C4⋊C4C2×D4×C8311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42C24×C8311yescharacteristic
510C23—21no—
511C23—21no—
512C23—21no—
513C23—41no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—81no—
519Q8—81no—
520Q8#135×C8312yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—81no—
533D4—161no—
534D4—161no—
535D4—161no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4C22×D4×C8311yescharacteristic
553C2×C4C22×D4×C8311yescharacteristic
554C2×C4H(5,𝔽2)×C8311yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C8311yescharacteristic
577C4—22no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4C2×#135×C8311yescharacteristic
587C4#575×C8311yescharacteristic
588C4#576×C8311yescharacteristic
589C4#578×C8311yescharacteristic
590C2—81no—
591C2—81no—
592C2—81no—
593C2—161no—
594C2C83×#326911yescharacteristic
595C2C83×#328011yescharacteristic
596C2C83×#328811yescharacteristic
subgroupG/H
center, socleC22×C83D42
commutator, Frattini, cosocleC42C24×C83
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×#3358C2semidirect
2. C83×#3341C2semidirect
3. C83×#3329C2semidirect
4. C83×#3305C2semidirect
5. C83×#1719C2semidirect
6. C83×#1697C2semidirect
7. C83×#1683C2semidirect
8. C83×#1681C2semidirect
9. C83×#1676C2semidirect
10. C83×#1646C2semidirect
11. C83×#1637C2semidirect
12. C83×#1631C2semidirect
13. C83×#1624C2semidirect
14. C83×#1581C2semidirect
15. C83×SD16⋊C8C2semidirect
291. #19784C83direct (N × H)
299. #3358C2×C83semidirect
300. #3341C2×C83semidirect
301. #3329C2×C83semidirect
302. #3305C2×C83semidirect
303. #1719C2×C83semidirect
304. #1697C2×C83semidirect
305. #1683C2×C83semidirect
306. #1681C2×C83semidirect
307. #1676C2×C83semidirect
308. #1646C2×C83semidirect
309. #1637C2×C83semidirect
310. #1631C2×C83semidirect
311. #1624C2×C83semidirect
312. #1581C2×C83semidirect
313. SD16⋊C8C2×C83semidirect
314. C83#19784direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#33582
C83×#33412
C83×#33292
C83×#33052
C83×#17192
C83×#16972
C83×#16832
C83×#16812
C83×#16762
C83×#16462
C83×#16372
C83×#16312
C83×#16242
C83×#15812
C83×SD16⋊C82
#1978483