Finite Group Databasebeta

← C83×#61886 #35289710

Subgroups — C83×#61886 #35289710

Order 21248.

1796 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3522C211yesmaximal, characteristic, complemented
2C83×#3480C211yesmaximal, characteristic, complemented
3C83×#3396C213yesmaximal, complemented
4C83×#3394C213yesmaximal, complemented
5C83×#3392C211yesmaximal, characteristic, complemented
6C83×#3391C211yesmaximal, characteristic, complemented
7C83×#3363C211yesmaximal, characteristic, complemented
8C83×#3362C211yesmaximal, characteristic, complemented
9C83×#3361C213yesmaximal, complemented
10C83×#3360C213yesmaximal, complemented
11C83×#3212C213yesmaximal, complemented
12C83×#3207C213yesmaximal, complemented
13C83×#3106C213yesmaximal, complemented
14C83×#3102C213yesmaximal, complemented
15C83×#2982C211yesmaximal, characteristic, complemented
16#559×C83C2213yes—
17#559×C83C2213yes—
18Q82×C83C2211yescharacteristic
19#557×C83C2211yescharacteristic
20#556×C83C2213yes—
21#554×C83C2213yes—
22#553×C83—23no—
23#550×C83C2211yescharacteristic
24#550×C83C2211yescharacteristic
25#548×C83—21no—
26#548×C83—21no—
27#547×C83—23no—
28#542×C83—23no—
29#532×C83C2213yes—
30#532×C83C2213yes—
31#529×C83—23no—
32#529×C83C2213yes—
33#520×C83—21no—
34C4×#41×C83—21no—
35C4×#41×C83C2213yes—
36C2×C4×Q8×C83C2211yescharacteristic
37#495×C83C2216yes—
38#493×C83C2213yes—
39#492×C83C2213yes—
40#488×C83C2216yes—
41#487×C83C2213yes—
42#486×C83C2213yes—
43#485×C83C2211yescharacteristic
44#482×C83C2213yes—
45#479×C83C2213yes—
46#478×C83C2213yes—
47#477×C83C2213yes—
48#476×C83C2213yes—
49#464×C83C2213yes—
50#463×C83C2213yes—
51#463×C83C2216yes—
52#463×C83C2216yes—
53#462×C83C2213yes—
54#461×C83C2213yes—
55#460×C83C2213yes—
56#460×C83C2213yes—
57#459×C83C2213yes—
58#459×C83C2213yes—
59#452×C83C2213yes—
60#449×C83C2213yes—
61#449×C83C2216yes—
62C8×Q8×C83C2213yes—
63C8×Q8×C83C2213yes—
64C8×Q8×C83C2211yescharacteristic
65C8×Q8×C83C2211yescharacteristic
66C4×Q16×C83C2213yes—
67C4×SD16×C83C2213yes—
68C4×SD16×C83C2213yes—
69C4×SD16×C83C2216yes—
70C4×D8×C83C2213yes—
71C4×D8×C83C2216yes—
72#431×C83C2213yes—
73#431×C83C2213yes—
74C2×#41×C83—21no—
75C2×#41×C83—21no—
76C2×#41×C83—23no—
77C2×#41×C83C2313yes—
78C22×Q8×C83D411yescharacteristic
79C2×Q16×C83C2313yes—
80C2×SD16×C83C2313yes—
81C2×SD16×C83C2316yes—
82C2×SD16×C83C2313yes—
83C2×D8×C83C2313yes—
84C2×D8×C83C2316yes—
85C4⋊Q8×C83—23no—
86C4⋊Q8×C83C2313yes—
87C4⋊Q8×C83C2313yes—
88#127×C83C2313yes—
89#127×C83C2313yes—
90#126×C83—26no—
91#126×C83—23no—
92#125×C83—23no—
93#125×C83C2313yes—
94#124×C83—23no—
95#124×C83—23no—
96#124×C83—23no—
97#124×C83C2316yes—
98#124×C83C2313yes—
99#123×C83—23no—
100#123×C83—26no—
101#123×C83—26no—
102C22⋊Q8×C83—23no—
103C22⋊Q8×C83—23no—
104C22⋊Q8×C83—26no—
105C22⋊Q8×C83C2311yescharacteristic
106#121×C83—23no—
107#121×C83—23no—
108#121×C83—23no—
109#121×C83—23no—
110#121×C83—23no—
111#121×C83C2313yes—
112C4×Q8×C83—21no—
113C4×Q8×C83—21no—
114C4×Q8×C83D411yescharacteristic
115C4×Q8×C83D413yes—
116C4×Q8×C83C2313yes—
117C4×Q8×C83C2313yes—
118C4×Q8×C83C2313yes—
119C4×Q8×C83C2311yescharacteristic
120C4×Q8×C83C2313yes—
121C4×D4×C83—23no—
122C4×D4×C83—23no—
123C4×D4×C83—23no—
124C4×D4×C83—23no—
125C4×D4×C83—23no—
126C4×D4×C83—23no—
127C4×D4×C83—23no—
128C4×D4×C83—23no—
129C4×D4×C83C2316yes—
130C4×D4×C83C2313yes—
131C4×D4×C83C2313yes—
132C4×D4×C83C2313yes—
133#117×C83—23no—
134#117×C83—23no—
135#117×C83—23no—
136#117×C83C2311yescharacteristic
137C2×C4⋊C4×C83—23no—
138C2×C4⋊C4×C83D413yes—
139C2×C42×C83—23no—
140C2×C42×C83C2313yes—
141#107×C83C2313yes—
142#107×C83C2311yescharacteristic
143#106×C83C2313yes—
144#106×C83C2311yescharacteristic
145C4⋊C8×C83C2313yes—
146C4⋊C8×C83C2313yes—
147C4⋊C8×C83C2313yes—
148C4⋊C8×C83C2313yes—
149#103×C83C2311yescharacteristic
150#103×C83C2313yes—
151#103×C83C2316yes—
152#103×C83C2311yescharacteristic
153#103×C83C2313yes—
154#102×C83C2313yes—
155#102×C83C2316yes—
156#102×C83C2313yes—
157#102×C83C2313yes—
158#102×C83C2313yes—
159C22⋊C8×C83C2313yes—
160C22⋊C8×C83C2311yescharacteristic
161C4×C8×C83C2313yes—
162C4×C8×C83C2313yes—
163C4×C8×C83C2316yes—
164#41×C83—43no—
165#41×C83—43no—
166#41×C83—44no—
167#41×C83—44no—
168#41×C83—86no—
169C2×Q8×C83—24no—
170C2×Q8×C83—23no—
171C2×Q8×C83C2×D413yes—
172C2×Q8×C83C2×D411yescharacteristic
173C2×Q8×C83C2413yes—
174C2×Q8×C83C2411yescharacteristic
175C2×D4×C83—23no—
176C2×D4×C83—23no—
177C2×D4×C83—23no—
178C2×D4×C83—23no—
179C2×D4×C83—23no—
180C2×D4×C83—23no—
181C2×D4×C83C2413yes—
182C2×D4×C83C2413yes—
183C22×C4×C83—23no—
184C22×C4×C83—23no—
185C22×C4×C83—23no—
186C22×C4×C83—23no—
187C22×C4×C83—26no—
188C22×C4×C83C2×D413yes—
189C22×C4×C83C2×D413yes—
190C22×C4×C83C2411yescharacteristic
191Q16×C83—43no—
192SD16×C83—43no—
193SD16×C83—46no—
194SD16×C83—43no—
195D8×C83—43no—
196D8×C83—46no—
197C2×C8×C83C2411yescharacteristic
198C2×C8×C83C2413yes—
199C2×C8×C83C2413yes—
200C2×C8×C83C2411yescharacteristic
201C4⋊C4×C83—23no—
202C4⋊C4×C83—23no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83—23no—
205C4⋊C4×C83—23no—
206C4⋊C4×C83—23no—
207C4⋊C4×C83—23no—
208C4⋊C4×C83—23no—
209C4⋊C4×C83—23no—
210C4⋊C4×C83C2×D413yes—
211C4⋊C4×C83C2×D413yes—
212C4⋊C4×C83C2×D416yes—
213C4⋊C4×C83C2411yescharacteristic
214C4⋊C4×C83C2413yes—
215C4⋊C4×C83C2411yescharacteristic
216C4⋊C4×C83C2411yescharacteristic
217C22⋊C4×C83—21no—
218C22⋊C4×C83—21no—
219C22⋊C4×C83—26no—
220C22⋊C4×C83—23no—
221C22⋊C4×C83—23no—
222C22⋊C4×C83—23no—
223C22⋊C4×C83—23no—
224C22⋊C4×C83—26no—
225C22⋊C4×C83—23no—
226C22⋊C4×C83—23no—
227C22⋊C4×C83—26no—
228C42×C83—21no—
229C42×C83—23no—
230C42×C83—23no—
231C42×C83—23no—
232C42×C83C2×D413yes—
233C42×C83C2×D413yes—
234C42×C83C2413yes—
235C42×C83C2413yes—
236C23×C83—23no—
237C23×C83—23no—
238C23×C83C22×D411yescharacteristic
239Q8×C83—26no—
240Q8×C83—21no—
241Q8×C83—23no—
242Q8×C83—23no—
243Q8×C83—21no—
244Q8×C83—83no—
245Q8×C83#13514yes—
246D4×C83—23no—
247D4×C83—23no—
248D4×C83—23no—
249D4×C83—23no—
250D4×C83—46no—
251D4×C83—46no—
252D4×C83—46no—
253D4×C83—46no—
254D4×C83—83no—
255D4×C83—83no—
256C2×C4×C83—26no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—21no—
260C2×C4×C83—21no—
261C2×C4×C83—21no—
262C2×C4×C83—23no—
263C2×C4×C83—23no—
264C2×C4×C83—21no—
265C2×C4×C83—43no—
266C2×C4×C83—46no—
267C2×C4×C83—46no—
268C2×C4×C83—46no—
269C2×C4×C83—83no—
270C2×C4×C83—86no—
271C2×C4×C83C22×D411yescharacteristic
272C2×C4×C83C22×D413yes—
273C2×C4×C83C22×D413yes—
274C2×C4×C83C22×D413yes—
275C2×C4×C83C22×D413yes—
276C2×C4×C83C2511yescharacteristic
277C8×C83—21no—
278C8×C83—23no—
279C8×C83—23no—
280C8×C83—21no—
281C22×C83—21no—
282C22×C83—21no—
283C22×C83—21no—
284C22×C83—43no—
285C22×C83—43no—
286C22×C83—43no—
287C22×C83—43no—
288C22×C83—43no—
289C22×C83—43no—
290C22×C83C23×D411yescharacteristic
291C4×C83—23no—
292C4×C83—23no—
293C4×C83—21no—
294C4×C83—23no—
295C4×C83—41no—
296C4×C83—43no—
297C4×C83—43no—
298C4×C83—41no—
299C4×C83—41no—
300C4×C83—41no—
301C4×C83C2×#13516yes—
302C4×C83#58511yescharacteristic
303C4×C83#58511yescharacteristic
304#61886C8311yesmaximal, characteristic, direct product factor, Sylow
305C2×C83—41no—
306C2×C83—83no—
307C2×C83—83no—
308C2×C83#348711yescharacteristic
309C2×C83C22×#13511yescharacteristic
310C2×C83#358511yescharacteristic
311#3522C2×C8311yescharacteristic, complemented
312#3480C2×C8311yescharacteristic, complemented
313#3396C2×C8313yescomplemented
314#3394C2×C8313yescomplemented
315#3392C2×C8311yescharacteristic, complemented
316#3391C2×C8311yescharacteristic, complemented
317#3363C2×C8311yescharacteristic, complemented
318#3362C2×C8311yescharacteristic, complemented
319#3361C2×C8313yescomplemented
320#3360C2×C8313yescomplemented
321#3212C2×C8313yescomplemented
322#3207C2×C8313yescomplemented
323#3106C2×C8313yescomplemented
324#3102C2×C8313yescomplemented
325#2982C2×C8311yescharacteristic, complemented
326C83#6188611yescharacteristic, direct product factor, Sylow
327#559C22×C8313yes—
328#559C22×C8313yes—
329Q82C22×C8311yescharacteristic
330#557C22×C8311yescharacteristic
331#556C22×C8313yes—
332#554C22×C8313yes—
333#553—23no—
334#550C22×C8311yescharacteristic
335#550C22×C8311yescharacteristic
336#548—21no—
337#548—21no—
338#547—23no—
339#542—23no—
340#532C22×C8313yes—
341#532C22×C8313yes—
342#529—23no—
343#529C22×C8313yes—
344#520—21no—
345C4×#41—21no—
346C4×#41C22×C8313yes—
347C2×C4×Q8C22×C8311yescharacteristic
348#495C22×C8316yes—
349#493C22×C8313yes—
350#492C22×C8313yes—
351#488C22×C8316yes—
352#487C22×C8313yes—
353#486C22×C8313yes—
354#485C22×C8311yescharacteristic
355#482C22×C8313yes—
356#479C22×C8313yes—
357#478C22×C8313yes—
358#477C22×C8313yes—
359#476C22×C8313yes—
360#464C22×C8313yes—
361#463C22×C8313yes—
362#463C22×C8316yes—
363#463C22×C8316yes—
364#462C22×C8313yes—
365#461C22×C8313yes—
366#460C22×C8313yes—
367#460C22×C8313yes—
368#459C22×C8313yes—
369#459C22×C8313yes—
370#452C22×C8313yes—
371#449C22×C8313yes—
372#449C22×C8316yes—
373C8×Q8C22×C8313yes—
374C8×Q8C22×C8313yes—
375C8×Q8C22×C8311yescharacteristic
376C8×Q8C22×C8311yescharacteristic
377C4×Q16C22×C8313yes—
378C4×SD16C22×C8313yes—
379C4×SD16C22×C8313yes—
380C4×SD16C22×C8316yes—
381C4×D8C22×C8313yes—
382C4×D8C22×C8316yes—
383#431C22×C8313yes—
384#431C22×C8313yes—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—23no—
388C2×#41C23×C8313yes—
389C22×Q8D4×C8311yescharacteristic
390C2×Q16C23×C8313yes—
391C2×SD16C23×C8316yes—
392C2×SD16C23×C8313yes—
393C2×SD16C23×C8313yes—
394C2×D8C23×C8316yes—
395C2×D8C23×C8313yes—
396C4⋊Q8—23no—
397C4⋊Q8C23×C8313yes—
398C4⋊Q8C23×C8313yes—
399#127C23×C8313yes—
400#127C23×C8313yes—
401#126—26no—
402#126—23no—
403#125—23no—
404#125C23×C8313yes—
405#124—23no—
406#124—23no—
407#124—23no—
408#124C23×C8313yes—
409#124C23×C8316yes—
410#123—23no—
411#123—26no—
412#123—26no—
413C22⋊Q8—23no—
414C22⋊Q8—23no—
415C22⋊Q8—26no—
416C22⋊Q8C23×C8311yescharacteristic
417#121—23no—
418#121—23no—
419#121—23no—
420#121—23no—
421#121—23no—
422#121C23×C8313yes—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8D4×C8311yescharacteristic
426C4×Q8D4×C8313yes—
427C4×Q8C23×C8313yes—
428C4×Q8C23×C8313yes—
429C4×Q8C23×C8313yes—
430C4×Q8C23×C8311yescharacteristic
431C4×Q8C23×C8313yes—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4—23no—
436C4×D4—23no—
437C4×D4—23no—
438C4×D4—23no—
439C4×D4—23no—
440C4×D4C23×C8313yes—
441C4×D4C23×C8313yes—
442C4×D4C23×C8313yes—
443C4×D4C23×C8316yes—
444#117—23no—
445#117—23no—
446#117—23no—
447#117C23×C8311yescharacteristic
448C2×C4⋊C4—23no—
449C2×C4⋊C4D4×C8313yes—
450C2×C42—23no—
451C2×C42C23×C8313yes—
452#107C23×C8311yescharacteristic
453#107C23×C8313yes—
454#106C23×C8313yes—
455#106C23×C8311yescharacteristic
456C4⋊C8C23×C8313yes—
457C4⋊C8C23×C8313yes—
458C4⋊C8C23×C8313yes—
459C4⋊C8C23×C8313yes—
460#103C23×C8311yescharacteristic
461#103C23×C8316yes—
462#103C23×C8313yes—
463#103C23×C8311yescharacteristic
464#103C23×C8313yes—
465#102C23×C8313yes—
466#102C23×C8313yes—
467#102C23×C8316yes—
468#102C23×C8313yes—
469#102C23×C8313yes—
470C22⋊C8C23×C8311yescharacteristic
471C22⋊C8C23×C8313yes—
472C4×C8C23×C8316yes—
473C4×C8C23×C8313yes—
474C4×C8C23×C8313yes—
475#41—43no—
476#41—43no—
477#41—44no—
478#41—44no—
479#41—86no—
480C2×Q8—24no—
481C2×Q8—23no—
482C2×Q8C2×D4×C8313yes—
483C2×Q8C2×D4×C8311yescharacteristic
484C2×Q8C24×C8313yes—
485C2×Q8C24×C8311yescharacteristic
486C2×D4—23no—
487C2×D4—23no—
488C2×D4—23no—
489C2×D4—23no—
490C2×D4—23no—
491C2×D4—23no—
492C2×D4C24×C8313yes—
493C2×D4C24×C8313yes—
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—23no—
497C22×C4—23no—
498C22×C4—26no—
499C22×C4C2×D4×C8313yes—
500C22×C4C2×D4×C8313yes—
501C22×C4C24×C8311yescharacteristic
502Q16—43no—
503SD16—43no—
504SD16—46no—
505SD16—43no—
506D8—43no—
507D8—46no—
508C2×C8C24×C8313yes—
509C2×C8C24×C8311yescharacteristic
510C2×C8C24×C8313yes—
511C2×C8C24×C8311yescharacteristic
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—21no—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—23no—
520C4⋊C4—23no—
521C4⋊C4C2×D4×C8313yes—
522C4⋊C4C2×D4×C8313yes—
523C4⋊C4C2×D4×C8316yes—
524C4⋊C4C24×C8311yescharacteristic
525C4⋊C4C24×C8313yes—
526C4⋊C4C24×C8311yescharacteristic
527C4⋊C4C24×C8311yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—26no—
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—23no—
534C22⋊C4—23no—
535C22⋊C4—26no—
536C22⋊C4—23no—
537C22⋊C4—23no—
538C22⋊C4—26no—
539C42—21no—
540C42—23no—
541C42—23no—
542C42—23no—
543C42C2×D4×C8313yes—
544C42C2×D4×C8313yes—
545C42C24×C8313yes—
546C42C24×C8313yes—
547C23—23no—
548C23—23no—
549C23C22×D4×C8311yescharacteristic
550Q8—26no—
551Q8—21no—
552Q8—23no—
553Q8—23no—
554Q8—21no—
555Q8—83no—
556Q8#135×C8314yes—
557D4—23no—
558D4—23no—
559D4—23no—
560D4—23no—
561D4—46no—
562D4—46no—
563D4—46no—
564D4—46no—
565D4—83no—
566D4—83no—
567C2×C4—26no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—43no—
577C2×C4—46no—
578C2×C4—46no—
579C2×C4—46no—
580C2×C4—86no—
581C2×C4—83no—
582C2×C4C22×D4×C8311yescharacteristic
583C2×C4C22×D4×C8313yes—
584C2×C4C22×D4×C8313yes—
585C2×C4C22×D4×C8313yes—
586C2×C4C22×D4×C8313yes—
587C2×C4C25×C8311yescharacteristic
588C8—21no—
589C8—23no—
590C8—23no—
591C8—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—43no—
596C22—43no—
597C22—43no—
598C22—43no—
599C22—43no—
600C22—43no—
601C22C23×D4×C8311yescharacteristic
602C4—23no—
603C4—23no—
604C4—23no—
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—43no—
610C4—43no—
611C4—41no—
612C4C2×#135×C8316yes—
613C4#585×C8311yescharacteristic
614C4#585×C8311yescharacteristic
615C2—41no—
616C2—83no—
617C2—83no—
618C2C83×#348711yescharacteristic
619C2C22×#135×C8311yescharacteristic
620C2C83×#358511yescharacteristic
subgroupG/H
center, socleC22×C83C23×D4
commutator, Frattini, cosocleC2×C4C25×C83
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C4×Q8×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3522C2semidirect
2. C83×#3480C2semidirect
3. C83×#3396C2semidirect
4. C83×#3394C2semidirect
5. C83×#3392C2semidirect
6. C83×#3391C2semidirect
7. C83×#3363C2semidirect
8. C83×#3362C2semidirect
9. C83×#3361C2semidirect
10. C83×#3360C2semidirect
11. C83×#3212C2semidirect
12. C83×#3207C2semidirect
13. C83×#3106C2semidirect
14. C83×#3102C2semidirect
15. C83×#2982C2semidirect
304. #61886C83direct (N × H)
311. #3522C2×C83semidirect
312. #3480C2×C83semidirect
313. #3396C2×C83semidirect
314. #3394C2×C83semidirect
315. #3392C2×C83semidirect
316. #3391C2×C83semidirect
317. #3363C2×C83semidirect
318. #3362C2×C83semidirect
319. #3361C2×C83semidirect
320. #3360C2×C83semidirect
321. #3212C2×C83semidirect
322. #3207C2×C83semidirect
323. #3106C2×C83semidirect
324. #3102C2×C83semidirect
325. #2982C2×C83semidirect
326. C83#61886direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#35222
C83×#34802
C83×#33962
C83×#33942
C83×#33922
C83×#33912
C83×#33632
C83×#33622
C83×#33612
C83×#33602
C83×#32122
C83×#32072
C83×#31062
C83×#31022
C83×#29822
#6188683