Finite Group Databasebeta

← C83×#61887 #35289711

Subgroups — C83×#61887 #35289711

Order 21248.

1740 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3523C211yesmaximal, characteristic, complemented
2C83×#3480C211yesmaximal, characteristic, complemented
3C83×#3395C211yesmaximal, characteristic, complemented
4C83×#3394C213yesmaximal, complemented
5C83×#3393C213yesmaximal, complemented
6C83×#3392C211yesmaximal, characteristic, complemented
7C83×#3365C213yesmaximal, complemented
8C83×#3364C213yesmaximal, complemented
9C83×#3359C211yesmaximal, characteristic, complemented
10C83×#3358C211yesmaximal, characteristic, complemented
11C83×#3212C213yesmaximal, complemented
12C83×#3210C213yesmaximal, complemented
13C83×#3107C213yesmaximal, complemented
14C83×#3102C213yesmaximal, complemented
15C83×#2982C211yesmaximal, characteristic, complemented
16#559×C83C2213yes—
17#557×C83C2211yescharacteristic
18#557×C83C2211yescharacteristic
19#557×C83C2213yes—
20#556×C83C2213yes—
21#556×C83C2213yes—
22#553×C83—23no—
23#552×C83—23no—
24#550×C83C2211yescharacteristic
25D4×Q8×C83—21no—
26D4×Q8×C83C2211yescharacteristic
27#548×C83—21no—
28#541×C83—23no—
29#533×C83C2213yes—
30#532×C83C2213yes—
31#529×C83—23no—
32#529×C83C2213yes—
33#519×C83—21no—
34C4×#41×C83—21no—
35C4×#41×C83C2213yes—
36C2×C4×Q8×C83C2211yescharacteristic
37#495×C83C2216yes—
38#494×C83C2213yes—
39#492×C83C2213yes—
40#488×C83C2216yes—
41#487×C83C2213yes—
42#486×C83C2213yes—
43#485×C83C2213yes—
44#482×C83C2211yescharacteristic
45#479×C83C2213yes—
46#478×C83C2213yes—
47#475×C83C2213yes—
48#474×C83C2213yes—
49#464×C83C2213yes—
50#464×C83C2216yes—
51#464×C83C2216yes—
52#463×C83C2213yes—
53#462×C83C2213yes—
54#462×C83C2213yes—
55#461×C83C2213yes—
56#461×C83C2213yes—
57#460×C83C2213yes—
58#459×C83C2213yes—
59#452×C83C2213yes—
60#452×C83C2216yes—
61#449×C83C2213yes—
62C8×Q8×C83C2211yescharacteristic
63C8×Q8×C83C2211yescharacteristic
64C8×Q8×C83C2213yes—
65C8×Q8×C83C2213yes—
66C4×Q16×C83C2213yes—
67C4×Q16×C83C2216yes—
68C4×SD16×C83C2213yes—
69C4×SD16×C83C2213yes—
70C4×SD16×C83C2216yes—
71C4×D8×C83C2213yes—
72#431×C83C2213yes—
73#431×C83C2213yes—
74C2×#41×C83—21no—
75C2×#41×C83C2313yes—
76C22×Q8×C83—21no—
77C22×Q8×C83D411yescharacteristic
78C2×Q16×C83C2313yes—
79C2×Q16×C83C2316yes—
80C2×SD16×C83C2313yes—
81C2×SD16×C83C2316yes—
82C2×SD16×C83C2313yes—
83C2×D8×C83C2313yes—
84C4⋊Q8×C83—23no—
85C4⋊Q8×C83C2313yes—
86C4⋊Q8×C83C2313yes—
87C4⋊Q8×C83C2313yes—
88#127×C83C2313yes—
89#126×C83—26no—
90#126×C83—26no—
91#126×C83—23no—
92#125×C83—23no—
93#125×C83—26no—
94#125×C83—23no—
95#125×C83—23no—
96#125×C83C2313yes—
97#124×C83—23no—
98#124×C83C2313yes—
99#124×C83C2316yes—
100#123×C83—23no—
101#123×C83—26no—
102C22⋊Q8×C83—23no—
103C22⋊Q8×C83—23no—
104C22⋊Q8×C83—23no—
105C22⋊Q8×C83—23no—
106C22⋊Q8×C83C2313yes—
107#121×C83—23no—
108#121×C83—23no—
109#121×C83—23no—
110#121×C83C2311yescharacteristic
111C4×Q8×C83—21no—
112C4×Q8×C83—21no—
113C4×Q8×C83—23no—
114C4×Q8×C83—23no—
115C4×Q8×C83D411yescharacteristic
116C4×Q8×C83D413yes—
117C4×Q8×C83C2316yes—
118C4×Q8×C83C2313yes—
119C4×Q8×C83C2313yes—
120C4×Q8×C83C2313yes—
121C4×Q8×C83C2311yescharacteristic
122C4×Q8×C83C2313yes—
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×C83C2313yes—
130C4×D4×C83C2313yes—
131C4×D4×C83C2313yes—
132#117×C83—23no—
133#117×C83—23no—
134#117×C83—23no—
135#117×C83—23no—
136#117×C83—23no—
137#117×C83C2311yescharacteristic
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×C83C2313yes—
150#103×C83C2313yes—
151#103×C83C2316yes—
152#103×C83C2313yes—
153#103×C83C2313yes—
154#102×C83C2311yescharacteristic
155#102×C83C2311yescharacteristic
156#102×C83C2313yes—
157#102×C83C2316yes—
158#102×C83C2313yes—
159C22⋊C8×C83C2311yescharacteristic
160C22⋊C8×C83C2313yes—
161C4×C8×C83C2313yes—
162C4×C8×C83C2313yes—
163C4×C8×C83C2316yes—
164#41×C83—43no—
165#41×C83—43no—
166#41×C83—44no—
167C2×Q8×C83—24no—
168C2×Q8×C83—23no—
169C2×Q8×C83—44no—
170C2×Q8×C83C2×D413yes—
171C2×Q8×C83C2×D411yescharacteristic
172C2×Q8×C83C2413yes—
173C2×Q8×C83C2413yes—
174C2×D4×C83—21no—
175C2×D4×C83—23no—
176C2×D4×C83—23no—
177C2×D4×C83—23no—
178C2×D4×C83C2413yes—
179C2×D4×C83C2411yescharacteristic
180C22×C4×C83—23no—
181C22×C4×C83—23no—
182C22×C4×C83—23no—
183C22×C4×C83—23no—
184C22×C4×C83C2×D413yes—
185C22×C4×C83C2×D413yes—
186C22×C4×C83C2411yescharacteristic
187Q16×C83—46no—
188Q16×C83—43no—
189SD16×C83—43no—
190SD16×C83—43no—
191SD16×C83—46no—
192D8×C83—43no—
193C2×C8×C83C2411yescharacteristic
194C2×C8×C83C2413yes—
195C2×C8×C83C2411yescharacteristic
196C2×C8×C83C2413yes—
197C4⋊C4×C83—23no—
198C4⋊C4×C83—23no—
199C4⋊C4×C83—23no—
200C4⋊C4×C83—23no—
201C4⋊C4×C83—23no—
202C4⋊C4×C83—23no—
203C4⋊C4×C83—23no—
204C4⋊C4×C83—23no—
205C4⋊C4×C83—23no—
206C4⋊C4×C83—23no—
207C4⋊C4×C83—26no—
208C4⋊C4×C83—23no—
209C4⋊C4×C83C2×D413yes—
210C4⋊C4×C83C2×D413yes—
211C4⋊C4×C83C2×D416yes—
212C4⋊C4×C83C2413yes—
213C4⋊C4×C83C2411yescharacteristic
214C4⋊C4×C83C2411yescharacteristic
215C4⋊C4×C83C2411yescharacteristic
216C22⋊C4×C83—23no—
217C22⋊C4×C83—21no—
218C22⋊C4×C83—21no—
219C22⋊C4×C83—23no—
220C22⋊C4×C83—26no—
221C22⋊C4×C83—23no—
222C22⋊C4×C83—23no—
223C22⋊C4×C83—26no—
224C22⋊C4×C83—23no—
225C22⋊C4×C83—23no—
226C42×C83—21no—
227C42×C83—23no—
228C42×C83—23no—
229C42×C83—26no—
230C42×C83—23no—
231C42×C83C2×D413yes—
232C42×C83C2×D413yes—
233C42×C83C2413yes—
234C42×C83C2413yes—
235C23×C83—21no—
236C23×C83—23no—
237C23×C83C22×D411yescharacteristic
238Q8×C83—26no—
239Q8×C83—23no—
240Q8×C83—23no—
241Q8×C83—23no—
242Q8×C83—23no—
243Q8×C83—46no—
244Q8×C83#13514yes—
245D4×C83—21no—
246D4×C83—23no—
247D4×C83—21no—
248D4×C83—23no—
249D4×C83—42no—
250D4×C83—46no—
251D4×C83—46no—
252D4×C83—83no—
253C2×C4×C83—26no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—23no—
259C2×C4×C83—21no—
260C2×C4×C83—23no—
261C2×C4×C83—23no—
262C2×C4×C83—43no—
263C2×C4×C83—46no—
264C2×C4×C83—46no—
265C2×C4×C83—46no—
266C2×C4×C83—83no—
267C2×C4×C83C22×D413yes—
268C2×C4×C83C22×D411yescharacteristic
269C2×C4×C83C22×D413yes—
270C2×C4×C83C22×D413yes—
271C2×C4×C83C22×D413yes—
272C2×C4×C83C2511yescharacteristic
273C8×C83—23no—
274C8×C83—21no—
275C8×C83—23no—
276C8×C83—21no—
277C22×C83—21no—
278C22×C83—21no—
279C22×C83—21no—
280C22×C83—43no—
281C22×C83—41no—
282C22×C83—43no—
283C22×C83—41no—
284C22×C83—41no—
285C22×C83—43no—
286C22×C83C23×D411yescharacteristic
287C4×C83—23no—
288C4×C83—23no—
289C4×C83—21no—
290C4×C83—23no—
291C4×C83—41no—
292C4×C83—41no—
293C4×C83—43no—
294C4×C83—43no—
295C4×C83—41no—
296C4×C83—43no—
297C4×C83C2×#13516yes—
298C4×C83#58511yescharacteristic
299C4×C83#58511yescharacteristic
300#61887C8311yesmaximal, characteristic, direct product factor, Sylow
301C2×C83—41no—
302C2×C83—83no—
303C2×C83—81no—
304C2×C83#348711yescharacteristic
305C2×C83C22×#13511yescharacteristic
306C2×C83#358611yescharacteristic
307#3523C2×C8311yescharacteristic, complemented
308#3480C2×C8311yescharacteristic, complemented
309#3395C2×C8311yescharacteristic, complemented
310#3394C2×C8313yescomplemented
311#3393C2×C8313yescomplemented
312#3392C2×C8311yescharacteristic, complemented
313#3365C2×C8313yescomplemented
314#3364C2×C8313yescomplemented
315#3359C2×C8311yescharacteristic, complemented
316#3358C2×C8311yescharacteristic, complemented
317#3212C2×C8313yescomplemented
318#3210C2×C8313yescomplemented
319#3107C2×C8313yescomplemented
320#3102C2×C8313yescomplemented
321#2982C2×C8311yescharacteristic, complemented
322C83#6188711yescharacteristic, direct product factor, Sylow
323#559C22×C8313yes—
324#557C22×C8311yescharacteristic
325#557C22×C8311yescharacteristic
326#557C22×C8313yes—
327#556C22×C8313yes—
328#556C22×C8313yes—
329#553—23no—
330#552—23no—
331#550C22×C8311yescharacteristic
332D4×Q8—21no—
333D4×Q8C22×C8311yescharacteristic
334#548—21no—
335#541—23no—
336#533C22×C8313yes—
337#532C22×C8313yes—
338#529—23no—
339#529C22×C8313yes—
340#519—21no—
341C4×#41—21no—
342C4×#41C22×C8313yes—
343C2×C4×Q8C22×C8311yescharacteristic
344#495C22×C8316yes—
345#494C22×C8313yes—
346#492C22×C8313yes—
347#488C22×C8316yes—
348#487C22×C8313yes—
349#486C22×C8313yes—
350#485C22×C8313yes—
351#482C22×C8311yescharacteristic
352#479C22×C8313yes—
353#478C22×C8313yes—
354#475C22×C8313yes—
355#474C22×C8313yes—
356#464C22×C8313yes—
357#464C22×C8316yes—
358#464C22×C8316yes—
359#463C22×C8313yes—
360#462C22×C8313yes—
361#462C22×C8313yes—
362#461C22×C8313yes—
363#461C22×C8313yes—
364#460C22×C8313yes—
365#459C22×C8313yes—
366#452C22×C8313yes—
367#452C22×C8316yes—
368#449C22×C8313yes—
369C8×Q8C22×C8311yescharacteristic
370C8×Q8C22×C8311yescharacteristic
371C8×Q8C22×C8313yes—
372C8×Q8C22×C8313yes—
373C4×Q16C22×C8313yes—
374C4×Q16C22×C8316yes—
375C4×SD16C22×C8313yes—
376C4×SD16C22×C8313yes—
377C4×SD16C22×C8316yes—
378C4×D8C22×C8313yes—
379#431C22×C8313yes—
380#431C22×C8313yes—
381C2×#41—21no—
382C2×#41C23×C8313yes—
383C22×Q8—21no—
384C22×Q8D4×C8311yescharacteristic
385C2×Q16C23×C8316yes—
386C2×Q16C23×C8313yes—
387C2×SD16C23×C8313yes—
388C2×SD16C23×C8316yes—
389C2×SD16C23×C8313yes—
390C2×D8C23×C8313yes—
391C4⋊Q8—23no—
392C4⋊Q8C23×C8313yes—
393C4⋊Q8C23×C8313yes—
394C4⋊Q8C23×C8313yes—
395#127C23×C8313yes—
396#126—26no—
397#126—26no—
398#126—23no—
399#125—23no—
400#125—26no—
401#125—23no—
402#125—23no—
403#125C23×C8313yes—
404#124—23no—
405#124C23×C8313yes—
406#124C23×C8316yes—
407#123—23no—
408#123—26no—
409C22⋊Q8—23no—
410C22⋊Q8—23no—
411C22⋊Q8—23no—
412C22⋊Q8—23no—
413C22⋊Q8C23×C8313yes—
414#121—23no—
415#121—23no—
416#121—23no—
417#121C23×C8311yescharacteristic
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—23no—
421C4×Q8—23no—
422C4×Q8D4×C8311yescharacteristic
423C4×Q8D4×C8313yes—
424C4×Q8C23×C8313yes—
425C4×Q8C23×C8313yes—
426C4×Q8C23×C8313yes—
427C4×Q8C23×C8316yes—
428C4×Q8C23×C8311yescharacteristic
429C4×Q8C23×C8313yes—
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4—23no—
436C4×D4C23×C8313yes—
437C4×D4C23×C8313yes—
438C4×D4C23×C8313yes—
439#117—23no—
440#117—23no—
441#117—23no—
442#117—23no—
443#117—23no—
444#117C23×C8311yescharacteristic
445C2×C4⋊C4D4×C8313yes—
446C2×C42—23no—
447C2×C42C23×C8313yes—
448#107C23×C8313yes—
449#107C23×C8311yescharacteristic
450#106C23×C8313yes—
451#106C23×C8311yescharacteristic
452C4⋊C8C23×C8313yes—
453C4⋊C8C23×C8313yes—
454C4⋊C8C23×C8313yes—
455C4⋊C8C23×C8313yes—
456#103C23×C8313yes—
457#103C23×C8313yes—
458#103C23×C8313yes—
459#103C23×C8313yes—
460#103C23×C8316yes—
461#102C23×C8311yescharacteristic
462#102C23×C8313yes—
463#102C23×C8311yescharacteristic
464#102C23×C8313yes—
465#102C23×C8316yes—
466C22⋊C8C23×C8313yes—
467C22⋊C8C23×C8311yescharacteristic
468C4×C8C23×C8313yes—
469C4×C8C23×C8313yes—
470C4×C8C23×C8316yes—
471#41—43no—
472#41—43no—
473#41—44no—
474C2×Q8—24no—
475C2×Q8—23no—
476C2×Q8—44no—
477C2×Q8C2×D4×C8313yes—
478C2×Q8C2×D4×C8311yescharacteristic
479C2×Q8C24×C8313yes—
480C2×Q8C24×C8313yes—
481C2×D4—21no—
482C2×D4—23no—
483C2×D4—23no—
484C2×D4—23no—
485C2×D4C24×C8313yes—
486C2×D4C24×C8311yescharacteristic
487C22×C4—23no—
488C22×C4—23no—
489C22×C4—23no—
490C22×C4—23no—
491C22×C4C2×D4×C8313yes—
492C22×C4C2×D4×C8313yes—
493C22×C4C24×C8311yescharacteristic
494Q16—46no—
495Q16—43no—
496SD16—43no—
497SD16—43no—
498SD16—46no—
499D8—43no—
500C2×C8C24×C8311yescharacteristic
501C2×C8C24×C8313yes—
502C2×C8C24×C8311yescharacteristic
503C2×C8C24×C8313yes—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—23no—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—26no—
515C4⋊C4—23no—
516C4⋊C4C2×D4×C8313yes—
517C4⋊C4C2×D4×C8313yes—
518C4⋊C4C2×D4×C8316yes—
519C4⋊C4C24×C8313yes—
520C4⋊C4C24×C8311yescharacteristic
521C4⋊C4C24×C8311yescharacteristic
522C4⋊C4C24×C8311yescharacteristic
523C22⋊C4—23no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—23no—
527C22⋊C4—26no—
528C22⋊C4—23no—
529C22⋊C4—23no—
530C22⋊C4—26no—
531C22⋊C4—23no—
532C22⋊C4—23no—
533C42—21no—
534C42—23no—
535C42—23no—
536C42—26no—
537C42—23no—
538C42C2×D4×C8313yes—
539C42C2×D4×C8313yes—
540C42C24×C8313yes—
541C42C24×C8313yes—
542C23—21no—
543C23—23no—
544C23C22×D4×C8311yescharacteristic
545Q8—26no—
546Q8—23no—
547Q8—23no—
548Q8—23no—
549Q8—23no—
550Q8—46no—
551Q8#135×C8314yes—
552D4—21no—
553D4—23no—
554D4—21no—
555D4—23no—
556D4—46no—
557D4—42no—
558D4—46no—
559D4—83no—
560C2×C4—26no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—23no—
566C2×C4—21no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—43no—
570C2×C4—46no—
571C2×C4—46no—
572C2×C4—46no—
573C2×C4—83no—
574C2×C4C22×D4×C8313yes—
575C2×C4C22×D4×C8311yescharacteristic
576C2×C4C22×D4×C8313yes—
577C2×C4C22×D4×C8313yes—
578C2×C4C22×D4×C8313yes—
579C2×C4C25×C8311yescharacteristic
580C8—23no—
581C8—21no—
582C8—23no—
583C8—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—41no—
588C22—43no—
589C22—43no—
590C22—41no—
591C22—43no—
592C22—41no—
593C22C23×D4×C8311yescharacteristic
594C4—23no—
595C4—23no—
596C4—23no—
597C4—21no—
598C4—41no—
599C4—43no—
600C4—41no—
601C4—41no—
602C4—43no—
603C4—43no—
604C4C2×#135×C8316yes—
605C4#585×C8311yescharacteristic
606C4#585×C8311yescharacteristic
607C2—41no—
608C2—81no—
609C2—83no—
610C2C83×#348711yescharacteristic
611C2C22×#135×C8311yescharacteristic
612C2C83×#358611yescharacteristic
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×#3523C2semidirect
2. C83×#3480C2semidirect
3. C83×#3395C2semidirect
4. C83×#3394C2semidirect
5. C83×#3393C2semidirect
6. C83×#3392C2semidirect
7. C83×#3365C2semidirect
8. C83×#3364C2semidirect
9. C83×#3359C2semidirect
10. C83×#3358C2semidirect
11. C83×#3212C2semidirect
12. C83×#3210C2semidirect
13. C83×#3107C2semidirect
14. C83×#3102C2semidirect
15. C83×#2982C2semidirect
300. #61887C83direct (N × H)
307. #3523C2×C83semidirect
308. #3480C2×C83semidirect
309. #3395C2×C83semidirect
310. #3394C2×C83semidirect
311. #3393C2×C83semidirect
312. #3392C2×C83semidirect
313. #3365C2×C83semidirect
314. #3364C2×C83semidirect
315. #3359C2×C83semidirect
316. #3358C2×C83semidirect
317. #3212C2×C83semidirect
318. #3210C2×C83semidirect
319. #3107C2×C83semidirect
320. #3102C2×C83semidirect
321. #2982C2×C83semidirect
322. C83#61887direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#35232
C83×#34802
C83×#33952
C83×#33942
C83×#33932
C83×#33922
C83×#33652
C83×#33642
C83×#33592
C83×#33582
C83×#32122
C83×#32102
C83×#31072
C83×#31022
C83×#29822
#6188783