Finite Group Databasebeta

← C83×#61903 #35289727

Subgroups — C83×#61903 #35289727

Order 21248.

1974 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3497C211yesmaximal, characteristic, complemented
2C83×#3480C211yesmaximal, characteristic, complemented
3C83×#3399C213yesmaximal, complemented
4C83×#3397C213yesmaximal, complemented
5C83×#3392C211yesmaximal, characteristic, complemented
6C83×#3391C211yesmaximal, characteristic, complemented
7C83×#3373C213yesmaximal, complemented
8C83×#3367C213yesmaximal, complemented
9C83×#3359C211yesmaximal, characteristic, complemented
10C83×#3358C211yesmaximal, characteristic, complemented
11C83×#3214C213yesmaximal, complemented
12C83×#3207C213yesmaximal, complemented
13C83×#3115C213yesmaximal, complemented
14C83×#3106C213yesmaximal, complemented
15C83×#2984C211yesmaximal, characteristic, complemented
16C2×2−1+4×C83—21no—
17#559×C83C2213yes—
18#557×C83C2211yescharacteristic
19#556×C83C2213yes—
20#553×C83—23no—
21#550×C83C2211yescharacteristic
22#550×C83C2211yescharacteristic
23#550×C83C2213yes—
24D4×Q8×C83C2211yescharacteristic
25D4×Q8×C83C2213yes—
26#548×C83—21no—
27#548×C83—21no—
28#548×C83—23no—
29#537×C83—23no—
30#532×C83C2213yes—
31#532×C83C2213yes—
32#532×C83C2213yes—
33#529×C83—23no—
34C4×#41×C83—21no—
35C4×#41×C83C2213yes—
36C2×C4×Q8×C83C2211yescharacteristic
37#496×C83C2216yes—
38#493×C83C2213yes—
39#492×C83C2213yes—
40#489×C83C2216yes—
41#487×C83C2213yes—
42#486×C83C2213yes—
43#482×C83C2211yescharacteristic
44#482×C83C2213yes—
45#477×C83C2213yes—
46#476×C83C2213yes—
47#475×C83C2213yes—
48#474×C83C2213yes—
49#463×C83C2216yes—
50#463×C83C2216yes—
51#461×C83C2213yes—
52#461×C83C2213yes—
53#460×C83C2213yes—
54#460×C83C2213yes—
55#459×C83C2213yes—
56#459×C83C2213yes—
57#459×C83C2213yes—
58#459×C83C2213yes—
59#449×C83C2213yes—
60#449×C83C2213yes—
61#449×C83C2216yes—
62#446×C83C2213yes—
63#446×C83C2213yes—
64C8×Q8×C83C2211yescharacteristic
65C8×Q8×C83C2211yescharacteristic
66#442×C83C2216yes—
67#440×C83C2216yes—
68C4×SD16×C83C2213yes—
69C4×SD16×C83C2213yes—
70C4×D8×C83C2213yes—
71C4×D8×C83C2213yes—
72#432×C83C2213yes—
73#431×C83C2213yes—
742−1+4×C83—48no—
75C2×#41×C83—21no—
76C2×#41×C83—23no—
77C2×#41×C83—21no—
78C2×#41×C83—23no—
79C2×#41×C83—23no—
80C2×#41×C83C2313yes—
81C22×Q8×C83—23no—
82C22×Q8×C83—21no—
83C22×Q8×C83D411yescharacteristic
84C2×SD16×C83C2313yes—
85C2×SD16×C83C2316yes—
86C2×SD16×C83C2313yes—
87C2×D8×C83C2313yes—
88C2×D8×C83C2316yes—
89C2×D8×C83C2313yes—
90C4⋊Q8×C83C2313yes—
91C4⋊Q8×C83C2313yes—
92C4⋊Q8×C83C2313yes—
93#127×C83C2313yes—
94#127×C83C2313yes—
95#127×C83C2313yes—
96#126×C83—26no—
97#125×C83—23no—
98#124×C83—23no—
99#124×C83—23no—
100#124×C83—23no—
101#124×C83C2316yes—
102#123×C83—26no—
103C22⋊Q8×C83—23no—
104C22⋊Q8×C83—23no—
105C22⋊Q8×C83—23no—
106C22⋊Q8×C83—26no—
107#121×C83—23no—
108#121×C83—23no—
109#121×C83—23no—
110#121×C83—23no—
111#121×C83—23no—
112#121×C83—23no—
113#121×C83—23no—
114#121×C83—26no—
115#121×C83C2311yescharacteristic
116#121×C83C2313yes—
117C4×Q8×C83—21no—
118C4×Q8×C83D411yescharacteristic
119C4×Q8×C83D413yes—
120C4×Q8×C83C2313yes—
121C4×Q8×C83C2313yes—
122C4×Q8×C83C2311yescharacteristic
123C4×Q8×C83C2313yes—
124C4×D4×C83—23no—
125C4×D4×C83—23no—
126C4×D4×C83—23no—
127C4×D4×C83—23no—
128C4×D4×C83—23no—
129C4×D4×C83—23no—
130C4×D4×C83—23no—
131C4×D4×C83C2316yes—
132C4×D4×C83C2313yes—
133C4×D4×C83C2313yes—
134C4×D4×C83C2313yes—
135C4×D4×C83C2313yes—
136#117×C83—23no—
137#117×C83—23no—
138#117×C83C2311yescharacteristic
139C2×C4⋊C4×C83D413yes—
140C2×C42×C83—23no—
141C2×C42×C83C2313yes—
142#107×C83C2313yes—
143#107×C83C2311yescharacteristic
144#106×C83C2313yes—
145#106×C83C2311yescharacteristic
146C4⋊C8×C83C2313yes—
147C4⋊C8×C83C2313yes—
148C4⋊C8×C83C2313yes—
149C4⋊C8×C83C2313yes—
150#103×C83C2313yes—
151#103×C83C2316yes—
152#103×C83C2313yes—
153#102×C83C2313yes—
154#102×C83C2316yes—
155#102×C83C2313yes—
156#102×C83C2311yescharacteristic
157#102×C83C2313yes—
158#102×C83C2311yescharacteristic
159#102×C83C2313yes—
160C22⋊C8×C83C2311yescharacteristic
161C22⋊C8×C83C2313yes—
162#97×C83C2316yes—
163C4×C8×C83C2313yes—
164C4×C8×C83C2313yes—
165#41×C83—43no—
166#41×C83—43no—
167#41×C83—412no—
168#41×C83—412no—
169#41×C83—412no—
170#41×C83—44no—
171#41×C83—44no—
172C2×Q8×C83—24no—
173C2×Q8×C83—23no—
174C2×Q8×C83—23no—
175C2×Q8×C83—412no—
176C2×Q8×C83—44no—
177C2×Q8×C83C2×D413yes—
178C2×Q8×C83C2×D411yescharacteristic
179C2×Q8×C83C2413yes—
180C2×D4×C83—23no—
181C2×D4×C83—21no—
182C2×D4×C83—23no—
183C2×D4×C83—23no—
184C2×D4×C83—23no—
185C2×D4×C83—23no—
186C2×D4×C83—23no—
187C2×D4×C83—23no—
188C2×D4×C83—23no—
189C2×D4×C83C2413yes—
190C2×D4×C83C2411yescharacteristic
191C2×D4×C83C2413yes—
192C22×C4×C83—23no—
193C22×C4×C83—23no—
194C22×C4×C83—26no—
195C22×C4×C83—23no—
196C22×C4×C83—23no—
197C22×C4×C83—23no—
198C22×C4×C83C2×D413yes—
199C22×C4×C83C2×D413yes—
200C22×C4×C83C2411yescharacteristic
201SD16×C83—43no—
202SD16×C83—46no—
203SD16×C83—43no—
204D8×C83—43no—
205D8×C83—46no—
206D8×C83—43no—
207C2×C8×C83C2411yescharacteristic
208C2×C8×C83C2411yescharacteristic
209C2×C8×C83C2413yes—
210C2×C8×C83C2413yes—
211C4⋊C4×C83—23no—
212C4⋊C4×C83—23no—
213C4⋊C4×C83—23no—
214C4⋊C4×C83—23no—
215C4⋊C4×C83—23no—
216C4⋊C4×C83—23no—
217C4⋊C4×C83C2×D413yes—
218C4⋊C4×C83C2×D413yes—
219C4⋊C4×C83C2×D416yes—
220C4⋊C4×C83C2411yescharacteristic
221C4⋊C4×C83C2411yescharacteristic
222C4⋊C4×C83C2413yes—
223C4⋊C4×C83C2411yescharacteristic
224C22⋊C4×C83—21no—
225C22⋊C4×C83—26no—
226C22⋊C4×C83—23no—
227C22⋊C4×C83—23no—
228C22⋊C4×C83—21no—
229C22⋊C4×C83—23no—
230C22⋊C4×C83—26no—
231C22⋊C4×C83—26no—
232C22⋊C4×C83—23no—
233C22⋊C4×C83—23no—
234C42×C83—21no—
235C42×C83—23no—
236C42×C83—23no—
237C42×C83C2×D413yes—
238C42×C83C2×D413yes—
239C42×C83C2413yes—
240C42×C83C2413yes—
241C23×C83—23no—
242C23×C83—21no—
243C23×C83—23no—
244C23×C83C22×D411yescharacteristic
245Q8×C83—26no—
246Q8×C83—23no—
247Q8×C83—23no—
248Q8×C83—46no—
249Q8×C83—46no—
250Q8×C83AGL(1,ℤ/8)14yes—
251D4×C83—21no—
252D4×C83—23no—
253D4×C83—23no—
254D4×C83—23no—
255D4×C83—23no—
256D4×C83—21no—
257D4×C83—46no—
258D4×C83—46no—
259D4×C83—46no—
260D4×C83—42no—
261D4×C83—46no—
262D4×C83—46no—
263D4×C83—83no—
264D4×C83—83no—
265D4×C83—83no—
266C2×C4×C83—26no—
267C2×C4×C83—21no—
268C2×C4×C83—21no—
269C2×C4×C83—21no—
270C2×C4×C83—21no—
271C2×C4×C83—23no—
272C2×C4×C83—23no—
273C2×C4×C83—21no—
274C2×C4×C83—43no—
275C2×C4×C83—412no—
276C2×C4×C83—46no—
277C2×C4×C83—46no—
278C2×C4×C83—46no—
279C2×C4×C83—46no—
280C2×C4×C83—83no—
281C2×C4×C83C22×D411yescharacteristic
282C2×C4×C83C22×D413yes—
283C2×C4×C83C22×D413yes—
284C2×C4×C83C22×D413yes—
285C2×C4×C83C22×D413yes—
286C2×C4×C83C2511yescharacteristic
287C8×C83—21no—
288C8×C83—23no—
289C8×C83—23no—
290C8×C83—21no—
291C22×C83—21no—
292C22×C83—21no—
293C22×C83—21no—
294C22×C83—43no—
295C22×C83—41no—
296C22×C83—43no—
297C22×C83—43no—
298C22×C83—41no—
299C22×C83—43no—
300C22×C83—43no—
301C22×C83—41no—
302C22×C83—43no—
303C22×C83C23×D411yescharacteristic
304C4×C83—23no—
305C4×C83—23no—
306C4×C83—21no—
307C4×C83—23no—
308C4×C83—41no—
309C4×C83—43no—
310C4×C83—41no—
311C4×C83—43no—
312C4×C83—41no—
313C4×C83C2×AGL(1,ℤ/8)16yes—
314C4×C83#58511yescharacteristic
315C4×C83#58511yescharacteristic
316#61903C8311yesmaximal, characteristic, direct product factor, Sylow
317C2×C83—41no—
318C2×C83—83no—
319C2×C83—81no—
320C2×C83—83no—
321C2×C83#348711yescharacteristic
322C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
323C2×C83#358411yescharacteristic
324#3497C2×C8311yescharacteristic, complemented
325#3480C2×C8311yescharacteristic, complemented
326#3399C2×C8313yescomplemented
327#3397C2×C8313yescomplemented
328#3392C2×C8311yescharacteristic, complemented
329#3391C2×C8311yescharacteristic, complemented
330#3373C2×C8313yescomplemented
331#3367C2×C8313yescomplemented
332#3359C2×C8311yescharacteristic, complemented
333#3358C2×C8311yescharacteristic, complemented
334#3214C2×C8313yescomplemented
335#3207C2×C8313yescomplemented
336#3115C2×C8313yescomplemented
337#3106C2×C8313yescomplemented
338#2984C2×C8311yescharacteristic, complemented
339C83#6190311yescharacteristic, direct product factor, Sylow
340C2×2−1+4—21no—
341#559C22×C8313yes—
342#557C22×C8311yescharacteristic
343#556C22×C8313yes—
344#553—23no—
345#550C22×C8311yescharacteristic
346#550C22×C8311yescharacteristic
347#550C22×C8313yes—
348D4×Q8C22×C8311yescharacteristic
349D4×Q8C22×C8313yes—
350#548—21no—
351#548—21no—
352#548—23no—
353#537—23no—
354#532C22×C8313yes—
355#532C22×C8313yes—
356#532C22×C8313yes—
357#529—23no—
358C4×#41—21no—
359C4×#41C22×C8313yes—
360C2×C4×Q8C22×C8311yescharacteristic
361#496C22×C8316yes—
362#493C22×C8313yes—
363#492C22×C8313yes—
364#489C22×C8316yes—
365#487C22×C8313yes—
366#486C22×C8313yes—
367#482C22×C8311yescharacteristic
368#482C22×C8313yes—
369#477C22×C8313yes—
370#476C22×C8313yes—
371#475C22×C8313yes—
372#474C22×C8313yes—
373#463C22×C8316yes—
374#463C22×C8316yes—
375#461C22×C8313yes—
376#461C22×C8313yes—
377#460C22×C8313yes—
378#460C22×C8313yes—
379#459C22×C8313yes—
380#459C22×C8313yes—
381#459C22×C8313yes—
382#459C22×C8313yes—
383#449C22×C8313yes—
384#449C22×C8313yes—
385#449C22×C8316yes—
386#446C22×C8313yes—
387#446C22×C8313yes—
388C8×Q8C22×C8311yescharacteristic
389C8×Q8C22×C8311yescharacteristic
390#442C22×C8316yes—
391#440C22×C8316yes—
392C4×SD16C22×C8313yes—
393C4×SD16C22×C8313yes—
394C4×D8C22×C8313yes—
395C4×D8C22×C8313yes—
396#432C22×C8313yes—
397#431C22×C8313yes—
3982−1+4—48no—
399C2×#41—21no—
400C2×#41—23no—
401C2×#41—21no—
402C2×#41—23no—
403C2×#41—23no—
404C2×#41C23×C8313yes—
405C22×Q8—23no—
406C22×Q8—21no—
407C22×Q8D4×C8311yescharacteristic
408C2×SD16C23×C8313yes—
409C2×SD16C23×C8313yes—
410C2×SD16C23×C8316yes—
411C2×D8C23×C8313yes—
412C2×D8C23×C8313yes—
413C2×D8C23×C8316yes—
414C4⋊Q8C23×C8313yes—
415C4⋊Q8C23×C8313yes—
416C4⋊Q8C23×C8313yes—
417#127C23×C8313yes—
418#127C23×C8313yes—
419#127C23×C8313yes—
420#126—26no—
421#125—23no—
422#124—23no—
423#124—23no—
424#124—23no—
425#124C23×C8316yes—
426#123—26no—
427C22⋊Q8—23no—
428C22⋊Q8—23no—
429C22⋊Q8—23no—
430C22⋊Q8—26no—
431#121—23no—
432#121—23no—
433#121—23no—
434#121—23no—
435#121—23no—
436#121—23no—
437#121—23no—
438#121—26no—
439#121C23×C8311yescharacteristic
440#121C23×C8313yes—
441C4×Q8—21no—
442C4×Q8D4×C8311yescharacteristic
443C4×Q8D4×C8313yes—
444C4×Q8C23×C8313yes—
445C4×Q8C23×C8313yes—
446C4×Q8C23×C8311yescharacteristic
447C4×Q8C23×C8313yes—
448C4×D4—23no—
449C4×D4—23no—
450C4×D4—23no—
451C4×D4—23no—
452C4×D4—23no—
453C4×D4—23no—
454C4×D4—23no—
455C4×D4C23×C8313yes—
456C4×D4C23×C8313yes—
457C4×D4C23×C8313yes—
458C4×D4C23×C8313yes—
459C4×D4C23×C8316yes—
460#117—23no—
461#117—23no—
462#117C23×C8311yescharacteristic
463C2×C4⋊C4D4×C8313yes—
464C2×C42—23no—
465C2×C42C23×C8313yes—
466#107C23×C8311yescharacteristic
467#107C23×C8313yes—
468#106C23×C8311yescharacteristic
469#106C23×C8313yes—
470C4⋊C8C23×C8313yes—
471C4⋊C8C23×C8313yes—
472C4⋊C8C23×C8313yes—
473C4⋊C8C23×C8313yes—
474#103C23×C8313yes—
475#103C23×C8313yes—
476#103C23×C8316yes—
477#102C23×C8311yescharacteristic
478#102C23×C8313yes—
479#102C23×C8313yes—
480#102C23×C8313yes—
481#102C23×C8311yescharacteristic
482#102C23×C8313yes—
483#102C23×C8316yes—
484C22⋊C8C23×C8311yescharacteristic
485C22⋊C8C23×C8313yes—
486#97C23×C8316yes—
487C4×C8C23×C8313yes—
488C4×C8C23×C8313yes—
489#41—43no—
490#41—43no—
491#41—412no—
492#41—412no—
493#41—412no—
494#41—44no—
495#41—44no—
496C2×Q8—24no—
497C2×Q8—23no—
498C2×Q8—23no—
499C2×Q8—412no—
500C2×Q8—44no—
501C2×Q8C2×D4×C8313yes—
502C2×Q8C2×D4×C8311yescharacteristic
503C2×Q8C24×C8313yes—
504C2×D4—23no—
505C2×D4—21no—
506C2×D4—23no—
507C2×D4—23no—
508C2×D4—23no—
509C2×D4—23no—
510C2×D4—23no—
511C2×D4—23no—
512C2×D4—23no—
513C2×D4C24×C8313yes—
514C2×D4C24×C8311yescharacteristic
515C2×D4C24×C8313yes—
516C22×C4—23no—
517C22×C4—23no—
518C22×C4—26no—
519C22×C4—23no—
520C22×C4—23no—
521C22×C4—23no—
522C22×C4C2×D4×C8313yes—
523C22×C4C2×D4×C8313yes—
524C22×C4C24×C8311yescharacteristic
525SD16—43no—
526SD16—46no—
527SD16—43no—
528D8—43no—
529D8—46no—
530D8—43no—
531C2×C8C24×C8311yescharacteristic
532C2×C8C24×C8311yescharacteristic
533C2×C8C24×C8313yes—
534C2×C8C24×C8313yes—
535C4⋊C4—23no—
536C4⋊C4—23no—
537C4⋊C4—23no—
538C4⋊C4—23no—
539C4⋊C4—23no—
540C4⋊C4—23no—
541C4⋊C4C2×D4×C8313yes—
542C4⋊C4C2×D4×C8313yes—
543C4⋊C4C2×D4×C8316yes—
544C4⋊C4C24×C8311yescharacteristic
545C4⋊C4C24×C8311yescharacteristic
546C4⋊C4C24×C8311yescharacteristic
547C4⋊C4C24×C8313yes—
548C22⋊C4—21no—
549C22⋊C4—26no—
550C22⋊C4—23no—
551C22⋊C4—23no—
552C22⋊C4—21no—
553C22⋊C4—23no—
554C22⋊C4—26no—
555C22⋊C4—26no—
556C22⋊C4—23no—
557C22⋊C4—23no—
558C42—21no—
559C42—23no—
560C42—23no—
561C42C2×D4×C8313yes—
562C42C2×D4×C8313yes—
563C42C24×C8313yes—
564C42C24×C8313yes—
565C23—23no—
566C23—23no—
567C23—21no—
568C23C22×D4×C8311yescharacteristic
569Q8—26no—
570Q8—23no—
571Q8—23no—
572Q8—46no—
573Q8—46no—
574Q8AGL(1,ℤ/8)×C8314yes—
575D4—21no—
576D4—23no—
577D4—23no—
578D4—23no—
579D4—23no—
580D4—21no—
581D4—46no—
582D4—46no—
583D4—42no—
584D4—46no—
585D4—46no—
586D4—46no—
587D4—83no—
588D4—83no—
589D4—83no—
590C2×C4—26no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—23no—
596C2×C4—23no—
597C2×C4—21no—
598C2×C4—43no—
599C2×C4—412no—
600C2×C4—46no—
601C2×C4—46no—
602C2×C4—46no—
603C2×C4—46no—
604C2×C4—83no—
605C2×C4C22×D4×C8311yescharacteristic
606C2×C4C22×D4×C8313yes—
607C2×C4C22×D4×C8313yes—
608C2×C4C22×D4×C8313yes—
609C2×C4C22×D4×C8313yes—
610C2×C4C25×C8311yescharacteristic
611C8—21no—
612C8—23no—
613C8—23no—
614C8—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—43no—
619C22—41no—
620C22—43no—
621C22—43no—
622C22—41no—
623C22—43no—
624C22—43no—
625C22—41no—
626C22—43no—
627C22C23×D4×C8311yescharacteristic
628C4—23no—
629C4—23no—
630C4—23no—
631C4—21no—
632C4—43no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—43no—
637C4C2×AGL(1,ℤ/8)×C8316yes—
638C4#585×C8311yescharacteristic
639C4#585×C8311yescharacteristic
640C2—41no—
641C2—83no—
642C2—81no—
643C2—83no—
644C2C83×#348711yescharacteristic
645C2C22×AGL(1,ℤ/8)×C8311yescharacteristic
646C2C83×#358411yescharacteristic
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×#3497C2semidirect
2. C83×#3480C2semidirect
3. C83×#3399C2semidirect
4. C83×#3397C2semidirect
5. C83×#3392C2semidirect
6. C83×#3391C2semidirect
7. C83×#3373C2semidirect
8. C83×#3367C2semidirect
9. C83×#3359C2semidirect
10. C83×#3358C2semidirect
11. C83×#3214C2semidirect
12. C83×#3207C2semidirect
13. C83×#3115C2semidirect
14. C83×#3106C2semidirect
15. C83×#2984C2semidirect
316. #61903C83direct (N × H)
324. #3497C2×C83semidirect
325. #3480C2×C83semidirect
326. #3399C2×C83semidirect
327. #3397C2×C83semidirect
328. #3392C2×C83semidirect
329. #3391C2×C83semidirect
330. #3373C2×C83semidirect
331. #3367C2×C83semidirect
332. #3359C2×C83semidirect
333. #3358C2×C83semidirect
334. #3214C2×C83semidirect
335. #3207C2×C83semidirect
336. #3115C2×C83semidirect
337. #3106C2×C83semidirect
338. #2984C2×C83semidirect
339. C83#61903direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#34972
C83×#34802
C83×#33992
C83×#33972
C83×#33922
C83×#33912
C83×#33732
C83×#33672
C83×#33592
C83×#33582
C83×#32142
C83×#32072
C83×#31152
C83×#31062
C83×#29842
#6190383