Finite Group Databasebeta

← C83×#19010 #35246834

Subgroups — C83×#19010 #35246834

Order 21248.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3529C211yesmaximal, characteristic, complemented
2C83×#3219C211yesmaximal, characteristic, complemented
3C83×#3214C211yesmaximal, characteristic, complemented
4C83×#3180C211yesmaximal, characteristic, complemented
5C83×#1664C211yesmaximal, characteristic, complemented
6C83×#1662C211yesmaximal, characteristic, complemented
7C83×#1661C211yesmaximal, characteristic, complemented
8C83×#1659C211yesmaximal, characteristic, complemented
9C83×#1657C211yesmaximal, characteristic, complemented
10C83×#1656C211yesmaximal, characteristic, complemented
11C83×#1656C211yesmaximal, characteristic, complemented
12C83×#1655C211yesmaximal, characteristic, complemented
13C83×#1535C211yesmaximal, characteristic, complemented
14C83×#1532C211yesmaximal, characteristic, complemented
15C83×#1530C211yesmaximal, characteristic, complemented
16#563×C83—21no—
17#563×C83C2211yescharacteristic
18#562×C83—21no—
19#562×C83—21no—
20#562×C83C2211yescharacteristic
21#562×C83C2211yescharacteristic
22H(3,𝔽4)×C83C2211yescharacteristic
23#560×C83—21no—
24#560×C83—21no—
25#560×C83—21no—
26#532×C83—21no—
27#532×C83C2211yescharacteristic
28#532×C83C2211yescharacteristic, complemented
29#529×C83—21no—
30#529×C83—21no—
31#529×C83C2211yescharacteristic
32#529×C83C2211yescharacteristic
33#525×C83—21no—
34#525×C83—21no—
35#525×C83—21no—
36#501×C83C2211yescharacteristic, complemented
37#497×C83C2211yescharacteristic
38#496×C83C2211yescharacteristic
39#496×C83C2211yescharacteristic
40#496×C83C2211yescharacteristic
41#496×C83C2211yescharacteristic, complemented
42#491×C83C2211yescharacteristic, complemented
43#490×C83C2211yescharacteristic, complemented
44#490×C83C2211yescharacteristic, complemented
45#489×C83C2211yescharacteristic
46#489×C83C2211yescharacteristic
47#489×C83C2211yescharacteristic, complemented
48#466×C83—21no—
49#465×C83—21no—
50#464×C83—21no—
51#463×C83—21no—
52#461×C83—21no—
53#459×C83—21no—
54#452×C83—21no—
55#449×C83—21no—
56#449×C83—21no—
57#449×C83—21no—
58#442×C83—21no—
59#440×C83—21no—
60#432×C83C2211yescharacteristic, complemented
61#432×C83C2211yescharacteristic, complemented
62C2×#97×C83C2211yescharacteristic, complemented
63#330×C83C2211yescharacteristic, complemented
64#330×C83C2211yescharacteristic, complemented
65#330×C83C2211yescharacteristic, complemented
66#330×C83C2211yescharacteristic, complemented
67#329×C83C2211yescharacteristic
68#329×C83C2211yescharacteristic
69#329×C83C2211yescharacteristic
70#329×C83C2211yescharacteristic
71#329×C83C2211yescharacteristic
72#329×C83C2211yescharacteristic
73#329×C83C2211yescharacteristic, complemented
74#329×C83C2211yescharacteristic, complemented
75C2×#41×C83—21no—
76C2×#41×C83—21no—
77C2×#41×C83D411yescharacteristic
78C2×#41×C83D411yescharacteristic
79C23×C4×C83—21no—
80C2×Q16×C83—21no—
81C2×SD16×C83—21no—
82C2×SD16×C83—21no—
83C2×SD16×C83—21no—
84C2×SD16×C83—21no—
85C2×SD16×C83—21no—
86C2×D8×C83—21no—
87C2×D8×C83—21no—
88C2×D8×C83—21no—
89C2×D8×C83—21no—
90C22×C8×C83—21no—
91C4⋊Q8×C83—21no—
92C4⋊Q8×C83D411yescharacteristic
93C4⋊Q8×C83C2311yescharacteristic
94#127×C83—21no—
95#127×C83D411yescharacteristic
96#127×C83C2311yescharacteristic
97#126×C83—21no—
98#126×C83—21no—
99#126×C83—21no—
100#126×C83—21no—
101#126×C83—21no—
102#126×C83—21no—
103#125×C83—21no—
104#125×C83—21no—
105#125×C83C2311yescharacteristic
106#125×C83C2311yescharacteristic
107#124×C83—21no—
108#124×C83—21no—
109#124×C83—21no—
110#124×C83—21no—
111#124×C83—21no—
112#124×C83C2311yescharacteristic
113#124×C83C2311yescharacteristic
114#124×C83C2311yescharacteristic
115#124×C83C2311yescharacteristic
116#123×C83—21no—
117#123×C83—21no—
118#123×C83—21no—
119#123×C83—21no—
120#123×C83—21no—
121#123×C83—21no—
122#123×C83—21no—
123#123×C83—21no—
124#123×C83—21no—
125#123×C83—21no—
126#123×C83—21no—
127#123×C83—21no—
128C22⋊Q8×C83—21no—
129C22⋊Q8×C83—21no—
130C22⋊Q8×C83—21no—
131C22⋊Q8×C83—21no—
132C22⋊Q8×C83—21no—
133C22⋊Q8×C83—21no—
134C22⋊Q8×C83—21no—
135C22⋊Q8×C83—21no—
136C22⋊Q8×C83D411yescharacteristic
137C22⋊Q8×C83D411yescharacteristic
138#121×C83—21no—
139#121×C83—21no—
140#121×C83—21no—
141#121×C83—21no—
142#121×C83—21no—
143#121×C83—21no—
144#121×C83—21no—
145#121×C83—21no—
146#121×C83—21no—
147#121×C83—21no—
148#121×C83—21no—
149#121×C83—21no—
150#121×C83—21no—
151#121×C83—21no—
152#121×C83—21no—
153#121×C83—21no—
154#121×C83D411yescharacteristic
155#121×C83D411yescharacteristic
156#120×C83—21no—
157#120×C83—21no—
158#120×C83—21no—
159#120×C83—21no—
160#120×C83—21no—
161#120×C83—21no—
162C4×Q8×C83D411yescharacteristic
163C4×Q8×C83D411yescharacteristic
164C4×D4×C83—21no—
165C4×D4×C83—21no—
166C4×D4×C83—21no—
167C4×D4×C83—21no—
168C4×D4×C83—21no—
169C4×D4×C83—21no—
170C4×D4×C83—21no—
171C4×D4×C83—21no—
172C4×D4×C83—21no—
173C4×D4×C83—21no—
174C4×D4×C83D411yescharacteristic
175C4×D4×C83D411yescharacteristic
176#117×C83—21no—
177#117×C83—21no—
178#117×C83—21no—
179C2×C42×C83—21no—
180C2×C42×C83C2311yescharacteristic
181#107×C83—21no—
182#106×C83—21no—
183C4⋊C8×C83—21no—
184C4⋊C8×C83—21no—
185#103×C83—21no—
186#103×C83—21no—
187#103×C83—21no—
188#103×C83—21no—
189#103×C83—21no—
190#102×C83—21no—
191#102×C83—21no—
192#102×C83—21no—
193#102×C83—21no—
194#102×C83—21no—
195#102×C83—21no—
196#102×C83—21no—
197C22⋊C8×C83—21no—
198C22⋊C8×C83—21no—
199#97×C83—21no—
200#97×C83C2311yescharacteristic
201#97×C83C2311yescharacteristic
202#97×C83C2311yescharacteristic
203#97×C83C2311yescharacteristic
204#97×C83C2311yescharacteristic
205#97×C83C2311yescharacteristic
206C24×C83—21no—
207#41×C83—81no—
208#41×C83—81no—
209#41×C83—82no—
210#41×C83—81no—
211#41×C83—81no—
212C2×Q8×C83—21no—
213C2×Q8×C83—21no—
214C2×Q8×C83C2×D411yescharacteristic
215C2×Q8×C83C2×D411yescharacteristic
216C2×Q8×C83C2×D411yescharacteristic
217C2×Q8×C83C2×D411yescharacteristic
218C2×D4×C83—21no—
219C2×D4×C83—21no—
220C2×D4×C83—21no—
221C2×D4×C83—21no—
222C2×D4×C83—21no—
223C2×D4×C83—21no—
224C2×D4×C83—21no—
225C2×D4×C83—21no—
226C2×D4×C83—21no—
227C2×D4×C83—21no—
228C2×D4×C83—21no—
229C2×D4×C83—21no—
230C2×D4×C83—21no—
231C2×D4×C83—21no—
232C2×D4×C83—21no—
233C2×D4×C83—21no—
234C2×D4×C83—41no—
235C2×D4×C83C2×D411yescharacteristic
236C2×D4×C83C2×D411yescharacteristic
237C2×D4×C83C2×D411yescharacteristic
238C2×D4×C83C2×D411yescharacteristic
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—41no—
249C22×C4×C83—82no—
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253Q16×C83—81no—
254SD16×C83—42no—
255SD16×C83—81no—
256SD16×C83—81no—
257SD16×C83—81no—
258SD16×C83—81no—
259D8×C83—42no—
260D8×C83—81no—
261D8×C83—81no—
262D8×C83—81no—
263C2×C8×C83—21no—
264C2×C8×C83—21no—
265C2×C8×C83—21no—
266C2×C8×C83—21no—
267C2×C8×C83—21no—
268C2×C8×C83—21no—
269C2×C8×C83—42no—
270C4⋊C4×C83—21no—
271C4⋊C4×C83—21no—
272C4⋊C4×C83—21no—
273C4⋊C4×C83—21no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—21no—
280C4⋊C4×C83—21no—
281C4⋊C4×C83—21no—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—21no—
284C4⋊C4×C83—21no—
285C4⋊C4×C83—21no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—21no—
288C4⋊C4×C83C2×D411yescharacteristic
289C4⋊C4×C83C2×D411yescharacteristic
290C4⋊C4×C83C2×D411yescharacteristic
291C4⋊C4×C83C2×D411yescharacteristic
292C22⋊C4×C83—21no—
293C22⋊C4×C83—21no—
294C22⋊C4×C83—21no—
295C22⋊C4×C83—21no—
296C22⋊C4×C83—21no—
297C22⋊C4×C83—21no—
298C22⋊C4×C83—21no—
299C22⋊C4×C83—21no—
300C22⋊C4×C83—21no—
301C22⋊C4×C83—21no—
302C22⋊C4×C83—21no—
303C22⋊C4×C83—21no—
304C22⋊C4×C83—21no—
305C22⋊C4×C83—21no—
306C22⋊C4×C83—21no—
307C22⋊C4×C83—21no—
308C22⋊C4×C83—21no—
309C22⋊C4×C83—21no—
310C22⋊C4×C83—21no—
311C22⋊C4×C83—21no—
312C22⋊C4×C83—21no—
313C22⋊C4×C83—21no—
314C22⋊C4×C83—21no—
315C22⋊C4×C83—21no—
316C22⋊C4×C83—41no—
317C22⋊C4×C83—41no—
318C42×C83—21no—
319C42×C83—21no—
320C42×C83—21no—
321C42×C83—21no—
322C42×C83C2×D411yescharacteristic
323C42×C83C2×D411yescharacteristic
324C42×C83C2×D411yescharacteristic
325C42×C83C2411yescharacteristic
326C23×C83—21no—
327C23×C83—21no—
328C23×C83—21no—
329C23×C83—21no—
330C23×C83—41no—
331C23×C83—81no—
332C23×C83—81no—
333C23×C83—81no—
334C23×C83#12011yescharacteristic
335Q8×C83—41no—
336Q8×C83—41no—
337Q8×C83—41no—
338Q8×C83—41no—
339Q8×C83—41no—
340Q8×C83—41no—
341Q8×C83—81no—
342D4×C83—41no—
343D4×C83—41no—
344D4×C83—41no—
345D4×C83—41no—
346D4×C83—41no—
347D4×C83—41no—
348D4×C83—41no—
349D4×C83—41no—
350D4×C83—41no—
351D4×C83—41no—
352D4×C83—81no—
353D4×C83—81no—
354D4×C83—81no—
355D4×C83—81no—
356D4×C83—81no—
357D4×C83—81no—
358D4×C83—81no—
359D4×C83—81no—
360D4×C83—81no—
361D4×C83—81no—
362D4×C83—81no—
363D4×C83—81no—
364D4×C83—81no—
365D4×C83—82no—
366C2×C4×C83—21no—
367C2×C4×C83—21no—
368C2×C4×C83—21no—
369C2×C4×C83—21no—
370C2×C4×C83—21no—
371C2×C4×C83—21no—
372C2×C4×C83—21no—
373C2×C4×C83—21no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
377C2×C4×C83—42no—
378C2×C4×C83—42no—
379C2×C4×C83—42no—
380C2×C4×C83—42no—
381C2×C4×C83—41no—
382C2×C4×C83—82no—
383C2×C4×C83—81no—
384C2×C4×C83—81no—
385C2×C4×C83—81no—
386C2×C4×C83—81no—
387C2×C4×C83—81no—
388C2×C4×C83#12011yescharacteristic
389C2×C4×C83#12011yescharacteristic
390C2×C4×C83#12011yescharacteristic
391C2×C4×C83C22×D411yescharacteristic
392C2×C4×C83C22×D411yescharacteristic
393C2×C4×C83C22×D411yescharacteristic
394C8×C83—22no—
395C8×C83—41no—
396C8×C83—41no—
397C8×C83—41no—
398C8×C83—41no—
399C8×C83—41no—
400C22×C83—21no—
401C22×C83—21no—
402C22×C83—21no—
403C22×C83—41no—
404C22×C83—41no—
405C22×C83—41no—
406C22×C83—41no—
407C22×C83—41no—
408C22×C83—41no—
409C22×C83—41no—
410C22×C83—41no—
411C22×C83—41no—
412C22×C83—41no—
413C22×C83—41no—
414C22×C83—41no—
415C22×C83—84no—
416C22×C83—81no—
417C22×C83—81no—
418C22×C83—81no—
419C22×C83C2×#12011yescharacteristic
420C4×C83—21no—
421C4×C83—21no—
422C4×C83—21no—
423C4×C83—21no—
424C4×C83—21no—
425C4×C83—21no—
426C4×C83—41no—
427C4×C83—41no—
428C4×C83—41no—
429C4×C83—41no—
430C4×C83—41no—
431C4×C83—41no—
432C4×C83—41no—
433C4×C83—41no—
434C4×C83—81no—
435#19010C8311yesmaximal, characteristic, direct product factor, Sylow
436C2×C83—41no—
437C2×C83—81no—
438C2×C83—81no—
439C2×C83—81no—
440C2×C83—81no—
441C2×C83—161no—
442C2×C83#301811yescharacteristic
443C2×C83#301911yescharacteristic
444C2×C83#302111yescharacteristic
445#3529C2×C8311yescharacteristic, complemented
446#3219C2×C8311yescharacteristic, complemented
447#3214C2×C8311yescharacteristic, complemented
448#3180C2×C8311yescharacteristic, complemented
449#1664C2×C8311yescharacteristic, complemented
450#1662C2×C8311yescharacteristic, complemented
451#1661C2×C8311yescharacteristic, complemented
452#1659C2×C8311yescharacteristic, complemented
453#1657C2×C8311yescharacteristic, complemented
454#1656C2×C8311yescharacteristic, complemented
455#1656C2×C8311yescharacteristic, complemented
456#1655C2×C8311yescharacteristic, complemented
457#1535C2×C8311yescharacteristic, complemented
458#1532C2×C8311yescharacteristic, complemented
459#1530C2×C8311yescharacteristic, complemented
460C83#1901011yescharacteristic, direct product factor, Sylow
461#563—21no—
462#563C22×C8311yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C8311yescharacteristic
466#562C22×C8311yescharacteristic
467H(3,𝔽4)C22×C8311yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C8311yescharacteristic
473#532C22×C8311yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C8311yescharacteristic
477#529C22×C8311yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C8311yescharacteristic, complemented
482#497C22×C8311yescharacteristic
483#496C22×C8311yescharacteristic
484#496C22×C8311yescharacteristic
485#496C22×C8311yescharacteristic
486#496C22×C8311yescharacteristic, complemented
487#491C22×C8311yescharacteristic, complemented
488#490C22×C8311yescharacteristic, complemented
489#490C22×C8311yescharacteristic, complemented
490#489C22×C8311yescharacteristic
491#489C22×C8311yescharacteristic
492#489C22×C8311yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C8311yescharacteristic, complemented
506#432C22×C8311yescharacteristic, complemented
507C2×#97C22×C8311yescharacteristic, complemented
508#330C22×C8311yescharacteristic, complemented
509#330C22×C8311yescharacteristic, complemented
510#330C22×C8311yescharacteristic, complemented
511#330C22×C8311yescharacteristic, complemented
512#329C22×C8311yescharacteristic
513#329C22×C8311yescharacteristic
514#329C22×C8311yescharacteristic
515#329C22×C8311yescharacteristic
516#329C22×C8311yescharacteristic
517#329C22×C8311yescharacteristic
518#329C22×C8311yescharacteristic, complemented
519#329C22×C8311yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C8311yescharacteristic
523C2×#41D4×C8311yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C8311yescharacteristic
538C4⋊Q8C23×C8311yescharacteristic
539#127—21no—
540#127D4×C8311yescharacteristic
541#127C23×C8311yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C8311yescharacteristic
551#125C23×C8311yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C8311yescharacteristic
558#124C23×C8311yescharacteristic
559#124C23×C8311yescharacteristic
560#124C23×C8311yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C8311yescharacteristic
582C22⋊Q8D4×C8311yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C8311yescharacteristic
600#121D4×C8311yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C8311yescharacteristic
608C4×Q8D4×C8311yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C8311yescharacteristic
620C4×D4D4×C8311yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C8311yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C8311yescharacteristic
646#97C23×C8311yescharacteristic
647#97C23×C8311yescharacteristic
648#97C23×C8311yescharacteristic
649#97C23×C8311yescharacteristic
650#97C23×C8311yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C8311yescharacteristic
660C2×Q8C2×D4×C8311yescharacteristic
661C2×Q8C2×D4×C8311yescharacteristic
662C2×Q8C2×D4×C8311yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C8311yescharacteristic
681C2×D4C2×D4×C8311yescharacteristic
682C2×D4C2×D4×C8311yescharacteristic
683C2×D4C2×D4×C8311yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C8311yescharacteristic
696C22×C4C2×D4×C8311yescharacteristic
697C22×C4C2×D4×C8311yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C8311yescharacteristic
734C4⋊C4C2×D4×C8311yescharacteristic
735C4⋊C4C2×D4×C8311yescharacteristic
736C4⋊C4C2×D4×C8311yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C8311yescharacteristic
768C42C2×D4×C8311yescharacteristic
769C42C2×D4×C8311yescharacteristic
770C42C24×C8311yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C8311yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C8311yescharacteristic
834C2×C4#120×C8311yescharacteristic
835C2×C4#120×C8311yescharacteristic
836C2×C4C22×D4×C8311yescharacteristic
837C2×C4C22×D4×C8311yescharacteristic
838C2×C4C22×D4×C8311yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C8311yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C83×#301811yescharacteristic
887C2C83×#301911yescharacteristic
888C2C83×#302111yescharacteristic
subgroupG/H
center, socleC22×C83C2×#120
commutator, Frattini, cosocleC42C24×C83
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3529C2semidirect
2. C83×#3219C2semidirect
3. C83×#3214C2semidirect
4. C83×#3180C2semidirect
5. C83×#1664C2semidirect
6. C83×#1662C2semidirect
7. C83×#1661C2semidirect
8. C83×#1659C2semidirect
9. C83×#1657C2semidirect
10. C83×#1656C2semidirect
11. C83×#1656C2semidirect
12. C83×#1655C2semidirect
13. C83×#1535C2semidirect
14. C83×#1532C2semidirect
15. C83×#1530C2semidirect
28. #532×C83C22semidirect
36. #501×C83C22semidirect
41. #496×C83C22semidirect
42. #491×C83C22semidirect
43. #490×C83C22semidirect
44. #490×C83C22semidirect
47. #489×C83C22semidirect
60. #432×C83C22semidirect
61. #432×C83C22semidirect
62. C2×#97×C83C22semidirect
63. #330×C83C22semidirect
64. #330×C83C22semidirect
65. #330×C83C22semidirect
66. #330×C83C22semidirect
73. #329×C83C22semidirect
74. #329×C83C22semidirect
435. #19010C83direct (N × H)
445. #3529C2×C83semidirect
446. #3219C2×C83semidirect
447. #3214C2×C83semidirect
448. #3180C2×C83semidirect
449. #1664C2×C83semidirect
450. #1662C2×C83semidirect
451. #1661C2×C83semidirect
452. #1659C2×C83semidirect
453. #1657C2×C83semidirect
454. #1656C2×C83semidirect
455. #1656C2×C83semidirect
456. #1655C2×C83semidirect
457. #1535C2×C83semidirect
458. #1532C2×C83semidirect
459. #1530C2×C83semidirect
460. C83#19010direct (N × H)
473. #532C22×C83semidirect
481. #501C22×C83semidirect
486. #496C22×C83semidirect
487. #491C22×C83semidirect
488. #490C22×C83semidirect
489. #490C22×C83semidirect
492. #489C22×C83semidirect
505. #432C22×C83semidirect
506. #432C22×C83semidirect
507. C2×#97C22×C83semidirect
508. #330C22×C83semidirect
509. #330C22×C83semidirect
510. #330C22×C83semidirect
511. #330C22×C83semidirect
518. #329C22×C83semidirect
519. #329C22×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35292
C83×#32192
C83×#32142
C83×#31802
C83×#16642
C83×#16622
C83×#16612
C83×#16592
C83×#16572
C83×#16562
C83×#16552
C83×#15352
C83×#15322
C83×#15302
#1901083