Finite Group Databasebeta

← C83×#18450 #35246274

Subgroups — C83×#18450 #35246274

Order 21248.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3537C211yesmaximal, characteristic, complemented
2C83×#3194C211yesmaximal, characteristic, complemented
3C83×#3186C211yesmaximal, characteristic, complemented
4C83×#2815C211yesmaximal, characteristic, complemented
5C83×#1612C212yesmaximal, complemented
6C83×#1607C212yesmaximal, complemented
7C83×#1600C212yesmaximal, complemented
8C83×#1595C212yesmaximal, complemented
9C83×#1516C211yesmaximal, characteristic, complemented
10C83×#1510C211yesmaximal, characteristic, complemented
11C83×#1471C211yesmaximal, characteristic, complemented
12#560×C83—22no—
13#553×C83—21no—
14#553×C83—21no—
15D42×C83—22no—
16D42×C83—21no—
17D42×C83—21no—
18#540×C83—21no—
19#538×C83—21no—
20#538×C83C2212yes—
21#535×C83—21no—
22#534×C83—21no—
23#534×C83C2212yes—
24#525×C83C2211yescharacteristic
25C2×#121×C83C2211yescharacteristic
26C2×#121×C83C2211yescharacteristic
27C2×#121×C83C2211yescharacteristic, complemented
28#483×C83C2211yescharacteristic, complemented
29#482×C83—21no—
30#480×C83—21no—
31#480×C83C2211yescharacteristic, complemented
32#480×C83C2212yescomplemented
33#469×C83—21no—
34#468×C83—21no—
35#466×C83—22no—
36#450×C83C2211yescharacteristic, complemented
37#449×C83—21no—
38#447×C83—21no—
39#447×C83C2211yescharacteristic, complemented
40#447×C83C2212yescomplemented
41#407×C83C2211yescharacteristic, complemented
42C2×C22⋊C8×C83C2211yescharacteristic, complemented
43#397×C83—21no—
44#397×C83C2212yescomplemented
45#392×C83—21no—
46#392×C83—22no—
47#392×C83C2212yescomplemented
48#381×C83C2211yescharacteristic, complemented
49#328×C83C2212yescomplemented
50#327×C83C2212yescomplemented
51#327×C83C2212yescomplemented
52#327×C83C2212yescomplemented
53#323×C83C2212yescomplemented
54#323×C83C2212yescomplemented
55C2×#41×C83D411yescharacteristic, complemented
56C22×D4×C83—22no—
57C22×D4×C83—21no—
58C22×D4×C83—21no—
59C22×D4×C83—22no—
60C22×D4×C83—21no—
61C22×D4×C83—22no—
62C22×D4×C83D412yes—
63C22×D4×C83D411yescharacteristic
64C22×D4×C83D411yescharacteristic, complemented
65C22×D4×C83C2311yescharacteristic
66C23×C4×C83C2311yescharacteristic
67C2×SD16×C83—21no—
68C2×D8×C83—22no—
69C2×D8×C83—21no—
70C2×M16×C83—21no—
71C22×C8×C83—21no—
72#127×C83—22no—
73#127×C83—21no—
74#126×C83—22no—
75#126×C83—22no—
76#125×C83—21no—
77#124×C83—22no—
78#123×C83—22no—
79#123×C83—21no—
80#123×C83—22no—
81#123×C83—22no—
82#123×C83—22no—
83C22⋊Q8×C83D411yescharacteristic, complemented
84C22⋊Q8×C83C2311yescharacteristic
85#121×C83—22no—
86#121×C83—21no—
87#121×C83—21no—
88#121×C83—22no—
89#121×C83—22no—
90#121×C83—22no—
91#121×C83—22no—
92#121×C83—21no—
93#121×C83—21no—
94#121×C83—21no—
95#121×C83—21no—
96#121×C83—21no—
97#121×C83—21no—
98#121×C83—22no—
99#121×C83—21no—
100#121×C83—21no—
101#121×C83—21no—
102#121×C83—21no—
103#121×C83D412yescomplemented
104#121×C83D411yescharacteristic, complemented
105#121×C83C2312yes—
106#121×C83C2311yescharacteristic
107#120×C83—22no—
108#120×C83—22no—
109#120×C83—22no—
110#120×C83—21no—
111#120×C83—22no—
112#120×C83—22no—
113#120×C83—22no—
114C4×D4×C83—22no—
115C4×D4×C83—21no—
116C4×D4×C83—21no—
117C4×D4×C83—21no—
118C4×D4×C83—21no—
119C4×D4×C83—22no—
120#117×C83—21no—
121#117×C83D411yescharacteristic, complemented
122C2×C4⋊C4×C83D411yescharacteristic
123C2×C4⋊C4×C83D411yescharacteristic, complemented
124C2×C4⋊C4×C83C2311yescharacteristic
125C2×C22⋊C4×C83—21no—
126C2×C22⋊C4×C83—21no—
127C2×C22⋊C4×C83—21no—
128C2×C22⋊C4×C83—22no—
129C2×C22⋊C4×C83—22no—
130C2×C22⋊C4×C83C2312yes—
131#107×C83—22no—
132#107×C83—21no—
133#106×C83—21no—
134#103×C83—21no—
135#102×C83—22no—
136#102×C83—21no—
137#102×C83—22no—
138#102×C83—21no—
139#102×C83—21no—
140C22⋊C8×C83—21no—
141C22⋊C8×C83—21no—
142C22⋊C8×C83C2311yescharacteristic
143C22⋊C8×C83C2312yes—
144C22⋊C8×C83C2311yescharacteristic
145#95×C83—21no—
146#95×C83—22no—
147#95×C83C2312yes—
148C24×C83—22no—
149C24×C83—21no—
150C24×C83—21no—
151C24×C83C2×D412yes—
152C24×C83C2×D411yescharacteristic
153#41×C83—81no—
154C2×Q8×C83C2×D411yescharacteristic
155C2×D4×C83—22no—
156C2×D4×C83—21no—
157C2×D4×C83—21no—
158C2×D4×C83—22no—
159C2×D4×C83—22no—
160C2×D4×C83—22no—
161C2×D4×C83—22no—
162C2×D4×C83—22no—
163C2×D4×C83—22no—
164C2×D4×C83—21no—
165C2×D4×C83—22no—
166C2×D4×C83—22no—
167C2×D4×C83—21no—
168C2×D4×C83—21no—
169C2×D4×C83—21no—
170C2×D4×C83—21no—
171C2×D4×C83—21no—
172C2×D4×C83—41no—
173C2×D4×C83—41no—
174C2×D4×C83—81no—
175C2×D4×C83—81no—
176C2×D4×C83—82no—
177C2×D4×C83—81no—
178C2×D4×C83—82no—
179C2×D4×C83—82no—
180C2×D4×C83—82no—
181C2×D4×C83—82no—
182C2×D4×C83—82no—
183C2×D4×C83—82no—
184C2×D4×C83—82no—
185C2×D4×C83—82no—
186C2×D4×C83—84no—
187C2×D4×C83C2×D411yescharacteristic
188C2×D4×C83C2×D412yes—
189C22×C4×C83—22no—
190C22×C4×C83—22no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—22no—
194C22×C4×C83—21no—
195C22×C4×C83—81no—
196C22×C4×C83C2×D412yes—
197C22×C4×C83C2×D411yescharacteristic
198C22×C4×C83C2×D411yescharacteristic
199C22×C4×C83C2×D411yescharacteristic
200C22×C4×C83C2×D411yescharacteristic
201C22×C4×C83C2×D411yescharacteristic
202C22×C4×C83C2411yescharacteristic
203SD16×C83—81no—
204D8×C83—82no—
205D8×C83—81no—
206M16×C83—81no—
207C2×C8×C83—22no—
208C2×C8×C83—21no—
209C2×C8×C83—21no—
210C2×C8×C83—81no—
211C4⋊C4×C83—22no—
212C4⋊C4×C83—22no—
213C4⋊C4×C83—21no—
214C4⋊C4×C83—21no—
215C4⋊C4×C83—21no—
216C4⋊C4×C83—21no—
217C4⋊C4×C83—21no—
218C4⋊C4×C83—21no—
219C4⋊C4×C83—21no—
220C4⋊C4×C83C2×D411yescharacteristic
221C4⋊C4×C83C2×D412yes—
222C4⋊C4×C83C2×D411yescharacteristic
223C22⋊C4×C83—22no—
224C22⋊C4×C83—22no—
225C22⋊C4×C83—22no—
226C22⋊C4×C83—22no—
227C22⋊C4×C83—22no—
228C22⋊C4×C83—21no—
229C22⋊C4×C83—21no—
230C22⋊C4×C83—21no—
231C22⋊C4×C83—22no—
232C22⋊C4×C83—21no—
233C22⋊C4×C83—22no—
234C22⋊C4×C83—22no—
235C22⋊C4×C83—22no—
236C22⋊C4×C83—21no—
237C22⋊C4×C83—41no—
238C22⋊C4×C83—41no—
239C22⋊C4×C83—82no—
240C22⋊C4×C83—82no—
241C22⋊C4×C83—81no—
242C42×C83—22no—
243C42×C83—21no—
244C23×C83—22no—
245C23×C83—22no—
246C23×C83—22no—
247C23×C83—21no—
248C23×C83—22no—
249C23×C83—22no—
250C23×C83—41no—
251C23×C83—41no—
252C23×C83—42no—
253C23×C83—42no—
254C23×C83—42no—
255C23×C83—41no—
256C23×C83—41no—
257C23×C83—42no—
258C23×C83—41no—
259C23×C83—42no—
260C23×C83—81no—
261C23×C83—81no—
262C23×C83—82no—
263C23×C83—82no—
264C23×C83—82no—
265C23×C83#12011yescharacteristic
266C23×C83#12011yescharacteristic
267C23×C83C22×D411yescharacteristic
268Q8×C83—41no—
269D4×C83—42no—
270D4×C83—41no—
271D4×C83—42no—
272D4×C83—42no—
273D4×C83—42no—
274D4×C83—41no—
275D4×C83—41no—
276D4×C83—44no—
277D4×C83—42no—
278D4×C83—42no—
279D4×C83—42no—
280D4×C83—42no—
281D4×C83—81no—
282D4×C83—82no—
283D4×C83—82no—
284D4×C83—81no—
285D4×C83—82no—
286D4×C83—82no—
287D4×C83—82no—
288D4×C83—82no—
289D4×C83—82no—
290D4×C83—82no—
291D4×C83—82no—
292D4×C83—88no—
293C2×C4×C83—21no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—21no—
297C2×C4×C83—21no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83—41no—
301C2×C4×C83—41no—
302C2×C4×C83—41no—
303C2×C4×C83—41no—
304C2×C4×C83—42no—
305C2×C4×C83—42no—
306C2×C4×C83—42no—
307C2×C4×C83—42no—
308C2×C4×C83—41no—
309C2×C4×C83—42no—
310C2×C4×C83—42no—
311C2×C4×C83—81no—
312C2×C4×C83—82no—
313C2×C4×C83—82no—
314C2×C4×C83#12011yescharacteristic
315C2×C4×C83#12011yescharacteristic
316C2×C4×C83C22×D411yescharacteristic
317C2×C4×C83C22×D411yescharacteristic
318C8×C83—42no—
319C8×C83—41no—
320C8×C83—41no—
321C22×C83—21no—
322C22×C83—21no—
323C22×C83—21no—
324C22×C83—21no—
325C22×C83—21no—
326C22×C83—21no—
327C22×C83—21no—
328C22×C83—21no—
329C22×C83—42no—
330C22×C83—42no—
331C22×C83—41no—
332C22×C83—42no—
333C22×C83—42no—
334C22×C83—41no—
335C22×C83—41no—
336C22×C83—42no—
337C22×C83—42no—
338C22×C83—82no—
339C22×C83—82no—
340C22×C83—82no—
341C22×C83—82no—
342C22×C83—82no—
343C22×C83—81no—
344C22×C83—81no—
345C22×C83—81no—
346C22×C83—162no—
347C22×C83—164no—
348C22×C83C2×#12011yescharacteristic
349C22×C83#57612yes—
350C4×C83—21no—
351C4×C83—21no—
352C4×C83—21no—
353C4×C83—21no—
354C4×C83—42no—
355C4×C83—41no—
356C4×C83—42no—
357C4×C83—41no—
358C4×C83—41no—
359C4×C83—82no—
360C4×C83—81no—
361#18450C8311yesmaximal, characteristic, direct product factor, Sylow
362C2×C83—22no—
363C2×C83—41no—
364C2×C83—41no—
365C2×C83—82no—
366C2×C83—82no—
367C2×C83—81no—
368C2×C83—161no—
369C2×C83#300811yescharacteristic
370C2×C83#301911yescharacteristic
371C2×C83#302611yescharacteristic
372#3537C2×C8311yescharacteristic, complemented
373#3194C2×C8311yescharacteristic, complemented
374#3186C2×C8311yescharacteristic, complemented
375#2815C2×C8311yescharacteristic, complemented
376#1612C2×C8312yescomplemented
377#1607C2×C8312yescomplemented
378#1600C2×C8312yescomplemented
379#1595C2×C8312yescomplemented
380#1516C2×C8311yescharacteristic, complemented
381#1510C2×C8311yescharacteristic, complemented
382#1471C2×C8311yescharacteristic, complemented
383C83#1845011yescharacteristic, direct product factor, Sylow
384#560—22no—
385#553—21no—
386#553—21no—
387D42—22no—
388D42—21no—
389D42—21no—
390#540—21no—
391#538—21no—
392#538C22×C8312yes—
393#535—21no—
394#534—21no—
395#534C22×C8312yes—
396#525C22×C8311yescharacteristic
397C2×#121C22×C8311yescharacteristic
398C2×#121C22×C8311yescharacteristic
399C2×#121C22×C8311yescharacteristic, complemented
400#483C22×C8311yescharacteristic, complemented
401#482—21no—
402#480—21no—
403#480C22×C8311yescharacteristic, complemented
404#480C22×C8312yescomplemented
405#469—21no—
406#468—21no—
407#466—22no—
408#450C22×C8311yescharacteristic, complemented
409#449—21no—
410#447—21no—
411#447C22×C8311yescharacteristic, complemented
412#447C22×C8312yescomplemented
413#407C22×C8311yescharacteristic, complemented
414C2×C22⋊C8C22×C8311yescharacteristic, complemented
415#397—21no—
416#397C22×C8312yescomplemented
417#392—21no—
418#392—22no—
419#392C22×C8312yescomplemented
420#381C22×C8311yescharacteristic, complemented
421#328C22×C8312yescomplemented
422#327C22×C8312yescomplemented
423#327C22×C8312yescomplemented
424#327C22×C8312yescomplemented
425#323C22×C8312yescomplemented
426#323C22×C8312yescomplemented
427C2×#41D4×C8311yescharacteristic, complemented
428C22×D4—22no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—22no—
432C22×D4—21no—
433C22×D4—22no—
434C22×D4D4×C8312yes—
435C22×D4D4×C8311yescharacteristic
436C22×D4D4×C8311yescharacteristic, complemented
437C22×D4C23×C8311yescharacteristic
438C23×C4C23×C8311yescharacteristic
439C2×SD16—21no—
440C2×D8—22no—
441C2×D8—21no—
442C2×M16—21no—
443C22×C8—21no—
444#127—22no—
445#127—21no—
446#126—22no—
447#126—22no—
448#125—21no—
449#124—22no—
450#123—22no—
451#123—21no—
452#123—22no—
453#123—22no—
454#123—22no—
455C22⋊Q8D4×C8311yescharacteristic, complemented
456C22⋊Q8C23×C8311yescharacteristic
457#121—22no—
458#121—21no—
459#121—21no—
460#121—22no—
461#121—22no—
462#121—22no—
463#121—22no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—22no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121D4×C8312yescomplemented
476#121D4×C8311yescharacteristic, complemented
477#121C23×C8312yes—
478#121C23×C8311yescharacteristic
479#120—22no—
480#120—22no—
481#120—22no—
482#120—21no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—22no—
492#117—21no—
493#117D4×C8311yescharacteristic, complemented
494C2×C4⋊C4D4×C8311yescharacteristic
495C2×C4⋊C4D4×C8311yescharacteristic, complemented
496C2×C4⋊C4C23×C8311yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4C23×C8312yes—
503#107—22no—
504#107—21no—
505#106—21no—
506#103—21no—
507#102—22no—
508#102—21no—
509#102—22no—
510#102—21no—
511#102—21no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8C23×C8311yescharacteristic
515C22⋊C8C23×C8311yescharacteristic
516C22⋊C8C23×C8312yes—
517#95—21no—
518#95—22no—
519#95C23×C8312yes—
520C24—22no—
521C24—21no—
522C24—21no—
523C24C2×D4×C8312yes—
524C24C2×D4×C8311yescharacteristic
525#41—81no—
526C2×Q8C2×D4×C8311yescharacteristic
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—82no—
549C2×D4—81no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—84no—
559C2×D4C2×D4×C8311yescharacteristic
560C2×D4C2×D4×C8312yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—81no—
568C22×C4C2×D4×C8312yes—
569C22×C4C2×D4×C8311yescharacteristic
570C22×C4C2×D4×C8311yescharacteristic
571C22×C4C2×D4×C8311yescharacteristic
572C22×C4C2×D4×C8311yescharacteristic
573C22×C4C2×D4×C8311yescharacteristic
574C22×C4C24×C8311yescharacteristic
575SD16—81no—
576D8—82no—
577D8—81no—
578M16—81no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—81no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4C2×D4×C8311yescharacteristic
593C4⋊C4C2×D4×C8312yes—
594C4⋊C4C2×D4×C8311yescharacteristic
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—81no—
614C42—22no—
615C42—21no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—81no—
633C23—81no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23#120×C8311yescharacteristic
638C23#120×C8311yescharacteristic
639C23C22×D4×C8311yescharacteristic
640Q8—41no—
641D4—42no—
642D4—41no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—41no—
647D4—41no—
648D4—44no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—81no—
654D4—82no—
655D4—82no—
656D4—81no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
661D4—82no—
662D4—82no—
663D4—82no—
664D4—88no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—81no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4#120×C8311yescharacteristic
687C2×C4#120×C8311yescharacteristic
688C2×C4C22×D4×C8311yescharacteristic
689C2×C4C22×D4×C8311yescharacteristic
690C8—42no—
691C8—41no—
692C8—41no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—41no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—162no—
719C22—164no—
720C22C2×#120×C8311yescharacteristic
721C22#576×C8312yes—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—42no—
730C4—41no—
731C4—82no—
732C4—81no—
733C2—22no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—81no—
739C2—161no—
740C2C83×#300811yescharacteristic
741C2C83×#301911yescharacteristic
742C2C83×#302611yescharacteristic
subgroupG/H
center, socleC22×C83C2×#120
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3537C2semidirect
2. C83×#3194C2semidirect
3. C83×#3186C2semidirect
4. C83×#2815C2semidirect
5. C83×#1612C2semidirect
6. C83×#1607C2semidirect
7. C83×#1600C2semidirect
8. C83×#1595C2semidirect
9. C83×#1516C2semidirect
10. C83×#1510C2semidirect
11. C83×#1471C2semidirect
27. C2×#121×C83C22semidirect
28. #483×C83C22semidirect
31. #480×C83C22semidirect
32. #480×C83C22semidirect
36. #450×C83C22semidirect
39. #447×C83C22semidirect
40. #447×C83C22semidirect
41. #407×C83C22semidirect
42. C2×C22⋊C8×C83C22semidirect
44. #397×C83C22semidirect
47. #392×C83C22semidirect
48. #381×C83C22semidirect
49. #328×C83C22semidirect
50. #327×C83C22semidirect
51. #327×C83C22semidirect
52. #327×C83C22semidirect
53. #323×C83C22semidirect
54. #323×C83C22semidirect
55. C2×#41×C83D4semidirect
64. C22×D4×C83D4semidirect
83. C22⋊Q8×C83D4semidirect
103. #121×C83D4semidirect
104. #121×C83D4semidirect
121. #117×C83D4semidirect
123. C2×C4⋊C4×C83D4semidirect
361. #18450C83direct (N × H)
372. #3537C2×C83semidirect
373. #3194C2×C83semidirect
374. #3186C2×C83semidirect
375. #2815C2×C83semidirect
376. #1612C2×C83semidirect
377. #1607C2×C83semidirect
378. #1600C2×C83semidirect
379. #1595C2×C83semidirect
380. #1516C2×C83semidirect
381. #1510C2×C83semidirect
382. #1471C2×C83semidirect
383. C83#18450direct (N × H)
399. C2×#121C22×C83semidirect
400. #483C22×C83semidirect
403. #480C22×C83semidirect
404. #480C22×C83semidirect
408. #450C22×C83semidirect
411. #447C22×C83semidirect
412. #447C22×C83semidirect
413. #407C22×C83semidirect
414. C2×C22⋊C8C22×C83semidirect
416. #397C22×C83semidirect
419. #392C22×C83semidirect
420. #381C22×C83semidirect
421. #328C22×C83semidirect
422. #327C22×C83semidirect
423. #327C22×C83semidirect
424. #327C22×C83semidirect
425. #323C22×C83semidirect
426. #323C22×C83semidirect
427. C2×#41D4×C83semidirect
436. C22×D4D4×C83semidirect
455. C22⋊Q8D4×C83semidirect
475. #121D4×C83semidirect
476. #121D4×C83semidirect
493. #117D4×C83semidirect
495. C2×C4⋊C4D4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35372
C83×#31942
C83×#31862
C83×#28152
C83×#16122
C83×#16072
C83×#16002
C83×#15952
C83×#15162
C83×#15102
C83×#14712
#1845083