Finite Group Databasebeta

← C83×#18418 #35246242

Subgroups — C83×#18418 #35246242

Order 21248.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3537C211yesmaximal, characteristic, complemented
2C83×#3192C211yesmaximal, characteristic, complemented
3C83×#3188C211yesmaximal, characteristic, complemented
4C83×#2656C211yesmaximal, characteristic, complemented
5C83×#1618C212yesmaximal, complemented
6C83×#1613C212yesmaximal, complemented
7C83×#1600C212yesmaximal, complemented
8C83×#1595C212yesmaximal, complemented
9C83×#1504C211yesmaximal, characteristic, complemented
10C2×#327×C83C211yesmaximal, 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×C83—22no—
26C2×#121×C83C2211yescharacteristic
27C2×#121×C83C2211yescharacteristic
28C2×#121×C83C2211yescharacteristic, complemented
29#484×C83C2211yescharacteristic, complemented
30#482×C83—21no—
31#481×C83—21no—
32#481×C83C2211yescharacteristic, complemented
33#481×C83C2212yescomplemented
34#469×C83—22no—
35#466×C83—21no—
36#465×C83—21no—
37#450×C83C2211yescharacteristic, complemented
38#449×C83—21no—
39#447×C83—21no—
40#447×C83C2211yescharacteristic, complemented
41#447×C83C2212yescomplemented
42#407×C83C2211yescharacteristic, complemented
43C2×C22⋊C8×C83C2211yescharacteristic, complemented
44#399×C83—21no—
45#399×C83C2212yescomplemented
46#392×C83—21no—
47#392×C83C2212yescomplemented
48C2×#95×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×C83—21no—
67C23×C4×C83C2311yescharacteristic
68C2×SD16×C83—21no—
69C2×D8×C83—21no—
70C2×D8×C83—22no—
71C2×M16×C83—21no—
72C22×C8×C83—21no—
73#127×C83—22no—
74#127×C83—21no—
75#126×C83—22no—
76#126×C83—22no—
77#125×C83—21no—
78#124×C83—22no—
79#123×C83—22no—
80#123×C83—21no—
81#123×C83—22no—
82#123×C83—22no—
83#123×C83—22no—
84C22⋊Q8×C83D411yescharacteristic, complemented
85C22⋊Q8×C83C2311yescharacteristic
86#121×C83—22no—
87#121×C83—21no—
88#121×C83—21no—
89#121×C83—22no—
90#121×C83—22no—
91#121×C83—22no—
92#121×C83—22no—
93#121×C83—21no—
94#121×C83—21no—
95#121×C83—21no—
96#121×C83—21no—
97#121×C83—21no—
98#121×C83—21no—
99#121×C83—22no—
100#121×C83—21no—
101#121×C83—21no—
102#121×C83—21no—
103#121×C83—21no—
104#121×C83—48no—
105#121×C83D411yescharacteristic, complemented
106#121×C83D412yescomplemented
107#121×C83C2312yes—
108#121×C83C2311yescharacteristic
109#120×C83—22no—
110#120×C83—22no—
111#120×C83—22no—
112#120×C83—21no—
113#120×C83—22no—
114#120×C83—22no—
115#120×C83—22no—
116C4×D4×C83—22no—
117C4×D4×C83—21no—
118C4×D4×C83—21no—
119C4×D4×C83—21no—
120C4×D4×C83—21no—
121C4×D4×C83—22no—
122#117×C83—21no—
123#117×C83D411yescharacteristic, complemented
124C2×C4⋊C4×C83—22no—
125C2×C4⋊C4×C83D411yescharacteristic
126C2×C4⋊C4×C83D411yescharacteristic, complemented
127C2×C4⋊C4×C83C2311yescharacteristic
128C2×C22⋊C4×C83—21no—
129C2×C22⋊C4×C83—22no—
130C2×C22⋊C4×C83—22no—
131C2×C22⋊C4×C83—21no—
132C2×C22⋊C4×C83C2312yes—
133#107×C83—21no—
134#106×C83—21no—
135#106×C83—22no—
136#103×C83—21no—
137#102×C83—21no—
138#102×C83—22no—
139#102×C83—21no—
140#102×C83—21no—
141#102×C83—22no—
142C22⋊C8×C83—21no—
143C22⋊C8×C83—21no—
144C22⋊C8×C83C2311yescharacteristic
145C22⋊C8×C83C2312yes—
146C22⋊C8×C83C2311yescharacteristic
147#95×C83—21no—
148#95×C83C2312yes—
149C24×C83—22no—
150C24×C83—21no—
151C24×C83—21no—
152C24×C83C2×D411yescharacteristic
153C24×C83C2×D412yes—
154#41×C83—81no—
155C2×Q8×C83C2×D411yescharacteristic
156C2×D4×C83—22no—
157C2×D4×C83—21no—
158C2×D4×C83—21no—
159C2×D4×C83—22no—
160C2×D4×C83—22no—
161C2×D4×C83—22no—
162C2×D4×C83—22no—
163C2×D4×C83—22no—
164C2×D4×C83—22no—
165C2×D4×C83—21no—
166C2×D4×C83—22no—
167C2×D4×C83—22no—
168C2×D4×C83—21no—
169C2×D4×C83—21no—
170C2×D4×C83—21no—
171C2×D4×C83—21no—
172C2×D4×C83—21no—
173C2×D4×C83—44no—
174C2×D4×C83—44no—
175C2×D4×C83—44no—
176C2×D4×C83—41no—
177C2×D4×C83—41no—
178C2×D4×C83—81no—
179C2×D4×C83—81no—
180C2×D4×C83—82no—
181C2×D4×C83—81no—
182C2×D4×C83—82no—
183C2×D4×C83—82no—
184C2×D4×C83—81no—
185C2×D4×C83—81no—
186C2×D4×C83—82no—
187C2×D4×C83—82no—
188C2×D4×C83—84no—
189C2×D4×C83C2×D411yescharacteristic
190C2×D4×C83C2×D412yes—
191C22×C4×C83—22no—
192C22×C4×C83—22no—
193C22×C4×C83—22no—
194C22×C4×C83—24no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—81no—
199C22×C4×C83—81no—
200C22×C4×C83—81no—
201C22×C4×C83C2×D412yes—
202C22×C4×C83C2×D411yescharacteristic
203C22×C4×C83C2×D411yescharacteristic
204C22×C4×C83C2×D411yescharacteristic
205C22×C4×C83C2×D411yescharacteristic
206C22×C4×C83C2×D411yescharacteristic
207C22×C4×C83C2411yescharacteristic
208SD16×C83—81no—
209D8×C83—81no—
210D8×C83—82no—
211M16×C83—81no—
212C2×C8×C83—21no—
213C2×C8×C83—22no—
214C2×C8×C83—21no—
215C2×C8×C83—81no—
216C4⋊C4×C83—22no—
217C4⋊C4×C83—22no—
218C4⋊C4×C83—21no—
219C4⋊C4×C83—21no—
220C4⋊C4×C83—21no—
221C4⋊C4×C83—21no—
222C4⋊C4×C83—21no—
223C4⋊C4×C83—21no—
224C4⋊C4×C83—21no—
225C4⋊C4×C83—44no—
226C4⋊C4×C83C2×D412yes—
227C4⋊C4×C83C2×D411yescharacteristic
228C4⋊C4×C83C2×D411yescharacteristic
229C22⋊C4×C83—22no—
230C22⋊C4×C83—22no—
231C22⋊C4×C83—22no—
232C22⋊C4×C83—22no—
233C22⋊C4×C83—22no—
234C22⋊C4×C83—21no—
235C22⋊C4×C83—21no—
236C22⋊C4×C83—21no—
237C22⋊C4×C83—22no—
238C22⋊C4×C83—21no—
239C22⋊C4×C83—22no—
240C22⋊C4×C83—22no—
241C22⋊C4×C83—22no—
242C22⋊C4×C83—21no—
243C22⋊C4×C83—44no—
244C22⋊C4×C83—44no—
245C22⋊C4×C83—41no—
246C22⋊C4×C83—41no—
247C42×C83—22no—
248C42×C83—21no—
249C23×C83—21no—
250C23×C83—21no—
251C23×C83—22no—
252C23×C83—22no—
253C23×C83—22no—
254C23×C83—21no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83—41no—
258C23×C83—42no—
259C23×C83—42no—
260C23×C83—42no—
261C23×C83—42no—
262C23×C83—42no—
263C23×C83—41no—
264C23×C83—41no—
265C23×C83—41no—
266C23×C83—81no—
267C23×C83—81no—
268C23×C83—82no—
269C23×C83—82no—
270C23×C83—82no—
271C23×C83#12011yescharacteristic
272C23×C83#12011yescharacteristic
273C23×C83C22×D411yescharacteristic
274Q8×C83—41no—
275D4×C83—42no—
276D4×C83—41no—
277D4×C83—42no—
278D4×C83—42no—
279D4×C83—42no—
280D4×C83—41no—
281D4×C83—41no—
282D4×C83—42no—
283D4×C83—41no—
284D4×C83—42no—
285D4×C83—41no—
286D4×C83—44no—
287D4×C83—42no—
288D4×C83—81no—
289D4×C83—82no—
290D4×C83—82no—
291D4×C83—81no—
292D4×C83—82no—
293D4×C83—82no—
294D4×C83—82no—
295D4×C83—82no—
296D4×C83—82no—
297D4×C83—88no—
298D4×C83—82no—
299D4×C83—82no—
300C2×C4×C83—24no—
301C2×C4×C83—21no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—21no—
305C2×C4×C83—21no—
306C2×C4×C83—41no—
307C2×C4×C83—41no—
308C2×C4×C83—41no—
309C2×C4×C83—41no—
310C2×C4×C83—41no—
311C2×C4×C83—41no—
312C2×C4×C83—42no—
313C2×C4×C83—42no—
314C2×C4×C83—42no—
315C2×C4×C83—42no—
316C2×C4×C83—42no—
317C2×C4×C83—41no—
318C2×C4×C83—81no—
319C2×C4×C83—84no—
320C2×C4×C83—82no—
321C2×C4×C83—82no—
322C2×C4×C83#12011yescharacteristic
323C2×C4×C83#12011yescharacteristic
324C2×C4×C83C22×D411yescharacteristic
325C2×C4×C83C22×D411yescharacteristic
326C8×C83—41no—
327C8×C83—41no—
328C8×C83—42no—
329C22×C83—21no—
330C22×C83—21no—
331C22×C83—21no—
332C22×C83—21no—
333C22×C83—21no—
334C22×C83—21no—
335C22×C83—21no—
336C22×C83—42no—
337C22×C83—42no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83—41no—
341C22×C83—42no—
342C22×C83—42no—
343C22×C83—41no—
344C22×C83—41no—
345C22×C83—42no—
346C22×C83—42no—
347C22×C83—82no—
348C22×C83—82no—
349C22×C83—82no—
350C22×C83—82no—
351C22×C83—81no—
352C22×C83—81no—
353C22×C83—81no—
354C22×C83—162no—
355C22×C83—164no—
356C22×C83#45312yes—
357C22×C83C2×#12011yescharacteristic
358C22×C83#57611yescharacteristic
359C22×C83#57711yescharacteristic
360C4×C83—21no—
361C4×C83—21no—
362C4×C83—21no—
363C4×C83—21no—
364C4×C83—44no—
365C4×C83—42no—
366C4×C83—41no—
367C4×C83—42no—
368C4×C83—41no—
369C4×C83—41no—
370C4×C83—81no—
371#18418C8311yesmaximal, characteristic, direct product factor, Sylow
372C2×C83—21no—
373C2×C83—21no—
374C2×C83—22no—
375C2×C83—41no—
376C2×C83—82no—
377C2×C83—82no—
378C2×C83—81no—
379C2×C83—161no—
380C2×C83#301211yescharacteristic
381C2×C83C2×#45311yescharacteristic
382C2×C83#302611yescharacteristic
383#3537C2×C8311yescharacteristic, complemented
384#3192C2×C8311yescharacteristic, complemented
385#3188C2×C8311yescharacteristic, complemented
386#2656C2×C8311yescharacteristic, complemented
387#1618C2×C8312yescomplemented
388#1613C2×C8312yescomplemented
389#1600C2×C8312yescomplemented
390#1595C2×C8312yescomplemented
391#1504C2×C8311yescharacteristic, complemented
392C2×#327C2×C8311yescharacteristic, complemented
393#1471C2×C8311yescharacteristic, complemented
394C83#1841811yescharacteristic, direct product factor, Sylow
395#560—22no—
396#553—21no—
397#553—21no—
398D42—22no—
399D42—21no—
400D42—21no—
401#540—21no—
402#538—21no—
403#538C22×C8312yes—
404#535—21no—
405#534—21no—
406#534C22×C8312yes—
407#525C22×C8311yescharacteristic
408C2×#121—22no—
409C2×#121C22×C8311yescharacteristic
410C2×#121C22×C8311yescharacteristic
411C2×#121C22×C8311yescharacteristic, complemented
412#484C22×C8311yescharacteristic, complemented
413#482—21no—
414#481—21no—
415#481C22×C8311yescharacteristic, complemented
416#481C22×C8312yescomplemented
417#469—22no—
418#466—21no—
419#465—21no—
420#450C22×C8311yescharacteristic, complemented
421#449—21no—
422#447—21no—
423#447C22×C8311yescharacteristic, complemented
424#447C22×C8312yescomplemented
425#407C22×C8311yescharacteristic, complemented
426C2×C22⋊C8C22×C8311yescharacteristic, complemented
427#399—21no—
428#399C22×C8312yescomplemented
429#392—21no—
430#392C22×C8312yescomplemented
431C2×#95C22×C8311yescharacteristic, complemented
432#328C22×C8312yescomplemented
433#327C22×C8312yescomplemented
434#327C22×C8312yescomplemented
435#327C22×C8312yescomplemented
436#323C22×C8312yescomplemented
437#323C22×C8312yescomplemented
438C2×#41D4×C8311yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C8312yes—
446C22×D4D4×C8311yescharacteristic
447C22×D4D4×C8311yescharacteristic, complemented
448C22×D4C23×C8311yescharacteristic
449C23×C4—21no—
450C23×C4C23×C8311yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C8311yescharacteristic, complemented
468C22⋊Q8C23×C8311yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C8312yescomplemented
489#121D4×C8311yescharacteristic, complemented
490#121C23×C8312yes—
491#121C23×C8311yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C8311yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C8311yescharacteristic
509C2×C4⋊C4D4×C8311yescharacteristic, complemented
510C2×C4⋊C4C23×C8311yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C8312yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C8311yescharacteristic
528C22⋊C8C23×C8311yescharacteristic
529C22⋊C8C23×C8312yes—
530#95—21no—
531#95C23×C8312yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C8311yescharacteristic
536C24C2×D4×C8312yes—
537#41—81no—
538C2×Q8C2×D4×C8311yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C8311yescharacteristic
573C2×D4C2×D4×C8312yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C8312yes—
585C22×C4C2×D4×C8311yescharacteristic
586C22×C4C2×D4×C8311yescharacteristic
587C22×C4C2×D4×C8311yescharacteristic
588C22×C4C2×D4×C8311yescharacteristic
589C22×C4C2×D4×C8311yescharacteristic
590C22×C4C24×C8311yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C8312yes—
610C4⋊C4C2×D4×C8311yescharacteristic
611C4⋊C4C2×D4×C8311yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C8311yescharacteristic
655C23#120×C8311yescharacteristic
656C23C22×D4×C8311yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—42no—
666D4—41no—
667D4—42no—
668D4—41no—
669D4—44no—
670D4—42no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C8311yescharacteristic
706C2×C4#120×C8311yescharacteristic
707C2×C4C22×D4×C8311yescharacteristic
708C2×C4C22×D4×C8311yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22#453×C8312yes—
740C22C2×#120×C8311yescharacteristic
741C22#576×C8311yescharacteristic
742C22#577×C8311yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—41no—
749C4—42no—
750C4—41no—
751C4—42no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—81no—
760C2—82no—
761C2—161no—
762C2C83×#301211yescharacteristic
763C2C2×#453×C8311yescharacteristic
764C2C83×#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×#3192C2semidirect
3. C83×#3188C2semidirect
4. C83×#2656C2semidirect
5. C83×#1618C2semidirect
6. C83×#1613C2semidirect
7. C83×#1600C2semidirect
8. C83×#1595C2semidirect
9. C83×#1504C2semidirect
10. C2×#327×C83C2semidirect
11. C83×#1471C2semidirect
28. C2×#121×C83C22semidirect
29. #484×C83C22semidirect
32. #481×C83C22semidirect
33. #481×C83C22semidirect
37. #450×C83C22semidirect
40. #447×C83C22semidirect
41. #447×C83C22semidirect
42. #407×C83C22semidirect
43. C2×C22⋊C8×C83C22semidirect
45. #399×C83C22semidirect
47. #392×C83C22semidirect
48. C2×#95×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
84. C22⋊Q8×C83D4semidirect
105. #121×C83D4semidirect
106. #121×C83D4semidirect
123. #117×C83D4semidirect
126. C2×C4⋊C4×C83D4semidirect
371. #18418C83direct (N × H)
383. #3537C2×C83semidirect
384. #3192C2×C83semidirect
385. #3188C2×C83semidirect
386. #2656C2×C83semidirect
387. #1618C2×C83semidirect
388. #1613C2×C83semidirect
389. #1600C2×C83semidirect
390. #1595C2×C83semidirect
391. #1504C2×C83semidirect
392. C2×#327C2×C83semidirect
393. #1471C2×C83semidirect
394. C83#18418direct (N × H)
411. C2×#121C22×C83semidirect
412. #484C22×C83semidirect
415. #481C22×C83semidirect
416. #481C22×C83semidirect
420. #450C22×C83semidirect
423. #447C22×C83semidirect
424. #447C22×C83semidirect
425. #407C22×C83semidirect
426. C2×C22⋊C8C22×C83semidirect
428. #399C22×C83semidirect
430. #392C22×C83semidirect
431. C2×#95C22×C83semidirect
432. #328C22×C83semidirect
433. #327C22×C83semidirect
434. #327C22×C83semidirect
435. #327C22×C83semidirect
436. #323C22×C83semidirect
437. #323C22×C83semidirect
438. C2×#41D4×C83semidirect
447. C22×D4D4×C83semidirect
467. C22⋊Q8D4×C83semidirect
488. #121D4×C83semidirect
489. #121D4×C83semidirect
506. #117D4×C83semidirect
509. 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×#31922
C83×#31882
C83×#26562
C83×#16182
C83×#16132
C83×#16002
C83×#15952
C83×#15042
C2×#327×C832
C83×#14712
#1841883