Finite Group Databasebeta

← C83×#61466 #35289290

Subgroups — C83×#61466 #35289290

Order 21248.

2102 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3482C211yesmaximal, characteristic, complemented
2D4×#41×C83C211yesmaximal, characteristic, complemented
3C83×#3392C211yesmaximal, characteristic, complemented
4Q8×D8×C83C211yesmaximal, characteristic, complemented
5C83×#3359C211yesmaximal, characteristic, complemented
6C83×#3358C211yesmaximal, characteristic, complemented
7C83×#3353C213yesmaximal, complemented
8C83×#3330C213yesmaximal, complemented
9C83×#3324C213yesmaximal, complemented
10C83×#3272C213yesmaximal, complemented
11C83×#3182C213yesmaximal, complemented
12C83×#3115C213yesmaximal, complemented
13C83×#3110C213yesmaximal, complemented
14C83×#2971C211yesmaximal, characteristic, complemented
15C4×AGL(1,ℤ/8)×C83C213yesmaximal, complemented
16C22×#41×C83—21no—
17C2×AGL(1,ℤ/8)×C83C2213yes—
18#557×C83C2211yescharacteristic, complemented
19#556×C83C2213yescomplemented
20#552×C83—23no—
21#550×C83C2211yescharacteristic
22D4×Q8×C83C2211yescharacteristic
23D4×Q8×C83C2211yescharacteristic, complemented
24#548×C83—21no—
25#548×C83—21no—
26#547×C83C2213yes—
27#547×C83C2213yescomplemented
28#546×C83—23no—
29D42×C83C2213yes—
30#533×C83C2213yescomplemented
31#532×C83C2213yes—
32#529×C83—23no—
33#525×C83—23no—
34C4×#41×C83C2211yescharacteristic
35C4×#41×C83C2213yescomplemented
36C2×C4×Q8×C83—21no—
37C2×C4×D4×C83C2213yes—
38#500×C83C2213yescomplemented
39#492×C83C2213yescomplemented
40#487×C83C2213yescomplemented
41#486×C83C2213yescomplemented
42#484×C83C2216yescomplemented
43#482×C83C2216yescomplemented
44#475×C83C2213yescomplemented
45#474×C83C2213yes—
46#474×C83C2213yescomplemented
47#474×C83C2213yescomplemented
48#468×C83C2216yescomplemented
49#468×C83C2216yescomplemented
50#461×C83C2213yes—
51#461×C83C2213yescomplemented
52#460×C83C2213yescomplemented
53#459×C83C2213yescomplemented
54#450×C83C2216yes—
55#449×C83C2216yescomplemented
56C8×Q8×C83C2211yescharacteristic, complemented
57C8×Q8×C83C2211yescharacteristic, complemented
58#442×C83C2211yescharacteristic
59#442×C83C2213yescomplemented
60#440×C83C2213yes—
61#440×C83C2216yescomplemented
62#440×C83C2213yescomplemented
63C4×SD16×C83C2213yes—
64C4×SD16×C83C2213yescomplemented
65C4×D8×C83C2213yes—
66C4×D8×C83C2213yescomplemented
67#436×C83C2213yescomplemented
68#436×C83C2213yescomplemented
69#432×C83C2213yescomplemented
70#428×C83C2213yescomplemented
71#418×C83C2213yes—
72#417×C83C2213yescomplemented
73C4×M16×C83C2213yescomplemented
74C2×#41×C83—21no—
75C2×#41×C83—23no—
76C2×#41×C83—23no—
77C2×#41×C83—48no—
78C2×#41×C83D411yescharacteristic
79C2×#41×C83C2313yes—
80C22×Q8×C83—21no—
81C22×Q8×C83—21no—
82C22×D4×C83—23no—
83C22×D4×C83C2313yes—
84C23×C4×C83—23no—
85AGL(1,ℤ/8)×C83—212no—
86C2×SD16×C83C2313yes—
87C2×SD16×C83C2313yes—
88C2×SD16×C83C2316yes—
89C2×D8×C83C2313yes—
90C2×D8×C83C2311yescharacteristic
91C2×M16×C83C2313yes—
92C2×M16×C83C2313yes—
93C4⋊Q8×C83C2313yes—
94C4⋊Q8×C83C2313yes—
95C4⋊Q8×C83C2313yes—
96#127×C83C2313yes—
97#126×C83—26no—
98#125×C83—23no—
99#125×C83—23no—
100#124×C83—23no—
101#124×C83—23no—
102#123×C83—26no—
103#123×C83—26no—
104C22⋊Q8×C83—23no—
105C22⋊Q8×C83—23no—
106C22⋊Q8×C83—23no—
107C22⋊Q8×C83—23no—
108C22⋊Q8×C83C2316yes—
109#121×C83—23no—
110#121×C83—23no—
111#121×C83—23no—
112#121×C83—23no—
113#121×C83C2316yes—
114#120×C83—26no—
115C4×Q8×C83—21no—
116C4×Q8×C83—23no—
117C4×Q8×C83—23no—
118C4×Q8×C83D411yescharacteristic
119C4×Q8×C83C2313yes—
120C4×Q8×C83C2313yes—
121C4×Q8×C83C2311yescharacteristic
122C4×D4×C83—23no—
123C4×D4×C83—23no—
124C4×D4×C83—23no—
125C4×D4×C83—23no—
126C4×D4×C83—23no—
127C4×D4×C83D413yes—
128C4×D4×C83C2313yes—
129C4×D4×C83C2313yes—
130C4×D4×C83C2313yes—
131C4×D4×C83C2311yescharacteristic
132C4×D4×C83C2313yes—
133C4×D4×C83C2311yescharacteristic
134C4×D4×C83C2313yes—
135#117×C83—23no—
136#117×C83—23no—
137#117×C83D413yes—
138#117×C83C2313yes—
139C2×C4⋊C4×C83—23no—
140C2×C4⋊C4×C83C2313yes—
141C2×C22⋊C4×C83—23no—
142C2×C42×C83—23no—
143C2×C42×C83C2313yes—
144#107×C83C2313yes—
145#107×C83C2316yes—
146#107×C83C2313yes—
147#106×C83C2313yes—
148#106×C83C2311yescharacteristic
149C4⋊C8×C83C2313yes—
150C4⋊C8×C83C2313yes—
151#103×C83C2313yes—
152#103×C83C2316yes—
153#103×C83C2313yes—
154#102×C83C2313yes—
155#102×C83C2316yes—
156#102×C83C2313yes—
157#102×C83C2313yes—
158#102×C83C2313yes—
159#102×C83C2311yescharacteristic
160#102×C83C2311yescharacteristic
161C22⋊C8×C83C2316yes—
162#97×C83C2311yescharacteristic
163#97×C83C2313yes—
164C4×C8×C83C2313yes—
165C4×C8×C83C2313yes—
166C24×C83—23no—
167#41×C83—24no—
168#41×C83—26no—
169#41×C83—43no—
170#41×C83—412no—
171#41×C83—412no—
172#41×C83—44no—
173C2×Q8×C83—23no—
174C2×Q8×C83—23no—
175C2×Q8×C83—44no—
176C2×Q8×C83—44no—
177C2×Q8×C83C2×D411yescharacteristic
178C2×Q8×C83C2413yes—
179C2×D4×C83—26no—
180C2×D4×C83—23no—
181C2×D4×C83—26no—
182C2×D4×C83—23no—
183C2×D4×C83—23no—
184C2×D4×C83—23no—
185C2×D4×C83—43no—
186C2×D4×C83—412no—
187C2×D4×C83C2×D413yes—
188C2×D4×C83C2413yes—
189C2×D4×C83C2411yescharacteristic
190C2×D4×C83C2411yescharacteristic
191C22×C4×C83—23no—
192C22×C4×C83—21no—
193C22×C4×C83—23no—
194C22×C4×C83—23no—
195C22×C4×C83—21no—
196C22×C4×C83—23no—
197C22×C4×C83—23no—
198C22×C4×C83—23no—
199C22×C4×C83—412no—
200C22×C4×C83C2×D413yes—
201C22×C4×C83C2×D413yes—
202C22×C4×C83C2413yes—
203SD16×C83—26no—
204SD16×C83—26no—
205SD16×C83—46no—
206D8×C83—26no—
207D8×C83#4114yescomplemented
208M16×C83—26no—
209M16×C83—43no—
210C2×C8×C83C2411yescharacteristic
211C2×C8×C83C2413yes—
212C2×C8×C83C2413yes—
213C2×C8×C83C2411yescharacteristic
214C4⋊C4×C83—23no—
215C4⋊C4×C83—26no—
216C4⋊C4×C83—23no—
217C4⋊C4×C83—23no—
218C4⋊C4×C83—23no—
219C4⋊C4×C83—23no—
220C4⋊C4×C83—23no—
221C4⋊C4×C83—23no—
222C4⋊C4×C83C2×D413yes—
223C4⋊C4×C83C2×D413yes—
224C4⋊C4×C83C2411yescharacteristic
225C4⋊C4×C83C2413yes—
226C4⋊C4×C83C2411yescharacteristic
227C4⋊C4×C83C2413yes—
228C22⋊C4×C83—26no—
229C22⋊C4×C83—23no—
230C22⋊C4×C83—21no—
231C22⋊C4×C83—23no—
232C22⋊C4×C83—23no—
233C22⋊C4×C83—23no—
234C22⋊C4×C83—21no—
235C22⋊C4×C83—23no—
236C22⋊C4×C83—26no—
237C22⋊C4×C83C2×D416yes—
238C42×C83—23no—
239C42×C83—23no—
240C42×C83—23no—
241C42×C83C2×D413yes—
242C42×C83C2×D413yes—
243C42×C83C2413yes—
244C42×C83C2411yescharacteristic
245C23×C83—21no—
246C23×C83—21no—
247C23×C83—23no—
248C23×C83—46no—
249C23×C83—46no—
250C23×C83—83no—
251C23×C83C22×D413yes—
252Q8×C83—23no—
253Q8×C83—23no—
254Q8×C83—46no—
255Q8×C83—46no—
256Q8×C83AGL(1,ℤ/8)14yescomplemented
257D4×C83—26no—
258D4×C83—23no—
259D4×C83—21no—
260D4×C83—21no—
261D4×C83—23no—
262D4×C83—46no—
263D4×C83—46no—
264D4×C83—412no—
265D4×C83—46no—
266D4×C83—83no—
267D4×C83C2×#4112yes—
268D4×C83C2×#4112yescomplemented
269C2×C4×C83—26no—
270C2×C4×C83—23no—
271C2×C4×C83—23no—
272C2×C4×C83—21no—
273C2×C4×C83—23no—
274C2×C4×C83—23no—
275C2×C4×C83—21no—
276C2×C4×C83—23no—
277C2×C4×C83—43no—
278C2×C4×C83—46no—
279C2×C4×C83—42no—
280C2×C4×C83—42no—
281C2×C4×C83—46no—
282C2×C4×C83—46no—
283C2×C4×C83—46no—
284C2×C4×C83—46no—
285C2×C4×C83—46no—
286C2×C4×C83C22×D411yescharacteristic
287C2×C4×C83C22×D413yes—
288C2×C4×C83C22×D411yescharacteristic
289C2×C4×C83C22×D413yes—
290C2×C4×C83C22×D413yes—
291C2×C4×C83C2511yescharacteristic
292C8×C83—23no—
293C8×C83—21no—
294C8×C83—23no—
295C8×C83C2×#4112yescomplemented
296C22×C83—23no—
297C22×C83—23no—
298C22×C83—22no—
299C22×C83—22no—
300C22×C83—23no—
301C22×C83—41no—
302C22×C83—41no—
303C22×C83—41no—
304C22×C83—41no—
305C22×C83—43no—
306C22×C83—43no—
307C22×C83—43no—
308C22×C83—812no—
309C22×C83C23×D411yescharacteristic
310C4×C83—21no—
311C4×C83—23no—
312C4×C83—23no—
313C4×C83—21no—
314C4×C83—41no—
315C4×C83—43no—
316C4×C83—41no—
317C4×C83—43no—
318C4×C83—43no—
319C4×C83C2×AGL(1,ℤ/8)16yes—
320C4×C83C22×#4111yescharacteristic
321C4×C83#58511yescharacteristic
322#61466C8311yesmaximal, characteristic, direct product factor, Sylow
323C2×C83—43no—
324C2×C83—42no—
325C2×C83—42no—
326C2×C83—83no—
327C2×C83D4×#4111yescharacteristic
328C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
329C2×C83#358611yescharacteristic
330#3482C2×C8311yescharacteristic, complemented
331D4×#41C2×C8311yescharacteristic, complemented
332#3392C2×C8311yescharacteristic, complemented
333Q8×D8C2×C8311yescharacteristic, complemented
334#3359C2×C8311yescharacteristic, complemented
335#3358C2×C8311yescharacteristic, complemented
336#3353C2×C8313yescomplemented
337#3330C2×C8313yescomplemented
338#3324C2×C8313yescomplemented
339#3272C2×C8313yescomplemented
340#3182C2×C8313yescomplemented
341#3115C2×C8313yescomplemented
342#3110C2×C8313yescomplemented
343#2971C2×C8311yescharacteristic, complemented
344C4×AGL(1,ℤ/8)C2×C8313yescomplemented
345C83#6146611yescharacteristic, direct product factor, Sylow
346C22×#41—21no—
347C2×AGL(1,ℤ/8)C22×C8313yes—
348#557C22×C8311yescharacteristic, complemented
349#556C22×C8313yescomplemented
350#552—23no—
351#550C22×C8311yescharacteristic
352D4×Q8C22×C8311yescharacteristic
353D4×Q8C22×C8311yescharacteristic, complemented
354#548—21no—
355#548—21no—
356#547C22×C8313yes—
357#547C22×C8313yescomplemented
358#546—23no—
359D42C22×C8313yes—
360#533C22×C8313yescomplemented
361#532C22×C8313yes—
362#529—23no—
363#525—23no—
364C4×#41C22×C8311yescharacteristic
365C4×#41C22×C8313yescomplemented
366C2×C4×Q8—21no—
367C2×C4×D4C22×C8313yes—
368#500C22×C8313yescomplemented
369#492C22×C8313yescomplemented
370#487C22×C8313yescomplemented
371#486C22×C8313yescomplemented
372#484C22×C8316yescomplemented
373#482C22×C8316yescomplemented
374#475C22×C8313yescomplemented
375#474C22×C8313yes—
376#474C22×C8313yescomplemented
377#474C22×C8313yescomplemented
378#468C22×C8316yescomplemented
379#468C22×C8316yescomplemented
380#461C22×C8313yes—
381#461C22×C8313yescomplemented
382#460C22×C8313yescomplemented
383#459C22×C8313yescomplemented
384#450C22×C8316yes—
385#449C22×C8316yescomplemented
386C8×Q8C22×C8311yescharacteristic, complemented
387C8×Q8C22×C8311yescharacteristic, complemented
388#442C22×C8311yescharacteristic
389#442C22×C8313yescomplemented
390#440C22×C8313yes—
391#440C22×C8316yescomplemented
392#440C22×C8313yescomplemented
393C4×SD16C22×C8313yes—
394C4×SD16C22×C8313yescomplemented
395C4×D8C22×C8313yes—
396C4×D8C22×C8313yescomplemented
397#436C22×C8313yescomplemented
398#436C22×C8313yescomplemented
399#432C22×C8313yescomplemented
400#428C22×C8313yescomplemented
401#418C22×C8313yes—
402#417C22×C8313yescomplemented
403C4×M16C22×C8313yescomplemented
404C2×#41—21no—
405C2×#41—23no—
406C2×#41—23no—
407C2×#41—48no—
408C2×#41D4×C8311yescharacteristic
409C2×#41C23×C8313yes—
410C22×Q8—21no—
411C22×Q8—21no—
412C22×D4—23no—
413C22×D4C23×C8313yes—
414C23×C4—23no—
415AGL(1,ℤ/8)—212no—
416C2×SD16C23×C8313yes—
417C2×SD16C23×C8313yes—
418C2×SD16C23×C8316yes—
419C2×D8C23×C8313yes—
420C2×D8C23×C8311yescharacteristic
421C2×M16C23×C8313yes—
422C2×M16C23×C8313yes—
423C4⋊Q8C23×C8313yes—
424C4⋊Q8C23×C8313yes—
425C4⋊Q8C23×C8313yes—
426#127C23×C8313yes—
427#126—26no—
428#125—23no—
429#125—23no—
430#124—23no—
431#124—23no—
432#123—26no—
433#123—26no—
434C22⋊Q8—23no—
435C22⋊Q8—23no—
436C22⋊Q8—23no—
437C22⋊Q8—23no—
438C22⋊Q8C23×C8316yes—
439#121—23no—
440#121—23no—
441#121—23no—
442#121—23no—
443#121C23×C8316yes—
444#120—26no—
445C4×Q8—21no—
446C4×Q8—23no—
447C4×Q8—23no—
448C4×Q8D4×C8311yescharacteristic
449C4×Q8C23×C8313yes—
450C4×Q8C23×C8313yes—
451C4×Q8C23×C8311yescharacteristic
452C4×D4—23no—
453C4×D4—23no—
454C4×D4—23no—
455C4×D4—23no—
456C4×D4—23no—
457C4×D4D4×C8313yes—
458C4×D4C23×C8311yescharacteristic
459C4×D4C23×C8313yes—
460C4×D4C23×C8313yes—
461C4×D4C23×C8313yes—
462C4×D4C23×C8311yescharacteristic
463C4×D4C23×C8313yes—
464C4×D4C23×C8313yes—
465#117—23no—
466#117—23no—
467#117D4×C8313yes—
468#117C23×C8313yes—
469C2×C4⋊C4—23no—
470C2×C4⋊C4C23×C8313yes—
471C2×C22⋊C4—23no—
472C2×C42—23no—
473C2×C42C23×C8313yes—
474#107C23×C8313yes—
475#107C23×C8313yes—
476#107C23×C8316yes—
477#106C23×C8311yescharacteristic
478#106C23×C8313yes—
479C4⋊C8C23×C8313yes—
480C4⋊C8C23×C8313yes—
481#103C23×C8313yes—
482#103C23×C8313yes—
483#103C23×C8316yes—
484#102C23×C8311yescharacteristic
485#102C23×C8313yes—
486#102C23×C8311yescharacteristic
487#102C23×C8313yes—
488#102C23×C8313yes—
489#102C23×C8313yes—
490#102C23×C8316yes—
491C22⋊C8C23×C8316yes—
492#97C23×C8311yescharacteristic
493#97C23×C8313yes—
494C4×C8C23×C8313yes—
495C4×C8C23×C8313yes—
496C24—23no—
497#41—24no—
498#41—26no—
499#41—43no—
500#41—412no—
501#41—412no—
502#41—44no—
503C2×Q8—23no—
504C2×Q8—23no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8C2×D4×C8311yescharacteristic
508C2×Q8C24×C8313yes—
509C2×D4—26no—
510C2×D4—23no—
511C2×D4—26no—
512C2×D4—23no—
513C2×D4—23no—
514C2×D4—23no—
515C2×D4—43no—
516C2×D4—412no—
517C2×D4C2×D4×C8313yes—
518C2×D4C24×C8313yes—
519C2×D4C24×C8311yescharacteristic
520C2×D4C24×C8311yescharacteristic
521C22×C4—23no—
522C22×C4—21no—
523C22×C4—23no—
524C22×C4—23no—
525C22×C4—21no—
526C22×C4—23no—
527C22×C4—23no—
528C22×C4—23no—
529C22×C4—412no—
530C22×C4C2×D4×C8313yes—
531C22×C4C2×D4×C8313yes—
532C22×C4C24×C8313yes—
533SD16—26no—
534SD16—26no—
535SD16—46no—
536D8—26no—
537D8#41×C8314yescomplemented
538M16—26no—
539M16—43no—
540C2×C8C24×C8311yescharacteristic
541C2×C8C24×C8313yes—
542C2×C8C24×C8313yes—
543C2×C8C24×C8311yescharacteristic
544C4⋊C4—23no—
545C4⋊C4—26no—
546C4⋊C4—23no—
547C4⋊C4—23no—
548C4⋊C4—23no—
549C4⋊C4—23no—
550C4⋊C4—23no—
551C4⋊C4—23no—
552C4⋊C4C2×D4×C8313yes—
553C4⋊C4C2×D4×C8313yes—
554C4⋊C4C24×C8311yescharacteristic
555C4⋊C4C24×C8313yes—
556C4⋊C4C24×C8311yescharacteristic
557C4⋊C4C24×C8313yes—
558C22⋊C4—26no—
559C22⋊C4—23no—
560C22⋊C4—21no—
561C22⋊C4—23no—
562C22⋊C4—23no—
563C22⋊C4—23no—
564C22⋊C4—21no—
565C22⋊C4—23no—
566C22⋊C4—26no—
567C22⋊C4C2×D4×C8316yes—
568C42—23no—
569C42—23no—
570C42—23no—
571C42C2×D4×C8313yes—
572C42C2×D4×C8313yes—
573C42C24×C8313yes—
574C42C24×C8311yescharacteristic
575C23—21no—
576C23—21no—
577C23—23no—
578C23—46no—
579C23—46no—
580C23—83no—
581C23C22×D4×C8313yes—
582Q8—23no—
583Q8—23no—
584Q8—46no—
585Q8—46no—
586Q8AGL(1,ℤ/8)×C8314yescomplemented
587D4—26no—
588D4—23no—
589D4—21no—
590D4—21no—
591D4—23no—
592D4—46no—
593D4—46no—
594D4—412no—
595D4—46no—
596D4—83no—
597D4C2×#41×C8312yes—
598D4C2×#41×C8312yescomplemented
599C2×C4—26no—
600C2×C4—23no—
601C2×C4—23no—
602C2×C4—21no—
603C2×C4—23no—
604C2×C4—23no—
605C2×C4—21no—
606C2×C4—23no—
607C2×C4—43no—
608C2×C4—46no—
609C2×C4—42no—
610C2×C4—46no—
611C2×C4—42no—
612C2×C4—46no—
613C2×C4—46no—
614C2×C4—46no—
615C2×C4—46no—
616C2×C4C22×D4×C8311yescharacteristic
617C2×C4C22×D4×C8313yes—
618C2×C4C22×D4×C8311yescharacteristic
619C2×C4C22×D4×C8313yes—
620C2×C4C22×D4×C8313yes—
621C2×C4C25×C8311yescharacteristic
622C8—23no—
623C8—21no—
624C8—23no—
625C8C2×#41×C8312yescomplemented
626C22—23no—
627C22—23no—
628C22—23no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—43no—
636C22—43no—
637C22—43no—
638C22—812no—
639C22C23×D4×C8311yescharacteristic
640C4—21no—
641C4—21no—
642C4—23no—
643C4—23no—
644C4—41no—
645C4—43no—
646C4—43no—
647C4—41no—
648C4—43no—
649C4C2×AGL(1,ℤ/8)×C8316yes—
650C4C22×#41×C8311yescharacteristic
651C4#585×C8311yescharacteristic
652C2—43no—
653C2—42no—
654C2—42no—
655C2—83no—
656C2D4×#41×C8311yescharacteristic
657C2C22×AGL(1,ℤ/8)×C8311yescharacteristic
658C2C83×#358611yescharacteristic
subgroupG/H
center, socleC22×C83C23×D4
commutator, Frattini, cosocleC2×C4C25×C83
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C4×#41×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3482C2semidirect
2. D4×#41×C83C2semidirect
3. C83×#3392C2semidirect
4. Q8×D8×C83C2semidirect
5. C83×#3359C2semidirect
6. C83×#3358C2semidirect
7. C83×#3353C2semidirect
8. C83×#3330C2semidirect
9. C83×#3324C2semidirect
10. C83×#3272C2semidirect
11. C83×#3182C2semidirect
12. C83×#3115C2semidirect
13. C83×#3110C2semidirect
14. C83×#2971C2semidirect
15. C4×AGL(1,ℤ/8)×C83C2semidirect
18. #557×C83C22semidirect
19. #556×C83C22semidirect
23. D4×Q8×C83C22semidirect
27. #547×C83C22semidirect
30. #533×C83C22semidirect
35. C4×#41×C83C22semidirect
38. #500×C83C22semidirect
39. #492×C83C22semidirect
40. #487×C83C22semidirect
41. #486×C83C22semidirect
42. #484×C83C22semidirect
43. #482×C83C22semidirect
44. #475×C83C22semidirect
46. #474×C83C22semidirect
47. #474×C83C22semidirect
48. #468×C83C22semidirect
49. #468×C83C22semidirect
51. #461×C83C22semidirect
52. #460×C83C22semidirect
53. #459×C83C22semidirect
55. #449×C83C22semidirect
56. C8×Q8×C83C22semidirect
57. C8×Q8×C83C22semidirect
59. #442×C83C22semidirect
61. #440×C83C22semidirect
62. #440×C83C22semidirect
64. C4×SD16×C83C22semidirect
66. C4×D8×C83C22semidirect
67. #436×C83C22semidirect
68. #436×C83C22semidirect
69. #432×C83C22semidirect
70. #428×C83C22semidirect
72. #417×C83C22semidirect
73. C4×M16×C83C22semidirect
207. D8×C83#41semidirect
256. Q8×C83AGL(1,ℤ/8)semidirect
268. D4×C83C2×#41semidirect
295. C8×C83C2×#41semidirect
322. #61466C83direct (N × H)
330. #3482C2×C83semidirect
331. D4×#41C2×C83semidirect
332. #3392C2×C83semidirect
333. Q8×D8C2×C83semidirect
334. #3359C2×C83semidirect
335. #3358C2×C83semidirect
336. #3353C2×C83semidirect
337. #3330C2×C83semidirect
338. #3324C2×C83semidirect
339. #3272C2×C83semidirect
340. #3182C2×C83semidirect
341. #3115C2×C83semidirect
342. #3110C2×C83semidirect
343. #2971C2×C83semidirect
344. C4×AGL(1,ℤ/8)C2×C83semidirect
345. C83#61466direct (N × H)
348. #557C22×C83semidirect
349. #556C22×C83semidirect
353. D4×Q8C22×C83semidirect
357. #547C22×C83semidirect
360. #533C22×C83semidirect
365. C4×#41C22×C83semidirect
368. #500C22×C83semidirect
369. #492C22×C83semidirect
370. #487C22×C83semidirect
371. #486C22×C83semidirect
372. #484C22×C83semidirect
373. #482C22×C83semidirect
374. #475C22×C83semidirect
376. #474C22×C83semidirect
377. #474C22×C83semidirect
378. #468C22×C83semidirect
379. #468C22×C83semidirect
381. #461C22×C83semidirect
382. #460C22×C83semidirect
383. #459C22×C83semidirect
385. #449C22×C83semidirect
386. C8×Q8C22×C83semidirect
387. C8×Q8C22×C83semidirect
389. #442C22×C83semidirect
391. #440C22×C83semidirect
392. #440C22×C83semidirect
394. C4×SD16C22×C83semidirect
396. C4×D8C22×C83semidirect
397. #436C22×C83semidirect
398. #436C22×C83semidirect
399. #432C22×C83semidirect
400. #428C22×C83semidirect
402. #417C22×C83semidirect
403. C4×M16C22×C83semidirect
537. D8#41×C83semidirect
586. Q8AGL(1,ℤ/8)×C83semidirect
598. D4C2×#41×C83semidirect
625. C8C2×#41×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#34822
D4×#41×C832
C83×#33922
Q8×D8×C832
C83×#33592
C83×#33582
C83×#33532
C83×#33302
C83×#33242
C83×#32722
C83×#31822
C83×#31152
C83×#31102
C83×#29712
C4×AGL(1,ℤ/8)×C832
#6146683