Finite Group Databasebeta

← C83×#18518 #35246342

Subgroups — C83×#18518 #35246342

Order 21248.

968 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
1Q8×#41×C83C211yesmaximal, characteristic, complemented
2C83×#3167C211yesmaximal, characteristic, complemented
3C83×#3103C211yesmaximal, characteristic, complemented
4C83×#3035C211yesmaximal, characteristic
5C83×#1653C211yesmaximal, characteristic, complemented
6C83×#1651C211yesmaximal, characteristic, complemented
7C83×#1645C211yesmaximal, characteristic, complemented
8C83×#1643C211yesmaximal, characteristic, complemented
9C83×#1627C211yesmaximal, characteristic, complemented
10C83×#1626C211yesmaximal, characteristic, complemented
11C83×#1623C211yesmaximal, characteristic, complemented
12C83×#1622C211yesmaximal, characteristic, complemented
13C83×#1542C211yesmaximal, characteristic, complemented
14C83×#1476C211yesmaximal, characteristic, complemented
15C2×Q8⋊C8×C83C211yesmaximal, characteristic, complemented
16C2×#135×C83—21no—
17Q82×C83C2211yescharacteristic
18#557×C83—21no—
19#557×C83C2211yescharacteristic
20#554×C83—22no—
21#554×C83—21no—
22#554×C83—21no—
23#554×C83C2211yescharacteristic
24D4×Q8×C83—21no—
25D4×Q8×C83C2211yescharacteristic
26#533×C83—22no—
27#533×C83—21no—
28#533×C83—21no—
29#533×C83C2211yescharacteristic
30#532×C83C2211yescharacteristic
31C4×#41×C83—21no—
32C4×#41×C83C2211yescharacteristic
33C2×C4×Q8×C83—21no—
34C2×C4×Q8×C83C2211yescharacteristic
35#498×C83C2211yescharacteristic
36#492×C83C2211yescharacteristic
37#487×C83C2211yescharacteristic
38#486×C83C2211yescharacteristic
39#481×C83—21no—
40#475×C83C2211yescharacteristic
41#475×C83C2211yescharacteristic
42#465×C83—22no—
43#464×C83—21no—
44#463×C83—21no—
45#462×C83C2211yescharacteristic
46#461×C83C2211yescharacteristic
47#460×C83C2211yescharacteristic
48#460×C83C2211yescharacteristic
49#460×C83C2211yescharacteristic
50#459×C83C2211yescharacteristic
51#448×C83—21no—
52C4×SD16×C83—21no—
53C4×SD16×C83—21no—
54C4×SD16×C83—22no—
55#431×C83C2211yescharacteristic
56C2×C4⋊C8×C83C2211yescharacteristic
57#416×C83—21no—
58C2×C4×C8×C83C2211yescharacteristic
59#333×C83C2211yescharacteristic
60#333×C83C2211yescharacteristic
61#332×C83C2211yescharacteristic
62#332×C83C2211yescharacteristic
63Q8⋊C8×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66Q8⋊C8×C83C2211yescharacteristic
67Q8⋊C8×C83C2211yescharacteristic
68Q8⋊C8×C83C2211yescharacteristic
69D4⋊C8×C83C2211yescharacteristic
70D4⋊C8×C83C2211yescharacteristic
71C2×#41×C83—21no—
72C2×#41×C83D411yescharacteristic
73C22×Q8×C83—21no—
74C22×Q8×C83D411yescharacteristic
75#135×C83—44no—
76C2×Q16×C83—21no—
77C2×SD16×C83—21no—
78C2×SD16×C83—22no—
79C2×SD16×C83—21no—
80C2×SD16×C83—21no—
81C2×SD16×C83—21no—
82C2×D8×C83—21no—
83C22×C8×C83—21no—
84C22×C8×C83—21no—
85C4⋊Q8×C83—22no—
86C4⋊Q8×C83—21no—
87C4⋊Q8×C83—22no—
88C4⋊Q8×C83—21no—
89C4⋊Q8×C83—21no—
90C4⋊Q8×C83—21no—
91C4⋊Q8×C83C2311yescharacteristic
92C4⋊Q8×C83C2311yescharacteristic
93C4⋊Q8×C83C2311yescharacteristic
94#127×C83C2311yescharacteristic
95#125×C83—22no—
96#125×C83—22no—
97#125×C83—22no—
98#125×C83—21no—
99#125×C83—21no—
100#125×C83—21no—
101#124×C83—21no—
102C22⋊Q8×C83—22no—
103C22⋊Q8×C83—22no—
104C22⋊Q8×C83—22no—
105C22⋊Q8×C83—22no—
106C22⋊Q8×C83—22no—
107C22⋊Q8×C83—21no—
108C22⋊Q8×C83—22no—
109C22⋊Q8×C83—21no—
110C22⋊Q8×C83—21no—
111C22⋊Q8×C83—22no—
112C22⋊Q8×C83D412yes—
113#121×C83—21no—
114#121×C83—21no—
115C4×Q8×C83—22no—
116C4×Q8×C83—22no—
117C4×Q8×C83—22no—
118C4×Q8×C83—21no—
119C4×Q8×C83—21no—
120C4×Q8×C83—21no—
121C4×Q8×C83—21no—
122C4×Q8×C83—21no—
123C4×Q8×C83—21no—
124C4×Q8×C83—21no—
125C4×Q8×C83D411yescharacteristic
126C4×Q8×C83D411yescharacteristic
127C4×Q8×C83D411yescharacteristic
128C4×Q8×C83D412yes—
129C4×Q8×C83C2311yescharacteristic
130C4×Q8×C83C2311yescharacteristic
131C4×Q8×C83C2311yescharacteristic
132C4×D4×C83—22no—
133C4×D4×C83—22no—
134C4×D4×C83—21no—
135C4×D4×C83—21no—
136C4×D4×C83—21no—
137C4×D4×C83—21no—
138C4×D4×C83—21no—
139C4×D4×C83—21no—
140C4×D4×C83D411yescharacteristic
141C4×D4×C83C2311yescharacteristic
142#117×C83—22no—
143#117×C83—21no—
144#117×C83—21no—
145#117×C83D411yescharacteristic
146C2×C4⋊C4×C83—22no—
147C2×C4⋊C4×C83—21no—
148C2×C4⋊C4×C83—21no—
149C2×C4⋊C4×C83D411yescharacteristic
150C2×C42×C83—22no—
151C2×C42×C83—21no—
152C2×C42×C83—21no—
153C2×C42×C83C2311yescharacteristic
154#106×C83—22no—
155#106×C83—21no—
156#106×C83—21no—
157C4⋊C8×C83—21no—
158C4⋊C8×C83C2311yescharacteristic
159C4⋊C8×C83C2311yescharacteristic
160C4⋊C8×C83C2311yescharacteristic
161C4⋊C8×C83C2311yescharacteristic
162#103×C83—22no—
163#103×C83—21no—
164#103×C83—21no—
165#103×C83—21no—
166#103×C83—21no—
167#102×C83—21no—
168#102×C83—21no—
169#102×C83—22no—
170#102×C83—21no—
171#102×C83—21no—
172C22⋊C8×C83—21no—
173C4×C8×C83—21no—
174C4×C8×C83—21no—
175C4×C8×C83C2311yescharacteristic
176C4×C8×C83C2311yescharacteristic
177#41×C83—22no—
178#41×C83—42no—
179#41×C83—42no—
180#41×C83SD1614yescomplemented
181C2×Q8×C83—22no—
182C2×Q8×C83—22no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—22no—
186C2×Q8×C83—21no—
187C2×Q8×C83—41no—
188C2×Q8×C83—42no—
189C2×Q8×C83—42no—
190C2×Q8×C83C2×D411yescharacteristic
191C2×Q8×C83C2×D411yescharacteristic
192C2×Q8×C83C2×D411yescharacteristic
193C2×Q8×C83C2×D412yes—
194C2×D4×C83—21no—
195C2×D4×C83—21no—
196C2×D4×C83—21no—
197C2×D4×C83—21no—
198C2×D4×C83—41no—
199C2×D4×C83C2×D411yescharacteristic
200C22×C4×C83—21no—
201C22×C4×C83—22no—
202C22×C4×C83—21no—
203C22×C4×C83—22no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—41no—
208C22×C4×C83C2×D411yescharacteristic
209C22×C4×C83C2×D411yescharacteristic
210C22×C4×C83C2×D411yescharacteristic
211Q16×C83—42no—
212SD16×C83—44no—
213SD16×C83—42no—
214SD16×C83—42no—
215SD16×C83—42no—
216SD16×C83—42no—
217D8×C83—42no—
218C2×C8×C83—21no—
219C2×C8×C83—21no—
220C2×C8×C83—21no—
221C2×C8×C83—21no—
222C2×C8×C83—21no—
223C2×C8×C83—21no—
224C2×C8×C83—42no—
225C2×C8×C83—42no—
226C4⋊C4×C83—22no—
227C4⋊C4×C83—22no—
228C4⋊C4×C83—22no—
229C4⋊C4×C83—22no—
230C4⋊C4×C83—22no—
231C4⋊C4×C83—22no—
232C4⋊C4×C83—22no—
233C4⋊C4×C83—22no—
234C4⋊C4×C83—21no—
235C4⋊C4×C83—22no—
236C4⋊C4×C83—21no—
237C4⋊C4×C83—21no—
238C4⋊C4×C83—21no—
239C4⋊C4×C83—22no—
240C4⋊C4×C83—21no—
241C4⋊C4×C83—21no—
242C4⋊C4×C83—21no—
243C4⋊C4×C83—21no—
244C4⋊C4×C83—21no—
245C4⋊C4×C83—21no—
246C4⋊C4×C83—21no—
247C4⋊C4×C83—21no—
248C4⋊C4×C83C2×D411yescharacteristic
249C4⋊C4×C83C2×D411yescharacteristic
250C4⋊C4×C83C2×D411yescharacteristic
251C4⋊C4×C83C2×D411yescharacteristic
252C4⋊C4×C83C2×D412yes—
253C22⋊C4×C83—22no—
254C22⋊C4×C83—22no—
255C22⋊C4×C83—22no—
256C22⋊C4×C83—21no—
257C22⋊C4×C83—21no—
258C22⋊C4×C83—21no—
259C22⋊C4×C83—41no—
260C22⋊C4×C83—41no—
261C42×C83—22no—
262C42×C83—22no—
263C42×C83—21no—
264C42×C83—21no—
265C42×C83—22no—
266C42×C83—21no—
267C42×C83—21no—
268C42×C83—21no—
269C42×C83—21no—
270C42×C83—21no—
271C42×C83C2×D411yescharacteristic
272C42×C83C2×D411yescharacteristic
273C42×C83C2×D411yescharacteristic
274C42×C83C2411yescharacteristic
275C23×C83—21no—
276C23×C83—41no—
277C23×C83#12011yescharacteristic
278Q8×C83—21no—
279Q8×C83—21no—
280Q8×C83—21no—
281Q8×C83—21no—
282Q8×C83—42no—
283Q8×C83—42no—
284Q8×C83—44no—
285Q8×C83—41no—
286Q8×C83—41no—
287Q8×C83—41no—
288Q8×C83—41no—
289Q8×C83—82no—
290Q8×C83C2×SD1612yes—
291Q8×C83#13512yescomplemented
292D4×C83—24no—
293D4×C83—21no—
294D4×C83—42no—
295D4×C83—41no—
296D4×C83—41no—
297D4×C83—41no—
298D4×C83—41no—
299D4×C83—82no—
300D4×C83C2×SD1612yes—
301C2×C4×C83—21no—
302C2×C4×C83—21no—
303C2×C4×C83—21no—
304C2×C4×C83—21no—
305C2×C4×C83—24no—
306C2×C4×C83—21no—
307C2×C4×C83—21no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—21no—
311C2×C4×C83—21no—
312C2×C4×C83—21no—
313C2×C4×C83—41no—
314C2×C4×C83—42no—
315C2×C4×C83—44no—
316C2×C4×C83—41no—
317C2×C4×C83—41no—
318C2×C4×C83—41no—
319C2×C4×C83—81no—
320C2×C4×C83—81no—
321C2×C4×C83—82no—
322C2×C4×C83—82no—
323C2×C4×C83#12011yescharacteristic
324C2×C4×C83#12011yescharacteristic
325C2×C4×C83#12011yescharacteristic
326C2×C4×C83C2×SD1612yes—
327C2×C4×C83#13712yes—
328C2×C4×C83C22×D411yescharacteristic
329C2×C4×C83C22×D411yescharacteristic
330C2×C4×C83C22×D411yescharacteristic
331C8×C83—22no—
332C8×C83—41no—
333C8×C83—41no—
334C8×C83—41no—
335C8×C83—41no—
336C8×C83—41no—
337C22×C83—21no—
338C22×C83—21no—
339C22×C83—22no—
340C22×C83—41no—
341C22×C83—41no—
342C22×C83—81no—
343C22×C83—81no—
344C22×C83—81no—
345C22×C83#44812yes—
346C22×C83C2×#12011yescharacteristic
347C4×C83—22no—
348C4×C83—21no—
349C4×C83—22no—
350C4×C83—21no—
351C4×C83—21no—
352C4×C83—41no—
353C4×C83—42no—
354C4×C83—41no—
355C4×C83—41no—
356C4×C83—42no—
357C4×C83—41no—
358C4×C83—41no—
359C4×C83—81no—
360C4×C83#44812yes—
361C4×C83C22×SD1611yescharacteristic
362C4×C83C2×#13511yescharacteristic
363C4×C83C2×#13711yescharacteristic
364C4×C83#57511yescharacteristic
365#18518C8311yesmaximal, characteristic, direct product factor, Sylow
366C2×C83—22no—
367C2×C83—42no—
368C2×C83—161no—
369C2×C83C2×#44811yescharacteristic
370C2×C83#300211yescharacteristic
371C2×C83#301811yescharacteristic
372Q8×#41C2×C8311yescharacteristic, complemented
373#3167C2×C8311yescharacteristic, complemented
374#3103C2×C8311yescharacteristic, complemented
375#3035C2×C8311yescharacteristic
376#1653C2×C8311yescharacteristic, complemented
377#1651C2×C8311yescharacteristic, complemented
378#1645C2×C8311yescharacteristic, complemented
379#1643C2×C8311yescharacteristic, complemented
380#1627C2×C8311yescharacteristic, complemented
381#1626C2×C8311yescharacteristic, complemented
382#1623C2×C8311yescharacteristic, complemented
383#1622C2×C8311yescharacteristic, complemented
384#1542C2×C8311yescharacteristic, complemented
385#1476C2×C8311yescharacteristic, complemented
386C2×Q8⋊C8C2×C8311yescharacteristic, complemented
387C83#1851811yescharacteristic, direct product factor, Sylow
388C2×#135—21no—
389Q82C22×C8311yescharacteristic
390#557—21no—
391#557C22×C8311yescharacteristic
392#554—22no—
393#554—21no—
394#554—21no—
395#554C22×C8311yescharacteristic
396D4×Q8—21no—
397D4×Q8C22×C8311yescharacteristic
398#533—22no—
399#533—21no—
400#533—21no—
401#533C22×C8311yescharacteristic
402#532C22×C8311yescharacteristic
403C4×#41—21no—
404C4×#41C22×C8311yescharacteristic
405C2×C4×Q8—21no—
406C2×C4×Q8C22×C8311yescharacteristic
407#498C22×C8311yescharacteristic
408#492C22×C8311yescharacteristic
409#487C22×C8311yescharacteristic
410#486C22×C8311yescharacteristic
411#481—21no—
412#475C22×C8311yescharacteristic
413#475C22×C8311yescharacteristic
414#465—22no—
415#464—21no—
416#463—21no—
417#462C22×C8311yescharacteristic
418#461C22×C8311yescharacteristic
419#460C22×C8311yescharacteristic
420#460C22×C8311yescharacteristic
421#460C22×C8311yescharacteristic
422#459C22×C8311yescharacteristic
423#448—21no—
424C4×SD16—21no—
425C4×SD16—21no—
426C4×SD16—22no—
427#431C22×C8311yescharacteristic
428C2×C4⋊C8C22×C8311yescharacteristic
429#416—21no—
430C2×C4×C8C22×C8311yescharacteristic
431#333C22×C8311yescharacteristic
432#333C22×C8311yescharacteristic
433#332C22×C8311yescharacteristic
434#332C22×C8311yescharacteristic
435Q8⋊C8C22×C8311yescharacteristic
436Q8⋊C8C22×C8311yescharacteristic
437Q8⋊C8C22×C8311yescharacteristic
438Q8⋊C8C22×C8311yescharacteristic
439Q8⋊C8C22×C8311yescharacteristic
440Q8⋊C8C22×C8311yescharacteristic
441D4⋊C8C22×C8311yescharacteristic
442D4⋊C8C22×C8311yescharacteristic
443C2×#41—21no—
444C2×#41D4×C8311yescharacteristic
445C22×Q8—21no—
446C22×Q8D4×C8311yescharacteristic
447#135—44no—
448C2×Q16—21no—
449C2×SD16—21no—
450C2×SD16—21no—
451C2×SD16—21no—
452C2×SD16—22no—
453C2×SD16—21no—
454C2×D8—21no—
455C22×C8—21no—
456C22×C8—21no—
457C4⋊Q8—22no—
458C4⋊Q8—21no—
459C4⋊Q8—22no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8—21no—
463C4⋊Q8C23×C8311yescharacteristic
464C4⋊Q8C23×C8311yescharacteristic
465C4⋊Q8C23×C8311yescharacteristic
466#127C23×C8311yescharacteristic
467#125—22no—
468#125—22no—
469#125—22no—
470#125—21no—
471#125—21no—
472#125—21no—
473#124—21no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—22no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8D4×C8312yes—
485#121—21no—
486#121—21no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8D4×C8311yescharacteristic
498C4×Q8D4×C8311yescharacteristic
499C4×Q8D4×C8311yescharacteristic
500C4×Q8D4×C8312yes—
501C4×Q8C23×C8311yescharacteristic
502C4×Q8C23×C8311yescharacteristic
503C4×Q8C23×C8311yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4D4×C8311yescharacteristic
513C4×D4C23×C8311yescharacteristic
514#117—22no—
515#117—21no—
516#117—21no—
517#117D4×C8311yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4D4×C8311yescharacteristic
522C2×C42—22no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42C23×C8311yescharacteristic
526#106—22no—
527#106—21no—
528#106—21no—
529C4⋊C8—21no—
530C4⋊C8C23×C8311yescharacteristic
531C4⋊C8C23×C8311yescharacteristic
532C4⋊C8C23×C8311yescharacteristic
533C4⋊C8C23×C8311yescharacteristic
534#103—21no—
535#103—21no—
536#103—22no—
537#103—21no—
538#103—21no—
539#102—21no—
540#102—21no—
541#102—21no—
542#102—21no—
543#102—22no—
544C22⋊C8—21no—
545C4×C8—21no—
546C4×C8—21no—
547C4×C8C23×C8311yescharacteristic
548C4×C8C23×C8311yescharacteristic
549#41—22no—
550#41—42no—
551#41—42no—
552#41SD16×C8314yescomplemented
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8—41no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8C2×D4×C8311yescharacteristic
563C2×Q8C2×D4×C8311yescharacteristic
564C2×Q8C2×D4×C8311yescharacteristic
565C2×Q8C2×D4×C8312yes—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—41no—
571C2×D4C2×D4×C8311yescharacteristic
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—41no—
580C22×C4C2×D4×C8311yescharacteristic
581C22×C4C2×D4×C8311yescharacteristic
582C22×C4C2×D4×C8311yescharacteristic
583Q16—42no—
584SD16—44no—
585SD16—42no—
586SD16—42no—
587SD16—42no—
588SD16—42no—
589D8—42no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—42no—
597C2×C8—42no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4C2×D4×C8311yescharacteristic
621C4⋊C4C2×D4×C8311yescharacteristic
622C4⋊C4C2×D4×C8311yescharacteristic
623C4⋊C4C2×D4×C8311yescharacteristic
624C4⋊C4C2×D4×C8312yes—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—41no—
632C22⋊C4—41no—
633C42—22no—
634C42—22no—
635C42—21no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×D4×C8311yescharacteristic
644C42C2×D4×C8311yescharacteristic
645C42C2×D4×C8311yescharacteristic
646C42C24×C8311yescharacteristic
647C23—21no—
648C23—41no—
649C23#120×C8311yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—42no—
655Q8—42no—
656Q8—44no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—82no—
662Q8C2×SD16×C8312yes—
663Q8#135×C8312yescomplemented
664D4—24no—
665D4—21no—
666D4—42no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—82no—
672D4C2×SD16×C8312yes—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—24no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4#120×C8311yescharacteristic
696C2×C4#120×C8311yescharacteristic
697C2×C4#120×C8311yescharacteristic
698C2×C4C2×SD16×C8312yes—
699C2×C4#137×C8312yes—
700C2×C4C22×D4×C8311yescharacteristic
701C2×C4C22×D4×C8311yescharacteristic
702C2×C4C22×D4×C8311yescharacteristic
703C8—22no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C22—21no—
710C22—21no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22#448×C8312yes—
718C22C2×#120×C8311yescharacteristic
719C4—22no—
720C4—21no—
721C4—22no—
722C4—21no—
723C4—21no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—81no—
732C4#448×C8312yes—
733C4C22×SD16×C8311yescharacteristic
734C4C2×#135×C8311yescharacteristic
735C4C2×#137×C8311yescharacteristic
736C4#575×C8311yescharacteristic
737C2—22no—
738C2—42no—
739C2—161no—
740C2C2×#448×C8311yescharacteristic
741C2C83×#300211yescharacteristic
742C2C83×#301811yescharacteristic
subgroupG/H
centerC2×C4×C83#120
commutator, Frattini, cosocleC42C24×C83
socleC22×C83C2×#120
prime radicalC83×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. Q8×#41×C83C2semidirect
2. C83×#3167C2semidirect
3. C83×#3103C2semidirect
5. C83×#1653C2semidirect
6. C83×#1651C2semidirect
7. C83×#1645C2semidirect
8. C83×#1643C2semidirect
9. C83×#1627C2semidirect
10. C83×#1626C2semidirect
11. C83×#1623C2semidirect
12. C83×#1622C2semidirect
13. C83×#1542C2semidirect
14. C83×#1476C2semidirect
15. C2×Q8⋊C8×C83C2semidirect
180. #41×C83SD16semidirect
291. Q8×C83#135semidirect
365. #18518C83direct (N × H)
372. Q8×#41C2×C83semidirect
373. #3167C2×C83semidirect
374. #3103C2×C83semidirect
376. #1653C2×C83semidirect
377. #1651C2×C83semidirect
378. #1645C2×C83semidirect
379. #1643C2×C83semidirect
380. #1627C2×C83semidirect
381. #1626C2×C83semidirect
382. #1623C2×C83semidirect
383. #1622C2×C83semidirect
384. #1542C2×C83semidirect
385. #1476C2×C83semidirect
386. C2×Q8⋊C8C2×C83semidirect
387. C83#18518direct (N × H)
552. #41SD16×C83semidirect
663. Q8#135×C83semidirect

Maximal subgroups

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

subgroupindex
Q8×#41×C832
C83×#31672
C83×#31032
C83×#30352
C83×#16532
C83×#16512
C83×#16452
C83×#16432
C83×#16272
C83×#16262
C83×#16232
C83×#16222
C83×#15422
C83×#14762
C2×Q8⋊C8×C832
#1851883