Finite Group Databasebeta

← C83×#62929 #35290753

Subgroups — C83×#62929 #35290753

Order 21248.

6566 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3565C218yesmaximal, complemented
2C83×#3561C218yesmaximal, complemented
3C83×#3547C214yesmaximal, complemented
4C83×#3547C218yesmaximal, complemented
5C83×#3544C214yesmaximal, complemented
6C83×#3536C214yesmaximal, complemented
7C83×#3518C214yesmaximal, complemented
8C83×#3511C214yesmaximal, complemented
9C83×#3503C212yesmaximal, complemented
10C83×#3501C211yesmaximal, characteristic, complemented
11C83×#3495C214yesmaximal, complemented
12C83×#3494C214yesmaximal, complemented
13C83×#3493C212yesmaximal, complemented
14C83×#3475C212yesmaximal, complemented
15C2×#555×C83C211yesmaximal, characteristic, complemented
16C83×#3460C211yesmaximal, characteristic, complemented
17C83×#3458C212yesmaximal, complemented
18#563×C83C22116yescomplemented
19#562×C83C22116yescomplemented
20#562×C83C22116yescomplemented
21Q82×C83C2214yescomplemented
22#557×C83C2214yescomplemented
23#556×C83C22116yescomplemented
24#556×C83C2218yescomplemented
25#556×C83C2212yescomplemented
26#556×C83C2218yescomplemented
27#555×C83C2214yes—
28#555×C83C2218yes—
29#555×C83C2214yes—
30#555×C83C2218yescomplemented
31#555×C83C2218yescomplemented
32#555×C83C2212yescomplemented
33#554×C83C2218yes—
34#554×C83C2212yescomplemented
35#554×C83C2214yescomplemented
36#554×C83C2218yescomplemented
37#554×C83C2214yescomplemented
38#553×C83C2214yescomplemented
39#553×C83C2218yescomplemented
40#553×C83C2218yescomplemented
41#553×C83C2218yescomplemented
42#552×C83C2214yes—
43#552×C83C2218yescomplemented
44#552×C83C2218yescomplemented
45#552×C83C22116yescomplemented
46#552×C83C2214yescomplemented
47#551×C83C2218yes—
48#551×C83C22116yes—
49D4×Q8×C83C2218yes—
50D4×Q8×C83C2214yescomplemented
51D4×Q8×C83C2214yescomplemented
52#548×C83C2218yescomplemented
53#548×C83C22116yescomplemented
54#547×C83C2218yescomplemented
55#547×C83C2218yescomplemented
56#547×C83C2212yescomplemented
57#546×C83C2214yes—
58#546×C83C22116yes—
59#544×C83C2211yescharacteristic
60#544×C83C2212yes—
61#544×C83C2214yes—
62#544×C83C2214yescomplemented
63#544×C83C2218yescomplemented
64#544×C83C2218yescomplemented
65#544×C83C2218yescomplemented
66#543×C83C2218yes—
67#543×C83C2214yes—
68#542×C83C2218yescomplemented
69#542×C83C2218yescomplemented
70#542×C83C2218yescomplemented
71#542×C83C22116yescomplemented
72#542×C83C22116yescomplemented
73#542×C83C22116yescomplemented
74#542×C83C2214yescomplemented
75#541×C83C2218yescomplemented
76#540×C83C2214yescomplemented
77#540×C83C2218yescomplemented
78#539×C83C2218yescomplemented
79#538×C83C2218yes—
80#538×C83C2214yes—
81#537×C83C2211yescharacteristic
82#537×C83C2218yescomplemented
83#537×C83C2218yescomplemented
84#536×C83C22116yescomplemented
85#536×C83C2214yescomplemented
86#535×C83C2212yes—
87#533×C83C2218yes—
88#533×C83C2212yes—
89#533×C83C2218yescomplemented
90#533×C83C2214yescomplemented
91#533×C83C2218yescomplemented
92#532×C83C2214yescomplemented
93#532×C83C2218yescomplemented
94C2×C4⋊Q8×C83C2211yescharacteristic
95C2×C4⋊Q8×C83C2214yescomplemented
96#529×C83C2218yes—
97#529×C83C2214yescomplemented
98#529×C83C2214yescomplemented
99#529×C83C2218yescomplemented
100#529×C83C2218yescomplemented
101C2×#124×C83C2214yes—
102#525×C83C2214yes—
103#525×C83C2214yes—
104C2×C22⋊Q8×C83C2214yes—
105C2×#121×C83C2212yes—
106C2×#121×C83C2212yes—
107#520×C83C2214yes—
108#520×C83C2214yescomplemented
109#519×C83C2214yescomplemented
110#518×C83C2212yes—
111C4×#41×C83C2212yes—
112C4×#41×C83C2214yescomplemented
113C2×C4×D4×C83C2211yescharacteristic
114C2×C4×D4×C83C2211yescharacteristic
115C2×#117×C83C2212yes—
116C2×#117×C83C2214yes—
117C2×#117×C83C2212yes—
118C2×#41×C83C2312yes—
119C2×#41×C83C2314yes—
120C2×#41×C83C2314yes—
121C2×#41×C83C23116yes—
122C22×Q8×C83C2314yes—
123C22×Q8×C83C2312yes—
124C22×Q8×C83C2318yes—
125C22×D4×C83C2311yescharacteristic
126C22×D4×C83C2311yescharacteristic
127C22×D4×C83C2314yes—
128C23×C4×C83C2312yes—
129C23×C4×C83C2312yes—
130C4⋊Q8×C83C2314yes—
131C4⋊Q8×C83C2314yes—
132C4⋊Q8×C83C2312yes—
133C4⋊Q8×C83C2318yes—
134C4⋊Q8×C83C2318yes—
135C4⋊Q8×C83C2318yes—
136C4⋊Q8×C83C2314yes—
137C4⋊Q8×C83C2312yes—
138C4⋊Q8×C83C2318yes—
139C4⋊Q8×C83C2318yes—
140C4⋊Q8×C83C2318yes—
141C4⋊Q8×C83C2318yes—
142C4⋊Q8×C83C23116yes—
143#127×C83C2314yes—
144#126×C83C23116yes—
145#126×C83C2318yes—
146#126×C83C23116yes—
147#126×C83C2318yes—
148#126×C83C2318yes—
149#126×C83C2318yes—
150#126×C83C23116yes—
151#126×C83C23116yes—
152#125×C83C2318yes—
153#125×C83C2314yes—
154#125×C83C2318yes—
155#125×C83C2318yes—
156#125×C83C2314yes—
157#125×C83C23116yes—
158#125×C83C2314yes—
159#125×C83C2318yes—
160#125×C83C2318yes—
161#125×C83C23116yes—
162#124×C83C23116yes—
163#124×C83C23116yes—
164#124×C83C2318yes—
165#124×C83C2314yes—
166#124×C83C2314yes—
167#124×C83C2318yes—
168#124×C83C2318yes—
169#124×C83C23116yes—
170#124×C83C23116yes—
171#124×C83C23116yes—
172#123×C83C2318yes—
173#123×C83C2318yes—
174#123×C83C2318yes—
175#123×C83C2318yes—
176#123×C83C2318yes—
177#123×C83C23116yes—
178#123×C83C2318yes—
179#123×C83C23116yes—
180#123×C83C23116yes—
181#123×C83C23116yes—
182#123×C83C23116yes—
183C22⋊Q8×C83C2314yes—
184C22⋊Q8×C83C2318yes—
185C22⋊Q8×C83C2318yes—
186C22⋊Q8×C83C2318yes—
187C22⋊Q8×C83C2314yes—
188C22⋊Q8×C83C2314yes—
189C22⋊Q8×C83C2314yes—
190C22⋊Q8×C83C2314yes—
191C22⋊Q8×C83C2314yes—
192C22⋊Q8×C83C2318yes—
193C22⋊Q8×C83C2314yes—
194C22⋊Q8×C83C2314yes—
195C22⋊Q8×C83C23116yes—
196C22⋊Q8×C83C23116yes—
197C22⋊Q8×C83C2318yes—
198C22⋊Q8×C83C23116yes—
199C22⋊Q8×C83C2318yes—
200C22⋊Q8×C83C23116yes—
201C22⋊Q8×C83C23116yes—
202C22⋊Q8×C83C23116yes—
203C22⋊Q8×C83C23116yes—
204C22⋊Q8×C83C23116yes—
205C22⋊Q8×C83C23116yes—
206C22⋊Q8×C83C23116yes—
207#121×C83C2318yes—
208#121×C83C2318yes—
209#121×C83C2318yes—
210#121×C83C2318yes—
211#121×C83C2314yes—
212#121×C83C2314yes—
213#121×C83C2314yes—
214#121×C83C2314yes—
215#121×C83C2314yes—
216#121×C83C2314yes—
217#121×C83C2318yes—
218#121×C83C2314yes—
219#121×C83C2314yes—
220#121×C83C23116yes—
221#121×C83C2318yes—
222#121×C83C23116yes—
223#121×C83C23116yes—
224#121×C83C23116yes—
225#120×C83C2318yes—
226#120×C83C2318yes—
227C4×Q8×C83C2312yes—
228C4×Q8×C83C2312yes—
229C4×Q8×C83C2314yes—
230C4×Q8×C83C2314yes—
231C4×Q8×C83C2318yes—
232C4×Q8×C83C2318yes—
233C4×Q8×C83C2318yes—
234C4×Q8×C83C2318yes—
235C4×Q8×C83C2318yes—
236C4×Q8×C83C2314yes—
237C4×Q8×C83C23116yes—
238C4×Q8×C83C2318yes—
239C4×D4×C83C2312yes—
240C4×D4×C83C2312yes—
241C4×D4×C83C2314yes—
242C4×D4×C83C2314yes—
243C4×D4×C83C2314yes—
244C4×D4×C83C2314yes—
245C4×D4×C83C2312yes—
246C4×D4×C83C2314yes—
247C4×D4×C83C2312yes—
248C4×D4×C83C2318yes—
249C4×D4×C83C2314yes—
250C4×D4×C83C2318yes—
251C4×D4×C83C2318yes—
252C4×D4×C83C2318yes—
253C4×D4×C83C23116yes—
254C4×D4×C83C2318yes—
255C4×D4×C83C2318yes—
256C4×D4×C83C23116yes—
257C4×D4×C83C2318yes—
258C4×D4×C83C2318yes—
259C4×D4×C83C23116yes—
260#117×C83C2312yes—
261#117×C83C2314yes—
262#117×C83C2314yes—
263#117×C83C2318yes—
264#117×C83C2318yes—
265#117×C83C2314yes—
266#117×C83C2318yes—
267#117×C83C2314yes—
268#117×C83C2314yes—
269#117×C83C2318yes—
270#117×C83C2318yes—
271#117×C83C2314yes—
272#117×C83C2314yes—
273#117×C83C2318yes—
274#117×C83C2314yes—
275#117×C83C23116yes—
276#117×C83C2318yes—
277#117×C83C23116yes—
278C2×C4⋊C4×C83C2311yescharacteristic
279C2×C4⋊C4×C83C2311yescharacteristic
280C2×C4⋊C4×C83C2312yes—
281C2×C4⋊C4×C83C2312yes—
282C2×C4⋊C4×C83C2314yes—
283C2×C4⋊C4×C83C2314yes—
284C2×C4⋊C4×C83C2318yes—
285C2×C4⋊C4×C83C2314yes—
286C2×C4⋊C4×C83C2318yes—
287C2×C4⋊C4×C83C2318yes—
288C2×C22⋊C4×C83C2314yes—
289C2×C22⋊C4×C83C2314yes—
290C2×C22⋊C4×C83C2318yes—
291C2×C22⋊C4×C83C2312yes—
292C2×C22⋊C4×C83C2312yes—
293C2×C22⋊C4×C83C2318yes—
294C2×C42×C83C2314yes—
295C2×C42×C83C2318yes—
296C2×C42×C83C2311yescharacteristic
297C2×C42×C83C2314yes—
298C24×C83C2412yes—
299C24×C83C2412yes—
300#41×C83—28no—
301#41×C83—48no—
302#41×C83—48no—
303#41×C83—816no—
304C2×Q8×C83—48no—
305C2×Q8×C83—82no—
306C2×Q8×C83—88no—
307C2×Q8×C83C2412yes—
308C2×Q8×C83C2414yes—
309C2×Q8×C83C2418yes—
310C2×Q8×C83C2414yes—
311C2×Q8×C83C2414yes—
312C2×Q8×C83C24116yes—
313C2×Q8×C83C2418yes—
314C2×D4×C83—24no—
315C2×D4×C83—42no—
316C2×D4×C83—84no—
317C2×D4×C83C2414yes—
318C2×D4×C83C2414yes—
319C2×D4×C83C2412yes—
320C2×D4×C83C2412yes—
321C2×D4×C83C2418yes—
322C2×D4×C83C2418yes—
323C2×D4×C83C2414yes—
324C2×D4×C83C2412yes—
325C2×D4×C83C2418yes—
326C2×D4×C83C2418yes—
327C2×D4×C83C24116yes—
328C22×C4×C83—28no—
329C22×C4×C83—44no—
330C22×C4×C83C2412yes—
331C22×C4×C83C2414yes—
332C22×C4×C83C2411yescharacteristic
333C22×C4×C83C2414yes—
334C22×C4×C83C2414yes—
335C22×C4×C83C2414yes—
336C22×C4×C83C2414yes—
337C22×C4×C83C2412yes—
338C22×C4×C83C2411yescharacteristic
339C22×C4×C83C2414yes—
340C22×C4×C83C2418yes—
341C22×C4×C83C2418yes—
342C22×C4×C83C2414yes—
343C22×C4×C83C2418yes—
344C22×C4×C83C2418yes—
345C22×C4×C83C2414yes—
346C22×C4×C83C24116yes—
347C22×C4×C83C2411yescharacteristic
348C4⋊C4×C83C2414yes—
349C4⋊C4×C83C2414yes—
350C4⋊C4×C83C2414yes—
351C4⋊C4×C83C2412yes—
352C4⋊C4×C83C2418yes—
353C4⋊C4×C83C2412yes—
354C4⋊C4×C83C2418yes—
355C4⋊C4×C83C2411yescharacteristic
356C4⋊C4×C83C2414yes—
357C4⋊C4×C83C2414yes—
358C4⋊C4×C83C2411yescharacteristic
359C4⋊C4×C83C2412yes—
360C4⋊C4×C83C2414yes—
361C4⋊C4×C83C2418yes—
362C4⋊C4×C83C2418yes—
363C4⋊C4×C83C24116yes—
364C4⋊C4×C83C24116yes—
365C4⋊C4×C83C2418yes—
366C4⋊C4×C83C24116yes—
367C4⋊C4×C83C2418yes—
368C4⋊C4×C83C2418yes—
369C4⋊C4×C83C2418yes—
370C4⋊C4×C83C2414yes—
371C4⋊C4×C83C2414yes—
372C4⋊C4×C83C2414yes—
373C4⋊C4×C83C24116yes—
374C4⋊C4×C83C2414yes—
375C4⋊C4×C83C2418yes—
376C4⋊C4×C83C24116yes—
377C4⋊C4×C83C2414yes—
378C22⋊C4×C83C2418yes—
379C22⋊C4×C83C2414yes—
380C22⋊C4×C83C2418yes—
381C22⋊C4×C83C2414yes—
382C22⋊C4×C83C2418yes—
383C22⋊C4×C83C24116yes—
384C22⋊C4×C83C2418yes—
385C22⋊C4×C83C2418yes—
386C22⋊C4×C83C24116yes—
387C22⋊C4×C83C2418yes—
388C22⋊C4×C83C2414yes—
389C22⋊C4×C83C2418yes—
390C22⋊C4×C83C2418yes—
391C22⋊C4×C83C2418yes—
392C22⋊C4×C83C2418yes—
393C22⋊C4×C83C2418yes—
394C22⋊C4×C83C2414yes—
395C22⋊C4×C83C24116yes—
396C22⋊C4×C83C2414yes—
397C22⋊C4×C83C2418yes—
398C22⋊C4×C83C2418yes—
399C42×C83C2414yes—
400C42×C83C2412yes—
401C42×C83C2418yes—
402C42×C83C2418yes—
403C42×C83C2418yes—
404C42×C83C2418yes—
405C42×C83C2412yes—
406C42×C83C2418yes—
407C42×C83C2414yes—
408C42×C83C2414yes—
409C42×C83C24116yes—
410C23×C83—24no—
411C23×C83—24no—
412C23×C83—42no—
413C23×C83—42no—
414C23×C83—42no—
415C23×C83—42no—
416C23×C83C2514yes—
417C23×C83C2514yes—
418C23×C83C2514yes—
419C23×C83C2511yescharacteristic
420Q8×C83—24no—
421Q8×C83—28no—
422Q8×C83—48no—
423Q8×C83—44no—
424Q8×C83—48no—
425Q8×C83—416no—
426Q8×C83—44no—
427D4×C83—28no—
428D4×C83—28no—
429D4×C83—24no—
430D4×C83—24no—
431D4×C83—42no—
432D4×C83—416no—
433D4×C83—48no—
434D4×C83—44no—
435D4×C83—48no—
436D4×C83—48no—
437D4×C83—48no—
438C2×C4×C83—24no—
439C2×C4×C83—28no—
440C2×C4×C83—28no—
441C2×C4×C83—28no—
442C2×C4×C83—22no—
443C2×C4×C83—28no—
444C2×C4×C83—28no—
445C2×C4×C83—44no—
446C2×C4×C83—42no—
447C2×C4×C83—44no—
448C2×C4×C83—48no—
449C2×C4×C83—44no—
450C2×C4×C83—41no—
451C2×C4×C83—416no—
452C2×C4×C83—48no—
453C2×C4×C83—48no—
454C2×C4×C83—48no—
455C2×C4×C832−1+414yes—
456C2×C4×C83C2512yes—
457C2×C4×C83C2514yes—
458C2×C4×C83C2512yes—
459C2×C4×C83C2512yes—
460C2×C4×C83C2514yes—
461C2×C4×C83C2518yes—
462C2×C4×C83C2514yes—
463C2×C4×C83C2514yes—
464C2×C4×C83C2518yes—
465C2×C4×C83C2518yes—
466C2×C4×C83C2511yescharacteristic
467C2×C4×C83C2512yes—
468C2×C4×C83C2511yescharacteristic
469C22×C83—21no—
470C22×C83—21no—
471C22×C83—24no—
472C22×C83—24no—
473C22×C83—24no—
474C22×C83—24no—
475C22×C83—24no—
476C22×C83—24no—
477C22×C83—24no—
478C22×C83—24no—
479C22×C83—24no—
480C22×C83—84no—
481C22×C83—84no—
482C22×C83C2×2−1+412yes—
483C22×C83C2611yescharacteristic
484C4×C83—22no—
485C4×C83—22no—
486C4×C83—24no—
487C4×C83—21no—
488C4×C83—24no—
489C4×C83—24no—
490C4×C83—28no—
491C4×C83—28no—
492C4×C83—28no—
493C4×C83—24no—
494C4×C83—22no—
495C4×C83C2×2−1+414yes—
496C4×C83#58512yes—
497#62929C8311yesmaximal, characteristic, direct product factor, Sylow
498C2×C83—22no—
499C2×C83—44no—
500C2×C83—44no—
501C2×C83—44no—
502C2×C83C22×2−1+411yescharacteristic
503C2×C83C2×#58511yescharacteristic
504C2×C83H(7,𝔽2)11yescharacteristic
505#3565C2×C8318yescomplemented
506#3561C2×C8318yescomplemented
507#3547C2×C8314yescomplemented
508#3547C2×C8318yescomplemented
509#3544C2×C8314yescomplemented
510#3536C2×C8314yescomplemented
511#3518C2×C8314yescomplemented
512#3511C2×C8314yescomplemented
513#3503C2×C8312yescomplemented
514#3501C2×C8311yescharacteristic, complemented
515#3495C2×C8314yescomplemented
516#3494C2×C8314yescomplemented
517#3493C2×C8312yescomplemented
518#3475C2×C8312yescomplemented
519C2×#555C2×C8311yescharacteristic, complemented
520#3460C2×C8311yescharacteristic, complemented
521#3458C2×C8312yescomplemented
522C83#6292911yescharacteristic, direct product factor, Sylow
523#563C22×C83116yescomplemented
524#562C22×C83116yescomplemented
525#562C22×C83116yescomplemented
526Q82C22×C8314yescomplemented
527#557C22×C8314yescomplemented
528#556C22×C8312yescomplemented
529#556C22×C8318yescomplemented
530#556C22×C8318yescomplemented
531#556C22×C83116yescomplemented
532#555C22×C8314yes—
533#555C22×C8314yes—
534#555C22×C8318yes—
535#555C22×C8312yescomplemented
536#555C22×C8318yescomplemented
537#555C22×C8318yescomplemented
538#554C22×C8318yes—
539#554C22×C8312yescomplemented
540#554C22×C8314yescomplemented
541#554C22×C8318yescomplemented
542#554C22×C8314yescomplemented
543#553C22×C8314yescomplemented
544#553C22×C8318yescomplemented
545#553C22×C8318yescomplemented
546#553C22×C8318yescomplemented
547#552C22×C8314yes—
548#552C22×C8314yescomplemented
549#552C22×C8318yescomplemented
550#552C22×C8318yescomplemented
551#552C22×C83116yescomplemented
552#551C22×C8318yes—
553#551C22×C83116yes—
554D4×Q8C22×C8318yes—
555D4×Q8C22×C8314yescomplemented
556D4×Q8C22×C8314yescomplemented
557#548C22×C83116yescomplemented
558#548C22×C8318yescomplemented
559#547C22×C8312yescomplemented
560#547C22×C8318yescomplemented
561#547C22×C8318yescomplemented
562#546C22×C8314yes—
563#546C22×C83116yes—
564#544C22×C8311yescharacteristic
565#544C22×C8312yes—
566#544C22×C8314yes—
567#544C22×C8318yescomplemented
568#544C22×C8318yescomplemented
569#544C22×C8314yescomplemented
570#544C22×C8318yescomplemented
571#543C22×C8318yes—
572#543C22×C8314yes—
573#542C22×C8314yescomplemented
574#542C22×C8318yescomplemented
575#542C22×C8318yescomplemented
576#542C22×C83116yescomplemented
577#542C22×C8318yescomplemented
578#542C22×C83116yescomplemented
579#542C22×C83116yescomplemented
580#541C22×C8318yescomplemented
581#540C22×C8314yescomplemented
582#540C22×C8318yescomplemented
583#539C22×C8318yescomplemented
584#538C22×C8314yes—
585#538C22×C8318yes—
586#537C22×C8311yescharacteristic
587#537C22×C8318yescomplemented
588#537C22×C8318yescomplemented
589#536C22×C8314yescomplemented
590#536C22×C83116yescomplemented
591#535C22×C8312yes—
592#533C22×C8318yes—
593#533C22×C8312yes—
594#533C22×C8318yescomplemented
595#533C22×C8318yescomplemented
596#533C22×C8314yescomplemented
597#532C22×C8314yescomplemented
598#532C22×C8318yescomplemented
599C2×C4⋊Q8C22×C8311yescharacteristic
600C2×C4⋊Q8C22×C8314yescomplemented
601#529C22×C8318yes—
602#529C22×C8314yescomplemented
603#529C22×C8314yescomplemented
604#529C22×C8318yescomplemented
605#529C22×C8318yescomplemented
606C2×#124C22×C8314yes—
607#525C22×C8314yes—
608#525C22×C8314yes—
609C2×C22⋊Q8C22×C8314yes—
610C2×#121C22×C8312yes—
611C2×#121C22×C8312yes—
612#520C22×C8314yes—
613#520C22×C8314yescomplemented
614#519C22×C8314yescomplemented
615#518C22×C8312yes—
616C4×#41C22×C8312yes—
617C4×#41C22×C8314yescomplemented
618C2×C4×D4C22×C8311yescharacteristic
619C2×C4×D4C22×C8311yescharacteristic
620C2×#117C22×C8312yes—
621C2×#117C22×C8314yes—
622C2×#117C22×C8312yes—
623C2×#41C23×C8312yes—
624C2×#41C23×C8314yes—
625C2×#41C23×C8314yes—
626C2×#41C23×C83116yes—
627C22×Q8C23×C8314yes—
628C22×Q8C23×C8312yes—
629C22×Q8C23×C8318yes—
630C22×D4C23×C8311yescharacteristic
631C22×D4C23×C8311yescharacteristic
632C22×D4C23×C8314yes—
633C23×C4C23×C8312yes—
634C23×C4C23×C8312yes—
635C4⋊Q8C23×C8314yes—
636C4⋊Q8C23×C8314yes—
637C4⋊Q8C23×C8312yes—
638C4⋊Q8C23×C8318yes—
639C4⋊Q8C23×C8318yes—
640C4⋊Q8C23×C8318yes—
641C4⋊Q8C23×C8314yes—
642C4⋊Q8C23×C8312yes—
643C4⋊Q8C23×C8318yes—
644C4⋊Q8C23×C8318yes—
645C4⋊Q8C23×C8318yes—
646C4⋊Q8C23×C8318yes—
647C4⋊Q8C23×C83116yes—
648#127C23×C8314yes—
649#126C23×C83116yes—
650#126C23×C8318yes—
651#126C23×C83116yes—
652#126C23×C8318yes—
653#126C23×C8318yes—
654#126C23×C8318yes—
655#126C23×C83116yes—
656#126C23×C83116yes—
657#125C23×C8318yes—
658#125C23×C8314yes—
659#125C23×C8318yes—
660#125C23×C8318yes—
661#125C23×C8314yes—
662#125C23×C83116yes—
663#125C23×C8314yes—
664#125C23×C8318yes—
665#125C23×C8318yes—
666#125C23×C83116yes—
667#124C23×C83116yes—
668#124C23×C83116yes—
669#124C23×C8318yes—
670#124C23×C8314yes—
671#124C23×C8314yes—
672#124C23×C8318yes—
673#124C23×C8318yes—
674#124C23×C83116yes—
675#124C23×C83116yes—
676#124C23×C83116yes—
677#123C23×C8318yes—
678#123C23×C8318yes—
679#123C23×C8318yes—
680#123C23×C8318yes—
681#123C23×C8318yes—
682#123C23×C83116yes—
683#123C23×C8318yes—
684#123C23×C83116yes—
685#123C23×C83116yes—
686#123C23×C83116yes—
687#123C23×C83116yes—
688C22⋊Q8C23×C8314yes—
689C22⋊Q8C23×C8318yes—
690C22⋊Q8C23×C8318yes—
691C22⋊Q8C23×C8318yes—
692C22⋊Q8C23×C8314yes—
693C22⋊Q8C23×C8314yes—
694C22⋊Q8C23×C8314yes—
695C22⋊Q8C23×C8314yes—
696C22⋊Q8C23×C8314yes—
697C22⋊Q8C23×C8318yes—
698C22⋊Q8C23×C8314yes—
699C22⋊Q8C23×C8314yes—
700C22⋊Q8C23×C83116yes—
701C22⋊Q8C23×C83116yes—
702C22⋊Q8C23×C8318yes—
703C22⋊Q8C23×C83116yes—
704C22⋊Q8C23×C8318yes—
705C22⋊Q8C23×C83116yes—
706C22⋊Q8C23×C83116yes—
707C22⋊Q8C23×C83116yes—
708C22⋊Q8C23×C83116yes—
709C22⋊Q8C23×C83116yes—
710C22⋊Q8C23×C83116yes—
711C22⋊Q8C23×C83116yes—
712#121C23×C8318yes—
713#121C23×C8318yes—
714#121C23×C8318yes—
715#121C23×C8318yes—
716#121C23×C8314yes—
717#121C23×C8314yes—
718#121C23×C8314yes—
719#121C23×C8314yes—
720#121C23×C8314yes—
721#121C23×C8314yes—
722#121C23×C8318yes—
723#121C23×C8314yes—
724#121C23×C8314yes—
725#121C23×C83116yes—
726#121C23×C8318yes—
727#121C23×C83116yes—
728#121C23×C83116yes—
729#121C23×C83116yes—
730#120C23×C8318yes—
731#120C23×C8318yes—
732C4×Q8C23×C8312yes—
733C4×Q8C23×C8312yes—
734C4×Q8C23×C8314yes—
735C4×Q8C23×C8314yes—
736C4×Q8C23×C8318yes—
737C4×Q8C23×C8318yes—
738C4×Q8C23×C8318yes—
739C4×Q8C23×C8318yes—
740C4×Q8C23×C8318yes—
741C4×Q8C23×C8314yes—
742C4×Q8C23×C83116yes—
743C4×Q8C23×C8318yes—
744C4×D4C23×C8312yes—
745C4×D4C23×C8312yes—
746C4×D4C23×C8314yes—
747C4×D4C23×C8314yes—
748C4×D4C23×C8314yes—
749C4×D4C23×C8314yes—
750C4×D4C23×C8312yes—
751C4×D4C23×C8314yes—
752C4×D4C23×C8312yes—
753C4×D4C23×C8318yes—
754C4×D4C23×C8314yes—
755C4×D4C23×C8318yes—
756C4×D4C23×C8318yes—
757C4×D4C23×C8318yes—
758C4×D4C23×C83116yes—
759C4×D4C23×C8318yes—
760C4×D4C23×C8318yes—
761C4×D4C23×C83116yes—
762C4×D4C23×C8318yes—
763C4×D4C23×C8318yes—
764C4×D4C23×C83116yes—
765#117C23×C8312yes—
766#117C23×C8314yes—
767#117C23×C8314yes—
768#117C23×C8318yes—
769#117C23×C8318yes—
770#117C23×C8314yes—
771#117C23×C8318yes—
772#117C23×C8314yes—
773#117C23×C8314yes—
774#117C23×C8318yes—
775#117C23×C8318yes—
776#117C23×C8314yes—
777#117C23×C8314yes—
778#117C23×C8318yes—
779#117C23×C8314yes—
780#117C23×C83116yes—
781#117C23×C8318yes—
782#117C23×C83116yes—
783C2×C4⋊C4C23×C8311yescharacteristic
784C2×C4⋊C4C23×C8311yescharacteristic
785C2×C4⋊C4C23×C8312yes—
786C2×C4⋊C4C23×C8312yes—
787C2×C4⋊C4C23×C8314yes—
788C2×C4⋊C4C23×C8314yes—
789C2×C4⋊C4C23×C8318yes—
790C2×C4⋊C4C23×C8314yes—
791C2×C4⋊C4C23×C8318yes—
792C2×C4⋊C4C23×C8318yes—
793C2×C22⋊C4C23×C8314yes—
794C2×C22⋊C4C23×C8314yes—
795C2×C22⋊C4C23×C8318yes—
796C2×C22⋊C4C23×C8312yes—
797C2×C22⋊C4C23×C8312yes—
798C2×C22⋊C4C23×C8318yes—
799C2×C42C23×C8314yes—
800C2×C42C23×C8318yes—
801C2×C42C23×C8311yescharacteristic
802C2×C42C23×C8314yes—
803C24C24×C8312yes—
804C24C24×C8312yes—
805#41—28no—
806#41—48no—
807#41—48no—
808#41—816no—
809C2×Q8—48no—
810C2×Q8—82no—
811C2×Q8—88no—
812C2×Q8C24×C8312yes—
813C2×Q8C24×C8314yes—
814C2×Q8C24×C8318yes—
815C2×Q8C24×C8314yes—
816C2×Q8C24×C8314yes—
817C2×Q8C24×C83116yes—
818C2×Q8C24×C8318yes—
819C2×D4—24no—
820C2×D4—42no—
821C2×D4—84no—
822C2×D4C24×C8314yes—
823C2×D4C24×C8314yes—
824C2×D4C24×C8312yes—
825C2×D4C24×C8312yes—
826C2×D4C24×C8318yes—
827C2×D4C24×C8318yes—
828C2×D4C24×C8314yes—
829C2×D4C24×C8312yes—
830C2×D4C24×C8318yes—
831C2×D4C24×C8318yes—
832C2×D4C24×C83116yes—
833C22×C4—28no—
834C22×C4—44no—
835C22×C4C24×C8312yes—
836C22×C4C24×C8314yes—
837C22×C4C24×C8311yescharacteristic
838C22×C4C24×C8314yes—
839C22×C4C24×C8314yes—
840C22×C4C24×C8314yes—
841C22×C4C24×C8314yes—
842C22×C4C24×C8312yes—
843C22×C4C24×C8311yescharacteristic
844C22×C4C24×C8314yes—
845C22×C4C24×C8318yes—
846C22×C4C24×C8318yes—
847C22×C4C24×C8314yes—
848C22×C4C24×C8318yes—
849C22×C4C24×C8318yes—
850C22×C4C24×C8314yes—
851C22×C4C24×C83116yes—
852C22×C4C24×C8311yescharacteristic
853C4⋊C4C24×C8314yes—
854C4⋊C4C24×C8314yes—
855C4⋊C4C24×C8314yes—
856C4⋊C4C24×C8312yes—
857C4⋊C4C24×C8318yes—
858C4⋊C4C24×C8312yes—
859C4⋊C4C24×C8318yes—
860C4⋊C4C24×C8311yescharacteristic
861C4⋊C4C24×C8314yes—
862C4⋊C4C24×C8314yes—
863C4⋊C4C24×C8311yescharacteristic
864C4⋊C4C24×C8312yes—
865C4⋊C4C24×C8314yes—
866C4⋊C4C24×C8318yes—
867C4⋊C4C24×C8318yes—
868C4⋊C4C24×C83116yes—
869C4⋊C4C24×C83116yes—
870C4⋊C4C24×C8318yes—
871C4⋊C4C24×C83116yes—
872C4⋊C4C24×C8318yes—
873C4⋊C4C24×C8318yes—
874C4⋊C4C24×C8318yes—
875C4⋊C4C24×C8314yes—
876C4⋊C4C24×C8314yes—
877C4⋊C4C24×C8314yes—
878C4⋊C4C24×C83116yes—
879C4⋊C4C24×C8314yes—
880C4⋊C4C24×C8318yes—
881C4⋊C4C24×C83116yes—
882C4⋊C4C24×C8314yes—
883C22⋊C4C24×C8318yes—
884C22⋊C4C24×C8314yes—
885C22⋊C4C24×C8318yes—
886C22⋊C4C24×C8314yes—
887C22⋊C4C24×C8318yes—
888C22⋊C4C24×C83116yes—
889C22⋊C4C24×C8318yes—
890C22⋊C4C24×C8318yes—
891C22⋊C4C24×C83116yes—
892C22⋊C4C24×C8318yes—
893C22⋊C4C24×C8314yes—
894C22⋊C4C24×C8318yes—
895C22⋊C4C24×C8318yes—
896C22⋊C4C24×C8318yes—
897C22⋊C4C24×C8318yes—
898C22⋊C4C24×C8318yes—
899C22⋊C4C24×C8314yes—
900C22⋊C4C24×C83116yes—
901C22⋊C4C24×C8314yes—
902C22⋊C4C24×C8318yes—
903C22⋊C4C24×C8318yes—
904C42C24×C8314yes—
905C42C24×C8312yes—
906C42C24×C8318yes—
907C42C24×C8318yes—
908C42C24×C8318yes—
909C42C24×C8318yes—
910C42C24×C8312yes—
911C42C24×C8318yes—
912C42C24×C8314yes—
913C42C24×C8314yes—
914C42C24×C83116yes—
915C23—24no—
916C23—24no—
917C23—42no—
918C23—42no—
919C23—42no—
920C23—42no—
921C23C25×C8314yes—
922C23C25×C8314yes—
923C23C25×C8314yes—
924C23C25×C8311yescharacteristic
925Q8—24no—
926Q8—28no—
927Q8—48no—
928Q8—44no—
929Q8—48no—
930Q8—416no—
931Q8—44no—
932D4—28no—
933D4—28no—
934D4—24no—
935D4—24no—
936D4—42no—
937D4—416no—
938D4—48no—
939D4—44no—
940D4—48no—
941D4—48no—
942D4—48no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—28no—
949C2×C4—28no—
950C2×C4—44no—
951C2×C4—42no—
952C2×C4—44no—
953C2×C4—48no—
954C2×C4—44no—
955C2×C4—41no—
956C2×C4—416no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—48no—
960C2×C42−1+4×C8314yes—
961C2×C4C25×C8312yes—
962C2×C4C25×C8314yes—
963C2×C4C25×C8312yes—
964C2×C4C25×C8312yes—
965C2×C4C25×C8314yes—
966C2×C4C25×C8318yes—
967C2×C4C25×C8314yes—
968C2×C4C25×C8314yes—
969C2×C4C25×C8318yes—
970C2×C4C25×C8318yes—
971C2×C4C25×C8311yescharacteristic
972C2×C4C25×C8312yes—
973C2×C4C25×C8311yescharacteristic
974C22—21no—
975C22—21no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—84no—
986C22—84no—
987C22C2×2−1+4×C8312yes—
988C22C26×C8311yescharacteristic
989C4—22no—
990C4—22no—
991C4—24no—
992C4—21no—
993C4—24no—
994C4—24no—
995C4—28no—
996C4—28no—
997C4—28no—
998C4—24no—
999C4—22no—
1000C4C2×2−1+4×C8314yes—
1001C4#585×C8312yes—
1002C2—22no—
1003C2—44no—
1004C2—44no—
1005C2—44no—
1006C2C22×2−1+4×C8311yescharacteristic
1007C2C2×#585×C8311yescharacteristic
1008C2C83×H(7,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C83C26
commutator, Frattini, cosocleC22C26×C83
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3565C2semidirect
2. C83×#3561C2semidirect
3. C83×#3547C2semidirect
4. C83×#3547C2semidirect
5. C83×#3544C2semidirect
6. C83×#3536C2semidirect
7. C83×#3518C2semidirect
8. C83×#3511C2semidirect
9. C83×#3503C2semidirect
10. C83×#3501C2semidirect
11. C83×#3495C2semidirect
12. C83×#3494C2semidirect
13. C83×#3493C2semidirect
14. C83×#3475C2semidirect
15. C2×#555×C83C2semidirect
16. C83×#3460C2semidirect
17. C83×#3458C2semidirect
18. #563×C83C22semidirect
19. #562×C83C22semidirect
20. #562×C83C22semidirect
21. Q82×C83C22semidirect
22. #557×C83C22semidirect
23. #556×C83C22semidirect
24. #556×C83C22semidirect
25. #556×C83C22semidirect
26. #556×C83C22semidirect
30. #555×C83C22semidirect
31. #555×C83C22semidirect
32. #555×C83C22semidirect
34. #554×C83C22semidirect
35. #554×C83C22semidirect
36. #554×C83C22semidirect
37. #554×C83C22semidirect
38. #553×C83C22semidirect
39. #553×C83C22semidirect
40. #553×C83C22semidirect
41. #553×C83C22semidirect
43. #552×C83C22semidirect
44. #552×C83C22semidirect
45. #552×C83C22semidirect
46. #552×C83C22semidirect
50. D4×Q8×C83C22semidirect
51. D4×Q8×C83C22semidirect
52. #548×C83C22semidirect
53. #548×C83C22semidirect
54. #547×C83C22semidirect
55. #547×C83C22semidirect
56. #547×C83C22semidirect
62. #544×C83C22semidirect
63. #544×C83C22semidirect
64. #544×C83C22semidirect
65. #544×C83C22semidirect
68. #542×C83C22semidirect
69. #542×C83C22semidirect
70. #542×C83C22semidirect
71. #542×C83C22semidirect
72. #542×C83C22semidirect
73. #542×C83C22semidirect
74. #542×C83C22semidirect
75. #541×C83C22semidirect
76. #540×C83C22semidirect
77. #540×C83C22semidirect
78. #539×C83C22semidirect
82. #537×C83C22semidirect
83. #537×C83C22semidirect
84. #536×C83C22semidirect
85. #536×C83C22semidirect
89. #533×C83C22semidirect
90. #533×C83C22semidirect
91. #533×C83C22semidirect
92. #532×C83C22semidirect
93. #532×C83C22semidirect
95. C2×C4⋊Q8×C83C22semidirect
97. #529×C83C22semidirect
98. #529×C83C22semidirect
99. #529×C83C22semidirect
100. #529×C83C22semidirect
108. #520×C83C22semidirect
109. #519×C83C22semidirect
112. C4×#41×C83C22semidirect
497. #62929C83direct (N × H)
505. #3565C2×C83semidirect
506. #3561C2×C83semidirect
507. #3547C2×C83semidirect
508. #3547C2×C83semidirect
509. #3544C2×C83semidirect
510. #3536C2×C83semidirect
511. #3518C2×C83semidirect
512. #3511C2×C83semidirect
513. #3503C2×C83semidirect
514. #3501C2×C83semidirect
515. #3495C2×C83semidirect
516. #3494C2×C83semidirect
517. #3493C2×C83semidirect
518. #3475C2×C83semidirect
519. C2×#555C2×C83semidirect
520. #3460C2×C83semidirect
521. #3458C2×C83semidirect
522. C83#62929direct (N × H)
523. #563C22×C83semidirect
524. #562C22×C83semidirect
525. #562C22×C83semidirect
526. Q82C22×C83semidirect
527. #557C22×C83semidirect
528. #556C22×C83semidirect
529. #556C22×C83semidirect
530. #556C22×C83semidirect
531. #556C22×C83semidirect
535. #555C22×C83semidirect
536. #555C22×C83semidirect
537. #555C22×C83semidirect
539. #554C22×C83semidirect
540. #554C22×C83semidirect
541. #554C22×C83semidirect
542. #554C22×C83semidirect
543. #553C22×C83semidirect
544. #553C22×C83semidirect
545. #553C22×C83semidirect
546. #553C22×C83semidirect
548. #552C22×C83semidirect
549. #552C22×C83semidirect
550. #552C22×C83semidirect
551. #552C22×C83semidirect
555. D4×Q8C22×C83semidirect
556. D4×Q8C22×C83semidirect
557. #548C22×C83semidirect
558. #548C22×C83semidirect
559. #547C22×C83semidirect
560. #547C22×C83semidirect
561. #547C22×C83semidirect
567. #544C22×C83semidirect
568. #544C22×C83semidirect
569. #544C22×C83semidirect
570. #544C22×C83semidirect
573. #542C22×C83semidirect
574. #542C22×C83semidirect
575. #542C22×C83semidirect
576. #542C22×C83semidirect
577. #542C22×C83semidirect
578. #542C22×C83semidirect
579. #542C22×C83semidirect
580. #541C22×C83semidirect
581. #540C22×C83semidirect
582. #540C22×C83semidirect
583. #539C22×C83semidirect
587. #537C22×C83semidirect
588. #537C22×C83semidirect
589. #536C22×C83semidirect
590. #536C22×C83semidirect
594. #533C22×C83semidirect
595. #533C22×C83semidirect
596. #533C22×C83semidirect
597. #532C22×C83semidirect
598. #532C22×C83semidirect
600. C2×C4⋊Q8C22×C83semidirect
602. #529C22×C83semidirect
603. #529C22×C83semidirect
604. #529C22×C83semidirect
605. #529C22×C83semidirect
613. #520C22×C83semidirect
614. #519C22×C83semidirect
617. C4×#41C22×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35652
C83×#35612
C83×#35472
C83×#35442
C83×#35362
C83×#35182
C83×#35112
C83×#35032
C83×#35012
C83×#34952
C83×#34942
C83×#34932
C83×#34752
C2×#555×C832
C83×#34602
C83×#34582
#6292983