Finite Group Databasebeta

← C83×#62959 #35290783

Subgroups — C83×#62959 #35290783

Order 21248.

6354 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3565C218yesmaximal, complemented
2C83×#3564C218yesmaximal, complemented
3C83×#3561C214yesmaximal, complemented
4C83×#3555C218yesmaximal, complemented
5C83×#3555C214yesmaximal, complemented
6C83×#3552C214yesmaximal, complemented
7C83×#3523C214yesmaximal, complemented
8C83×#3518C214yesmaximal, complemented
9C83×#3509C214yesmaximal, complemented
10C83×#3503C212yesmaximal, complemented
11C83×#3502C211yesmaximal, characteristic, complemented
12C83×#3495C214yesmaximal, complemented
13C83×#3493C212yesmaximal, complemented
14C83×#3475C212yesmaximal, complemented
15C2×#556×C83C211yesmaximal, characteristic, complemented
16C83×#3461C211yesmaximal, characteristic, complemented
17C83×#3458C212yesmaximal, complemented
18#563×C83C2218yes—
19#563×C83C22116yescomplemented
20#563×C83C22116yescomplemented
21#562×C83C2218yes—
22Q82×C83C2214yescomplemented
23Q82×C83C2214yescomplemented
24#557×C83C2214yescomplemented
25#557×C83C2214yescomplemented
26#557×C83C2218yescomplemented
27#557×C83C2218yescomplemented
28#557×C83C2214yescomplemented
29#557×C83C2214yescomplemented
30#556×C83C2214yes—
31#556×C83C2218yes—
32#556×C83C2218yes—
33#556×C83C2214yes—
34#556×C83C2212yes—
35#556×C83C2218yescomplemented
36#556×C83C22116yescomplemented
37#556×C83C2218yescomplemented
38#556×C83C2218yescomplemented
39#556×C83C2214yescomplemented
40#555×C83C2212yes—
41#555×C83C2218yescomplemented
42#554×C83C2212yes—
43#554×C83C2218yes—
44#554×C83C2218yescomplemented
45#554×C83C2214yescomplemented
46#553×C83C2214yes—
47#553×C83C2218yescomplemented
48#552×C83C2214yes—
49#552×C83C22116yes—
50#552×C83C2214yes—
51#552×C83C2218yescomplemented
52#552×C83C2218yescomplemented
53#552×C83C22116yescomplemented
54#552×C83C2218yescomplemented
55#551×C83C22116yes—
56#551×C83C2218yes—
57D4×Q8×C83C2218yes—
58D4×Q8×C83C2214yescomplemented
59D4×Q8×C83C2214yescomplemented
60#548×C83C2218yes—
61#547×C83C2212yes—
62#546×C83C2214yes—
63#544×C83C2214yes—
64#544×C83C2211yescharacteristic
65#544×C83C2212yes—
66#544×C83C2214yes—
67#544×C83C2218yescomplemented
68#544×C83C2218yescomplemented
69#544×C83C2218yescomplemented
70#543×C83C2218yes—
71#542×C83C22116yes—
72#542×C83C2218yes—
73#542×C83C2218yescomplemented
74#542×C83C22116yescomplemented
75#542×C83C2214yescomplemented
76#541×C83C2218yescomplemented
77#541×C83C22116yescomplemented
78#541×C83C2214yescomplemented
79#541×C83C2218yescomplemented
80#541×C83C22116yescomplemented
81#541×C83C22116yescomplemented
82#539×C83C2214yes—
83#539×C83C22116yescomplemented
84#538×C83C2218yes—
85#537×C83C2211yescharacteristic
86#536×C83C2218yes—
87#536×C83C2212yes—
88#533×C83C2214yes—
89#533×C83C2218yes—
90#533×C83C2212yes—
91#533×C83C2218yescomplemented
92#533×C83C2214yescomplemented
93#533×C83C2218yescomplemented
94#533×C83C2214yescomplemented
95#533×C83C2218yescomplemented
96C2×C4⋊Q8×C83C2211yescharacteristic
97C2×C4⋊Q8×C83C2214yescomplemented
98#529×C83C2214yes—
99#529×C83C2218yes—
100#529×C83C2214yes—
101#529×C83C2218yes—
102#529×C83C2214yescomplemented
103#529×C83C2218yescomplemented
104C2×#126×C83C2214yes—
105C2×#124×C83C2212yes—
106#525×C83C2214yes—
107C2×C22⋊Q8×C83C2212yes—
108#520×C83C2214yes—
109#519×C83C2212yes—
110#519×C83C2218yescomplemented
111C4×#41×C83C2212yes—
112C4×#41×C83C2214yes—
113C2×C4×Q8×C83C2211yescharacteristic
114C2×C4×Q8×C83C2212yes—
115C2×C4×D4×C83C2211yescharacteristic
116C2×#117×C83C2212yes—
117C2×#117×C83C2214yes—
118C2×#41×C83C2312yes—
119C2×#41×C83C2314yes—
120C22×Q8×C83C2311yescharacteristic
121C22×Q8×C83C2312yes—
122C22×Q8×C83C2318yes—
123C22×D4×C83C2311yescharacteristic
124C23×C4×C83C2312yes—
125C4⋊Q8×C83C2314yes—
126C4⋊Q8×C83C2314yes—
127C4⋊Q8×C83C2312yes—
128C4⋊Q8×C83C2318yes—
129C4⋊Q8×C83C2318yes—
130C4⋊Q8×C83C2318yes—
131C4⋊Q8×C83C2312yes—
132C4⋊Q8×C83C2314yes—
133C4⋊Q8×C83C2314yes—
134C4⋊Q8×C83C2318yes—
135C4⋊Q8×C83C2318yes—
136C4⋊Q8×C83C2314yes—
137C4⋊Q8×C83C2314yes—
138C4⋊Q8×C83C2318yes—
139C4⋊Q8×C83C2318yes—
140C4⋊Q8×C83C23116yes—
141C4⋊Q8×C83C23116yes—
142#126×C83C23116yes—
143#126×C83C23116yes—
144#126×C83C2318yes—
145#126×C83C2318yes—
146#126×C83C2318yes—
147#126×C83C2318yes—
148#126×C83C23116yes—
149#126×C83C2318yes—
150#126×C83C23116yes—
151#126×C83C23116yes—
152#126×C83C23116yes—
153#126×C83C23116yes—
154#126×C83C23116yes—
155#125×C83C2318yes—
156#125×C83C2314yes—
157#125×C83C2318yes—
158#125×C83C2314yes—
159#125×C83C2314yes—
160#125×C83C2318yes—
161#125×C83C23116yes—
162#125×C83C2318yes—
163#125×C83C2314yes—
164#125×C83C2318yes—
165#125×C83C23116yes—
166#125×C83C2318yes—
167#125×C83C2318yes—
168#125×C83C23116yes—
169#125×C83C23116yes—
170#125×C83C23116yes—
171#125×C83C23116yes—
172#124×C83C2318yes—
173#124×C83C2318yes—
174#124×C83C2314yes—
175#124×C83C2318yes—
176#124×C83C2318yes—
177#124×C83C2314yes—
178#124×C83C2314yes—
179#124×C83C23116yes—
180#124×C83C23116yes—
181#123×C83C2318yes—
182#123×C83C2318yes—
183#123×C83C2318yes—
184#123×C83C2318yes—
185#123×C83C2318yes—
186#123×C83C2318yes—
187#123×C83C23116yes—
188#123×C83C23116yes—
189#123×C83C23116yes—
190C22⋊Q8×C83C2318yes—
191C22⋊Q8×C83C2318yes—
192C22⋊Q8×C83C2314yes—
193C22⋊Q8×C83C2314yes—
194C22⋊Q8×C83C2318yes—
195C22⋊Q8×C83C2314yes—
196C22⋊Q8×C83C2314yes—
197C22⋊Q8×C83C2318yes—
198C22⋊Q8×C83C2314yes—
199C22⋊Q8×C83C2314yes—
200C22⋊Q8×C83C23116yes—
201C22⋊Q8×C83C2314yes—
202C22⋊Q8×C83C23116yes—
203C22⋊Q8×C83C23116yes—
204C22⋊Q8×C83C2314yes—
205C22⋊Q8×C83C2314yes—
206C22⋊Q8×C83C2318yes—
207C22⋊Q8×C83C23116yes—
208C22⋊Q8×C83C2318yes—
209C22⋊Q8×C83C2318yes—
210C22⋊Q8×C83C23116yes—
211C22⋊Q8×C83C23116yes—
212C22⋊Q8×C83C23116yes—
213C22⋊Q8×C83C23116yes—
214C22⋊Q8×C83C23116yes—
215#121×C83C2314yes—
216#121×C83C2314yes—
217#121×C83C2314yes—
218#121×C83C2314yes—
219#121×C83C2318yes—
220#121×C83C2314yes—
221#121×C83C23116yes—
222#120×C83C2318yes—
223C4×Q8×C83C2314yes—
224C4×Q8×C83C2314yes—
225C4×Q8×C83C2314yes—
226C4×Q8×C83C2318yes—
227C4×Q8×C83C2314yes—
228C4×Q8×C83C2314yes—
229C4×Q8×C83C2314yes—
230C4×Q8×C83C2312yes—
231C4×Q8×C83C2312yes—
232C4×Q8×C83C2318yes—
233C4×Q8×C83C2318yes—
234C4×Q8×C83C23116yes—
235C4×Q8×C83C2318yes—
236C4×Q8×C83C23116yes—
237C4×Q8×C83C2318yes—
238C4×Q8×C83C2318yes—
239C4×Q8×C83C2314yes—
240C4×Q8×C83C2314yes—
241C4×Q8×C83C2318yes—
242C4×Q8×C83C2318yes—
243C4×Q8×C83C2318yes—
244C4×Q8×C83C2318yes—
245C4×Q8×C83C2318yes—
246C4×D4×C83C2312yes—
247C4×D4×C83C2312yes—
248C4×D4×C83C2314yes—
249C4×D4×C83C2318yes—
250C4×D4×C83C2314yes—
251C4×D4×C83C2312yes—
252C4×D4×C83C2314yes—
253C4×D4×C83C2314yes—
254C4×D4×C83C2318yes—
255C4×D4×C83C2312yes—
256C4×D4×C83C23116yes—
257C4×D4×C83C2318yes—
258C4×D4×C83C2318yes—
259C4×D4×C83C2314yes—
260C4×D4×C83C2318yes—
261C4×D4×C83C23116yes—
262#117×C83C2312yes—
263#117×C83C2314yes—
264#117×C83C2318yes—
265#117×C83C2318yes—
266#117×C83C2314yes—
267#117×C83C2314yes—
268#117×C83C2318yes—
269#117×C83C2318yes—
270#117×C83C2314yes—
271#117×C83C2314yes—
272#117×C83C2318yes—
273#117×C83C2318yes—
274#117×C83C2318yes—
275#117×C83C23116yes—
276#117×C83C23116yes—
277#117×C83C2318yes—
278#117×C83C23116yes—
279C2×C4⋊C4×C83C2311yescharacteristic
280C2×C4⋊C4×C83C2312yes—
281C2×C4⋊C4×C83C2314yes—
282C2×C4⋊C4×C83C2314yes—
283C2×C4⋊C4×C83C2311yescharacteristic
284C2×C4⋊C4×C83C2314yes—
285C2×C4⋊C4×C83C2312yes—
286C2×C4⋊C4×C83C2318yes—
287C2×C4⋊C4×C83C2312yes—
288C2×C4⋊C4×C83C2318yes—
289C2×C22⋊C4×C83C2314yes—
290C2×C22⋊C4×C83C2318yes—
291C2×C22⋊C4×C83C2312yes—
292C2×C22⋊C4×C83C2314yes—
293C2×C42×C83C2314yes—
294C2×C42×C83C2318yes—
295C2×C42×C83C2311yescharacteristic
296C2×C42×C83C2312yes—
297C2×C42×C83C2314yes—
298C24×C83C2412yes—
299#41×C83—28no—
300#41×C83—48no—
301C2×Q8×C83—24no—
302C2×Q8×C83—44no—
303C2×Q8×C83—416no—
304C2×Q8×C83C2414yes—
305C2×Q8×C83C2412yes—
306C2×Q8×C83C2414yes—
307C2×Q8×C83C2414yes—
308C2×Q8×C83C2414yes—
309C2×Q8×C83C2414yes—
310C2×Q8×C83C2418yes—
311C2×Q8×C83C24116yes—
312C2×Q8×C83C2414yes—
313C2×D4×C83—42no—
314C2×D4×C83C2414yes—
315C2×D4×C83C2412yes—
316C2×D4×C83C2412yes—
317C2×D4×C83C2418yes—
318C2×D4×C83C2414yes—
319C2×D4×C83C2418yes—
320C2×D4×C83C2412yes—
321C22×C4×C83—28no—
322C22×C4×C83C2411yescharacteristic
323C22×C4×C83C2412yes—
324C22×C4×C83C2414yes—
325C22×C4×C83C2412yes—
326C22×C4×C83C2414yes—
327C22×C4×C83C2414yes—
328C22×C4×C83C2414yes—
329C22×C4×C83C2412yes—
330C22×C4×C83C2411yescharacteristic
331C22×C4×C83C2414yes—
332C22×C4×C83C2418yes—
333C22×C4×C83C2418yes—
334C22×C4×C83C2414yes—
335C22×C4×C83C24116yes—
336C22×C4×C83C2411yescharacteristic
337C4⋊C4×C83C2414yes—
338C4⋊C4×C83C2412yes—
339C4⋊C4×C83C2418yes—
340C4⋊C4×C83C2412yes—
341C4⋊C4×C83C2418yes—
342C4⋊C4×C83C2414yes—
343C4⋊C4×C83C2411yescharacteristic
344C4⋊C4×C83C2414yes—
345C4⋊C4×C83C2414yes—
346C4⋊C4×C83C2418yes—
347C4⋊C4×C83C2418yes—
348C4⋊C4×C83C2418yes—
349C4⋊C4×C83C24116yes—
350C4⋊C4×C83C2411yescharacteristic
351C4⋊C4×C83C2412yes—
352C4⋊C4×C83C24116yes—
353C4⋊C4×C83C2418yes—
354C4⋊C4×C83C2418yes—
355C4⋊C4×C83C2418yes—
356C4⋊C4×C83C2418yes—
357C4⋊C4×C83C2414yes—
358C4⋊C4×C83C2414yes—
359C4⋊C4×C83C2418yes—
360C4⋊C4×C83C2414yes—
361C4⋊C4×C83C24116yes—
362C4⋊C4×C83C2418yes—
363C4⋊C4×C83C24116yes—
364C4⋊C4×C83C2418yes—
365C4⋊C4×C83C2418yes—
366C4⋊C4×C83C2418yes—
367C4⋊C4×C83C2414yes—
368C4⋊C4×C83C24116yes—
369C4⋊C4×C83C2418yes—
370C4⋊C4×C83C2418yes—
371C4⋊C4×C83C2418yes—
372C4⋊C4×C83C2414yes—
373C22⋊C4×C83C2414yes—
374C22⋊C4×C83C2418yes—
375C22⋊C4×C83C2414yes—
376C22⋊C4×C83C2418yes—
377C22⋊C4×C83C24116yes—
378C22⋊C4×C83C2418yes—
379C22⋊C4×C83C24116yes—
380C22⋊C4×C83C2414yes—
381C22⋊C4×C83C2418yes—
382C22⋊C4×C83C2418yes—
383C22⋊C4×C83C2418yes—
384C22⋊C4×C83C2418yes—
385C22⋊C4×C83C2418yes—
386C22⋊C4×C83C2414yes—
387C22⋊C4×C83C24116yes—
388C22⋊C4×C83C2414yes—
389C22⋊C4×C83C2418yes—
390C22⋊C4×C83C2418yes—
391C42×C83C2414yes—
392C42×C83C2412yes—
393C42×C83C2418yes—
394C42×C83C2418yes—
395C42×C83C2418yes—
396C42×C83C2418yes—
397C42×C83C2412yes—
398C42×C83C2414yes—
399C42×C83C2414yes—
400C42×C83C2414yes—
401C42×C83C2418yes—
402C42×C83C2414yes—
403C42×C83C24116yes—
404C42×C83C24116yes—
405C23×C83—24no—
406C23×C83—42no—
407C23×C83—42no—
408C23×C83C2514yes—
409C23×C83C2514yes—
410C23×C83C2511yescharacteristic
411Q8×C83—28no—
412Q8×C83—24no—
413Q8×C83—28no—
414Q8×C83—28no—
415Q8×C83—416no—
416Q8×C83—44no—
417Q8×C83—44no—
418Q8×C83—44no—
419Q8×C83—48no—
420D4×C83—28no—
421D4×C83—24no—
422D4×C83—24no—
423D4×C83—42no—
424D4×C83—48no—
425D4×C83—44no—
426D4×C83—48no—
427C2×C4×C83—24no—
428C2×C4×C83—24no—
429C2×C4×C83—28no—
430C2×C4×C83—28no—
431C2×C4×C83—28no—
432C2×C4×C83—22no—
433C2×C4×C83—28no—
434C2×C4×C83—41no—
435C2×C4×C83—44no—
436C2×C4×C83—48no—
437C2×C4×C83—42no—
438C2×C4×C83—416no—
439C2×C4×C83—44no—
440C2×C4×C83—48no—
441C2×C4×C832−1+414yes—
442C2×C4×C83C2512yes—
443C2×C4×C83C2514yes—
444C2×C4×C83C2514yes—
445C2×C4×C83C2514yes—
446C2×C4×C83C2518yes—
447C2×C4×C83C2511yescharacteristic
448C2×C4×C83C2512yes—
449C2×C4×C83C2514yes—
450C2×C4×C83C2512yes—
451C2×C4×C83C2514yes—
452C2×C4×C83C2518yes—
453C2×C4×C83C2518yes—
454C2×C4×C83C2512yes—
455C2×C4×C83C2511yescharacteristic
456C22×C83—21no—
457C22×C83—21no—
458C22×C83—24no—
459C22×C83—24no—
460C22×C83—24no—
461C22×C83—24no—
462C22×C83—24no—
463C22×C83—24no—
464C22×C83—84no—
465C22×C83C2×2−1+412yes—
466C22×C83C2611yescharacteristic
467C4×C83—22no—
468C4×C83—22no—
469C4×C83—24no—
470C4×C83—24no—
471C4×C83—24no—
472C4×C83—21no—
473C4×C83—28no—
474C4×C83—28no—
475C4×C83—22no—
476C4×C83—24no—
477C4×C83—28no—
478C4×C83—24no—
479C4×C83C2×2−1+414yes—
480C4×C83#58512yes—
481#62959C8311yesmaximal, characteristic, direct product factor, Sylow
482C2×C83—22no—
483C2×C83—44no—
484C2×C83—44no—
485C2×C83C22×2−1+411yescharacteristic
486C2×C83C2×#58511yescharacteristic
487C2×C832−1+611yescharacteristic
488#3565C2×C8318yescomplemented
489#3564C2×C8318yescomplemented
490#3561C2×C8314yescomplemented
491#3555C2×C8318yescomplemented
492#3555C2×C8314yescomplemented
493#3552C2×C8314yescomplemented
494#3523C2×C8314yescomplemented
495#3518C2×C8314yescomplemented
496#3509C2×C8314yescomplemented
497#3503C2×C8312yescomplemented
498#3502C2×C8311yescharacteristic, complemented
499#3495C2×C8314yescomplemented
500#3493C2×C8312yescomplemented
501#3475C2×C8312yescomplemented
502C2×#556C2×C8311yescharacteristic, complemented
503#3461C2×C8311yescharacteristic, complemented
504#3458C2×C8312yescomplemented
505C83#6295911yescharacteristic, direct product factor, Sylow
506#563C22×C8318yes—
507#563C22×C83116yescomplemented
508#563C22×C83116yescomplemented
509#562C22×C8318yes—
510Q82C22×C8314yescomplemented
511Q82C22×C8314yescomplemented
512#557C22×C8314yescomplemented
513#557C22×C8318yescomplemented
514#557C22×C8314yescomplemented
515#557C22×C8314yescomplemented
516#557C22×C8314yescomplemented
517#557C22×C8318yescomplemented
518#556C22×C8314yes—
519#556C22×C8314yes—
520#556C22×C8318yes—
521#556C22×C8312yes—
522#556C22×C8318yes—
523#556C22×C8318yescomplemented
524#556C22×C8318yescomplemented
525#556C22×C8314yescomplemented
526#556C22×C83116yescomplemented
527#556C22×C8318yescomplemented
528#555C22×C8312yes—
529#555C22×C8318yescomplemented
530#554C22×C8312yes—
531#554C22×C8318yes—
532#554C22×C8318yescomplemented
533#554C22×C8314yescomplemented
534#553C22×C8314yes—
535#553C22×C8318yescomplemented
536#552C22×C8314yes—
537#552C22×C8314yes—
538#552C22×C83116yes—
539#552C22×C8318yescomplemented
540#552C22×C8318yescomplemented
541#552C22×C8318yescomplemented
542#552C22×C83116yescomplemented
543#551C22×C8318yes—
544#551C22×C83116yes—
545D4×Q8C22×C8318yes—
546D4×Q8C22×C8314yescomplemented
547D4×Q8C22×C8314yescomplemented
548#548C22×C8318yes—
549#547C22×C8312yes—
550#546C22×C8314yes—
551#544C22×C8311yescharacteristic
552#544C22×C8312yes—
553#544C22×C8314yes—
554#544C22×C8314yes—
555#544C22×C8318yescomplemented
556#544C22×C8318yescomplemented
557#544C22×C8318yescomplemented
558#543C22×C8318yes—
559#542C22×C8318yes—
560#542C22×C83116yes—
561#542C22×C8314yescomplemented
562#542C22×C8318yescomplemented
563#542C22×C83116yescomplemented
564#541C22×C8314yescomplemented
565#541C22×C8318yescomplemented
566#541C22×C83116yescomplemented
567#541C22×C8318yescomplemented
568#541C22×C83116yescomplemented
569#541C22×C83116yescomplemented
570#539C22×C8314yes—
571#539C22×C83116yescomplemented
572#538C22×C8318yes—
573#537C22×C8311yescharacteristic
574#536C22×C8312yes—
575#536C22×C8318yes—
576#533C22×C8318yes—
577#533C22×C8312yes—
578#533C22×C8314yes—
579#533C22×C8318yescomplemented
580#533C22×C8318yescomplemented
581#533C22×C8314yescomplemented
582#533C22×C8318yescomplemented
583#533C22×C8314yescomplemented
584C2×C4⋊Q8C22×C8311yescharacteristic
585C2×C4⋊Q8C22×C8314yescomplemented
586#529C22×C8314yes—
587#529C22×C8314yes—
588#529C22×C8318yes—
589#529C22×C8318yes—
590#529C22×C8314yescomplemented
591#529C22×C8318yescomplemented
592C2×#126C22×C8314yes—
593C2×#124C22×C8312yes—
594#525C22×C8314yes—
595C2×C22⋊Q8C22×C8312yes—
596#520C22×C8314yes—
597#519C22×C8312yes—
598#519C22×C8318yescomplemented
599C4×#41C22×C8312yes—
600C4×#41C22×C8314yes—
601C2×C4×Q8C22×C8311yescharacteristic
602C2×C4×Q8C22×C8312yes—
603C2×C4×D4C22×C8311yescharacteristic
604C2×#117C22×C8312yes—
605C2×#117C22×C8314yes—
606C2×#41C23×C8312yes—
607C2×#41C23×C8314yes—
608C22×Q8C23×C8311yescharacteristic
609C22×Q8C23×C8312yes—
610C22×Q8C23×C8318yes—
611C22×D4C23×C8311yescharacteristic
612C23×C4C23×C8312yes—
613C4⋊Q8C23×C8314yes—
614C4⋊Q8C23×C8314yes—
615C4⋊Q8C23×C8312yes—
616C4⋊Q8C23×C8318yes—
617C4⋊Q8C23×C8318yes—
618C4⋊Q8C23×C8318yes—
619C4⋊Q8C23×C8312yes—
620C4⋊Q8C23×C8314yes—
621C4⋊Q8C23×C8314yes—
622C4⋊Q8C23×C8318yes—
623C4⋊Q8C23×C8318yes—
624C4⋊Q8C23×C8314yes—
625C4⋊Q8C23×C8314yes—
626C4⋊Q8C23×C8318yes—
627C4⋊Q8C23×C8318yes—
628C4⋊Q8C23×C83116yes—
629C4⋊Q8C23×C83116yes—
630#126C23×C83116yes—
631#126C23×C83116yes—
632#126C23×C8318yes—
633#126C23×C8318yes—
634#126C23×C8318yes—
635#126C23×C8318yes—
636#126C23×C83116yes—
637#126C23×C8318yes—
638#126C23×C83116yes—
639#126C23×C83116yes—
640#126C23×C83116yes—
641#126C23×C83116yes—
642#126C23×C83116yes—
643#125C23×C8318yes—
644#125C23×C8314yes—
645#125C23×C8318yes—
646#125C23×C8314yes—
647#125C23×C8314yes—
648#125C23×C8318yes—
649#125C23×C83116yes—
650#125C23×C8318yes—
651#125C23×C8314yes—
652#125C23×C8318yes—
653#125C23×C83116yes—
654#125C23×C8318yes—
655#125C23×C8318yes—
656#125C23×C83116yes—
657#125C23×C83116yes—
658#125C23×C83116yes—
659#125C23×C83116yes—
660#124C23×C8318yes—
661#124C23×C8318yes—
662#124C23×C8314yes—
663#124C23×C8318yes—
664#124C23×C8318yes—
665#124C23×C8314yes—
666#124C23×C8314yes—
667#124C23×C83116yes—
668#124C23×C83116yes—
669#123C23×C8318yes—
670#123C23×C8318yes—
671#123C23×C8318yes—
672#123C23×C8318yes—
673#123C23×C8318yes—
674#123C23×C8318yes—
675#123C23×C83116yes—
676#123C23×C83116yes—
677#123C23×C83116yes—
678C22⋊Q8C23×C8318yes—
679C22⋊Q8C23×C8318yes—
680C22⋊Q8C23×C8314yes—
681C22⋊Q8C23×C8314yes—
682C22⋊Q8C23×C8318yes—
683C22⋊Q8C23×C8314yes—
684C22⋊Q8C23×C8314yes—
685C22⋊Q8C23×C8318yes—
686C22⋊Q8C23×C8314yes—
687C22⋊Q8C23×C8314yes—
688C22⋊Q8C23×C83116yes—
689C22⋊Q8C23×C8314yes—
690C22⋊Q8C23×C83116yes—
691C22⋊Q8C23×C83116yes—
692C22⋊Q8C23×C8314yes—
693C22⋊Q8C23×C8314yes—
694C22⋊Q8C23×C8318yes—
695C22⋊Q8C23×C83116yes—
696C22⋊Q8C23×C8318yes—
697C22⋊Q8C23×C8318yes—
698C22⋊Q8C23×C83116yes—
699C22⋊Q8C23×C83116yes—
700C22⋊Q8C23×C83116yes—
701C22⋊Q8C23×C83116yes—
702C22⋊Q8C23×C83116yes—
703#121C23×C8314yes—
704#121C23×C8314yes—
705#121C23×C8314yes—
706#121C23×C8314yes—
707#121C23×C8318yes—
708#121C23×C8314yes—
709#121C23×C83116yes—
710#120C23×C8318yes—
711C4×Q8C23×C8314yes—
712C4×Q8C23×C8314yes—
713C4×Q8C23×C8314yes—
714C4×Q8C23×C8318yes—
715C4×Q8C23×C8314yes—
716C4×Q8C23×C8314yes—
717C4×Q8C23×C8314yes—
718C4×Q8C23×C8312yes—
719C4×Q8C23×C8312yes—
720C4×Q8C23×C8318yes—
721C4×Q8C23×C8318yes—
722C4×Q8C23×C83116yes—
723C4×Q8C23×C8318yes—
724C4×Q8C23×C83116yes—
725C4×Q8C23×C8318yes—
726C4×Q8C23×C8318yes—
727C4×Q8C23×C8314yes—
728C4×Q8C23×C8314yes—
729C4×Q8C23×C8318yes—
730C4×Q8C23×C8318yes—
731C4×Q8C23×C8318yes—
732C4×Q8C23×C8318yes—
733C4×Q8C23×C8318yes—
734C4×D4C23×C8312yes—
735C4×D4C23×C8312yes—
736C4×D4C23×C8314yes—
737C4×D4C23×C8318yes—
738C4×D4C23×C8314yes—
739C4×D4C23×C8312yes—
740C4×D4C23×C8314yes—
741C4×D4C23×C8314yes—
742C4×D4C23×C8318yes—
743C4×D4C23×C8312yes—
744C4×D4C23×C83116yes—
745C4×D4C23×C8318yes—
746C4×D4C23×C8318yes—
747C4×D4C23×C8314yes—
748C4×D4C23×C8318yes—
749C4×D4C23×C83116yes—
750#117C23×C8312yes—
751#117C23×C8314yes—
752#117C23×C8318yes—
753#117C23×C8318yes—
754#117C23×C8314yes—
755#117C23×C8314yes—
756#117C23×C8318yes—
757#117C23×C8318yes—
758#117C23×C8314yes—
759#117C23×C8314yes—
760#117C23×C8318yes—
761#117C23×C8318yes—
762#117C23×C8318yes—
763#117C23×C83116yes—
764#117C23×C83116yes—
765#117C23×C8318yes—
766#117C23×C83116yes—
767C2×C4⋊C4C23×C8311yescharacteristic
768C2×C4⋊C4C23×C8312yes—
769C2×C4⋊C4C23×C8314yes—
770C2×C4⋊C4C23×C8314yes—
771C2×C4⋊C4C23×C8311yescharacteristic
772C2×C4⋊C4C23×C8314yes—
773C2×C4⋊C4C23×C8312yes—
774C2×C4⋊C4C23×C8318yes—
775C2×C4⋊C4C23×C8312yes—
776C2×C4⋊C4C23×C8318yes—
777C2×C22⋊C4C23×C8314yes—
778C2×C22⋊C4C23×C8318yes—
779C2×C22⋊C4C23×C8312yes—
780C2×C22⋊C4C23×C8314yes—
781C2×C42C23×C8314yes—
782C2×C42C23×C8318yes—
783C2×C42C23×C8311yescharacteristic
784C2×C42C23×C8312yes—
785C2×C42C23×C8314yes—
786C24C24×C8312yes—
787#41—28no—
788#41—48no—
789C2×Q8—24no—
790C2×Q8—44no—
791C2×Q8—416no—
792C2×Q8C24×C8314yes—
793C2×Q8C24×C8312yes—
794C2×Q8C24×C8314yes—
795C2×Q8C24×C8314yes—
796C2×Q8C24×C8314yes—
797C2×Q8C24×C8314yes—
798C2×Q8C24×C8318yes—
799C2×Q8C24×C83116yes—
800C2×Q8C24×C8314yes—
801C2×D4—42no—
802C2×D4C24×C8314yes—
803C2×D4C24×C8312yes—
804C2×D4C24×C8312yes—
805C2×D4C24×C8318yes—
806C2×D4C24×C8314yes—
807C2×D4C24×C8318yes—
808C2×D4C24×C8312yes—
809C22×C4—28no—
810C22×C4C24×C8311yescharacteristic
811C22×C4C24×C8312yes—
812C22×C4C24×C8314yes—
813C22×C4C24×C8312yes—
814C22×C4C24×C8314yes—
815C22×C4C24×C8314yes—
816C22×C4C24×C8314yes—
817C22×C4C24×C8312yes—
818C22×C4C24×C8311yescharacteristic
819C22×C4C24×C8314yes—
820C22×C4C24×C8318yes—
821C22×C4C24×C8318yes—
822C22×C4C24×C8314yes—
823C22×C4C24×C83116yes—
824C22×C4C24×C8311yescharacteristic
825C4⋊C4C24×C8314yes—
826C4⋊C4C24×C8312yes—
827C4⋊C4C24×C8318yes—
828C4⋊C4C24×C8312yes—
829C4⋊C4C24×C8318yes—
830C4⋊C4C24×C8314yes—
831C4⋊C4C24×C8311yescharacteristic
832C4⋊C4C24×C8314yes—
833C4⋊C4C24×C8314yes—
834C4⋊C4C24×C8318yes—
835C4⋊C4C24×C8318yes—
836C4⋊C4C24×C8318yes—
837C4⋊C4C24×C83116yes—
838C4⋊C4C24×C8311yescharacteristic
839C4⋊C4C24×C8312yes—
840C4⋊C4C24×C83116yes—
841C4⋊C4C24×C8318yes—
842C4⋊C4C24×C8318yes—
843C4⋊C4C24×C8318yes—
844C4⋊C4C24×C8318yes—
845C4⋊C4C24×C8314yes—
846C4⋊C4C24×C8314yes—
847C4⋊C4C24×C8318yes—
848C4⋊C4C24×C8314yes—
849C4⋊C4C24×C83116yes—
850C4⋊C4C24×C8318yes—
851C4⋊C4C24×C83116yes—
852C4⋊C4C24×C8318yes—
853C4⋊C4C24×C8318yes—
854C4⋊C4C24×C8318yes—
855C4⋊C4C24×C8314yes—
856C4⋊C4C24×C83116yes—
857C4⋊C4C24×C8318yes—
858C4⋊C4C24×C8318yes—
859C4⋊C4C24×C8318yes—
860C4⋊C4C24×C8314yes—
861C22⋊C4C24×C8314yes—
862C22⋊C4C24×C8318yes—
863C22⋊C4C24×C8314yes—
864C22⋊C4C24×C8318yes—
865C22⋊C4C24×C83116yes—
866C22⋊C4C24×C8318yes—
867C22⋊C4C24×C83116yes—
868C22⋊C4C24×C8314yes—
869C22⋊C4C24×C8318yes—
870C22⋊C4C24×C8318yes—
871C22⋊C4C24×C8318yes—
872C22⋊C4C24×C8318yes—
873C22⋊C4C24×C8318yes—
874C22⋊C4C24×C8314yes—
875C22⋊C4C24×C83116yes—
876C22⋊C4C24×C8314yes—
877C22⋊C4C24×C8318yes—
878C22⋊C4C24×C8318yes—
879C42C24×C8314yes—
880C42C24×C8312yes—
881C42C24×C8318yes—
882C42C24×C8318yes—
883C42C24×C8318yes—
884C42C24×C8318yes—
885C42C24×C8312yes—
886C42C24×C8314yes—
887C42C24×C8314yes—
888C42C24×C8314yes—
889C42C24×C8318yes—
890C42C24×C8314yes—
891C42C24×C83116yes—
892C42C24×C83116yes—
893C23—24no—
894C23—42no—
895C23—42no—
896C23C25×C8314yes—
897C23C25×C8314yes—
898C23C25×C8311yescharacteristic
899Q8—28no—
900Q8—24no—
901Q8—28no—
902Q8—28no—
903Q8—416no—
904Q8—44no—
905Q8—44no—
906Q8—44no—
907Q8—48no—
908D4—28no—
909D4—24no—
910D4—24no—
911D4—42no—
912D4—48no—
913D4—48no—
914D4—44no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—28no—
922C2×C4—416no—
923C2×C4—44no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—44no—
927C2×C4—48no—
928C2×C4—42no—
929C2×C42−1+4×C8314yes—
930C2×C4C25×C8312yes—
931C2×C4C25×C8314yes—
932C2×C4C25×C8314yes—
933C2×C4C25×C8314yes—
934C2×C4C25×C8318yes—
935C2×C4C25×C8311yescharacteristic
936C2×C4C25×C8312yes—
937C2×C4C25×C8314yes—
938C2×C4C25×C8312yes—
939C2×C4C25×C8314yes—
940C2×C4C25×C8318yes—
941C2×C4C25×C8318yes—
942C2×C4C25×C8312yes—
943C2×C4C25×C8311yescharacteristic
944C22—21no—
945C22—21no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—84no—
953C22C2×2−1+4×C8312yes—
954C22C26×C8311yescharacteristic
955C4—22no—
956C4—22no—
957C4—24no—
958C4—24no—
959C4—24no—
960C4—21no—
961C4—28no—
962C4—28no—
963C4—22no—
964C4—24no—
965C4—28no—
966C4—24no—
967C4C2×2−1+4×C8314yes—
968C4#585×C8312yes—
969C2—22no—
970C2—44no—
971C2—44no—
972C2C22×2−1+4×C8311yescharacteristic
973C2C2×#585×C8311yescharacteristic
974C2C83×2−1+611yescharacteristic
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×#3564C2semidirect
3. C83×#3561C2semidirect
4. C83×#3555C2semidirect
5. C83×#3555C2semidirect
6. C83×#3552C2semidirect
7. C83×#3523C2semidirect
8. C83×#3518C2semidirect
9. C83×#3509C2semidirect
10. C83×#3503C2semidirect
11. C83×#3502C2semidirect
12. C83×#3495C2semidirect
13. C83×#3493C2semidirect
14. C83×#3475C2semidirect
15. C2×#556×C83C2semidirect
16. C83×#3461C2semidirect
17. C83×#3458C2semidirect
19. #563×C83C22semidirect
20. #563×C83C22semidirect
22. Q82×C83C22semidirect
23. Q82×C83C22semidirect
24. #557×C83C22semidirect
25. #557×C83C22semidirect
26. #557×C83C22semidirect
27. #557×C83C22semidirect
28. #557×C83C22semidirect
29. #557×C83C22semidirect
35. #556×C83C22semidirect
36. #556×C83C22semidirect
37. #556×C83C22semidirect
38. #556×C83C22semidirect
39. #556×C83C22semidirect
41. #555×C83C22semidirect
44. #554×C83C22semidirect
45. #554×C83C22semidirect
47. #553×C83C22semidirect
51. #552×C83C22semidirect
52. #552×C83C22semidirect
53. #552×C83C22semidirect
54. #552×C83C22semidirect
58. D4×Q8×C83C22semidirect
59. D4×Q8×C83C22semidirect
67. #544×C83C22semidirect
68. #544×C83C22semidirect
69. #544×C83C22semidirect
73. #542×C83C22semidirect
74. #542×C83C22semidirect
75. #542×C83C22semidirect
76. #541×C83C22semidirect
77. #541×C83C22semidirect
78. #541×C83C22semidirect
79. #541×C83C22semidirect
80. #541×C83C22semidirect
81. #541×C83C22semidirect
83. #539×C83C22semidirect
91. #533×C83C22semidirect
92. #533×C83C22semidirect
93. #533×C83C22semidirect
94. #533×C83C22semidirect
95. #533×C83C22semidirect
97. C2×C4⋊Q8×C83C22semidirect
102. #529×C83C22semidirect
103. #529×C83C22semidirect
110. #519×C83C22semidirect
481. #62959C83direct (N × H)
488. #3565C2×C83semidirect
489. #3564C2×C83semidirect
490. #3561C2×C83semidirect
491. #3555C2×C83semidirect
492. #3555C2×C83semidirect
493. #3552C2×C83semidirect
494. #3523C2×C83semidirect
495. #3518C2×C83semidirect
496. #3509C2×C83semidirect
497. #3503C2×C83semidirect
498. #3502C2×C83semidirect
499. #3495C2×C83semidirect
500. #3493C2×C83semidirect
501. #3475C2×C83semidirect
502. C2×#556C2×C83semidirect
503. #3461C2×C83semidirect
504. #3458C2×C83semidirect
505. C83#62959direct (N × H)
507. #563C22×C83semidirect
508. #563C22×C83semidirect
510. Q82C22×C83semidirect
511. Q82C22×C83semidirect
512. #557C22×C83semidirect
513. #557C22×C83semidirect
514. #557C22×C83semidirect
515. #557C22×C83semidirect
516. #557C22×C83semidirect
517. #557C22×C83semidirect
523. #556C22×C83semidirect
524. #556C22×C83semidirect
525. #556C22×C83semidirect
526. #556C22×C83semidirect
527. #556C22×C83semidirect
529. #555C22×C83semidirect
532. #554C22×C83semidirect
533. #554C22×C83semidirect
535. #553C22×C83semidirect
539. #552C22×C83semidirect
540. #552C22×C83semidirect
541. #552C22×C83semidirect
542. #552C22×C83semidirect
546. D4×Q8C22×C83semidirect
547. D4×Q8C22×C83semidirect
555. #544C22×C83semidirect
556. #544C22×C83semidirect
557. #544C22×C83semidirect
561. #542C22×C83semidirect
562. #542C22×C83semidirect
563. #542C22×C83semidirect
564. #541C22×C83semidirect
565. #541C22×C83semidirect
566. #541C22×C83semidirect
567. #541C22×C83semidirect
568. #541C22×C83semidirect
569. #541C22×C83semidirect
571. #539C22×C83semidirect
579. #533C22×C83semidirect
580. #533C22×C83semidirect
581. #533C22×C83semidirect
582. #533C22×C83semidirect
583. #533C22×C83semidirect
585. C2×C4⋊Q8C22×C83semidirect
590. #529C22×C83semidirect
591. #529C22×C83semidirect
598. #519C22×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#35652
C83×#35642
C83×#35612
C83×#35552
C83×#35522
C83×#35232
C83×#35182
C83×#35092
C83×#35032
C83×#35022
C83×#34952
C83×#34932
C83×#34752
C2×#556×C832
C83×#34612
C83×#34582
#6295983