Finite Group Databasebeta

← #7683866

Subgroups — #7683866

Order 512.

5110 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60009C214yesmaximal, complemented
2#59958C214yesmaximal, complemented
3#59941C212yesmaximal, complemented
4#59886C212yesmaximal, complemented
5#59761C214yesmaximal, complemented
6#59704C214yesmaximal, complemented
7#59340C212yesmaximal, complemented
8#59329C211yesmaximal, characteristic, complemented
9#59313C211yesmaximal, characteristic, complemented
10#44841C212yesmaximal, complemented
11#44831C212yesmaximal, complemented
12#44825C214yesmaximal, complemented
13#44465C214yesmaximal, complemented
14#44450C214yesmaximal, complemented
15#43462C212yesmaximal, complemented
16#43432C212yesmaximal, complemented
17#43390C214yesmaximal, complemented
18#35461C214yesmaximal, complemented
19#35357C212yesmaximal, complemented
20#34875C212yesmaximal, complemented
21C2×#2499C211yesmaximal, characteristic, complemented
22#34289C214yesmaximal, complemented
23#34277C212yesmaximal, complemented
24C2×#547C2214yes—
25C2×#538C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C2×#520C2212yes—
28C2×C4×#41C2212yes—
29C22×#117C2211yescharacteristic
30#2806C2212yescomplemented
31#2805C2212yescomplemented
32#2804C2212yescomplemented
33#2799C2212yescomplemented
34#2796C2214yes—
35#2796C2214yes—
36#2794C2212yescomplemented
37#2794C2212yescomplemented
38#2789C2212yescomplemented
39#2782C2212yescomplemented
40#2777C2214yes—
41#2777C2214yes—
42#2772C2214yes—
43#2772C2214yes—
44#2745C2214yescomplemented
45#2744C2214yescomplemented
46#2741C2214yes—
47#2741C2214yes—
48#2732C2212yescomplemented
49#2728C2212yescomplemented
50#2716C2214yes—
51#2716C2214yes—
52#2706C2214yes—
53#2706C2214yes—
54#2700C2214yes—
55#2700C2214yes—
56#2688C2214yes—
57#2688C2214yes—
58#2680C2212yescomplemented
59#2680C2212yescomplemented
60#2612C2212yescomplemented
61#2609C2214yes—
62#2609C2214yes—
63#2609C2212yescomplemented
64#2605C2214yescomplemented
65#2599C2212yes—
66#2599C2212yes—
67#2598C2212yes—
68#2598C2212yes—
69#2597C2214yes—
70#2597C2214yes—
71#2596C2214yes—
72#2596C2214yes—
73#2594C2214yes—
74#2594C2214yes—
75#2590C2214yescomplemented
76#2589C2214yescomplemented
77#2588C2214yescomplemented
78#2586C2212yescomplemented
79#2582C2211yescharacteristic, complemented
80#2579C2214yes—
81#2577C2214yescomplemented
82#2576C2214yescomplemented
83#2575C2214yescomplemented
84#2574C2214yescomplemented
85#2572C2212yescomplemented
86#2571C2211yescharacteristic, complemented
87#2570C2214yescomplemented
88#2569C2214yes—
89#2564C2214yes—
90#2557C2214yes—
91#2557C2214yes—
92#2551C2211yescharacteristic, complemented
93#2537C2211yescharacteristic, complemented
94#2534C2214yes—
95#2534C2214yes—
96#2533C2214yescomplemented
97#2533C2214yescomplemented
98#2530C2214yescomplemented
99#2528C2214yescomplemented
100#2528C2214yescomplemented
101#2527C2214yescomplemented
102#2527C2214yescomplemented
103#2524C2214yescomplemented
104#2523C2214yescomplemented
105#2520C2214yescomplemented
106#2520C2214yescomplemented
107#2520C2214yescomplemented
108#2517C2214yescomplemented
109#2515C2214yescomplemented
110#2511C2214yescomplemented
111#2510C2214yes—
112#2510C2214yes—
113#2505C2214yescomplemented
114#2505C2214yescomplemented
115#2503C2214yes—
116#2499C2214yes—
117#2499C2212yes—
118#2499C2212yes—
119#2499C2212yes—
120#2499C2214yes—
121#2499C2212yes—
122#2493C2214yes—
123#2493C2214yes—
124#2493C2214yescomplemented
125#2488C2214yes—
126#2488C2214yes—
127#2486C2214yes—
128#2484C2212yes—
129#2484C2212yes—
130#2482C2212yes—
131#2482C2212yes—
132#2481C2214yes—
133#2481C2214yes—
134#2477C2214yes—
135#2477C2214yes—
136#2477C2214yescomplemented
137#2465C2214yes—
138#2465C2214yes—
139#2465C2214yescomplemented
140#2463C2214yes—
141#2463C2214yes—
142#2450C2214yescomplemented
143#2449C2214yes—
144#2449C2214yes—
145#2444C2214yes—
146#2444C2214yes—
147#2440C2214yescomplemented
148#2438C2214yescomplemented
149#2422C2214yescomplemented
150#2419C2214yes—
151#2419C2214yes—
152#2409C2214yes—
153#2406C2212yes—
154#2406C2212yes—
155#2404C2212yes—
156#2404C2212yes—
157#2396C2212yes—
158#2396C2212yes—
159#2392C2212yes—
160#2392C2212yes—
161C2×#397C2214yes—
162#2374C2214yes—
163#2373C2214yes—
164#2373C2214yes—
165#2372C2214yes—
166#2368C2214yescomplemented
167#2368C2214yescomplemented
168#2367C2214yes—
169#2365C2214yescomplemented
170#2364C2214yes—
171#2364C2214yes—
172#2364C2214yescomplemented
173#2363C2214yes—
174#2362C2214yescomplemented
175#2360C2214yescomplemented
176#2359C2214yes—
177#2359C2214yes—
178#2359C2214yes—
179#2359C2214yescomplemented
180#2359C2214yescomplemented
181#2355C2212yescomplemented
182#2352C2214yescomplemented
183#2349C2214yes—
184D4×C4⋊C4C2212yescomplemented
185#2344C2214yes—
186#2344C2214yescomplemented
187#2343C2214yescomplemented
188#2339C2214yes—
189#2339C2214yes—
190#2329C2212yes—
191#2327C2214yescomplemented
192#2325C2212yes—
193#2325C2214yescomplemented
194#2323C2214yescomplemented
195#2322C2214yes—
196#2322C2214yescomplemented
197#2321C2214yes—
198#2313C2212yes—
199#2312C2212yes—
200C4×C22⋊Q8C2212yes—
201C4×C22⋊Q8C2214yescomplemented
202C4×#123C2214yes—
203C4×#123C2214yescomplemented
204C4×#121C2212yes—
205C4×#120C2214yes—
206C2×#391C2211yescharacteristic
207C2×#391C2211yescharacteristic
208#2290C2214yes—
209#2290C2214yes—
210#2290C2214yes—
211#2290C2214yescomplemented
212C2×#387C2214yes—
213C2×#387C2214yescomplemented
214C2×#384C2211yescharacteristic
215#2283C2212yes—
216C2×#382C2211yescharacteristic
217#2275C2214yes—
218C2×C4×C22⋊C4C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2312yes—
221C23×Q8C2311yescharacteristic
222C24×C4C2311yescharacteristic
223#547—232no—
224#538—216no—
225C2×C4⋊Q8C2314yes—
226C2×#126C2314yes—
227C2×#124C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×C22⋊Q8—44no—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2312yes—
245C2×#120C2314yes—
246#520—48no—
247C4×#41—48no—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×#117—44no—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2312yes—
270C2×#117C2312yes—
271C2×#117C2314yes—
272C2×#117C2312yes—
273C2×#117C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C42C2312yes—
285C22×C42C2314yes—
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288#401C2314yes—
289#401C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2312yes—
296#400C2312yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2312yes—
307#400C2314yes—
308#400C2314yes—
309#399C2314yes—
310#399C2312yes—
311#399C2314yes—
312#399C2312yes—
313#398C2314yes—
314#398C2314yes—
315#398C2312yes—
316#398C2312yes—
317#398C2314yes—
318#398C2314yes—
319#398C2312yes—
320#398C2312yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2312yes—
334#397C2312yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2312yes—
351#395C2314yes—
352#395C2312yes—
353#395C2312yes—
354#395C2312yes—
355#394C2312yes—
356#394C2312yes—
357#394C2314yes—
358#394C2314yes—
359#394C2312yes—
360#394C2314yes—
361#394C2312yes—
362#394C2314yes—
363#393C2314yes—
364#393C2314yes—
365#393C2314yes—
366#393C2312yes—
367#393C2312yes—
368#393C2314yes—
369#392C2312yes—
370#392C2312yes—
371#392C2314yes—
372#391C2312yes—
373#391C2312yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2312yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#391C2312yes—
389#390C2314yes—
390#390C2314yes—
391#390C2312yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#384C2314yes—
536#384C2311yescharacteristic
537#384C2311yescharacteristic
538#384C2311yescharacteristic
539#384C2311yescharacteristic
540#383C2314yes—
541#383C2312yes—
542#383C2312yes—
543#383C2314yes—
544#382C2314yes—
545#382C2314yes—
546#382C2314yes—
547#382C2312yes—
548#382C2312yes—
549#382C2314yes—
550#382C2312yes—
551#382C2312yes—
552#381C2312yes—
553#381C2312yes—
554#381C2314yes—
555#381C2314yes—
556#381C2314yes—
557#381C2314yes—
558#381C2314yes—
559#381C2314yes—
560#381C2312yes—
561#381C2312yes—
562#380C2314yes—
563#380C2314yes—
564#380C2312yes—
565#380C2312yes—
566#380C2314yes—
567#380C2314yes—
568#380C2314yes—
569#380C2314yes—
570#380C2314yes—
571#379C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609#376C2314yes—
610#376C2314yes—
611#376C2314yes—
612C2×#95C2314yes—
613C2×#95C2312yes—
614C2×#95C2314yes—
615C2×#95C2314yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C2×#95C2314yes—
619C2×#95C2314yes—
620C25C2411yescharacteristic
621C2×#41—216no—
622C2×#41—216no—
623C2×#41—44no—
624C2×#41—44no—
625C22×Q8—42no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2412yes—
639C23×C4—24no—
640C23×C4—42no—
641C23×C4—42no—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2411yescharacteristic
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2411yescharacteristic
659C4⋊Q8—216no—
660#126—216no—
661#124—216no—
662#123—216no—
663#123—216no—
664#123—216no—
665#123—216no—
666#123—216no—
667C22⋊Q8—28no—
668C22⋊Q8—216no—
669C22⋊Q8—216no—
670C22⋊Q8—48no—
671C22⋊Q8—48no—
672C22⋊Q8—44no—
673C22⋊Q8—48no—
674C22⋊Q8—44no—
675#121—216no—
676#121—216no—
677#121#41116yes—
678#120—216no—
679C4×Q8—44no—
680C4×Q8—44no—
681C4×Q8—44no—
682C4×Q8—48no—
683C4×D4—216no—
684C4×D4—216no—
685C4×D4—216no—
686C4×D4—216no—
687C4×D4—44no—
688C4×D4—44no—
689C4×D4—44no—
690C4×D4—48no—
691C4×D4—48no—
692C4×D4—48no—
693C4×D4—48no—
694C4×D4—48no—
695#117—44no—
696#117—44no—
697#117—44no—
698#117—44no—
699#117—48no—
700#117—48no—
701#117—48no—
702#117—44no—
703#117—44no—
704C2×C4⋊C4—216no—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—216no—
707C2×C4⋊C4—48no—
708C2×C4⋊C4—42no—
709C2×C4⋊C4—42no—
710C2×C4⋊C4—42no—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C22⋊C4—28no—
759C2×C22⋊C4—44no—
760C2×C22⋊C4—44no—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C42—28no—
797C2×C42—48no—
798C2×C42—42no—
799C2×C42—42no—
800C2×C42C2412yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2411yescharacteristic
808C2×C42C2414yes—
809C2×C42C2411yescharacteristic
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
869#95C2412yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2412yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884C24—22no—
885C24—24no—
886C24—41no—
887C24—41no—
888C24—42no—
889C24C2512yes—
890C24C2514yes—
891C24C2511yescharacteristic
892#41—432no—
893#41—432no—
894C2×Q8—28no—
895C2×Q8—28no—
896C2×Q8—24no—
897C2×Q8—24no—
898C2×Q8—24no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—42no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—88no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4C2×#41116yes—
923C2×D4C2×#4118yes—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—28no—
928C22×C4—28no—
929C22×C4—28no—
930C22×C4—28no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—28no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—44no—
946C22×C4—42no—
947C22×C4—44no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—42no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—42no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—416no—
971C22×C4C2×#4118yes—
972C22×C4H(5,𝔽2)14yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2514yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—42no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—44no—
1018C4⋊C4—41no—
1019C4⋊C4—42no—
1020C4⋊C4—41no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—44no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4C2×#4118yes—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4C2×#41116yes—
1075C42—28no—
1076C42—28no—
1077C42—24no—
1078C42—24no—
1079C42—24no—
1080C42—24no—
1081C42—28no—
1082C42—24no—
1083C42—22no—
1084C42—22no—
1085C42—42no—
1086C42—42no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C23—21no—
1098C23—21no—
1099C23—22no—
1100C23—24no—
1101C23—24no—
1102C23—24no—
1103C23—24no—
1104C23—24no—
1105C23—24no—
1106C23—24no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—24no—
1111C23—44no—
1112C23—44no—
1113C23—44no—
1114C23—84no—
1115C23—84no—
1116C23C22×#4118yes—
1117C23C22×#4114yes—
1118C23C2×H(5,𝔽2)12yes—
1119C23C2611yescharacteristic
1120Q8—48no—
1121Q8—48no—
1122Q8—84no—
1123Q8—84no—
1124Q8—84no—
1125D4—232no—
1126D4—48no—
1127D4—48no—
1128D4—48no—
1129D4—88no—
1130D4—88no—
1131C2×C4—28no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—44no—
1181C2×C4—48no—
1182C2×C4—48no—
1183C2×C4—48no—
1184C2×C4—416no—
1185C2×C4—416no—
1186C2×C4—48no—
1187C2×C4—48no—
1188C2×C4—88no—
1189C2×C4—88no—
1190C2×C4—84no—
1191C2×C4—88no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—88no—
1195C2×C4—164no—
1196C2×C4C22×#4114yes—
1197C2×C4C22×#4118yes—
1198C2×C4C22×#4114yes—
1199C2×C4C2×H(5,𝔽2)14yes—
1200C2×C4#58512yes—
1201C2×C4#58512yes—
1202C22—24no—
1203C22—24no—
1204C22—22no—
1205C22—22no—
1206C22—28no—
1207C22—28no—
1208C22—28no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—88no—
1219C22#348114yes—
1220C22C23×#4112yes—
1221C22C22×H(5,𝔽2)11yescharacteristic
1222C22C2×#58511yescharacteristic
1223C22C2×#58511yescharacteristic
1224C222−1+612yes—
1225C4—24no—
1226C4—24no—
1227C4—22no—
1228C4—22no—
1229C4—24no—
1230C4—28no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—44no—
1235C4—44no—
1236C4—44no—
1237C4—44no—
1238C4—42no—
1239C4—44no—
1240C4—42no—
1241C4—42no—
1242C4—42no—
1243C4—42no—
1244C4—42no—
1245C2—24no—
1246C2—48no—
1247C2—82no—
1248C2C2×#348111yescharacteristic
1249C2#6282011yescharacteristic
1250C2#6288611yescharacteristic
1251C2#6299112yes—
1252C2#6299512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60009C2semidirect
2. #59958C2semidirect
3. #59941C2semidirect
4. #59886C2semidirect
5. #59761C2semidirect
6. #59704C2semidirect
7. #59340C2semidirect
8. #59329C2semidirect
9. #59313C2semidirect
10. #44841C2semidirect
11. #44831C2semidirect
12. #44825C2semidirect
13. #44465C2semidirect
14. #44450C2semidirect
15. #43462C2semidirect
16. #43432C2semidirect
17. #43390C2semidirect
18. #35461C2semidirect
19. #35357C2semidirect
20. #34875C2semidirect
21. C2×#2499C2semidirect
22. #34289C2semidirect
23. #34277C2semidirect
30. #2806C22semidirect
31. #2805C22semidirect
32. #2804C22semidirect
33. #2799C22semidirect
36. #2794C22semidirect
37. #2794C22semidirect
38. #2789C22semidirect
39. #2782C22semidirect
44. #2745C22semidirect
45. #2744C22semidirect
48. #2732C22semidirect
49. #2728C22semidirect
58. #2680C22semidirect
59. #2680C22semidirect
60. #2612C22semidirect
63. #2609C22semidirect
64. #2605C22semidirect
75. #2590C22semidirect
76. #2589C22semidirect
77. #2588C22semidirect
78. #2586C22semidirect
79. #2582C22semidirect
81. #2577C22semidirect
82. #2576C22semidirect
83. #2575C22semidirect
84. #2574C22semidirect
85. #2572C22semidirect
86. #2571C22semidirect
87. #2570C22semidirect
92. #2551C22semidirect
93. #2537C22semidirect
96. #2533C22semidirect
97. #2533C22semidirect
98. #2530C22semidirect
99. #2528C22semidirect
100. #2528C22semidirect
101. #2527C22semidirect
102. #2527C22semidirect
103. #2524C22semidirect
104. #2523C22semidirect
105. #2520C22semidirect
106. #2520C22semidirect
107. #2520C22semidirect
108. #2517C22semidirect
109. #2515C22semidirect
110. #2511C22semidirect
113. #2505C22semidirect
114. #2505C22semidirect
124. #2493C22semidirect
136. #2477C22semidirect
139. #2465C22semidirect
142. #2450C22semidirect
147. #2440C22semidirect
148. #2438C22semidirect
149. #2422C22semidirect
166. #2368C22semidirect
167. #2368C22semidirect
169. #2365C22semidirect
172. #2364C22semidirect
174. #2362C22semidirect
175. #2360C22semidirect
179. #2359C22semidirect
180. #2359C22semidirect
181. #2355C22semidirect
182. #2352C22semidirect
184. D4×C4⋊C4C22semidirect
186. #2344C22semidirect
187. #2343C22semidirect
191. #2327C22semidirect
193. #2325C22semidirect
194. #2323C22semidirect
196. #2322C22semidirect
201. C4×C22⋊Q8C22semidirect
203. C4×#123C22semidirect
211. #2290C22semidirect
213. C2×#387C22semidirect

Maximal subgroups

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

subgroupindex
#600092
#599582
#599412
#598862
#597612
#597042
#593402
#593292
#593132
#448412
#448312
#448252
#444652
#444502
#434622
#434322
#433902
#354612
#353572
#348752
C2×#24992
#342892
#342772