Finite Group Databasebeta

← #7727002

Subgroups — #7727002

Order 512.

4320 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52062C214yesmaximal, complemented
2#52024C214yesmaximal, complemented
3#47790C214yesmaximal, complemented
4#47696C214yesmaximal, complemented
5#44465C212yesmaximal, complemented
6#43965C212yesmaximal, complemented
7#43514C212yesmaximal, complemented
8#43082C212yesmaximal, complemented
9#40235C214yesmaximal, complemented
10#38635C214yesmaximal, complemented
11#38397C214yesmaximal, complemented
12#37959C212yesmaximal, complemented
13#37950C212yesmaximal
14#37896C212yesmaximal, complemented
15#37885C212yesmaximal, complemented
16#37562C211yesmaximal, characteristic, complemented
17#37028C212yesmaximal, complemented
18#37026C212yesmaximal, complemented
19#36343C214yesmaximal, complemented
20#35510C212yesmaximal, complemented
21#35494C212yesmaximal, complemented
22#35247C211yesmaximal, characteristic, complemented
23#35118C211yesmaximal, characteristic
24C2×#2599C211yesmaximal, characteristic, complemented
25#34401C211yesmaximal, characteristic, complemented
26#34196C211yesmaximal, characteristic, complemented
27#34048C211yesmaximal, characteristic, complemented
28C2×#529C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2865C2214yescomplemented
32#2863C2214yescomplemented
33#2855C2212yes—
34#2854C2212yes—
35#2853C2212yes—
36#2849C2212yes—
37#2843C2214yescomplemented
38#2809C2214yescomplemented
39#2808C2214yes—
40#2796C2214yes—
41#2793C2214yes—
42#2793C2214yescomplemented
43#2790C2214yescomplemented
44#2789C2214yescomplemented
45#2788C2214yes—
46#2787C2214yes—
47#2785C2214yes—
48#2783C2214yescomplemented
49#2781C2214yes—
50#2781C2214yes—
51#2780C2214yes—
52#2777C2214yes—
53#2775C2214yes—
54#2774C2214yescomplemented
55#2773C2214yes—
56#2772C2214yes—
57#2770C2214yes—
58#2769C2214yescomplemented
59#2768C2214yes—
60#2767C2214yescomplemented
61#2766C2214yescomplemented
62#2762C2214yescomplemented
63#2762C2214yescomplemented
64#2761C2214yescomplemented
65#2759C2214yes—
66#2759C2214yes—
67#2758C2214yescomplemented
68#2756C2214yes—
69#2754C2214yes—
70#2750C2214yes—
71#2745C2214yescomplemented
72#2744C2214yescomplemented
73#2741C2214yes—
74#2721C2214yes—
75#2715C2214yes—
76#2700C2214yes—
77#2690C2214yescomplemented
78#2666C2214yescomplemented
79#2666C2214yescomplemented
80#2659C2212yes—
81#2652C2214yes—
82#2649C2214yes—
83#2646C2212yes—
84#2637C2212yescomplemented
85#2637C2212yescomplemented
86#2627C2211yescharacteristic
87#2626C2211yescharacteristic
88#2618C2211yescharacteristic
89#2617C2211yescharacteristic
90#2612C2214yescomplemented
91#2611C2212yes—
92#2610C2212yes—
93#2610C2214yes—
94#2609C2214yes—
95#2606C2212yescomplemented
96#2605C2214yescomplemented
97#2605C2212yescomplemented
98#2601C2214yes—
99#2599C2214yes—
100#2599C2212yes—
101#2599C2212yes—
102#2599C2214yes—
103#2599C2212yes—
104#2599C2212yes—
105#2599C2212yes—
106#2599C2214yescomplemented
107#2598C2212yes—
108#2597C2214yes—
109#2597C2214yes—
110#2597C2214yescomplemented
111#2596C2214yes—
112#2594C2214yes—
113#2594C2214yescomplemented
114#2594C2214yescomplemented
115#2593C2214yes—
116#2592C2214yes—
117#2592C2211yescharacteristic, complemented
118#2592C2211yescharacteristic, complemented
119#2589C2214yes—
120#2588C2214yescomplemented
121#2588C2214yescomplemented
122#2587C2214yes—
123#2585C2214yescomplemented
124#2585C2214yescomplemented
125#2584C2211yescharacteristic, complemented
126#2584C2211yescharacteristic, complemented
127#2582C2212yescomplemented
128#2576C2214yes—
129#2574C2214yescomplemented
130#2574C2214yescomplemented
131#2573C2214yescomplemented
132#2569C2212yes—
133#2560C2214yes—
134#2549C2212yes—
135#2538C2212yescomplemented
136#2534C2214yes—
137#2532C2214yes—
138#2532C2214yes—
139#2532C2214yescomplemented
140#2532C2214yescomplemented
141#2530C2214yescomplemented
142#2529C2214yes—
143#2529C2214yes—
144#2528C2214yescomplemented
145#2528C2214yescomplemented
146#2528C2214yescomplemented
147#2528C2214yescomplemented
148#2525C2214yes—
149#2525C2214yescomplemented
150#2524C2214yescomplemented
151#2524C2214yescomplemented
152#2520C2214yescomplemented
153#2519C2214yes—
154#2510C2214yes—
155#2510C2214yes—
156#2508C2214yescomplemented
157#2503C2214yes—
158#2493C2214yes—
159#2493C2214yes—
160#2488C2214yes—
161#2486C2212yes—
162#2482C2214yes—
163#2480C2214yes—
164#2475C2214yescomplemented
165#2474C2214yes—
166#2473C2214yes—
167#2472C2214yes—
168#2469C2214yes—
169#2462C2214yescomplemented
170#2438C2214yes—
171#2438C2214yescomplemented
172#2419C2214yes—
173#2413C2214yes—
174#2413C2214yes—
175#2409C2212yes—
176C2×#398C2211yescharacteristic
177C2×#397C2211yescharacteristic
178C2×#395C2211yescharacteristic
179C2×#393C2211yescharacteristic
180#2383C2214yescomplemented
181#2368C2214yes—
182#2359C2214yes—
183#2359C2214yes—
184#2355C2212yescomplemented
185#2355C2212yescomplemented
186#2355C2212yescomplemented
187#2353C2212yes—
188#2352C2214yes—
189Q8×C4⋊C4C2212yescomplemented
190#2349C2212yes—
191#2347C2212yescomplemented
192#2344C2212yes—
193#2344C2214yes—
194#2343C2214yes—
195#2343C2212yescomplemented
196Q8×C22⋊C4C2212yes—
197#2337C2214yes—
198#2337C2212yescomplemented
199#2336C2212yescomplemented
200#2334C2214yes—
201#2329C2212yes—
202#2325C2212yes—
203#2323C2214yescomplemented
204#2322C2212yes—
205#2321C2212yes—
206#2320C2214yescomplemented
207#2320C2212yescomplemented
208#2320C2212yescomplemented
209#2318C2212yescomplemented
210#2314C2214yes—
211#2314C2214yes—
212#2313C2212yes—
213#2313C2212yes—
214#2312C2212yes—
215#2312C2212yes—
216C4×#125C2214yescomplemented
217#2298C2212yes—
218#2298C2212yes—
219#2298C2212yes—
220#2298C2212yes—
221#2298C2214yescomplemented
222C2×#388C2212yes—
223C2×#387C2212yes—
224C2×#387C2212yes—
225C2×#385C2212yes—
226#2285C2211yescharacteristic
227#2285C2211yescharacteristic
228#2285C2212yes—
229#2283C2211yescharacteristic
230#2283C2212yes—
231C2×#383C2211yescharacteristic
232#2280C2212yes—
233#2276C2212yescomplemented
234C4×#117C2212yes—
235C23×Q8C2311yescharacteristic
236C24×C4C2311yescharacteristic
237#529—28no—
238C2×#126C2312yes—
239C2×#126C2314yes—
240C2×#125C2311yescharacteristic
241C2×#125C2314yes—
242C2×#124C2311yescharacteristic
243C2×#124C2314yes—
244C2×#123C2312yes—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×#121C2311yescharacteristic
251C2×#120C2312yes—
252C2×C4×Q8—28no—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2314yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×#117—28no—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C2×#117C2312yes—
273C2×#117C2312yes—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C42C2311yescharacteristic
285C22×C42C2312yes—
286C22×C42C2311yescharacteristic
287#401C2314yes—
288#401C2314yes—
289#401C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2312yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2312yes—
320#398C2312yes—
321#398C2312yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2312yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2312yes—
341#397C2312yes—
342#397C2312yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2312yes—
347#397C2312yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2312yes—
365#395C2312yes—
366#395C2314yes—
367#395C2314yes—
368#395C2312yes—
369#395C2314yes—
370#395C2312yes—
371#395C2312yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2312yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2312yes—
382#393C2312yes—
383#393C2312yes—
384#393C2312yes—
385#393C2312yes—
386#392C2312yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2312yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#390C2314yes—
402#390C2314yes—
403#390C2312yes—
404#390C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
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#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2312yes—
536#386C2312yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2312yes—
547#385C2312yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#384C2312yes—
560#384C2312yes—
561#384C2312yes—
562#384C2312yes—
563#383C2314yes—
564#383C2312yes—
565#383C2312yes—
566#383C2314yes—
567#383C2312yes—
568#383C2312yes—
569#383C2314yes—
570#383C2314yes—
571#383C2312yes—
572#383C2312yes—
573#383C2314yes—
574#382C2314yes—
575#382C2312yes—
576#382C2312yes—
577#382C2314yes—
578#382C2314yes—
579#382C2314yes—
580#382C2312yes—
581#382C2314yes—
582#382C2314yes—
583#382C2312yes—
584#382C2312yes—
585#382C2312yes—
586#381C2314yes—
587#381C2314yes—
588#381C2312yes—
589#381C2312yes—
590#381C2312yes—
591#381C2314yes—
592#381C2314yes—
593#380C2312yes—
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2311yescharacteristic
605#380C2311yescharacteristic
606#379C2314yes—
607#379C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2311yescharacteristic
622C4×C4⋊C4C2311yescharacteristic
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2311yescharacteristic
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2311yescharacteristic
631C4×C4⋊C4C2312yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2314yes—
644#376C2312yes—
645#376C2312yes—
646#376C2314yes—
647#376C2314yes—
648#376C2312yes—
649#376C2312yes—
650C2×#95C2311yescharacteristic
651C2×#95C2312yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2311yescharacteristic
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C43C2312yes—
660C43C2312yes—
661C25C2411yescharacteristic
662C22×Q8—24no—
663C22×Q8—44no—
664C22×Q8C2411yescharacteristic
665C22×Q8C2412yes—
666C22×Q8C2411yescharacteristic
667C22×Q8C2411yescharacteristic
668C22×Q8C2414yes—
669C22×D4C2412yes—
670C22×D4C2411yescharacteristic
671C22×D4C2414yes—
672C23×C4—24no—
673C23×C4—42no—
674C23×C4—42no—
675C23×C4C2412yes—
676C23×C4C2411yescharacteristic
677C23×C4C2412yes—
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C23×C4C2412yes—
681C23×C4C2412yes—
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2414yes—
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689#126—28no—
690#126—48no—
691#125—24no—
692#125—48no—
693#124—24no—
694#124—48no—
695#123—28no—
696#123—44no—
697#123—48no—
698C22⋊Q8—24no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701#121—24no—
702#120—44no—
703C4×Q8—28no—
704C4×Q8—28no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—48no—
711C4×D4—28no—
712C4×D4—24no—
713C4×D4—48no—
714#117—28no—
715#117—28no—
716#117—28no—
717#117—28no—
718#117—28no—
719#117—48no—
720#117—44no—
721#117—48no—
722#117—44no—
723C2×C4⋊C4—24no—
724C2×C4⋊C4—24no—
725C2×C4⋊C4—24no—
726C2×C4⋊C4—28no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4—44no—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C22⋊C4—24no—
784C2×C22⋊C4—24no—
785C2×C22⋊C4—44no—
786C2×C22⋊C4—44no—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C42—24no—
822C2×C42—28no—
823C2×C42#4118yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2412yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920C24—22no—
921C24—22no—
922C24—22no—
923C24—42no—
924C24—42no—
925C24C2512yes—
926C24C2512yes—
927C24C2511yescharacteristic
928C2×Q8—22no—
929C2×Q8—24no—
930C2×Q8—22no—
931C2×Q8—22no—
932C2×Q8—24no—
933C2×Q8—24no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×Q8—42no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×Q8—44no—
940C2×Q8—416no—
941C2×D4—24no—
942C2×D4—24no—
943C2×D4—24no—
944C2×D4—22no—
945C2×D4—42no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—22no—
954C22×C4—24no—
955C22×C4—22no—
956C22×C4—24no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—42no—
980C22×C4—44no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—416no—
984C22×C4C2×#4114yes—
985C22×C4C2×#4114yes—
986C22×C4C2×#4114yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2511yescharacteristic
1010C22×C4C2512yes—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—22no—
1025C4⋊C4—24no—
1026C4⋊C4—22no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—24no—
1068C22⋊C4—28no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—24no—
1074C22⋊C4—24no—
1075C22⋊C4—24no—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C42—24no—
1100C42—24no—
1101C42—24no—
1102C42—24no—
1103C42—24no—
1104C42—24no—
1105C42—24no—
1106C42—28no—
1107C42—44no—
1108C42—44no—
1109C42—44no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C42—44no—
1115C42—44no—
1116C42—44no—
1117C42—44no—
1118C42—44no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C42C2×#4114yes—
1123C42C2×#4114yes—
1124C42C2×#4114yes—
1125C42C2×#4114yes—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—24no—
1137C23—24no—
1138C23—48no—
1139C23—44no—
1140C23—82no—
1141C23—82no—
1142C23—84no—
1143C23C22×#4112yes—
1144C23#58512yes—
1145C23#58512yes—
1146C23C2611yescharacteristic
1147Q8—28no—
1148Q8—48no—
1149Q8—44no—
1150Q8—82no—
1151Q8—164no—
1152D4—48no—
1153D4—82no—
1154D4—164no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—28no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—48no—
1216C2×C4—48no—
1217C2×C4—48no—
1218C2×C4—48no—
1219C2×C4—44no—
1220C2×C4—84no—
1221C2×C4—82no—
1222C2×C4—82no—
1223C2×C4—84no—
1224C2×C4—84no—
1225C2×C4—88no—
1226C2×C4C22×#4112yes—
1227C2×C4C22×#4112yes—
1228C2×C4C22×#4112yes—
1229C2×C4C22×#4112yes—
1230C2×C4C22×#4112yes—
1231C2×C4C22×#4112yes—
1232C2×C4#58514yes—
1233C22—22no—
1234C22—22no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—88no—
1248C22#349314yes—
1249C22C23×#4111yescharacteristic
1250C22C2×#58511yescharacteristic
1251C22C2×#58511yescharacteristic
1252C22C2×#58512yes—
1253C222−1+612yes—
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—22no—
1258C4—24no—
1259C4—22no—
1260C4—22no—
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—44no—
1271C4—44no—
1272C4—44no—
1273C4—44no—
1274C4—44no—
1275C4—44no—
1276C4—44no—
1277C4—44no—
1278C2—24no—
1279C2—82no—
1280C2—82no—
1281C2C2×#349311yescharacteristic
1282C2#6281411yescharacteristic
1283C2#6286011yescharacteristic
1284C2#6290712yes—
1285C2#6296412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2617C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52062C2semidirect
2. #52024C2semidirect
3. #47790C2semidirect
4. #47696C2semidirect
5. #44465C2semidirect
6. #43965C2semidirect
7. #43514C2semidirect
8. #43082C2semidirect
9. #40235C2semidirect
10. #38635C2semidirect
11. #38397C2semidirect
12. #37959C2semidirect
14. #37896C2semidirect
15. #37885C2semidirect
16. #37562C2semidirect
17. #37028C2semidirect
18. #37026C2semidirect
19. #36343C2semidirect
20. #35510C2semidirect
21. #35494C2semidirect
22. #35247C2semidirect
24. C2×#2599C2semidirect
25. #34401C2semidirect
26. #34196C2semidirect
27. #34048C2semidirect
31. #2865C22semidirect
32. #2863C22semidirect
37. #2843C22semidirect
38. #2809C22semidirect
42. #2793C22semidirect
43. #2790C22semidirect
44. #2789C22semidirect
48. #2783C22semidirect
54. #2774C22semidirect
58. #2769C22semidirect
60. #2767C22semidirect
61. #2766C22semidirect
62. #2762C22semidirect
63. #2762C22semidirect
64. #2761C22semidirect
67. #2758C22semidirect
71. #2745C22semidirect
72. #2744C22semidirect
77. #2690C22semidirect
78. #2666C22semidirect
79. #2666C22semidirect
84. #2637C22semidirect
85. #2637C22semidirect
90. #2612C22semidirect
95. #2606C22semidirect
96. #2605C22semidirect
97. #2605C22semidirect
106. #2599C22semidirect
110. #2597C22semidirect
113. #2594C22semidirect
114. #2594C22semidirect
117. #2592C22semidirect
118. #2592C22semidirect
120. #2588C22semidirect
121. #2588C22semidirect
123. #2585C22semidirect
124. #2585C22semidirect
125. #2584C22semidirect
126. #2584C22semidirect
127. #2582C22semidirect
129. #2574C22semidirect
130. #2574C22semidirect
131. #2573C22semidirect
135. #2538C22semidirect
139. #2532C22semidirect
140. #2532C22semidirect
141. #2530C22semidirect
144. #2528C22semidirect
145. #2528C22semidirect
146. #2528C22semidirect
147. #2528C22semidirect
149. #2525C22semidirect
150. #2524C22semidirect
151. #2524C22semidirect
152. #2520C22semidirect
156. #2508C22semidirect
164. #2475C22semidirect
169. #2462C22semidirect
171. #2438C22semidirect
180. #2383C22semidirect
184. #2355C22semidirect
185. #2355C22semidirect
186. #2355C22semidirect
189. Q8×C4⋊C4C22semidirect
191. #2347C22semidirect
195. #2343C22semidirect
198. #2337C22semidirect
199. #2336C22semidirect
203. #2323C22semidirect
206. #2320C22semidirect
207. #2320C22semidirect
208. #2320C22semidirect
209. #2318C22semidirect
216. C4×#125C22semidirect
221. #2298C22semidirect
233. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#520622
#520242
#477902
#476962
#444652
#439652
#435142
#430822
#402352
#386352
#383972
#379592
#379502
#378962
#378852
#375622
#370282
#370262
#363432
#355102
#354942
#352472
#351182
C2×#25992
#344012
#341962
#340482