Finite Group Databasebeta

← #7658893

Subgroups — #7658893

Order 512.

4330 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42396C212yesmaximal, complemented
2#42352C214yesmaximal, complemented
3#42078C214yesmaximal, complemented
4#41979C212yesmaximal, complemented
5#41969C214yesmaximal, complemented
6#41710C214yesmaximal, complemented
7#41695C214yesmaximal, complemented
8#41025C214yesmaximal, complemented
9#41014C214yesmaximal, complemented
10#40655C212yesmaximal, complemented
11#40652C212yesmaximal, complemented
12#37610C212yesmaximal, complemented
13#37607C211yesmaximal, characteristic, complemented
14#37600C212yesmaximal, complemented
15#37600C212yesmaximal, complemented
16#37564C211yesmaximal, characteristic, complemented
17#37539C211yesmaximal, characteristic, complemented
18#36695C212yesmaximal, complemented
19#36687C211yesmaximal, characteristic
20#36081C212yesmaximal, complemented
21#35943C212yesmaximal, complemented
22#35925C212yesmaximal, complemented
23#35775C214yesmaximal, complemented
24#35690C212yesmaximal, complemented
25#34239C211yesmaximal, characteristic, complemented
26#34232C211yesmaximal, characteristic, complemented
27#34227C211yesmaximal, characteristic, complemented
28C2×#532C2211yescharacteristic
29C2×#529C2211yescharacteristic
30C22×#125C2211yescharacteristic
31#2845C2212yes—
32#2845C2212yes—
33#2837C2214yes—
34#2837C2214yes—
35#2831C2214yes—
36#2831C2214yes—
37#2829C2214yes—
38#2829C2214yes—
39#2822C2212yes—
40#2821C2212yes—
41#2820C2211yescharacteristic
42#2820C2211yescharacteristic
43#2820C2212yes—
44#2820C2212yes—
45#2820C2212yes—
46#2819C2211yescharacteristic
47#2819C2211yescharacteristic
48#2818C2212yes—
49#2816C2212yes—
50#2815C2212yes—
51#2813C2214yes—
52#2803C2214yes—
53#2803C2214yes—
54#2802C2214yes—
55#2800C2214yes—
56#2796C2214yes—
57#2794C2214yes—
58#2786C2214yes—
59#2783C2214yes—
60#2777C2214yes—
61#2773C2214yes—
62#2767C2214yes—
63#2761C2214yes—
64#2752C2214yes—
65#2752C2214yes—
66#2749C2214yes—
67#2743C2214yes—
68#2727C2214yes—
69#2726C2214yes—
70#2721C2214yes—
71#2706C2214yes—
72#2705C2214yes—
73#2705C2214yes—
74#2695C2214yes—
75#2694C2214yes—
76#2667C2212yes—
77#2667C2214yes—
78#2667C2212yes—
79#2667C2214yes—
80#2667C2214yes—
81#2667C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2664C2214yes—
85#2664C2214yes—
86#2664C2214yes—
87#2660C2212yes—
88#2654C2214yes—
89#2654C2214yes—
90#2652C2214yes—
91#2652C2214yes—
92#2651C2214yes—
93#2651C2214yes—
94#2651C2214yes—
95#2651C2214yes—
96#2641C2212yes—
97#2637C2214yes—
98#2637C2214yes—
99#2634C2212yes—
100#2633C2212yes—
101#2633C2214yes—
102#2630C2214yes—
103#2630C2214yes—
104#2623C2212yes—
105#2623C2212yes—
106#2618C2214yes—
107#2611C2214yes—
108#2609C2214yes—
109#2606C2214yes—
110#2606C2212yes—
111#2606C2214yes—
112#2606C2212yes—
113#2602C2214yes—
114#2601C2214yes—
115#2600C2214yes—
116#2598C2214yes—
117#2591C2212yes—
118#2590C2214yes—
119#2583C2212yes—
120#2579C2212yes—
121#2579C2212yes—
122#2577C2214yes—
123#2577C2214yes—
124#2574C2214yes—
125#2574C2214yes—
126#2573C2214yes—
127#2570C2214yes—
128#2566C2212yes—
129#2566C2212yes—
130#2558C2214yes—
131#2554C2214yes—
132#2554C2214yes—
133#2553C2214yes—
134#2553C2214yes—
135#2553C2214yes—
136#2525C2214yes—
137#2525C2214yes—
138#2524C2214yes—
139#2522C2214yes—
140#2522C2214yes—
141#2522C2214yes—
142#2519C2214yes—
143#2519C2214yes—
144#2517C2214yes—
145#2517C2214yes—
146#2516C2214yes—
147#2515C2214yes—
148#2515C2214yes—
149#2515C2214yes—
150#2508C2214yes—
151#2505C2214yes—
152#2504C2212yes—
153#2501C2212yes—
154#2485C2214yes—
155#2479C2214yes—
156#2478C2214yes—
157#2471C2214yes—
158#2471C2214yes—
159#2468C2214yes—
160#2468C2214yes—
161#2468C2214yes—
162#2467C2214yes—
163#2466C2214yes—
164#2466C2214yes—
165#2466C2214yes—
166#2462C2214yes—
167#2462C2214yes—
168#2460C2214yes—
169#2457C2214yes—
170#2455C2214yes—
171#2454C2214yes—
172#2441C2214yes—
173#2419C2214yes—
174#2406C2212yes—
175#2406C2212yes—
176#2398C2212yes—
177#2397C2212yes—
178#2396C2214yes—
179#2396C2214yes—
180#2395C2214yes—
181#2395C2214yes—
182#2392C2214yes—
183#2392C2214yes—
184#2392C2214yes—
185#2388C2212yes—
186#2388C2212yes—
187#2374C2214yes—
188#2373C2214yes—
189#2373C2214yes—
190#2371C2212yes—
191#2371C2212yes—
192#2370C2212yes—
193#2370C2212yes—
194#2366C2212yes—
195#2365C2212yes—
196#2363C2214yes—
197#2359C2214yes—
198#2357C2212yes—
199#2353C2212yes—
200#2353C2212yes—
201#2353C2212yes—
202#2349C2214yes—
203#2347C2212yes—
204#2345C2212yes—
205#2344C2214yes—
206#2344C2212yes—
207#2343C2214yes—
208#2343C2212yes—
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2339C2211yescharacteristic
212#2339C2211yescharacteristic
213#2336C2214yes—
214#2333C2214yes—
215#2324C2212yes—
216#2323C2212yes—
217#2320C2211yescharacteristic
218#2319C2211yescharacteristic
219#2319C2212yes—
220#2313C2212yes—
221C4×#125C2212yes—
222C4×#125C2212yes—
223C4×#125C2212yes—
224C4×#124C2212yes—
225C4×#124C2212yes—
226C4×#124C2212yes—
227#2283C2211yescharacteristic
228#2283C2211yescharacteristic
229#2283C2211yescharacteristic
230#2276C2211yescharacteristic
231#2275C2211yescharacteristic
232#2275C2212yes—
233#2274C2212yes—
234C4×#117C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2311yescharacteristic
237#532—28no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×#127C2311yescharacteristic
240#529—28no—
241C2×#126C2312yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125—28no—
247C2×#125C2312yes—
248C2×#125C2311yescharacteristic
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2314yes—
253C2×#125C2314yes—
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#123C2312yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×C22⋊Q8C2311yescharacteristic
263C2×#121C2312yes—
264C2×#121C2311yescharacteristic
265C2×#121C2312yes—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2314yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C42C2311yescharacteristic
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#399C2312yes—
305#399C2312yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2312yes—
349#397C2312yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#395C2312yes—
383#395C2312yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2312yes—
391#394C2312yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#393C2312yes—
409#393C2312yes—
410#393C2312yes—
411#393C2312yes—
412#392C2312yes—
413#392C2312yes—
414#392C2314yes—
415#392C2314yes—
416#392C2312yes—
417#392C2312yes—
418#392C2314yes—
419#392C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2312yes—
434#390C2314yes—
435#390C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
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#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#386C2312yes—
535#386C2312yes—
536#386C2312yes—
537#386C2312yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2312yes—
555#385C2312yes—
556#385C2312yes—
557#385C2312yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#384C2312yes—
565#384C2312yes—
566#383C2312yes—
567#383C2312yes—
568#383C2314yes—
569#383C2312yes—
570#383C2312yes—
571#383C2314yes—
572#382C2311yescharacteristic
573#382C2311yescharacteristic
574#382C2312yes—
575#382C2312yes—
576#382C2312yes—
577#382C2312yes—
578#382C2314yes—
579#382C2314yes—
580#382C2314yes—
581#382C2312yes—
582#382C2314yes—
583#381C2312yes—
584#381C2314yes—
585#381C2312yes—
586#381C2312yes—
587#381C2312yes—
588#381C2312yes—
589#381C2314yes—
590#381C2312yes—
591#381C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2311yescharacteristic
600#380C2311yescharacteristic
601#380C2312yes—
602#380C2314yes—
603#380C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2311yescharacteristic
617C4×C4⋊C4C2311yescharacteristic
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2311yescharacteristic
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2311yescharacteristic
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2314yes—
630C4×C22⋊C4C2311yescharacteristic
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2311yescharacteristic
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2312yes—
651#376C2311yescharacteristic
652#376C2312yes—
653#376C2312yes—
654#376C2312yes—
655#376C2312yes—
656#376C2311yescharacteristic
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C43C2312yes—
661C2×#41—24no—
662C2×#41—24no—
663C2×#41—82no—
664C2×#41—82no—
665C22×Q8C2411yescharacteristic
666C22×Q8C2411yescharacteristic
667C22×Q8C2411yescharacteristic
668C22×D4C2411yescharacteristic
669C22×D4C2412yes—
670C22×D4C2411yescharacteristic
671C22×D4C2411yescharacteristic
672C22×D4C2412yes—
673C22×D4C2412yes—
674C22×D4C2412yes—
675C22×D4C2412yes—
676C22×D4C2414yes—
677C22×D4C2414yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2414yes—
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C4⋊Q8—24no—
690#127—24no—
691#126—28no—
692#126—48no—
693#126—84no—
694#126—84no—
695#126—84no—
696#125—28no—
697#125—28no—
698#125—28no—
699#125—28no—
700#125—24no—
701#125—84no—
702#125—84no—
703#124—24no—
704#124—24no—
705#124—24no—
706#123—28no—
707#123—48no—
708#123—84no—
709#123—84no—
710#123—84no—
711C22⋊Q8—24no—
712#121—24no—
713#121—28no—
714#121—28no—
715C4×Q8—24no—
716C4×Q8—44no—
717C4×Q8—82no—
718C4×Q8—82no—
719C4×D4—28no—
720C4×D4—24no—
721C4×D4—28no—
722C4×D4—28no—
723C4×D4—48no—
724C4×D4—44no—
725C4×D4—48no—
726C4×D4—84no—
727C4×D4—84no—
728C4×D4—84no—
729C4×D4—82no—
730C4×D4—82no—
731#117—28no—
732#117—48no—
733#117—48no—
734#117—44no—
735#117—84no—
736C2×C4⋊C4—24no—
737C2×C4⋊C4—28no—
738C2×C4⋊C4—28no—
739C2×C4⋊C4—24no—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C42#4118yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2412yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2412yes—
867#95C2414yes—
868#95C2414yes—
869#95C2412yes—
870#95C2414yes—
871#95C2411yescharacteristic
872#95C2412yes—
873#95C2412yes—
874#95C2414yes—
875#95C2411yescharacteristic
876#95C2414yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
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—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924C24C2512yes—
925C24C2512yes—
926C24C2512yes—
927C24C2511yescharacteristic
928#41—88no—
929#41—88no—
930C2×Q8—22no—
931C2×Q8—22no—
932C2×Q8—22no—
933C2×Q8—42no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×D4—24no—
937C2×D4—24no—
938C2×D4—24no—
939C2×D4—22no—
940C2×D4—24no—
941C2×D4—22no—
942C2×D4—22no—
943C2×D4—24no—
944C2×D4—42no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—42no—
949C2×D4—42no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—44no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—28no—
966C22×C4—28no—
967C22×C4—42no—
968C22×C4—44no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4C2×#4114yes—
984C22×C4C2×#4114yes—
985C22×C4C2×#4114yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2514yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2512yes—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—22no—
1022C4⋊C4—24no—
1023C4⋊C4—22no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—44no—
1042C4⋊C4—42no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
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—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—24no—
1074C22⋊C4—28no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—42no—
1080C22⋊C4—44no—
1081C22⋊C4—42no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
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—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C42—24no—
1109C42—28no—
1110C42—24no—
1111C42—28no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—44no—
1117C42—42no—
1118C42—44no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C42—44no—
1123C42—42no—
1124C42—42no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C42C2×#4114yes—
1129C42C2×#4114yes—
1130C42C2×#4114yes—
1131C42C2×#4114yes—
1132C23—22no—
1133C23—22no—
1134C23—21no—
1135C23—21no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—24no—
1140C23—24no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—24no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23C22×#4112yes—
1152C23C2611yescharacteristic
1153Q8—44no—
1154Q8—44no—
1155Q8—44no—
1156D4—48no—
1157D4—44no—
1158D4—44no—
1159D4—44no—
1160D4—416no—
1161D4—84no—
1162D4—84no—
1163D4—84no—
1164D4—84no—
1165D4—88no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—48no—
1224C2×C4—88no—
1225C2×C4—88no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4—84no—
1229C2×C4—84no—
1230C2×C4—164no—
1231C2×C4C22×#4112yes—
1232C2×C4C22×#4112yes—
1233C2×C4C22×#4112yes—
1234C2×C4C22×#4112yes—
1235C2×C4C22×#4112yes—
1236C2×C4C22×#4112yes—
1237C2×C4#58514yes—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—42no—
1242C22—42no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22C23×#4111yescharacteristic
1259C22C2×#58512yes—
1260C22H(7,𝔽2)12yes—
1261C222−1+611yescharacteristic
1262C222−1+611yescharacteristic
1263C4—24no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—42no—
1271C4—44no—
1272C4—42no—
1273C4—44no—
1274C4—44no—
1275C4—44no—
1276C4—44no—
1277C4—42no—
1278C4—44no—
1279C4—42no—
1280C4—44no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—42no—
1286C2—42no—
1287C2—82no—
1288C2—82no—
1289C2—82no—
1290C2#6268611yescharacteristic
1291C2#6285511yescharacteristic
1292C2#6286011yescharacteristic
1293C2#6304712yes—
1294C2#6305012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36687C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42396C2semidirect
2. #42352C2semidirect
3. #42078C2semidirect
4. #41979C2semidirect
5. #41969C2semidirect
6. #41710C2semidirect
7. #41695C2semidirect
8. #41025C2semidirect
9. #41014C2semidirect
10. #40655C2semidirect
11. #40652C2semidirect
12. #37610C2semidirect
13. #37607C2semidirect
14. #37600C2semidirect
15. #37600C2semidirect
16. #37564C2semidirect
17. #37539C2semidirect
18. #36695C2semidirect
20. #36081C2semidirect
21. #35943C2semidirect
22. #35925C2semidirect
23. #35775C2semidirect
24. #35690C2semidirect
25. #34239C2semidirect
26. #34232C2semidirect
27. #34227C2semidirect

Maximal subgroups

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

subgroupindex
#423962
#423522
#420782
#419792
#419692
#417102
#416952
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