Finite Group Databasebeta

← #9912962

Subgroups — #9912962

Order 512.

4613 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58489C214yesmaximal, complemented
2#58010C214yesmaximal, complemented
3#56306C214yesmaximal, complemented
4#55379C214yesmaximal, complemented
5#54928C214yesmaximal, complemented
6#54928C214yesmaximal, complemented
7#53872C214yesmaximal, complemented
8#53521C212yesmaximal, complemented
9#53348C212yesmaximal, complemented
10#53180C214yesmaximal, complemented
11#51930C212yesmaximal, complemented
12#51930C212yesmaximal, complemented
13#51794C212yesmaximal, complemented
14#50638C214yesmaximal, complemented
15#47836C212yesmaximal, complemented
16#46318C212yesmaximal, complemented
17#46240C211yesmaximal, characteristic, complemented
18#46172C214yesmaximal, complemented
19#45957C212yesmaximal, complemented
20#38956C211yesmaximal, characteristic, complemented
21#38089C212yesmaximal, complemented
22#37425C212yesmaximal, complemented
23#37216C211yesmaximal, characteristic, complemented
24C2×#553C2212yes—
25C2×#550C2211yescharacteristic
26C2×#547C2211yescharacteristic
27C2×#539C2212yes—
28#2864C2212yes—
29#2860C2212yes—
30#2858C2211yescharacteristic
31#2856C2212yes—
32#2854C2214yes—
33#2851C2214yes—
34#2845C2212yes—
35#2837C2214yes—
36#2837C2214yes—
37#2829C2214yes—
38#2828C2214yes—
39#2827C2214yes—
40#2826C2212yes—
41#2813C2214yes—
42#2813C2214yes—
43#2813C2214yes—
44#2809C2211yescharacteristic
45#2809C2212yes—
46#2809C2212yes—
47#2809C2212yes—
48#2790C2214yes—
49#2790C2214yes—
50#2782C2212yes—
51#2780C2214yes—
52#2780C2214yes—
53#2780C2214yes—
54#2780C2214yes—
55#2780C2214yes—
56#2777C2214yes—
57#2773C2214yes—
58#2770C2214yes—
59#2768C2214yes—
60#2768C2214yes—
61#2753C2214yes—
62#2753C2214yes—
63#2748C2214yes—
64#2748C2214yes—
65#2748C2212yes—
66#2733C2211yescharacteristic
67#2733C2212yes—
68#2729C2214yes—
69#2727C2214yes—
70#2727C2212yes—
71#2727C2212yes—
72#2727C2212yes—
73#2726C2212yes—
74#2724C2212yes—
75#2724C2214yes—
76#2723C2214yes—
77#2718C2214yes—
78#2718C2214yes—
79#2718C2214yes—
80#2715C2214yes—
81#2714C2214yes—
82#2714C2214yes—
83#2714C2214yes—
84#2711C2214yes—
85#2711C2214yes—
86#2711C2214yes—
87#2710C2214yes—
88#2708C2214yes—
89#2706C2214yes—
90#2706C2214yes—
91#2706C2214yes—
92#2706C2214yes—
93#2705C2214yes—
94#2705C2214yes—
95#2704C2214yes—
96#2703C2214yes—
97#2703C2214yes—
98#2703C2214yes—
99#2703C2214yes—
100#2701C2214yes—
101#2695C2214yes—
102#2694C2214yes—
103#2694C2214yes—
104#2691C2214yes—
105#2691C2214yes—
106#2682C2214yes—
107#2682C2214yes—
108#2682C2212yes—
109#2682C2212yes—
110#2682C2212yes—
111#2682C2212yes—
112#2682C2214yes—
113#2682C2214yes—
114#2682C2214yes—
115#2676C2214yes—
116#2675C2212yes—
117#2675C2214yes—
118#2675C2212yes—
119#2675C2214yes—
120#2673C2214yes—
121#2673C2214yes—
122#2673C2214yes—
123#2673C2214yes—
124#2673C2214yes—
125#2673C2214yes—
126#2672C2214yes—
127#2671C2214yes—
128#2671C2214yes—
129#2671C2214yes—
130#2671C2214yes—
131#2671C2214yes—
132#2671C2214yes—
133#2671C2214yes—
134#2671C2214yes—
135#2661C2214yes—
136#2661C2214yes—
137#2656C2214yes—
138#2647C2214yes—
139#2641C2212yes—
140#2635C2212yes—
141#2633C2214yes—
142#2630C2214yes—
143#2630C2214yes—
144#2629C2214yes—
145#2619C2212yes—
146#2619C2212yes—
147#2615C2212yes—
148#2612C2214yes—
149#2603C2214yes—
150#2603C2214yes—
151#2598C2214yes—
152#2589C2214yes—
153#2587C2214yes—
154#2579C2212yes—
155#2568C2211yescharacteristic
156#2565C2212yes—
157#2553C2214yes—
158#2553C2214yes—
159#2541C2211yescharacteristic
160#2541C2212yes—
161#2537C2214yes—
162#2531C2214yes—
163#2531C2214yes—
164#2526C2214yes—
165#2522C2214yes—
166#2518C2214yes—
167#2518C2214yes—
168#2505C2214yes—
169#2505C2214yes—
170#2504C2212yes—
171#2501C2212yes—
172#2500C2212yes—
173#2476C2214yes—
174#2476C2214yes—
175#2473C2214yes—
176#2467C2214yes—
177#2467C2214yes—
178#2464C2214yes—
179#2464C2214yes—
180#2464C2214yes—
181#2464C2214yes—
182#2464C2214yes—
183#2455C2212yes—
184#2455C2214yes—
185#2455C2214yes—
186#2450C2214yes—
187#2443C2214yes—
188#2443C2214yes—
189#2442C2214yes—
190#2442C2214yes—
191#2441C2214yes—
192#2441C2214yes—
193#2431C2214yes—
194#2431C2212yes—
195#2431C2212yes—
196#2431C2212yes—
197#2428C2214yes—
198#2428C2214yes—
199#2427C2214yes—
200#2425C2214yes—
201#2425C2214yes—
202#2425C2214yes—
203#2416C2214yes—
204#2407C2214yes—
205#2406C2212yes—
206#2383C2214yes—
207#2379C2212yes—
208#2379C2211yescharacteristic
209#2379C2211yescharacteristic
210#2378C2212yes—
211#2372C2212yes—
212#2326C2212yes—
213#2311C2212yes—
214#2311C2212yes—
215C4×#124C2211yescharacteristic
216#2297C2212yes—
217#2293C2211yescharacteristic
218#2290C2212yes—
219C22×#41C2312yes—
220C22×#41C2312yes—
221#553—48no—
222#550—44no—
223#547—44no—
224#539—48no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2312yes—
228C2×#127C2312yes—
229C2×#127C2312yes—
230C2×#127C2312yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#125C2312yes—
236C2×#125C2314yes—
237C2×#125C2314yes—
238C2×#124C2312yes—
239C2×#124C2311yescharacteristic
240C2×#124C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2314yes—
256C2×#121C2312yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×D4C2312yes—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×#117C2312yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C42C2312yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#399C2312yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
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#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#395C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2312yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#393C2314yes—
401#392C2312yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2312yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2311yescharacteristic
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2311yescharacteristic
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
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#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
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#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2312yes—
529#386C2312yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#385C2312yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2312yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#384C2312yes—
580#384C2312yes—
581#384C2314yes—
582#383C2314yes—
583#382C2312yes—
584#382C2312yes—
585#382C2311yescharacteristic
586#382C2312yes—
587#382C2312yes—
588#382C2314yes—
589#382C2314yes—
590#381C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2311yescharacteristic
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614#376C2312yes—
615#376C2314yes—
616C2×#95C2314yes—
617C43C2311yescharacteristic
618C2×#41—28no—
619C2×#41—44no—
620C2×#41—44no—
621C2×#41—82no—
622C2×#41—84no—
623C22×Q8C2412yes—
624C22×Q8C2411yescharacteristic
625C22×D4C2412yes—
626C22×D4C2411yescharacteristic
627C22×D4C2412yes—
628C22×D4C2411yescharacteristic
629C22×D4C2412yes—
630C22×D4C2412yes—
631C22×D4C2412yes—
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2412yes—
638C22×D4C2411yescharacteristic
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2411yescharacteristic
648C22×D4C2414yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2414yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C4⋊Q8—42no—
662#127—44no—
663#127—42no—
664#127—82no—
665#127—82no—
666#127—82no—
667#126—216no—
668#126—84no—
669#126—84no—
670#126—84no—
671#125—48no—
672#125—44no—
673#125—84no—
674#124—28no—
675#124—24no—
676#124—84no—
677#123—48no—
678#123—48no—
679#123—48no—
680#123—48no—
681#123—84no—
682#123—84no—
683#123—84no—
684#123—84no—
685#123—84no—
686#123—84no—
687#123—84no—
688#123—84no—
689#123—84no—
690C22⋊Q8—28no—
691C22⋊Q8—48no—
692#121—44no—
693#121—44no—
694#121—44no—
695#121—44no—
696#121—44no—
697#121—44no—
698#121—44no—
699#121—48no—
700#121—84no—
701#121—84no—
702#121—84no—
703#121—84no—
704#121—84no—
705#121—84no—
706#121—84no—
707#121—84no—
708#121—84no—
709#121—84no—
710#121—84no—
711#121—84no—
712#121—84no—
713#121—84no—
714#121—84no—
715#121—84no—
716#121—84no—
717C4×Q8—42no—
718C4×D4—24no—
719C4×D4—28no—
720C4×D4—48no—
721C4×D4—48no—
722C4×D4—44no—
723C4×D4—42no—
724C4×D4—84no—
725C4×D4—84no—
726#117—44no—
727#117—82no—
728#117—82no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—44no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
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×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⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C42—82no—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839C2×C42C2412yes—
840C2×C42C2411yescharacteristic
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2412yes—
847C2×C42C2414yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
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#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890C24C2514yes—
891C24C2512yes—
892C24C2512yes—
893C24C2512yes—
894C24C2512yes—
895#41—816no—
896#41—816no—
897C2×Q8—24no—
898C2×Q8—41no—
899C2×Q8—41no—
900C2×Q8—44no—
901C2×Q82−1+414yes—
902C2×D4—22no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—22no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—41no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—41no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—44no—
937C2×D4—41no—
938C2×D4—41no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—44no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—42no—
966C2×D4—44no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—42no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2511yescharacteristic
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2511yescharacteristic
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—41no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—42no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
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—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4H(5,𝔽2)14yes—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—42no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—42no—
1085C22⋊C4—44no—
1086C22⋊C4—42no—
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—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C42—28no—
1121C42—24no—
1122C42—22no—
1123C42—22no—
1124C42—24no—
1125C42—42no—
1126C42—44no—
1127C42—42no—
1128C42—41no—
1129C42—42no—
1130C42—42no—
1131C42—44no—
1132C42—44no—
1133C42—42no—
1134C42—42no—
1135C23—24no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—24no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—24no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—24no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—22no—
1156C23—22no—
1157C23—24no—
1158C23—24no—
1159C23—22no—
1160C23—24no—
1161C23—22no—
1162C23C2611yescharacteristic
1163Q8—44no—
1164Q8—84no—
1165D4—44no—
1166D4—84no—
1167D4—84no—
1168D4—82no—
1169D4—84no—
1170D4—84no—
1171D4—84no—
1172D4—88no—
1173D4—88no—
1174D4—88no—
1175D4—88no—
1176D4—88no—
1177D4—164no—
1178D4—164no—
1179D4—164no—
1180D4—164no—
1181D4—164no—
1182D4—162no—
1183D4—164no—
1184D4—162no—
1185D4—162no—
1186D4—161no—
1187D4—161no—
1188D4—162no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—48no—
1236C2×C4—48no—
1237C2×C4—48no—
1238C2×C4—84no—
1239C2×C4—88no—
1240C2×C4—84no—
1241C2×C4—88no—
1242C2×C4—164no—
1243C2×C4—164no—
1244C2×C4—164no—
1245C2×C4—164no—
1246C2×C4—162no—
1247C2×C4C2×H(5,𝔽2)12yes—
1248C2×C4C2×H(5,𝔽2)14yes—
1249C2×C4C2×2−1+412yes—
1250C2×C4C2×2−1+414yes—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—42no—
1258C22—42no—
1259C22—44no—
1260C22—42no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—42no—
1269C22—42no—
1270C22—44no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—44no—
1277C22—42no—
1278C22C22×H(5,𝔽2)11yescharacteristic
1279C22C22×2−1+411yescharacteristic
1280C22H(7,𝔽2)11yescharacteristic
1281C22H(7,𝔽2)12yes—
1282C22H(7,𝔽2)12yes—
1283C4—22no—
1284C4—24no—
1285C4—24no—
1286C4—22no—
1287C4—44no—
1288C4—44no—
1289C4—44no—
1290C4—44no—
1291C4—42no—
1292C4—44no—
1293C4—44no—
1294C4—42no—
1295C4—41no—
1296C4—42no—
1297C4—44no—
1298C4—42no—
1299C4—44no—
1300C4—44no—
1301C2—82no—
1302C2—84no—
1303C2—82no—
1304C2—82no—
1305C2—82no—
1306C2#6287411yescharacteristic
1307C2#6289411yescharacteristic
1308C2#6297612yes—
1309C2#6306611yescharacteristic
1310C2#6307012yes—
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. #58489C2semidirect
2. #58010C2semidirect
3. #56306C2semidirect
4. #55379C2semidirect
5. #54928C2semidirect
6. #54928C2semidirect
7. #53872C2semidirect
8. #53521C2semidirect
9. #53348C2semidirect
10. #53180C2semidirect
11. #51930C2semidirect
12. #51930C2semidirect
13. #51794C2semidirect
14. #50638C2semidirect
15. #47836C2semidirect
16. #46318C2semidirect
17. #46240C2semidirect
18. #46172C2semidirect
19. #45957C2semidirect
20. #38956C2semidirect
21. #38089C2semidirect
22. #37425C2semidirect
23. #37216C2semidirect

Maximal subgroups

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

subgroupindex
#584892
#580102
#563062
#553792
#549282
#538722
#535212
#533482
#531802
#519302
#517942
#506382
#478362
#463182
#462402
#461722
#459572
#389562
#380892
#374252
#372162