Finite Group Databasebeta

← #8701606

Subgroups — #8701606

Order 512.

4099 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59873C212yesmaximal, complemented
2#59569C212yesmaximal, complemented
3#59299C212yesmaximal, complemented
4#59222C212yesmaximal, complemented
5#57385C214yesmaximal, complemented
6#54726C214yesmaximal, complemented
7#54245C214yesmaximal, complemented
8#52303C211yesmaximal, characteristic, complemented
9#51011C214yesmaximal, complemented
10#50976C214yesmaximal, complemented
11#50606C214yesmaximal, complemented
12#46158C211yesmaximal, characteristic, complemented
13#46158C211yesmaximal, characteristic, complemented
14#46157C211yesmaximal, characteristic, complemented
15#45178C212yesmaximal, complemented
16#44944C212yesmaximal, complemented
17#44912C212yesmaximal, complemented
18#42630C212yesmaximal, complemented
19#42501C212yesmaximal, complemented
20#42461C212yesmaximal, complemented
21#40168C212yesmaximal, complemented
22#40011C212yesmaximal, complemented
23#39907C212yesmaximal, complemented
24#37218C212yesmaximal, complemented
25#37168C212yesmaximal, complemented
26#37141C212yesmaximal, complemented
27#36464C211yesmaximal, characteristic, complemented
28#36453C211yesmaximal, characteristic, complemented
29#36290C211yesmaximal, characteristic, complemented
30#2859C2211yescharacteristic
31#2859C2211yescharacteristic
32#2859C2211yescharacteristic
33#2855C2212yes—
34#2854C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2836C2214yes—
38#2827C2214yes—
39#2826C2214yes—
40#2822C2212yes—
41#2820C2212yes—
42#2820C2212yes—
43#2810C2212yes—
44#2808C2211yescharacteristic
45#2806C2211yescharacteristic
46#2805C2212yes—
47#2805C2212yes—
48#2802C2214yes—
49#2797C2214yes—
50#2796C2214yes—
51#2796C2214yes—
52#2793C2214yes—
53#2791C2214yes—
54#2787C2214yes—
55#2786C2214yes—
56#2786C2214yes—
57#2783C2214yes—
58#2783C2212yes—
59#2781C2212yes—
60#2780C2214yes—
61#2780C2214yes—
62#2780C2214yes—
63#2773C2214yes—
64#2773C2214yes—
65#2773C2214yes—
66#2772C2214yes—
67#2771C2214yes—
68#2770C2214yes—
69#2769C2214yes—
70#2768C2214yes—
71#2767C2214yes—
72#2766C2214yes—
73#2758C2214yes—
74#2757C2214yes—
75#2757C2214yes—
76#2756C2214yes—
77#2750C2214yes—
78#2750C2214yes—
79#2749C2214yes—
80#2748C2214yes—
81#2744C2214yes—
82#2744C2212yes—
83#2739C2214yes—
84#2739C2214yes—
85#2738C2214yes—
86#2738C2214yes—
87#2732C2211yescharacteristic
88#2730C2212yes—
89#2727C2212yes—
90#2727C2212yes—
91#2726C2212yes—
92#2725C2214yes—
93#2725C2214yes—
94#2725C2214yes—
95#2720C2214yes—
96#2719C2214yes—
97#2718C2214yes—
98#2714C2214yes—
99#2711C2214yes—
100#2706C2214yes—
101#2705C2214yes—
102#2694C2214yes—
103#2694C2212yes—
104#2689C2214yes—
105#2686C2212yes—
106#2682C2211yescharacteristic
107#2655C2214yes—
108#2652C2214yes—
109#2652C2214yes—
110#2652C2214yes—
111#2651C2214yes—
112#2636C2214yes—
113#2634C2214yes—
114#2630C2214yes—
115#2629C2212yes—
116#2623C2214yes—
117#2597C2214yes—
118#2596C2214yes—
119#2594C2214yes—
120#2591C2214yes—
121#2587C2214yes—
122#2584C2212yes—
123#2584C2212yes—
124#2578C2214yes—
125#2577C2214yes—
126#2576C2214yes—
127#2573C2214yes—
128#2571C2211yescharacteristic
129#2571C2212yes—
130#2570C2212yes—
131#2570C2212yes—
132#2570C2212yes—
133#2564C2214yes—
134#2558C2214yes—
135#2558C2214yes—
136#2556C2214yes—
137#2553C2214yes—
138#2552C2211yescharacteristic
139#2538C2211yescharacteristic
140#2538C2211yescharacteristic
141#2537C2211yescharacteristic
142#2537C2211yescharacteristic
143#2535C2212yes—
144#2535C2212yes—
145#2533C2214yes—
146#2533C2214yes—
147#2533C2214yes—
148#2531C2214yes—
149#2524C2214yes—
150#2524C2214yes—
151#2522C2214yes—
152#2518C2214yes—
153#2517C2214yes—
154#2515C2214yes—
155#2509C2212yes—
156#2509C2212yes—
157#2509C2212yes—
158#2508C2212yes—
159#2507C2212yes—
160#2507C2212yes—
161#2506C2214yes—
162#2506C2212yes—
163#2506C2212yes—
164#2505C2214yes—
165#2505C2214yes—
166#2497C2212yes—
167#2497C2214yes—
168#2497C2212yes—
169#2497C2212yes—
170#2496C2212yes—
171#2496C2212yes—
172#2496C2212yes—
173#2495C2212yes—
174#2495C2214yes—
175#2495C2212yes—
176#2495C2212yes—
177#2495C2212yes—
178#2494C2212yes—
179#2494C2212yes—
180#2486C2212yes—
181#2485C2212yes—
182#2485C2212yes—
183#2485C2212yes—
184#2485C2212yes—
185#2485C2212yes—
186#2481C2214yes—
187#2481C2214yes—
188#2481C2214yes—
189#2473C2214yes—
190#2469C2214yes—
191#2466C2214yes—
192#2464C2214yes—
193#2460C2214yes—
194#2457C2214yes—
195#2454C2214yes—
196#2454C2214yes—
197#2454C2212yes—
198#2454C2212yes—
199#2449C2214yes—
200#2444C2214yes—
201#2442C2212yes—
202#2442C2212yes—
203#2442C2212yes—
204#2441C2212yes—
205#2441C2212yes—
206#2441C2212yes—
207#2441C2212yes—
208#2441C2212yes—
209#2427C2212yes—
210#2426C2212yes—
211#2422C2212yes—
212#2420C2212yes—
213#2396C2212yes—
214#2395C2212yes—
215#2392C2212yes—
216#2382C2212yes—
217#2382C2212yes—
218#2382C2212yes—
219#2373C2214yes—
220#2370C2212yes—
221#2370C2212yes—
222#2363C2212yes—
223#2363C2212yes—
224#2363C2212yes—
225#2361C2212yes—
226#2355C2211yescharacteristic
227#2354C2211yescharacteristic
228#2354C2212yes—
229#2353C2214yes—
230#2352C2212yes—
231Q8×C4⋊C4C2211yescharacteristic
232#2349C2212yes—
233D4×C4⋊C4C2211yescharacteristic
234D4×C4⋊C4C2212yes—
235D4×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2211yescharacteristic
237#2347C2212yes—
238#2345C2212yes—
239#2345C2214yes—
240#2336C2214yes—
241#2334C2214yes—
242#2324C2212yes—
243#2322C2214yes—
244#2317C2212yes—
245#2314C2212yes—
246C4×#125C2211yescharacteristic
247C4×#124C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×#123C2212yes—
252C4×#121C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255#2296C2212yes—
256C2×#389C2212yes—
257#2283C2212yes—
258C42×D4C2211yescharacteristic
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#125C2311yescharacteristic
263C2×#125C2312yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2312yes—
270C2×#125C2314yes—
271C2×#124C2311yescharacteristic
272C2×#124C2311yescharacteristic
273C2×#123C2314yes—
274C2×#123C2312yes—
275C2×#123C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2312yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×#117C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C42C2312yes—
308C22×C42C2312yes—
309#401C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2312yes—
342#399C2312yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2312yes—
382#397C2312yes—
383#397C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2312yes—
404#396C2312yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2312yes—
409#394C2314yes—
410#394C2314yes—
411#394C2312yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2312yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2312yes—
420#394C2312yes—
421#394C2312yes—
422#394C2314yes—
423#393C2312yes—
424#392C2314yes—
425#392C2312yes—
426#392C2314yes—
427#391C2311yescharacteristic
428#391C2312yes—
429#391C2312yes—
430#391C2311yescharacteristic
431#390C2314yes—
432#390C2312yes—
433#390C2311yescharacteristic
434#390C2312yes—
435#390C2314yes—
436#390C2312yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2311yescharacteristic
442#389C2311yescharacteristic
443#389C2311yescharacteristic
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2314yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#387C2312yes—
529#387C2312yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2312yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2312yes—
590#386C2312yes—
591#386C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2312yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#384C2312yes—
615#384C2311yescharacteristic
616#384C2311yescharacteristic
617#384C2312yes—
618#384C2311yescharacteristic
619#384C2314yes—
620#384C2311yescharacteristic
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#383C2314yes—
624#383C2314yes—
625#383C2314yes—
626#383C2314yes—
627#383C2314yes—
628#382C2311yescharacteristic
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2314yes—
640#382C2311yescharacteristic
641#382C2311yescharacteristic
642#381C2314yes—
643#381C2314yes—
644#381C2312yes—
645#381C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2314yes—
710C2×#95C2314yes—
711C43C2311yescharacteristic
712C22×Q8C2411yescharacteristic
713C22×Q8C2411yescharacteristic
714C22×D4C2411yescharacteristic
715C22×D4C2411yescharacteristic
716C22×D4C2411yescharacteristic
717C22×D4C2414yes—
718C22×D4C2414yes—
719C22×D4C2412yes—
720C22×D4C2412yes—
721C23×C4C2412yes—
722C23×C4C2412yes—
723C23×C4C2412yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2414yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731#126—48no—
732#126—48no—
733#126—84no—
734#125—44no—
735#125—44no—
736#125—44no—
737#125—44no—
738#125—42no—
739#125—44no—
740#125—48no—
741#125—82no—
742#125—84no—
743#124—42no—
744#124—42no—
745#123—44no—
746#123—48no—
747#123—84no—
748C22⋊Q8—44no—
749C22⋊Q8—44no—
750C22⋊Q8—82no—
751#121—28no—
752#121—28no—
753#121—44no—
754#121—44no—
755#121—82no—
756C4×Q8—42no—
757C4×Q8—42no—
758C4×Q8—82no—
759C4×D4—24no—
760C4×D4—44no—
761C4×D4—44no—
762C4×D4—42no—
763C4×D4—42no—
764C4×D4—44no—
765C4×D4—44no—
766C4×D4—42no—
767C4×D4—42no—
768C4×D4—48no—
769C4×D4—82no—
770C4×D4—84no—
771#117—44no—
772#117—44no—
773#117—44no—
774#117—44no—
775C2×C4⋊C4—44no—
776C2×C4⋊C4—48no—
777C2×C4⋊C4—44no—
778C2×C4⋊C4—82no—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C42—44no—
896C2×C42—82no—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991C24C2512yes—
992C24C2512yes—
993C24C2512yes—
994C2×Q8—22no—
995C2×Q8—22no—
996C2×Q8—41no—
997C2×Q8—41no—
998C2×Q8—41no—
999C2×Q8—41no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—22no—
1005C2×D4—22no—
1006C2×D4—41no—
1007C2×D4—41no—
1008C2×D4—41no—
1009C2×D4—42no—
1010C2×D4—42no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—42no—
1014C2×D4—44no—
1015C2×D4—42no—
1016C2×D4—41no—
1017C2×D4—44no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C2×D42−1+414yes—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C4⋊C4—22no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—22no—
1081C4⋊C4—24no—
1082C4⋊C4—22no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—22no—
1095C4⋊C4—28no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—41no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—41no—
1106C4⋊C4—41no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C22⋊C4—24no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C22⋊C4—42no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C42—22no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—22no—
1199C42—22no—
1200C42—22no—
1201C42—22no—
1202C42—22no—
1203C42—42no—
1204C42—42no—
1205C42—41no—
1206C42—42no—
1207C42—42no—
1208C42—42no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23C2×2−1+414yes—
1239C23C2611yescharacteristic
1240Q8—44no—
1241Q8—82no—
1242D4—28no—
1243D4—44no—
1244D4—82no—
1245D4—88no—
1246D4—88no—
1247D4—84no—
1248D4—84no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—48no—
1322C2×C4—48no—
1323C2×C4—48no—
1324C2×C4—84no—
1325C2×C4—84no—
1326C2×C4—88no—
1327C2×C4—84no—
1328C2×C4—84no—
1329C2×C4—164no—
1330C2×C4—164no—
1331C2×C4C2×2−1+412yes—
1332C2×C4#58512yes—
1333C2×C4#58512yes—
1334C2×C4#58512yes—
1335C2×C4#58512yes—
1336C2×C4#58512yes—
1337C22—24no—
1338C22—24no—
1339C22—24no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—42no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22C22×2−1+411yescharacteristic
1359C22C2×#58511yescharacteristic
1360C22C2×#58511yescharacteristic
1361C22C2×#58511yescharacteristic
1362C22C2×#58511yescharacteristic
1363C22C2×#58511yescharacteristic
1364C22H(7,𝔽2)11yescharacteristic
1365C4—22no—
1366C4—22no—
1367C4—22no—
1368C4—42no—
1369C4—42no—
1370C4—41no—
1371C4—44no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—44no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—44no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—44no—
1390C4#355314yes—
1391C2—44no—
1392C2—82no—
1393C2—82no—
1394C2C2×#355311yescharacteristic
1395C2#6290811yescharacteristic
1396C2#6290811yescharacteristic
1397C2#6294811yescharacteristic
1398C2#6302511yescharacteristic
1399C2#6303111yescharacteristic
1400C2#6303111yescharacteristic
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. #59873C2semidirect
2. #59569C2semidirect
3. #59299C2semidirect
4. #59222C2semidirect
5. #57385C2semidirect
6. #54726C2semidirect
7. #54245C2semidirect
8. #52303C2semidirect
9. #51011C2semidirect
10. #50976C2semidirect
11. #50606C2semidirect
12. #46158C2semidirect
13. #46158C2semidirect
14. #46157C2semidirect
15. #45178C2semidirect
16. #44944C2semidirect
17. #44912C2semidirect
18. #42630C2semidirect
19. #42501C2semidirect
20. #42461C2semidirect
21. #40168C2semidirect
22. #40011C2semidirect
23. #39907C2semidirect
24. #37218C2semidirect
25. #37168C2semidirect
26. #37141C2semidirect
27. #36464C2semidirect
28. #36453C2semidirect
29. #36290C2semidirect

Maximal subgroups

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

subgroupindex
#598732
#595692
#592992
#592222
#573852
#547262
#542452
#523032
#510112
#509762
#506062
#461582
#461572
#451782
#449442
#449122
#426302
#425012
#424612
#401682
#400112
#399072
#372182
#371682
#371412
#364642
#364532
#362902