Finite Group Databasebeta

← #8701632

Subgroups — #8701632

Order 512.

3941 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59877C212yesmaximal, complemented
2#59756C212yesmaximal, complemented
3#59298C212yesmaximal, complemented
4#59221C212yesmaximal, complemented
5#55295C214yesmaximal, complemented
6#54752C214yesmaximal, complemented
7#54250C214yesmaximal, complemented
8#52303C211yesmaximal, characteristic
9#51008C214yesmaximal, complemented
10#50613C214yesmaximal, complemented
11#50558C214yesmaximal, complemented
12#46158C211yesmaximal, characteristic, complemented
13#46158C211yesmaximal, characteristic, complemented
14#46157C211yesmaximal, characteristic, complemented
15#45262C212yesmaximal, complemented
16#45180C212yesmaximal, complemented
17#44902C212yesmaximal, complemented
18#42870C212yesmaximal, complemented
19#42507C212yesmaximal, complemented
20#42461C212yesmaximal, complemented
21#40195C212yesmaximal, complemented
22#40011C212yesmaximal, complemented
23#39928C212yesmaximal, complemented
24#37200C212yesmaximal
25#37164C212yesmaximal, complemented
26#37146C212yesmaximal, complemented
27#36447C211yesmaximal, characteristic, complemented
28#36312C211yesmaximal, characteristic, complemented
29#36299C211yesmaximal, characteristic, complemented
30#2863C2212yes—
31#2860C2212yes—
32#2859C2212yes—
33#2859C2211yescharacteristic
34#2859C2211yescharacteristic
35#2859C2211yescharacteristic
36#2851C2212yes—
37#2837C2214yes—
38#2836C2214yes—
39#2827C2214yes—
40#2822C2212yes—
41#2820C2212yes—
42#2820C2212yes—
43#2810C2212yes—
44#2808C2211yescharacteristic
45#2807C2214yes—
46#2807C2214yes—
47#2806C2211yescharacteristic
48#2805C2212yes—
49#2805C2212yes—
50#2803C2214yes—
51#2802C2214yes—
52#2800C2214yes—
53#2796C2214yes—
54#2795C2214yes—
55#2795C2214yes—
56#2794C2214yes—
57#2793C2214yes—
58#2791C2214yes—
59#2791C2214yes—
60#2790C2214yes—
61#2790C2214yes—
62#2787C2214yes—
63#2783C2214yes—
64#2783C2212yes—
65#2783C2214yes—
66#2781C2214yes—
67#2781C2212yes—
68#2776C2214yes—
69#2776C2214yes—
70#2774C2214yes—
71#2773C2214yes—
72#2773C2214yes—
73#2773C2214yes—
74#2773C2214yes—
75#2772C2214yes—
76#2771C2214yes—
77#2768C2214yes—
78#2767C2214yes—
79#2767C2214yes—
80#2766C2214yes—
81#2765C2214yes—
82#2765C2214yes—
83#2762C2214yes—
84#2761C2214yes—
85#2757C2214yes—
86#2757C2214yes—
87#2744C2212yes—
88#2744C2214yes—
89#2743C2214yes—
90#2732C2211yescharacteristic
91#2730C2212yes—
92#2727C2212yes—
93#2727C2212yes—
94#2726C2212yes—
95#2725C2214yes—
96#2725C2214yes—
97#2725C2214yes—
98#2721C2214yes—
99#2721C2214yes—
100#2719C2214yes—
101#2718C2214yes—
102#2711C2214yes—
103#2698C2214yes—
104#2694C2212yes—
105#2686C2212yes—
106#2682C2211yescharacteristic
107#2655C2214yes—
108#2655C2214yes—
109#2654C2214yes—
110#2652C2214yes—
111#2652C2214yes—
112#2651C2214yes—
113#2649C2214yes—
114#2636C2214yes—
115#2634C2214yes—
116#2629C2212yes—
117#2611C2214yes—
118#2596C2214yes—
119#2596C2214yes—
120#2594C2214yes—
121#2594C2214yes—
122#2594C2214yes—
123#2594C2214yes—
124#2593C2214yes—
125#2590C2214yes—
126#2590C2214yes—
127#2588C2214yes—
128#2587C2214yes—
129#2585C2214yes—
130#2584C2212yes—
131#2584C2212yes—
132#2582C2211yescharacteristic
133#2582C2211yescharacteristic
134#2576C2214yes—
135#2575C2214yes—
136#2574C2214yes—
137#2571C2212yes—
138#2571C2211yescharacteristic
139#2571C2212yes—
140#2570C2214yes—
141#2570C2212yes—
142#2570C2212yes—
143#2570C2212yes—
144#2559C2214yes—
145#2556C2214yes—
146#2552C2211yescharacteristic
147#2552C2212yes—
148#2538C2211yescharacteristic
149#2538C2211yescharacteristic
150#2536C2212yes—
151#2536C2212yes—
152#2533C2214yes—
153#2529C2214yes—
154#2529C2214yes—
155#2528C2214yes—
156#2528C2214yes—
157#2528C2214yes—
158#2528C2214yes—
159#2522C2214yes—
160#2522C2214yes—
161#2519C2214yes—
162#2516C2214yes—
163#2515C2214yes—
164#2515C2214yes—
165#2509C2212yes—
166#2509C2212yes—
167#2508C2212yes—
168#2508C2212yes—
169#2508C2212yes—
170#2508C2214yes—
171#2508C2214yes—
172#2508C2212yes—
173#2507C2214yes—
174#2507C2214yes—
175#2507C2212yes—
176#2507C2212yes—
177#2506C2212yes—
178#2506C2214yes—
179#2506C2212yes—
180#2497C2212yes—
181#2497C2212yes—
182#2497C2212yes—
183#2496C2212yes—
184#2496C2212yes—
185#2496C2212yes—
186#2495C2212yes—
187#2494C2212yes—
188#2494C2212yes—
189#2494C2212yes—
190#2487C2212yes—
191#2485C2212yes—
192#2485C2212yes—
193#2485C2212yes—
194#2485C2212yes—
195#2485C2212yes—
196#2479C2214yes—
197#2475C2214yes—
198#2470C2214yes—
199#2469C2214yes—
200#2460C2214yes—
201#2453C2212yes—
202#2453C2212yes—
203#2448C2212yes—
204#2447C2212yes—
205#2442C2212yes—
206#2441C2212yes—
207#2441C2212yes—
208#2441C2212yes—
209#2441C2212yes—
210#2441C2212yes—
211#2423C2212yes—
212#2421C2212yes—
213#2396C2212yes—
214#2395C2212yes—
215#2392C2212yes—
216#2382C2212yes—
217#2382C2212yes—
218#2382C2212yes—
219#2373C2214yes—
220#2370C2212yes—
221#2370C2214yes—
222#2370C2212yes—
223#2362C2212yes—
224#2362C2212yes—
225#2362C2212yes—
226#2360C2212yes—
227#2355C2211yescharacteristic
228#2354C2211yescharacteristic
229#2354C2212yes—
230#2352C2212yes—
231#2351C2212yes—
232Q8×C4⋊C4C2211yescharacteristic
233Q8×C4⋊C4C2212yes—
234Q8×C4⋊C4C2211yescharacteristic
235Q8×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2211yescharacteristic
237#2346C2212yes—
238#2346C2214yes—
239#2344C2212yes—
240#2336C2214yes—
241#2334C2214yes—
242#2334C2214yes—
243#2323C2212yes—
244#2317C2212yes—
245#2314C2212yes—
246C4×#125C2212yes—
247C4×#125C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×#123C2212yes—
253C4×#121C2212yes—
254#2296C2212yes—
255#2295C2212yes—
256#2293C2212yes—
257#2283C2212yes—
258C42×Q8C2211yescharacteristic
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#125C2311yescharacteristic
263C2×#125C2312yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#124C2311yescharacteristic
272C2×#124C2311yescharacteristic
273C2×#123C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×#121C2312yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C42C2312yes—
298#401C2314yes—
299#401C2314yes—
300#401C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
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#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2312yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#397C2312yes—
378#397C2314yes—
379#397C2312yes—
380#397C2312yes—
381#397C2314yes—
382#397C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2312yes—
392#396C2312yes—
393#396C2314yes—
394#396C2314yes—
395#396C2312yes—
396#396C2314yes—
397#396C2312yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2312yes—
402#394C2314yes—
403#394C2314yes—
404#394C2312yes—
405#394C2314yes—
406#394C2314yes—
407#394C2312yes—
408#394C2314yes—
409#394C2312yes—
410#394C2312yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#393C2312yes—
415#392C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2311yescharacteristic
422#391C2312yes—
423#391C2311yescharacteristic
424#390C2312yes—
425#390C2311yescharacteristic
426#390C2312yes—
427#390C2312yes—
428#390C2314yes—
429#390C2312yes—
430#390C2311yescharacteristic
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
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#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2312yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#387C2314yes—
538#387C2312yes—
539#387C2314yes—
540#387C2312yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#386C2314yes—
599#386C2312yes—
600#386C2314yes—
601#386C2312yes—
602#386C2312yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2312yes—
615#385C2314yes—
616#385C2314yes—
617#384C2312yes—
618#384C2311yescharacteristic
619#384C2311yescharacteristic
620#384C2312yes—
621#384C2314yes—
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2312yes—
628#384C2314yes—
629#383C2314yes—
630#383C2314yes—
631#382C2312yes—
632#382C2311yescharacteristic
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2314yes—
641#382C2314yes—
642#382C2314yes—
643#382C2312yes—
644#382C2314yes—
645#382C2314yes—
646#382C2314yes—
647#382C2311yescharacteristic
648#382C2311yescharacteristic
649#381C2312yes—
650#381C2314yes—
651#381C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708#376C2314yes—
709#376C2314yes—
710C43C2311yescharacteristic
711C43C2312yes—
712C22×Q8C2411yescharacteristic
713C22×Q8C2411yescharacteristic
714C22×Q8C2411yescharacteristic
715C22×D4C2411yescharacteristic
716C22×D4C2411yescharacteristic
717C22×D4C2412yes—
718C22×D4C2412yes—
719C23×C4C2412yes—
720C23×C4C2412yes—
721C23×C4C2414yes—
722C23×C4C2412yes—
723C23×C4C2412yes—
724#126—48no—
725#126—48no—
726#126—48no—
727#125—44no—
728#125—44no—
729#125—44no—
730#125—48no—
731#125—44no—
732#125—44no—
733#125—44no—
734#125—42no—
735#125—48no—
736#124—42no—
737#124—42no—
738#123—44no—
739C22⋊Q8—28no—
740C22⋊Q8—28no—
741C22⋊Q8—44no—
742#121—44no—
743C4×Q8—24no—
744C4×Q8—42no—
745C4×Q8—42no—
746C4×Q8—44no—
747C4×Q8—44no—
748C4×Q8—42no—
749C4×Q8—42no—
750C4×Q8—44no—
751C4×D4—44no—
752C4×D4—44no—
753C4×D4—44no—
754C4×D4—42no—
755C4×D4—42no—
756#117—44no—
757#117—48no—
758#117—44no—
759#117—44no—
760#117—44no—
761C2×C4⋊C4—44no—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C42—44no—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2411yescharacteristic
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2412yes—
915#95C2412yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980C24C2512yes—
981C24C2512yes—
982C2×Q8—22no—
983C2×Q8—22no—
984C2×Q8—22no—
985C2×Q8—22no—
986C2×Q8—41no—
987C2×Q8—41no—
988C2×Q8—41no—
989C2×Q8—41no—
990C2×Q82−1+414yes—
991C2×D4—22no—
992C2×D4—22no—
993C2×D4—41no—
994C2×D4—41no—
995C2×D4—41no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—42no—
1000C2×D4—42no—
1001C2×D4—41no—
1002C2×D4—42no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C4⋊C4—24no—
1046C4⋊C4—22no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—22no—
1052C4⋊C4—24no—
1053C4⋊C4—22no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—44no—
1068C4⋊C4—41no—
1069C4⋊C4—42no—
1070C4⋊C4—41no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—24no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—42no—
1145C22⋊C4—42no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C42—24no—
1160C42—22no—
1161C42—24no—
1162C42—24no—
1163C42—24no—
1164C42—24no—
1165C42—24no—
1166C42—22no—
1167C42—22no—
1168C42—24no—
1169C42—24no—
1170C42—22no—
1171C42—22no—
1172C42—22no—
1173C42—42no—
1174C42—42no—
1175C42—41no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—44no—
1180C42—44no—
1181C42—42no—
1182C42—42no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23C2611yescharacteristic
1204Q8—28no—
1205Q8—44no—
1206Q8—82no—
1207D4—44no—
1208D4—82no—
1209D4—84no—
1210D4—84no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—48no—
1286C2×C4—48no—
1287C2×C4—88no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4C2×2−1+414yes—
1291C2×C4C2×2−1+412yes—
1292C2×C4#58512yes—
1293C2×C4#58512yes—
1294C2×C4#58512yes—
1295C2×C4#58512yes—
1296C2×C4#58512yes—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22C22×2−1+411yescharacteristic
1312C22C2×#58511yescharacteristic
1313C22C2×#58511yescharacteristic
1314C22C2×#58511yescharacteristic
1315C22C2×#58511yescharacteristic
1316C22C2×#58511yescharacteristic
1317C222−1+611yescharacteristic
1318C4—24no—
1319C4—22no—
1320C4—22no—
1321C4—22no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—41no—
1327C4—41no—
1328C4—42no—
1329C4—44no—
1330C4—42no—
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—41no—
1336C4—44no—
1337C4—44no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C4#355314yes—
1345C2—82no—
1346C2—82no—
1347C2C2×#355311yescharacteristic
1348C2#6290711yescharacteristic
1349C2#6290711yescharacteristic
1350C2#6294911yescharacteristic
1351C2#6303111yescharacteristic
1352C2#6303111yescharacteristic
1353C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2682C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59877C2semidirect
2. #59756C2semidirect
3. #59298C2semidirect
4. #59221C2semidirect
5. #55295C2semidirect
6. #54752C2semidirect
7. #54250C2semidirect
9. #51008C2semidirect
10. #50613C2semidirect
11. #50558C2semidirect
12. #46158C2semidirect
13. #46158C2semidirect
14. #46157C2semidirect
15. #45262C2semidirect
16. #45180C2semidirect
17. #44902C2semidirect
18. #42870C2semidirect
19. #42507C2semidirect
20. #42461C2semidirect
21. #40195C2semidirect
22. #40011C2semidirect
23. #39928C2semidirect
25. #37164C2semidirect
26. #37146C2semidirect
27. #36447C2semidirect
28. #36312C2semidirect
29. #36299C2semidirect

Maximal subgroups

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

subgroupindex
#598772
#597562
#592982
#592212
#552952
#547522
#542502
#523032
#510082
#506132
#505582
#461582
#461572
#452622
#451802
#449022
#428702
#425072
#424612
#401952
#400112
#399282
#372002
#371642
#371462
#364472
#363122
#362992