Finite Group Databasebeta

← #7743821

Subgroups — #7743821

Order 512.

4030 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51484C214yesmaximal, complemented
2#51351C214yesmaximal, complemented
3#51227C212yesmaximal, complemented
4#51089C212yesmaximal, complemented
5#50915C212yesmaximal, complemented
6#50714C212yesmaximal, complemented
7#48891C214yesmaximal
8#48884C214yesmaximal
9#45809C214yesmaximal
10#45517C214yesmaximal
11#39683C212yesmaximal, complemented
12#39681C212yesmaximal, complemented
13#39082C212yesmaximal
14#39078C212yesmaximal
15#38267C212yesmaximal
16#38263C212yesmaximal
17#38243C212yesmaximal, complemented
18#38239C212yesmaximal, complemented
19#37635C211yesmaximal, characteristic
20#37635C211yesmaximal, characteristic
21#37404C212yesmaximal, complemented
22#37359C212yesmaximal, complemented
23#35643C212yesmaximal, complemented
24#35583C212yesmaximal, complemented
25#35235C211yesmaximal, characteristic
26#35173C211yesmaximal, characteristic
27#34403C211yesmaximal, characteristic
28#34348C211yesmaximal, characteristic
29#34235C211yesmaximal, characteristic
30C2×#533C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#533C2211yescharacteristic
33#2864C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2859C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2855C2214yes—
40#2817C2212yes—
41#2817C2214yes—
42#2817C2212yes—
43#2810C2214yes—
44#2806C2214yes—
45#2805C2214yes—
46#2805C2214yes—
47#2799C2214yes—
48#2794C2214yes—
49#2794C2214yes—
50#2791C2214yes—
51#2791C2214yes—
52#2789C2214yes—
53#2789C2214yes—
54#2789C2214yes—
55#2787C2214yes—
56#2787C2214yes—
57#2776C2214yes—
58#2776C2214yes—
59#2776C2214yes—
60#2776C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2774C2214yes—
64#2770C2214yes—
65#2770C2214yes—
66#2769C2214yes—
67#2769C2214yes—
68#2767C2214yes—
69#2767C2214yes—
70#2766C2214yes—
71#2766C2214yes—
72#2766C2214yes—
73#2762C2214yes—
74#2762C2214yes—
75#2762C2214yes—
76#2758C2214yes—
77#2758C2214yes—
78#2758C2214yes—
79#2758C2214yes—
80#2758C2214yes—
81#2755C2214yes—
82#2755C2214yes—
83#2747C2214yes—
84#2747C2214yes—
85#2719C2214yes—
86#2719C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2690C2214yes—
90#2690C2214yes—
91#2666C2214yes—
92#2660C2211yescharacteristic
93#2660C2211yescharacteristic
94#2660C2212yes—
95#2659C2214yes—
96#2647C2212yes—
97#2647C2212yes—
98#2645C2212yes—
99#2645C2212yes—
100#2642C2212yes—
101#2642C2211yescharacteristic
102#2642C2211yescharacteristic
103#2634C2212yes—
104#2634C2212yes—
105#2634C2214yes—
106#2625C2212yes—
107#2625C2212yes—
108#2625C2212yes—
109#2625C2212yes—
110#2612C2214yes—
111#2612C2214yes—
112#2612C2214yes—
113#2606C2214yes—
114#2606C2212yes—
115#2606C2214yes—
116#2605C2214yes—
117#2605C2212yes—
118#2605C2214yes—
119#2605C2214yes—
120#2605C2214yes—
121#2590C2214yes—
122#2588C2214yes—
123#2588C2214yes—
124#2588C2214yes—
125#2588C2214yes—
126#2586C2214yes—
127#2585C2214yes—
128#2585C2214yes—
129#2584C2212yes—
130#2584C2212yes—
131#2584C2214yes—
132#2584C2214yes—
133#2581C2214yes—
134#2581C2212yes—
135#2581C2214yes—
136#2581C2212yes—
137#2577C2214yes—
138#2577C2214yes—
139#2570C2212yes—
140#2570C2214yes—
141#2569C2212yes—
142#2568C2212yes—
143#2568C2212yes—
144#2567C2212yes—
145#2567C2212yes—
146#2567C2212yes—
147#2567C2211yescharacteristic
148#2567C2211yescharacteristic
149#2565C2214yes—
150#2550C2214yes—
151#2550C2212yes—
152#2549C2212yes—
153#2546C2212yes—
154#2546C2211yescharacteristic
155#2546C2211yescharacteristic
156#2533C2214yes—
157#2533C2214yes—
158#2533C2214yes—
159#2533C2214yes—
160#2530C2214yes—
161#2530C2214yes—
162#2528C2214yes—
163#2528C2214yes—
164#2524C2214yes—
165#2520C2214yes—
166#2520C2214yes—
167#2514C2212yes—
168#2514C2214yes—
169#2514C2212yes—
170#2511C2214yes—
171#2511C2212yes—
172#2511C2212yes—
173#2509C2212yes—
174#2509C2212yes—
175#2509C2214yes—
176#2508C2212yes—
177#2508C2212yes—
178#2507C2212yes—
179#2507C2212yes—
180#2506C2212yes—
181#2506C2214yes—
182#2506C2212yes—
183#2499C2212yes—
184#2499C2212yes—
185#2499C2214yes—
186#2495C2214yes—
187#2494C2214yes—
188#2489C2214yes—
189#2462C2214yes—
190#2462C2214yes—
191#2462C2214yes—
192#2462C2214yes—
193#2453C2212yes—
194#2453C2212yes—
195#2451C2212yes—
196#2451C2212yes—
197#2451C2214yes—
198#2442C2212yes—
199#2440C2212yes—
200#2421C2214yes—
201#2382C2212yes—
202#2382C2212yes—
203#2381C2211yescharacteristic
204#2381C2211yescharacteristic
205#2381C2211yescharacteristic
206#2381C2211yescharacteristic
207#2378C2212yes—
208#2378C2212yes—
209#2378C2212yes—
210#2378C2212yes—
211#2378C2214yes—
212#2370C2212yes—
213#2370C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2360C2212yes—
217#2360C2212yes—
218#2356C2212yes—
219#2356C2212yes—
220#2356C2212yes—
221#2351C2212yes—
222#2347C2211yescharacteristic
223#2347C2211yescharacteristic
224#2346C2211yescharacteristic
225#2346C2211yescharacteristic
226#2343C2214yes—
227#2336C2212yes—
228#2336C2212yes—
229#2332C2214yes—
230#2331C2212yes—
231#2331C2212yes—
232#2331C2212yes—
233#2331C2212yes—
234#2330C2212yes—
235#2330C2212yes—
236#2320C2212yes—
237#2320C2212yes—
238#2320C2212yes—
239#2320C2212yes—
240#2320C2212yes—
241#2316C2212yes—
242#2316C2212yes—
243C4×C4⋊Q8C2212yes—
244C4×#125C2212yes—
245C4×C22⋊Q8C2214yes—
246#2298C2212yes—
247#2298C2212yes—
248#2295C2212yes—
249#2295C2212yes—
250#2295C2212yes—
251#2295C2212yes—
252#2295C2212yes—
253#2295C2212yes—
254#2283C2211yescharacteristic
255#2283C2211yescharacteristic
256#2283C2211yescharacteristic
257#2276C2212yes—
258C2×C4×C4⋊C4C2211yescharacteristic
259#533—28no—
260#533—28no—
261#533—28no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2314yes—
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C2×#117C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C42C2312yes—
304C22×C42C2311yescharacteristic
305#401C2314yes—
306#401C2314yes—
307#401C2314yes—
308#401C2314yes—
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#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#387C2314yes—
516#387C2314yes—
517#387C2312yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
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#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
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#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#384C2312yes—
616#384C2314yes—
617#384C2312yes—
618#384C2312yes—
619#384C2312yes—
620#384C2312yes—
621#383C2312yes—
622#383C2314yes—
623#383C2314yes—
624#383C2314yes—
625#383C2312yes—
626#383C2312yes—
627#383C2311yescharacteristic
628#383C2311yescharacteristic
629#383C2311yescharacteristic
630#383C2314yes—
631#383C2311yescharacteristic
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#382C2312yes—
636#382C2314yes—
637#382C2312yes—
638#382C2314yes—
639#382C2314yes—
640#382C2312yes—
641#382C2314yes—
642#382C2312yes—
643#382C2311yescharacteristic
644#382C2311yescharacteristic
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2312yes—
650#382C2314yes—
651#381C2312yes—
652#381C2312yes—
653#381C2312yes—
654#380C2311yescharacteristic
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2311yescharacteristic
661#380C2311yescharacteristic
662#380C2311yescharacteristic
663#380C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701#376C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2312yes—
705#376C2312yes—
706#376C2311yescharacteristic
707#376C2311yescharacteristic
708#376C2314yes—
709#376C2314yes—
710#376C2312yes—
711#376C2314yes—
712C2×#95C2312yes—
713C43C2312yes—
714C43C2312yes—
715C22×Q8C2412yes—
716C22×Q8C2412yes—
717C22×Q8C2411yescharacteristic
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C23×C4C2411yescharacteristic
724C23×C4C2414yes—
725C23×C4C2411yescharacteristic
726C23×C4C2411yescharacteristic
727C4⋊Q8—28no—
728C4⋊Q8—24no—
729C4⋊Q8—24no—
730C4⋊Q8—24no—
731C4⋊Q8—24no—
732C4⋊Q8—24no—
733C4⋊Q8—24no—
734C4⋊Q8—82no—
735C4⋊Q8—82no—
736#125—28no—
737#125—28no—
738#125—24no—
739#125—24no—
740#125—28no—
741#125—84no—
742#125—84no—
743#125—84no—
744C22⋊Q8—28no—
745C22⋊Q8—28no—
746C22⋊Q8—28no—
747C22⋊Q8—28no—
748C22⋊Q8—24no—
749C22⋊Q8—28no—
750C22⋊Q8—24no—
751C22⋊Q8—84no—
752C4×Q8—28no—
753C4×Q8—28no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—28no—
757C4×Q8—24no—
758C4×Q8—24no—
759C4×Q8—28no—
760C4×Q8—28no—
761C4×Q8—84no—
762C4×Q8—84no—
763#117—24no—
764#117—24no—
765#117—28no—
766#117—28no—
767C2×C4⋊C4—28no—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C42—82no—
855C2×C42#4118yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2411yescharacteristic
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2412yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2411yescharacteristic
928#95C2411yescharacteristic
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
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—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987C24C2511yescharacteristic
988C2×Q8—24no—
989C2×Q8—24no—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—22no—
993C2×Q8—22no—
994C2×Q8—24no—
995C2×Q8—24no—
996C2×Q8—24no—
997C2×Q8—28no—
998C2×Q8—42no—
999C2×Q8—42no—
1000C2×Q8—44no—
1001C2×Q8—42no—
1002C2×Q8—41no—
1003C2×Q8—41no—
1004C2×Q8—42no—
1005C2×Q8—42no—
1006C2×Q8—44no—
1007C2×Q8—44no—
1008C2×Q8—42no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C22×C4—24no—
1012C22×C4—28no—
1013C22×C4—41no—
1014C22×C4—42no—
1015C22×C4—41no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4C2×#4114yes—
1019C22×C4C2×#4114yes—
1020C22×C4C2×#4114yes—
1021C22×C4C2514yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2514yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2514yes—
1048C22×C4C2511yescharacteristic
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
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⋊C42−1+418yes—
1124C22⋊C4—28no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C42—24no—
1136C42—24no—
1137C42—28no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—28no—
1143C42—28no—
1144C42—24no—
1145C42—24no—
1146C42—44no—
1147C42—42no—
1148C42—42no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—42no—
1153C42—42no—
1154C42—44no—
1155C42—42no—
1156C42—42no—
1157C42—42no—
1158C42—42no—
1159C42—44no—
1160C42—42no—
1161C42—44no—
1162C42—44no—
1163C42—42no—
1164C42C2×#4114yes—
1165C42C2×#4114yes—
1166C42C2×#4114yes—
1167C42C2×#4114yes—
1168C23—22no—
1169C23—21no—
1170C23—21no—
1171C23—22no—
1172C23C22×#4112yes—
1173C23C2611yescharacteristic
1174Q8—48no—
1175Q8—48no—
1176Q8—88no—
1177Q8—84no—
1178Q8—82no—
1179Q8—82no—
1180Q8—84no—
1181Q8—84no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—28no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—44no—
1254C2×C4—44no—
1255C2×C4—88no—
1256C2×C4C22×#4112yes—
1257C2×C4C22×#4112yes—
1258C2×C4C22×#4112yes—
1259C2×C4C22×#4112yes—
1260C2×C4C22×#4112yes—
1261C2×C4C22×#4112yes—
1262C2×C4C2×2−1+418yes—
1263C2×C4C2×2−1+414yes—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—42no—
1268C22—42no—
1269C22C23×#4111yescharacteristic
1270C22C22×2−1+412yes—
1271C22H(7,𝔽2)11yescharacteristic
1272C222−1+611yescharacteristic
1273C222−1+612yes—
1274C4—28no—
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—44no—
1289C4—44no—
1290C4—42no—
1291C4—44no—
1292C4—44no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4#350914yes—
1302C2—42no—
1303C2C2×#350911yescharacteristic
1304C2#6285611yescharacteristic
1305C2#6286011yescharacteristic
1306C2#6305712yes—
1307C2#6305812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51484C2semidirect
2. #51351C2semidirect
3. #51227C2semidirect
4. #51089C2semidirect
5. #50915C2semidirect
6. #50714C2semidirect
11. #39683C2semidirect
12. #39681C2semidirect
17. #38243C2semidirect
18. #38239C2semidirect
21. #37404C2semidirect
22. #37359C2semidirect
23. #35643C2semidirect
24. #35583C2semidirect

Maximal subgroups

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

subgroupindex
#514842
#513512
#512272
#510892
#509152
#507142
#488912
#488842
#458092
#455172
#396832
#396812
#390822
#390782
#382672
#382632
#382432
#382392
#376352
#374042
#373592
#356432
#355832
#352352
#351732
#344032
#343482
#342352