Finite Group Databasebeta

← #8125443

Subgroups — #8125443

Order 512.

3792 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58541C214yesmaximal, complemented
2#58288C214yesmaximal, complemented
3#55660C214yesmaximal
4#54093C214yesmaximal
5#53131C212yesmaximal, complemented
6#53034C212yesmaximal, complemented
7#47820C214yesmaximal
8#47789C214yesmaximal
9#47474C214yesmaximal, complemented
10#47323C214yesmaximal, complemented
11#45306C212yesmaximal, complemented
12#45280C212yesmaximal, complemented
13#40082C212yesmaximal, complemented
14#39979C212yesmaximal, complemented
15#39695C212yesmaximal
16#39475C212yesmaximal
17#39003C212yesmaximal, complemented
18#38986C212yesmaximal, complemented
19#37981C212yesmaximal
20#37981C212yesmaximal
21#37428C211yesmaximal, characteristic
22#37394C211yesmaximal, characteristic
23#35337C211yesmaximal, characteristic
24#35323C211yesmaximal, characteristic
25#35181C211yesmaximal, characteristic
26#35087C211yesmaximal, characteristic
27#34815C211yesmaximal, characteristic
28#2863C2212yes—
29#2862C2211yescharacteristic
30#2859C2211yescharacteristic
31#2857C2211yescharacteristic
32#2855C2212yes—
33#2851C2211yescharacteristic
34#2851C2211yescharacteristic
35#2851C2212yes—
36#2851C2211yescharacteristic
37#2843C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2833C2214yes—
43#2833C2214yes—
44#2822C2214yes—
45#2809C2214yes—
46#2807C2214yes—
47#2807C2214yes—
48#2805C2214yes—
49#2802C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2799C2214yes—
53#2794C2214yes—
54#2794C2214yes—
55#2792C2214yes—
56#2791C2214yes—
57#2791C2214yes—
58#2791C2214yes—
59#2789C2214yes—
60#2789C2214yes—
61#2787C2214yes—
62#2787C2214yes—
63#2776C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2776C2214yes—
67#2776C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2774C2214yes—
73#2770C2214yes—
74#2770C2214yes—
75#2769C2214yes—
76#2769C2214yes—
77#2767C2214yes—
78#2767C2214yes—
79#2767C2214yes—
80#2767C2214yes—
81#2766C2214yes—
82#2766C2214yes—
83#2763C2214yes—
84#2763C2214yes—
85#2762C2214yes—
86#2758C2214yes—
87#2758C2214yes—
88#2758C2214yes—
89#2758C2214yes—
90#2758C2214yes—
91#2758C2214yes—
92#2755C2214yes—
93#2745C2214yes—
94#2745C2214yes—
95#2738C2214yes—
96#2738C2214yes—
97#2726C2214yes—
98#2726C2214yes—
99#2719C2214yes—
100#2719C2214yes—
101#2666C2214yes—
102#2655C2214yes—
103#2655C2214yes—
104#2655C2214yes—
105#2647C2212yes—
106#2647C2211yescharacteristic
107#2646C2214yes—
108#2645C2214yes—
109#2642C2211yescharacteristic
110#2628C2212yes—
111#2628C2212yes—
112#2625C2212yes—
113#2625C2212yes—
114#2612C2214yes—
115#2612C2214yes—
116#2612C2214yes—
117#2611C2214yes—
118#2611C2214yes—
119#2606C2214yes—
120#2599C2214yes—
121#2599C2214yes—
122#2590C2214yes—
123#2589C2214yes—
124#2589C2214yes—
125#2589C2214yes—
126#2589C2214yes—
127#2588C2214yes—
128#2588C2214yes—
129#2588C2214yes—
130#2586C2214yes—
131#2582C2214yes—
132#2577C2214yes—
133#2577C2214yes—
134#2571C2212yes—
135#2571C2212yes—
136#2571C2212yes—
137#2571C2212yes—
138#2570C2212yes—
139#2570C2212yes—
140#2570C2212yes—
141#2570C2214yes—
142#2570C2214yes—
143#2568C2212yes—
144#2567C2212yes—
145#2567C2212yes—
146#2565C2212yes—
147#2552C2212yes—
148#2552C2212yes—
149#2550C2212yes—
150#2550C2212yes—
151#2550C2212yes—
152#2533C2214yes—
153#2533C2214yes—
154#2533C2214yes—
155#2533C2214yes—
156#2533C2214yes—
157#2533C2214yes—
158#2530C2214yes—
159#2530C2214yes—
160#2528C2214yes—
161#2528C2214yes—
162#2524C2214yes—
163#2524C2214yes—
164#2514C2212yes—
165#2514C2212yes—
166#2514C2212yes—
167#2514C2212yes—
168#2514C2212yes—
169#2514C2214yes—
170#2511C2212yes—
171#2511C2212yes—
172#2511C2212yes—
173#2509C2214yes—
174#2509C2212yes—
175#2509C2212yes—
176#2509C2212yes—
177#2508C2212yes—
178#2508C2212yes—
179#2507C2212yes—
180#2507C2212yes—
181#2507C2212yes—
182#2507C2212yes—
183#2507C2212yes—
184#2506C2212yes—
185#2506C2212yes—
186#2506C2212yes—
187#2506C2212yes—
188#2505C2212yes—
189#2505C2212yes—
190#2493C2214yes—
191#2473C2214yes—
192#2473C2212yes—
193#2473C2212yes—
194#2462C2214yes—
195#2462C2214yes—
196#2462C2214yes—
197#2462C2214yes—
198#2453C2212yes—
199#2453C2212yes—
200#2453C2212yes—
201#2453C2214yes—
202#2453C2214yes—
203#2451C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2402C2212yes—
207#2402C2212yes—
208#2370C2212yes—
209#2369C2212yes—
210#2365C2212yes—
211#2365C2212yes—
212#2356C2212yes—
213#2356C2212yes—
214#2356C2212yes—
215#2351C2212yes—
216#2336C2214yes—
217#2331C2212yes—
218#2330C2214yes—
219#2330C2214yes—
220#2330C2211yescharacteristic
221#2327C2211yescharacteristic
222#2323C2212yes—
223#2323C2212yes—
224#2320C2214yes—
225#2320C2214yes—
226#2317C2214yes—
227#2314C2212yes—
228#2314C2212yes—
229C4×#125C2211yescharacteristic
230C4×#125C2211yescharacteristic
231C4×#125C2212yes—
232C4×#125C2212yes—
233C4×C22⋊Q8C2212yes—
234#2296C2211yescharacteristic
235#2296C2211yescharacteristic
236#2296C2211yescharacteristic
237#2296C2211yescharacteristic
238#2295C2212yes—
239#2285C2211yescharacteristic
240#2285C2212yes—
241C4×#117C2211yescharacteristic
242C2×C4×C4⋊C4C2211yescharacteristic
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2311yescharacteristic
246C2×#125C2311yescharacteristic
247C2×#125C2311yescharacteristic
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#125C2314yes—
253C2×#125C2311yescharacteristic
254C2×#125C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2314yes—
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2314yes—
265C2×#117C2311yescharacteristic
266C22×C4⋊C4C2312yes—
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270#401C2314yes—
271#401C2314yes—
272#401C2314yes—
273#401C2314yes—
274#401C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2312yes—
294#400C2312yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2312yes—
325#400C2312yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#399C2314yes—
330#399C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
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#398C2312yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#393C2314yes—
389#393C2314yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2314yes—
396#391C2312yes—
397#391C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2312yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2312yes—
413#391C2314yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#387C2312yes—
485#387C2312yes—
486#387C2314yes—
487#387C2314yes—
488#387C2312yes—
489#387C2312yes—
490#387C2312yes—
491#387C2312yes—
492#387C2312yes—
493#387C2312yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#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#387C2314yes—
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#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2312yes—
573#385C2312yes—
574#385C2311yescharacteristic
575#385C2314yes—
576#385C2312yes—
577#385C2311yescharacteristic
578#385C2314yes—
579#385C2312yes—
580#385C2312yes—
581#385C2311yescharacteristic
582#385C2312yes—
583#385C2311yescharacteristic
584#384C2312yes—
585#384C2312yes—
586#384C2312yes—
587#384C2312yes—
588#384C2314yes—
589#384C2314yes—
590#384C2311yescharacteristic
591#384C2311yescharacteristic
592#384C2311yescharacteristic
593#383C2314yes—
594#383C2314yes—
595#383C2314yes—
596#383C2314yes—
597#383C2314yes—
598#383C2314yes—
599#383C2314yes—
600#383C2314yes—
601#383C2314yes—
602#382C2311yescharacteristic
603#382C2311yescharacteristic
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2314yes—
608#382C2312yes—
609#382C2312yes—
610#382C2312yes—
611#382C2314yes—
612#382C2314yes—
613#382C2312yes—
614#382C2311yescharacteristic
615#382C2314yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2311yescharacteristic
620#382C2311yescharacteristic
621#381C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2314yes—
627#380C2314yes—
628#380C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665#376C2314yes—
666#376C2314yes—
667#376C2311yescharacteristic
668#376C2314yes—
669#376C2314yes—
670#376C2311yescharacteristic
671C2×#95C2312yes—
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C22×Q8C2412yes—
675C22×Q8C2414yes—
676C22×Q8C2414yes—
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C23×C4C2412yes—
681C23×C4C2412yes—
682C4⋊Q8—28no—
683C4⋊Q8—44no—
684C4⋊Q8—42no—
685#125—44no—
686#125—42no—
687#125—42no—
688#125—42no—
689#125—48no—
690#125—48no—
691#125—44no—
692#125—44no—
693#125—48no—
694C22⋊Q8—28no—
695C4×Q8—28no—
696C4×Q8—48no—
697C4×Q8—48no—
698C4×Q8—44no—
699C4×Q8—44no—
700#117—24no—
701#117—24no—
702#117—24no—
703#117—48no—
704#117—42no—
705C2×C4⋊C4—44no—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2414yes—
792C2×C42—24no—
793C2×C42—42no—
794C2×C42—42no—
795C2×C42C2414yes—
796C2×C42C2412yes—
797C2×C42C2414yes—
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2414yes—
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2412yes—
807C2×C42C2412yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2414yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2411yescharacteristic
822C2×C42C2412yes—
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825#95C2412yes—
826#95C2412yes—
827#95C2412yes—
828#95C2412yes—
829#95C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2412yes—
833#95C2412yes—
834#95C2412yes—
835#95C2412yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2412yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2412yes—
865#95C2414yes—
866#95C2412yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2414yes—
885#95C2412yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916C24C2511yescharacteristic
917C2×Q8—24no—
918C2×Q8—24no—
919C2×Q8—28no—
920C2×Q8—24no—
921C2×Q8—44no—
922C2×Q8—44no—
923C2×Q8—44no—
924C2×Q8—44no—
925C2×Q8—44no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—24no—
930C22×C4—22no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C42−1+414yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2511yescharacteristic
942C22×C4C2512yes—
943C22×C4C2511yescharacteristic
944C22×C4C2514yes—
945C22×C4C2514yes—
946C22×C4C2512yes—
947C22×C4C2514yes—
948C22×C4C2512yes—
949C22×C4C2511yescharacteristic
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2511yescharacteristic
954C22×C4C2514yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2511yescharacteristic
963C22×C4C2512yes—
964C22×C4C2511yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—24no—
971C4⋊C4—28no—
972C4⋊C4—24no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—42no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—42no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—24no—
1044C22⋊C4—28no—
1045C22⋊C4—24no—
1046C22⋊C4—44no—
1047C22⋊C4—41no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—41no—
1051C42—24no—
1052C42—24no—
1053C42—22no—
1054C42—22no—
1055C42—24no—
1056C42—22no—
1057C42—28no—
1058C42—24no—
1059C42—22no—
1060C42—22no—
1061C42—28no—
1062C42—24no—
1063C42—28no—
1064C42—41no—
1065C42—42no—
1066C42—41no—
1067C42—42no—
1068C42—42no—
1069C42—44no—
1070C42—44no—
1071C42—44no—
1072C42—44no—
1073C42—44no—
1074C42—44no—
1075C42—44no—
1076C42—44no—
1077C42—42no—
1078C42—42no—
1079C42—44no—
1080C422−1+414yes—
1081C23—21no—
1082C23—22no—
1083C23—21no—
1084C23—22no—
1085C23C2×2−1+412yes—
1086C23C2611yescharacteristic
1087Q8—48no—
1088Q8—88no—
1089Q8—88no—
1090C2×C4—28no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—28no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—82no—
1161C2×C4—84no—
1162C2×C4—84no—
1163C2×C4C2×2−1+414yes—
1164C2×C4C2×2−1+412yes—
1165C2×C4C2×2−1+412yes—
1166C2×C4C2×2−1+412yes—
1167C2×C4#58514yes—
1168C2×C4#58512yes—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—42no—
1173C22—42no—
1174C22C22×2−1+411yescharacteristic
1175C22C22×2−1+411yescharacteristic
1176C22C2×#58511yescharacteristic
1177C22C2×#58512yes—
1178C222−1+612yes—
1179C4—22no—
1180C4—24no—
1181C4—24no—
1182C4—44no—
1183C4—41no—
1184C4—42no—
1185C4—41no—
1186C4—44no—
1187C4—41no—
1188C4—42no—
1189C4—41no—
1190C4—42no—
1191C4—42no—
1192C4—44no—
1193C4—44no—
1194C4—44no—
1195C4—42no—
1196C4—44no—
1197C4—42no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—44no—
1202C4—44no—
1203C4—42no—
1204C4#356314yes—
1205C2—42no—
1206C2C2×#356311yescharacteristic
1207C2#6282511yescharacteristic
1208C2#6288911yescharacteristic
1209C2#6293212yes—
1210C2#6293612yes—
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. #58541C2semidirect
2. #58288C2semidirect
5. #53131C2semidirect
6. #53034C2semidirect
9. #47474C2semidirect
10. #47323C2semidirect
11. #45306C2semidirect
12. #45280C2semidirect
13. #40082C2semidirect
14. #39979C2semidirect
17. #39003C2semidirect
18. #38986C2semidirect

Maximal subgroups

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

subgroupindex
#585412
#582882
#556602
#540932
#531312
#530342
#478202
#477892
#474742
#473232
#453062
#452802
#400822
#399792
#396952
#394752
#390032
#389862
#379812
#374282
#373942
#353372
#353232
#351812
#350872
#348152