Finite Group Databasebeta

← #9712241

Subgroups — #9712241

Order 512.

3814 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58774C213yesmaximal, complemented
2#58723C211yesmaximal, characteristic, complemented
3#58705C213yesmaximal, complemented
4#57107C213yesmaximal, complemented
5#56737C213yesmaximal, complemented
6#55918C213yesmaximal, complemented
7#54778C213yesmaximal, complemented
8#53388C211yesmaximal, characteristic, complemented
9#53255C211yesmaximal, characteristic, complemented
10#51728C213yesmaximal, complemented
11#51129C213yesmaximal, complemented
12#49427C213yesmaximal, complemented
13#49014C213yesmaximal, complemented
14#47267C213yesmaximal, complemented
15#46908C213yesmaximal, complemented
16#43703C213yesmaximal, complemented
17#43604C213yesmaximal, complemented
18#41782C213yesmaximal, complemented
19#40887C213yesmaximal
20#40060C213yesmaximal, complemented
21#39476C213yesmaximal, complemented
22#38690C213yesmaximal, complemented
23#38339C213yesmaximal, complemented
24#2865C2213yes—
25#2855C2213yes—
26#2841C2213yes—
27#2839C2213yes—
28#2838C2213yes—
29#2836C2213yes—
30#2836C2213yes—
31#2834C2213yes—
32#2832C2213yes—
33#2831C2213yes—
34#2825C2211yescharacteristic
35#2810C2211yescharacteristic
36#2806C2213yes—
37#2806C2213yes—
38#2806C2213yes—
39#2802C2213yes—
40#2802C2213yes—
41#2800C2213yes—
42#2799C2213yes—
43#2798C2213yes—
44#2798C2213yes—
45#2794C2213yes—
46#2794C2213yes—
47#2793C2213yes—
48#2793C2213yes—
49#2791C2213yes—
50#2791C2213yes—
51#2789C2213yes—
52#2789C2213yes—
53#2789C2213yes—
54#2787C2213yes—
55#2787C2213yes—
56#2786C2213yes—
57#2780C2213yes—
58#2779C2213yes—
59#2776C2213yes—
60#2776C2213yes—
61#2776C2213yes—
62#2776C2213yes—
63#2776C2213yes—
64#2775C2213yes—
65#2774C2213yes—
66#2773C2213yes—
67#2772C2213yes—
68#2770C2213yes—
69#2769C2213yes—
70#2769C2213yes—
71#2767C2213yes—
72#2767C2213yes—
73#2766C2213yes—
74#2762C2213yes—
75#2762C2213yes—
76#2762C2213yes—
77#2762C2213yes—
78#2762C2213yes—
79#2761C2213yes—
80#2759C2213yes—
81#2759C2213yes—
82#2756C2213yes—
83#2755C2213yes—
84#2754C2213yes—
85#2754C2213yes—
86#2754C2213yes—
87#2753C2213yes—
88#2750C2213yes—
89#2749C2213yes—
90#2746C2213yes—
91#2746C2213yes—
92#2745C2213yes—
93#2745C2213yes—
94#2744C2213yes—
95#2742C2213yes—
96#2741C2213yes—
97#2740C2213yes—
98#2739C2213yes—
99#2739C2213yes—
100#2738C2213yes—
101#2738C2213yes—
102#2729C2213yes—
103#2727C2213yes—
104#2723C2213yes—
105#2721C2213yes—
106#2721C2213yes—
107#2721C2213yes—
108#2719C2213yes—
109#2717C2213yes—
110#2713C2213yes—
111#2713C2213yes—
112#2698C2213yes—
113#2698C2213yes—
114#2698C2213yes—
115#2696C2213yes—
116#2695C2213yes—
117#2690C2213yes—
118#2689C2213yes—
119#2687C2213yes—
120#2674C2213yes—
121#2667C2213yes—
122#2666C2213yes—
123#2666C2213yes—
124#2664C2213yes—
125#2655C2213yes—
126#2655C2213yes—
127#2655C2213yes—
128#2654C2213yes—
129#2653C2213yes—
130#2653C2213yes—
131#2651C2213yes—
132#2651C2213yes—
133#2649C2213yes—
134#2623C2213yes—
135#2623C2213yes—
136#2607C2213yes—
137#2606C2213yes—
138#2605C2213yes—
139#2604C2213yes—
140#2590C2213yes—
141#2590C2213yes—
142#2589C2213yes—
143#2589C2213yes—
144#2588C2213yes—
145#2588C2213yes—
146#2585C2213yes—
147#2585C2213yes—
148#2577C2213yes—
149#2577C2213yes—
150#2577C2213yes—
151#2577C2213yes—
152#2576C2213yes—
153#2575C2213yes—
154#2574C2213yes—
155#2574C2213yes—
156#2573C2213yes—
157#2570C2213yes—
158#2565C2213yes—
159#2564C2213yes—
160#2557C2213yes—
161#2553C2213yes—
162#2533C2213yes—
163#2533C2213yes—
164#2532C2213yes—
165#2531C2213yes—
166#2530C2213yes—
167#2529C2213yes—
168#2528C2213yes—
169#2528C2213yes—
170#2528C2213yes—
171#2527C2213yes—
172#2527C2213yes—
173#2527C2213yes—
174#2525C2213yes—
175#2524C2213yes—
176#2523C2213yes—
177#2522C2213yes—
178#2522C2213yes—
179#2521C2213yes—
180#2520C2213yes—
181#2520C2213yes—
182#2520C2213yes—
183#2520C2213yes—
184#2517C2213yes—
185#2516C2213yes—
186#2515C2213yes—
187#2514C2213yes—
188#2514C2213yes—
189#2514C2213yes—
190#2511C2213yes—
191#2507C2213yes—
192#2506C2213yes—
193#2505C2213yes—
194#2499C2213yes—
195#2496C2213yes—
196#2495C2213yes—
197#2494C2213yes—
198#2494C2213yes—
199#2494C2213yes—
200#2493C2213yes—
201#2492C2213yes—
202#2481C2213yes—
203#2481C2213yes—
204#2477C2213yes—
205#2475C2213yes—
206#2473C2213yes—
207#2473C2213yes—
208#2469C2213yes—
209#2467C2213yes—
210#2466C2213yes—
211#2459C2213yes—
212#2455C2213yes—
213#2454C2213yes—
214#2447C2213yes—
215#2446C2213yes—
216#2442C2213yes—
217#2441C2213yes—
218#2423C2213yes—
219#2419C2213yes—
220#2417C2213yes—
221#2401C2211yescharacteristic
222#2395C2213yes—
223#2383C2211yescharacteristic
224#2382C2213yes—
225#2374C2213yes—
226#2373C2213yes—
227#2371C2213yes—
228#2370C2213yes—
229#2360C2213yes—
230#2353C2213yes—
231#2352C2213yes—
232#2343C2213yes—
233#2337C2213yes—
234#2334C2213yes—
235#2334C2213yes—
236#2332C2213yes—
237#2331C2213yes—
238#2329C2213yes—
239#2313C2213yes—
240#2313C2213yes—
241C4×#126C2211yescharacteristic
242C4×#123C2213yes—
243#2295C2213yes—
244C2×#384C2211yescharacteristic
245C2×C4⋊Q8C2313yes—
246C2×#126C2311yescharacteristic
247C2×#126C2313yes—
248C2×#126C2313yes—
249C2×#126C2313yes—
250C2×#126C2311yescharacteristic
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#124C2313yes—
255C2×#123C2313yes—
256C2×#123C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C4×Q8C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2313yes—
263C2×#117C2313yes—
264C22×C4⋊C4C2313yes—
265C22×C4⋊C4C2313yes—
266C22×C42C2311yescharacteristic
267#401C2311yescharacteristic
268#401C2313yes—
269#401C2313yes—
270#401C2313yes—
271#401C2313yes—
272#401C2313yes—
273#401C2313yes—
274#401C2311yescharacteristic
275#401C2313yes—
276#400C2313yes—
277#400C2313yes—
278#400C2313yes—
279#400C2313yes—
280#400C2313yes—
281#400C2313yes—
282#400C2313yes—
283#400C2313yes—
284#400C2313yes—
285#400C2313yes—
286#400C2313yes—
287#400C2313yes—
288#400C2313yes—
289#400C2313yes—
290#400C2313yes—
291#400C2313yes—
292#400C2313yes—
293#400C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2313yes—
298#400C2313yes—
299#400C2313yes—
300#400C2313yes—
301#400C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#399C2313yes—
317#399C2313yes—
318#399C2313yes—
319#399C2313yes—
320#399C2313yes—
321#399C2313yes—
322#399C2313yes—
323#399C2313yes—
324#399C2313yes—
325#398C2313yes—
326#398C2313yes—
327#398C2313yes—
328#398C2313yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#398C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#397C2313yes—
385#397C2313yes—
386#397C2313yes—
387#397C2313yes—
388#396C2311yescharacteristic
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2313yes—
395#396C2313yes—
396#396C2313yes—
397#396C2313yes—
398#396C2311yescharacteristic
399#395C2313yes—
400#395C2313yes—
401#395C2313yes—
402#395C2313yes—
403#395C2313yes—
404#395C2313yes—
405#395C2313yes—
406#395C2313yes—
407#395C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#393C2313yes—
417#393C2313yes—
418#393C2313yes—
419#393C2313yes—
420#393C2313yes—
421#393C2313yes—
422#393C2313yes—
423#392C2313yes—
424#392C2311yescharacteristic
425#391C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#390C2313yes—
448#390C2313yes—
449#390C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2313yes—
528#387C2313yes—
529#387C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#387C2313yes—
538#387C2313yes—
539#387C2313yes—
540#387C2313yes—
541#387C2313yes—
542#387C2313yes—
543#387C2313yes—
544#387C2313yes—
545#387C2313yes—
546#387C2313yes—
547#387C2313yes—
548#387C2313yes—
549#387C2313yes—
550#387C2313yes—
551#387C2313yes—
552#387C2313yes—
553#387C2313yes—
554#387C2313yes—
555#387C2313yes—
556#387C2313yes—
557#387C2313yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2313yes—
563#387C2313yes—
564#387C2313yes—
565#387C2313yes—
566#387C2313yes—
567#387C2313yes—
568#387C2313yes—
569#387C2313yes—
570#387C2313yes—
571#387C2313yes—
572#387C2313yes—
573#387C2313yes—
574#387C2313yes—
575#387C2313yes—
576#387C2313yes—
577#387C2313yes—
578#387C2313yes—
579#387C2313yes—
580#387C2313yes—
581#387C2313yes—
582#387C2313yes—
583#387C2313yes—
584#387C2313yes—
585#387C2313yes—
586#387C2313yes—
587#387C2313yes—
588#387C2313yes—
589#387C2313yes—
590#387C2313yes—
591#387C2313yes—
592#387C2313yes—
593#387C2313yes—
594#387C2313yes—
595#387C2313yes—
596#387C2313yes—
597#387C2313yes—
598#387C2313yes—
599#387C2313yes—
600#387C2313yes—
601#387C2313yes—
602#387C2313yes—
603#387C2313yes—
604#387C2313yes—
605#387C2313yes—
606#387C2313yes—
607#387C2313yes—
608#387C2313yes—
609#387C2313yes—
610#387C2313yes—
611#387C2313yes—
612#387C2313yes—
613#386C2313yes—
614#386C2313yes—
615#386C2313yes—
616#386C2313yes—
617#386C2313yes—
618#386C2313yes—
619#386C2313yes—
620#386C2313yes—
621#386C2313yes—
622#386C2313yes—
623#385C2313yes—
624#385C2313yes—
625#385C2313yes—
626#385C2313yes—
627#385C2313yes—
628#385C2313yes—
629#385C2313yes—
630#385C2313yes—
631#385C2313yes—
632#385C2313yes—
633#385C2313yes—
634#385C2313yes—
635#385C2313yes—
636#385C2313yes—
637#385C2313yes—
638#385C2313yes—
639#385C2313yes—
640#385C2313yes—
641#384C2313yes—
642#384C2311yescharacteristic
643#384C2313yes—
644#384C2311yescharacteristic
645#384C2311yescharacteristic
646#383C2311yescharacteristic
647#383C2313yes—
648#383C2313yes—
649#383C2313yes—
650#383C2313yes—
651#383C2313yes—
652#383C2313yes—
653#383C2311yescharacteristic
654#383C2313yes—
655#382C2313yes—
656#382C2313yes—
657#382C2313yes—
658#382C2313yes—
659#382C2313yes—
660#382C2313yes—
661#382C2313yes—
662#382C2313yes—
663#382C2313yes—
664#382C2313yes—
665#381C2313yes—
666#381C2313yes—
667#381C2313yes—
668#381C2313yes—
669#381C2313yes—
670#381C2313yes—
671#381C2313yes—
672#380C2313yes—
673#380C2313yes—
674#380C2313yes—
675#380C2313yes—
676#380C2313yes—
677#380C2313yes—
678#380C2313yes—
679#380C2313yes—
680#380C2313yes—
681#380C2313yes—
682#380C2313yes—
683#380C2313yes—
684C4×C4⋊C4C2313yes—
685C4×C4⋊C4C2313yes—
686C4×C4⋊C4C2313yes—
687C4×C4⋊C4C2313yes—
688C4×C4⋊C4C2313yes—
689C4×C4⋊C4C2313yes—
690C4×C4⋊C4C2313yes—
691C4×C4⋊C4C2313yes—
692C4×C4⋊C4C2313yes—
693C4×C4⋊C4C2313yes—
694C4×C4⋊C4C2313yes—
695C4×C4⋊C4C2313yes—
696C4×C4⋊C4C2313yes—
697C4×C4⋊C4C2313yes—
698C4×C4⋊C4C2313yes—
699C4×C4⋊C4C2313yes—
700C4×C4⋊C4C2313yes—
701C4×C22⋊C4C2313yes—
702C4×C22⋊C4C2313yes—
703C4×C22⋊C4C2313yes—
704C4×C22⋊C4C2313yes—
705C4×C22⋊C4C2313yes—
706C4×C22⋊C4C2313yes—
707C4×C22⋊C4C2313yes—
708C4×C22⋊C4C2313yes—
709C4×C22⋊C4C2313yes—
710C4×C22⋊C4C2313yes—
711C4×C22⋊C4C2313yes—
712C4×C22⋊C4C2313yes—
713C4×C22⋊C4C2313yes—
714#376C2313yes—
715#376C2311yescharacteristic
716#376C2313yes—
717#376C2313yes—
718C2×#95C2313yes—
719C43C2311yescharacteristic
720C22×Q8C2413yes—
721C22×Q8C2413yes—
722C22×Q8C2413yes—
723C22×D4C2413yes—
724C22×D4C2413yes—
725C23×C4C2413yes—
726C23×C4C2413yes—
727C23×C4C2411yescharacteristic
728C23×C4C2413yes—
729C23×C4C2413yes—
730C23×C4C2413yes—
731C4⋊Q8—46no—
732#126—46no—
733#126—42no—
734#126—42no—
735#126—46no—
736#126—46no—
737#125—46no—
738#125—46no—
739#125—46no—
740#124—46no—
741#123—46no—
742#123—46no—
743C22⋊Q8—46no—
744C22⋊Q8—46no—
745C22⋊Q8—46no—
746C4×Q8—46no—
747C4×D4—46no—
748C4×D4—46no—
749#117—46no—
750C2×C4⋊C4—46no—
751C2×C4⋊C4—46no—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C42—42no—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2411yescharacteristic
857C2×C42C2413yes—
858C2×C42C2413yes—
859C2×C42C2411yescharacteristic
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2411yescharacteristic
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2413yes—
933#95C2413yes—
934#95C2413yes—
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2411yescharacteristic
947#95C2413yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963C24C2513yes—
964C24C2511yescharacteristic
965C2×Q8—26no—
966C2×Q8—43no—
967C2×Q8—43no—
968C2×Q8—43no—
969C2×Q8—43no—
970C2×Q8—43no—
971C2×Q8—43no—
972C2×Q8—43no—
973C2×Q8—43no—
974C2×D4—26no—
975C2×D4—43no—
976C2×D4—43no—
977C2×D4—43no—
978C2×D4—43no—
979C2×D4—43no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—43no—
984C22×C4—43no—
985C22×C4—43no—
986C22×C4—43no—
987C22×C4—43no—
988C22×C4—43no—
989C22×C4—43no—
990C22×C4—43no—
991C22×C4—43no—
992C22×C4—43no—
993C22×C4—43no—
994C22×C4—43no—
995C22×C4—43no—
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2513yes—
1000C22×C4C2513yes—
1001C22×C4C2513yes—
1002C22×C4C2513yes—
1003C22×C4C2513yes—
1004C22×C4C2513yes—
1005C22×C4C2513yes—
1006C22×C4C2513yes—
1007C22×C4C2513yes—
1008C22×C4C2513yes—
1009C22×C4C2513yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2513yes—
1013C22×C4C2513yes—
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C22⋊C4—26no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—26no—
1082C22⋊C4—26no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C22⋊C4—43no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C42—26no—
1111C42—43no—
1112C42—41no—
1113C42—43no—
1114C42—43no—
1115C42—43no—
1116C42—43no—
1117C42—43no—
1118C42—43no—
1119C42—43no—
1120C42—43no—
1121C42—43no—
1122C42—43no—
1123C42—43no—
1124C42—43no—
1125C42—43no—
1126C42—43no—
1127C42—43no—
1128C42—41no—
1129C42—43no—
1130C42—43no—
1131C42—41no—
1132C42—43no—
1133C23—23no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23#58512yes—
1143C23C2611yescharacteristic
1144Q8—86no—
1145Q8—163no—
1146Q8—163no—
1147D4—86no—
1148D4—86no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—412no—
1208C2×C4—86no—
1209C2×C4—161no—
1210C2×C4—163no—
1211C2×C4—163no—
1212C2×C4—163no—
1213C2×C4#58516yes—
1214C22—26no—
1215C22—41no—
1216C22—43no—
1217C22—43no—
1218C22—43no—
1219C22—43no—
1220C22—43no—
1221C22—43no—
1222C22—43no—
1223C22—43no—
1224C22C2×#58513yes—
1225C22C2×#58511yescharacteristic
1226C222−1+613yes—
1227C4—26no—
1228C4—43no—
1229C4—41no—
1230C4—41no—
1231C4—43no—
1232C4—43no—
1233C4—43no—
1234C4—43no—
1235C4—43no—
1236C4—43no—
1237C4—43no—
1238C4—43no—
1239C4—43no—
1240C4—43no—
1241C4—43no—
1242C4—43no—
1243C4—43no—
1244C4—43no—
1245C4—43no—
1246C4—43no—
1247C4—43no—
1248C2—42no—
1249C2—83no—
1250C2#6289113yes—
1251C2#6290913yes—
1252C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2825C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58774C2semidirect
2. #58723C2semidirect
3. #58705C2semidirect
4. #57107C2semidirect
5. #56737C2semidirect
6. #55918C2semidirect
7. #54778C2semidirect
8. #53388C2semidirect
9. #53255C2semidirect
10. #51728C2semidirect
11. #51129C2semidirect
12. #49427C2semidirect
13. #49014C2semidirect
14. #47267C2semidirect
15. #46908C2semidirect
16. #43703C2semidirect
17. #43604C2semidirect
18. #41782C2semidirect
20. #40060C2semidirect
21. #39476C2semidirect
22. #38690C2semidirect
23. #38339C2semidirect

Maximal subgroups

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

subgroupindex
#587742
#587232
#587052
#571072
#567372
#559182
#547782
#533882
#532552
#517282
#511292
#494272
#490142
#472672
#469082
#437032
#436042
#417822
#408872
#400602
#394762
#386902
#383392