Finite Group Databasebeta

← #8429566

Subgroups — #8429566

Order 512.

4153 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60049C211yesmaximal, characteristic, complemented
2#59610C213yesmaximal, complemented
3#59525C213yesmaximal, complemented
4#58734C213yesmaximal, complemented
5#58723C211yesmaximal, characteristic, complemented
6#55244C211yesmaximal, characteristic, complemented
7#53787C213yesmaximal, complemented
8#52602C213yesmaximal, complemented
9#52557C213yesmaximal, complemented
10#52531C213yesmaximal, complemented
11#52488C213yesmaximal, complemented
12#40848C213yesmaximal, complemented
13#40833C213yesmaximal, complemented
14#40749C213yesmaximal, complemented
15#40709C213yesmaximal, complemented
16#39842C213yesmaximal, complemented
17#39824C213yesmaximal, complemented
18#39331C213yesmaximal, complemented
19#39303C213yesmaximal, complemented
20#37595C213yesmaximal, complemented
21#37531C213yesmaximal, complemented
22#36369C213yesmaximal, complemented
23#34961C213yesmaximal, complemented
24#2860C2213yes—
25#2856C2211yescharacteristic
26#2854C2213yes—
27#2841C2213yes—
28#2839C2213yes—
29#2836C2213yes—
30#2830C2213yes—
31#2830C2213yes—
32#2829C2213yes—
33#2829C2213yes—
34#2829C2213yes—
35#2829C2213yes—
36#2828C2213yes—
37#2828C2213yes—
38#2827C2213yes—
39#2826C2213yes—
40#2825C2213yes—
41#2824C2213yes—
42#2823C2211yescharacteristic
43#2818C2211yescharacteristic
44#2816C2213yes—
45#2814C2213yes—
46#2813C2213yes—
47#2810C2211yescharacteristic
48#2802C2213yes—
49#2802C2213yes—
50#2801C2213yes—
51#2800C2213yes—
52#2797C2213yes—
53#2796C2213yes—
54#2791C2213yes—
55#2783C2213yes—
56#2781C2213yes—
57#2780C2213yes—
58#2777C2213yes—
59#2776C2213yes—
60#2776C2213yes—
61#2776C2213yes—
62#2774C2213yes—
63#2770C2213yes—
64#2766C2213yes—
65#2761C2213yes—
66#2757C2213yes—
67#2757C2213yes—
68#2756C2213yes—
69#2753C2213yes—
70#2752C2213yes—
71#2752C2213yes—
72#2751C2213yes—
73#2751C2213yes—
74#2747C2213yes—
75#2740C2213yes—
76#2740C2213yes—
77#2726C2213yes—
78#2725C2213yes—
79#2723C2213yes—
80#2719C2213yes—
81#2714C2213yes—
82#2711C2213yes—
83#2711C2213yes—
84#2708C2213yes—
85#2707C2213yes—
86#2707C2213yes—
87#2705C2213yes—
88#2701C2213yes—
89#2701C2213yes—
90#2694C2213yes—
91#2694C2213yes—
92#2691C2213yes—
93#2690C2213yes—
94#2688C2213yes—
95#2681C2213yes—
96#2673C2213yes—
97#2666C2213yes—
98#2664C2213yes—
99#2664C2213yes—
100#2664C2213yes—
101#2663C2213yes—
102#2663C2213yes—
103#2655C2213yes—
104#2654C2213yes—
105#2654C2213yes—
106#2653C2213yes—
107#2651C2213yes—
108#2651C2213yes—
109#2650C2213yes—
110#2649C2213yes—
111#2648C2213yes—
112#2648C2213yes—
113#2644C2213yes—
114#2644C2211yescharacteristic
115#2643C2211yescharacteristic
116#2643C2213yes—
117#2638C2213yes—
118#2636C2213yes—
119#2633C2213yes—
120#2630C2213yes—
121#2602C2213yes—
122#2602C2213yes—
123#2601C2213yes—
124#2601C2213yes—
125#2597C2213yes—
126#2597C2213yes—
127#2596C2213yes—
128#2596C2213yes—
129#2595C2213yes—
130#2595C2213yes—
131#2594C2213yes—
132#2594C2213yes—
133#2593C2213yes—
134#2593C2213yes—
135#2589C2213yes—
136#2587C2213yes—
137#2585C2213yes—
138#2585C2213yes—
139#2585C2213yes—
140#2585C2213yes—
141#2578C2213yes—
142#2578C2213yes—
143#2577C2213yes—
144#2576C2213yes—
145#2576C2213yes—
146#2575C2213yes—
147#2573C2213yes—
148#2573C2213yes—
149#2573C2213yes—
150#2573C2213yes—
151#2559C2213yes—
152#2559C2213yes—
153#2556C2213yes—
154#2556C2213yes—
155#2554C2213yes—
156#2554C2213yes—
157#2554C2213yes—
158#2554C2213yes—
159#2553C2213yes—
160#2553C2213yes—
161#2533C2213yes—
162#2532C2213yes—
163#2529C2213yes—
164#2528C2213yes—
165#2525C2213yes—
166#2523C2213yes—
167#2522C2213yes—
168#2517C2213yes—
169#2516C2213yes—
170#2515C2213yes—
171#2512C2213yes—
172#2507C2213yes—
173#2497C2213yes—
174#2494C2213yes—
175#2478C2213yes—
176#2478C2213yes—
177#2478C2213yes—
178#2477C2213yes—
179#2476C2213yes—
180#2476C2213yes—
181#2475C2213yes—
182#2475C2213yes—
183#2475C2213yes—
184#2470C2213yes—
185#2469C2213yes—
186#2466C2213yes—
187#2466C2213yes—
188#2466C2213yes—
189#2465C2213yes—
190#2464C2213yes—
191#2464C2213yes—
192#2463C2213yes—
193#2463C2213yes—
194#2460C2213yes—
195#2460C2213yes—
196#2460C2213yes—
197#2458C2213yes—
198#2457C2213yes—
199#2456C2213yes—
200#2456C2213yes—
201#2455C2213yes—
202#2455C2213yes—
203#2450C2213yes—
204#2445C2213yes—
205#2445C2213yes—
206#2444C2213yes—
207#2428C2213yes—
208#2425C2213yes—
209#2421C2213yes—
210#2419C2213yes—
211#2414C2213yes—
212#2414C2213yes—
213#2396C2213yes—
214#2395C2213yes—
215#2395C2213yes—
216#2392C2213yes—
217#2374C2213yes—
218#2374C2213yes—
219#2370C2213yes—
220#2370C2213yes—
221#2363C2213yes—
222#2363C2213yes—
223#2363C2213yes—
224#2363C2213yes—
225#2353C2213yes—
226#2353C2213yes—
227#2343C2213yes—
228#2343C2213yes—
229#2335C2213yes—
230#2335C2213yes—
231#2334C2213yes—
232#2334C2213yes—
233C4×#125C2213yes—
234C4×#125C2213yes—
235C4×#126C2213yes—
236C4×#126C2213yes—
237C4×C22⋊Q8C2213yes—
238C4×C22⋊Q8C2213yes—
239C4×#123C2213yes—
240C4×#123C2213yes—
241C4×#121C2213yes—
242#2296C2213yes—
243#2293C2213yes—
244C42×D4C2213yes—
245C2×#127C2311yescharacteristic
246C2×#127C2311yescharacteristic
247C2×#126C2313yes—
248C2×#126C2313yes—
249C2×#126C2313yes—
250C2×#126C2313yes—
251C2×#126C2311yescharacteristic
252C2×#126C2311yescharacteristic
253C2×#126C2311yescharacteristic
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#123C2313yes—
259C2×#123C2313yes—
260C2×#123C2313yes—
261C2×#123C2313yes—
262C2×#123C2313yes—
263C2×#123C2313yes—
264C2×#123C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×C4×Q8C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×#117C2313yes—
284C2×#117C2313yes—
285C2×#117C2313yes—
286C2×#117C2313yes—
287C22×C42C2313yes—
288C22×C42C2311yescharacteristic
289#401C2313yes—
290#401C2313yes—
291#401C2311yescharacteristic
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#399C2313yes—
314#399C2313yes—
315#399C2313yes—
316#399C2313yes—
317#399C2313yes—
318#399C2313yes—
319#399C2313yes—
320#399C2313yes—
321#398C2313yes—
322#398C2313yes—
323#398C2313yes—
324#398C2313yes—
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#397C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2313yes—
350#397C2313yes—
351#397C2313yes—
352#397C2313yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
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#396C2313yes—
377#396C2313yes—
378#396C2313yes—
379#396C2311yescharacteristic
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2311yescharacteristic
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2311yescharacteristic
394#396C2313yes—
395#396C2313yes—
396#396C2313yes—
397#395C2313yes—
398#395C2313yes—
399#395C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#394C2313yes—
424#394C2313yes—
425#394C2313yes—
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2313yes—
434#393C2313yes—
435#393C2313yes—
436#393C2313yes—
437#393C2313yes—
438#393C2313yes—
439#392C2313yes—
440#392C2313yes—
441#392C2313yes—
442#392C2313yes—
443#392C2313yes—
444#392C2313yes—
445#392C2313yes—
446#392C2313yes—
447#392C2313yes—
448#392C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#390C2313yes—
453#390C2313yes—
454#390C2313yes—
455#390C2313yes—
456#390C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
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#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#388C2313yes—
537#388C2313yes—
538#388C2313yes—
539#388C2313yes—
540#388C2313yes—
541#388C2313yes—
542#388C2313yes—
543#388C2313yes—
544#388C2313yes—
545#388C2313yes—
546#388C2313yes—
547#388C2313yes—
548#388C2313yes—
549#388C2313yes—
550#388C2313yes—
551#388C2313yes—
552#388C2313yes—
553#388C2313yes—
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#386C2313yes—
608#386C2313yes—
609#386C2313yes—
610#386C2313yes—
611#386C2313yes—
612#386C2313yes—
613#386C2313yes—
614#386C2313yes—
615#386C2313yes—
616#386C2313yes—
617#386C2313yes—
618#386C2313yes—
619#386C2313yes—
620#386C2313yes—
621#386C2313yes—
622#386C2313yes—
623#386C2313yes—
624#386C2313yes—
625#386C2313yes—
626#386C2313yes—
627#386C2313yes—
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#385C2313yes—
642#385C2313yes—
643#385C2313yes—
644#385C2313yes—
645#385C2313yes—
646#385C2313yes—
647#385C2313yes—
648#385C2313yes—
649#385C2313yes—
650#385C2313yes—
651#384C2311yescharacteristic
652#384C2311yescharacteristic
653#383C2313yes—
654#383C2313yes—
655#383C2311yescharacteristic
656#383C2313yes—
657#383C2313yes—
658#382C2313yes—
659#382C2313yes—
660#382C2313yes—
661#382C2313yes—
662#381C2313yes—
663#381C2313yes—
664#381C2313yes—
665#381C2313yes—
666#381C2313yes—
667#380C2313yes—
668#380C2313yes—
669#380C2313yes—
670#380C2313yes—
671#380C2313yes—
672#380C2313yes—
673#380C2313yes—
674C4×C4⋊C4C2313yes—
675C4×C4⋊C4C2313yes—
676C4×C4⋊C4C2313yes—
677C4×C4⋊C4C2313yes—
678C4×C4⋊C4C2313yes—
679C4×C4⋊C4C2313yes—
680C4×C4⋊C4C2313yes—
681C4×C4⋊C4C2313yes—
682C4×C4⋊C4C2313yes—
683C4×C4⋊C4C2313yes—
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×C22⋊C4C2313yes—
696C4×C22⋊C4C2313yes—
697C4×C22⋊C4C2313yes—
698C4×C22⋊C4C2313yes—
699C4×C22⋊C4C2313yes—
700C4×C22⋊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—
714C4×C22⋊C4C2313yes—
715#376C2313yes—
716#376C2311yescharacteristic
717C2×#95C2311yescharacteristic
718C2×#95C2313yes—
719C43C2313yes—
720C22×Q8C2413yes—
721C22×D4C2413yes—
722C22×D4C2413yes—
723C22×D4C2413yes—
724C22×D4C2413yes—
725C22×D4C2413yes—
726C22×D4C2413yes—
727C22×D4C2411yescharacteristic
728C22×D4C2413yes—
729C22×D4C2413yes—
730C22×D4C2413yes—
731C23×C4C2413yes—
732C23×C4C2413yes—
733C23×C4C2413yes—
734C23×C4C2413yes—
735C23×C4C2413yes—
736C23×C4C2413yes—
737C23×C4C2413yes—
738C23×C4C2413yes—
739#127—81no—
740#127—81no—
741#126—46no—
742#126—46no—
743#126—46no—
744#126—46no—
745#126—81no—
746#126—81no—
747#126—81no—
748#125—46no—
749#125—46no—
750#125—46no—
751#125—46no—
752#123—46no—
753#123—46no—
754#123—46no—
755#123—46no—
756#123—46no—
757#123—46no—
758#123—83no—
759C22⋊Q8—46no—
760C22⋊Q8—46no—
761C22⋊Q8—83no—
762#121—46no—
763#121—46no—
764#121—46no—
765#121—46no—
766#121—46no—
767#121—83no—
768C4×Q8—83no—
769C4×D4—46no—
770C4×D4—46no—
771C4×D4—46no—
772C4×D4—46no—
773C4×D4—46no—
774C4×D4—46no—
775C4×D4—83no—
776C4×D4—83no—
777#117—46no—
778#117—46no—
779#117—46no—
780#117—83no—
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×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊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×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C42—81no—
891C2×C42—83no—
892C2×C42C2413yes—
893C2×C42C2413yes—
894C2×C42C2413yes—
895C2×C42C2413yes—
896C2×C42C2413yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2413yes—
900C2×C42C2413yes—
901C2×C42C2413yes—
902C2×C42C2413yes—
903C2×C42C2413yes—
904C2×C42C2413yes—
905C2×C42C2413yes—
906C2×C42C2413yes—
907C2×C42C2413yes—
908C2×C42C2413yes—
909C2×C42C2413yes—
910C2×C42C2413yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2411yescharacteristic
920#95C2413yes—
921#95C2413yes—
922#95C2411yescharacteristic
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#95C2413yes—
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—
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985C24C2513yes—
986C24C2513yes—
987C24C2511yescharacteristic
988C24C2511yescharacteristic
989C2×Q8—43no—
990C2×Q8—43no—
991C2×Q8—43no—
992C2×D4—26no—
993C2×D4—26no—
994C2×D4—43no—
995C2×D4—43no—
996C2×D4—43no—
997C2×D4—43no—
998C2×D4—43no—
999C2×D4—43no—
1000C2×D4—43no—
1001C2×D4—43no—
1002C2×D4—43no—
1003C2×D4—43no—
1004C2×D4—43no—
1005C2×D4—43no—
1006C2×D4—43no—
1007C2×D4—43no—
1008C2×D4—43no—
1009C2×D4—43no—
1010C2×D4—43no—
1011C2×D4—43no—
1012C2×D4—43no—
1013C2×D4—43no—
1014C2×D4—43no—
1015C2×D4—43no—
1016C2×D4—43no—
1017C2×D4—43no—
1018C2×D4—43no—
1019C2×D4—43no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—43no—
1026C22×C4—43no—
1027C22×C4—43no—
1028C22×C4—43no—
1029C22×C4—43no—
1030C22×C4—43no—
1031C22×C4—43no—
1032C22×C4—43no—
1033C22×C4—43no—
1034C22×C4—43no—
1035C22×C4—43no—
1036C22×C4—43no—
1037C22×C4—43no—
1038C22×C4—43no—
1039C22×C4—43no—
1040C22×C4—43no—
1041C22×C4—43no—
1042C22×C4—43no—
1043C22×C4—43no—
1044C22×C4C2513yes—
1045C22×C4C2513yes—
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2513yes—
1053C22×C4C2513yes—
1054C22×C4C2513yes—
1055C22×C4C2513yes—
1056C22×C4C2513yes—
1057C22×C4C2513yes—
1058C22×C4C2513yes—
1059C22×C4C2513yes—
1060C22×C4C2513yes—
1061C22×C4C2513yes—
1062C22×C4C2513yes—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—43no—
1100C4⋊C4—43no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—43no—
1104C4⋊C4—43no—
1105C4⋊C4—43no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—43no—
1110C4⋊C4—43no—
1111C4⋊C4—43no—
1112C4⋊C4—43no—
1113C4⋊C4—43no—
1114C4⋊C4—43no—
1115C4⋊C4—43no—
1116C22⋊C4—26no—
1117C22⋊C4—26no—
1118C22⋊C4—26no—
1119C22⋊C4—26no—
1120C22⋊C4—26no—
1121C22⋊C4—26no—
1122C22⋊C4—26no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C42—26no—
1173C42—26no—
1174C42—26no—
1175C42—43no—
1176C42—43no—
1177C42—43no—
1178C42—43no—
1179C42—41no—
1180C42—43no—
1181C42—43no—
1182C42—43no—
1183C42—43no—
1184C42—43no—
1185C42—43no—
1186C42—43no—
1187C42—43no—
1188C42—43no—
1189C42—43no—
1190C42—43no—
1191C42—43no—
1192C42—43no—
1193C42—41no—
1194C42—41no—
1195C23—23no—
1196C23—23no—
1197C23—23no—
1198C23—23no—
1199C23—23no—
1200C23—23no—
1201C23—23no—
1202C23—23no—
1203C23—23no—
1204C23—23no—
1205C23—23no—
1206C23—23no—
1207C23—23no—
1208C23—23no—
1209C23—23no—
1210C23—23no—
1211C23—21no—
1212C23—23no—
1213C23—21no—
1214C23—23no—
1215C23C2611yescharacteristic
1216Q8—86no—
1217D4—412no—
1218D4—86no—
1219D4—86no—
1220D4—86no—
1221D4—86no—
1222D4—86no—
1223D4—163no—
1224D4—161no—
1225D4—163no—
1226D4—163no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—412no—
1281C2×C4—86no—
1282C2×C4—86no—
1283C2×C4—86no—
1284C2×C4—86no—
1285C2×C4—86no—
1286C2×C4—163no—
1287C2×C4—163no—
1288C2×C4#58516yes—
1289C2×C4#58516yes—
1290C22—43no—
1291C22—43no—
1292C22—43no—
1293C22—43no—
1294C22—43no—
1295C22—43no—
1296C22—43no—
1297C22—43no—
1298C22—41no—
1299C22—43no—
1300C22—41no—
1301C22—43no—
1302C22—43no—
1303C22—43no—
1304C22—43no—
1305C22—43no—
1306C22—43no—
1307C22—43no—
1308C22—43no—
1309C22—43no—
1310C22C2×#58513yes—
1311C22C2×#58513yes—
1312C22H(7,𝔽2)11yescharacteristic
1313C4—26no—
1314C4—26no—
1315C4—43no—
1316C4—43no—
1317C4—43no—
1318C4—43no—
1319C4—43no—
1320C4—43no—
1321C4—43no—
1322C4—43no—
1323C4—43no—
1324C4—41no—
1325C4—43no—
1326C4—43no—
1327C4—43no—
1328C4—43no—
1329C4—43no—
1330C4—43no—
1331C4—43no—
1332C2—81no—
1333C2—83no—
1334C2—81no—
1335C2—83no—
1336C2#6276213yes—
1337C2#6296313yes—
1338C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60049C2semidirect
2. #59610C2semidirect
3. #59525C2semidirect
4. #58734C2semidirect
5. #58723C2semidirect
6. #55244C2semidirect
7. #53787C2semidirect
8. #52602C2semidirect
9. #52557C2semidirect
10. #52531C2semidirect
11. #52488C2semidirect
12. #40848C2semidirect
13. #40833C2semidirect
14. #40749C2semidirect
15. #40709C2semidirect
16. #39842C2semidirect
17. #39824C2semidirect
18. #39331C2semidirect
19. #39303C2semidirect
20. #37595C2semidirect
21. #37531C2semidirect
22. #36369C2semidirect
23. #34961C2semidirect

Maximal subgroups

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

subgroupindex
#600492
#596102
#595252
#587342
#587232
#552442
#537872
#526022
#525572
#525312
#524882
#408482
#408332
#407492
#407092
#398422
#398242
#393312
#393032
#375952
#375312
#363692
#349612