Finite Group Databasebeta

← #8926048

Subgroups — #8926048

Order 512.

4291 conjugacy classes of subgroups.

The subgroup lattice has 1409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58975C211yesmaximal, characteristic, complemented
2#56306C213yesmaximal, complemented
3#56114C213yesmaximal, complemented
4#56019C213yesmaximal, complemented
5#55603C213yesmaximal, complemented
6#55244C211yesmaximal, characteristic, complemented
7#54694C211yesmaximal, characteristic, complemented
8#54531C213yesmaximal, complemented
9#53828C213yesmaximal, complemented
10#53790C213yesmaximal, complemented
11#47659C213yesmaximal, complemented
12#47631C213yesmaximal, complemented
13#47499C213yesmaximal, complemented
14#46950C213yesmaximal, complemented
15#46622C213yesmaximal, complemented
16#46563C213yesmaximal, complemented
17#37361C213yesmaximal, complemented
18#37217C213yesmaximal, complemented
19#37036C213yesmaximal, complemented
20#36917C213yesmaximal, complemented
21#36853C213yesmaximal, complemented
22#36770C213yesmaximal, complemented
23#35405C213yesmaximal, complemented
24#2854C2213yes—
25#2854C2213yes—
26#2851C2213yes—
27#2850C2213yes—
28#2839C2213yes—
29#2833C2213yes—
30#2829C2213yes—
31#2828C2213yes—
32#2828C2213yes—
33#2827C2213yes—
34#2825C2213yes—
35#2818C2211yescharacteristic
36#2818C2211yescharacteristic
37#2818C2211yescharacteristic
38#2813C2213yes—
39#2813C2213yes—
40#2810C2211yescharacteristic
41#2805C2213yes—
42#2803C2213yes—
43#2802C2213yes—
44#2801C2211yescharacteristic
45#2801C2213yes—
46#2801C2213yes—
47#2800C2213yes—
48#2799C2213yes—
49#2796C2213yes—
50#2781C2213yes—
51#2781C2213yes—
52#2781C2213yes—
53#2781C2213yes—
54#2780C2213yes—
55#2779C2213yes—
56#2778C2213yes—
57#2778C2213yes—
58#2778C2213yes—
59#2778C2213yes—
60#2778C2213yes—
61#2778C2213yes—
62#2777C2213yes—
63#2775C2213yes—
64#2773C2213yes—
65#2771C2213yes—
66#2770C2213yes—
67#2766C2213yes—
68#2766C2213yes—
69#2762C2213yes—
70#2761C2213yes—
71#2761C2213yes—
72#2757C2213yes—
73#2753C2213yes—
74#2753C2213yes—
75#2753C2213yes—
76#2750C2213yes—
77#2750C2213yes—
78#2749C2213yes—
79#2749C2213yes—
80#2748C2213yes—
81#2746C2213yes—
82#2746C2213yes—
83#2746C2213yes—
84#2741C2213yes—
85#2739C2213yes—
86#2733C2213yes—
87#2727C2213yes—
88#2725C2213yes—
89#2715C2213yes—
90#2714C2213yes—
91#2714C2213yes—
92#2714C2213yes—
93#2710C2213yes—
94#2709C2213yes—
95#2708C2213yes—
96#2708C2213yes—
97#2708C2213yes—
98#2707C2213yes—
99#2707C2213yes—
100#2706C2213yes—
101#2706C2213yes—
102#2705C2213yes—
103#2705C2213yes—
104#2704C2213yes—
105#2703C2213yes—
106#2703C2213yes—
107#2703C2213yes—
108#2703C2213yes—
109#2703C2213yes—
110#2703C2213yes—
111#2702C2213yes—
112#2701C2213yes—
113#2701C2213yes—
114#2695C2213yes—
115#2695C2213yes—
116#2695C2213yes—
117#2694C2213yes—
118#2694C2213yes—
119#2693C2213yes—
120#2691C2213yes—
121#2691C2213yes—
122#2688C2213yes—
123#2688C2213yes—
124#2682C2213yes—
125#2682C2213yes—
126#2673C2213yes—
127#2673C2213yes—
128#2673C2213yes—
129#2673C2213yes—
130#2673C2213yes—
131#2673C2213yes—
132#2673C2213yes—
133#2673C2213yes—
134#2673C2213yes—
135#2672C2213yes—
136#2672C2213yes—
137#2671C2213yes—
138#2671C2213yes—
139#2671C2213yes—
140#2661C2213yes—
141#2649C2213yes—
142#2645C2213yes—
143#2641C2213yes—
144#2636C2213yes—
145#2636C2213yes—
146#2635C2213yes—
147#2635C2213yes—
148#2630C2213yes—
149#2630C2213yes—
150#2630C2213yes—
151#2630C2213yes—
152#2612C2213yes—
153#2603C2213yes—
154#2603C2213yes—
155#2602C2213yes—
156#2595C2213yes—
157#2594C2213yes—
158#2594C2213yes—
159#2591C2213yes—
160#2588C2213yes—
161#2578C2213yes—
162#2578C2213yes—
163#2577C2213yes—
164#2576C2213yes—
165#2576C2213yes—
166#2574C2213yes—
167#2559C2213yes—
168#2558C2213yes—
169#2557C2213yes—
170#2555C2213yes—
171#2555C2213yes—
172#2554C2213yes—
173#2554C2213yes—
174#2553C2213yes—
175#2553C2213yes—
176#2541C2213yes—
177#2535C2213yes—
178#2533C2213yes—
179#2526C2213yes—
180#2525C2213yes—
181#2522C2213yes—
182#2521C2213yes—
183#2521C2213yes—
184#2519C2213yes—
185#2519C2213yes—
186#2518C2213yes—
187#2513C2213yes—
188#2510C2213yes—
189#2510C2213yes—
190#2508C2213yes—
191#2505C2213yes—
192#2494C2213yes—
193#2494C2213yes—
194#2493C2213yes—
195#2489C2213yes—
196#2481C2213yes—
197#2478C2213yes—
198#2473C2213yes—
199#2471C2213yes—
200#2471C2213yes—
201#2470C2213yes—
202#2468C2213yes—
203#2467C2213yes—
204#2464C2213yes—
205#2464C2213yes—
206#2459C2213yes—
207#2457C2213yes—
208#2457C2213yes—
209#2456C2213yes—
210#2456C2213yes—
211#2455C2213yes—
212#2455C2213yes—
213#2447C2213yes—
214#2445C2213yes—
215#2444C2213yes—
216#2444C2213yes—
217#2442C2213yes—
218#2431C2213yes—
219#2431C2213yes—
220#2431C2213yes—
221#2430C2213yes—
222#2428C2213yes—
223#2428C2213yes—
224#2425C2213yes—
225#2425C2213yes—
226#2419C2213yes—
227#2416C2213yes—
228#2407C2213yes—
229#2406C2213yes—
230#2337C2213yes—
231#2337C2213yes—
232#2335C2213yes—
233#2335C2213yes—
234#2335C2213yes—
235#2334C2213yes—
236#2334C2213yes—
237#2333C2213yes—
238#2325C2213yes—
239#2324C2213yes—
240#2311C2213yes—
241C4×#123C2213yes—
242C4×#121C2213yes—
243#2290C2213yes—
244#2275C2211yescharacteristic
245C22×#41C2313yes—
246C2×#127C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#127C2311yescharacteristic
249C2×#127C2313yes—
250C2×#127C2313yes—
251C2×#126C2313yes—
252C2×#126C2313yes—
253C2×#126C2311yescharacteristic
254C2×#126C2311yescharacteristic
255C2×#126C2311yescharacteristic
256C2×#126C2313yes—
257C2×#126C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#123C2313yes—
264C2×#123C2313yes—
265C2×#123C2313yes—
266C2×#123C2313yes—
267C2×#123C2313yes—
268C2×#123C2313yes—
269C2×#123C2313yes—
270C2×#123C2313yes—
271C2×#123C2313yes—
272C2×#123C2313yes—
273C2×#123C2313yes—
274C2×#123C2313yes—
275C2×#123C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×#117C2313yes—
300C22×C4⋊C4C2313yes—
301C22×C42C2313yes—
302#401C2313yes—
303#401C2313yes—
304#401C2313yes—
305#401C2313yes—
306#401C2311yescharacteristic
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#399C2313yes—
329#399C2313yes—
330#399C2313yes—
331#399C2313yes—
332#399C2311yescharacteristic
333#399C2313yes—
334#399C2313yes—
335#399C2313yes—
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#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#396C2313yes—
376#396C2313yes—
377#396C2313yes—
378#396C2313yes—
379#396C2313yes—
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2311yescharacteristic
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#395C2313yes—
393#395C2313yes—
394#395C2313yes—
395#394C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
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#394C2313yes—
435#394C2313yes—
436#393C2313yes—
437#392C2313yes—
438#392C2313yes—
439#392C2313yes—
440#392C2313yes—
441#392C2313yes—
442#392C2313yes—
443#392C2313yes—
444#392C2313yes—
445#392C2313yes—
446#392C2313yes—
447#392C2313yes—
448#392C2313yes—
449#392C2313yes—
450#392C2313yes—
451#392C2313yes—
452#392C2313yes—
453#392C2313yes—
454#392C2313yes—
455#392C2313yes—
456#392C2313yes—
457#392C2313yes—
458#392C2313yes—
459#392C2313yes—
460#392C2313yes—
461#392C2313yes—
462#392C2313yes—
463#392C2313yes—
464#391C2313yes—
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
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#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
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#388C2313yes—
555#388C2313yes—
556#388C2313yes—
557#388C2313yes—
558#388C2313yes—
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#386C2313yes—
591#386C2313yes—
592#386C2313yes—
593#386C2313yes—
594#386C2313yes—
595#386C2313yes—
596#386C2313yes—
597#386C2313yes—
598#386C2313yes—
599#386C2313yes—
600#386C2313yes—
601#386C2313yes—
602#386C2313yes—
603#386C2313yes—
604#386C2313yes—
605#386C2313yes—
606#386C2313yes—
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#386C2313yes—
629#386C2313yes—
630#386C2313yes—
631#386C2313yes—
632#386C2313yes—
633#386C2313yes—
634#386C2313yes—
635#386C2313yes—
636#386C2313yes—
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#385C2313yes—
652#385C2313yes—
653#385C2313yes—
654#385C2313yes—
655#385C2313yes—
656#385C2313yes—
657#385C2313yes—
658#385C2313yes—
659#385C2313yes—
660#385C2313yes—
661#385C2313yes—
662#385C2313yes—
663#385C2313yes—
664#383C2311yescharacteristic
665#383C2311yescharacteristic
666#383C2311yescharacteristic
667#383C2313yes—
668#383C2313yes—
669#382C2313yes—
670#382C2313yes—
671#382C2313yes—
672#382C2313yes—
673#382C2313yes—
674#382C2313yes—
675#381C2313yes—
676#381C2313yes—
677#381C2313yes—
678#381C2313yes—
679#381C2313yes—
680#380C2313yes—
681#380C2313yes—
682#380C2313yes—
683#380C2313yes—
684#380C2313yes—
685#380C2313yes—
686#380C2313yes—
687#380C2313yes—
688#380C2313yes—
689#380C2313yes—
690#380C2313yes—
691#380C2313yes—
692#380C2313yes—
693#380C2313yes—
694#380C2313yes—
695#380C2313yes—
696C4×C4⋊C4C2313yes—
697C4×C4⋊C4C2313yes—
698C4×C4⋊C4C2313yes—
699C4×C4⋊C4C2313yes—
700C4×C4⋊C4C2313yes—
701C4×C4⋊C4C2313yes—
702C4×C4⋊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#376C2311yescharacteristic
716#376C2313yes—
717C2×#95C2313yes—
718C2×#95C2311yescharacteristic
719C2×#95C2311yescharacteristic
720C2×#41—46no—
721C2×#41—83no—
722C2×#41—83no—
723C22×Q8C2413yes—
724C22×D4C2413yes—
725C22×D4C2413yes—
726C22×D4C2411yescharacteristic
727C22×D4C2413yes—
728C22×D4C2413yes—
729C22×D4C2413yes—
730C22×D4C2413yes—
731C22×D4C2413yes—
732C22×D4C2413yes—
733C22×D4C2413yes—
734C22×D4C2413yes—
735C22×D4C2413yes—
736C22×D4C2413yes—
737C22×D4C2413yes—
738C22×D4C2413yes—
739C22×D4C2413yes—
740C22×D4C2413yes—
741C22×D4C2413yes—
742C22×D4C2413yes—
743C23×C4C2413yes—
744C23×C4C2413yes—
745C23×C4C2413yes—
746C23×C4C2413yes—
747C23×C4C2413yes—
748C23×C4C2413yes—
749C23×C4C2413yes—
750C23×C4C2413yes—
751C23×C4C2413yes—
752C23×C4C2413yes—
753C23×C4C2413yes—
754#127—83no—
755#127—83no—
756#127—81no—
757#127—81no—
758#127—81no—
759#126—46no—
760#126—46no—
761#126—83no—
762#126—83no—
763#126—81no—
764#126—81no—
765#126—81no—
766#125—83no—
767#125—83no—
768#124—46no—
769#124—46no—
770#124—83no—
771#123—46no—
772#123—46no—
773#123—46no—
774#123—46no—
775#123—83no—
776#123—83no—
777#123—83no—
778#123—83no—
779#123—83no—
780#123—83no—
781#123—83no—
782#123—83no—
783#123—83no—
784C22⋊Q8—83no—
785#121—46no—
786#121—46no—
787#121—46no—
788#121—46no—
789#121—83no—
790#121—83no—
791#121—83no—
792#121—83no—
793#121—83no—
794#121—83no—
795#121—83no—
796#121—83no—
797#121—83no—
798#121—83no—
799#121—83no—
800C4×D4—46no—
801C4×D4—46no—
802C4×D4—83no—
803C4×D4—83no—
804C4×D4—83no—
805C4×D4—83no—
806C4×D4—83no—
807#117—83no—
808C2×C4⋊C4—83no—
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×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊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×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2413yes—
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2413yes—
919C2×C42—83no—
920C2×C42C2413yes—
921C2×C42C2413yes—
922C2×C42C2413yes—
923C2×C42C2413yes—
924C2×C42C2413yes—
925C2×C42C2413yes—
926C2×C42C2413yes—
927C2×C42C2413yes—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2413yes—
936#95C2411yescharacteristic
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—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2413yes—
994#95C2413yes—
995#95C2413yes—
996#95C2413yes—
997#95C2413yes—
998#95C2413yes—
999#95C2411yescharacteristic
1000C24C2513yes—
1001C24C2513yes—
1002C24C2513yes—
1003C24C2511yescharacteristic
1004C24C2511yescharacteristic
1005#41—824no—
1006C2×Q8—26no—
1007C2×Q8—43no—
1008C2×Q8—43no—
1009C2×D4—26no—
1010C2×D4—26no—
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—
1020C2×D4—43no—
1021C2×D4—43no—
1022C2×D4—43no—
1023C2×D4—43no—
1024C2×D4—43no—
1025C2×D4—43no—
1026C2×D4—43no—
1027C2×D4—43no—
1028C2×D4—43no—
1029C2×D4—43no—
1030C2×D4—43no—
1031C2×D4—43no—
1032C2×D4—43no—
1033C2×D4—43no—
1034C2×D4—43no—
1035C2×D4—43no—
1036C2×D4—43no—
1037C2×D4—43no—
1038C2×D4—43no—
1039C2×D4—43no—
1040C2×D4—43no—
1041C2×D4—43no—
1042C2×D4—43no—
1043C2×D4—43no—
1044C2×D4—43no—
1045C2×D4—43no—
1046C2×D4—43no—
1047C2×D4—43no—
1048C2×D4—43no—
1049C2×D4—43no—
1050C2×D4—43no—
1051C2×D4—43no—
1052C2×D4—43no—
1053C2×D4—43no—
1054C2×D4—43no—
1055C2×D4—43no—
1056C2×D4—43no—
1057C2×D4—43no—
1058C2×D4—43no—
1059C2×D4—43no—
1060C2×D4—43no—
1061C2×D4—43no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C22×C4—26no—
1065C22×C4—26no—
1066C22×C4—43no—
1067C22×C4—43no—
1068C22×C4—43no—
1069C22×C4—43no—
1070C22×C4—43no—
1071C22×C4—43no—
1072C22×C4—43no—
1073C22×C4—43no—
1074C22×C4—43no—
1075C22×C4—43no—
1076C22×C4—43no—
1077C22×C4—43no—
1078C22×C4—43no—
1079C22×C4—43no—
1080C22×C4—43no—
1081C22×C4—43no—
1082C22×C4—43no—
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×C4C2513yes—
1098C22×C4C2513yes—
1099C22×C4C2513yes—
1100C22×C4C2513yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2513yes—
1103C22×C4C2513yes—
1104C22×C4C2513yes—
1105C22×C4C2513yes—
1106C22×C4C2513yes—
1107C22×C4C2513yes—
1108C22×C4C2513yes—
1109C22×C4C2513yes—
1110C22×C4C2513yes—
1111C22×C4C2513yes—
1112C22×C4C2513yes—
1113C22×C4C2513yes—
1114C22×C4C2513yes—
1115C4⋊C4—26no—
1116C4⋊C4—26no—
1117C4⋊C4—26no—
1118C4⋊C4—26no—
1119C4⋊C4—43no—
1120C4⋊C4—43no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4—43no—
1124C4⋊C4—43no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—43no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—43no—
1133C4⋊C4—43no—
1134C4⋊C4—43no—
1135C4⋊C4—43no—
1136C4⋊C4—43no—
1137C4⋊C4—43no—
1138C4⋊C4—43no—
1139C4⋊C4—43no—
1140C4⋊C4—43no—
1141C4⋊C4—43no—
1142C4⋊C4—43no—
1143C4⋊C4—43no—
1144C4⋊C4—43no—
1145C4⋊C4—43no—
1146C4⋊C4—43no—
1147C4⋊C4—43no—
1148C4⋊C4—43no—
1149C4⋊C4—43no—
1150C4⋊C4—43no—
1151C4⋊C4—43no—
1152C4⋊C4—43no—
1153C4⋊C4—43no—
1154C4⋊C4—43no—
1155C4⋊C4—43no—
1156C4⋊C4—43no—
1157C4⋊C4—43no—
1158C4⋊C4—43no—
1159C22⋊C4—26no—
1160C22⋊C4—26no—
1161C22⋊C4—26no—
1162C22⋊C4—26no—
1163C22⋊C4—26no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—43no—
1178C22⋊C4—43no—
1179C22⋊C4—43no—
1180C22⋊C4—43no—
1181C22⋊C4—43no—
1182C22⋊C4—43no—
1183C22⋊C4—43no—
1184C22⋊C4—43no—
1185C22⋊C4—43no—
1186C22⋊C4—43no—
1187C22⋊C4—43no—
1188C22⋊C4—43no—
1189C22⋊C4—43no—
1190C22⋊C4—43no—
1191C22⋊C4—43no—
1192C22⋊C4—43no—
1193C22⋊C4—43no—
1194C22⋊C4—43no—
1195C22⋊C4—43no—
1196C22⋊C4—43no—
1197C22⋊C4—43no—
1198C22⋊C4—43no—
1199C22⋊C4—43no—
1200C22⋊C4—43no—
1201C22⋊C4—43no—
1202C22⋊C4—43no—
1203C22⋊C4—43no—
1204C22⋊C4—43no—
1205C22⋊C4—43no—
1206C22⋊C4—43no—
1207C22⋊C4—43no—
1208C22⋊C4—43no—
1209C22⋊C4—43no—
1210C22⋊C4—43no—
1211C22⋊C4—43no—
1212C22⋊C4—43no—
1213C22⋊C4—43no—
1214C22⋊C4—43no—
1215C22⋊C4—43no—
1216C22⋊C4—43no—
1217C22⋊C4—43no—
1218C22⋊C4—43no—
1219C22⋊C4—43no—
1220C22⋊C4—43no—
1221C22⋊C4—43no—
1222C22⋊C4—43no—
1223C22⋊C4—43no—
1224C22⋊C4—43no—
1225C42—26no—
1226C42—43no—
1227C42—43no—
1228C42—43no—
1229C42—43no—
1230C42—43no—
1231C42—43no—
1232C42—43no—
1233C42—43no—
1234C42—43no—
1235C42—43no—
1236C42—43no—
1237C42—43no—
1238C42—41no—
1239C42—41no—
1240C42—41no—
1241C23—23no—
1242C23—23no—
1243C23—23no—
1244C23—23no—
1245C23—23no—
1246C23—23no—
1247C23—23no—
1248C23—23no—
1249C23—23no—
1250C23—23no—
1251C23—23no—
1252C23—21no—
1253C23—23no—
1254C23—23no—
1255C23—23no—
1256C23—23no—
1257C23—23no—
1258C23—23no—
1259C23—21no—
1260C23—23no—
1261C23—23no—
1262C23—23no—
1263C23—23no—
1264C23—23no—
1265C23—23no—
1266C23—23no—
1267C23—23no—
1268C23C2611yescharacteristic
1269Q8—86no—
1270D4—44no—
1271D4—86no—
1272D4—86no—
1273D4—86no—
1274D4—86no—
1275D4—86no—
1276D4—86no—
1277D4—86no—
1278D4—86no—
1279D4—86no—
1280D4—163no—
1281D4—163no—
1282D4—163no—
1283D4—163no—
1284D4—163no—
1285D4—163no—
1286D4—163no—
1287D4—163no—
1288D4—163no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—23no—
1317C2×C4—23no—
1318C2×C4—23no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—23no—
1322C2×C4—23no—
1323C2×C4—23no—
1324C2×C4—23no—
1325C2×C4—23no—
1326C2×C4—23no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—23no—
1334C2×C4—23no—
1335C2×C4—23no—
1336C2×C4—23no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—23no—
1340C2×C4—412no—
1341C2×C4—86no—
1342C2×C4—86no—
1343C2×C4—86no—
1344C2×C4—86no—
1345C2×C4—86no—
1346C2×C4—163no—
1347C2×C4—163no—
1348C2×C4—163no—
1349C2×C4—163no—
1350C2×C4—163no—
1351C2×C4#58516yes—
1352C22—41no—
1353C22—41no—
1354C22—43no—
1355C22—43no—
1356C22—43no—
1357C22—43no—
1358C22—43no—
1359C22—43no—
1360C22—43no—
1361C22—43no—
1362C22—43no—
1363C22—43no—
1364C22—43no—
1365C22—43no—
1366C22—43no—
1367C22—43no—
1368C22—43no—
1369C22—43no—
1370C22—43no—
1371C22—43no—
1372C22—43no—
1373C22—43no—
1374C22—43no—
1375C22—43no—
1376C22—43no—
1377C22—43no—
1378C22—43no—
1379C22C2×#58513yes—
1380C22H(7,𝔽2)11yescharacteristic
1381C22H(7,𝔽2)13yes—
1382C4—26no—
1383C4—43no—
1384C4—41no—
1385C4—43no—
1386C4—43no—
1387C4—43no—
1388C4—43no—
1389C4—43no—
1390C4—43no—
1391C4—43no—
1392C4—43no—
1393C4—43no—
1394C4—43no—
1395C4—43no—
1396C4—43no—
1397C4—43no—
1398C4—43no—
1399C4—43no—
1400C2—81no—
1401C2—81no—
1402C2—83no—
1403C2—83no—
1404C2—83no—
1405C2#6284011yescharacteristic
1406C2#6286713yes—
1407C2#6288313yes—
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. #58975C2semidirect
2. #56306C2semidirect
3. #56114C2semidirect
4. #56019C2semidirect
5. #55603C2semidirect
6. #55244C2semidirect
7. #54694C2semidirect
8. #54531C2semidirect
9. #53828C2semidirect
10. #53790C2semidirect
11. #47659C2semidirect
12. #47631C2semidirect
13. #47499C2semidirect
14. #46950C2semidirect
15. #46622C2semidirect
16. #46563C2semidirect
17. #37361C2semidirect
18. #37217C2semidirect
19. #37036C2semidirect
20. #36917C2semidirect
21. #36853C2semidirect
22. #36770C2semidirect
23. #35405C2semidirect

Maximal subgroups

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

subgroupindex
#589752
#563062
#561142
#560192
#556032
#552442
#546942
#545312
#538282
#537902
#476592
#476312
#474992
#469502
#466222
#465632
#373612
#372172
#370362
#369172
#368532
#367702
#354052