Finite Group Databasebeta

← #9210392

Subgroups — #9210392

Order 512.

4928 conjugacy classes of subgroups.

The subgroup lattice has 1446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#56538C213yesmaximal, complemented
2#56431C213yesmaximal, complemented
3#53498C213yesmaximal, complemented
4#53445C213yesmaximal, complemented
5#53443C213yesmaximal, complemented
6#52682C213yesmaximal, complemented
7#50339C213yesmaximal, complemented
8#49555C213yesmaximal, complemented
9#49036C213yesmaximal, complemented
10#48376C213yesmaximal, complemented
11#47841C213yesmaximal, complemented
12#47841C213yesmaximal, complemented
13#47691C213yesmaximal, complemented
14#47207C213yesmaximal, complemented
15#46103C213yesmaximal, complemented
16#45874C213yesmaximal, complemented
17#43015C213yesmaximal, complemented
18#41287C213yesmaximal, complemented
19#39397C213yesmaximal, complemented
20#39348C213yesmaximal, complemented
21#35927C211yesmaximal, characteristic, complemented
22#35498C211yesmaximal, characteristic, complemented
23#35432C211yesmaximal, characteristic, complemented
24C2×D4×Q8C2213yes—
25C2×#548C2213yes—
26C2×#540C2213yes—
27C2×#539C2213yes—
28C2×#539C2213yes—
29C2×#539C2213yes—
30#2860C2213yes—
31#2854C2213yes—
32#2837C2213yes—
33#2837C2213yes—
34#2836C2213yes—
35#2829C2213yes—
36#2829C2213yes—
37#2828C2213yes—
38#2828C2213yes—
39#2827C2213yes—
40#2825C2211yescharacteristic
41#2818C2213yes—
42#2813C2213yes—
43#2807C2213yes—
44#2803C2213yes—
45#2803C2213yes—
46#2794C2213yes—
47#2790C2213yes—
48#2780C2213yes—
49#2777C2213yes—
50#2771C2213yes—
51#2768C2213yes—
52#2753C2213yes—
53#2749C2213yes—
54#2748C2213yes—
55#2746C2213yes—
56#2743C2213yes—
57#2741C2213yes—
58#2738C2213yes—
59#2730C2213yes—
60#2730C2213yes—
61#2729C2213yes—
62#2729C2213yes—
63#2729C2213yes—
64#2729C2213yes—
65#2721C2213yes—
66#2721C2213yes—
67#2720C2213yes—
68#2720C2213yes—
69#2720C2213yes—
70#2718C2213yes—
71#2718C2213yes—
72#2718C2213yes—
73#2716C2213yes—
74#2716C2213yes—
75#2714C2213yes—
76#2713C2213yes—
77#2713C2213yes—
78#2711C2213yes—
79#2711C2213yes—
80#2711C2213yes—
81#2711C2213yes—
82#2705C2213yes—
83#2705C2213yes—
84#2705C2213yes—
85#2704C2213yes—
86#2704C2213yes—
87#2703C2213yes—
88#2702C2213yes—
89#2702C2213yes—
90#2701C2213yes—
91#2699C2213yes—
92#2699C2213yes—
93#2696C2213yes—
94#2696C2213yes—
95#2696C2213yes—
96#2694C2213yes—
97#2691C2213yes—
98#2691C2213yes—
99#2689C2213yes—
100#2689C2213yes—
101#2687C2213yes—
102#2687C2213yes—
103#2686C2213yes—
104#2686C2213yes—
105#2682C2213yes—
106#2681C2213yes—
107#2681C2213yes—
108#2681C2213yes—
109#2680C2213yes—
110#2680C2213yes—
111#2680C2213yes—
112#2676C2213yes—
113#2676C2213yes—
114#2673C2213yes—
115#2673C2213yes—
116#2673C2213yes—
117#2673C2213yes—
118#2673C2213yes—
119#2672C2213yes—
120#2672C2213yes—
121#2671C2213yes—
122#2671C2213yes—
123#2667C2213yes—
124#2658C2213yes—
125#2654C2213yes—
126#2651C2213yes—
127#2649C2213yes—
128#2636C2213yes—
129#2636C2213yes—
130#2630C2213yes—
131#2630C2213yes—
132#2630C2213yes—
133#2623C2213yes—
134#2623C2213yes—
135#2614C2213yes—
136#2602C2213yes—
137#2602C2213yes—
138#2601C2213yes—
139#2600C2213yes—
140#2600C2213yes—
141#2600C2213yes—
142#2598C2213yes—
143#2596C2213yes—
144#2595C2213yes—
145#2593C2213yes—
146#2593C2213yes—
147#2590C2213yes—
148#2590C2213yes—
149#2585C2213yes—
150#2560C2213yes—
151#2559C2213yes—
152#2558C2213yes—
153#2557C2213yes—
154#2556C2213yes—
155#2552C2213yes—
156#2542C2213yes—
157#2542C2213yes—
158#2542C2213yes—
159#2541C2213yes—
160#2540C2213yes—
161#2540C2213yes—
162#2540C2213yes—
163#2533C2213yes—
164#2531C2213yes—
165#2528C2213yes—
166#2526C2213yes—
167#2524C2213yes—
168#2521C2213yes—
169#2516C2213yes—
170#2512C2213yes—
171#2512C2213yes—
172#2506C2213yes—
173#2506C2213yes—
174#2501C2213yes—
175#2496C2213yes—
176#2487C2213yes—
177#2479C2213yes—
178#2474C2213yes—
179#2468C2213yes—
180#2468C2213yes—
181#2468C2213yes—
182#2467C2213yes—
183#2467C2213yes—
184#2464C2213yes—
185#2463C2213yes—
186#2463C2213yes—
187#2463C2213yes—
188#2462C2213yes—
189#2462C2213yes—
190#2460C2213yes—
191#2459C2213yes—
192#2458C2213yes—
193#2458C2213yes—
194#2457C2213yes—
195#2457C2213yes—
196#2456C2213yes—
197#2456C2213yes—
198#2456C2213yes—
199#2455C2213yes—
200#2455C2213yes—
201#2452C2213yes—
202#2452C2213yes—
203#2450C2213yes—
204#2449C2213yes—
205#2449C2213yes—
206#2449C2213yes—
207#2445C2213yes—
208#2445C2213yes—
209#2445C2213yes—
210#2445C2213yes—
211#2444C2213yes—
212#2443C2213yes—
213#2443C2213yes—
214#2443C2213yes—
215#2441C2213yes—
216#2440C2213yes—
217#2440C2213yes—
218#2438C2213yes—
219#2430C2213yes—
220#2428C2213yes—
221#2422C2213yes—
222#2419C2213yes—
223#2416C2213yes—
224#2409C2213yes—
225#2409C2213yes—
226#2409C2213yes—
227#2397C2213yes—
228#2388C2211yescharacteristic
229#2383C2211yescharacteristic
230#2378C2213yes—
231#2378C2213yes—
232#2377C2213yes—
233#2368C2213yes—
234#2366C2213yes—
235#2361C2213yes—
236D4×C4⋊C4C2213yes—
237#2336C2213yes—
238#2335C2213yes—
239#2325C2213yes—
240C4×#127C2211yescharacteristic
241C4×#125C2213yes—
242C4×#123C2213yes—
243C2×#384C2211yescharacteristic
244#2276C2211yescharacteristic
245C22×#41C2311yescharacteristic
246C23×Q8C2313yes—
247D4×Q8—412no—
248#548—412no—
249#540—412no—
250#539—412no—
251#539—412no—
252#539—412no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×#127C2311yescharacteristic
257C2×#127C2313yes—
258C2×#127C2313yes—
259C2×#126C2313yes—
260C2×#126C2313yes—
261C2×#126C2313yes—
262C2×#126C2313yes—
263C2×#126C2311yescharacteristic
264C2×#126C2313yes—
265C2×#126C2313yes—
266C2×#125C2313yes—
267C2×#125C2313yes—
268C2×#125C2313yes—
269C2×#125C2313yes—
270C2×#125C2313yes—
271C2×#124C2313yes—
272C2×#124C2313yes—
273C2×#124C2313yes—
274C2×#123C2313yes—
275C2×#123C2313yes—
276C2×#123C2313yes—
277C2×#123C2313yes—
278C2×#123C2313yes—
279C2×#123C2313yes—
280C2×#123C2313yes—
281C2×#123C2313yes—
282C2×#123C2313yes—
283C2×#123C2313yes—
284C2×#123C2313yes—
285C2×#123C2313yes—
286C2×#123C2313yes—
287C2×#123C2313yes—
288C2×C22⋊Q8C2313yes—
289C2×C22⋊Q8C2313yes—
290C2×C22⋊Q8C2313yes—
291C2×C22⋊Q8C2313yes—
292C2×C22⋊Q8C2313yes—
293C2×C22⋊Q8C2313yes—
294C2×C22⋊Q8C2313yes—
295C2×C22⋊Q8C2313yes—
296C2×C22⋊Q8C2313yes—
297C2×C22⋊Q8C2313yes—
298C2×C22⋊Q8C2313yes—
299C2×C22⋊Q8C2313yes—
300C2×C22⋊Q8C2313yes—
301C2×C22⋊Q8C2313yes—
302C2×C22⋊Q8C2313yes—
303C2×#121C2313yes—
304C2×#121C2313yes—
305C2×#121C2313yes—
306C2×#121C2313yes—
307C2×#121C2313yes—
308C2×#121C2313yes—
309C2×#121C2313yes—
310C2×#121C2313yes—
311C2×#121C2313yes—
312C2×#121C2313yes—
313C2×#121C2313yes—
314C2×#121C2313yes—
315C2×#121C2313yes—
316C2×C4×Q8C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×C4×D4C2313yes—
330C2×C4×D4C2313yes—
331C2×C4×D4C2313yes—
332C2×#117C2313yes—
333C22×C4⋊C4C2313yes—
334C22×C4⋊C4C2313yes—
335C22×C4⋊C4C2313yes—
336C22×C42C2311yescharacteristic
337#401C2311yescharacteristic
338#400C2313yes—
339#400C2313yes—
340#400C2313yes—
341#400C2313yes—
342#400C2313yes—
343#400C2313yes—
344#400C2313yes—
345#400C2313yes—
346#400C2313yes—
347#400C2313yes—
348#400C2313yes—
349#400C2313yes—
350#400C2313yes—
351#400C2313yes—
352#400C2313yes—
353#399C2313yes—
354#399C2313yes—
355#399C2313yes—
356#399C2313yes—
357#399C2313yes—
358#399C2313yes—
359#399C2313yes—
360#399C2313yes—
361#399C2313yes—
362#399C2313yes—
363#399C2313yes—
364#399C2313yes—
365#399C2313yes—
366#399C2313yes—
367#399C2313yes—
368#399C2313yes—
369#398C2313yes—
370#398C2313yes—
371#398C2313yes—
372#398C2313yes—
373#398C2313yes—
374#398C2313yes—
375#398C2313yes—
376#398C2313yes—
377#398C2313yes—
378#398C2313yes—
379#398C2313yes—
380#398C2313yes—
381#398C2313yes—
382#398C2313yes—
383#398C2313yes—
384#398C2313yes—
385#398C2313yes—
386#398C2313yes—
387#398C2313yes—
388#398C2313yes—
389#398C2313yes—
390#398C2313yes—
391#397C2313yes—
392#397C2313yes—
393#397C2313yes—
394#397C2313yes—
395#397C2313yes—
396#397C2313yes—
397#397C2313yes—
398#397C2313yes—
399#397C2313yes—
400#397C2313yes—
401#397C2313yes—
402#397C2313yes—
403#397C2313yes—
404#397C2313yes—
405#397C2313yes—
406#396C2311yescharacteristic
407#396C2313yes—
408#396C2313yes—
409#396C2313yes—
410#396C2313yes—
411#396C2313yes—
412#396C2313yes—
413#396C2313yes—
414#396C2313yes—
415#396C2313yes—
416#396C2313yes—
417#396C2313yes—
418#396C2313yes—
419#396C2313yes—
420#396C2313yes—
421#396C2313yes—
422#396C2313yes—
423#395C2313yes—
424#395C2313yes—
425#395C2313yes—
426#395C2313yes—
427#395C2311yescharacteristic
428#395C2313yes—
429#395C2313yes—
430#395C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2313yes—
434#394C2313yes—
435#394C2313yes—
436#394C2313yes—
437#394C2313yes—
438#394C2313yes—
439#394C2313yes—
440#394C2313yes—
441#394C2313yes—
442#394C2313yes—
443#394C2313yes—
444#394C2313yes—
445#394C2313yes—
446#394C2313yes—
447#394C2313yes—
448#394C2313yes—
449#394C2313yes—
450#394C2313yes—
451#394C2313yes—
452#394C2313yes—
453#394C2313yes—
454#394C2313yes—
455#394C2313yes—
456#394C2313yes—
457#394C2313yes—
458#394C2313yes—
459#394C2313yes—
460#394C2313yes—
461#394C2313yes—
462#394C2313yes—
463#394C2313yes—
464#394C2313yes—
465#394C2313yes—
466#394C2313yes—
467#394C2313yes—
468#394C2313yes—
469#393C2313yes—
470#393C2313yes—
471#393C2313yes—
472#393C2313yes—
473#393C2313yes—
474#393C2311yescharacteristic
475#393C2313yes—
476#393C2313yes—
477#392C2313yes—
478#392C2313yes—
479#392C2313yes—
480#392C2313yes—
481#392C2313yes—
482#392C2313yes—
483#392C2311yescharacteristic
484#392C2313yes—
485#392C2313yes—
486#392C2313yes—
487#392C2313yes—
488#392C2313yes—
489#392C2313yes—
490#392C2313yes—
491#392C2313yes—
492#392C2313yes—
493#392C2313yes—
494#392C2313yes—
495#391C2313yes—
496#391C2313yes—
497#391C2313yes—
498#391C2313yes—
499#391C2313yes—
500#391C2313yes—
501#390C2313yes—
502#390C2313yes—
503#390C2313yes—
504#390C2313yes—
505#390C2313yes—
506#390C2313yes—
507#390C2313yes—
508#390C2313yes—
509#390C2313yes—
510#390C2313yes—
511#390C2313yes—
512#390C2313yes—
513#390C2313yes—
514#390C2313yes—
515#390C2313yes—
516#390C2313yes—
517#390C2313yes—
518#390C2313yes—
519#390C2313yes—
520#389C2313yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2313yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#389C2313yes—
529#389C2313yes—
530#389C2313yes—
531#389C2313yes—
532#389C2313yes—
533#389C2313yes—
534#389C2313yes—
535#389C2313yes—
536#389C2313yes—
537#389C2313yes—
538#389C2313yes—
539#389C2313yes—
540#389C2313yes—
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#388C2313yes—
560#388C2313yes—
561#388C2313yes—
562#388C2313yes—
563#388C2313yes—
564#388C2313yes—
565#388C2313yes—
566#388C2313yes—
567#388C2313yes—
568#388C2313yes—
569#388C2313yes—
570#388C2313yes—
571#388C2313yes—
572#388C2313yes—
573#388C2313yes—
574#388C2313yes—
575#388C2313yes—
576#388C2313yes—
577#388C2313yes—
578#388C2313yes—
579#388C2313yes—
580#388C2313yes—
581#388C2313yes—
582#388C2313yes—
583#388C2313yes—
584#388C2313yes—
585#388C2313yes—
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#387C2313yes—
614#387C2313yes—
615#387C2313yes—
616#387C2313yes—
617#387C2313yes—
618#387C2313yes—
619#387C2313yes—
620#387C2313yes—
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#386C2313yes—
638#386C2313yes—
639#386C2313yes—
640#386C2313yes—
641#386C2313yes—
642#386C2313yes—
643#386C2313yes—
644#386C2313yes—
645#386C2313yes—
646#386C2313yes—
647#386C2313yes—
648#386C2313yes—
649#386C2313yes—
650#386C2313yes—
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#385C2313yes—
665#385C2313yes—
666#385C2313yes—
667#385C2313yes—
668#385C2313yes—
669#385C2313yes—
670#385C2313yes—
671#385C2313yes—
672#385C2313yes—
673#385C2313yes—
674#385C2313yes—
675#385C2313yes—
676#385C2313yes—
677#385C2313yes—
678#385C2313yes—
679#384C2311yescharacteristic
680#384C2313yes—
681#384C2311yescharacteristic
682#384C2313yes—
683#384C2313yes—
684#384C2313yes—
685#384C2311yescharacteristic
686#384C2311yescharacteristic
687#383C2313yes—
688#383C2311yescharacteristic
689#382C2313yes—
690#381C2313yes—
691#381C2313yes—
692#381C2313yes—
693#381C2313yes—
694#381C2313yes—
695#381C2313yes—
696#380C2313yes—
697#380C2313yes—
698#380C2313yes—
699#380C2313yes—
700#380C2313yes—
701#380C2313yes—
702#380C2313yes—
703#380C2313yes—
704#380C2313yes—
705#380C2313yes—
706C4×C4⋊C4C2313yes—
707C4×C4⋊C4C2313yes—
708C4×C4⋊C4C2313yes—
709C4×C4⋊C4C2313yes—
710C4×C4⋊C4C2313yes—
711C4×C4⋊C4C2313yes—
712C4×C4⋊C4C2313yes—
713C4×C4⋊C4C2313yes—
714C4×C4⋊C4C2313yes—
715C4×C4⋊C4C2313yes—
716C4×C4⋊C4C2313yes—
717C4×C22⋊C4C2313yes—
718C4×C22⋊C4C2313yes—
719C4×C22⋊C4C2313yes—
720C4×C22⋊C4C2313yes—
721C4×C22⋊C4C2313yes—
722C4×C22⋊C4C2313yes—
723#376C2313yes—
724C2×#95C2313yes—
725C43C2311yescharacteristic
726C2×#41—46no—
727C22×Q8—46no—
728C22×Q8—46no—
729C22×Q8—46no—
730C22×Q8C2411yescharacteristic
731C22×Q8C2413yes—
732C22×Q8C2413yes—
733C22×Q8C2413yes—
734C22×D4C2413yes—
735C22×D4C2413yes—
736C22×D4C2413yes—
737C22×D4C2413yes—
738C22×D4C2413yes—
739C22×D4C2413yes—
740C22×D4C2413yes—
741C22×D4C2413yes—
742C22×D4C2413yes—
743C22×D4C2413yes—
744C22×D4C2413yes—
745C22×D4C2413yes—
746C22×D4C2413yes—
747C22×D4C2413yes—
748C22×D4C2413yes—
749C23×C4C2413yes—
750C23×C4C2413yes—
751C23×C4C2413yes—
752C23×C4C2413yes—
753C23×C4C2413yes—
754C23×C4C2413yes—
755C23×C4C2411yescharacteristic
756C23×C4C2413yes—
757C23×C4C2413yes—
758C23×C4C2413yes—
759C23×C4C2413yes—
760C23×C4C2413yes—
761C4⋊Q8—46no—
762C4⋊Q8—46no—
763C4⋊Q8—46no—
764#127—46no—
765#127—42no—
766#127—46no—
767#126—46no—
768#126—46no—
769#126—46no—
770#126—42no—
771#126—46no—
772#126—46no—
773#126—46no—
774#125—212no—
775#125—212no—
776#125—46no—
777#125—46no—
778#125—46no—
779#124—46no—
780#124—46no—
781#124—46no—
782#123—212no—
783#123—212no—
784#123—46no—
785#123—46no—
786#123—46no—
787#123—46no—
788#123—46no—
789#123—46no—
790#123—46no—
791#123—46no—
792#123—46no—
793#123—46no—
794#123—46no—
795#123—46no—
796C22⋊Q8—212no—
797C22⋊Q8—212no—
798C22⋊Q8—212no—
799C22⋊Q8—46no—
800C22⋊Q8—46no—
801C22⋊Q8—46no—
802C22⋊Q8—46no—
803C22⋊Q8—46no—
804C22⋊Q8—46no—
805C22⋊Q8—46no—
806C22⋊Q8—46no—
807C22⋊Q8—46no—
808C22⋊Q8—46no—
809C22⋊Q8—46no—
810C22⋊Q8—46no—
811#121—212no—
812#121—46no—
813#121—46no—
814#121—46no—
815#121—46no—
816#121—46no—
817#121—46no—
818#121—46no—
819#121—46no—
820#121—46no—
821#121—46no—
822#121—46no—
823#121—46no—
824C4×Q8—212no—
825C4×D4—46no—
826C4×D4—46no—
827C4×D4—46no—
828C4×D4—46no—
829C4×D4—46no—
830C4×D4—46no—
831C4×D4—46no—
832C4×D4—46no—
833C4×D4—46no—
834C4×D4—46no—
835C4×D4—46no—
836C4×D4—46no—
837C4×D4—46no—
838C4×D4—46no—
839C4×D4—46no—
840#117—46no—
841C2×C4⋊C4—46no—
842C2×C4⋊C4—46no—
843C2×C4⋊C4—46no—
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×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2413yes—
873C2×C4⋊C4C2413yes—
874C2×C4⋊C4C2413yes—
875C2×C4⋊C4C2413yes—
876C2×C4⋊C4C2413yes—
877C2×C4⋊C4C2413yes—
878C2×C4⋊C4C2413yes—
879C2×C4⋊C4C2413yes—
880C2×C4⋊C4C2413yes—
881C2×C4⋊C4C2413yes—
882C2×C4⋊C4C2413yes—
883C2×C4⋊C4C2413yes—
884C2×C4⋊C4C2413yes—
885C2×C4⋊C4C2413yes—
886C2×C4⋊C4C2413yes—
887C2×C4⋊C4C2413yes—
888C2×C4⋊C4C2413yes—
889C2×C4⋊C4C2413yes—
890C2×C4⋊C4C2413yes—
891C2×C4⋊C4C2413yes—
892C2×C4⋊C4C2413yes—
893C2×C4⋊C4C2413yes—
894C2×C4⋊C4C2413yes—
895C2×C4⋊C4C2413yes—
896C2×C4⋊C4C2413yes—
897C2×C4⋊C4C2413yes—
898C2×C4⋊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×C22⋊C4C2413yes—
920C2×C22⋊C4C2413yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2413yes—
925C2×C22⋊C4C2413yes—
926C2×C22⋊C4C2413yes—
927C2×C22⋊C4C2413yes—
928C2×C22⋊C4C2413yes—
929C2×C22⋊C4C2413yes—
930C2×C22⋊C4C2413yes—
931C2×C22⋊C4C2413yes—
932C2×C22⋊C4C2413yes—
933C2×C22⋊C4C2413yes—
934C2×C22⋊C4C2413yes—
935C2×C22⋊C4C2413yes—
936C2×C22⋊C4C2413yes—
937C2×C22⋊C4C2413yes—
938C2×C22⋊C4C2413yes—
939C2×C22⋊C4C2413yes—
940C2×C22⋊C4C2413yes—
941C2×C22⋊C4C2413yes—
942C2×C22⋊C4C2413yes—
943C2×C22⋊C4C2413yes—
944C2×C22⋊C4C2413yes—
945C2×C22⋊C4C2413yes—
946C2×C22⋊C4C2413yes—
947C2×C22⋊C4C2413yes—
948C2×C22⋊C4C2413yes—
949C2×C22⋊C4C2413yes—
950C2×C22⋊C4C2413yes—
951C2×C22⋊C4C2413yes—
952C2×C22⋊C4C2413yes—
953C2×C22⋊C4C2413yes—
954C2×C22⋊C4C2413yes—
955C2×C22⋊C4C2413yes—
956C2×C22⋊C4C2413yes—
957C2×C22⋊C4C2413yes—
958C2×C22⋊C4C2413yes—
959C2×C22⋊C4C2413yes—
960C2×C22⋊C4C2413yes—
961C2×C42—42no—
962C2×C42C2413yes—
963C2×C42C2413yes—
964C2×C42C2413yes—
965C2×C42C2413yes—
966C2×C42C2413yes—
967C2×C42C2413yes—
968C2×C42C2413yes—
969C2×C42C2413yes—
970C2×C42C2413yes—
971C2×C42C2413yes—
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2413yes—
975C2×C42C2413yes—
976C2×C42C2411yescharacteristic
977C2×C42C2413yes—
978C2×C42C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2411yescharacteristic
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#95C2413yes—
1000#95C2413yes—
1001#95C2413yes—
1002#95C2413yes—
1003#95C2413yes—
1004#95C2413yes—
1005#95C2413yes—
1006#95C2413yes—
1007#95C2413yes—
1008#95C2413yes—
1009#95C2413yes—
1010#95C2413yes—
1011#95C2413yes—
1012#95C2413yes—
1013#95C2413yes—
1014#95C2413yes—
1015#95C2413yes—
1016#95C2413yes—
1017#95C2413yes—
1018#95C2413yes—
1019#95C2413yes—
1020#95C2413yes—
1021#95C2413yes—
1022#95C2413yes—
1023#95C2413yes—
1024#95C2413yes—
1025#95C2413yes—
1026#95C2413yes—
1027#95C2413yes—
1028#95C2413yes—
1029#95C2413yes—
1030#95C2413yes—
1031#95C2413yes—
1032#95C2413yes—
1033#95C2413yes—
1034#95C2413yes—
1035C24C2513yes—
1036C24C2513yes—
1037C24C2513yes—
1038C24C2511yescharacteristic
1039#41—88no—
1040C2×Q8—26no—
1041C2×Q8—26no—
1042C2×Q8—26no—
1043C2×Q8—26no—
1044C2×Q8—43no—
1045C2×Q8—43no—
1046C2×Q8—43no—
1047C2×Q8—43no—
1048C2×Q8—43no—
1049C2×Q8—43no—
1050C2×Q8—824no—
1051C2×D4—26no—
1052C2×D4—26no—
1053C2×D4—26no—
1054C2×D4—26no—
1055C2×D4—26no—
1056C2×D4—26no—
1057C2×D4—26no—
1058C2×D4—26no—
1059C2×D4—43no—
1060C2×D4—43no—
1061C2×D4—43no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—43no—
1065C2×D4—43no—
1066C2×D4—43no—
1067C2×D4—43no—
1068C2×D4—43no—
1069C2×D4—43no—
1070C2×D4—43no—
1071C2×D4—43no—
1072C2×D4—43no—
1073C2×D4—43no—
1074C2×D4—43no—
1075C2×D4—43no—
1076C2×D4—43no—
1077C2×D4—43no—
1078C2×D4—43no—
1079C2×D4—43no—
1080C2×D4—43no—
1081C2×D4—43no—
1082C2×D4—43no—
1083C2×D4—43no—
1084C2×D4—43no—
1085C2×D4—43no—
1086C2×D4—43no—
1087C2×D4—43no—
1088C2×D4—43no—
1089C2×D4—43no—
1090C2×D4—43no—
1091C2×D4—43no—
1092C2×D4—43no—
1093C2×D4—43no—
1094C2×D4—43no—
1095C2×D4—43no—
1096C22×C4—26no—
1097C22×C4—26no—
1098C22×C4—26no—
1099C22×C4—26no—
1100C22×C4—26no—
1101C22×C4—26no—
1102C22×C4—26no—
1103C22×C4—43no—
1104C22×C4—43no—
1105C22×C4—43no—
1106C22×C4—43no—
1107C22×C4—43no—
1108C22×C4—43no—
1109C22×C4—43no—
1110C22×C4—43no—
1111C22×C4—43no—
1112C22×C4—43no—
1113C22×C4—43no—
1114C22×C4—43no—
1115C22×C4—43no—
1116C22×C4—43no—
1117C22×C4—43no—
1118C22×C4—43no—
1119C22×C4—43no—
1120C22×C4—43no—
1121C22×C4—43no—
1122C22×C4—43no—
1123C22×C4—43no—
1124C22×C4—43no—
1125C22×C4—43no—
1126C22×C4—43no—
1127C22×C4—43no—
1128C22×C4—43no—
1129C22×C4—43no—
1130C22×C4C2513yes—
1131C22×C4C2513yes—
1132C22×C4C2513yes—
1133C22×C4C2513yes—
1134C22×C4C2513yes—
1135C22×C4C2513yes—
1136C22×C4C2513yes—
1137C22×C4C2513yes—
1138C22×C4C2513yes—
1139C22×C4C2513yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2513yes—
1143C22×C4C2513yes—
1144C22×C4C2513yes—
1145C22×C4C2513yes—
1146C22×C4C2513yes—
1147C22×C4C2513yes—
1148C22×C4C2513yes—
1149C4⋊C4—26no—
1150C4⋊C4—26no—
1151C4⋊C4—26no—
1152C4⋊C4—26no—
1153C4⋊C4—26no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—26no—
1158C4⋊C4—26no—
1159C4⋊C4—26no—
1160C4⋊C4—26no—
1161C4⋊C4—26no—
1162C4⋊C4—26no—
1163C4⋊C4—26no—
1164C4⋊C4—26no—
1165C4⋊C4—26no—
1166C4⋊C4—26no—
1167C4⋊C4—26no—
1168C4⋊C4—26no—
1169C4⋊C4—43no—
1170C4⋊C4—43no—
1171C4⋊C4—43no—
1172C4⋊C4—43no—
1173C4⋊C4—43no—
1174C4⋊C4—43no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4—43no—
1178C4⋊C4—43no—
1179C4⋊C4—43no—
1180C4⋊C4—43no—
1181C4⋊C4—43no—
1182C4⋊C4—43no—
1183C4⋊C4—43no—
1184C4⋊C4—43no—
1185C4⋊C4—43no—
1186C4⋊C4—43no—
1187C4⋊C4—43no—
1188C4⋊C4—43no—
1189C4⋊C4—43no—
1190C4⋊C4—43no—
1191C4⋊C4—43no—
1192C4⋊C4—43no—
1193C4⋊C4—43no—
1194C4⋊C4—43no—
1195C4⋊C4—43no—
1196C4⋊C4—43no—
1197C4⋊C4—43no—
1198C4⋊C4—43no—
1199C4⋊C4—43no—
1200C4⋊C4—43no—
1201C4⋊C4—43no—
1202C4⋊C4—43no—
1203C4⋊C4H(5,𝔽2)112yes—
1204C22⋊C4—26no—
1205C22⋊C4—26no—
1206C22⋊C4—26no—
1207C22⋊C4—26no—
1208C22⋊C4—26no—
1209C22⋊C4—26no—
1210C22⋊C4—26no—
1211C22⋊C4—26no—
1212C22⋊C4—26no—
1213C22⋊C4—26no—
1214C22⋊C4—26no—
1215C22⋊C4—26no—
1216C22⋊C4—26no—
1217C22⋊C4—26no—
1218C22⋊C4—26no—
1219C22⋊C4—43no—
1220C22⋊C4—43no—
1221C22⋊C4—43no—
1222C22⋊C4—43no—
1223C22⋊C4—43no—
1224C22⋊C4—43no—
1225C22⋊C4—43no—
1226C22⋊C4—43no—
1227C22⋊C4—43no—
1228C22⋊C4—43no—
1229C22⋊C4—43no—
1230C22⋊C4—43no—
1231C22⋊C4—43no—
1232C22⋊C4—43no—
1233C22⋊C4—43no—
1234C22⋊C4—43no—
1235C22⋊C4—43no—
1236C22⋊C4—43no—
1237C22⋊C4—43no—
1238C22⋊C4—43no—
1239C22⋊C4—43no—
1240C22⋊C4—43no—
1241C22⋊C4—43no—
1242C22⋊C4—43no—
1243C22⋊C4—43no—
1244C22⋊C4—43no—
1245C22⋊C4—43no—
1246C22⋊C4—43no—
1247C22⋊C4—43no—
1248C22⋊C4—43no—
1249C22⋊C4—43no—
1250C22⋊C4—43no—
1251C22⋊C4—43no—
1252C22⋊C4—43no—
1253C22⋊C4—43no—
1254C22⋊C4—43no—
1255C22⋊C4—43no—
1256C22⋊C4—43no—
1257C22⋊C4—43no—
1258C22⋊C4—43no—
1259C22⋊C4—43no—
1260C22⋊C4—43no—
1261C22⋊C4—43no—
1262C22⋊C4—43no—
1263C22⋊C4—43no—
1264C22⋊C4—43no—
1265C22⋊C4—43no—
1266C42—26no—
1267C42—26no—
1268C42—26no—
1269C42—26no—
1270C42—26no—
1271C42—41no—
1272C42—43no—
1273C42—43no—
1274C42—43no—
1275C42—43no—
1276C42—43no—
1277C42—43no—
1278C42—43no—
1279C42—43no—
1280C42—41no—
1281C42—41no—
1282C42—43no—
1283C23—23no—
1284C23—23no—
1285C23—23no—
1286C23—23no—
1287C23—23no—
1288C23—23no—
1289C23—23no—
1290C23—23no—
1291C23—23no—
1292C23—23no—
1293C23—23no—
1294C23—23no—
1295C23—23no—
1296C23—23no—
1297C23—23no—
1298C23—23no—
1299C23—23no—
1300C23—23no—
1301C23—23no—
1302C23—23no—
1303C23—23no—
1304C23—23no—
1305C23—23no—
1306C23#58512yes—
1307C23C2611yescharacteristic
1308Q8—28no—
1309Q8—86no—
1310Q8—86no—
1311Q8—86no—
1312D4—412no—
1313D4—412no—
1314D4—86no—
1315D4—86no—
1316D4—86no—
1317D4—86no—
1318D4—86no—
1319D4—86no—
1320D4—86no—
1321D4—86no—
1322D4—86no—
1323D4—86no—
1324D4—163no—
1325D4—163no—
1326D4—163no—
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—23no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—23no—
1345C2×C4—23no—
1346C2×C4—23no—
1347C2×C4—23no—
1348C2×C4—23no—
1349C2×C4—23no—
1350C2×C4—23no—
1351C2×C4—23no—
1352C2×C4—23no—
1353C2×C4—23no—
1354C2×C4—23no—
1355C2×C4—23no—
1356C2×C4—23no—
1357C2×C4—23no—
1358C2×C4—23no—
1359C2×C4—23no—
1360C2×C4—23no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—23no—
1364C2×C4—23no—
1365C2×C4—23no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—23no—
1371C2×C4—23no—
1372C2×C4—23no—
1373C2×C4—23no—
1374C2×C4—23no—
1375C2×C4—23no—
1376C2×C4—23no—
1377C2×C4—412no—
1378C2×C4—86no—
1379C2×C4—86no—
1380C2×C4—86no—
1381C2×C4—86no—
1382C2×C4—86no—
1383C2×C4—86no—
1384C2×C4—161no—
1385C2×C4—163no—
1386C2×C4—163no—
1387C2×C4—163no—
1388C2×C4—163no—
1389C2×C4C2×H(5,𝔽2)16yes—
1390C2×C4C2×H(5,𝔽2)16yes—
1391C2×C4C2×H(5,𝔽2)16yes—
1392C22—26no—
1393C22—43no—
1394C22—41no—
1395C22—43no—
1396C22—43no—
1397C22—43no—
1398C22—43no—
1399C22—43no—
1400C22—43no—
1401C22—43no—
1402C22—43no—
1403C22—43no—
1404C22—43no—
1405C22—43no—
1406C22—43no—
1407C22—43no—
1408C22—43no—
1409C22—43no—
1410C22—43no—
1411C22—43no—
1412C22—43no—
1413C22—43no—
1414C22—43no—
1415C22—43no—
1416C22C22×H(5,𝔽2)13yes—
1417C22C2×#58511yescharacteristic
1418C222−1+613yes—
1419C4—26no—
1420C4—26no—
1421C4—26no—
1422C4—43no—
1423C4—43no—
1424C4—43no—
1425C4—43no—
1426C4—43no—
1427C4—41no—
1428C4—43no—
1429C4—43no—
1430C4—43no—
1431C4—41no—
1432C4—43no—
1433C4—43no—
1434C4—43no—
1435C4—43no—
1436C4—43no—
1437C4—43no—
1438C2—42no—
1439C2—83no—
1440C2—83no—
1441C2—83no—
1442C2#6283211yescharacteristic
1443C2#6289813yes—
1444C2#6304413yes—
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. #56538C2semidirect
2. #56431C2semidirect
3. #53498C2semidirect
4. #53445C2semidirect
5. #53443C2semidirect
6. #52682C2semidirect
7. #50339C2semidirect
8. #49555C2semidirect
9. #49036C2semidirect
10. #48376C2semidirect
11. #47841C2semidirect
12. #47841C2semidirect
13. #47691C2semidirect
14. #47207C2semidirect
15. #46103C2semidirect
16. #45874C2semidirect
17. #43015C2semidirect
18. #41287C2semidirect
19. #39397C2semidirect
20. #39348C2semidirect
21. #35927C2semidirect
22. #35498C2semidirect
23. #35432C2semidirect

Maximal subgroups

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

subgroupindex
#565382
#564312
#534982
#534452
#534432
#526822
#503392
#495552
#490362
#483762
#478412
#476912
#472072
#461032
#458742
#430152
#412872
#393972
#393482
#359272
#354982
#354322