Finite Group Databasebeta

← #8105556

Subgroups — #8105556

Order 512.

4190 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58849C211yesmaximal, characteristic, complemented
2#58781C213yesmaximal, complemented
3#58460C211yesmaximal, characteristic, complemented
4#58333C213yesmaximal, complemented
5#57589C213yesmaximal, complemented
6#57096C213yesmaximal, complemented
7#57090C213yesmaximal, complemented
8#56596C213yesmaximal, complemented
9#55472C213yesmaximal, complemented
10#54631C213yesmaximal, complemented
11#54623C213yesmaximal, complemented
12#53870C213yesmaximal, complemented
13#52294C211yesmaximal, characteristic, complemented
14#52284C213yesmaximal, complemented
15#52243C213yesmaximal, complemented
16#52233C213yesmaximal, complemented
17#52197C213yesmaximal, complemented
18#52185C213yesmaximal, complemented
19#36697C213yesmaximal, complemented
20#34968C213yesmaximal, complemented
21#34902C213yesmaximal, complemented
22#34811C213yesmaximal, complemented
23#34589C213yesmaximal, complemented
24#2843C2213yescomplemented
25#2839C2213yescomplemented
26#2839C2213yescomplemented
27#2838C2213yes—
28#2838C2213yescomplemented
29#2837C2213yes—
30#2837C2213yes—
31#2836C2213yes—
32#2836C2213yescomplemented
33#2833C2213yescomplemented
34#2832C2213yes—
35#2831C2213yes—
36#2831C2213yescomplemented
37#2823C2213yes—
38#2821C2213yes—
39#2821C2213yescomplemented
40#2800C2213yes—
41#2799C2213yescomplemented
42#2793C2213yes—
43#2789C2213yescomplemented
44#2788C2213yes—
45#2788C2213yescomplemented
46#2787C2213yescomplemented
47#2786C2213yes—
48#2786C2213yes—
49#2783C2213yes—
50#2781C2213yes—
51#2780C2213yes—
52#2779C2213yescomplemented
53#2778C2213yes—
54#2777C2213yes—
55#2777C2213yes—
56#2775C2213yes—
57#2773C2213yescomplemented
58#2770C2213yes—
59#2767C2213yescomplemented
60#2767C2213yescomplemented
61#2765C2213yes—
62#2765C2213yescomplemented
63#2763C2213yes—
64#2762C2213yescomplemented
65#2759C2213yes—
66#2759C2213yes—
67#2759C2213yescomplemented
68#2758C2213yescomplemented
69#2758C2213yescomplemented
70#2757C2213yescomplemented
71#2756C2213yes—
72#2755C2213yescomplemented
73#2754C2213yes—
74#2753C2213yes—
75#2753C2213yes—
76#2753C2213yes—
77#2752C2213yes—
78#2751C2213yes—
79#2751C2213yes—
80#2751C2213yescomplemented
81#2750C2213yescomplemented
82#2749C2213yes—
83#2749C2213yes—
84#2748C2213yes—
85#2747C2213yes—
86#2747C2213yes—
87#2746C2213yes—
88#2746C2213yes—
89#2746C2213yescomplemented
90#2745C2213yes—
91#2745C2213yes—
92#2745C2213yescomplemented
93#2744C2213yes—
94#2744C2213yes—
95#2743C2213yes—
96#2743C2213yes—
97#2743C2213yes—
98#2740C2213yes—
99#2740C2213yescomplemented
100#2736C2211yescharacteristic
101#2735C2213yes—
102#2735C2213yes—
103#2735C2213yes—
104#2731C2213yes—
105#2730C2213yes—
106#2729C2213yescomplemented
107#2723C2213yescomplemented
108#2718C2213yescomplemented
109#2717C2213yes—
110#2715C2213yes—
111#2715C2213yes—
112#2712C2213yes—
113#2710C2213yes—
114#2705C2213yes—
115#2700C2213yes—
116#2697C2213yes—
117#2696C2213yes—
118#2695C2213yes—
119#2689C2213yescomplemented
120#2686C2213yes—
121#2685C2213yes—
122#2684C2213yes—
123#2684C2213yes—
124#2678C2213yes—
125#2670C2213yes—
126#2666C2213yescomplemented
127#2665C2213yescomplemented
128#2662C2213yes—
129#2661C2213yes—
130#2653C2213yes—
131#2653C2213yescomplemented
132#2651C2213yescomplemented
133#2650C2213yes—
134#2649C2213yescomplemented
135#2648C2213yes—
136#2648C2213yes—
137#2648C2213yescomplemented
138#2636C2213yescomplemented
139#2635C2213yes—
140#2631C2213yes—
141#2630C2213yescomplemented
142#2596C2213yes—
143#2596C2213yescomplemented
144#2594C2213yes—
145#2594C2213yescomplemented
146#2592C2213yes—
147#2581C2213yescomplemented
148#2570C2213yescomplemented
149#2545C2213yes—
150#2533C2213yescomplemented
151#2532C2213yes—
152#2531C2213yes—
153#2530C2213yescomplemented
154#2529C2213yes—
155#2528C2213yescomplemented
156#2527C2213yescomplemented
157#2526C2213yes—
158#2525C2213yes—
159#2525C2213yes—
160#2525C2213yes—
161#2525C2213yescomplemented
162#2521C2213yes—
163#2521C2213yes—
164#2520C2213yescomplemented
165#2520C2213yescomplemented
166#2515C2213yescomplemented
167#2515C2213yescomplemented
168#2514C2213yescomplemented
169#2512C2213yes—
170#2510C2213yes—
171#2505C2213yescomplemented
172#2493C2213yescomplemented
173#2488C2213yes—
174#2469C2213yes—
175#2469C2213yescomplemented
176#2468C2213yescomplemented
177#2468C2213yescomplemented
178#2465C2213yescomplemented
179#2465C2213yescomplemented
180#2461C2213yes—
181#2461C2213yes—
182#2458C2213yes—
183#2458C2213yes—
184#2450C2213yescomplemented
185#2448C2213yes—
186#2446C2213yescomplemented
187#2444C2213yes—
188#2425C2213yes—
189#2419C2213yescomplemented
190#2402C2213yescomplemented
191#2401C2213yes—
192#2401C2213yes—
193#2401C2213yes—
194#2401C2213yescomplemented
195#2401C2213yescomplemented
196#2399C2213yescomplemented
197#2398C2213yes—
198#2398C2213yes—
199#2398C2213yescomplemented
200#2396C2213yes—
201#2396C2213yes—
202#2396C2213yes—
203#2396C2213yescomplemented
204#2396C2213yescomplemented
205#2395C2213yes—
206#2395C2213yes—
207#2395C2213yes—
208#2392C2213yes—
209#2392C2213yes—
210#2388C2213yes—
211#2388C2211yescharacteristic, complemented
212C4×C4⋊Q8C2213yescomplemented
213C4×#126C2213yes—
214C4×#126C2213yescomplemented
215C4×#126C2211yescharacteristic, complemented
216C4×#126C2213yescomplemented
217C4×#126C2211yescharacteristic, complemented
218C4×#124C2213yes—
219C4×#124C2213yes—
220C4×#124C2213yes—
221C4×#124C2213yes—
222C4×C22⋊Q8C2213yescomplemented
223C4×C22⋊Q8C2213yescomplemented
224C4×#123C2213yes—
225C4×#123C2213yes—
226C4×#123C2213yescomplemented
227C4×#121C2213yes—
228C4×#120C2211yescharacteristic
229C4×#120C2213yes—
230#2298C2213yes—
231#2298C2213yes—
232#2298C2213yescomplemented
233#2297C2213yescomplemented
234#2295C2213yescomplemented
235#2295C2213yescomplemented
236#2293C2213yes—
237#2290C2213yes—
238#2290C2213yes—
239#2290C2213yes—
240#2283C2213yescomplemented
241#2280C2213yes—
242C42×Q8C2213yescomplemented
243C42×D4C2213yescomplemented
244C2×#376C2211yescharacteristic, complemented
245C22×#41C2311yescharacteristic
246C24×C4C2311yescharacteristic
247C2×C4⋊Q8C2313yes—
248C2×#126C2313yes—
249C2×#126C2313yes—
250C2×#126C2313yes—
251C2×#126C2311yescharacteristic
252C2×#126C2311yescharacteristic
253C2×#124C2313yes—
254C2×#124C2313yes—
255C2×#124C2313yes—
256C2×#124C2313yes—
257C2×#123C2313yes—
258C2×#123C2313yes—
259C2×#123C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×#121C2313yes—
263C2×#120C2313yes—
264C2×#120C2311yescharacteristic
265C2×C4×Q8C2313yes—
266C2×C4×Q8C2313yes—
267C2×C4×Q8C2313yes—
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2313yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×#117C2313yes—
278C2×#117C2313yes—
279C2×#117C2313yes—
280C22×C42C2313yes—
281C22×C42C2313yes—
282#401C2313yes—
283#401C2313yes—
284#401C2313yes—
285#401C2313yes—
286#401C2313yes—
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#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#399C2313yes—
321#399C2313yes—
322#399C2313yes—
323#399C2313yes—
324#399C2313yes—
325#399C2313yes—
326#399C2313yes—
327#399C2313yes—
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#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#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#397C2313yes—
382#397C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2313yes—
395#396C2313yes—
396#396C2313yes—
397#396C2313yes—
398#396C2313yes—
399#396C2313yes—
400#396C2313yes—
401#396C2313yes—
402#395C2313yes—
403#395C2313yes—
404#395C2313yes—
405#395C2313yes—
406#395C2313yes—
407#395C2313yes—
408#395C2313yes—
409#395C2313yes—
410#395C2313yes—
411#395C2313yes—
412#395C2311yescharacteristic
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#393C2313yes—
436#393C2313yes—
437#393C2313yes—
438#393C2313yes—
439#393C2313yes—
440#393C2313yes—
441#393C2313yes—
442#393C2313yes—
443#393C2313yes—
444#393C2311yescharacteristic
445#393C2313yes—
446#393C2313yes—
447#393C2313yes—
448#392C2313yes—
449#392C2313yes—
450#392C2313yes—
451#392C2313yes—
452#392C2313yes—
453#392C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2313yes—
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
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#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#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#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#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#385C2313yes—
614#385C2313yes—
615#385C2313yes—
616#385C2313yes—
617#385C2313yes—
618#385C2313yes—
619#385C2313yes—
620#385C2313yes—
621#385C2313yes—
622#385C2313yes—
623#385C2313yes—
624#385C2313yes—
625#385C2313yes—
626#385C2313yes—
627#385C2313yes—
628#385C2313yes—
629#385C2313yes—
630#384C2313yes—
631#383C2313yes—
632#383C2313yes—
633#383C2313yes—
634#383C2311yescharacteristic
635#383C2311yescharacteristic
636#383C2313yes—
637#383C2313yes—
638#382C2313yes—
639#382C2313yes—
640#382C2313yes—
641#382C2313yes—
642#382C2313yes—
643#382C2313yes—
644#381C2313yes—
645#381C2313yes—
646#381C2313yes—
647#381C2313yes—
648#381C2313yes—
649#381C2313yes—
650#381C2313yes—
651#380C2313yes—
652#380C2313yes—
653#380C2313yes—
654#380C2313yes—
655#380C2313yes—
656#380C2313yes—
657#380C2313yes—
658#380C2313yes—
659#380C2313yes—
660#379C2313yes—
661#379C2313yes—
662#379C2313yes—
663#379C2311yescharacteristic
664C4×C4⋊C4C2313yes—
665C4×C4⋊C4C2313yes—
666C4×C4⋊C4C2313yes—
667C4×C4⋊C4C2313yes—
668C4×C4⋊C4C2313yes—
669C4×C4⋊C4C2313yes—
670C4×C4⋊C4C2313yes—
671C4×C4⋊C4C2313yes—
672C4×C4⋊C4C2313yes—
673C4×C4⋊C4C2313yes—
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×C22⋊C4C2313yes—
687C4×C22⋊C4C2313yes—
688C4×C22⋊C4C2313yes—
689C4×C22⋊C4C2313yes—
690C4×C22⋊C4C2313yes—
691C4×C22⋊C4C2313yes—
692C4×C22⋊C4C2313yes—
693C4×C22⋊C4C2313yes—
694C4×C22⋊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—
708#376C2311yescharacteristic
709#376C2313yes—
710#376C2313yes—
711#376C2313yes—
712#376C2313yes—
713#376C2311yescharacteristic
714C2×#95C2313yes—
715C2×#95C2311yescharacteristic
716C43C2313yes—
717C43C2313yes—
718C43C2311yescharacteristic
719C43C2311yescharacteristic
720C25C2411yescharacteristic
721C2×#41—46no—
722C22×Q8C2413yes—
723C22×Q8C2413yes—
724C22×Q8C2413yes—
725C22×Q8C2411yescharacteristic
726C22×D4C2413yes—
727C22×D4C2413yes—
728C22×D4C2413yes—
729C22×D4C2413yes—
730C22×D4C2413yes—
731C22×D4C2413yes—
732C23×C4—46no—
733C23×C4C2413yes—
734C23×C4C2413yes—
735C23×C4C2411yescharacteristic
736C23×C4C2413yes—
737C23×C4C2413yes—
738C23×C4C2413yes—
739C23×C4C2413yes—
740C23×C4C2413yes—
741C4⋊Q8—46no—
742#126—46no—
743#126—46no—
744#126—46no—
745#126—42no—
746#126—42no—
747#124—46no—
748#124—46no—
749#124—46no—
750#124—46no—
751#123—46no—
752#123—46no—
753#123—46no—
754C22⋊Q8—46no—
755C22⋊Q8—46no—
756#121—46no—
757#120—46no—
758#120—42no—
759C4×Q8—46no—
760C4×Q8—46no—
761C4×Q8—46no—
762C4×Q8—46no—
763C4×Q8—46no—
764C4×D4—46no—
765C4×D4—46no—
766C4×D4—46no—
767C4×D4—46no—
768C4×D4—46no—
769C4×D4—46no—
770C4×D4—46no—
771#117—46no—
772#117—46no—
773#117—46no—
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×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×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×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×C42—46no—
875C2×C42—46no—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879C2×C42C2413yes—
880C2×C42C2413yes—
881C2×C42C2413yes—
882C2×C42C2413yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2413yes—
886C2×C42C2413yes—
887C2×C42C2413yes—
888C2×C42C2413yes—
889C2×C42C2413yes—
890C2×C42C2413yes—
891C2×C42C2413yes—
892C2×C42C2413yes—
893C2×C42C2413yes—
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2413yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2411yescharacteristic
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#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—
978C24—43no—
979C24—41no—
980C24—43no—
981C24C2513yes—
982C24C2513yes—
983C24C2511yescharacteristic
984#41—88no—
985C2×Q8—26no—
986C2×Q8—26no—
987C2×Q8—43no—
988C2×Q8—43no—
989C2×Q8—43no—
990C2×Q8—43no—
991C2×Q8—43no—
992C2×Q8—43no—
993C2×Q8—43no—
994C2×Q8—43no—
995C2×D4—26no—
996C2×D4—26no—
997C2×D4—26no—
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—
1013C22×C4—26no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—43no—
1022C22×C4—43no—
1023C22×C4—43no—
1024C22×C4—43no—
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—88no—
1036C22×C4C2513yes—
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2513yes—
1053C22×C4C2513yes—
1054C22×C4C2513yes—
1055C22×C4C2511yescharacteristic
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—26no—
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—
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—
1104C22⋊C4—26no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—26no—
1109C22⋊C4—26no—
1110C22⋊C4—26no—
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⋊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—
1156C42—26no—
1157C42—26no—
1158C42—26no—
1159C42—26no—
1160C42—26no—
1161C42—26no—
1162C42—26no—
1163C42—26no—
1164C42—26no—
1165C42—26no—
1166C42—26no—
1167C42—43no—
1168C42—43no—
1169C42—43no—
1170C42—43no—
1171C42—43no—
1172C42—43no—
1173C42—43no—
1174C42—43no—
1175C42—43no—
1176C42—43no—
1177C42—43no—
1178C42—41no—
1179C42—41no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23—23no—
1195C23—23no—
1196C23—82no—
1197C23—86no—
1198C23—86no—
1199C23#58512yes—
1200C23C2611yescharacteristic
1201Q8—412no—
1202Q8—86no—
1203Q8—86no—
1204Q8—82no—
1205D4—412no—
1206D4—86no—
1207D4—86no—
1208D4—86no—
1209D4—86no—
1210D4—86no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
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—44no—
1266C2×C4—412no—
1267C2×C4—412no—
1268C2×C4—86no—
1269C2×C4—86no—
1270C2×C4—86no—
1271C2×C4—86no—
1272C2×C4—86no—
1273C2×C4#58516yes—
1274C2×C4#58516yes—
1275C22—26no—
1276C22—41no—
1277C22—43no—
1278C22—43no—
1279C22—43no—
1280C22—43no—
1281C22—43no—
1282C22—43no—
1283C22—43no—
1284C22—43no—
1285C22—43no—
1286C22—43no—
1287C22—43no—
1288C22—43no—
1289C22—43no—
1290C22—43no—
1291C22—43no—
1292C22—88no—
1293C22C2×#58513yes—
1294C22C2×#58511yescharacteristic
1295C22C2×#58513yes—
1296C4—26no—
1297C4—41no—
1298C4—43no—
1299C4—43no—
1300C4—43no—
1301C4—43no—
1302C4—43no—
1303C4—43no—
1304C4—43no—
1305C4—43no—
1306C4—43no—
1307C4—43no—
1308C4—43no—
1309C4—43no—
1310C4—43no—
1311C4—43no—
1312C4—43no—
1313C4—43no—
1314C4—43no—
1315C4#356814yes—
1316C2—42no—
1317C2—83no—
1318C2—83no—
1319C2C2×#356811yescharacteristic
1320C2#6274313yes—
1321C2#6274313yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58849C2semidirect
2. #58781C2semidirect
3. #58460C2semidirect
4. #58333C2semidirect
5. #57589C2semidirect
6. #57096C2semidirect
7. #57090C2semidirect
8. #56596C2semidirect
9. #55472C2semidirect
10. #54631C2semidirect
11. #54623C2semidirect
12. #53870C2semidirect
13. #52294C2semidirect
14. #52284C2semidirect
15. #52243C2semidirect
16. #52233C2semidirect
17. #52197C2semidirect
18. #52185C2semidirect
19. #36697C2semidirect
20. #34968C2semidirect
21. #34902C2semidirect
22. #34811C2semidirect
23. #34589C2semidirect
24. #2843C22semidirect
25. #2839C22semidirect
26. #2839C22semidirect
28. #2838C22semidirect
32. #2836C22semidirect
33. #2833C22semidirect
36. #2831C22semidirect
39. #2821C22semidirect
41. #2799C22semidirect
43. #2789C22semidirect
45. #2788C22semidirect
46. #2787C22semidirect
52. #2779C22semidirect
57. #2773C22semidirect
59. #2767C22semidirect
60. #2767C22semidirect
62. #2765C22semidirect
64. #2762C22semidirect
67. #2759C22semidirect
68. #2758C22semidirect
69. #2758C22semidirect
70. #2757C22semidirect
72. #2755C22semidirect
80. #2751C22semidirect
81. #2750C22semidirect
89. #2746C22semidirect
92. #2745C22semidirect
99. #2740C22semidirect
106. #2729C22semidirect
107. #2723C22semidirect
108. #2718C22semidirect
119. #2689C22semidirect
126. #2666C22semidirect
127. #2665C22semidirect
131. #2653C22semidirect
132. #2651C22semidirect
134. #2649C22semidirect
137. #2648C22semidirect
138. #2636C22semidirect
141. #2630C22semidirect
143. #2596C22semidirect
145. #2594C22semidirect
147. #2581C22semidirect
148. #2570C22semidirect
150. #2533C22semidirect
153. #2530C22semidirect
155. #2528C22semidirect
156. #2527C22semidirect
161. #2525C22semidirect
164. #2520C22semidirect
165. #2520C22semidirect
166. #2515C22semidirect
167. #2515C22semidirect
168. #2514C22semidirect
171. #2505C22semidirect
172. #2493C22semidirect
175. #2469C22semidirect
176. #2468C22semidirect
177. #2468C22semidirect
178. #2465C22semidirect
179. #2465C22semidirect
184. #2450C22semidirect
186. #2446C22semidirect
189. #2419C22semidirect
190. #2402C22semidirect
194. #2401C22semidirect
195. #2401C22semidirect
196. #2399C22semidirect
199. #2398C22semidirect
203. #2396C22semidirect
204. #2396C22semidirect
211. #2388C22semidirect
212. C4×C4⋊Q8C22semidirect
214. C4×#126C22semidirect
215. C4×#126C22semidirect
216. C4×#126C22semidirect
217. C4×#126C22semidirect
222. C4×C22⋊Q8C22semidirect
223. C4×C22⋊Q8C22semidirect
226. C4×#123C22semidirect
232. #2298C22semidirect
233. #2297C22semidirect
234. #2295C22semidirect
235. #2295C22semidirect
240. #2283C22semidirect
242. C42×Q8C22semidirect
243. C42×D4C22semidirect
244. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
#588492
#587812
#584602
#583332
#575892
#570962
#570902
#565962
#554722
#546312
#546232
#538702
#522942
#522842
#522432
#522332
#521972
#521852
#366972
#349682
#349022
#348112
#345892