Finite Group Databasebeta

← #8926227

Subgroups — #8926227

Order 512.

4778 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58256C212yesmaximal, complemented
2#58032C214yesmaximal, complemented
3#57954C214yesmaximal, complemented
4#57756C214yesmaximal, complemented
5#57661C214yesmaximal, complemented
6#56584C212yesmaximal, complemented
7#56411C214yesmaximal, complemented
8#47226C212yesmaximal, complemented
9#47093C214yesmaximal, complemented
10#46544C214yesmaximal, complemented
11#46504C214yesmaximal, complemented
12#46356C212yesmaximal, complemented
13#46354C212yesmaximal, complemented
14#37418C212yesmaximal, complemented
15#37148C214yesmaximal, complemented
16#36844C214yesmaximal, complemented
17#36822C212yesmaximal, complemented
18#36731C212yesmaximal, complemented
19#36731C212yesmaximal, complemented
20#36721C211yesmaximal, characteristic, complemented
21#36710C211yesmaximal, characteristic, complemented
22#35455C211yesmaximal, characteristic, complemented
23#35422C212yesmaximal, complemented
24C2×#543C2211yescharacteristic, complemented
25C2×#537C2212yes—
26C2×#537C2211yescharacteristic, complemented
27C2×#534C2211yescharacteristic
28C22×#123C2211yescharacteristic
29#2853C2214yescomplemented
30#2850C2212yescomplemented
31#2850C2212yescomplemented
32#2847C2212yes—
33#2847C2211yescharacteristic, complemented
34#2847C2211yescharacteristic, complemented
35#2839C2214yescomplemented
36#2837C2214yescomplemented
37#2835C2212yescomplemented
38#2828C2214yescomplemented
39#2826C2214yescomplemented
40#2825C2214yes—
41#2816C2212yes—
42#2816C2214yescomplemented
43#2812C2212yescomplemented
44#2803C2214yescomplemented
45#2798C2214yescomplemented
46#2798C2214yescomplemented
47#2796C2214yescomplemented
48#2796C2214yescomplemented
49#2781C2214yescomplemented
50#2780C2214yescomplemented
51#2779C2214yescomplemented
52#2778C2214yescomplemented
53#2773C2214yescomplemented
54#2767C2214yescomplemented
55#2765C2214yescomplemented
56#2753C2214yes—
57#2753C2214yescomplemented
58#2752C2214yescomplemented
59#2750C2214yescomplemented
60#2746C2214yescomplemented
61#2743C2214yescomplemented
62#2743C2214yescomplemented
63#2743C2214yescomplemented
64#2743C2214yescomplemented
65#2743C2214yescomplemented
66#2740C2214yescomplemented
67#2740C2214yescomplemented
68#2740C2214yescomplemented
69#2740C2214yescomplemented
70#2736C2212yescomplemented
71#2732C2214yescomplemented
72#2730C2214yescomplemented
73#2728C2214yescomplemented
74#2728C2214yescomplemented
75#2722C2212yescomplemented
76#2716C2214yescomplemented
77#2714C2214yes—
78#2714C2214yescomplemented
79#2710C2214yescomplemented
80#2706C2214yes—
81#2706C2214yes—
82#2699C2214yes—
83#2699C2214yescomplemented
84#2699C2214yescomplemented
85#2699C2214yescomplemented
86#2699C2214yescomplemented
87#2698C2214yescomplemented
88#2697C2214yes—
89#2696C2214yescomplemented
90#2696C2214yescomplemented
91#2696C2214yescomplemented
92#2693C2212yescomplemented
93#2692C2214yescomplemented
94#2688C2214yes—
95#2688C2214yes—
96#2688C2214yescomplemented
97#2688C2214yescomplemented
98#2688C2214yescomplemented
99#2688C2214yescomplemented
100#2688C2214yescomplemented
101#2688C2214yescomplemented
102#2687C2214yescomplemented
103#2686C2214yescomplemented
104#2685C2214yes—
105#2685C2214yescomplemented
106#2681C2214yescomplemented
107#2678C2214yes—
108#2678C2214yes—
109#2676C2214yescomplemented
110#2676C2214yescomplemented
111#2673C2214yes—
112#2673C2214yescomplemented
113#2673C2214yescomplemented
114#2672C2214yescomplemented
115#2670C2212yescomplemented
116#2669C2214yescomplemented
117#2669C2214yescomplemented
118#2668C2214yescomplemented
119#2668C2214yescomplemented
120#2656C2212yescomplemented
121#2656C2212yescomplemented
122#2651C2214yescomplemented
123#2650C2214yescomplemented
124#2649C2214yescomplemented
125#2646C2212yescomplemented
126#2646C2212yescomplemented
127#2636C2214yescomplemented
128#2635C2214yescomplemented
129#2621C2212yescomplemented
130#2619C2212yescomplemented
131#2618C2212yes—
132#2617C2211yescharacteristic
133#2617C2211yescharacteristic
134#2608C2212yescomplemented
135#2603C2214yes—
136#2600C2214yescomplemented
137#2595C2214yescomplemented
138#2591C2212yescomplemented
139#2589C2214yescomplemented
140#2576C2214yescomplemented
141#2561C2212yes—
142#2561C2212yes—
143#2559C2214yescomplemented
144#2554C2214yescomplemented
145#2540C2214yescomplemented
146#2539C2212yes—
147#2529C2214yescomplemented
148#2528C2214yescomplemented
149#2527C2214yescomplemented
150#2526C2214yescomplemented
151#2526C2214yescomplemented
152#2517C2214yescomplemented
153#2516C2214yescomplemented
154#2504C2212yes—
155#2504C2212yescomplemented
156#2503C2212yescomplemented
157#2503C2212yescomplemented
158#2503C2212yescomplemented
159#2488C2214yescomplemented
160#2488C2214yescomplemented
161#2488C2214yescomplemented
162#2488C2214yescomplemented
163#2483C2212yescomplemented
164#2479C2214yescomplemented
165#2476C2214yescomplemented
166#2472C2214yescomplemented
167#2468C2214yescomplemented
168#2467C2214yescomplemented
169#2464C2214yescomplemented
170#2463C2212yescomplemented
171#2459C2214yescomplemented
172#2459C2214yescomplemented
173#2457C2214yescomplemented
174#2456C2214yes—
175#2452C2214yescomplemented
176#2449C2214yescomplemented
177#2444C2214yescomplemented
178#2444C2214yescomplemented
179#2444C2214yescomplemented
180#2444C2214yescomplemented
181#2443C2214yescomplemented
182#2433C2212yes—
183#2432C2212yescomplemented
184#2432C2212yescomplemented
185#2431C2212yes—
186#2431C2212yescomplemented
187#2428C2214yes—
188#2428C2214yescomplemented
189#2424C2214yescomplemented
190#2424C2214yescomplemented
191#2424C2214yescomplemented
192#2424C2214yescomplemented
193#2424C2214yescomplemented
194#2418C2214yescomplemented
195#2410C2214yes—
196#2408C2214yes—
197#2407C2214yescomplemented
198#2405C2212yes—
199#2404C2212yes—
200#2404C2214yescomplemented
201#2404C2212yescomplemented
202#2403C2212yes—
203#2333C2212yes—
204#2333C2214yescomplemented
205#2332C2212yescomplemented
206#2328C2214yescomplemented
207#2325C2212yescomplemented
208#2325C2212yescomplemented
209#2325C2212yescomplemented
210#2325C2212yescomplemented
211#2321C2214yescomplemented
212#2313C2211yescharacteristic, complemented
213#2312C2211yescharacteristic
214#2308C2212yes—
215C4×#121C2214yescomplemented
216#2297C2212yescomplemented
217C2×#381C2212yescomplemented
218#2273C2211yescharacteristic, complemented
219C22×#41C2312yes—
220C22×#41C2312yes—
221C23×D4C2311yescharacteristic
222C23×D4C2312yes—
223C24×C4C2311yescharacteristic
224#543—44no—
225#537—44no—
226#537—48no—
227#534—44no—
228C2×C4⋊Q8C2312yes—
229C2×#127C2314yes—
230C2×#127C2312yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#124C2312yes—
234C2×#124C2312yes—
235C2×#124C2314yes—
236C2×#123—44no—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2312yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2311yescharacteristic
260C2×#121C2311yescharacteristic
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#120C2314yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277C2×#120C2312yes—
278C2×#120C2312yes—
279C2×#120C2312yes—
280C2×#120C2312yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×#117C2312yes—
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2312yes—
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2314yes—
299C22×C42C2312yes—
300#401C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#397C2312yes—
335#397C2314yes—
336#397C2312yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2312yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2312yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#395C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2314yes—
397#393C2312yes—
398#393C2314yes—
399#393C2314yes—
400#393C2312yes—
401#393C2314yes—
402#393C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2312yes—
413#392C2312yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2314yes—
442#390C2312yes—
443#390C2312yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2312yes—
533#386C2312yes—
534#386C2312yes—
535#386C2312yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2312yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2312yes—
568#385C2314yes—
569#382C2314yes—
570#382C2312yes—
571#382C2312yes—
572#382C2312yes—
573#382C2312yes—
574#382C2314yes—
575#381C2312yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2314yes—
587#380C2312yes—
588#380C2311yescharacteristic
589#380C2311yescharacteristic
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#379C2314yes—
598#379C2312yes—
599#379C2314yes—
600#379C2312yes—
601#379C2312yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614#376C2314yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C25C2412yes—
622C2×#41—28no—
623C2×#41—44no—
624C2×#41—82no—
625C2×#41—82no—
626C2×#41—82no—
627C2×#41—82no—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×D4—42no—
632C22×D4—44no—
633C22×D4—44no—
634C22×D4—84no—
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2411yescharacteristic
654C22×D4C2411yescharacteristic
655C22×D4C2412yes—
656C23×C4—42no—
657C23×C4—44no—
658C23×C4C2411yescharacteristic
659C23×C4C2411yescharacteristic
660C23×C4C2411yescharacteristic
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2412yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2412yes—
672C23×C4C2414yes—
673C23×C4C2414yes—
674C23×C4C2412yes—
675C23×C4C2411yescharacteristic
676C4⋊Q8—82no—
677#127—48no—
678#127—82no—
679#126—84no—
680#126—84no—
681#124—82no—
682#124—82no—
683#124—84no—
684#123—48no—
685#123—48no—
686#123—48no—
687#123—84no—
688#123—84no—
689C22⋊Q8—28no—
690C22⋊Q8—44no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—44no—
695C22⋊Q8—44no—
696C22⋊Q8—44no—
697C22⋊Q8—84no—
698#121—28no—
699#121—48no—
700#121—48no—
701#121—48no—
702#121—48no—
703#121—48no—
704#121—44no—
705#121—44no—
706#121—44no—
707#121—44no—
708#121—44no—
709#121—44no—
710#121—44no—
711#121—44no—
712#121—42no—
713#121—42no—
714#121—44no—
715#121—84no—
716#121—84no—
717#121—84no—
718#121—84no—
719#121—84no—
720#121—84no—
721#120—48no—
722#120—48no—
723#120—82no—
724#120—82no—
725#120—82no—
726#120—84no—
727#120—84no—
728#120—82no—
729#120—84no—
730C4×D4—84no—
731C4×D4—84no—
732C4×D4—84no—
733C4×D4—84no—
734C4×D4—84no—
735C4×D4—84no—
736#117—82no—
737C2×C4⋊C4—24no—
738C2×C4⋊C4—44no—
739C2×C4⋊C4—42no—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C22⋊C4—24no—
775C2×C22⋊C4—24no—
776C2×C22⋊C4—44no—
777C2×C22⋊C4—44no—
778C2×C22⋊C4—42no—
779C2×C22⋊C4—84no—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C42—82no—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2412yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897C24—22no—
898C24—24no—
899C24—22no—
900C24—42no—
901C24—41no—
902C24—41no—
903C24—42no—
904C24—42no—
905C24—44no—
906C24—42no—
907C24—44no—
908C24—41no—
909C24—41no—
910C24—42no—
911C24—42no—
912C24C2512yes—
913C24C2514yes—
914C24C2512yes—
915C24C2512yes—
916C24C2511yescharacteristic
917C24C2512yes—
918#41—816no—
919#41—816no—
920C2×Q8—24no—
921C2×Q8—24no—
922C2×Q8—42no—
923C2×Q8—42no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—44no—
928C2×D4—28no—
929C2×D4—24no—
930C2×D4—24no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—24no—
937C2×D4—24no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—44no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—44no—
970C2×D4—42no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—41no—
977C2×D4—41no—
978C2×D4—42no—
979C2×D4—44no—
980C2×D4—42no—
981C2×D4—42no—
982C2×D4—42no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—88no—
989C2×D4—816no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—88no—
1039C22×C4H(5,𝔽2)14yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C42—44no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C23—28no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—21no—
1170C23—21no—
1171C23—22no—
1172C23—22no—
1173C23—24no—
1174C23—22no—
1175C23—22no—
1176C23—24no—
1177C23—24no—
1178C23—24no—
1179C23—24no—
1180C23—24no—
1181C23—22no—
1182C23—22no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—24no—
1191C23—24no—
1192C23—24no—
1193C23—22no—
1194C23—44no—
1195C23—82no—
1196C23—84no—
1197C23—84no—
1198C23—82no—
1199C23—82no—
1200C23—82no—
1201C23—84no—
1202C23—88no—
1203C23—162no—
1204C23—162no—
1205C23—162no—
1206C23—162no—
1207C23—164no—
1208C23C2×H(5,𝔽2)12yes—
1209C23#58514yes—
1210C23C2611yescharacteristic
1211Q8—84no—
1212Q8—84no—
1213Q8—162no—
1214D4—84no—
1215D4—84no—
1216D4—88no—
1217D4—88no—
1218D4—88no—
1219D4—88no—
1220D4—88no—
1221D4—88no—
1222D4—84no—
1223D4—84no—
1224D4—88no—
1225D4—88no—
1226D4—88no—
1227D4—88no—
1228D4—161no—
1229D4—161no—
1230D4—162no—
1231D4—162no—
1232D4—164no—
1233D4—164no—
1234D4—164no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—44no—
1282C2×C4—48no—
1283C2×C4—48no—
1284C2×C4—82no—
1285C2×C4—82no—
1286C2×C4—82no—
1287C2×C4—84no—
1288C2×C4—84no—
1289C2×C4—82no—
1290C2×C4—88no—
1291C2×C4—84no—
1292C2×C4—88no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4—164no—
1296C2×C4—162no—
1297C2×C4—164no—
1298C2×C4—162no—
1299C2×C4C2×H(5,𝔽2)14yes—
1300C22—22no—
1301C22—24no—
1302C22—22no—
1303C22—24no—
1304C22—24no—
1305C22—22no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—42no—
1317C22—42no—
1318C22—44no—
1319C22—42no—
1320C22—44no—
1321C22—44no—
1322C22—44no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—42no—
1331C22—42no—
1332C22—44no—
1333C22—42no—
1334C22—88no—
1335C22—164no—
1336C22—168no—
1337C22C22×H(5,𝔽2)11yescharacteristic
1338C22C2×#58512yes—
1339C22H(7,𝔽2)11yescharacteristic
1340C22H(7,𝔽2)11yescharacteristic
1341C22H(7,𝔽2)12yes—
1342C4—24no—
1343C4—42no—
1344C4—41no—
1345C4—41no—
1346C4—42no—
1347C4—42no—
1348C4—42no—
1349C4—44no—
1350C4—44no—
1351C4—44no—
1352C4—44no—
1353C4—44no—
1354C4—44no—
1355C4—44no—
1356C4—44no—
1357C4—42no—
1358C4—44no—
1359C2—44no—
1360C2—42no—
1361C2—82no—
1362C2—82no—
1363C2—84no—
1364C2—82no—
1365C2#6282411yescharacteristic
1366C2#6286211yescharacteristic
1367C2#6287012yes—
1368C2#6287012yes—
1369C2#6287611yescharacteristic
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. #58256C2semidirect
2. #58032C2semidirect
3. #57954C2semidirect
4. #57756C2semidirect
5. #57661C2semidirect
6. #56584C2semidirect
7. #56411C2semidirect
8. #47226C2semidirect
9. #47093C2semidirect
10. #46544C2semidirect
11. #46504C2semidirect
12. #46356C2semidirect
13. #46354C2semidirect
14. #37418C2semidirect
15. #37148C2semidirect
16. #36844C2semidirect
17. #36822C2semidirect
18. #36731C2semidirect
19. #36731C2semidirect
20. #36721C2semidirect
21. #36710C2semidirect
22. #35455C2semidirect
23. #35422C2semidirect
24. C2×#543C22semidirect
26. C2×#537C22semidirect
29. #2853C22semidirect
30. #2850C22semidirect
31. #2850C22semidirect
33. #2847C22semidirect
34. #2847C22semidirect
35. #2839C22semidirect
36. #2837C22semidirect
37. #2835C22semidirect
38. #2828C22semidirect
39. #2826C22semidirect
42. #2816C22semidirect
43. #2812C22semidirect
44. #2803C22semidirect
45. #2798C22semidirect
46. #2798C22semidirect
47. #2796C22semidirect
48. #2796C22semidirect
49. #2781C22semidirect
50. #2780C22semidirect
51. #2779C22semidirect
52. #2778C22semidirect
53. #2773C22semidirect
54. #2767C22semidirect
55. #2765C22semidirect
57. #2753C22semidirect
58. #2752C22semidirect
59. #2750C22semidirect
60. #2746C22semidirect
61. #2743C22semidirect
62. #2743C22semidirect
63. #2743C22semidirect
64. #2743C22semidirect
65. #2743C22semidirect
66. #2740C22semidirect
67. #2740C22semidirect
68. #2740C22semidirect
69. #2740C22semidirect
70. #2736C22semidirect
71. #2732C22semidirect
72. #2730C22semidirect
73. #2728C22semidirect
74. #2728C22semidirect
75. #2722C22semidirect
76. #2716C22semidirect
78. #2714C22semidirect
79. #2710C22semidirect
83. #2699C22semidirect
84. #2699C22semidirect
85. #2699C22semidirect
86. #2699C22semidirect
87. #2698C22semidirect
89. #2696C22semidirect
90. #2696C22semidirect
91. #2696C22semidirect
92. #2693C22semidirect
93. #2692C22semidirect
96. #2688C22semidirect
97. #2688C22semidirect
98. #2688C22semidirect
99. #2688C22semidirect
100. #2688C22semidirect
101. #2688C22semidirect
102. #2687C22semidirect
103. #2686C22semidirect
105. #2685C22semidirect
106. #2681C22semidirect
109. #2676C22semidirect
110. #2676C22semidirect
112. #2673C22semidirect
113. #2673C22semidirect
114. #2672C22semidirect
115. #2670C22semidirect
116. #2669C22semidirect
117. #2669C22semidirect
118. #2668C22semidirect
119. #2668C22semidirect
120. #2656C22semidirect
121. #2656C22semidirect
122. #2651C22semidirect
123. #2650C22semidirect
124. #2649C22semidirect
125. #2646C22semidirect
126. #2646C22semidirect
127. #2636C22semidirect
128. #2635C22semidirect
129. #2621C22semidirect
130. #2619C22semidirect
134. #2608C22semidirect
136. #2600C22semidirect
137. #2595C22semidirect
138. #2591C22semidirect
139. #2589C22semidirect
140. #2576C22semidirect
143. #2559C22semidirect
144. #2554C22semidirect
145. #2540C22semidirect
147. #2529C22semidirect
148. #2528C22semidirect
149. #2527C22semidirect
150. #2526C22semidirect
151. #2526C22semidirect
152. #2517C22semidirect
153. #2516C22semidirect
155. #2504C22semidirect
156. #2503C22semidirect
157. #2503C22semidirect
158. #2503C22semidirect
159. #2488C22semidirect
160. #2488C22semidirect
161. #2488C22semidirect
162. #2488C22semidirect
163. #2483C22semidirect
164. #2479C22semidirect
165. #2476C22semidirect
166. #2472C22semidirect
167. #2468C22semidirect
168. #2467C22semidirect
169. #2464C22semidirect
170. #2463C22semidirect
171. #2459C22semidirect
172. #2459C22semidirect
173. #2457C22semidirect
175. #2452C22semidirect
176. #2449C22semidirect
177. #2444C22semidirect
178. #2444C22semidirect
179. #2444C22semidirect
180. #2444C22semidirect
181. #2443C22semidirect
183. #2432C22semidirect
184. #2432C22semidirect
186. #2431C22semidirect
188. #2428C22semidirect
189. #2424C22semidirect
190. #2424C22semidirect
191. #2424C22semidirect
192. #2424C22semidirect
193. #2424C22semidirect
194. #2418C22semidirect
197. #2407C22semidirect
200. #2404C22semidirect
201. #2404C22semidirect
204. #2333C22semidirect
205. #2332C22semidirect
206. #2328C22semidirect
207. #2325C22semidirect
208. #2325C22semidirect
209. #2325C22semidirect
210. #2325C22semidirect
211. #2321C22semidirect
212. #2313C22semidirect
215. C4×#121C22semidirect
216. #2297C22semidirect
217. C2×#381C22semidirect
218. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#582562
#580322
#579542
#577562
#576612
#565842
#564112
#472262
#470932
#465442
#465042
#463562
#463542
#374182
#371482
#368442
#368222
#367312
#367212
#367102
#354552
#354222