Finite Group Databasebeta

← #8757566

Subgroups — #8757566

Order 512.

4762 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58576C214yesmaximal, complemented
2#57426C214yesmaximal, complemented
3#56626C214yesmaximal, complemented
4#54946C214yesmaximal, complemented
5#53954C214yesmaximal, complemented
6#53407C214yesmaximal, complemented
7#50489C214yesmaximal, complemented
8#50255C212yesmaximal, complemented
9#50108C214yesmaximal, complemented
10#49703C212yesmaximal, complemented
11#47191C214yesmaximal, complemented
12#46831C214yesmaximal, complemented
13#46360C212yesmaximal, complemented
14#46356C212yesmaximal, complemented
15#46232C212yesmaximal, complemented
16#46230C212yesmaximal, complemented
17#46228C211yesmaximal, characteristic, complemented
18#46225C211yesmaximal, characteristic, complemented
19#45989C212yesmaximal, complemented
20#45975C212yesmaximal, complemented
21#45973C212yesmaximal, complemented
22#35328C211yesmaximal, characteristic, complemented
23#35189C212yesmaximal, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×H(3,𝔽4)C2211yescharacteristic
26C2×#543C2212yescomplemented
27C2×#539C2212yes—
28C2×#537C2211yescharacteristic
29C2×#537C2211yescharacteristic, complemented
30C2×#532C2211yescharacteristic
31C2×#529C2212yes—
32C2×C4×#41C2211yescharacteristic, complemented
33#2851C2212yescomplemented
34#2851C2212yescomplemented
35#2850C2212yes—
36#2850C2212yes—
37#2850C2212yes—
38#2850C2212yescomplemented
39#2844C2212yescomplemented
40#2837C2214yescomplemented
41#2836C2214yescomplemented
42#2830C2214yescomplemented
43#2825C2214yes—
44#2820C2212yes—
45#2820C2212yes—
46#2819C2212yes—
47#2816C2212yescomplemented
48#2815C2212yes—
49#2814C2214yes—
50#2812C2214yescomplemented
51#2803C2214yes—
52#2803C2214yes—
53#2801C2214yescomplemented
54#2797C2214yes—
55#2795C2214yescomplemented
56#2793C2214yescomplemented
57#2787C2214yescomplemented
58#2775C2214yescomplemented
59#2773C2214yescomplemented
60#2765C2214yescomplemented
61#2762C2214yescomplemented
62#2759C2214yescomplemented
63#2756C2214yes—
64#2756C2214yes—
65#2756C2214yescomplemented
66#2748C2212yescomplemented
67#2741C2214yescomplemented
68#2740C2214yescomplemented
69#2738C2214yescomplemented
70#2737C2214yescomplemented
71#2734C2212yescomplemented
72#2732C2214yes—
73#2731C2212yes—
74#2730C2214yes—
75#2730C2214yescomplemented
76#2730C2214yescomplemented
77#2728C2214yescomplemented
78#2723C2214yes—
79#2720C2214yescomplemented
80#2717C2214yescomplemented
81#2716C2214yescomplemented
82#2715C2214yes—
83#2714C2214yes—
84#2714C2214yescomplemented
85#2709C2212yes—
86#2709C2212yes—
87#2705C2214yescomplemented
88#2705C2214yescomplemented
89#2704C2214yescomplemented
90#2704C2214yescomplemented
91#2703C2214yes—
92#2703C2214yescomplemented
93#2703C2214yescomplemented
94#2702C2214yes—
95#2698C2214yescomplemented
96#2696C2214yescomplemented
97#2692C2214yescomplemented
98#2692C2214yescomplemented
99#2692C2214yescomplemented
100#2691C2214yescomplemented
101#2690C2214yescomplemented
102#2687C2214yes—
103#2685C2214yes—
104#2684C2212yescomplemented
105#2683C2212yescomplemented
106#2682C2214yes—
107#2681C2214yes—
108#2681C2214yescomplemented
109#2680C2214yescomplemented
110#2678C2214yes—
111#2676C2214yes—
112#2676C2214yes—
113#2676C2214yes—
114#2673C2214yes—
115#2672C2214yes—
116#2672C2214yes—
117#2672C2214yes—
118#2672C2214yescomplemented
119#2670C2214yescomplemented
120#2669C2212yes—
121#2669C2214yes—
122#2668C2214yes—
123#2661C2214yes—
124#2651C2214yescomplemented
125#2648C2214yes—
126#2644C2214yescomplemented
127#2635C2214yes—
128#2630C2214yescomplemented
129#2630C2214yescomplemented
130#2630C2214yescomplemented
131#2621C2212yescomplemented
132#2619C2212yes—
133#2610C2214yescomplemented
134#2606C2214yescomplemented
135#2601C2214yescomplemented
136#2601C2214yescomplemented
137#2598C2214yescomplemented
138#2597C2214yes—
139#2596C2214yescomplemented
140#2591C2212yescomplemented
141#2586C2214yescomplemented
142#2585C2214yescomplemented
143#2582C2212yescomplemented
144#2564C2214yescomplemented
145#2556C2214yescomplemented
146#2549C2214yescomplemented
147#2543C2214yescomplemented
148#2543C2214yescomplemented
149#2540C2214yes—
150#2539C2212yescomplemented
151#2538C2212yes—
152#2538C2212yescomplemented
153#2537C2212yes—
154#2536C2214yescomplemented
155#2535C2214yescomplemented
156#2534C2214yescomplemented
157#2532C2214yescomplemented
158#2532C2214yescomplemented
159#2531C2214yes—
160#2525C2214yescomplemented
161#2522C2214yescomplemented
162#2510C2214yescomplemented
163#2490C2214yescomplemented
164#2485C2214yescomplemented
165#2481C2214yescomplemented
166#2480C2214yescomplemented
167#2479C2214yescomplemented
168#2474C2214yes—
169#2474C2214yescomplemented
170#2470C2214yescomplemented
171#2469C2214yescomplemented
172#2466C2214yescomplemented
173#2464C2214yescomplemented
174#2463C2214yes—
175#2461C2214yes—
176#2461C2214yes—
177#2461C2214yescomplemented
178#2459C2214yes—
179#2456C2214yescomplemented
180#2452C2214yescomplemented
181#2449C2214yescomplemented
182#2449C2214yescomplemented
183#2448C2214yes—
184#2444C2214yes—
185#2432C2212yes—
186#2431C2212yes—
187#2427C2214yes—
188#2424C2214yes—
189#2424C2214yes—
190#2424C2214yescomplemented
191#2418C2214yes—
192#2418C2214yescomplemented
193#2417C2214yescomplemented
194#2415C2212yescomplemented
195#2415C2212yescomplemented
196#2415C2214yescomplemented
197#2414C2212yes—
198#2414C2212yes—
199#2411C2214yes—
200#2407C2214yescomplemented
201#2406C2212yescomplemented
202#2404C2212yes—
203#2382C2212yescomplemented
204#2379C2211yescharacteristic
205#2379C2212yes—
206#2379C2211yescharacteristic, complemented
207#2376C2212yescomplemented
208#2375C2212yescomplemented
209#2372C2212yescomplemented
210#2366C2212yes—
211#2332C2212yescomplemented
212#2332C2212yescomplemented
213#2324C2214yescomplemented
214#2323C2214yescomplemented
215#2311C2211yescharacteristic
216#2311C2211yescharacteristic, complemented
217#2285C2212yescomplemented
218C2×#382C2211yescharacteristic, complemented
219C22×#41C2311yescharacteristic
220C22×#41C2311yescharacteristic
221C22×#41C2311yescharacteristic
222#563—44no—
223H(3,𝔽4)—44no—
224#543—48no—
225#539—48no—
226#537—44no—
227#537—44no—
228#532—44no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×#127C2311yescharacteristic
232C2×#127C2312yes—
233#529—48no—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#125C2312yes—
238C2×#125C2314yes—
239C2×#124C2311yescharacteristic
240C2×#124C2312yes—
241C2×#124C2311yescharacteristic
242C2×#124C2312yes—
243C2×#124C2314yes—
244C2×#124C2312yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#123C2314yes—
248C2×#123C2312yes—
249C2×#123C2312yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#121C2312yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2312yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#120C2312yes—
285C2×#120C2312yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288C2×#120C2314yes—
289C4×#41—44no—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×#117C2311yescharacteristic
302C2×#117C2314yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2314yes—
311C22×C42C2312yes—
312C22×C42C2311yescharacteristic
313#401C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
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#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#390C2312yes—
445#390C2312yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2312yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2312yes—
542#386C2312yes—
543#386C2312yes—
544#386C2312yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2312yes—
557#386C2314yes—
558#386C2312yes—
559#386C2314yes—
560#386C2312yes—
561#386C2314yes—
562#386C2312yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#384C2312yes—
586#384C2312yes—
587#383C2314yes—
588#383C2314yes—
589#382C2312yes—
590#382C2312yes—
591#382C2312yes—
592#382C2312yes—
593#382C2314yes—
594#381C2312yes—
595#381C2312yes—
596#381C2314yes—
597#380C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2312yes—
604#380C2312yes—
605#380C2312yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#379C2314yes—
611#379C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621#376C2314yes—
622C2×#95C2314yes—
623C25C2412yes—
624C2×#41—24no—
625C2×#41—42no—
626C2×#41—42no—
627C2×#41—42no—
628C2×#41—42no—
629C2×#41—42no—
630C2×#41—42no—
631C2×#41—42no—
632C2×#41—42no—
633C22×Q8C2412yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2411yescharacteristic
636C22×Q8C2414yes—
637C22×Q8C2412yes—
638C22×Q8C2411yescharacteristic
639C22×D4C2412yes—
640C22×D4C2411yescharacteristic
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2411yescharacteristic
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2411yescharacteristic
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2412yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C23×C4C2411yescharacteristic
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2412yes—
669C23×C4C2412yes—
670C4⋊Q8—42no—
671C4⋊Q8—44no—
672#127—42no—
673#127—44no—
674#126—48no—
675#126—48no—
676#126—48no—
677#125—28no—
678#125—48no—
679#124—28no—
680#124—24no—
681#124—24no—
682#124—44no—
683#124—48no—
684#124—44no—
685#124—84no—
686#124—84no—
687#123—48no—
688#123—44no—
689#123—48no—
690#123—48no—
691#123—44no—
692#123—84no—
693#123—84no—
694C22⋊Q8—28no—
695C22⋊Q8—28no—
696C22⋊Q8—216no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—44no—
702C22⋊Q8—44no—
703C22⋊Q8—44no—
704C22⋊Q8—48no—
705C22⋊Q8—44no—
706C22⋊Q8—84no—
707C22⋊Q8—82no—
708C22⋊Q8—84no—
709C22⋊Q8—82no—
710#121—48no—
711#121—44no—
712#121—44no—
713#121—44no—
714#121—48no—
715#121—48no—
716#121—48no—
717#121—44no—
718#121—44no—
719#121—44no—
720#121—82no—
721#121—84no—
722#121—84no—
723#121—82no—
724#120—48no—
725#120—44no—
726#120—44no—
727#120—84no—
728#120—84no—
729C4×Q8—44no—
730C4×Q8—44no—
731C4×D4—48no—
732C4×D4—44no—
733C4×D4—44no—
734C4×D4—44no—
735C4×D4—44no—
736C4×D4—48no—
737C4×D4—48no—
738C4×D4—84no—
739C4×D4—84no—
740#117—42no—
741#117—44no—
742#117—48no—
743#117—82no—
744#117—82no—
745C2×C4⋊C4—42no—
746C2×C4⋊C4—42no—
747C2×C4⋊C4—44no—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C22⋊C4—48no—
792C2×C22⋊C4—44no—
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⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C42—28no—
850C2×C42—24no—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2411yescharacteristic
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2411yescharacteristic
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909C24—42no—
910C24—44no—
911C24—42no—
912C24—42no—
913C24—44no—
914C24C2514yes—
915C24C2512yes—
916C24C2512yes—
917C24C2512yes—
918C24C2511yescharacteristic
919#41—416no—
920#41—88no—
921#41—88no—
922C2×Q8—24no—
923C2×Q8—22no—
924C2×Q8—22no—
925C2×Q8—41no—
926C2×Q8—41no—
927C2×Q8—41no—
928C2×Q8—41no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—41no—
932C2×Q8—41no—
933C2×Q8—44no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×Q8—44no—
937C2×Q8—44no—
938C2×Q8—42no—
939C2×Q8H(5,𝔽2)14yes—
940C2×D4—24no—
941C2×D4—28no—
942C2×D4—24no—
943C2×D4—24no—
944C2×D4—24no—
945C2×D4—22no—
946C2×D4—24no—
947C2×D4—22no—
948C2×D4—22no—
949C2×D4—42no—
950C2×D4—41no—
951C2×D4—41no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—41no—
961C2×D4—41no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—41no—
975C2×D4—41no—
976C2×D4—44no—
977C2×D4—42no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—28no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—42no—
1008C22×C4—42no—
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—44no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—24no—
1053C4⋊C4—28no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—41no—
1108C22⋊C4—41no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
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—44no—
1123C22⋊C4—42no—
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—44no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—44no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C42—24no—
1147C42—24no—
1148C42—22no—
1149C42—24no—
1150C42—24no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—42no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42H(5,𝔽2)14yes—
1162C23—21no—
1163C23—21no—
1164C23—22no—
1165C23—22no—
1166C23—24no—
1167C23—22no—
1168C23—24no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—22no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—22no—
1188C23—22no—
1189C23—24no—
1190C23—48no—
1191C23—164no—
1192C23—162no—
1193C23—162no—
1194C23—164no—
1195C23#58512yes—
1196C23C2611yescharacteristic
1197Q8—44no—
1198Q8—84no—
1199Q8—82no—
1200Q8—82no—
1201Q8—164no—
1202Q8—162no—
1203D4—48no—
1204D4—44no—
1205D4—84no—
1206D4—82no—
1207D4—82no—
1208D4—88no—
1209D4—84no—
1210D4—84no—
1211D4—88no—
1212D4—88no—
1213D4—88no—
1214D4—88no—
1215D4—164no—
1216D4—164no—
1217D4—164no—
1218D4—162no—
1219D4—164no—
1220C2×C4—28no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—48no—
1272C2×C4—48no—
1273C2×C4—88no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—162no—
1280C2×C4—164no—
1281C2×C4—162no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4C2×H(5,𝔽2)14yes—
1285C2×C4C2×H(5,𝔽2)12yes—
1286C2×C4C2×H(5,𝔽2)14yes—
1287C2×C4C2×H(5,𝔽2)12yes—
1288C22—24no—
1289C22—22no—
1290C22—41no—
1291C22—41no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—44no—
1296C22—42no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—42no—
1301C22—42no—
1302C22—44no—
1303C22—42no—
1304C22—44no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—44no—
1311C22—42no—
1312C22—42no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22—168no—
1318C22C22×H(5,𝔽2)11yescharacteristic
1319C22C22×H(5,𝔽2)11yescharacteristic
1320C22C2×#58511yescharacteristic
1321C22H(7,𝔽2)12yes—
1322C222−1+612yes—
1323C4—22no—
1324C4—22no—
1325C4—24no—
1326C4—24no—
1327C4—44no—
1328C4—44no—
1329C4—44no—
1330C4—44no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—44no—
1341C2—42no—
1342C2—82no—
1343C2—82no—
1344C2—84no—
1345C2—82no—
1346C2#6281811yescharacteristic
1347C2#6287512yes—
1348C2#6304811yescharacteristic
1349C2#6305912yes—
1350C2#6306611yescharacteristic
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. #58576C2semidirect
2. #57426C2semidirect
3. #56626C2semidirect
4. #54946C2semidirect
5. #53954C2semidirect
6. #53407C2semidirect
7. #50489C2semidirect
8. #50255C2semidirect
9. #50108C2semidirect
10. #49703C2semidirect
11. #47191C2semidirect
12. #46831C2semidirect
13. #46360C2semidirect
14. #46356C2semidirect
15. #46232C2semidirect
16. #46230C2semidirect
17. #46228C2semidirect
18. #46225C2semidirect
19. #45989C2semidirect
20. #45975C2semidirect
21. #45973C2semidirect
22. #35328C2semidirect
23. #35189C2semidirect
24. C2×#563C22semidirect
26. C2×#543C22semidirect
29. C2×#537C22semidirect
32. C2×C4×#41C22semidirect
33. #2851C22semidirect
34. #2851C22semidirect
38. #2850C22semidirect
39. #2844C22semidirect
40. #2837C22semidirect
41. #2836C22semidirect
42. #2830C22semidirect
47. #2816C22semidirect
50. #2812C22semidirect
53. #2801C22semidirect
55. #2795C22semidirect
56. #2793C22semidirect
57. #2787C22semidirect
58. #2775C22semidirect
59. #2773C22semidirect
60. #2765C22semidirect
61. #2762C22semidirect
62. #2759C22semidirect
65. #2756C22semidirect
66. #2748C22semidirect
67. #2741C22semidirect
68. #2740C22semidirect
69. #2738C22semidirect
70. #2737C22semidirect
71. #2734C22semidirect
75. #2730C22semidirect
76. #2730C22semidirect
77. #2728C22semidirect
79. #2720C22semidirect
80. #2717C22semidirect
81. #2716C22semidirect
84. #2714C22semidirect
87. #2705C22semidirect
88. #2705C22semidirect
89. #2704C22semidirect
90. #2704C22semidirect
92. #2703C22semidirect
93. #2703C22semidirect
95. #2698C22semidirect
96. #2696C22semidirect
97. #2692C22semidirect
98. #2692C22semidirect
99. #2692C22semidirect
100. #2691C22semidirect
101. #2690C22semidirect
104. #2684C22semidirect
105. #2683C22semidirect
108. #2681C22semidirect
109. #2680C22semidirect
118. #2672C22semidirect
119. #2670C22semidirect
124. #2651C22semidirect
126. #2644C22semidirect
128. #2630C22semidirect
129. #2630C22semidirect
130. #2630C22semidirect
131. #2621C22semidirect
133. #2610C22semidirect
134. #2606C22semidirect
135. #2601C22semidirect
136. #2601C22semidirect
137. #2598C22semidirect
139. #2596C22semidirect
140. #2591C22semidirect
141. #2586C22semidirect
142. #2585C22semidirect
143. #2582C22semidirect
144. #2564C22semidirect
145. #2556C22semidirect
146. #2549C22semidirect
147. #2543C22semidirect
148. #2543C22semidirect
150. #2539C22semidirect
152. #2538C22semidirect
154. #2536C22semidirect
155. #2535C22semidirect
156. #2534C22semidirect
157. #2532C22semidirect
158. #2532C22semidirect
160. #2525C22semidirect
161. #2522C22semidirect
162. #2510C22semidirect
163. #2490C22semidirect
164. #2485C22semidirect
165. #2481C22semidirect
166. #2480C22semidirect
167. #2479C22semidirect
169. #2474C22semidirect
170. #2470C22semidirect
171. #2469C22semidirect
172. #2466C22semidirect
173. #2464C22semidirect
177. #2461C22semidirect
179. #2456C22semidirect
180. #2452C22semidirect
181. #2449C22semidirect
182. #2449C22semidirect
190. #2424C22semidirect
192. #2418C22semidirect
193. #2417C22semidirect
194. #2415C22semidirect
195. #2415C22semidirect
196. #2415C22semidirect
200. #2407C22semidirect
201. #2406C22semidirect
203. #2382C22semidirect
206. #2379C22semidirect
207. #2376C22semidirect
208. #2375C22semidirect
209. #2372C22semidirect
211. #2332C22semidirect
212. #2332C22semidirect
213. #2324C22semidirect
214. #2323C22semidirect
216. #2311C22semidirect
217. #2285C22semidirect
218. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#585762
#574262
#566262
#549462
#539542
#534072
#504892
#502552
#501082
#497032
#471912
#468312
#463602
#463562
#462322
#462302
#462282
#462252
#459892
#459752
#459732
#353282
#351892