Finite Group Databasebeta

← #9913062

Subgroups — #9913062

Order 512.

4789 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58384C212yesmaximal, complemented
2#58237C214yesmaximal, complemented
3#58149C214yesmaximal, complemented
4#57512C214yesmaximal, complemented
5#57201C214yesmaximal, complemented
6#55330C214yesmaximal, complemented
7#53636C214yesmaximal, complemented
8#53432C214yesmaximal, complemented
9#53348C212yesmaximal, complemented
10#53170C214yesmaximal, complemented
11#51940C212yesmaximal, complemented
12#50896C212yesmaximal, complemented
13#48330C214yesmaximal, complemented
14#48113C212yesmaximal, complemented
15#47962C212yesmaximal, complemented
16#46240C211yesmaximal, characteristic, complemented
17#45939C212yesmaximal, complemented
18#45568C212yesmaximal, complemented
19#45443C214yesmaximal, complemented
20#38957C211yesmaximal, characteristic, complemented
21#38020C212yesmaximal, complemented
22#37150C211yesmaximal, characteristic, complemented
23#36747C212yesmaximal, complemented
24C2×#562C2212yes—
25C2×#556C2211yescharacteristic, complemented
26C2×D42C2211yescharacteristic
27C22×#121C2212yescomplemented
28#2864C2212yescomplemented
29#2860C2212yescomplemented
30#2858C2211yescharacteristic, complemented
31#2849C2214yescomplemented
32#2849C2212yescomplemented
33#2848C2214yescomplemented
34#2845C2212yescomplemented
35#2838C2214yescomplemented
36#2837C2214yescomplemented
37#2837C2214yescomplemented
38#2829C2214yescomplemented
39#2824C2214yescomplemented
40#2819C2212yescomplemented
41#2816C2214yescomplemented
42#2816C2214yescomplemented
43#2813C2214yescomplemented
44#2810C2212yescomplemented
45#2809C2212yescomplemented
46#2808C2212yescomplemented
47#2804C2212yes—
48#2797C2214yescomplemented
49#2790C2214yescomplemented
50#2790C2214yescomplemented
51#2785C2212yescomplemented
52#2785C2212yescomplemented
53#2784C2214yescomplemented
54#2782C2214yescomplemented
55#2780C2214yescomplemented
56#2780C2214yescomplemented
57#2778C2214yescomplemented
58#2773C2214yescomplemented
59#2768C2214yescomplemented
60#2768C2214yescomplemented
61#2765C2214yescomplemented
62#2765C2214yescomplemented
63#2761C2214yescomplemented
64#2761C2214yescomplemented
65#2753C2214yescomplemented
66#2753C2214yescomplemented
67#2750C2214yescomplemented
68#2748C2212yes—
69#2748C2212yes—
70#2748C2214yescomplemented
71#2746C2214yescomplemented
72#2741C2214yescomplemented
73#2740C2214yescomplemented
74#2739C2214yescomplemented
75#2737C2214yescomplemented
76#2735C2214yescomplemented
77#2732C2214yescomplemented
78#2729C2214yescomplemented
79#2727C2212yescomplemented
80#2724C2212yescomplemented
81#2724C2212yescomplemented
82#2723C2214yescomplemented
83#2723C2214yescomplemented
84#2718C2214yescomplemented
85#2715C2214yescomplemented
86#2714C2214yescomplemented
87#2712C2214yescomplemented
88#2711C2214yescomplemented
89#2710C2214yescomplemented
90#2708C2214yescomplemented
91#2706C2214yescomplemented
92#2706C2214yescomplemented
93#2705C2214yescomplemented
94#2701C2214yescomplemented
95#2699C2214yescomplemented
96#2698C2214yescomplemented
97#2697C2214yescomplemented
98#2696C2214yescomplemented
99#2695C2214yescomplemented
100#2692C2214yescomplemented
101#2692C2214yescomplemented
102#2692C2214yescomplemented
103#2691C2214yescomplemented
104#2691C2214yescomplemented
105#2688C2214yes—
106#2687C2214yescomplemented
107#2687C2214yescomplemented
108#2686C2214yescomplemented
109#2685C2214yescomplemented
110#2685C2214yescomplemented
111#2685C2214yescomplemented
112#2685C2214yescomplemented
113#2684C2212yes—
114#2684C2214yescomplemented
115#2683C2211yescharacteristic
116#2683C2212yescomplemented
117#2682C2212yes—
118#2682C2212yescomplemented
119#2682C2212yescomplemented
120#2681C2214yescomplemented
121#2681C2214yescomplemented
122#2681C2214yescomplemented
123#2680C2212yescomplemented
124#2679C2211yescharacteristic
125#2678C2214yes—
126#2678C2214yescomplemented
127#2676C2214yescomplemented
128#2676C2214yescomplemented
129#2673C2214yescomplemented
130#2672C2214yescomplemented
131#2672C2214yescomplemented
132#2671C2214yescomplemented
133#2671C2214yescomplemented
134#2671C2214yescomplemented
135#2661C2214yescomplemented
136#2653C2214yescomplemented
137#2637C2214yescomplemented
138#2634C2212yescomplemented
139#2632C2212yescomplemented
140#2630C2214yescomplemented
141#2630C2214yescomplemented
142#2630C2214yescomplemented
143#2626C2214yescomplemented
144#2626C2214yescomplemented
145#2622C2212yescomplemented
146#2620C2212yescomplemented
147#2617C2212yescomplemented
148#2592C2212yescomplemented
149#2591C2212yescomplemented
150#2580C2214yescomplemented
151#2579C2212yes—
152#2576C2214yescomplemented
153#2574C2214yescomplemented
154#2565C2212yescomplemented
155#2561C2214yescomplemented
156#2553C2214yescomplemented
157#2548C2211yescharacteristic, complemented
158#2543C2214yescomplemented
159#2542C2211yescharacteristic
160#2539C2214yescomplemented
161#2537C2212yescomplemented
162#2536C2214yescomplemented
163#2534C2214yescomplemented
164#2522C2214yescomplemented
165#2518C2214yescomplemented
166#2500C2212yescomplemented
167#2488C2214yescomplemented
168#2488C2214yescomplemented
169#2476C2214yescomplemented
170#2473C2214yescomplemented
171#2472C2214yescomplemented
172#2472C2214yescomplemented
173#2471C2214yescomplemented
174#2467C2214yescomplemented
175#2466C2214yescomplemented
176#2465C2214yescomplemented
177#2463C2214yescomplemented
178#2461C2214yescomplemented
179#2459C2214yescomplemented
180#2458C2214yescomplemented
181#2449C2214yescomplemented
182#2444C2214yescomplemented
183#2438C2214yescomplemented
184#2438C2214yescomplemented
185#2437C2214yescomplemented
186#2437C2214yescomplemented
187#2437C2214yescomplemented
188#2435C2212yes—
189#2435C2214yescomplemented
190#2426C2214yescomplemented
191#2426C2214yescomplemented
192#2424C2214yes—
193#2423C2214yescomplemented
194#2421C2214yescomplemented
195#2418C2214yescomplemented
196#2418C2214yescomplemented
197#2410C2214yes—
198#2410C2212yescomplemented
199#2410C2214yescomplemented
200#2410C2212yescomplemented
201#2408C2214yescomplemented
202#2405C2214yescomplemented
203#2405C2214yescomplemented
204#2403C2212yes—
205#2403C2212yes—
206#2379C2211yescharacteristic
207#2379C2211yescharacteristic
208#2377C2214yescomplemented
209#2375C2212yes—
210#2358C2212yes—
211D4×C22⋊C4C2212yescomplemented
212#2337C2212yescomplemented
213#2321C2212yes—
214#2309C2212yes—
215#2308C2212yes—
216C4×#124C2211yescharacteristic
217#2293C2211yescharacteristic, complemented
218C2×#386C2212yes—
219C23×D4C2312yes—
220C23×D4C2312yes—
221C23×D4C2312yes—
222C23×D4C2312yes—
223C24×C4C2312yes—
224#562—48no—
225#556—44no—
226D42—44no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#125C2312yes—
233C2×#124C2312yes—
234C2×#124C2311yescharacteristic
235C2×#124C2312yes—
236C2×#124C2314yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×#121—48no—
258C2×#121C2314yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#120C2312yes—
270C2×#120C2312yes—
271C2×#120C2312yes—
272C2×#120C2314yes—
273C2×#120C2312yes—
274C2×#120C2312yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2314yes—
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×#117C2312yes—
286C2×#117C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2314yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2314yes—
294#401C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2312yes—
364#395C2312yes—
365#395C2314yes—
366#394C2314yes—
367#394C2312yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2312yes—
379#394C2312yes—
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#394C2314yes—
397#394C2314yes—
398#394C2312yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2311yescharacteristic
429#390C2311yescharacteristic
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
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#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#386C2312yes—
513#386C2312yes—
514#386C2312yes—
515#386C2312yes—
516#386C2314yes—
517#386C2314yes—
518#386C2312yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2312yes—
524#386C2312yes—
525#386C2312yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2312yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2312yes—
549#385C2312yes—
550#385C2312yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#384C2312yes—
573#384C2312yes—
574#383C2312yes—
575#382C2312yes—
576#382C2314yes—
577#382C2312yes—
578#382C2311yescharacteristic
579#382C2312yes—
580#382C2314yes—
581#382C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#379C2312yes—
599#379C2314yes—
600#379C2314yes—
601#379C2314yes—
602#379C2314yes—
603#379C2312yes—
604#379C2312yes—
605#379C2314yes—
606#379C2314yes—
607#379C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2311yescharacteristic
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C2×#95C2314yes—
617C43C2311yescharacteristic
618C25C2412yes—
619C25C2412yes—
620C25C2412yes—
621C22×Q8C2412yes—
622C22×Q8C2411yescharacteristic
623C22×Q8C2414yes—
624C22×Q8C2412yes—
625C22×D4—28no—
626C22×D4—28no—
627C22×D4—44no—
628C22×D4—44no—
629C22×D4—44no—
630C22×D4—82no—
631C22×D4—84no—
632C22×D4—84no—
633C22×D4—84no—
634C22×D4C2412yes—
635C22×D4C2414yes—
636C22×D4C2412yes—
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C22×D4C2414yes—
641C22×D4C2412yes—
642C22×D4C2412yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2411yescharacteristic
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2411yescharacteristic
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2411yescharacteristic
652C22×D4C2411yescharacteristic
653C23×C4—44no—
654C23×C4—84no—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2414yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2412yes—
665C23×C4C2414yes—
666C4⋊Q8—42no—
667#127—42no—
668#126—48no—
669#126—84no—
670#126—84no—
671#125—44no—
672#124—28no—
673#124—24no—
674#124—44no—
675#124—82no—
676#124—84no—
677#124—84no—
678#123—48no—
679#123—48no—
680#123—84no—
681#123—84no—
682#123—84no—
683#123—84no—
684#123—84no—
685#123—84no—
686C22⋊Q8—44no—
687C22⋊Q8—48no—
688C22⋊Q8—48no—
689C22⋊Q8—84no—
690C22⋊Q8—84no—
691C22⋊Q8—84no—
692C22⋊Q8—84no—
693C22⋊Q8—84no—
694C22⋊Q8—84no—
695C22⋊Q8—84no—
696#121—216no—
697#121—48no—
698#121—48no—
699#121—48no—
700#121—44no—
701#121—48no—
702#121—44no—
703#121—84no—
704#121—84no—
705#121—84no—
706#121—84no—
707#120—28no—
708#120—44no—
709#120—44no—
710#120—84no—
711#120—84no—
712#120—82no—
713#120—82no—
714#120—84no—
715C4×Q8—42no—
716C4×Q8—44no—
717C4×Q8—84no—
718C4×D4—24no—
719C4×D4—42no—
720C4×D4—84no—
721C4×D4—84no—
722C4×D4—84no—
723#117—44no—
724#117—82no—
725C2×C4⋊C4—44no—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C22⋊C4—44no—
770C2×C22⋊C4—44no—
771C2×C22⋊C4—82no—
772C2×C22⋊C4—82no—
773C2×C22⋊C4—84no—
774C2×C22⋊C4—84no—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
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×C42C2411yescharacteristic
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839C2×C42C2414yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2412yes—
863#95C2414yes—
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#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2414yes—
890C24—24no—
891C24—24no—
892C24—24no—
893C24—24no—
894C24—24no—
895C24—42no—
896C24—44no—
897C24—42no—
898C24—42no—
899C24—44no—
900C24—44no—
901C24—44no—
902C24—44no—
903C24—44no—
904C24—42no—
905C24C2514yes—
906C24C2512yes—
907C24C2512yes—
908C24C2512yes—
909C24C2512yes—
910C2×Q8—24no—
911C2×Q8—22no—
912C2×Q8—41no—
913C2×Q8—44no—
914C2×Q8—44no—
915C2×Q8—44no—
916C2×Q8—44no—
917C2×Q8—41no—
918C2×Q8—42no—
919C2×Q8—44no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—28no—
923C2×D4—28no—
924C2×D4—28no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—24no—
928C2×D4—24no—
929C2×D4—41no—
930C2×D4—44no—
931C2×D4—41no—
932C2×D4—42no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—42no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—42no—
955C2×D4—44no—
956C2×D4—41no—
957C2×D4—41no—
958C2×D4—42no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—816no—
969C2×D4—816no—
970C2×D4—816no—
971C2×D4—816no—
972C2×D4H(5,𝔽2)14yes—
973C2×D42−1+414yes—
974C22×C4—24no—
975C22×C4—28no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—44no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—816no—
1004C22×C4C2512yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2514yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C4⋊C4—28no—
1023C4⋊C4—22no—
1024C4⋊C4—44no—
1025C4⋊C4—41no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—41no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—24no—
1068C22⋊C4—28no—
1069C22⋊C4—24no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—42no—
1076C22⋊C4—44no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—42no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
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—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—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C42—22no—
1126C42—24no—
1127C42—22no—
1128C42—44no—
1129C42—41no—
1130C42—42no—
1131C42—42no—
1132C42—44no—
1133C42—44no—
1134C42—44no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—24no—
1142C23—24no—
1143C23—22no—
1144C23—24no—
1145C23—24no—
1146C23—24no—
1147C23—22no—
1148C23—22no—
1149C23—24no—
1150C23—22no—
1151C23—22no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—22no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—22no—
1161C23—24no—
1162C23—24no—
1163C23—48no—
1164C23—48no—
1165C23—48no—
1166C23—84no—
1167C23—88no—
1168C23—84no—
1169C23—84no—
1170C23—88no—
1171C23—88no—
1172C23—84no—
1173C23—88no—
1174C23—84no—
1175C23—84no—
1176C23—164no—
1177C23—164no—
1178C23C2×H(5,𝔽2)14yes—
1179C23C2×2−1+414yes—
1180C23C2611yescharacteristic
1181Q8—84no—
1182Q8—82no—
1183Q8—88no—
1184Q8—162no—
1185D4—44no—
1186D4—44no—
1187D4—48no—
1188D4—84no—
1189D4—84no—
1190D4—88no—
1191D4—88no—
1192D4—88no—
1193D4—84no—
1194D4—84no—
1195D4—84no—
1196D4—88no—
1197D4—88no—
1198D4—88no—
1199D4—164no—
1200D4—162no—
1201D4—161no—
1202D4—161no—
1203D4—162no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—48no—
1253C2×C4—48no—
1254C2×C4—84no—
1255C2×C4—88no—
1256C2×C4—88no—
1257C2×C4—84no—
1258C2×C4—84no—
1259C2×C4—164no—
1260C2×C4—164no—
1261C2×C4—164no—
1262C2×C4—164no—
1263C2×C4C2×H(5,𝔽2)12yes—
1264C2×C4C2×2−1+412yes—
1265C22—24no—
1266C22—28no—
1267C22—24no—
1268C22—24no—
1269C22—24no—
1270C22—44no—
1271C22—44no—
1272C22—42no—
1273C22—44no—
1274C22—42no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—42no—
1280C22—44no—
1281C22—42no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—44no—
1292C22—816no—
1293C22—168no—
1294C22—168no—
1295C22C22×H(5,𝔽2)11yescharacteristic
1296C22C22×2−1+411yescharacteristic
1297C22H(7,𝔽2)11yescharacteristic
1298C22H(7,𝔽2)12yes—
1299C22H(7,𝔽2)12yes—
1300C4—22no—
1301C4—22no—
1302C4—44no—
1303C4—44no—
1304C4—44no—
1305C4—44no—
1306C4—42no—
1307C4—44no—
1308C4—44no—
1309C4—41no—
1310C4—42no—
1311C4—42no—
1312C4—44no—
1313C4—44no—
1314C4—42no—
1315C4—44no—
1316C4—42no—
1317C4—42no—
1318C2—44no—
1319C2—44no—
1320C2—82no—
1321C2—82no—
1322C2—84no—
1323C2#6286211yescharacteristic
1324C2#6289411yescharacteristic
1325C2#6297612yes—
1326C2#6304511yescharacteristic
1327C2#6305412yes—
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. #58384C2semidirect
2. #58237C2semidirect
3. #58149C2semidirect
4. #57512C2semidirect
5. #57201C2semidirect
6. #55330C2semidirect
7. #53636C2semidirect
8. #53432C2semidirect
9. #53348C2semidirect
10. #53170C2semidirect
11. #51940C2semidirect
12. #50896C2semidirect
13. #48330C2semidirect
14. #48113C2semidirect
15. #47962C2semidirect
16. #46240C2semidirect
17. #45939C2semidirect
18. #45568C2semidirect
19. #45443C2semidirect
20. #38957C2semidirect
21. #38020C2semidirect
22. #37150C2semidirect
23. #36747C2semidirect
25. C2×#556C22semidirect
27. C22×#121C22semidirect
28. #2864C22semidirect
29. #2860C22semidirect
30. #2858C22semidirect
31. #2849C22semidirect
32. #2849C22semidirect
33. #2848C22semidirect
34. #2845C22semidirect
35. #2838C22semidirect
36. #2837C22semidirect
37. #2837C22semidirect
38. #2829C22semidirect
39. #2824C22semidirect
40. #2819C22semidirect
41. #2816C22semidirect
42. #2816C22semidirect
43. #2813C22semidirect
44. #2810C22semidirect
45. #2809C22semidirect
46. #2808C22semidirect
48. #2797C22semidirect
49. #2790C22semidirect
50. #2790C22semidirect
51. #2785C22semidirect
52. #2785C22semidirect
53. #2784C22semidirect
54. #2782C22semidirect
55. #2780C22semidirect
56. #2780C22semidirect
57. #2778C22semidirect
58. #2773C22semidirect
59. #2768C22semidirect
60. #2768C22semidirect
61. #2765C22semidirect
62. #2765C22semidirect
63. #2761C22semidirect
64. #2761C22semidirect
65. #2753C22semidirect
66. #2753C22semidirect
67. #2750C22semidirect
70. #2748C22semidirect
71. #2746C22semidirect
72. #2741C22semidirect
73. #2740C22semidirect
74. #2739C22semidirect
75. #2737C22semidirect
76. #2735C22semidirect
77. #2732C22semidirect
78. #2729C22semidirect
79. #2727C22semidirect
80. #2724C22semidirect
81. #2724C22semidirect
82. #2723C22semidirect
83. #2723C22semidirect
84. #2718C22semidirect
85. #2715C22semidirect
86. #2714C22semidirect
87. #2712C22semidirect
88. #2711C22semidirect
89. #2710C22semidirect
90. #2708C22semidirect
91. #2706C22semidirect
92. #2706C22semidirect
93. #2705C22semidirect
94. #2701C22semidirect
95. #2699C22semidirect
96. #2698C22semidirect
97. #2697C22semidirect
98. #2696C22semidirect
99. #2695C22semidirect
100. #2692C22semidirect
101. #2692C22semidirect
102. #2692C22semidirect
103. #2691C22semidirect
104. #2691C22semidirect
106. #2687C22semidirect
107. #2687C22semidirect
108. #2686C22semidirect
109. #2685C22semidirect
110. #2685C22semidirect
111. #2685C22semidirect
112. #2685C22semidirect
114. #2684C22semidirect
116. #2683C22semidirect
118. #2682C22semidirect
119. #2682C22semidirect
120. #2681C22semidirect
121. #2681C22semidirect
122. #2681C22semidirect
123. #2680C22semidirect
126. #2678C22semidirect
127. #2676C22semidirect
128. #2676C22semidirect
129. #2673C22semidirect
130. #2672C22semidirect
131. #2672C22semidirect
132. #2671C22semidirect
133. #2671C22semidirect
134. #2671C22semidirect
135. #2661C22semidirect
136. #2653C22semidirect
137. #2637C22semidirect
138. #2634C22semidirect
139. #2632C22semidirect
140. #2630C22semidirect
141. #2630C22semidirect
142. #2630C22semidirect
143. #2626C22semidirect
144. #2626C22semidirect
145. #2622C22semidirect
146. #2620C22semidirect
147. #2617C22semidirect
148. #2592C22semidirect
149. #2591C22semidirect
150. #2580C22semidirect
152. #2576C22semidirect
153. #2574C22semidirect
154. #2565C22semidirect
155. #2561C22semidirect
156. #2553C22semidirect
157. #2548C22semidirect
158. #2543C22semidirect
160. #2539C22semidirect
161. #2537C22semidirect
162. #2536C22semidirect
163. #2534C22semidirect
164. #2522C22semidirect
165. #2518C22semidirect
166. #2500C22semidirect
167. #2488C22semidirect
168. #2488C22semidirect
169. #2476C22semidirect
170. #2473C22semidirect
171. #2472C22semidirect
172. #2472C22semidirect
173. #2471C22semidirect
174. #2467C22semidirect
175. #2466C22semidirect
176. #2465C22semidirect
177. #2463C22semidirect
178. #2461C22semidirect
179. #2459C22semidirect
180. #2458C22semidirect
181. #2449C22semidirect
182. #2444C22semidirect
183. #2438C22semidirect
184. #2438C22semidirect
185. #2437C22semidirect
186. #2437C22semidirect
187. #2437C22semidirect
189. #2435C22semidirect
190. #2426C22semidirect
191. #2426C22semidirect
193. #2423C22semidirect
194. #2421C22semidirect
195. #2418C22semidirect
196. #2418C22semidirect
198. #2410C22semidirect
199. #2410C22semidirect
200. #2410C22semidirect
201. #2408C22semidirect
202. #2405C22semidirect
203. #2405C22semidirect
208. #2377C22semidirect
211. D4×C22⋊C4C22semidirect
212. #2337C22semidirect
217. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#583842
#582372
#581492
#575122
#572012
#553302
#536362
#534322
#533482
#531702
#519402
#508962
#483302
#481132
#479622
#462402
#459392
#455682
#454432
#389572
#380202
#371502
#367472