Finite Group Databasebeta

← #7714731

Subgroups — #7714731

Order 512.

5570 conjugacy classes of subgroups.

The subgroup lattice has 1383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51988C212yesmaximal, complemented
2#51984C212yesmaximal, complemented
3#51931C214yesmaximal, complemented
4#51930C212yesmaximal, complemented
5#51923C212yesmaximal, complemented
6#51922C214yesmaximal, complemented
7#46624C214yesmaximal, complemented
8#46620C214yesmaximal, complemented
9#46610C214yesmaximal, complemented
10#46606C214yesmaximal, complemented
11#39557C214yesmaximal, complemented
12#39429C214yesmaximal, complemented
13#37854C214yesmaximal, complemented
14#37666C214yesmaximal, complemented
15#37517C212yesmaximal, complemented
16#37198C212yesmaximal, complemented
17#37194C211yesmaximal, characteristic, complemented
18#37190C211yesmaximal, characteristic, complemented
19#35149C212yesmaximal, complemented
20#35093C212yesmaximal, complemented
21#34989C212yesmaximal, complemented
22#34409C212yesmaximal, complemented
23C2×#2311C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C2×#539C2212yes—
26C2×#538C2212yes—
27C2×#536C2212yes—
28C2×#535C2212yes—
29C2×#525C2212yes—
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32#2855C2212yes—
33#2854C2212yes—
34#2849C2214yes—
35#2849C2214yes—
36#2848C2212yes—
37#2847C2212yes—
38#2830C2212yescomplemented
39#2829C2214yescomplemented
40#2828C2212yescomplemented
41#2811C2211yescharacteristic, complemented
42#2809C2211yescharacteristic, complemented
43#2809C2212yescomplemented
44#2808C2212yescomplemented
45#2806C2214yescomplemented
46#2806C2212yescomplemented
47#2803C2214yescomplemented
48#2803C2214yescomplemented
49#2800C2214yescomplemented
50#2799C2214yescomplemented
51#2799C2212yescomplemented
52#2797C2214yescomplemented
53#2797C2214yescomplemented
54#2796C2214yescomplemented
55#2786C2214yescomplemented
56#2757C2214yescomplemented
57#2756C2214yescomplemented
58#2753C2214yescomplemented
59#2748C2214yescomplemented
60#2747C2214yescomplemented
61#2747C2214yescomplemented
62#2742C2214yescomplemented
63#2741C2214yescomplemented
64#2741C2214yescomplemented
65#2734C2211yescharacteristic, complemented
66#2733C2212yescomplemented
67#2733C2211yescharacteristic, complemented
68#2732C2212yescomplemented
69#2731C2212yescomplemented
70#2730C2214yescomplemented
71#2730C2214yescomplemented
72#2729C2214yescomplemented
73#2728C2212yescomplemented
74#2727C2212yescomplemented
75#2723C2214yescomplemented
76#2722C2214yescomplemented
77#2717C2214yescomplemented
78#2715C2214yescomplemented
79#2714C2214yescomplemented
80#2712C2214yescomplemented
81#2710C2214yescomplemented
82#2709C2214yescomplemented
83#2704C2214yescomplemented
84#2703C2214yescomplemented
85#2702C2214yescomplemented
86#2692C2214yescomplemented
87#2691C2214yescomplemented
88#2691C2214yescomplemented
89#2690C2214yescomplemented
90#2688C2214yescomplemented
91#2686C2214yescomplemented
92#2682C2212yescomplemented
93#2673C2214yescomplemented
94#2672C2214yescomplemented
95#2671C2214yescomplemented
96#2671C2214yescomplemented
97#2662C2214yescomplemented
98#2661C2214yescomplemented
99#2651C2214yescomplemented
100#2648C2214yescomplemented
101#2627C2212yes—
102#2627C2212yes—
103#2623C2214yes—
104#2622C2214yes—
105#2618C2212yes—
106#2618C2212yes—
107#2613C2214yes—
108#2613C2214yes—
109#2603C2214yescomplemented
110#2602C2214yescomplemented
111#2597C2214yescomplemented
112#2595C2214yescomplemented
113#2593C2212yescomplemented
114#2578C2214yescomplemented
115#2577C2214yescomplemented
116#2574C2214yescomplemented
117#2560C2214yescomplemented
118#2559C2214yescomplemented
119#2557C2214yescomplemented
120#2555C2214yescomplemented
121#2555C2212yescomplemented
122#2554C2214yescomplemented
123#2553C2214yescomplemented
124#2544C2214yescomplemented
125#2543C2214yescomplemented
126#2531C2214yescomplemented
127#2531C2214yescomplemented
128#2530C2214yescomplemented
129#2522C2214yescomplemented
130#2521C2214yescomplemented
131#2521C2214yescomplemented
132#2498C2214yes—
133#2481C2214yescomplemented
134#2481C2214yescomplemented
135#2480C2214yes—
136#2480C2214yes—
137#2478C2214yescomplemented
138#2478C2214yescomplemented
139#2476C2214yescomplemented
140#2476C2214yescomplemented
141#2474C2214yescomplemented
142#2474C2214yescomplemented
143#2473C2214yescomplemented
144#2473C2214yescomplemented
145#2472C2214yes—
146#2472C2214yes—
147#2470C2214yescomplemented
148#2470C2214yescomplemented
149#2468C2214yescomplemented
150#2467C2214yescomplemented
151#2467C2214yescomplemented
152#2461C2214yescomplemented
153#2460C2214yescomplemented
154#2457C2214yescomplemented
155#2454C2214yescomplemented
156#2450C2214yescomplemented
157#2449C2214yescomplemented
158#2449C2214yescomplemented
159#2443C2214yescomplemented
160#2443C2214yescomplemented
161#2438C2214yes—
162#2438C2214yes—
163#2432C2212yes—
164#2432C2212yes—
165#2432C2212yes—
166#2432C2212yes—
167#2431C2212yes—
168#2431C2212yes—
169#2431C2212yes—
170#2431C2212yes—
171#2430C2214yes—
172#2428C2214yescomplemented
173#2427C2214yescomplemented
174#2425C2214yescomplemented
175#2425C2214yescomplemented
176#2424C2214yes—
177#2424C2214yes—
178#2418C2214yes—
179#2418C2214yes—
180#2407C2214yes—
181#2407C2214yes—
182#2407C2214yes—
183#2407C2214yes—
184#2381C2212yescomplemented
185#2379C2212yescomplemented
186#2378C2214yescomplemented
187#2372C2212yescomplemented
188#2369C2212yescomplemented
189#2368C2214yescomplemented
190#2359C2214yes—
191#2359C2214yes—
192#2343C2214yes—
193#2339C2214yes—
194#2337C2214yescomplemented
195#2332C2214yescomplemented
196#2331C2214yescomplemented
197#2329C2214yescomplemented
198#2322C2214yes—
199#2322C2214yes—
200#2313C2212yes—
201#2312C2212yes—
202#2311C2214yes—
203#2311C2212yes—
204#2311C2212yes—
205#2311C2214yes—
206#2311C2212yes—
207#2311C2212yes—
208#2310C2212yes—
209#2309C2212yes—
210C4×#123C2214yes—
211C4×#120C2214yes—
212C2×#391C2211yescharacteristic
213C2×#391C2211yescharacteristic
214C2×#390C2211yescharacteristic
215C2×#390C2211yescharacteristic
216C2×#386C2214yes—
217#2280C2212yes—
218C2×#380C2214yes—
219C22×#41—28no—
220C22×#41—44no—
221C22×#41—44no—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2312yes—
227C23×Q8C2311yescharacteristic
228C23×D4C2312yes—
229C23×D4C2311yescharacteristic
230C24×C4C2311yescharacteristic
231C24×C4C2312yes—
232C24×C4C2312yes—
233#539—48no—
234#538—48no—
235#536—216no—
236#535—48no—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×#127C2312yes—
240C2×#127C2312yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#125C2314yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#124C2314yes—
251C2×#124C2314yes—
252C2×#124C2314yes—
253#525—48no—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281C2×#120C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×#117—44no—
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C22×C4⋊C4—44no—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2314yes—
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2312yes—
315#400C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#395C2314yes—
361#395C2312yes—
362#395C2312yes—
363#395C2314yes—
364#395C2314yes—
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#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2312yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#392C2314yes—
398#392C2314yes—
399#392C2314yes—
400#392C2314yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#391C2314yes—
409#391C2312yes—
410#391C2314yes—
411#391C2312yes—
412#391C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2311yescharacteristic
419#391C2314yes—
420#391C2311yescharacteristic
421#391C2311yescharacteristic
422#391C2311yescharacteristic
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#390C2314yes—
429#390C2314yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
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#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
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#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
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#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
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#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#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#383C2314yes—
577#382C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#379C2314yes—
600#379C2314yes—
601#379C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620#376C2314yes—
621C2×#95C2314yes—
622C2×#95C2314yes—
623C2×#95C2314yes—
624C25C2412yes—
625C25C2411yescharacteristic
626C2×#41—28no—
627C2×#41—28no—
628C2×#41—28no—
629C2×#41—28no—
630C2×#41—28no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41—44no—
634C2×#41—44no—
635C2×#41—44no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—44no—
639C2×#41—44no—
640C2×#41—44no—
641C2×#41—464no—
642C22×Q8—42no—
643C22×Q8—42no—
644C22×Q8#4118yes—
645C22×Q8C2412yes—
646C22×Q8C2412yes—
647C22×Q8C2412yes—
648C22×Q8C2411yescharacteristic
649C22×Q8C2412yes—
650C22×Q8C2411yescharacteristic
651C22×D4—28no—
652C22×D4—28no—
653C22×D4—24no—
654C22×D4—42no—
655C22×D4—42no—
656C22×D4—44no—
657C22×D4C2414yes—
658C22×D4C2412yes—
659C22×D4C2412yes—
660C22×D4C2412yes—
661C22×D4C2412yes—
662C22×D4C2414yes—
663C22×D4C2414yes—
664C22×D4C2412yes—
665C22×D4C2412yes—
666C22×D4C2411yescharacteristic
667C22×D4C2411yescharacteristic
668C22×D4C2414yes—
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2414yes—
672C22×D4C2412yes—
673C22×D4C2412yes—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—24no—
677C23×C4—28no—
678C23×C4—28no—
679C23×C4—44no—
680C23×C4—44no—
681C23×C4—84no—
682C23×C4C2412yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2411yescharacteristic
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C4⋊Q8—28no—
701C4⋊Q8—28no—
702#127—44no—
703#127—44no—
704#126—48no—
705#126—48no—
706#126—84no—
707#126—84no—
708#125—48no—
709#124—28no—
710#124—28no—
711#124—44no—
712#124—44no—
713#124—48no—
714#124—84no—
715#124—84no—
716#123—216no—
717#123—216no—
718#123—216no—
719#123—48no—
720#123—48no—
721#123—84no—
722#123—84no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—44no—
726C22⋊Q8—44no—
727C22⋊Q8—48no—
728C22⋊Q8—44no—
729C22⋊Q8—44no—
730C22⋊Q8—84no—
731#121—44no—
732#121—44no—
733#121—48no—
734#121—48no—
735#121—48no—
736#121—44no—
737#121—44no—
738#121—84no—
739#121—84no—
740#121—84no—
741#120—216no—
742#120—48no—
743#120—48no—
744C4×D4—48no—
745C4×D4—48no—
746C4×D4—48no—
747C4×D4—48no—
748C4×D4—84no—
749C4×D4—84no—
750#117—28no—
751#117—44no—
752#117—48no—
753#117—44no—
754#117—44no—
755#117—44no—
756C2×C4⋊C4—28no—
757C2×C4⋊C4—44no—
758C2×C4⋊C4—48no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4—42no—
761C2×C4⋊C4—42no—
762C2×C4⋊C4—44no—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C22⋊C4—28no—
805C2×C22⋊C4—84no—
806C2×C22⋊C4—84no—
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×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C42—42no—
857C2×C42—42no—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2411yescharacteristic
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
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—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920C24—22no—
921C24—22no—
922C24—24no—
923C24—24no—
924C24—24no—
925C24—42no—
926C24—42no—
927C24—44no—
928C24—44no—
929C24H(5,𝔽2)14yes—
930C24C2512yes—
931C24C2512yes—
932C24C2514yes—
933C24C2512yes—
934C24C2511yescharacteristic
935#41—432no—
936#41—432no—
937#41—432no—
938#41—432no—
939#41—816no—
940C2×Q8—24no—
941C2×Q8—416no—
942C2×Q8—41no—
943C2×Q8—42no—
944C2×Q8—41no—
945C2×Q8—41no—
946C2×Q8—42no—
947C2×Q8—41no—
948C2×Q8—42no—
949C2×Q8—42no—
950C2×Q8—42no—
951C2×Q8—42no—
952C2×Q8—44no—
953C2×Q8—42no—
954C2×Q8—42no—
955C2×Q8C2×#4114yes—
956C2×Q8C2×#4118yes—
957C2×Q8C2×#4114yes—
958C2×D4—28no—
959C2×D4—28no—
960C2×D4—28no—
961C2×D4—24no—
962C2×D4—24no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—24no—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—42no—
976C2×D4—41no—
977C2×D4—41no—
978C2×D4—42no—
979C2×D4—42no—
980C2×D4—41no—
981C2×D4—42no—
982C2×D4—41no—
983C2×D4—42no—
984C2×D4—42no—
985C2×D4—432no—
986C2×D4—416no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—42no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—42no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—42no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—42no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C22×C4—232no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—28no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—432no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—816no—
1062C22×C4C2×#4118yes—
1063C22×C4C2×#4114yes—
1064C22×C4H(5,𝔽2)14yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2511yescharacteristic
1082C22×C4C2512yes—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—41no—
1095C4⋊C4—42no—
1096C4⋊C4—41no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C42—24no—
1174C42—24no—
1175C42—42no—
1176C42—42no—
1177C42—41no—
1178C42—42no—
1179C42—41no—
1180C42—44no—
1181C42—44no—
1182C42—42no—
1183C42—42no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—24no—
1194C23—24no—
1195C23—28no—
1196C23—24no—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—22no—
1201C23—22no—
1202C23—24no—
1203C23—22no—
1204C23—22no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—48no—
1214C23—44no—
1215C23—48no—
1216C23—44no—
1217C23—416no—
1218C23—48no—
1219C23—88no—
1220C23—84no—
1221C23—84no—
1222C23C22×#4112yes—
1223C23C2×H(5,𝔽2)14yes—
1224C23C2×H(5,𝔽2)12yes—
1225C23C2×H(5,𝔽2)12yes—
1226C23C2611yescharacteristic
1227Q8—44no—
1228Q8—48no—
1229Q8—44no—
1230Q8—84no—
1231Q8—162no—
1232Q8—162no—
1233D4—48no—
1234D4—48no—
1235D4—48no—
1236D4—48no—
1237D4—48no—
1238D4—44no—
1239D4—44no—
1240D4—416no—
1241D4—84no—
1242D4—88no—
1243D4—88no—
1244D4—88no—
1245D4—88no—
1246D4—162no—
1247D4—164no—
1248D4—164no—
1249D4—162no—
1250C2×C4—216no—
1251C2×C4—216no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—28no—
1263C2×C4—28no—
1264C2×C4—216no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—48no—
1303C2×C4—48no—
1304C2×C4—48no—
1305C2×C4—48no—
1306C2×C4—88no—
1307C2×C4—84no—
1308C2×C4—84no—
1309C2×C4—84no—
1310C2×C4—84no—
1311C2×C4—88no—
1312C2×C4—88no—
1313C2×C4—164no—
1314C2×C4—164no—
1315C2×C4C22×#4114yes—
1316C2×C4C22×#4112yes—
1317C2×C4C22×#4112yes—
1318C2×C4C22×#4114yes—
1319C2×C4C2×H(5,𝔽2)14yes—
1320C22—24no—
1321C22—24no—
1322C22—22no—
1323C22—22no—
1324C22—24no—
1325C22—28no—
1326C22—416no—
1327C22—44no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—44no—
1333C22—44no—
1334C22—44no—
1335C22—44no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—44no—
1346C22—42no—
1347C22—816no—
1348C22#349014yes—
1349C22C23×#4111yescharacteristic
1350C22C22×H(5,𝔽2)11yescharacteristic
1351C22C22×H(5,𝔽2)11yescharacteristic
1352C22H(7,𝔽2)12yes—
1353C222−1+612yes—
1354C4—24no—
1355C4—22no—
1356C4—22no—
1357C4—24no—
1358C4—24no—
1359C4—44no—
1360C4—44no—
1361C4—44no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4—44no—
1367C4—44no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—44no—
1372C2—24no—
1373C2—44no—
1374C2—84no—
1375C2—82no—
1376C2—82no—
1377C2C2×#349011yescharacteristic
1378C2#6285112yes—
1379C2#6286612yes—
1380C2#6287411yescharacteristic
1381C2#6288611yescharacteristic
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. #51988C2semidirect
2. #51984C2semidirect
3. #51931C2semidirect
4. #51930C2semidirect
5. #51923C2semidirect
6. #51922C2semidirect
7. #46624C2semidirect
8. #46620C2semidirect
9. #46610C2semidirect
10. #46606C2semidirect
11. #39557C2semidirect
12. #39429C2semidirect
13. #37854C2semidirect
14. #37666C2semidirect
15. #37517C2semidirect
16. #37198C2semidirect
17. #37194C2semidirect
18. #37190C2semidirect
19. #35149C2semidirect
20. #35093C2semidirect
21. #34989C2semidirect
22. #34409C2semidirect
23. C2×#2311C2semidirect
38. #2830C22semidirect
39. #2829C22semidirect
40. #2828C22semidirect
41. #2811C22semidirect
42. #2809C22semidirect
43. #2809C22semidirect
44. #2808C22semidirect
45. #2806C22semidirect
46. #2806C22semidirect
47. #2803C22semidirect
48. #2803C22semidirect
49. #2800C22semidirect
50. #2799C22semidirect
51. #2799C22semidirect
52. #2797C22semidirect
53. #2797C22semidirect
54. #2796C22semidirect
55. #2786C22semidirect
56. #2757C22semidirect
57. #2756C22semidirect
58. #2753C22semidirect
59. #2748C22semidirect
60. #2747C22semidirect
61. #2747C22semidirect
62. #2742C22semidirect
63. #2741C22semidirect
64. #2741C22semidirect
65. #2734C22semidirect
66. #2733C22semidirect
67. #2733C22semidirect
68. #2732C22semidirect
69. #2731C22semidirect
70. #2730C22semidirect
71. #2730C22semidirect
72. #2729C22semidirect
73. #2728C22semidirect
74. #2727C22semidirect
75. #2723C22semidirect
76. #2722C22semidirect
77. #2717C22semidirect
78. #2715C22semidirect
79. #2714C22semidirect
80. #2712C22semidirect
81. #2710C22semidirect
82. #2709C22semidirect
83. #2704C22semidirect
84. #2703C22semidirect
85. #2702C22semidirect
86. #2692C22semidirect
87. #2691C22semidirect
88. #2691C22semidirect
89. #2690C22semidirect
90. #2688C22semidirect
91. #2686C22semidirect
92. #2682C22semidirect
93. #2673C22semidirect
94. #2672C22semidirect
95. #2671C22semidirect
96. #2671C22semidirect
97. #2662C22semidirect
98. #2661C22semidirect
99. #2651C22semidirect
100. #2648C22semidirect
109. #2603C22semidirect
110. #2602C22semidirect
111. #2597C22semidirect
112. #2595C22semidirect
113. #2593C22semidirect
114. #2578C22semidirect
115. #2577C22semidirect
116. #2574C22semidirect
117. #2560C22semidirect
118. #2559C22semidirect
119. #2557C22semidirect
120. #2555C22semidirect
121. #2555C22semidirect
122. #2554C22semidirect
123. #2553C22semidirect
124. #2544C22semidirect
125. #2543C22semidirect
126. #2531C22semidirect
127. #2531C22semidirect
128. #2530C22semidirect
129. #2522C22semidirect
130. #2521C22semidirect
131. #2521C22semidirect
133. #2481C22semidirect
134. #2481C22semidirect
137. #2478C22semidirect
138. #2478C22semidirect
139. #2476C22semidirect
140. #2476C22semidirect
141. #2474C22semidirect
142. #2474C22semidirect
143. #2473C22semidirect
144. #2473C22semidirect
147. #2470C22semidirect
148. #2470C22semidirect
149. #2468C22semidirect
150. #2467C22semidirect
151. #2467C22semidirect
152. #2461C22semidirect
153. #2460C22semidirect
154. #2457C22semidirect
155. #2454C22semidirect
156. #2450C22semidirect
157. #2449C22semidirect
158. #2449C22semidirect
159. #2443C22semidirect
160. #2443C22semidirect
172. #2428C22semidirect
173. #2427C22semidirect
174. #2425C22semidirect
175. #2425C22semidirect
184. #2381C22semidirect
185. #2379C22semidirect
186. #2378C22semidirect
187. #2372C22semidirect
188. #2369C22semidirect
189. #2368C22semidirect
194. #2337C22semidirect
195. #2332C22semidirect
196. #2331C22semidirect
197. #2329C22semidirect

Maximal subgroups

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

subgroupindex
#519882
#519842
#519312
#519302
#519232
#519222
#466242
#466202
#466102
#466062
#395572
#394292
#378542
#376662
#375172
#371982
#371942
#371902
#351492
#350932
#349892
#344092
C2×#23112