Finite Group Databasebeta

← #8935489

Subgroups — #8935489

Order 512.

5534 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58750C212yesmaximal, complemented
2#56487C212yesmaximal, complemented
3#55184C214yesmaximal, complemented
4#55180C214yesmaximal, complemented
5#51638C214yesmaximal, complemented
6#51336C212yesmaximal, complemented
7#49591C212yesmaximal, complemented
8#48662C214yesmaximal, complemented
9#47842C214yesmaximal, complemented
10#47832C212yesmaximal, complemented
11#47000C214yesmaximal, complemented
12#44869C214yesmaximal, complemented
13#43087C214yesmaximal, complemented
14#41997C214yesmaximal, complemented
15#40616C214yesmaximal, complemented
16#40504C212yesmaximal, complemented
17#37760C212yesmaximal, complemented
18#37745C212yesmaximal, complemented
19#36719C211yesmaximal, characteristic, complemented
20#36085C212yesmaximal, complemented
21#35924C212yesmaximal, complemented
22#35659C211yesmaximal, characteristic, complemented
23#35391C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C2×#547C2212yes—
26C2×#547C2214yescomplemented
27C2×#543C2211yescharacteristic
28C2×#539C2211yescharacteristic
29C2×#539C2212yes—
30C2×#537C2212yes—
31C2×#525C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33#2848C2211yescharacteristic
34#2847C2211yescharacteristic
35#2843C2212yescomplemented
36#2843C2214yescomplemented
37#2841C2214yes—
38#2841C2214yescomplemented
39#2832C2212yescomplemented
40#2821C2212yescomplemented
41#2814C2212yescomplemented
42#2811C2212yescomplemented
43#2806C2214yescomplemented
44#2806C2214yescomplemented
45#2799C2214yescomplemented
46#2792C2212yescomplemented
47#2784C2214yes—
48#2775C2214yescomplemented
49#2774C2214yescomplemented
50#2764C2214yes—
51#2764C2214yescomplemented
52#2764C2214yescomplemented
53#2763C2214yes—
54#2758C2214yescomplemented
55#2750C2214yes—
56#2749C2214yes—
57#2743C2214yes—
58#2739C2214yescomplemented
59#2738C2214yescomplemented
60#2737C2214yes—
61#2737C2214yescomplemented
62#2729C2214yes—
63#2728C2212yescomplemented
64#2720C2214yes—
65#2718C2214yescomplemented
66#2713C2214yescomplemented
67#2708C2214yes—
68#2708C2214yes—
69#2708C2214yes—
70#2707C2214yescomplemented
71#2706C2214yes—
72#2706C2214yes—
73#2704C2214yes—
74#2702C2214yes—
75#2701C2214yescomplemented
76#2701C2214yescomplemented
77#2698C2214yescomplemented
78#2696C2214yes—
79#2695C2214yes—
80#2693C2214yes—
81#2692C2214yes—
82#2692C2214yes—
83#2692C2214yescomplemented
84#2691C2214yescomplemented
85#2690C2214yescomplemented
86#2688C2214yes—
87#2687C2214yes—
88#2687C2214yes—
89#2687C2214yescomplemented
90#2687C2214yescomplemented
91#2683C2214yes—
92#2681C2214yes—
93#2681C2214yes—
94#2681C2214yes—
95#2680C2214yes—
96#2680C2212yescomplemented
97#2671C2214yes—
98#2666C2214yescomplemented
99#2665C2214yes—
100#2665C2212yes—
101#2665C2214yescomplemented
102#2660C2212yescomplemented
103#2659C2212yes—
104#2659C2212yescomplemented
105#2646C2214yescomplemented
106#2639C2212yes—
107#2638C2212yes—
108#2633C2212yescomplemented
109#2627C2211yescharacteristic
110#2627C2212yes—
111#2627C2212yes—
112#2627C2214yescomplemented
113#2618C2211yescharacteristic
114#2616C2212yes—
115#2616C2212yescomplemented
116#2614C2214yescomplemented
117#2609C2214yes—
118#2605C2214yescomplemented
119#2603C2212yescomplemented
120#2598C2214yes—
121#2583C2212yes—
122#2583C2212yes—
123#2579C2214yes—
124#2572C2214yes—
125#2572C2214yes—
126#2572C2214yes—
127#2572C2212yescomplemented
128#2553C2214yescomplemented
129#2549C2214yes—
130#2549C2214yes—
131#2549C2214yescomplemented
132#2549C2214yescomplemented
133#2537C2212yescomplemented
134#2534C2212yes—
135#2534C2214yes—
136#2523C2214yescomplemented
137#2505C2214yescomplemented
138#2502C2212yes—
139#2502C2214yescomplemented
140#2492C2214yescomplemented
141#2477C2214yes—
142#2477C2214yes—
143#2475C2214yes—
144#2473C2214yescomplemented
145#2468C2214yes—
146#2466C2214yescomplemented
147#2464C2214yes—
148#2464C2214yes—
149#2463C2214yes—
150#2457C2214yes—
151#2457C2214yes—
152#2457C2214yes—
153#2450C2214yes—
154#2450C2214yes—
155#2450C2214yescomplemented
156#2449C2214yes—
157#2449C2214yes—
158#2449C2214yescomplemented
159#2443C2214yes—
160#2442C2214yescomplemented
161#2440C2214yes—
162#2440C2214yes—
163#2438C2214yescomplemented
164#2438C2214yescomplemented
165#2434C2212yes—
166#2434C2214yescomplemented
167#2430C2214yes—
168#2430C2214yes—
169#2430C2212yescomplemented
170#2430C2214yescomplemented
171#2424C2214yes—
172#2422C2214yescomplemented
173#2419C2214yes—
174#2418C2214yes—
175#2417C2214yes—
176#2417C2214yescomplemented
177#2415C2214yescomplemented
178#2413C2212yes—
179#2411C2212yes—
180#2409C2214yes—
181#2409C2214yes—
182#2409C2212yes—
183#2409C2214yescomplemented
184#2407C2214yes—
185#2407C2214yes—
186#2407C2214yes—
187#2407C2214yes—
188#2406C2212yes—
189#2406C2212yes—
190#2406C2214yes—
191#2406C2214yes—
192#2406C2214yescomplemented
193#2404C2212yes—
194#2404C2212yes—
195#2404C2214yes—
196#2388C2212yes—
197#2388C2214yes—
198C2×#395C2214yescomplemented
199#2378C2212yes—
200#2376C2214yescomplemented
201#2363C2214yescomplemented
202#2353C2212yes—
203#2353C2214yes—
204D4×C4⋊C4C2214yes—
205#2339C2214yes—
206#2339C2214yes—
207#2339C2212yes—
208#2339C2214yescomplemented
209#2325C2212yes—
210#2325C2212yes—
211#2318C2214yes—
212#2316C2211yescharacteristic
213#2315C2212yes—
214#2311C2214yes—
215#2311C2212yes—
216#2310C2211yescharacteristic
217C2×#385C2212yes—
218#2273C2211yescharacteristic
219C2×2−1+4—44no—
220C2×2−1+4—48no—
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2314yes—
224C22×#41C2314yes—
225C22×#41C2312yes—
226C22×#41C2312yes—
227C23×Q8C2311yescharacteristic
228C23×Q8C2314yes—
229C24×C4C2311yescharacteristic
230#547—48no—
231#547—416no—
232#543—44no—
233#539—44no—
234#539—48no—
235#537—48no—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238C2×#126C2312yes—
239C2×#126C2314yes—
240C2×#125C2312yes—
241C2×#125C2314yes—
242#525—48no—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2312yes—
253C2×#123C2312yes—
254C2×C22⋊Q8—44no—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2311yescharacteristic
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#120C2314yes—
284C2×#120C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×#117C2312yes—
296C2×#117C2314yes—
297C2×#117C2312yes—
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2314yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2312yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2312yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2312yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#395C2312yes—
375#395C2312yes—
376#395C2312yes—
377#395C2312yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2312yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2312yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2312yes—
393#395C2314yes—
394#395C2314yes—
395#395C2312yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2312yes—
400#394C2312yes—
401#394C2314yes—
402#394C2312yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2312yes—
407#394C2314yes—
408#394C2314yes—
409#394C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#393C2312yes—
417#393C2312yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#392C2314yes—
429#392C2312yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
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#387C2314yes—
486#387C2314yes—
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#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
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#386C2312yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2312yes—
531#386C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2312yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
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#384C2314yes—
566#384C2312yes—
567#384C2312yes—
568#383C2312yes—
569#383C2314yes—
570#383C2314yes—
571#383C2314yes—
572#383C2314yes—
573#382C2314yes—
574#382C2314yes—
575#381C2312yes—
576#381C2312yes—
577#381C2312yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2311yescharacteristic
594#380C2311yescharacteristic
595#380C2312yes—
596#380C2314yes—
597#380C2312yes—
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2312yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#379C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617#376C2312yes—
618C2×#95C2314yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C2×#95C2314yes—
622C2×#95C2312yes—
623C2×#95C2314yes—
624C25C2411yescharacteristic
6252−1+4—464no—
626C2×#41—28no—
627C2×#41—216no—
628C2×#41—28no—
629C2×#41—216no—
630C2×#41—44no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41—48no—
634C2×#41—48no—
635C2×#41—48no—
636C2×#41—48no—
637C2×#41—48no—
638C2×#41—48no—
639C2×#41—44no—
640C2×#41—84no—
641C22×Q8—24no—
642C22×Q8—48no—
643C22×Q8—44no—
644C22×Q8—48no—
645C22×Q8—48no—
646C22×Q8C2414yes—
647C22×Q8C2412yes—
648C22×Q8C2414yes—
649C22×Q8C2412yes—
650C22×Q8C2412yes—
651C22×Q8C2411yescharacteristic
652C22×Q8C2412yes—
653C22×Q8C2412yes—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2412yes—
660C22×D4C2412yes—
661C22×D4C2414yes—
662C22×D4C2414yes—
663C22×D4C2411yescharacteristic
664C22×D4C2412yes—
665C23×C4—44no—
666C23×C4—42no—
667C23×C4C2411yescharacteristic
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2411yescharacteristic
672C23×C4C2411yescharacteristic
673C23×C4C2412yes—
674C23×C4C2411yescharacteristic
675C23×C4C2414yes—
676C23×C4C2411yescharacteristic
677C23×C4C2414yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2414yes—
681C23×C4C2412yes—
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2414yes—
686C23×C4C2411yescharacteristic
687C23×C4C2412yes—
688C4⋊Q8—44no—
689C4⋊Q8—48no—
690#126—44no—
691#126—48no—
692#125—44no—
693#125—48no—
694#123—216no—
695#123—48no—
696#123—48no—
697#123—48no—
698#123—48no—
699#123—44no—
700#123—48no—
701#123—48no—
702#123—44no—
703#123—48no—
704#123—82no—
705C22⋊Q8—28no—
706C22⋊Q8—48no—
707C22⋊Q8—42no—
708C22⋊Q8—48no—
709C22⋊Q8—44no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—48no—
715C22⋊Q8—48no—
716C22⋊Q8—48no—
717C22⋊Q8—44no—
718C22⋊Q8—44no—
719C22⋊Q8—44no—
720C22⋊Q8—44no—
721C22⋊Q8—44no—
722C22⋊Q8—84no—
723C22⋊Q8—84no—
724#121—28no—
725#121—28no—
726#121—216no—
727#121—44no—
728#121—48no—
729#121—48no—
730#121—48no—
731#121—48no—
732#121—42no—
733#120—48no—
734#120—82no—
735C4×D4—28no—
736C4×D4—216no—
737C4×D4—44no—
738C4×D4—48no—
739C4×D4—48no—
740C4×D4—48no—
741C4×D4—48no—
742C4×D4—48no—
743C4×D4—84no—
744C4×D4—84no—
745#117—44no—
746#117—82no—
747#117—84no—
748C2×C4⋊C4—24no—
749C2×C4⋊C4—44no—
750C2×C4⋊C4—44no—
751C2×C4⋊C4—48no—
752C2×C4⋊C4—48no—
753C2×C4⋊C4—42no—
754C2×C4⋊C4—42no—
755C2×C4⋊C4—48no—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C22⋊C4—24no—
805C2×C22⋊C4—28no—
806C2×C22⋊C4—44no—
807C2×C22⋊C4—42no—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914C24—22no—
915C24—24no—
916C24—42no—
917C24—41no—
918C24—41no—
919C24C2512yes—
920C24C2511yescharacteristic
921C24C2514yes—
922C24C2512yes—
923#41—432no—
924#41—432no—
925#41—464no—
926#41—432no—
927#41—832no—
928#41—816no—
929C2×Q8—28no—
930C2×Q8—24no—
931C2×Q8—28no—
932C2×Q8—24no—
933C2×Q8—24no—
934C2×Q8—28no—
935C2×Q8—44no—
936C2×Q8—42no—
937C2×Q8—44no—
938C2×Q8—42no—
939C2×Q8—44no—
940C2×Q8—42no—
941C2×Q8—44no—
942C2×Q8—44no—
943C2×Q8—44no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—41no—
947C2×Q8—42no—
948C2×Q8—42no—
949C2×Q8—416no—
950C2×Q8—464no—
951C2×D4—28no—
952C2×D4—28no—
953C2×D4—28no—
954C2×D4—28no—
955C2×D4—28no—
956C2×D4—28no—
957C2×D4—28no—
958C2×D4—28no—
959C2×D4—28no—
960C2×D4—24no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—28no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—42no—
971C2×D4—44no—
972C2×D4—42no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—42no—
978C2×D4—42no—
979C2×D4—41no—
980C2×D4H(5,𝔽2)18yes—
981C22×C4—22no—
982C22×C4—24no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—28no—
986C22×C4—28no—
987C22×C4—28no—
988C22×C4—28no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—28no—
992C22×C4—24no—
993C22×C4—28no—
994C22×C4—28no—
995C22×C4—28no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—28no—
1000C22×C4—28no—
1001C22×C4—42no—
1002C22×C4—41no—
1003C22×C4—44no—
1004C22×C4—41no—
1005C22×C4—42no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—42no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—41no—
1028C22×C4—42no—
1029C22×C4—41no—
1030C22×C4—44no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—88no—
1038C22×C4H(5,𝔽2)14yes—
1039C22×C42−1+418yescomplemented
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2512yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—41no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—41no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C22⋊C4—28no—
1108C22⋊C4—24no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—42no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
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—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C42—24no—
1151C42—28no—
1152C42—42no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—42no—
1159C23—28no—
1160C23—22no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—24no—
1165C23—24no—
1166C23—22no—
1167C23—22no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—21no—
1172C23—22no—
1173C23—24no—
1174C23—21no—
1175C23—22no—
1176C23—22no—
1177C23—24no—
1178C23—24no—
1179C23—22no—
1180C23—22no—
1181C23—82no—
1182C23—82no—
1183C23—84no—
1184C23—84no—
1185C23C2×H(5,𝔽2)12yes—
1186C23C2×H(5,𝔽2)18yes—
1187C23C2×2−1+414yes—
1188C23C2611yescharacteristic
1189Q8—416no—
1190Q8—48no—
1191Q8—48no—
1192Q8—48no—
1193Q8—84no—
1194Q8—88no—
1195Q8—161no—
1196Q8—162no—
1197D4—216no—
1198D4—48no—
1199D4—416no—
1200D4—416no—
1201D4—416no—
1202D4—48no—
1203D4—416no—
1204D4—84no—
1205D4—88no—
1206D4—88no—
1207D4—161no—
1208C2×C4—28no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—21no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—44no—
1258C2×C4—48no—
1259C2×C4—416no—
1260C2×C4—416no—
1261C2×C4—416no—
1262C2×C4—44no—
1263C2×C4—44no—
1264C2×C4—416no—
1265C2×C4—88no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—88no—
1270C2×C4—82no—
1271C2×C4—84no—
1272C2×C4—82no—
1273C2×C4—88no—
1274C2×C4—88no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4C2×H(5,𝔽2)14yes—
1278C2×C4C2×H(5,𝔽2)14yes—
1279C2×C4C2×2−1+418yes—
1280C22—22no—
1281C22—28no—
1282C22—22no—
1283C22—24no—
1284C22—22no—
1285C22—24no—
1286C22—28no—
1287C22—24no—
1288C22—28no—
1289C22—42no—
1290C22—44no—
1291C22—44no—
1292C22—42no—
1293C22—44no—
1294C22—42no—
1295C22—42no—
1296C22—44no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—44no—
1303C22—44no—
1304C22—88no—
1305C22C22×H(5,𝔽2)11yescharacteristic
1306C22C22×H(5,𝔽2)12yes—
1307C22C22×2−1+412yes—
1308C22H(7,𝔽2)11yescharacteristic
1309C222−1+611yescharacteristic
1310C4—24no—
1311C4—24no—
1312C4—28no—
1313C4—44no—
1314C4—42no—
1315C4—41no—
1316C4—41no—
1317C4—42no—
1318C4—44no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—42no—
1324C4—44no—
1325C4—44no—
1326C4—44no—
1327C4—44no—
1328C4—44no—
1329C2—48no—
1330C2—42no—
1331C2—44no—
1332C2—82no—
1333C2#6281711yescharacteristic
1334C2#6283311yescharacteristic
1335C2#6287511yescharacteristic
1336C2#6289412yes—
1337C2#6291512yes—
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. #58750C2semidirect
2. #56487C2semidirect
3. #55184C2semidirect
4. #55180C2semidirect
5. #51638C2semidirect
6. #51336C2semidirect
7. #49591C2semidirect
8. #48662C2semidirect
9. #47842C2semidirect
10. #47832C2semidirect
11. #47000C2semidirect
12. #44869C2semidirect
13. #43087C2semidirect
14. #41997C2semidirect
15. #40616C2semidirect
16. #40504C2semidirect
17. #37760C2semidirect
18. #37745C2semidirect
19. #36719C2semidirect
20. #36085C2semidirect
21. #35924C2semidirect
22. #35659C2semidirect
23. #35391C2semidirect
26. C2×#547C22semidirect
35. #2843C22semidirect
36. #2843C22semidirect
38. #2841C22semidirect
39. #2832C22semidirect
40. #2821C22semidirect
41. #2814C22semidirect
42. #2811C22semidirect
43. #2806C22semidirect
44. #2806C22semidirect
45. #2799C22semidirect
46. #2792C22semidirect
48. #2775C22semidirect
49. #2774C22semidirect
51. #2764C22semidirect
52. #2764C22semidirect
54. #2758C22semidirect
58. #2739C22semidirect
59. #2738C22semidirect
61. #2737C22semidirect
63. #2728C22semidirect
65. #2718C22semidirect
66. #2713C22semidirect
70. #2707C22semidirect
75. #2701C22semidirect
76. #2701C22semidirect
77. #2698C22semidirect
83. #2692C22semidirect
84. #2691C22semidirect
85. #2690C22semidirect
89. #2687C22semidirect
90. #2687C22semidirect
96. #2680C22semidirect
98. #2666C22semidirect
101. #2665C22semidirect
102. #2660C22semidirect
104. #2659C22semidirect
105. #2646C22semidirect
108. #2633C22semidirect
112. #2627C22semidirect
115. #2616C22semidirect
116. #2614C22semidirect
118. #2605C22semidirect
119. #2603C22semidirect
127. #2572C22semidirect
128. #2553C22semidirect
131. #2549C22semidirect
132. #2549C22semidirect
133. #2537C22semidirect
136. #2523C22semidirect
137. #2505C22semidirect
139. #2502C22semidirect
140. #2492C22semidirect
144. #2473C22semidirect
146. #2466C22semidirect
155. #2450C22semidirect
158. #2449C22semidirect
160. #2442C22semidirect
163. #2438C22semidirect
164. #2438C22semidirect
166. #2434C22semidirect
169. #2430C22semidirect
170. #2430C22semidirect
172. #2422C22semidirect
176. #2417C22semidirect
177. #2415C22semidirect
183. #2409C22semidirect
192. #2406C22semidirect
198. C2×#395C22semidirect
200. #2376C22semidirect
201. #2363C22semidirect
208. #2339C22semidirect
1039. C22×C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#587502
#564872
#551842
#551802
#516382
#513362
#495912
#486622
#478422
#478322
#470002
#448692
#430872
#419972
#406162
#405042
#377602
#377452
#367192
#360852
#359242
#356592
#353912