Finite Group Databasebeta

← #8943212

Subgroups — #8943212

Order 512.

5258 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58387C212yesmaximal, complemented
2#58296C214yesmaximal, complemented
3#57732C214yesmaximal, complemented
4#55926C212yesmaximal, complemented
5#51890C214yesmaximal, complemented
6#50784C214yesmaximal, complemented
7#50661C212yesmaximal, complemented
8#50166C212yesmaximal, complemented
9#49348C214yesmaximal, complemented
10#48795C212yesmaximal, complemented
11#46481C214yesmaximal, complemented
12#44250C214yesmaximal, complemented
13#44206C214yesmaximal, complemented
14#42580C214yesmaximal, complemented
15#42271C214yesmaximal, complemented
16#41386C212yesmaximal, complemented
17#37768C212yesmaximal, complemented
18#37760C212yesmaximal, complemented
19#36706C211yesmaximal, characteristic, complemented
20#36052C212yesmaximal, complemented
21#35995C212yesmaximal, complemented
22#35565C211yesmaximal, characteristic, complemented
23#35351C211yesmaximal, characteristic, complemented
24C2×#553C2212yes—
25C2×#553C2214yescomplemented
26C2×#539C2212yescomplemented
27C2×#539C2212yescomplemented
28C2×#538C2211yescharacteristic
29C2×#537C2211yescharacteristic
30C2×#535C2212yes—
31C2×#525C2212yes—
32C22×#121C2211yescharacteristic
33C2×#518C2211yescharacteristic
34#2848C2211yescharacteristic
35#2847C2211yescharacteristic
36#2841C2212yescomplemented
37#2827C2214yescomplemented
38#2826C2214yescomplemented
39#2826C2214yescomplemented
40#2820C2212yescomplemented
41#2815C2212yescomplemented
42#2815C2212yescomplemented
43#2807C2212yescomplemented
44#2797C2214yescomplemented
45#2796C2214yescomplemented
46#2780C2214yescomplemented
47#2771C2212yescomplemented
48#2768C2214yescomplemented
49#2752C2212yescomplemented
50#2740C2214yescomplemented
51#2732C2214yescomplemented
52#2724C2214yescomplemented
53#2723C2214yescomplemented
54#2721C2214yescomplemented
55#2720C2214yescomplemented
56#2715C2214yescomplemented
57#2714C2214yescomplemented
58#2714C2214yescomplemented
59#2714C2214yescomplemented
60#2711C2214yescomplemented
61#2708C2214yescomplemented
62#2708C2214yescomplemented
63#2706C2214yescomplemented
64#2706C2214yescomplemented
65#2706C2214yescomplemented
66#2705C2214yescomplemented
67#2703C2214yescomplemented
68#2703C2214yescomplemented
69#2701C2214yes—
70#2701C2214yescomplemented
71#2699C2214yescomplemented
72#2695C2214yes—
73#2694C2214yes—
74#2693C2212yescomplemented
75#2693C2214yescomplemented
76#2691C2214yes—
77#2691C2214yescomplemented
78#2690C2214yescomplemented
79#2689C2214yescomplemented
80#2688C2214yes—
81#2688C2214yescomplemented
82#2688C2214yescomplemented
83#2685C2214yes—
84#2682C2214yes—
85#2680C2214yes—
86#2678C2214yes—
87#2678C2214yes—
88#2678C2214yes—
89#2676C2214yes—
90#2675C2214yes—
91#2673C2214yescomplemented
92#2673C2214yescomplemented
93#2673C2214yescomplemented
94#2673C2214yescomplemented
95#2673C2214yescomplemented
96#2672C2214yescomplemented
97#2671C2214yes—
98#2671C2214yescomplemented
99#2667C2212yes—
100#2664C2212yescomplemented
101#2661C2212yescomplemented
102#2659C2212yescomplemented
103#2656C2212yescomplemented
104#2654C2214yescomplemented
105#2651C2214yescomplemented
106#2644C2214yescomplemented
107#2636C2214yescomplemented
108#2636C2212yescomplemented
109#2635C2212yes—
110#2635C2214yescomplemented
111#2627C2212yescomplemented
112#2626C2211yescharacteristic
113#2624C2212yes—
114#2623C2212yescomplemented
115#2618C2212yescomplemented
116#2618C2214yescomplemented
117#2617C2211yescharacteristic
118#2611C2214yescomplemented
119#2603C2214yescomplemented
120#2603C2214yescomplemented
121#2603C2214yescomplemented
122#2585C2214yescomplemented
123#2579C2212yes—
124#2575C2214yes—
125#2575C2214yescomplemented
126#2566C2214yescomplemented
127#2554C2214yescomplemented
128#2554C2214yescomplemented
129#2541C2214yes—
130#2541C2214yes—
131#2540C2214yes—
132#2540C2214yes—
133#2540C2212yescomplemented
134#2539C2212yes—
135#2539C2214yes—
136#2539C2212yes—
137#2535C2214yescomplemented
138#2534C2214yes—
139#2526C2214yes—
140#2526C2214yescomplemented
141#2519C2214yescomplemented
142#2516C2214yescomplemented
143#2512C2214yescomplemented
144#2508C2214yescomplemented
145#2501C2212yescomplemented
146#2484C2212yes—
147#2483C2212yes—
148#2482C2212yes—
149#2479C2214yes—
150#2479C2214yescomplemented
151#2475C2214yes—
152#2474C2214yescomplemented
153#2471C2214yescomplemented
154#2468C2214yescomplemented
155#2464C2214yescomplemented
156#2464C2214yescomplemented
157#2463C2212yescomplemented
158#2461C2214yescomplemented
159#2461C2214yescomplemented
160#2456C2214yescomplemented
161#2456C2214yescomplemented
162#2456C2214yescomplemented
163#2456C2214yescomplemented
164#2455C2212yescomplemented
165#2454C2214yescomplemented
166#2454C2214yescomplemented
167#2454C2214yescomplemented
168#2449C2214yescomplemented
169#2449C2214yescomplemented
170#2449C2214yescomplemented
171#2445C2214yescomplemented
172#2445C2214yescomplemented
173#2445C2214yescomplemented
174#2445C2214yescomplemented
175#2444C2214yes—
176#2444C2214yes—
177#2443C2214yes—
178#2443C2214yes—
179#2443C2214yescomplemented
180#2433C2212yes—
181#2433C2212yes—
182#2428C2214yescomplemented
183#2425C2214yescomplemented
184#2424C2214yes—
185#2424C2214yes—
186#2419C2214yescomplemented
187#2418C2214yes—
188#2418C2214yes—
189#2418C2214yes—
190#2411C2214yes—
191#2410C2212yes—
192#2410C2212yes—
193#2408C2212yes—
194#2407C2214yes—
195#2406C2214yes—
196#2405C2212yes—
197#2402C2214yescomplemented
198#2397C2214yescomplemented
199#2395C2212yes—
200#2377C2212yes—
201#2377C2214yescomplemented
202#2373C2214yescomplemented
203#2371C2214yescomplemented
204#2366C2214yescomplemented
205#2361C2214yescomplemented
206#2361C2214yescomplemented
207#2357C2212yes—
208D4×C4⋊C4C2214yescomplemented
209#2346C2212yes—
210#2329C2212yescomplemented
211#2328C2214yescomplemented
212#2325C2212yescomplemented
213#2324C2214yescomplemented
214#2315C2211yescharacteristic
215#2308C2212yes—
216#2308C2211yescharacteristic
217C2×#385C2212yes—
218#2274C2211yescharacteristic
219C22×#41C2312yes—
220C23×D4C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224#553—48no—
225#553—416no—
226#539—48no—
227#539—48no—
228#538—44no—
229#537—44no—
230#535—48no—
231C2×#127C2314yes—
232C2×#127C2314yes—
233C2×#127C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2312yes—
238C2×#126C2314yes—
239C2×#125C2314yes—
240C2×#125C2312yes—
241C2×#125C2314yes—
242C2×#124C2312yes—
243C2×#124C2314yes—
244#525—48no—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×#121—44no—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2311yescharacteristic
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#120C2312yes—
289C2×#120C2314yes—
290C2×#120C2314yes—
291C2×#120C2314yes—
292C2×#120C2312yes—
293C2×#120C2312yes—
294#518—44no—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2314yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C22⋊C4C2311yescharacteristic
318C22×C22⋊C4C2312yes—
319C22×C22⋊C4C2312yes—
320C22×C22⋊C4C2311yescharacteristic
321C22×C22⋊C4C2312yes—
322C22×C22⋊C4C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#399C2312yes—
333#399C2312yes—
334#399C2314yes—
335#399C2314yes—
336#399C2312yes—
337#399C2314yes—
338#399C2314yes—
339#399C2312yes—
340#399C2312yes—
341#399C2314yes—
342#399C2312yes—
343#399C2312yes—
344#399C2312yes—
345#399C2314yes—
346#399C2314yes—
347#399C2312yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#397C2312yes—
362#397C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
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#394C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#393C2312yes—
423#392C2312yes—
424#392C2314yes—
425#392C2312yes—
426#392C2314yes—
427#392C2314yes—
428#392C2312yes—
429#392C2314yes—
430#392C2312yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2312yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2312yes—
447#391C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
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#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#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2312yes—
530#386C2312yes—
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#386C2314yes—
553#385C2312yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2312yes—
563#385C2314yes—
564#385C2312yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2312yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#384C2314yes—
581#382C2312yes—
582#382C2314yes—
583#382C2314yes—
584#381C2314yes—
585#381C2312yes—
586#381C2312yes—
587#381C2312yes—
588#381C2314yes—
589#381C2314yes—
590#381C2312yes—
591#380C2312yes—
592#380C2311yescharacteristic
593#380C2311yescharacteristic
594#380C2314yes—
595#380C2312yes—
596#380C2312yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#379C2314yes—
603#379C2312yes—
604#379C2312yes—
605#379C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2312yes—
620#376C2314yes—
621#376C2314yes—
622C2×#95C2312yes—
623C2×#95C2312yes—
624C25C2411yescharacteristic
625C25C2411yescharacteristic
626C25C2411yescharacteristic
627C2×#41—44no—
628C2×#41—44no—
629C2×#41—44no—
630C22×Q8C2412yes—
631C22×Q8C2411yescharacteristic
632C22×D4—24no—
633C22×D4—44no—
634C22×D4—42no—
635C22×D4—42no—
636C22×D4—44no—
637C22×D4—44no—
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2412yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2412yes—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2411yescharacteristic
658C22×D4C2412yes—
659C23×C4—44no—
660C23×C4—42no—
661C23×C4C2411yescharacteristic
662C23×C4C2411yescharacteristic
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2411yescharacteristic
666C23×C4C2414yes—
667C23×C4C2412yes—
668C23×C4C2412yes—
669C23×C4C2412yes—
670C23×C4C2412yes—
671C23×C4C2414yes—
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2414yes—
676C23×C4C2414yes—
677C23×C4C2414yes—
678C23×C4C2411yescharacteristic
679#127—48no—
680#127—48no—
681#127—48no—
682#126—216no—
683#126—44no—
684#126—48no—
685#126—48no—
686#126—48no—
687#125—216no—
688#125—48no—
689#125—44no—
690#124—48no—
691#124—44no—
692#123—48no—
693#123—48no—
694#123—48no—
695#123—48no—
696#123—48no—
697#123—44no—
698#123—48no—
699#123—48no—
700#123—48no—
701#123—84no—
702#123—84no—
703#123—84no—
704#123—84no—
705C22⋊Q8—28no—
706C22⋊Q8—42no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709C22⋊Q8—48no—
710C22⋊Q8—44no—
711C22⋊Q8—44no—
712#121—28no—
713#121—28no—
714#121—216no—
715#121—44no—
716#121—44no—
717#121—48no—
718#121—48no—
719#121—48no—
720#121—48no—
721#121—48no—
722#121—48no—
723#121—48no—
724#121—48no—
725#121—48no—
726#121—44no—
727#121—48no—
728#121—44no—
729#121—48no—
730#121—44no—
731#121—42no—
732#121—84no—
733#121—84no—
734#120—48no—
735#120—48no—
736#120—48no—
737#120—44no—
738#120—82no—
739#120—82no—
740C4×D4—28no—
741C4×D4—48no—
742C4×D4—48no—
743C4×D4—48no—
744C4×D4—48no—
745C4×D4—48no—
746C4×D4—48no—
747C4×D4—48no—
748C4×D4—48no—
749C4×D4—48no—
750C4×D4—44no—
751C4×D4—48no—
752C4×D4—48no—
753C4×D4—48no—
754#117—28no—
755#117—28no—
756#117—48no—
757C2×C4⋊C4—24no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4—48no—
761C2×C4⋊C4—44no—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
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⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C22⋊C4—24no—
804C2×C22⋊C4—44no—
805C2×C22⋊C4—44no—
806C2×C22⋊C4—44no—
807C2×C22⋊C4—42no—
808C2×C22⋊C4—82no—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919C24—22no—
920C24—24no—
921C24—22no—
922C24—22no—
923C24—41no—
924C24—42no—
925C24—41no—
926C24—42no—
927C24—41no—
928C24—41no—
929C24—42no—
930C24—42no—
931C24—41no—
932C24—42no—
933C24—41no—
934C24C2512yes—
935C24C2512yes—
936C24C2512yes—
937C24C2514yes—
938C24C2511yescharacteristic
939C24C2512yes—
940#41—816no—
941C2×Q8—24no—
942C2×Q8—42no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—41no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—24no—
949C2×D4—28no—
950C2×D4—28no—
951C2×D4—28no—
952C2×D4—28no—
953C2×D4—28no—
954C2×D4—28no—
955C2×D4—28no—
956C2×D4—28no—
957C2×D4—24no—
958C2×D4—28no—
959C2×D4—24no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—42no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—42no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—42no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—42no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—41no—
995C2×D4—42no—
996C2×D4—44no—
997C2×D4—42no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—416no—
1005C2×D4—88no—
1006C2×D4—88no—
1007C22×C4—22no—
1008C22×C4—24no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—28no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—42no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
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—42no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—88no—
1055C22×C4H(5,𝔽2)14yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—41no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—41no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4H(5,𝔽2)18yes—
1114C22⋊C4—28no—
1115C22⋊C4—24no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—24no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
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—42no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—42no—
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—42no—
1173C22⋊C4—44no—
1174C42—28no—
1175C42—28no—
1176C42—28no—
1177C42—24no—
1178C42—28no—
1179C42—44no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C23—28no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—21no—
1192C23—22no—
1193C23—22no—
1194C23—21no—
1195C23—24no—
1196C23—22no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—22no—
1210C23—24no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—24no—
1217C23—44no—
1218C23—44no—
1219C23—82no—
1220C23—82no—
1221C23—84no—
1222C23—84no—
1223C23—82no—
1224C23—82no—
1225C23—82no—
1226C23—82no—
1227C23—162no—
1228C23—162no—
1229C23—162no—
1230C23—162no—
1231C23C2×H(5,𝔽2)12yes—
1232C23#58514yes—
1233C23C2611yescharacteristic
1234Q8—84no—
1235Q8—161no—
1236D4—416no—
1237D4—416no—
1238D4—84no—
1239D4—88no—
1240D4—88no—
1241D4—88no—
1242D4—84no—
1243D4—84no—
1244D4—88no—
1245D4—88no—
1246D4—88no—
1247D4—88no—
1248D4—88no—
1249D4—88no—
1250D4—88no—
1251D4—162no—
1252D4—162no—
1253D4—161no—
1254D4—162no—
1255D4—164no—
1256D4—164no—
1257C2×C4—28no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—44no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—88no—
1305C2×C4—84no—
1306C2×C4—84no—
1307C2×C4—82no—
1308C2×C4—82no—
1309C2×C4—88no—
1310C2×C4—88no—
1311C2×C4—164no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4—164no—
1315C2×C4—162no—
1316C2×C4—162no—
1317C2×C4C2×H(5,𝔽2)18yes—
1318C2×C4C2×H(5,𝔽2)14yes—
1319C2×C4C2×H(5,𝔽2)14yes—
1320C22—22no—
1321C22—24no—
1322C22—22no—
1323C22—22no—
1324C22—24no—
1325C22—24no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—44no—
1336C22—44no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—44no—
1343C22—42no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—88no—
1355C22—164no—
1356C22—164no—
1357C22C22×H(5,𝔽2)11yescharacteristic
1358C22C22×H(5,𝔽2)12yes—
1359C22C2×#58512yes—
1360C22H(7,𝔽2)11yescharacteristic
1361C222−1+611yescharacteristic
1362C4—24no—
1363C4—24no—
1364C4—28no—
1365C4—42no—
1366C4—42no—
1367C4—41no—
1368C4—41no—
1369C4—44no—
1370C4—44no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—44no—
1375C4—44no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C2—44no—
1380C2—42no—
1381C2—82no—
1382C2—84no—
1383C2—82no—
1384C2—82no—
1385C2#6282011yescharacteristic
1386C2#6283211yescharacteristic
1387C2#6287511yescharacteristic
1388C2#6289812yes—
1389C2#6289912yes—
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. #58387C2semidirect
2. #58296C2semidirect
3. #57732C2semidirect
4. #55926C2semidirect
5. #51890C2semidirect
6. #50784C2semidirect
7. #50661C2semidirect
8. #50166C2semidirect
9. #49348C2semidirect
10. #48795C2semidirect
11. #46481C2semidirect
12. #44250C2semidirect
13. #44206C2semidirect
14. #42580C2semidirect
15. #42271C2semidirect
16. #41386C2semidirect
17. #37768C2semidirect
18. #37760C2semidirect
19. #36706C2semidirect
20. #36052C2semidirect
21. #35995C2semidirect
22. #35565C2semidirect
23. #35351C2semidirect
25. C2×#553C22semidirect
26. C2×#539C22semidirect
27. C2×#539C22semidirect
36. #2841C22semidirect
37. #2827C22semidirect
38. #2826C22semidirect
39. #2826C22semidirect
40. #2820C22semidirect
41. #2815C22semidirect
42. #2815C22semidirect
43. #2807C22semidirect
44. #2797C22semidirect
45. #2796C22semidirect
46. #2780C22semidirect
47. #2771C22semidirect
48. #2768C22semidirect
49. #2752C22semidirect
50. #2740C22semidirect
51. #2732C22semidirect
52. #2724C22semidirect
53. #2723C22semidirect
54. #2721C22semidirect
55. #2720C22semidirect
56. #2715C22semidirect
57. #2714C22semidirect
58. #2714C22semidirect
59. #2714C22semidirect
60. #2711C22semidirect
61. #2708C22semidirect
62. #2708C22semidirect
63. #2706C22semidirect
64. #2706C22semidirect
65. #2706C22semidirect
66. #2705C22semidirect
67. #2703C22semidirect
68. #2703C22semidirect
70. #2701C22semidirect
71. #2699C22semidirect
74. #2693C22semidirect
75. #2693C22semidirect
77. #2691C22semidirect
78. #2690C22semidirect
79. #2689C22semidirect
81. #2688C22semidirect
82. #2688C22semidirect
91. #2673C22semidirect
92. #2673C22semidirect
93. #2673C22semidirect
94. #2673C22semidirect
95. #2673C22semidirect
96. #2672C22semidirect
98. #2671C22semidirect
100. #2664C22semidirect
101. #2661C22semidirect
102. #2659C22semidirect
103. #2656C22semidirect
104. #2654C22semidirect
105. #2651C22semidirect
106. #2644C22semidirect
107. #2636C22semidirect
108. #2636C22semidirect
110. #2635C22semidirect
111. #2627C22semidirect
114. #2623C22semidirect
115. #2618C22semidirect
116. #2618C22semidirect
118. #2611C22semidirect
119. #2603C22semidirect
120. #2603C22semidirect
121. #2603C22semidirect
122. #2585C22semidirect
125. #2575C22semidirect
126. #2566C22semidirect
127. #2554C22semidirect
128. #2554C22semidirect
133. #2540C22semidirect
137. #2535C22semidirect
140. #2526C22semidirect
141. #2519C22semidirect
142. #2516C22semidirect
143. #2512C22semidirect
144. #2508C22semidirect
145. #2501C22semidirect
150. #2479C22semidirect
152. #2474C22semidirect
153. #2471C22semidirect
154. #2468C22semidirect
155. #2464C22semidirect
156. #2464C22semidirect
157. #2463C22semidirect
158. #2461C22semidirect
159. #2461C22semidirect
160. #2456C22semidirect
161. #2456C22semidirect
162. #2456C22semidirect
163. #2456C22semidirect
164. #2455C22semidirect
165. #2454C22semidirect
166. #2454C22semidirect
167. #2454C22semidirect
168. #2449C22semidirect
169. #2449C22semidirect
170. #2449C22semidirect
171. #2445C22semidirect
172. #2445C22semidirect
173. #2445C22semidirect
174. #2445C22semidirect
179. #2443C22semidirect
182. #2428C22semidirect
183. #2425C22semidirect
186. #2419C22semidirect
197. #2402C22semidirect
198. #2397C22semidirect
201. #2377C22semidirect
202. #2373C22semidirect
203. #2371C22semidirect
204. #2366C22semidirect
205. #2361C22semidirect
206. #2361C22semidirect
208. D4×C4⋊C4C22semidirect
210. #2329C22semidirect
211. #2328C22semidirect
212. #2325C22semidirect
213. #2324C22semidirect

Maximal subgroups

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

subgroupindex
#583872
#582962
#577322
#559262
#518902
#507842
#506612
#501662
#493482
#487952
#464812
#442502
#442062
#425802
#422712
#413862
#377682
#377602
#367062
#360522
#359952
#355652
#353512