Finite Group Databasebeta

← #8141464

Subgroups — #8141464

Order 512.

5002 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#56769C214yesmaximal, complemented
2#56767C214yesmaximal, complemented
3#56267C214yesmaximal, complemented
4#55531C214yesmaximal, complemented
5#51974C214yesmaximal, complemented
6#51029C214yesmaximal, complemented
7#48983C214yesmaximal, complemented
8#48628C214yesmaximal, complemented
9#46088C212yesmaximal, complemented
10#45979C212yesmaximal, complemented
11#43020C214yesmaximal, complemented
12#40812C214yesmaximal, complemented
13#39548C212yesmaximal, complemented
14#39548C212yesmaximal, complemented
15#39486C212yesmaximal, complemented
16#37890C212yesmaximal, complemented
17#37673C212yesmaximal, complemented
18#37459C212yesmaximal, complemented
19#36749C212yesmaximal, complemented
20#36570C212yesmaximal, complemented
21#35003C211yesmaximal, characteristic, complemented
22#34994C211yesmaximal, characteristic, complemented
23C2×#2490C211yesmaximal, characteristic, complemented
24C2×#563C2212yescomplemented
25C2×#546C2214yes—
26C2×#538C2212yes—
27C2×#537C2212yes—
28C22×#125C2211yescharacteristic
29C22×#121C2211yescharacteristic
30#2857C2212yes—
31#2851C2212yes—
32#2851C2212yes—
33#2851C2212yes—
34#2850C2212yes—
35#2847C2212yes—
36#2837C2214yescomplemented
37#2837C2214yescomplemented
38#2829C2214yescomplemented
39#2828C2214yescomplemented
40#2827C2214yescomplemented
41#2822C2212yescomplemented
42#2820C2212yescomplemented
43#2808C2212yescomplemented
44#2798C2214yescomplemented
45#2796C2214yescomplemented
46#2796C2214yescomplemented
47#2790C2214yescomplemented
48#2790C2214yescomplemented
49#2788C2214yescomplemented
50#2786C2214yescomplemented
51#2781C2214yescomplemented
52#2768C2214yescomplemented
53#2761C2214yescomplemented
54#2753C2214yescomplemented
55#2753C2214yescomplemented
56#2750C2214yescomplemented
57#2747C2214yescomplemented
58#2744C2214yescomplemented
59#2742C2214yescomplemented
60#2740C2214yescomplemented
61#2732C2212yescomplemented
62#2729C2214yescomplemented
63#2728C2214yescomplemented
64#2725C2214yescomplemented
65#2724C2214yescomplemented
66#2724C2214yescomplemented
67#2721C2214yescomplemented
68#2720C2214yescomplemented
69#2720C2214yescomplemented
70#2718C2214yescomplemented
71#2715C2214yescomplemented
72#2714C2214yescomplemented
73#2714C2214yescomplemented
74#2713C2214yescomplemented
75#2711C2214yescomplemented
76#2711C2214yescomplemented
77#2711C2214yescomplemented
78#2708C2214yescomplemented
79#2707C2214yescomplemented
80#2706C2214yescomplemented
81#2706C2214yescomplemented
82#2701C2214yescomplemented
83#2701C2214yescomplemented
84#2693C2214yescomplemented
85#2691C2214yescomplemented
86#2691C2214yescomplemented
87#2690C2214yescomplemented
88#2686C2214yescomplemented
89#2682C2212yescomplemented
90#2682C2212yescomplemented
91#2682C2214yescomplemented
92#2682C2214yescomplemented
93#2677C2214yescomplemented
94#2676C2214yes—
95#2676C2214yescomplemented
96#2675C2214yes—
97#2672C2214yes—
98#2672C2214yescomplemented
99#2671C2214yes—
100#2671C2214yescomplemented
101#2661C2214yescomplemented
102#2659C2211yescharacteristic
103#2656C2212yes—
104#2656C2211yescharacteristic
105#2654C2214yescomplemented
106#2652C2214yescomplemented
107#2651C2214yescomplemented
108#2649C2214yescomplemented
109#2646C2212yes—
110#2646C2212yes—
111#2646C2212yescomplemented
112#2639C2214yescomplemented
113#2635C2214yescomplemented
114#2630C2214yescomplemented
115#2618C2212yes—
116#2618C2212yescomplemented
117#2617C2212yes—
118#2617C2212yes—
119#2617C2212yes—
120#2602C2214yescomplemented
121#2602C2214yescomplemented
122#2597C2214yescomplemented
123#2597C2214yescomplemented
124#2587C2214yescomplemented
125#2579C2214yes—
126#2574C2214yescomplemented
127#2569C2214yes—
128#2566C2212yescomplemented
129#2560C2214yescomplemented
130#2559C2214yescomplemented
131#2559C2214yescomplemented
132#2555C2214yescomplemented
133#2553C2214yescomplemented
134#2553C2214yescomplemented
135#2550C2212yescomplemented
136#2537C2214yescomplemented
137#2522C2214yescomplemented
138#2521C2214yescomplemented
139#2516C2214yescomplemented
140#2508C2212yescomplemented
141#2507C2212yescomplemented
142#2505C2214yescomplemented
143#2505C2214yescomplemented
144#2491C2214yescomplemented
145#2490C2214yes—
146#2490C2214yes—
147#2490C2214yes—
148#2490C2214yes—
149#2481C2214yes—
150#2481C2214yes—
151#2481C2214yescomplemented
152#2473C2214yescomplemented
153#2473C2214yescomplemented
154#2468C2214yescomplemented
155#2464C2214yescomplemented
156#2464C2214yescomplemented
157#2456C2214yescomplemented
158#2456C2214yescomplemented
159#2455C2214yescomplemented
160#2454C2212yescomplemented
161#2452C2212yescomplemented
162#2450C2214yes—
163#2449C2214yes—
164#2447C2214yescomplemented
165#2444C2214yes—
166#2443C2214yes—
167#2440C2214yes—
168#2437C2214yes—
169#2437C2214yes—
170#2432C2214yescomplemented
171#2432C2214yescomplemented
172#2430C2214yes—
173#2430C2214yescomplemented
174#2425C2214yescomplemented
175#2424C2214yes—
176#2424C2214yes—
177#2422C2214yescomplemented
178#2419C2214yescomplemented
179#2419C2214yescomplemented
180#2418C2214yes—
181#2418C2214yes—
182#2417C2214yes—
183#2416C2214yes—
184#2412C2214yes—
185#2412C2214yes—
186#2410C2214yes—
187#2410C2214yes—
188#2407C2214yescomplemented
189C2×#397C2212yes—
190C2×#394C2212yes—
191#2382C2212yescomplemented
192#2377C2214yescomplemented
193#2370C2212yescomplemented
194#2368C2214yescomplemented
195#2358C2214yes—
196#2358C2214yes—
197#2349C2214yes—
198#2349C2212yescomplemented
199#2325C2212yes—
200#2325C2212yes—
201#2325C2212yescomplemented
202#2315C2212yes—
203#2315C2211yescharacteristic
204#2315C2212yes—
205#2315C2211yescharacteristic
206#2313C2212yescomplemented
207#2312C2212yes—
208C4×#121C2212yes—
209C4×#121C2212yes—
210C4×#121C2212yes—
211C2×#390C2211yescharacteristic
212C2×#390C2212yes—
213C2×#390C2211yescharacteristic
214C2×#388C2212yes—
215C2×#385C2212yes—
216C2×#380C2211yescharacteristic
217C2×C4×C4⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2211yescharacteristic
219C22×#41C2314yes—
220C23×D4C2312yes—
221C23×D4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223#563—48no—
224#546—416no—
225#538—48no—
226#537—48no—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2312yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#125—44no—
233C2×#125C2312yes—
234C2×#125C2312yes—
235C2×#125C2312yes—
236C2×#125C2312yes—
237C2×#125C2314yes—
238C2×#125C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×#121—44no—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277C2×#120C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2314yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2312yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2312yes—
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2312yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#394C2314yes—
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#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2312yes—
423#391C2314yes—
424#390C2314yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2312yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#388C2314yes—
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#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#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
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#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
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#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
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#384C2312yes—
567#384C2314yes—
568#382C2312yes—
569#382C2312yes—
570#382C2312yes—
571#382C2314yes—
572#382C2312yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#380C2312yes—
577#380C2312yes—
578#380C2312yes—
579#380C2312yes—
580#380C2312yes—
581#380C2314yes—
582#380C2314yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2312yes—
590#380C2314yes—
591#380C2312yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#379C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C2×#95C2312yes—
614C2×#95C2311yescharacteristic
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2314yes—
619C2×#95C2311yescharacteristic
620C25C2412yes—
621C25C2411yescharacteristic
622C2×#41—48no—
623C2×#41—48no—
624C2×#41—84no—
625C22×Q8C2414yes—
626C22×Q8C2412yes—
627C22×D4—28no—
628C22×D4—42no—
629C22×D4—44no—
630C22×D4—42no—
631C22×D4—42no—
632C22×D4—82no—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C22×D4C2412yes—
646C22×D4C2412yes—
647C23×C4—42no—
648C23×C4—42no—
649C23×C4—42no—
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2411yescharacteristic
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C23×C4C2411yescharacteristic
657C23×C4C2411yescharacteristic
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2414yes—
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2412yes—
666C23×C4C2414yes—
667C23×C4C2414yes—
668C23×C4C2414yes—
669C23×C4C2411yescharacteristic
670C4⋊Q8—48no—
671C4⋊Q8—82no—
672#126—48no—
673#126—48no—
674#126—48no—
675#125—28no—
676#125—44no—
677#125—44no—
678#125—44no—
679#125—48no—
680#125—82no—
681#124—44no—
682#124—48no—
683#124—48no—
684#123—48no—
685#123—48no—
686#123—48no—
687#123—48no—
688#123—84no—
689#123—84no—
690#123—84no—
691#123—84no—
692C22⋊Q8—216no—
693C22⋊Q8—44no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697C22⋊Q8—84no—
698#121—28no—
699#121—28no—
700#121—44no—
701#121—48no—
702#121—44no—
703#121—48no—
704#121—48no—
705#121—48no—
706#121—48no—
707#121—48no—
708#121—48no—
709#121—48no—
710#121—44no—
711#121—44no—
712#121—44no—
713#121—48no—
714#121—84no—
715#121—84no—
716#120—216no—
717#120—48no—
718#120—48no—
719C4×D4—44no—
720C4×D4—48no—
721C4×D4—48no—
722C4×D4—48no—
723C4×D4—48no—
724C4×D4—82no—
725C4×D4—82no—
726C4×D4—84no—
727C4×D4—84no—
728C2×C4⋊C4—24no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—44no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4—42no—
733C2×C4⋊C4—44no—
734C2×C4⋊C4—42no—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C22⋊C4—24no—
787C2×C22⋊C4—28no—
788C2×C22⋊C4—24no—
789C2×C22⋊C4—28no—
790C2×C22⋊C4—44no—
791C2×C22⋊C4—44no—
792C2×C22⋊C4—48no—
793C2×C22⋊C4—82no—
794C2×C22⋊C4—82no—
795C2×C22⋊C4—82no—
796C2×C22⋊C4—82no—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
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×C42—42no—
847C2×C42—42no—
848C2×C42—82no—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862#95C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906C24—22no—
907C24—22no—
908C24—24no—
909C24—24no—
910C24—24no—
911C24—41no—
912C24—41no—
913C24—41no—
914C24—41no—
915C24—42no—
916C24—42no—
917C24—42no—
918C24—42no—
919C24H(5,𝔽2)14yes—
920C24C2514yes—
921C24C2514yes—
922C24C2512yes—
923C24C2511yescharacteristic
924#41—832no—
925C2×Q8—28no—
926C2×Q8—44no—
927C2×Q8—44no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—24no—
940C2×D4—24no—
941C2×D4—24no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—42no—
970C2×D4—42no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—88no—
974C2×D4—816no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—22no—
981C22×C4—24no—
982C22×C4—22no—
983C22×C4—24no—
984C22×C4—22no—
985C22×C4—24no—
986C22×C4—22no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—28no—
990C22×C4—24no—
991C22×C4—41no—
992C22×C4—41no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—42no—
1000C22×C4—41no—
1001C22×C4—44no—
1002C22×C4—42no—
1003C22×C4—41no—
1004C22×C4—42no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—41no—
1019C22×C4—44no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—42no—
1034C22×C4—88no—
1035C22×C42−1+414yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C4⋊C4—24no—
1056C4⋊C4—22no—
1057C4⋊C4—28no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—41no—
1065C4⋊C4—42no—
1066C4⋊C4—41no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4H(5,𝔽2)14yes—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
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—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—44no—
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—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—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—
1155C42—24no—
1156C42—24no—
1157C42—42no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42—42no—
1162C42—42no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—28no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—24no—
1191C23—24no—
1192C23—24no—
1193C23—44no—
1194C23—44no—
1195C23—48no—
1196C23—82no—
1197C23—82no—
1198C23—82no—
1199C23—82no—
1200C23—84no—
1201C23—84no—
1202C23—84no—
1203C23—84no—
1204C23—84no—
1205C23—84no—
1206C23C2×H(5,𝔽2)14yes—
1207C23C2×H(5,𝔽2)12yes—
1208C23C2×2−1+412yes—
1209C23#58512yes—
1210C23C2611yescharacteristic
1211Q8—88no—
1212Q8—162no—
1213D4—416no—
1214D4—48no—
1215D4—416no—
1216D4—84no—
1217D4—84no—
1218D4—88no—
1219D4—88no—
1220D4—88no—
1221D4—88no—
1222D4—88no—
1223D4—162no—
1224D4—164no—
1225D4—162no—
1226D4—164no—
1227C2×C4—28no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
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—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—44no—
1282C2×C4—48no—
1283C2×C4—48no—
1284C2×C4—84no—
1285C2×C4—84no—
1286C2×C4—88no—
1287C2×C4—84no—
1288C2×C4—82no—
1289C2×C4—82no—
1290C2×C4—84no—
1291C2×C4—82no—
1292C2×C4—84no—
1293C2×C4—82no—
1294C2×C4—88no—
1295C2×C4—162no—
1296C2×C4—164no—
1297C2×C4—162no—
1298C2×C4—164no—
1299C2×C4—164no—
1300C2×C4C2×H(5,𝔽2)12yes—
1301C2×C4C2×H(5,𝔽2)14yes—
1302C2×C4C2×2−1+414yes—
1303C2×C4#58512yes—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—24no—
1311C22—24no—
1312C22—24no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22—44no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—88no—
1332C22—168no—
1333C22#355914yes—
1334C22C22×H(5,𝔽2)11yescharacteristic
1335C22C22×H(5,𝔽2)11yescharacteristic
1336C22C22×2−1+411yescharacteristic
1337C22C2×#58511yescharacteristic
1338C22C2×#58511yescharacteristic
1339C22H(7,𝔽2)11yescharacteristic
1340C22H(7,𝔽2)11yescharacteristic
1341C4—22no—
1342C4—22no—
1343C4—24no—
1344C4—24no—
1345C4—44no—
1346C4—42no—
1347C4—44no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—44no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4—42no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—44no—
1360C2—24no—
1361C2—44no—
1362C2—84no—
1363C2—84no—
1364C2C2×#355911yescharacteristic
1365C2#6282411yescharacteristic
1366C2#6287011yescharacteristic
1367C2#6289211yescharacteristic
1368C2#6290211yescharacteristic
1369C2#6290511yescharacteristic
1370C2#6291711yescharacteristic
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. #56769C2semidirect
2. #56767C2semidirect
3. #56267C2semidirect
4. #55531C2semidirect
5. #51974C2semidirect
6. #51029C2semidirect
7. #48983C2semidirect
8. #48628C2semidirect
9. #46088C2semidirect
10. #45979C2semidirect
11. #43020C2semidirect
12. #40812C2semidirect
13. #39548C2semidirect
14. #39548C2semidirect
15. #39486C2semidirect
16. #37890C2semidirect
17. #37673C2semidirect
18. #37459C2semidirect
19. #36749C2semidirect
20. #36570C2semidirect
21. #35003C2semidirect
22. #34994C2semidirect
23. C2×#2490C2semidirect
24. C2×#563C22semidirect
36. #2837C22semidirect
37. #2837C22semidirect
38. #2829C22semidirect
39. #2828C22semidirect
40. #2827C22semidirect
41. #2822C22semidirect
42. #2820C22semidirect
43. #2808C22semidirect
44. #2798C22semidirect
45. #2796C22semidirect
46. #2796C22semidirect
47. #2790C22semidirect
48. #2790C22semidirect
49. #2788C22semidirect
50. #2786C22semidirect
51. #2781C22semidirect
52. #2768C22semidirect
53. #2761C22semidirect
54. #2753C22semidirect
55. #2753C22semidirect
56. #2750C22semidirect
57. #2747C22semidirect
58. #2744C22semidirect
59. #2742C22semidirect
60. #2740C22semidirect
61. #2732C22semidirect
62. #2729C22semidirect
63. #2728C22semidirect
64. #2725C22semidirect
65. #2724C22semidirect
66. #2724C22semidirect
67. #2721C22semidirect
68. #2720C22semidirect
69. #2720C22semidirect
70. #2718C22semidirect
71. #2715C22semidirect
72. #2714C22semidirect
73. #2714C22semidirect
74. #2713C22semidirect
75. #2711C22semidirect
76. #2711C22semidirect
77. #2711C22semidirect
78. #2708C22semidirect
79. #2707C22semidirect
80. #2706C22semidirect
81. #2706C22semidirect
82. #2701C22semidirect
83. #2701C22semidirect
84. #2693C22semidirect
85. #2691C22semidirect
86. #2691C22semidirect
87. #2690C22semidirect
88. #2686C22semidirect
89. #2682C22semidirect
90. #2682C22semidirect
91. #2682C22semidirect
92. #2682C22semidirect
93. #2677C22semidirect
95. #2676C22semidirect
98. #2672C22semidirect
100. #2671C22semidirect
101. #2661C22semidirect
105. #2654C22semidirect
106. #2652C22semidirect
107. #2651C22semidirect
108. #2649C22semidirect
111. #2646C22semidirect
112. #2639C22semidirect
113. #2635C22semidirect
114. #2630C22semidirect
116. #2618C22semidirect
120. #2602C22semidirect
121. #2602C22semidirect
122. #2597C22semidirect
123. #2597C22semidirect
124. #2587C22semidirect
126. #2574C22semidirect
128. #2566C22semidirect
129. #2560C22semidirect
130. #2559C22semidirect
131. #2559C22semidirect
132. #2555C22semidirect
133. #2553C22semidirect
134. #2553C22semidirect
135. #2550C22semidirect
136. #2537C22semidirect
137. #2522C22semidirect
138. #2521C22semidirect
139. #2516C22semidirect
140. #2508C22semidirect
141. #2507C22semidirect
142. #2505C22semidirect
143. #2505C22semidirect
144. #2491C22semidirect
151. #2481C22semidirect
152. #2473C22semidirect
153. #2473C22semidirect
154. #2468C22semidirect
155. #2464C22semidirect
156. #2464C22semidirect
157. #2456C22semidirect
158. #2456C22semidirect
159. #2455C22semidirect
160. #2454C22semidirect
161. #2452C22semidirect
164. #2447C22semidirect
170. #2432C22semidirect
171. #2432C22semidirect
173. #2430C22semidirect
174. #2425C22semidirect
177. #2422C22semidirect
178. #2419C22semidirect
179. #2419C22semidirect
188. #2407C22semidirect
191. #2382C22semidirect
192. #2377C22semidirect
193. #2370C22semidirect
194. #2368C22semidirect
198. #2349C22semidirect
201. #2325C22semidirect
206. #2313C22semidirect

Maximal subgroups

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

subgroupindex
#567692
#567672
#562672
#555312
#519742
#510292
#489832
#486282
#460882
#459792
#430202
#408122
#395482
#394862
#378902
#376732
#374592
#367492
#365702
#350032
#349942
C2×#24902