Finite Group Databasebeta

← #8119664

Subgroups — #8119664

Order 512.

4705 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58261C212yesmaximal, complemented
2#56164C212yesmaximal, complemented
3#56127C214yesmaximal, complemented
4#55616C212yesmaximal, complemented
5#53963C214yesmaximal, complemented
6#53491C212yesmaximal, complemented
7#52741C212yesmaximal, complemented
8#52414C212yesmaximal, complemented
9#47814C212yesmaximal, complemented
10#47241C214yesmaximal, complemented
11#46974C212yesmaximal, complemented
12#46898C214yesmaximal, complemented
13#46849C212yesmaximal, complemented
14#46548C212yesmaximal, complemented
15#43643C212yesmaximal, complemented
16#43621C212yesmaximal, complemented
17#38502C214yesmaximal, complemented
18#37941C212yesmaximal, complemented
19#37935C212yesmaximal, complemented
20#37909C214yesmaximal, complemented
21#37702C212yesmaximal, complemented
22#37698C212yesmaximal, complemented
23#36719C212yesmaximal, complemented
24#35237C211yesmaximal, characteristic
25#35084C211yesmaximal, characteristic, complemented
26#34997C212yesmaximal, complemented
27C2×#2564C211yesmaximal, characteristic, complemented
28C2×#539C2212yes—
29C2×#532C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33#2855C2212yes—
34#2849C2214yes—
35#2848C2212yes—
36#2847C2212yes—
37#2847C2212yes—
38#2844C2212yescomplemented
39#2841C2212yescomplemented
40#2838C2214yescomplemented
41#2838C2214yescomplemented
42#2831C2214yescomplemented
43#2830C2212yescomplemented
44#2829C2214yescomplemented
45#2827C2214yescomplemented
46#2826C2212yescomplemented
47#2817C2214yescomplemented
48#2796C2214yescomplemented
49#2789C2212yescomplemented
50#2788C2214yescomplemented
51#2784C2214yescomplemented
52#2784C2212yescomplemented
53#2783C2214yescomplemented
54#2780C2214yes—
55#2780C2214yescomplemented
56#2780C2214yescomplemented
57#2779C2214yescomplemented
58#2778C2214yescomplemented
59#2775C2214yescomplemented
60#2774C2214yescomplemented
61#2769C2214yescomplemented
62#2769C2212yescomplemented
63#2767C2214yescomplemented
64#2766C2214yescomplemented
65#2763C2212yescomplemented
66#2761C2214yes—
67#2760C2212yescomplemented
68#2759C2214yescomplemented
69#2758C2214yescomplemented
70#2753C2214yes—
71#2752C2212yescomplemented
72#2750C2214yescomplemented
73#2749C2214yes—
74#2749C2214yes—
75#2746C2214yescomplemented
76#2745C2214yescomplemented
77#2744C2214yescomplemented
78#2743C2214yescomplemented
79#2742C2212yescomplemented
80#2739C2214yescomplemented
81#2737C2214yescomplemented
82#2728C2214yescomplemented
83#2723C2214yescomplemented
84#2723C2214yescomplemented
85#2715C2214yescomplemented
86#2713C2214yescomplemented
87#2709C2214yes—
88#2709C2214yes—
89#2709C2214yescomplemented
90#2706C2214yes—
91#2704C2214yescomplemented
92#2704C2214yescomplemented
93#2702C2214yescomplemented
94#2702C2214yescomplemented
95#2701C2214yescomplemented
96#2700C2214yescomplemented
97#2696C2214yescomplemented
98#2696C2214yescomplemented
99#2695C2214yescomplemented
100#2690C2214yescomplemented
101#2689C2214yescomplemented
102#2683C2214yescomplemented
103#2683C2214yescomplemented
104#2683C2212yescomplemented
105#2681C2214yescomplemented
106#2681C2214yescomplemented
107#2681C2214yescomplemented
108#2665C2214yescomplemented
109#2648C2214yes—
110#2646C2212yes—
111#2643C2214yes—
112#2639C2212yes—
113#2638C2212yes—
114#2638C2212yes—
115#2631C2212yes—
116#2631C2212yes—
117#2630C2214yes—
118#2630C2214yescomplemented
119#2627C2212yes—
120#2618C2212yes—
121#2612C2214yescomplemented
122#2612C2212yescomplemented
123#2607C2212yescomplemented
124#2601C2214yescomplemented
125#2593C2212yescomplemented
126#2585C2214yescomplemented
127#2583C2212yes—
128#2578C2214yescomplemented
129#2574C2214yescomplemented
130#2572C2214yescomplemented
131#2564C2212yes—
132#2564C2212yes—
133#2564C2212yes—
134#2564C2212yes—
135#2564C2212yes—
136#2564C2212yes—
137#2564C2212yes—
138#2564C2212yes—
139#2564C2214yescomplemented
140#2563C2211yescharacteristic
141#2563C2211yescharacteristic
142#2561C2212yes—
143#2559C2214yescomplemented
144#2541C2211yescharacteristic
145#2541C2211yescharacteristic
146#2535C2212yes—
147#2535C2212yes—
148#2534C2214yes—
149#2533C2214yescomplemented
150#2528C2214yescomplemented
151#2526C2214yes—
152#2526C2214yescomplemented
153#2522C2214yescomplemented
154#2510C2214yescomplemented
155#2508C2214yescomplemented
156#2505C2214yes—
157#2505C2214yescomplemented
158#2504C2212yes—
159#2495C2214yescomplemented
160#2493C2214yes—
161#2493C2214yescomplemented
162#2488C2214yes—
163#2488C2214yescomplemented
164#2488C2214yescomplemented
165#2486C2211yescharacteristic
166#2486C2211yescharacteristic
167#2484C2214yes—
168#2483C2212yes—
169#2481C2214yes—
170#2481C2214yescomplemented
171#2470C2214yescomplemented
172#2467C2214yescomplemented
173#2466C2214yescomplemented
174#2463C2212yescomplemented
175#2460C2214yescomplemented
176#2457C2214yes—
177#2457C2214yes—
178#2450C2214yescomplemented
179#2450C2214yescomplemented
180#2450C2214yescomplemented
181#2449C2214yes—
182#2445C2214yes—
183#2444C2214yes—
184#2444C2214yescomplemented
185#2443C2214yescomplemented
186#2442C2214yescomplemented
187#2433C2212yes—
188#2425C2214yes—
189#2425C2214yescomplemented
190#2419C2214yescomplemented
191#2419C2214yescomplemented
192#2418C2214yes—
193#2415C2212yes—
194#2415C2212yes—
195#2413C2214yes—
196#2412C2214yes—
197#2411C2214yes—
198#2411C2214yes—
199#2409C2211yescharacteristic
200#2409C2211yescharacteristic
201#2409C2214yes—
202#2409C2214yescomplemented
203#2406C2214yes—
204#2405C2212yes—
205#2404C2212yes—
206#2404C2212yes—
207C2×#400C2211yescharacteristic
208C2×#399C2211yescharacteristic
209C2×#395C2211yescharacteristic
210C2×#393C2211yescharacteristic
211#2359C2214yes—
212#2358C2214yes—
213#2343C2214yes—
214#2339C2214yes—
215#2335C2214yes—
216#2335C2214yescomplemented
217#2329C2212yes—
218#2328C2214yes—
219#2328C2212yes—
220#2328C2212yes—
221#2325C2212yes—
222#2322C2212yes—
223#2322C2212yes—
224#2318C2214yes—
225#2318C2214yescomplemented
226#2316C2212yes—
227C4×#120C2214yes—
228C2×#387C2212yes—
229C2×#386C2212yes—
230C2×#385C2212yes—
231#2283C2211yescharacteristic
232#2280C2211yescharacteristic
233C2×#380C2212yes—
234C22×#95C2211yescharacteristic
235C22×#41C2312yes—
236C23×Q8C2311yescharacteristic
237C23×Q8C2311yescharacteristic
238C23×D4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240C24×C4C2311yescharacteristic
241C24×C4C2312yes—
242#539—48no—
243#532—44no—
244C2×C4⋊Q8C2311yescharacteristic
245C2×#127C2312yes—
246C2×#127C2312yes—
247C2×#127C2311yescharacteristic
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125C2314yes—
251C2×#124C2312yes—
252C2×#123C2312yes—
253C2×#123C2312yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×C22⋊Q8—44no—
261C2×C22⋊Q8—44no—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284C2×C4×D4—44no—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×#117C2314yes—
301C2×#117C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2312yes—
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2312yes—
315C22×C42C2311yescharacteristic
316#401C2314yes—
317#401C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2312yes—
325#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#399C2312yes—
343#399C2312yes—
344#399C2312yes—
345#399C2312yes—
346#399C2314yes—
347#399C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#397C2312yes—
363#397C2312yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
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#396C2314yes—
394#395C2312yes—
395#395C2312yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2312yes—
400#395C2312yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2312yes—
405#395C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#393C2312yes—
425#393C2312yes—
426#393C2312yes—
427#393C2312yes—
428#393C2312yes—
429#393C2312yes—
430#393C2312yes—
431#393C2312yes—
432#393C2312yes—
433#393C2312yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#392C2312yes—
439#392C2312yes—
440#392C2314yes—
441#392C2312yes—
442#392C2312yes—
443#392C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#390C2312yes—
453#390C2312yes—
454#390C2314yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2312yes—
459#390C2314yes—
460#390C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
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#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
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#386C2312yes—
544#386C2312yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2312yes—
571#385C2314yes—
572#385C2312yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#383C2314yes—
593#383C2314yes—
594#383C2314yes—
595#383C2312yes—
596#382C2312yes—
597#382C2312yes—
598#382C2314yes—
599#382C2314yes—
600#382C2314yes—
601#382C2314yes—
602#382C2312yes—
603#381C2314yes—
604#381C2314yes—
605#381C2312yes—
606#381C2314yes—
607#381C2314yes—
608#381C2314yes—
609#381C2312yes—
610#381C2314yes—
611#381C2314yes—
612#381C2312yes—
613#381C2312yes—
614#380C2312yes—
615#380C2312yes—
616#380C2312yes—
617#380C2312yes—
618#380C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2312yes—
625#380C2312yes—
626#380C2314yes—
627#380C2314yes—
628#380C2312yes—
629#380C2312yes—
630#380C2314yes—
631#380C2311yescharacteristic
632#380C2311yescharacteristic
633#380C2314yes—
634#379C2314yes—
635#379C2312yes—
636C4×C4⋊C4C2311yescharacteristic
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649#376C2312yes—
650#376C2314yes—
651C2×#95C2312yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2314yes—
656C2×#95C2311yescharacteristic
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2312yes—
661C2×#95C2311yescharacteristic
662C2×#95C2312yes—
663C25C2411yescharacteristic
664C25C2411yescharacteristic
665C2×#41—44no—
666C2×#41—48no—
667C22×Q8—42no—
668C22×Q8—42no—
669C22×Q8—82no—
670C22×Q8—82no—
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×D4—24no—
677C22×D4—42no—
678C22×D4—42no—
679C22×D4C2414yes—
680C22×D4C2411yescharacteristic
681C22×D4C2411yescharacteristic
682C22×D4C2411yescharacteristic
683C22×D4C2414yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C22×D4C2412yes—
687C22×D4C2412yes—
688C22×D4C2414yes—
689C22×D4C2412yes—
690C22×D4C2411yescharacteristic
691C23×C4—24no—
692C23×C4—24no—
693C23×C4—44no—
694C23×C4—44no—
695C23×C4—82no—
696C23×C4—82no—
697C23×C4—82no—
698C23×C4C2412yes—
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2411yescharacteristic
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C23×C4C2411yescharacteristic
709C23×C4C2411yescharacteristic
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C23×C4C2411yescharacteristic
713C23×C4C2411yescharacteristic
714C23×C4C2411yescharacteristic
715C23×C4C2414yes—
716C23×C4C2412yes—
717C23×C4C2414yes—
718C23×C4C2414yes—
719C23×C4C2414yes—
720C23×C4C2414yes—
721C23×C4C2411yescharacteristic
722C4⋊Q8—42no—
723#127—28no—
724#127—42no—
725#127—44no—
726#126—48no—
727#126—84no—
728#125—48no—
729#124—44no—
730#123—28no—
731#123—44no—
732#123—48no—
733#123—48no—
734#123—48no—
735#123—48no—
736#123—84no—
737#123—84no—
738C22⋊Q8—28no—
739C22⋊Q8—44no—
740C22⋊Q8—48no—
741C22⋊Q8—44no—
742C22⋊Q8—44no—
743C22⋊Q8—44no—
744C22⋊Q8—44no—
745C22⋊Q8—44no—
746C22⋊Q8—44no—
747C22⋊Q8—82no—
748C22⋊Q8—84no—
749C22⋊Q8—84no—
750C22⋊Q8—84no—
751C22⋊Q8—82no—
752#121—28no—
753#121—44no—
754#121—82no—
755#121—82no—
756#121—82no—
757#121—82no—
758#120—48no—
759#120—48no—
760C4×D4—44no—
761C4×D4—44no—
762C4×D4—42no—
763C4×D4—42no—
764C4×D4—42no—
765C4×D4—42no—
766C4×D4—42no—
767C4×D4—42no—
768C4×D4—42no—
769C4×D4—42no—
770C4×D4—48no—
771C4×D4—48no—
772C4×D4—48no—
773C4×D4—84no—
774C4×D4—84no—
775#117—48no—
776#117—82no—
777C2×C4⋊C4—28no—
778C2×C4⋊C4—44no—
779C2×C4⋊C4—42no—
780C2×C4⋊C4—44no—
781C2×C4⋊C4—42no—
782C2×C4⋊C4—42no—
783C2×C4⋊C4—82no—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C22⋊C4—44no—
829C2×C22⋊C4—44no—
830C2×C22⋊C4—42no—
831C2×C22⋊C4—42no—
832C2×C22⋊C4—44no—
833C2×C22⋊C4—82no—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2411yescharacteristic
843C2×C22⋊C4C2411yescharacteristic
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2411yescharacteristic
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C42—24no—
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955C24—22no—
956C24—22no—
957C24—22no—
958C24—22no—
959C24—24no—
960C24—22no—
961C24—24no—
962C24—42no—
963C24—42no—
964C24—41no—
965C24C2511yescharacteristic
966C24C2514yes—
967C24C2511yescharacteristic
968C24C2511yescharacteristic
969C24C2511yescharacteristic
970C24C2511yescharacteristic
971#41—816no—
972C2×Q8—24no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—42no—
976C2×Q8—42no—
977C2×Q8—42no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×Q8—44no—
981C2×Q8—42no—
982C2×Q8—44no—
983C2×Q8—88no—
984C2×Q8—88no—
985C2×D4—28no—
986C2×D4—22no—
987C2×D4—22no—
988C2×D4—28no—
989C2×D4—28no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—28no—
993C2×D4—28no—
994C2×D4—28no—
995C2×D4—24no—
996C2×D4—22no—
997C2×D4—24no—
998C2×D4—41no—
999C2×D4—41no—
1000C2×D4—41no—
1001C2×D4—41no—
1002C2×D4—41no—
1003C2×D4—41no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—42no—
1011C2×D4—42no—
1012C2×D4—44no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—416no—
1020C2×D42−1+414yes—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—24no—
1024C22×C4—22no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—22no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—28no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—41no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—42no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—88no—
1080C22×C4—88no—
1081C22×C4—816no—
1082C22×C4H(5,𝔽2)14yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2514yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—41no—
1113C4⋊C4—41no—
1114C4⋊C4—41no—
1115C4⋊C4—41no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—41no—
1158C22⋊C4—41no—
1159C22⋊C4—41no—
1160C22⋊C4—41no—
1161C22⋊C4—41no—
1162C22⋊C4—41no—
1163C22⋊C4—41no—
1164C22⋊C4—41no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C42—22no—
1198C42—22no—
1199C42—22no—
1200C42—22no—
1201C42—24no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—44no—
1209C42—42no—
1210C23—21no—
1211C23—21no—
1212C23—22no—
1213C23—28no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—22no—
1219C23—21no—
1220C23—22no—
1221C23—22no—
1222C23—21no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—24no—
1227C23—21no—
1228C23—24no—
1229C23—21no—
1230C23—22no—
1231C23—24no—
1232C23—24no—
1233C23—24no—
1234C23—21no—
1235C23—24no—
1236C23—24no—
1237C23—22no—
1238C23—48no—
1239C23—48no—
1240C23—44no—
1241C23—48no—
1242C23—44no—
1243C23—44no—
1244C23—44no—
1245C23—82no—
1246C23—84no—
1247C23C2×H(5,𝔽2)12yes—
1248C23C2×2−1+412yes—
1249C23C2×2−1+412yes—
1250C23#58512yes—
1251C23#58514yes—
1252C23C2611yescharacteristic
1253Q8—84no—
1254Q8—84no—
1255Q8—84no—
1256Q8—84no—
1257Q8—84no—
1258D4—44no—
1259D4—44no—
1260D4—44no—
1261D4—44no—
1262D4—416no—
1263D4—84no—
1264D4—84no—
1265D4—88no—
1266D4—88no—
1267D4—88no—
1268D4—84no—
1269D4—164no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—21no—
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—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—21no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—44no—
1323C2×C4—44no—
1324C2×C4—44no—
1325C2×C4—44no—
1326C2×C4—48no—
1327C2×C4—44no—
1328C2×C4—48no—
1329C2×C4—44no—
1330C2×C4—82no—
1331C2×C4—82no—
1332C2×C4—82no—
1333C2×C4—82no—
1334C2×C4—82no—
1335C2×C4—82no—
1336C2×C4—84no—
1337C2×C4—82no—
1338C2×C4—88no—
1339C2×C4—84no—
1340C2×C4—84no—
1341C2×C4—88no—
1342C2×C4—84no—
1343C2×C4—88no—
1344C2×C4—164no—
1345C2×C4—164no—
1346C2×C4C2×H(5,𝔽2)12yes—
1347C2×C4C2×H(5,𝔽2)12yes—
1348C2×C4C2×2−1+412yes—
1349C22—22no—
1350C22—22no—
1351C22—24no—
1352C22—24no—
1353C22—22no—
1354C22—22no—
1355C22—22no—
1356C22—24no—
1357C22—24no—
1358C22—24no—
1359C22—416no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—44no—
1370C22—41no—
1371C22—41no—
1372C22—44no—
1373C22—41no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—42no—
1378C22—44no—
1379C22—44no—
1380C22—42no—
1381C22—88no—
1382C22#355114yes—
1383C22C22×H(5,𝔽2)11yescharacteristic
1384C22C22×2−1+411yescharacteristic
1385C22C2×#58512yes—
1386C22C2×#58511yescharacteristic
1387C22H(7,𝔽2)12yes—
1388C4—22no—
1389C4—22no—
1390C4—22no—
1391C4—44no—
1392C4—41no—
1393C4—41no—
1394C4—44no—
1395C4—41no—
1396C4—44no—
1397C4—41no—
1398C4—41no—
1399C4—41no—
1400C4—41no—
1401C4—44no—
1402C4—44no—
1403C4—44no—
1404C4—44no—
1405C4—44no—
1406C4—44no—
1407C4—44no—
1408C4—44no—
1409C2—24no—
1410C2—42no—
1411C2—42no—
1412C2—42no—
1413C2—84no—
1414C2—81no—
1415C2C2×#355111yescharacteristic
1416C2#6281911yescharacteristic
1417C2#6286211yescharacteristic
1418C2#6290612yes—
1419C2#6294812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35237C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #58261C2semidirect
2. #56164C2semidirect
3. #56127C2semidirect
4. #55616C2semidirect
5. #53963C2semidirect
6. #53491C2semidirect
7. #52741C2semidirect
8. #52414C2semidirect
9. #47814C2semidirect
10. #47241C2semidirect
11. #46974C2semidirect
12. #46898C2semidirect
13. #46849C2semidirect
14. #46548C2semidirect
15. #43643C2semidirect
16. #43621C2semidirect
17. #38502C2semidirect
18. #37941C2semidirect
19. #37935C2semidirect
20. #37909C2semidirect
21. #37702C2semidirect
22. #37698C2semidirect
23. #36719C2semidirect
25. #35084C2semidirect
26. #34997C2semidirect
27. C2×#2564C2semidirect
38. #2844C22semidirect
39. #2841C22semidirect
40. #2838C22semidirect
41. #2838C22semidirect
42. #2831C22semidirect
43. #2830C22semidirect
44. #2829C22semidirect
45. #2827C22semidirect
46. #2826C22semidirect
47. #2817C22semidirect
48. #2796C22semidirect
49. #2789C22semidirect
50. #2788C22semidirect
51. #2784C22semidirect
52. #2784C22semidirect
53. #2783C22semidirect
55. #2780C22semidirect
56. #2780C22semidirect
57. #2779C22semidirect
58. #2778C22semidirect
59. #2775C22semidirect
60. #2774C22semidirect
61. #2769C22semidirect
62. #2769C22semidirect
63. #2767C22semidirect
64. #2766C22semidirect
65. #2763C22semidirect
67. #2760C22semidirect
68. #2759C22semidirect
69. #2758C22semidirect
71. #2752C22semidirect
72. #2750C22semidirect
75. #2746C22semidirect
76. #2745C22semidirect
77. #2744C22semidirect
78. #2743C22semidirect
79. #2742C22semidirect
80. #2739C22semidirect
81. #2737C22semidirect
82. #2728C22semidirect
83. #2723C22semidirect
84. #2723C22semidirect
85. #2715C22semidirect
86. #2713C22semidirect
89. #2709C22semidirect
91. #2704C22semidirect
92. #2704C22semidirect
93. #2702C22semidirect
94. #2702C22semidirect
95. #2701C22semidirect
96. #2700C22semidirect
97. #2696C22semidirect
98. #2696C22semidirect
99. #2695C22semidirect
100. #2690C22semidirect
101. #2689C22semidirect
102. #2683C22semidirect
103. #2683C22semidirect
104. #2683C22semidirect
105. #2681C22semidirect
106. #2681C22semidirect
107. #2681C22semidirect
108. #2665C22semidirect
118. #2630C22semidirect
121. #2612C22semidirect
122. #2612C22semidirect
123. #2607C22semidirect
124. #2601C22semidirect
125. #2593C22semidirect
126. #2585C22semidirect
128. #2578C22semidirect
129. #2574C22semidirect
130. #2572C22semidirect
139. #2564C22semidirect
143. #2559C22semidirect
149. #2533C22semidirect
150. #2528C22semidirect
152. #2526C22semidirect
153. #2522C22semidirect
154. #2510C22semidirect
155. #2508C22semidirect
157. #2505C22semidirect
159. #2495C22semidirect
161. #2493C22semidirect
163. #2488C22semidirect
164. #2488C22semidirect
170. #2481C22semidirect
171. #2470C22semidirect
172. #2467C22semidirect
173. #2466C22semidirect
174. #2463C22semidirect
175. #2460C22semidirect
178. #2450C22semidirect
179. #2450C22semidirect
180. #2450C22semidirect
184. #2444C22semidirect
185. #2443C22semidirect
186. #2442C22semidirect
189. #2425C22semidirect
190. #2419C22semidirect
191. #2419C22semidirect
202. #2409C22semidirect
216. #2335C22semidirect
225. #2318C22semidirect

Maximal subgroups

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

subgroupindex
#582612
#561642
#561272
#556162
#539632
#534912
#527412
#524142
#478142
#472412
#469742
#468982
#468492
#465482
#436432
#436212
#385022
#379412
#379352
#379092
#377022
#376982
#367192
#352372
#350842
#349972
C2×#25642