Finite Group Databasebeta

← #7713148

Subgroups — #7713148

Order 512.

4204 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49115C214yesmaximal, complemented
2#49045C214yesmaximal, complemented
3#48280C214yesmaximal, complemented
4#48198C214yesmaximal, complemented
5#47304C214yesmaximal, complemented
6#47124C214yesmaximal, complemented
7#46916C214yesmaximal, complemented
8#46554C214yesmaximal, complemented
9#39678C212yesmaximal, complemented
10#39639C212yesmaximal, complemented
11#39541C212yesmaximal, complemented
12#39508C212yesmaximal
13#37956C212yesmaximal
14#37933C212yesmaximal
15#37886C212yesmaximal, complemented
16#37885C212yesmaximal
17#37460C212yesmaximal
18#36977C212yesmaximal, complemented
19#36962C212yesmaximal
20#35167C211yesmaximal, characteristic, complemented
21#35033C211yesmaximal, characteristic
22#35015C211yesmaximal, characteristic, complemented
23#35015C211yesmaximal, characteristic, complemented
24#35015C211yesmaximal, characteristic, complemented
25#35014C211yesmaximal, characteristic
26#34432C212yesmaximal, complemented
27C2×#2334C211yesmaximal, characteristic
28C2×#544C2212yes—
29C22×#126C2211yescharacteristic
30#2857C2212yes—
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2855C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2851C2212yes—
39#2848C2212yes—
40#2836C2214yes—
41#2831C2214yes—
42#2809C2214yescomplemented
43#2802C2214yescomplemented
44#2802C2214yescomplemented
45#2799C2214yescomplemented
46#2798C2214yes—
47#2794C2214yescomplemented
48#2793C2214yes—
49#2793C2214yes—
50#2791C2214yescomplemented
51#2791C2214yescomplemented
52#2791C2214yescomplemented
53#2788C2214yes—
54#2787C2214yes—
55#2776C2214yescomplemented
56#2774C2214yescomplemented
57#2773C2214yes—
58#2770C2214yes—
59#2768C2214yes—
60#2767C2214yescomplemented
61#2766C2214yescomplemented
62#2766C2214yescomplemented
63#2766C2214yescomplemented
64#2762C2214yescomplemented
65#2762C2214yescomplemented
66#2762C2214yescomplemented
67#2759C2214yes—
68#2755C2214yescomplemented
69#2755C2214yescomplemented
70#2755C2214yescomplemented
71#2754C2214yes—
72#2745C2214yes—
73#2738C2214yes—
74#2726C2214yescomplemented
75#2721C2214yes—
76#2721C2214yes—
77#2721C2214yes—
78#2721C2214yes—
79#2721C2214yes—
80#2719C2214yescomplemented
81#2719C2214yescomplemented
82#2719C2214yescomplemented
83#2716C2214yes—
84#2716C2214yes—
85#2716C2214yes—
86#2716C2214yes—
87#2716C2214yes—
88#2698C2214yes—
89#2689C2214yes—
90#2664C2214yes—
91#2659C2212yes—
92#2659C2212yes—
93#2654C2214yes—
94#2650C2214yes—
95#2646C2212yes—
96#2646C2212yes—
97#2646C2212yes—
98#2646C2212yes—
99#2637C2214yes—
100#2627C2212yes—
101#2627C2212yes—
102#2627C2212yes—
103#2626C2212yes—
104#2626C2212yes—
105#2626C2212yes—
106#2611C2214yes—
107#2608C2214yes—
108#2607C2214yes—
109#2606C2214yescomplemented
110#2599C2214yes—
111#2596C2214yes—
112#2594C2214yes—
113#2590C2214yescomplemented
114#2590C2214yescomplemented
115#2590C2214yescomplemented
116#2590C2214yescomplemented
117#2589C2214yes—
118#2588C2214yescomplemented
119#2588C2214yescomplemented
120#2588C2214yescomplemented
121#2588C2214yescomplemented
122#2587C2214yes—
123#2582C2214yescomplemented
124#2577C2214yes—
125#2565C2214yescomplemented
126#2561C2214yes—
127#2556C2214yes—
128#2552C2212yescomplemented
129#2552C2214yescomplemented
130#2552C2212yescomplemented
131#2551C2212yescomplemented
132#2551C2212yescomplemented
133#2550C2214yescomplemented
134#2550C2214yescomplemented
135#2533C2214yescomplemented
136#2533C2214yescomplemented
137#2532C2214yes—
138#2530C2214yes—
139#2529C2214yes—
140#2528C2214yescomplemented
141#2525C2214yes—
142#2525C2214yes—
143#2524C2214yescomplemented
144#2520C2214yescomplemented
145#2520C2214yescomplemented
146#2519C2214yes—
147#2519C2214yes—
148#2511C2212yescomplemented
149#2511C2212yescomplemented
150#2511C2212yescomplemented
151#2511C2214yescomplemented
152#2507C2212yescomplemented
153#2507C2212yescomplemented
154#2507C2212yescomplemented
155#2506C2214yescomplemented
156#2505C2214yes—
157#2502C2214yes—
158#2497C2212yes—
159#2493C2214yes—
160#2493C2214yes—
161#2492C2212yes—
162#2484C2214yes—
163#2482C2214yes—
164#2480C2214yes—
165#2480C2214yes—
166#2478C2214yes—
167#2478C2214yes—
168#2473C2214yes—
169#2473C2214yes—
170#2473C2214yes—
171#2469C2214yes—
172#2469C2214yes—
173#2465C2214yes—
174#2462C2214yescomplemented
175#2451C2212yescomplemented
176#2451C2212yescomplemented
177#2451C2212yescomplemented
178#2446C2212yescomplemented
179#2446C2212yescomplemented
180#2446C2214yescomplemented
181#2446C2212yescomplemented
182#2441C2212yes—
183#2441C2212yes—
184#2439C2212yes—
185#2439C2212yes—
186#2429C2212yes—
187#2423C2212yes—
188#2382C2214yescomplemented
189#2381C2214yescomplemented
190#2371C2214yescomplemented
191#2368C2214yes—
192#2365C2214yescomplemented
193#2360C2214yes—
194#2343C2214yes—
195#2343C2214yes—
196#2336C2214yescomplemented
197#2336C2214yescomplemented
198#2334C2214yes—
199#2334C2214yes—
200#2334C2214yes—
201#2334C2214yes—
202#2331C2214yescomplemented
203#2329C2212yes—
204#2329C2212yes—
205#2329C2212yes—
206#2329C2212yes—
207#2329C2212yes—
208#2329C2212yes—
209#2327C2214yescomplemented
210#2316C2212yes—
211#2313C2212yes—
212#2313C2212yes—
213#2313C2212yes—
214#2312C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C4×C22⋊Q8C2212yes—
218C4×C22⋊Q8C2212yes—
219C2×#389C2211yescharacteristic
220C2×#389C2211yescharacteristic
221C2×#388C2211yescharacteristic
222C2×#388C2211yescharacteristic
223C2×#388C2211yescharacteristic
224C2×#387C2211yescharacteristic
225C2×#387C2211yescharacteristic
226C2×#387C2211yescharacteristic
227C2×#385C2211yescharacteristic
228C2×#385C2211yescharacteristic
229#2285C2212yes—
230C2×#382C2211yescharacteristic
231#2280C2212yes—
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×C4×C4⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C24×C4C2311yescharacteristic
236#544—216no—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2311yescharacteristic
244C2×#126—28no—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2314yes—
250C2×#125C2314yes—
251C2×#125C2314yes—
252C2×#125C2312yes—
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2314yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×#117C2314yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2311yescharacteristic
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2311yescharacteristic
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292#401C2314yes—
293#401C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
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#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2312yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2314yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2312yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#388C2314yes—
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#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#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#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#384C2314yes—
573#384C2311yescharacteristic
574#384C2311yescharacteristic
575#384C2311yescharacteristic
576#384C2311yescharacteristic
577#384C2312yes—
578#384C2314yes—
579#384C2312yes—
580#384C2312yes—
581#383C2314yes—
582#383C2314yes—
583#383C2314yes—
584#383C2314yes—
585#382C2314yes—
586#382C2314yes—
587#382C2314yes—
588#382C2314yes—
589#382C2314yes—
590#382C2312yes—
591#382C2314yes—
592#381C2314yes—
593#381C2314yes—
594#381C2314yes—
595#381C2314yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2312yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605#380C2312yes—
606#380C2312yes—
607#380C2314yes—
608#380C2312yes—
609#380C2312yes—
610#379C2314yes—
611#379C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2312yes—
646#376C2314yes—
647#376C2314yes—
648C2×#95C2311yescharacteristic
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2311yescharacteristic
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C25C2411yescharacteristic
661C22×Q8C2412yes—
662C22×Q8C2414yes—
663C22×Q8C2412yes—
664C22×Q8C2412yes—
665C22×Q8C2412yes—
666C23×C4—24no—
667C23×C4—81no—
668C23×C4—81no—
669C23×C4C2411yescharacteristic
670C23×C4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C23×C4C2411yescharacteristic
673C23×C4C2411yescharacteristic
674C23×C4C2411yescharacteristic
675C23×C4C2411yescharacteristic
676C23×C4C2411yescharacteristic
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C4⋊Q8—216no—
686C4⋊Q8—216no—
687C4⋊Q8—81no—
688C4⋊Q8—81no—
689C4⋊Q8—81no—
690C4⋊Q8—81no—
691C4⋊Q8—82no—
692#126—216no—
693#126—216no—
694#126—84no—
695#126—84no—
696#125—216no—
697#125—216no—
698#125—82no—
699#125—84no—
700#125—84no—
701#125—84no—
702C22⋊Q8—28no—
703C22⋊Q8—28no—
704C22⋊Q8—216no—
705C22⋊Q8—28no—
706C22⋊Q8—28no—
707C22⋊Q8—82no—
708C22⋊Q8—82no—
709C4×Q8—82no—
710C4×Q8—82no—
711C4×Q8—82no—
712C4×Q8—82no—
713C4×Q8—84no—
714#117—216no—
715#117—82no—
716#117—82no—
717C2×C4⋊C4—24no—
718C2×C4⋊C4—24no—
719C2×C4⋊C4—24no—
720C2×C4⋊C4—24no—
721C2×C4⋊C4—24no—
722C2×C4⋊C4—81no—
723C2×C4⋊C4—81no—
724C2×C4⋊C4—81no—
725C2×C4⋊C4—81no—
726C2×C4⋊C4#4118yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C22⋊C4—24no—
795C2×C22⋊C4—24no—
796C2×C22⋊C4—24no—
797C2×C22⋊C4—24no—
798C2×C22⋊C4—81no—
799C2×C22⋊C4—81no—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
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×C42—24no—
821C2×C42—24no—
822C2×C42—81no—
823C2×C42—81no—
824C2×C42—81no—
825C2×C42—81no—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846C2×C42C2411yescharacteristic
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2412yes—
855#95C2412yes—
856#95C2412yes—
857#95C2412yes—
858#95C2412yes—
859#95C2412yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
864#95C2414yes—
865#95C2412yes—
866#95C2412yes—
867#95C2414yes—
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—
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#95C2414yes—
923#95C2414yes—
924C24—22no—
925C24—22no—
926C24—22no—
927C24—41no—
928C24—41no—
929C24—41no—
930C24—41no—
931C24C2512yes—
932C24C2511yescharacteristic
933C2×Q8—24no—
934C2×Q8—24no—
935C2×Q8—28no—
936C2×Q8—24no—
937C2×Q8—24no—
938C2×Q8—42no—
939C2×Q8—42no—
940C2×Q8—42no—
941C2×Q8—44no—
942C2×Q8—42no—
943C2×Q8—42no—
944C2×Q8—44no—
945C2×Q8—42no—
946C2×Q8—42no—
947C2×Q8—42no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—41no—
977C22×C4—41no—
978C22×C4—41no—
979C22×C4—41no—
980C22×C4—41no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—41no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—41no—
989C22×C4—41no—
990C22×C4—41no—
991C22×C4—88no—
992C22×C4C2×#4114yes—
993C22×C4C2×#4114yes—
994C22×C4C2×#4114yes—
995C22×C42−1+414yes—
996C22×C42−1+414yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—24no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4C2×#4118yes—
1088C4⋊C4C2×#4118yes—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—24no—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C42—24no—
1110C42—24no—
1111C42—28no—
1112C42—28no—
1113C42—24no—
1114C42—24no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—41no—
1121C42—41no—
1122C42—42no—
1123C42—41no—
1124C42—41no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C42—44no—
1134C42—44no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—22no—
1140C23—22no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—44no—
1147C23—44no—
1148C23—44no—
1149C23—82no—
1150C23—82no—
1151C23—82no—
1152C23—82no—
1153C23C22×#4112yes—
1154C23C2×2−1+412yes—
1155C23C2×2−1+412yes—
1156C23C2611yescharacteristic
1157Q8—88no—
1158Q8—84no—
1159Q8—84no—
1160Q8—84no—
1161Q8—84no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—28no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—44no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—44no—
1234C2×C4—48no—
1235C2×C4—44no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—84no—
1239C2×C4—82no—
1240C2×C4—82no—
1241C2×C4—82no—
1242C2×C4—82no—
1243C2×C4—82no—
1244C2×C4—82no—
1245C2×C4C22×#4114yes—
1246C2×C4C22×#4112yes—
1247C2×C4C22×#4112yes—
1248C2×C4C22×#4114yes—
1249C2×C4C2×2−1+412yes—
1250C2×C4C2×2−1+412yes—
1251C2×C4C2×2−1+412yes—
1252C2×C4C2×2−1+412yes—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—88no—
1267C22#350914yes—
1268C22C23×#4111yescharacteristic
1269C22C22×2−1+411yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22H(7,𝔽2)11yescharacteristic
1272C22H(7,𝔽2)11yescharacteristic
1273C222−1+611yescharacteristic
1274C222−1+611yescharacteristic
1275C4—24no—
1276C4—24no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—42no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C4—44no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—44no—
1294C4—42no—
1295C4—44no—
1296C4—44no—
1297C4—42no—
1298C4—42no—
1299C4—44no—
1300C2—24no—
1301C2—82no—
1302C2C2×#350911yescharacteristic
1303C2#6284711yescharacteristic
1304C2#6285111yescharacteristic
1305C2#6286411yescharacteristic
1306C2#6286511yescharacteristic
1307C2#6287911yescharacteristic
1308C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #49115C2semidirect
2. #49045C2semidirect
3. #48280C2semidirect
4. #48198C2semidirect
5. #47304C2semidirect
6. #47124C2semidirect
7. #46916C2semidirect
8. #46554C2semidirect
9. #39678C2semidirect
10. #39639C2semidirect
11. #39541C2semidirect
15. #37886C2semidirect
18. #36977C2semidirect
20. #35167C2semidirect
22. #35015C2semidirect
23. #35015C2semidirect
24. #35015C2semidirect
26. #34432C2semidirect
42. #2809C22semidirect
43. #2802C22semidirect
44. #2802C22semidirect
45. #2799C22semidirect
47. #2794C22semidirect
50. #2791C22semidirect
51. #2791C22semidirect
52. #2791C22semidirect
55. #2776C22semidirect
56. #2774C22semidirect
60. #2767C22semidirect
61. #2766C22semidirect
62. #2766C22semidirect
63. #2766C22semidirect
64. #2762C22semidirect
65. #2762C22semidirect
66. #2762C22semidirect
68. #2755C22semidirect
69. #2755C22semidirect
70. #2755C22semidirect
74. #2726C22semidirect
80. #2719C22semidirect
81. #2719C22semidirect
82. #2719C22semidirect
109. #2606C22semidirect
113. #2590C22semidirect
114. #2590C22semidirect
115. #2590C22semidirect
116. #2590C22semidirect
118. #2588C22semidirect
119. #2588C22semidirect
120. #2588C22semidirect
121. #2588C22semidirect
123. #2582C22semidirect
125. #2565C22semidirect
128. #2552C22semidirect
129. #2552C22semidirect
130. #2552C22semidirect
131. #2551C22semidirect
132. #2551C22semidirect
133. #2550C22semidirect
134. #2550C22semidirect
135. #2533C22semidirect
136. #2533C22semidirect
140. #2528C22semidirect
143. #2524C22semidirect
144. #2520C22semidirect
145. #2520C22semidirect
148. #2511C22semidirect
149. #2511C22semidirect
150. #2511C22semidirect
151. #2511C22semidirect
152. #2507C22semidirect
153. #2507C22semidirect
154. #2507C22semidirect
155. #2506C22semidirect
174. #2462C22semidirect
175. #2451C22semidirect
176. #2451C22semidirect
177. #2451C22semidirect
178. #2446C22semidirect
179. #2446C22semidirect
180. #2446C22semidirect
181. #2446C22semidirect
188. #2382C22semidirect
189. #2381C22semidirect
190. #2371C22semidirect
192. #2365C22semidirect
196. #2336C22semidirect
197. #2336C22semidirect
202. #2331C22semidirect
209. #2327C22semidirect

Maximal subgroups

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

subgroupindex
#491152
#490452
#482802
#481982
#473042
#471242
#469162
#465542
#396782
#396392
#395412
#395082
#379562
#379332
#378862
#378852
#374602
#369772
#369622
#351672
#350332
#350152
#350142
#344322
C2×#23342