Finite Group Databasebeta

← #7658028

Subgroups — #7658028

Order 512.

4100 conjugacy classes of subgroups.

The subgroup lattice has 1233 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42379C214yesmaximal
2#42376C214yesmaximal, complemented
3#41920C214yesmaximal, complemented
4#41909C214yesmaximal
5#41591C214yesmaximal
6#41584C214yesmaximal, complemented
7#39802C212yesmaximal, complemented
8#39750C211yesmaximal, characteristic, complemented
9#39681C212yesmaximal, complemented
10#39612C211yesmaximal, characteristic, complemented
11#39591C212yesmaximal
12#37986C212yesmaximal
13#37981C212yesmaximal
14#37638C212yesmaximal, complemented
15#37580C212yesmaximal, complemented
16#37580C212yesmaximal, complemented
17#36608C211yesmaximal, characteristic, complemented
18#36567C211yesmaximal, characteristic, complemented
19#36199C212yesmaximal
20#36008C214yesmaximal, complemented
21#35835C214yesmaximal
22#35337C211yesmaximal, characteristic
23#35324C212yesmaximal
24#34629C211yesmaximal, characteristic
25#34625C212yesmaximal
26#34328C212yesmaximal, complemented
27#34145C211yesmaximal, characteristic
28C2×#557C2212yes—
29C2×#533C2211yescharacteristic
30#2864C2212yes—
31#2862C2211yescharacteristic
32#2862C2212yes—
33#2859C2211yescharacteristic
34#2855C2212yes—
35#2855C2212yes—
36#2851C2212yes—
37#2839C2214yes—
38#2839C2214yes—
39#2833C2214yes—
40#2833C2214yes—
41#2833C2214yes—
42#2833C2214yes—
43#2806C2214yes—
44#2799C2214yes—
45#2799C2214yes—
46#2791C2214yes—
47#2789C2214yes—
48#2774C2214yes—
49#2774C2214yes—
50#2769C2214yes—
51#2767C2214yes—
52#2766C2214yes—
53#2766C2214yes—
54#2765C2214yes—
55#2765C2214yes—
56#2762C2214yes—
57#2758C2214yes—
58#2755C2214yes—
59#2745C2214yes—
60#2738C2214yes—
61#2734C2214yes—
62#2734C2214yes—
63#2729C2214yes—
64#2726C2214yes—
65#2720C2214yes—
66#2713C2214yes—
67#2667C2214yes—
68#2666C2214yes—
69#2666C2214yes—
70#2666C2214yes—
71#2666C2214yes—
72#2665C2214yes—
73#2660C2212yes—
74#2660C2212yes—
75#2655C2214yes—
76#2655C2214yes—
77#2655C2214yes—
78#2655C2214yes—
79#2655C2214yes—
80#2655C2214yes—
81#2655C2214yes—
82#2652C2214yes—
83#2647C2211yescharacteristic
84#2647C2211yescharacteristic
85#2647C2212yes—
86#2647C2214yes—
87#2647C2211yescharacteristic
88#2647C2212yes—
89#2645C2212yes—
90#2645C2214yes—
91#2645C2212yes—
92#2645C2212yes—
93#2642C2211yescharacteristic
94#2634C2214yes—
95#2634C2214yes—
96#2629C2211yescharacteristic
97#2629C2212yes—
98#2628C2212yes—
99#2628C2212yes—
100#2625C2212yes—
101#2621C2211yescharacteristic
102#2611C2214yes—
103#2606C2214yes—
104#2605C2214yes—
105#2599C2214yes—
106#2590C2214yes—
107#2589C2214yes—
108#2589C2214yes—
109#2588C2214yes—
110#2588C2214yes—
111#2588C2214yes—
112#2588C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2585C2214yes—
116#2584C2212yes—
117#2584C2212yes—
118#2582C2212yes—
119#2581C2214yes—
120#2581C2212yes—
121#2581C2214yes—
122#2581C2212yes—
123#2575C2214yes—
124#2575C2214yes—
125#2573C2214yes—
126#2571C2212yes—
127#2570C2212yes—
128#2570C2212yes—
129#2567C2212yes—
130#2567C2212yes—
131#2565C2214yes—
132#2565C2212yes—
133#2565C2212yes—
134#2556C2214yes—
135#2533C2214yes—
136#2533C2214yes—
137#2533C2214yes—
138#2528C2214yes—
139#2528C2214yes—
140#2528C2214yes—
141#2528C2214yes—
142#2528C2214yes—
143#2528C2214yes—
144#2528C2214yes—
145#2527C2214yes—
146#2527C2214yes—
147#2524C2214yes—
148#2524C2214yes—
149#2524C2214yes—
150#2520C2214yes—
151#2520C2214yes—
152#2515C2214yes—
153#2514C2212yes—
154#2514C2212yes—
155#2514C2214yes—
156#2514C2214yes—
157#2514C2212yes—
158#2514C2214yes—
159#2514C2212yes—
160#2511C2212yes—
161#2511C2212yes—
162#2508C2212yes—
163#2508C2212yes—
164#2507C2212yes—
165#2507C2212yes—
166#2506C2212yes—
167#2506C2212yes—
168#2506C2214yes—
169#2506C2214yes—
170#2493C2214yes—
171#2484C2214yes—
172#2473C2214yes—
173#2465C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2462C2214yes—
177#2462C2214yes—
178#2462C2214yes—
179#2462C2214yes—
180#2402C2214yes—
181#2402C2214yes—
182#2401C2214yes—
183#2399C2214yes—
184#2396C2214yes—
185#2396C2214yes—
186#2371C2214yes—
187#2371C2214yes—
188#2371C2214yes—
189#2370C2212yes—
190#2370C2212yes—
191#2370C2212yes—
192#2370C2212yes—
193#2370C2214yes—
194#2369C2212yes—
195#2368C2212yes—
196#2368C2212yes—
197#2365C2212yes—
198#2365C2214yes—
199#2365C2212yes—
200#2360C2212yes—
201#2360C2212yes—
202#2356C2212yes—
203#2356C2214yes—
204#2356C2212yes—
205#2356C2214yes—
206#2355C2212yes—
207#2355C2212yes—
208#2343C2214yes—
209#2336C2214yes—
210#2336C2214yes—
211#2331C2212yes—
212#2331C2212yes—
213#2327C2214yes—
214#2327C2212yes—
215#2323C2212yes—
216#2323C2212yes—
217#2314C2211yescharacteristic
218#2314C2211yescharacteristic
219C4×C4⋊Q8C2212yes—
220C4×C4⋊Q8C2211yescharacteristic
221C4×C4⋊Q8C2212yes—
222C4×#125C2212yes—
223C4×#125C2212yes—
224C4×#125C2212yes—
225C4×#125C2211yescharacteristic
226C4×C22⋊Q8C2212yes—
227#2296C2212yes—
228#2295C2212yes—
229#2295C2212yes—
230#2295C2212yes—
231#2295C2212yes—
232#2295C2212yes—
233#2295C2211yescharacteristic
234#2295C2211yescharacteristic
235#2285C2212yes—
236#2283C2212yes—
237#2276C2214yes—
238C42×Q8C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2212yes—
242C2×C4×C4⋊C4C2211yescharacteristic
243#557—216no—
244#533—28no—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2311yescharacteristic
251C2×#125C2311yescharacteristic
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2311yescharacteristic
278C2×#117C2314yes—
279C22×C4⋊C4C2312yes—
280C22×C42C2311yescharacteristic
281C22×C42C2312yes—
282#401C2314yes—
283#401C2314yes—
284#401C2314yes—
285#401C2314yes—
286#401C2314yes—
287#401C2314yes—
288#401C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
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#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#399C2314yes—
329#399C2314yes—
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#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#393C2314yes—
385#393C2314yes—
386#391C2312yes—
387#391C2314yes—
388#391C2314yes—
389#391C2312yes—
390#391C2312yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2314yes—
431#389C2314yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2312yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
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#387C2312yes—
500#387C2312yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2312yes—
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#387C2312yes—
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#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#385C2312yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2312yes—
563#385C2312yes—
564#385C2312yes—
565#385C2314yes—
566#384C2311yescharacteristic
567#384C2312yes—
568#384C2311yescharacteristic
569#384C2312yes—
570#384C2314yes—
571#384C2311yescharacteristic
572#384C2312yes—
573#383C2314yes—
574#383C2314yes—
575#383C2314yes—
576#383C2314yes—
577#383C2314yes—
578#383C2314yes—
579#383C2314yes—
580#382C2312yes—
581#382C2312yes—
582#382C2312yes—
583#382C2311yescharacteristic
584#382C2312yes—
585#382C2314yes—
586#382C2311yescharacteristic
587#382C2311yescharacteristic
588#382C2312yes—
589#382C2314yes—
590#382C2314yes—
591#382C2314yes—
592#382C2314yes—
593#382C2314yes—
594#382C2314yes—
595#381C2314yes—
596#381C2314yes—
597#381C2314yes—
598#380C2312yes—
599#380C2312yes—
600#380C2312yes—
601#380C2314yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2311yescharacteristic
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660#376C2312yes—
661#376C2314yes—
662#376C2311yescharacteristic
663#376C2314yes—
664#376C2314yes—
665#376C2314yes—
666#376C2314yes—
667#376C2314yes—
668#376C2311yescharacteristic
669#376C2312yes—
670C2×#95C2311yescharacteristic
671C2×#95C2311yescharacteristic
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C43C2312yes—
675C43C2312yes—
676C22×Q8C2412yes—
677C22×Q8C2411yescharacteristic
678C22×Q8C2414yes—
679C22×Q8C2412yes—
680C22×Q8C2414yes—
681C22×Q8C2411yescharacteristic
682C23×C4C2412yes—
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2412yes—
686C23×C4C2411yescharacteristic
687C4⋊Q8—24no—
688C4⋊Q8—216no—
689C4⋊Q8—24no—
690C4⋊Q8—28no—
691C4⋊Q8—24no—
692C4⋊Q8—28no—
693#125—28no—
694#125—216no—
695#125—216no—
696#125—28no—
697#125—28no—
698#125—24no—
699#125—48no—
700#125—48no—
701C22⋊Q8—24no—
702C22⋊Q8—28no—
703C22⋊Q8—24no—
704C22⋊Q8—28no—
705C4×Q8—216no—
706C4×Q8—28no—
707C4×Q8—24no—
708C4×Q8—28no—
709C4×Q8—28no—
710C4×Q8—28no—
711C4×Q8—48no—
712C4×Q8—48no—
713C4×Q8—48no—
714C4×Q8—44no—
715C4×Q8—44no—
716C4×Q8#4118yes—
717#117—24no—
718#117—28no—
719#117—24no—
720#117—48no—
721C2×C4⋊C4—44no—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C42—28no—
800C2×C42—24no—
801C2×C42C2412yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815C2×C42C2411yescharacteristic
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2412yes—
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2412yes—
845#95C2414yes—
846#95C2412yes—
847#95C2414yes—
848#95C2412yes—
849#95C2412yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2412yes—
855#95C2412yes—
856#95C2412yes—
857#95C2412yes—
858#95C2412yes—
859#95C2412yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
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#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
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—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928C24C2511yescharacteristic
929C2×Q8—24no—
930C2×Q8—22no—
931C2×Q8—28no—
932C2×Q8—24no—
933C2×Q8—24no—
934C2×Q8—24no—
935C2×Q8—28no—
936C2×Q8—42no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×Q8—42no—
940C2×Q8—44no—
941C2×Q8—42no—
942C2×Q8—44no—
943C2×Q8—42no—
944C2×Q8C2×#4114yes—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—22no—
950C22×C4—24no—
951C22×C4—22no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C42−1+414yes—
958C22×C4C2514yes—
959C22×C4C2511yescharacteristic
960C22×C4C2512yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2514yes—
969C22×C4C2514yes—
970C22×C4C2512yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2511yescharacteristic
980C22×C4C2512yes—
981C22×C4C2511yescharacteristic
982C22×C4C2512yes—
983C22×C4C2511yescharacteristic
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—22no—
991C4⋊C4—28no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—44no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—42no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4C2×#4118yes—
1052C4⋊C4C2×#4114yes—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—24no—
1057C22⋊C4—24no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C42—22no—
1062C42—22no—
1063C42—22no—
1064C42—24no—
1065C42—28no—
1066C42—28no—
1067C42—28no—
1068C42—24no—
1069C42—24no—
1070C42—24no—
1071C42—24no—
1072C42—22no—
1073C42—22no—
1074C42—22no—
1075C42—28no—
1076C42—28no—
1077C42—24no—
1078C42—24no—
1079C42—28no—
1080C42—42no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—42no—
1088C42—42no—
1089C42—44no—
1090C42—42no—
1091C42—42no—
1092C42—44no—
1093C42—42no—
1094C42—42no—
1095C42—44no—
1096C42C2×#4114yes—
1097C42C2×#4118yes—
1098C422−1+414yes—
1099C23—21no—
1100C23—21no—
1101C23—22no—
1102C23—22no—
1103C23C2×2−1+412yes—
1104C23C2611yescharacteristic
1105Q8—44no—
1106Q8—44no—
1107Q8—416no—
1108Q8—48no—
1109Q8—84no—
1110Q8—88no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—28no—
1124C2×C4—24no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—48no—
1177C2×C4—44no—
1178C2×C4—82no—
1179C2×C4—84no—
1180C2×C4C22×#4112yes—
1181C2×C4C22×#4114yes—
1182C2×C4C22×#4114yes—
1183C2×C4C22×#4112yes—
1184C2×C4C22×#4112yes—
1185C2×C4C2×2−1+412yes—
1186C2×C4C2×2−1+414yes—
1187C2×C4C2×2−1+412yes—
1188C2×C4C2×2−1+412yes—
1189C2×C4#58514yes—
1190C22—22no—
1191C22—24no—
1192C22—41no—
1193C22—42no—
1194C22—41no—
1195C22C23×#4111yescharacteristic
1196C22C22×2−1+411yescharacteristic
1197C22C22×2−1+411yescharacteristic
1198C22C2×#58512yes—
1199C222−1+612yes—
1200C4—22no—
1201C4—22no—
1202C4—24no—
1203C4—24no—
1204C4—24no—
1205C4—22no—
1206C4—24no—
1207C4—44no—
1208C4—44no—
1209C4—41no—
1210C4—42no—
1211C4—42no—
1212C4—42no—
1213C4—44no—
1214C4—42no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—44no—
1219C4—44no—
1220C4—44no—
1221C4—41no—
1222C4—42no—
1223C4—44no—
1224C4—44no—
1225C4#352314yes—
1226C2—42no—
1227C2#6268611yescharacteristic
1228C2C2×#352311yescharacteristic
1229C2#6286111yescharacteristic
1230C2#6292812yes—
1231C2#6293212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42376C2semidirect
3. #41920C2semidirect
6. #41584C2semidirect
7. #39802C2semidirect
8. #39750C2semidirect
9. #39681C2semidirect
10. #39612C2semidirect
14. #37638C2semidirect
15. #37580C2semidirect
16. #37580C2semidirect
17. #36608C2semidirect
18. #36567C2semidirect
20. #36008C2semidirect
26. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#423792
#423762
#419202
#419092
#415912
#415842
#398022
#397502
#396812
#396122
#395912
#379862
#379812
#376382
#375802
#366082
#365672
#361992
#360082
#358352
#353372
#353242
#346292
#346252
#343282
#341452