Finite Group Databasebeta

← #7714743

Subgroups — #7714743

Order 512.

4448 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51789C214yesmaximal, complemented
2#51788C214yesmaximal, complemented
3#51595C214yesmaximal, complemented
4#51594C214yesmaximal, complemented
5#47022C214yesmaximal, complemented
6#47021C214yesmaximal, complemented
7#46846C214yesmaximal, complemented
8#46845C214yesmaximal, complemented
9#38963C214yesmaximal, complemented
10#38959C214yesmaximal
11#37877C212yesmaximal, complemented
12#37876C212yesmaximal
13#37689C212yesmaximal, complemented
14#37688C212yesmaximal
15#37478C212yesmaximal
16#37194C212yesmaximal, complemented
17#37135C212yesmaximal, complemented
18#35179C212yesmaximal, complemented
19#35151C211yesmaximal, characteristic
20#35090C211yesmaximal, characteristic
21#35013C212yesmaximal, complemented
22#34359C212yesmaximal
23C2×#2323C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#543C2211yescharacteristic
26C2×#533C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#2855C2212yes—
31#2855C2212yes—
32#2855C2212yes—
33#2855C2212yes—
34#2855C2212yes—
35#2855C2212yes—
36#2851C2214yes—
37#2841C2214yes—
38#2841C2214yes—
39#2811C2212yescomplemented
40#2809C2212yescomplemented
41#2809C2214yescomplemented
42#2806C2212yescomplemented
43#2806C2214yescomplemented
44#2806C2214yescomplemented
45#2806C2212yescomplemented
46#2806C2212yescomplemented
47#2805C2212yescomplemented
48#2802C2214yescomplemented
49#2799C2214yescomplemented
50#2799C2214yescomplemented
51#2799C2214yescomplemented
52#2792C2214yescomplemented
53#2792C2214yescomplemented
54#2792C2214yescomplemented
55#2792C2214yescomplemented
56#2791C2214yescomplemented
57#2791C2214yescomplemented
58#2791C2214yescomplemented
59#2791C2214yescomplemented
60#2790C2214yes—
61#2790C2214yes—
62#2788C2214yes—
63#2774C2214yescomplemented
64#2774C2214yescomplemented
65#2774C2214yescomplemented
66#2774C2214yescomplemented
67#2768C2214yes—
68#2768C2214yes—
69#2768C2214yes—
70#2763C2214yes—
71#2763C2214yes—
72#2755C2214yescomplemented
73#2755C2214yescomplemented
74#2755C2214yescomplemented
75#2755C2214yescomplemented
76#2742C2214yes—
77#2734C2212yescomplemented
78#2734C2214yescomplemented
79#2729C2214yes—
80#2726C2212yescomplemented
81#2726C2214yescomplemented
82#2720C2214yes—
83#2720C2214yes—
84#2720C2214yes—
85#2713C2214yescomplemented
86#2713C2214yescomplemented
87#2713C2214yescomplemented
88#2704C2214yes—
89#2704C2214yes—
90#2677C2214yes—
91#2667C2214yes—
92#2665C2214yes—
93#2659C2212yes—
94#2659C2212yes—
95#2659C2212yes—
96#2659C2212yes—
97#2646C2212yes—
98#2646C2212yes—
99#2627C2214yes—
100#2627C2212yes—
101#2627C2212yes—
102#2627C2214yes—
103#2627C2214yes—
104#2626C2212yes—
105#2626C2212yes—
106#2590C2214yescomplemented
107#2589C2214yes—
108#2589C2214yes—
109#2588C2214yescomplemented
110#2587C2214yes—
111#2587C2214yes—
112#2586C2214yescomplemented
113#2586C2214yescomplemented
114#2586C2214yescomplemented
115#2585C2214yescomplemented
116#2585C2214yescomplemented
117#2585C2214yescomplemented
118#2584C2214yescomplemented
119#2582C2212yescomplemented
120#2582C2212yescomplemented
121#2582C2212yescomplemented
122#2582C2212yescomplemented
123#2581C2214yescomplemented
124#2581C2214yescomplemented
125#2574C2214yes—
126#2574C2214yes—
127#2574C2214yes—
128#2569C2214yes—
129#2569C2214yes—
130#2568C2212yescomplemented
131#2568C2212yescomplemented
132#2567C2214yescomplemented
133#2567C2212yescomplemented
134#2567C2212yescomplemented
135#2565C2214yescomplemented
136#2565C2214yescomplemented
137#2556C2214yes—
138#2552C2214yescomplemented
139#2550C2214yescomplemented
140#2549C2214yes—
141#2549C2214yes—
142#2522C2214yes—
143#2520C2214yescomplemented
144#2520C2214yescomplemented
145#2509C2214yescomplemented
146#2508C2214yescomplemented
147#2508C2214yescomplemented
148#2507C2214yescomplemented
149#2497C2214yes—
150#2465C2214yes—
151#2465C2214yes—
152#2465C2214yes—
153#2462C2214yescomplemented
154#2462C2214yescomplemented
155#2462C2214yescomplemented
156#2462C2214yescomplemented
157#2451C2214yescomplemented
158#2446C2214yescomplemented
159#2442C2214yes—
160#2441C2214yes—
161#2441C2214yes—
162#2440C2214yes—
163#2439C2214yes—
164#2439C2214yes—
165#2438C2214yes—
166#2438C2214yes—
167#2438C2214yes—
168#2438C2214yes—
169#2438C2214yes—
170#2438C2214yes—
171#2438C2214yes—
172#2438C2214yes—
173#2438C2214yes—
174#2438C2214yes—
175#2437C2214yes—
176#2437C2214yes—
177#2429C2214yes—
178#2423C2214yes—
179#2423C2214yes—
180#2378C2214yes—
181#2378C2214yes—
182#2368C2214yes—
183#2368C2214yes—
184#2344C2214yes—
185#2344C2214yes—
186#2342C2214yes—
187#2342C2214yes—
188#2332C2214yes—
189#2332C2214yes—
190#2329C2212yes—
191#2329C2212yes—
192#2329C2212yes—
193#2329C2212yes—
194#2329C2212yes—
195#2329C2212yes—
196#2323C2214yes—
197#2323C2214yes—
198#2323C2214yes—
199#2323C2214yes—
200#2317C2214yes—
201#2317C2212yes—
202#2316C2211yescharacteristic
203#2315C2212yes—
204#2315C2211yescharacteristic
205#2313C2214yes—
206#2310C2214yes—
207C4×C22⋊Q8C2214yes—
208C2×#391C2211yescharacteristic
209C2×#389C2211yescharacteristic
210C2×#389C2212yes—
211C2×#388C2212yes—
212C2×#388C2212yes—
213C2×#387C2212yes—
214#2285C2212yes—
215#2280C2212yes—
216C2×#381C2212yes—
217C2×#380C2211yescharacteristic
218C2×C4×C4⋊C4C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C24×C4C2311yescharacteristic
221#544—44no—
222#543—44no—
223#533—48no—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2314yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×C22⋊Q8Q8116yescomplemented
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C4×Q8—44no—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2314yes—
255C2×#117—44no—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2314yes—
261C2×#117C2314yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2311yescharacteristic
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C42C2311yescharacteristic
277C22×C42C2312yes—
278C22×C42C2311yescharacteristic
279C22×C42C2312yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
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#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#393C2314yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2312yes—
387#391C2312yes—
388#391C2312yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2312yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#391C2314yes—
410#389C2314yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
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#389C2314yes—
431#389C2314yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
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#387C2314yes—
475#387C2314yes—
476#387C2314yes—
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#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#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#384C2314yes—
553#384C2314yes—
554#384C2314yes—
555#384C2312yes—
556#384C2312yes—
557#384C2314yes—
558#382C2314yes—
559#382C2314yes—
560#382C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#381C2314yes—
565#381C2314yes—
566#381C2314yes—
567#381C2314yes—
568#381C2314yes—
569#381C2314yes—
570#381C2314yes—
571#380C2314yes—
572#380C2314yes—
573#380C2312yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2312yes—
581#380C2312yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2314yes—
588#380C2312yes—
589#380C2312yes—
590#379C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C2×#95C2312yes—
612C2×#95C2312yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C2×#95C2312yes—
620C25C2411yescharacteristic
621C22×Q8—42no—
622C22×Q8—42no—
623C22×Q8C2×Q818yes—
624C22×Q8C2412yes—
625C22×Q8C2412yes—
626C22×Q8C2414yes—
627C22×Q8C2414yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2411yescharacteristic
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C23×C4—42no—
634C23×C4—42no—
635C23×C4C2×Q818yes—
636C23×C4C2412yes—
637C23×C4C2411yescharacteristic
638C23×C4C2411yescharacteristic
639C23×C4C2412yes—
640C23×C4C2411yescharacteristic
641C23×C4C2411yescharacteristic
642C23×C4C2411yescharacteristic
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C4⋊Q8—44no—
653C4⋊Q8—44no—
654C4⋊Q8—48no—
655C4⋊Q8—84no—
656#125—48no—
657#125—48no—
658#125—84no—
659#125—84no—
660C22⋊Q8—28no—
661C22⋊Q8—28no—
662C22⋊Q8—48no—
663C22⋊Q8—48no—
664C22⋊Q8—44no—
665C22⋊Q8—44no—
666C22⋊Q8—48no—
667C22⋊Q8—48no—
668C22⋊Q8—84no—
669C22⋊Q8—84no—
670C22⋊Q8C2×Q8116yes—
671C22⋊Q8C2×Q8116yes—
672C22⋊Q8C2×Q8132yes—
673C4×Q8—44no—
674C4×Q8—44no—
675C4×Q8—44no—
676C4×Q8—44no—
677C4×Q8—48no—
678C4×Q8—44no—
679C4×Q8—44no—
680C4×Q8—84no—
681#117—48no—
682#117—48no—
683#117—48no—
684#117—44no—
685#117—48no—
686#117—44no—
687C2×C4⋊C4—24no—
688C2×C4⋊C4—42no—
689C2×C4⋊C4—42no—
690C2×C4⋊C4—42no—
691C2×C4⋊C4—44no—
692C2×C4⋊C4—82no—
693C2×C4⋊C4C2×Q8116yes—
694C2×C4⋊C4C2×Q818yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C22⋊C4—24no—
767C2×C22⋊C4—44no—
768C2×C22⋊C4—44no—
769C2×C22⋊C4—42no—
770C2×C22⋊C4—82no—
771C2×C22⋊C4C2×Q8116yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C42—24no—
789C2×C42—28no—
790C2×C42—42no—
791C2×C42—82no—
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2412yes—
795C2×C42C2412yes—
796C2×C42C2412yes—
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
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—
874C24—22no—
875C24—22no—
876C24—41no—
877C24—41no—
878C24—41no—
879C24—41no—
880C24C22×Q814yes—
881C24C2512yes—
882C24C2511yescharacteristic
883C2×Q8—24no—
884C2×Q8—24no—
885C2×Q8—41no—
886C2×Q8—42no—
887C2×Q8—41no—
888C2×Q8—416no—
889C2×Q8—41no—
890C2×Q8—42no—
891C2×Q8—41no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—44no—
901C2×Q8—44no—
902C2×Q8—42no—
903C2×Q8—42no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—42no—
908C2×Q8C22×Q814yes—
909C2×Q8C22×Q814yes—
910C2×Q8C22×Q818yes—
911C22×C4—22no—
912C22×C4—24no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—24no—
917C22×C4—22no—
918C22×C4—24no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—24no—
922C22×C4—41no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—416no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—41no—
936C22×C4—42no—
937C22×C4—41no—
938C22×C4—42no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4C22×Q818yes—
954C22×C4C22×Q814yes—
955C22×C4C22×Q814yes—
956C22×C4C22×Q818yes—
957C22×C4C22×Q818yes—
958C22×C4C22×Q818yes—
959C22×C4H(5,𝔽2)14yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2512yes—
964C22×C4C2514yes—
965C22×C4C2514yes—
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2514yes—
973C22×C4C2512yes—
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2514yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—44no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—41no—
992C4⋊C4—42no—
993C4⋊C4—41no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—42no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
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—42no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4C22×Q818yes—
1049C4⋊C4C22×Q818yes—
1050C4⋊C4C22×Q8116yes—
1051C4⋊C4C22×Q8116yes—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4C22×Q8116yes—
1067C22⋊C4C22×Q8116yes—
1068C42—24no—
1069C42—24no—
1070C42—24no—
1071C42—24no—
1072C42—24no—
1073C42—24no—
1074C42—42no—
1075C42—42no—
1076C42—44no—
1077C42—44no—
1078C42—44no—
1079C42—44no—
1080C42—44no—
1081C42—44no—
1082C42—44no—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—28no—
1099C23—44no—
1100C23—44no—
1101C23—82no—
1102C23—82no—
1103C23—82no—
1104C23—82no—
1105C23C23×Q814yes—
1106C23C23×Q812yes—
1107C23C2×H(5,𝔽2)12yes—
1108C23#58512yes—
1109C23C2611yescharacteristic
1110Q8—44no—
1111Q8—48no—
1112Q8—44no—
1113Q8—84no—
1114Q8—84no—
1115Q8—88no—
1116Q8—88no—
1117Q8—162no—
1118Q8—162no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—28no—
1134C2×C4—28no—
1135C2×C4—216no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—48no—
1179C2×C4—48no—
1180C2×C4—48no—
1181C2×C4—44no—
1182C2×C4—44no—
1183C2×C4—84no—
1184C2×C4—82no—
1185C2×C4—84no—
1186C2×C4—82no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4C23×Q818yes—
1192C2×C4C23×Q814yes—
1193C2×C4C23×Q814yes—
1194C2×C4C23×Q814yes—
1195C2×C4C23×Q812yes—
1196C2×C4C23×Q812yes—
1197C2×C4C2×H(5,𝔽2)14yes—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—88no—
1212C22#350114yes—
1213C22C24×Q811yescharacteristic
1214C22C22×H(5,𝔽2)11yescharacteristic
1215C22C2×#58511yescharacteristic
1216C22H(7,𝔽2)11yescharacteristic
1217C222−1+611yescharacteristic
1218C222−1+611yescharacteristic
1219C222−1+611yescharacteristic
1220C4—24no—
1221C4—22no—
1222C4—22no—
1223C4—24no—
1224C4—24no—
1225C4—28no—
1226C4—24no—
1227C4—44no—
1228C4—44no—
1229C4—44no—
1230C4—42no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—44no—
1235C4—42no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—44no—
1240C4—44no—
1241C2—24no—
1242C2—44no—
1243C2C2×#350111yescharacteristic
1244C2#6284911yescharacteristic
1245C2#6285411yescharacteristic
1246C2#6286911yescharacteristic
1247C2#6287111yescharacteristic
1248C2#6287311yescharacteristic
1249C2#6287511yescharacteristic
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. #51789C2semidirect
2. #51788C2semidirect
3. #51595C2semidirect
4. #51594C2semidirect
5. #47022C2semidirect
6. #47021C2semidirect
7. #46846C2semidirect
8. #46845C2semidirect
9. #38963C2semidirect
11. #37877C2semidirect
13. #37689C2semidirect
16. #37194C2semidirect
17. #37135C2semidirect
18. #35179C2semidirect
21. #35013C2semidirect
39. #2811C22semidirect
40. #2809C22semidirect
41. #2809C22semidirect
42. #2806C22semidirect
43. #2806C22semidirect
44. #2806C22semidirect
45. #2806C22semidirect
46. #2806C22semidirect
47. #2805C22semidirect
48. #2802C22semidirect
49. #2799C22semidirect
50. #2799C22semidirect
51. #2799C22semidirect
52. #2792C22semidirect
53. #2792C22semidirect
54. #2792C22semidirect
55. #2792C22semidirect
56. #2791C22semidirect
57. #2791C22semidirect
58. #2791C22semidirect
59. #2791C22semidirect
63. #2774C22semidirect
64. #2774C22semidirect
65. #2774C22semidirect
66. #2774C22semidirect
72. #2755C22semidirect
73. #2755C22semidirect
74. #2755C22semidirect
75. #2755C22semidirect
77. #2734C22semidirect
78. #2734C22semidirect
80. #2726C22semidirect
81. #2726C22semidirect
85. #2713C22semidirect
86. #2713C22semidirect
87. #2713C22semidirect
106. #2590C22semidirect
109. #2588C22semidirect
112. #2586C22semidirect
113. #2586C22semidirect
114. #2586C22semidirect
115. #2585C22semidirect
116. #2585C22semidirect
117. #2585C22semidirect
118. #2584C22semidirect
119. #2582C22semidirect
120. #2582C22semidirect
121. #2582C22semidirect
122. #2582C22semidirect
123. #2581C22semidirect
124. #2581C22semidirect
130. #2568C22semidirect
131. #2568C22semidirect
132. #2567C22semidirect
133. #2567C22semidirect
134. #2567C22semidirect
135. #2565C22semidirect
136. #2565C22semidirect
138. #2552C22semidirect
139. #2550C22semidirect
143. #2520C22semidirect
144. #2520C22semidirect
145. #2509C22semidirect
146. #2508C22semidirect
147. #2508C22semidirect
148. #2507C22semidirect
153. #2462C22semidirect
154. #2462C22semidirect
155. #2462C22semidirect
156. #2462C22semidirect
157. #2451C22semidirect
158. #2446C22semidirect
232. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#517892
#517882
#515952
#515942
#470222
#470212
#468462
#468452
#389632
#389592
#378772
#378762
#376892
#376882
#374782
#371942
#371352
#351792
#351512
#350902
#350132
#343592
C2×#23232