Finite Group Databasebeta

← #8096541

Subgroups — #8096541

Order 512.

4271 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53131C212yesmaximal, complemented
2#53121C212yesmaximal, complemented
3#52996C212yesmaximal, complemented
4#52428C214yesmaximal, complemented
5#52428C214yesmaximal, complemented
6#52428C214yesmaximal, complemented
7#52305C211yesmaximal, characteristic, complemented
8C2×#2726C212yesmaximal, complemented
9#46200C212yesmaximal, complemented
10#46200C212yesmaximal, complemented
11#46200C214yesmaximal, complemented
12#46200C212yesmaximal, complemented
13#46181C212yesmaximal, complemented
14#46175C212yesmaximal, complemented
15#46169C214yesmaximal, complemented
16#46157C211yesmaximal, characteristic, complemented
17#46153C212yesmaximal, complemented
18#46153C211yesmaximal, characteristic, complemented
19C4⋊#564C211yesmaximal, characteristic, complemented
20C22⋊#564C214yesmaximal, complemented
21#36290C211yesmaximal, characteristic
22#36290C211yesmaximal, characteristic
23#36290C211yesmaximal, characteristic
24#36290C212yesmaximal
25#36239C212yesmaximal
26D4×#125C212yesmaximal
27#35858C212yesmaximal
28#35858C212yesmaximal
29#35858C212yesmaximal
30C2×#564C2212yes—
31C22×#125C2214yes—
32#2864C2212yes—
33#2859C2212yes—
34#2859C2211yescharacteristic
35#2859C2211yescharacteristic
36#2859C2211yescharacteristic
37#2859C2212yes—
38#2851C2214yes—
39#2851C2214yes—
40#2851C2214yes—
41#2851C2212yes—
42#2851C2212yes—
43#2851C2212yes—
44#2845C2212yes—
45#2845C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2839C2214yes—
51#2839C2214yes—
52#2839C2214yes—
53#2839C2214yes—
54#2839C2214yes—
55#2839C2214yes—
56#2839C2214yes—
57#2822C2214yes—
58#2822C2214yes—
59#2822C2212yes—
60#2822C2212yes—
61#2822C2214yes—
62#2810C2214yes—
63#2810C2212yes—
64#2810C2211yescharacteristic
65#2767C2214yes—
66#2767C2212yes—
67#2767C2212yes—
68#2767C2212yes—
69#2767C2214yes—
70#2767C2214yes—
71#2767C2214yes—
72#2767C2214yes—
73#2767C2214yes—
74#2767C2214yes—
75#2726C2214yes—
76#2726C2214yes—
77#2726C2214yes—
78#2726C2214yes—
79#2726C2214yes—
80#2726C2212yes—
81#2726C2212yes—
82#2726C2214yes—
83#2726C2212yes—
84#2726C2212yes—
85#2726C2214yes—
86#2726C2214yes—
87#2726C2214yes—
88#2726C2214yes—
89#2726C2212yes—
90#2726C2211yescharacteristic
91#2726C2211yescharacteristic
92#2726C2211yescharacteristic
93#2726C2214yes—
94#2726C2214yes—
95#2726C2214yes—
96#2726C2214yes—
97#2719C2214yes—
98#2719C2214yes—
99#2719C2212yes—
100#2719C2214yes—
101#2719C2214yes—
102#2719C2214yes—
103#2719C2214yes—
104#2719C2214yes—
105#2719C2214yes—
106#2719C2214yes—
107#2719C2212yes—
108#2719C2212yes—
109#2719C2214yes—
110#2719C2214yes—
111#2719C2214yes—
112#2719C2214yes—
113#2719C2214yes—
114#2647C2212yes—
115#2647C2212yes—
116#2647C2212yes—
117#2646C2214yes—
118#2646C2214yes—
119#2646C2214yes—
120#2571C2211yescharacteristic
121#2571C2211yescharacteristic
122#2571C2212yes—
123#2571C2211yescharacteristic
124#2570C2212yes—
125#2570C2212yes—
126#2570C2212yes—
127#2570C2212yes—
128#2570C2212yes—
129#2569C2214yes—
130#2569C2214yes—
131#2569C2214yes—
132#2569C2214yes—
133#2569C2214yes—
134#2552C2212yes—
135#2552C2212yes—
136#2552C2212yes—
137#2552C2212yes—
138#2552C2212yes—
139#2552C2212yes—
140#2552C2211yescharacteristic
141#2552C2211yescharacteristic
142#2552C2211yescharacteristic
143#2509C2212yes—
144#2509C2212yes—
145#2509C2212yes—
146#2509C2212yes—
147#2509C2212yes—
148#2509C2212yes—
149#2508C2212yes—
150#2508C2212yes—
151#2508C2212yes—
152#2508C2212yes—
153#2507C2212yes—
154#2507C2212yes—
155#2507C2212yes—
156#2507C2212yes—
157#2507C2212yes—
158#2507C2212yes—
159#2507C2212yes—
160#2507C2212yes—
161#2507C2212yes—
162#2507C2212yes—
163#2507C2212yes—
164#2507C2212yes—
165#2506C2212yes—
166#2506C2212yes—
167#2506C2212yes—
168#2506C2212yes—
169#2506C2212yes—
170#2506C2212yes—
171#2506C2212yes—
172#2506C2212yes—
173#2505C2214yes—
174#2505C2214yes—
175#2505C2214yes—
176#2505C2214yes—
177#2505C2214yes—
178#2505C2214yes—
179#2505C2214yes—
180#2505C2214yes—
181#2505C2214yes—
182#2505C2214yes—
183#2473C2214yes—
184#2473C2214yes—
185#2473C2214yes—
186#2473C2214yes—
187#2473C2214yes—
188#2473C2214yes—
189#2473C2214yes—
190#2473C2214yes—
191#2473C2214yes—
192#2473C2214yes—
193#2473C2214yes—
194#2473C2214yes—
195#2473C2214yes—
196#2473C2214yes—
197#2473C2214yes—
198#2473C2214yes—
199#2473C2214yes—
200#2473C2214yes—
201#2473C2214yes—
202#2473C2214yes—
203#2442C2214yes—
204#2442C2214yes—
205#2442C2214yes—
206#2442C2214yes—
207#2442C2214yes—
208#2442C2212yes—
209#2442C2214yes—
210#2442C2212yes—
211#2442C2212yes—
212#2442C2214yes—
213#2442C2212yes—
214#2442C2212yes—
215#2442C2212yes—
216#2402C2212yes—
217#2402C2212yes—
218#2402C2212yes—
219C2×#398C2214yes—
220C2×#398C2214yes—
221C2×#398C2214yes—
222#2382C2214yes—
223#2382C2212yes—
224#2382C2214yes—
225#2382C2212yes—
226#2382C2214yes—
227#2349C2212yes—
228#2349C2212yes—
229#2349C2212yes—
230#2349C2212yes—
231#2349C2212yes—
232D4×C4⋊C4C2211yescharacteristic
233D4×C4⋊C4C2212yes—
234D4×C4⋊C4C2212yes—
235D4×C4⋊C4C2212yes—
236D4×C4⋊C4C2212yes—
237D4×C4⋊C4C2212yes—
238D4×C4⋊C4C2211yescharacteristic
239D4×C4⋊C4C2211yescharacteristic
240D4×C4⋊C4C2211yescharacteristic
241D4×C4⋊C4C2212yes—
242D4×C4⋊C4C2212yes—
243D4×C4⋊C4C2211yescharacteristic
244D4×C4⋊C4C2211yescharacteristic
245C4×#125C2212yes—
246C4×#125C2211yescharacteristic
247C4×#125C2212yes—
248C4×#125C2211yescharacteristic
249C4×#125C2211yescharacteristic
250C4×#125C2212yes—
251C2×#389C2212yes—
252C2×#389C2212yes—
253C2×#389C2212yes—
254C2×#389C2214yes—
255C2×#387C2214yes—
256#2275C2212yes—
257C42×D4C2212yes—
258C42×D4C2211yescharacteristic
259#564—48no—
260C2×#125—416no—
261C2×#125C2311yescharacteristic
262C2×#125C2312yes—
263C2×#125C2312yes—
264C2×#125C2311yescharacteristic
265C2×#125C2314yes—
266C2×#125C2311yescharacteristic
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2314yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2314yes—
306C22×C4⋊C4C2314yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2314yes—
310C22×C4⋊C4C2312yes—
311C22×C42C2314yes—
312C22×C42C2312yes—
313#400C2312yes—
314#400C2312yes—
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#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#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2312yes—
364#400C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2312yes—
412#398C2312yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2312yes—
428#398C2312yes—
429#398C2312yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2312yes—
437#398C2312yes—
438#398C2312yes—
439#389C2312yes—
440#389C2311yescharacteristic
441#389C2311yescharacteristic
442#389C2311yescharacteristic
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2311yescharacteristic
447#389C2311yescharacteristic
448#389C2312yes—
449#389C2312yes—
450#389C2311yescharacteristic
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#387C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
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#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#384C2311yescharacteristic
615#384C2311yescharacteristic
616#384C2312yes—
617#384C2312yes—
618#384C2312yes—
619#384C2311yescharacteristic
620#384C2311yescharacteristic
621#384C2312yes—
622#384C2312yes—
623#384C2311yescharacteristic
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2312yes—
627#382C2311yescharacteristic
628#382C2311yescharacteristic
629#382C2312yes—
630#382C2312yes—
631#382C2311yescharacteristic
632#382C2312yes—
633#382C2314yes—
634#382C2314yes—
635#382C2312yes—
636#382C2314yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2314yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#380C2312yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2312yes—
668#380C2314yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705#376C2312yes—
706C2×#95C2314yes—
707C2×#95C2314yes—
708C2×#95C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C43C2311yescharacteristic
713C43C2312yes—
714C22×D4C2411yescharacteristic
715C23×C4C2412yes—
716C23×C4C2414yes—
717C23×C4C2412yes—
718C23×C4C2414yes—
719C23×C4C2412yes—
720C23×C4C2414yes—
721C23×C4C2414yes—
722C23×C4C2414yes—
723C23×C4C2414yes—
724#125—28no—
725#125—216no—
726#125—24no—
727#125—24no—
728#125—28no—
729#125—48no—
730#125—48no—
731#125—42no—
732#125—44no—
733#125—48no—
734#125—48no—
735#125—44no—
736#125—44no—
737#125—48no—
738#125—48no—
739#125—48no—
740#125—48no—
741#125—44no—
742#125—48no—
743#125—48no—
744#125—48no—
745#125—48no—
746#125—82no—
747#125—82no—
748#125—82no—
749#125—84no—
750#125—84no—
751#125—84no—
752C4×D4—24no—
753C4×D4—28no—
754C4×D4—24no—
755C4×D4—28no—
756C4×D4—24no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—28no—
760C4×D4—28no—
761C2×C4⋊C4—28no—
762C2×C4⋊C4—28no—
763C2×C4⋊C4—48no—
764C2×C4⋊C4—44no—
765C2×C4⋊C4—48no—
766C2×C4⋊C4—48no—
767C2×C4⋊C4—48no—
768C2×C4⋊C4—48no—
769C2×C4⋊C4—48no—
770C2×C4⋊C4—82no—
771C2×C4⋊C4—82no—
772C2×C4⋊C4—82no—
773C2×C4⋊C4—84no—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
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×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C42—48no—
885C2×C42—82no—
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2412yes—
891C2×C42C2411yescharacteristic
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2414yes—
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995C24C2512yes—
996C2×D42−1+414yes—
997C2×D42−1+414yes—
998C2×D42−1+414yes—
999C22×C4—24no—
1000C22×C4—28no—
1001C22×C4—24no—
1002C22×C4—28no—
1003C22×C4—24no—
1004C22×C4—28no—
1005C22×C4—28no—
1006C22×C4—28no—
1007C22×C4—28no—
1008C22×C4—28no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—44no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2512yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—22no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—22no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—22no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—41no—
1108C4⋊C4—41no—
1109C4⋊C4—41no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—41no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4H(5,𝔽2)14yes—
1154C4⋊C42−1+414yes—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—28no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C42—24no—
1165C42—28no—
1166C42—22no—
1167C42—24no—
1168C42—24no—
1169C42—22no—
1170C42—22no—
1171C42—22no—
1172C42—24no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—22no—
1177C42—24no—
1178C42—22no—
1179C42—44no—
1180C42—44no—
1181C42—41no—
1182C42—42no—
1183C42—42no—
1184C42—42no—
1185C42—42no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—42no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23C2×2−1+414yes—
1195C23C2×2−1+414yes—
1196C23C2×2−1+414yes—
1197C23C2611yescharacteristic
1198D4#564116yescomplemented
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—416no—
1276C2×C4—416no—
1277C2×C4—48no—
1278C2×C4—48no—
1279C2×C4—48no—
1280C2×C4—88no—
1281C2×C4—88no—
1282C2×C4—88no—
1283C2×C4—88no—
1284C2×C4C2×H(5,𝔽2)14yes—
1285C2×C4C2×H(5,𝔽2)12yes—
1286C2×C4C2×2−1+414yes—
1287C2×C4C2×2−1+412yes—
1288C2×C4C2×2−1+412yes—
1289C2×C4C2×2−1+412yes—
1290C2×C4C2×2−1+412yes—
1291C2×C4#58512yes—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22C2×#56418yes—
1299C22C22×H(5,𝔽2)11yescharacteristic
1300C22C22×2−1+411yescharacteristic
1301C22C22×2−1+411yescharacteristic
1302C22C22×2−1+411yescharacteristic
1303C22C22×2−1+411yescharacteristic
1304C22C2×#58511yescharacteristic
1305C22H(7,𝔽2)11yescharacteristic
1306C4—24no—
1307C4—24no—
1308C4—22no—
1309C4—22no—
1310C4—22no—
1311C4—41no—
1312C4—44no—
1313C4—44no—
1314C4—42no—
1315C4—41no—
1316C4—42no—
1317C4—44no—
1318C4—41no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—44no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—44no—
1332C4—42no—
1333C4C2×#56414yes—
1334C2—28no—
1335C2C22×#56411yescharacteristic
1336C2#6294411yescharacteristic
1337C2#6294511yescharacteristic
1338C2#6294811yescharacteristic
1339C2#6301311yescharacteristic
1340C2#6301611yescharacteristic
1341C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53131C2semidirect
2. #53121C2semidirect
3. #52996C2semidirect
4. #52428C2semidirect
5. #52428C2semidirect
6. #52428C2semidirect
7. #52305C2semidirect
8. C2×#2726C2semidirect
9. #46200C2semidirect
10. #46200C2semidirect
11. #46200C2semidirect
12. #46200C2semidirect
13. #46181C2semidirect
14. #46175C2semidirect
15. #46169C2semidirect
16. #46157C2semidirect
17. #46153C2semidirect
18. #46153C2semidirect
19. C4⋊#564C2semidirect
20. C22⋊#564C2semidirect
1198. D4#564semidirect

Maximal subgroups

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

subgroupindex
#531312
#531212
#529962
#524282
#523052
C2×#27262
#462002
#461812
#461752
#461692
#461572
#461532
C4⋊#5642
C22⋊#5642
#362902
#362392
D4×#1252
#358582