Finite Group Databasebeta

← #8093840

Subgroups — #8093840

Order 512.

5844 conjugacy classes of subgroups.

The subgroup lattice has 1428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52913C212yesmaximal, complemented
2#52912C212yesmaximal, complemented
3#52799C214yesmaximal, complemented
4#52549C214yesmaximal, complemented
5#52369C214yesmaximal, complemented
6#52369C214yesmaximal, complemented
7#52339C212yesmaximal, complemented
8#52309C212yesmaximal, complemented
9#45743C214yesmaximal, complemented
10#45550C214yesmaximal, complemented
11#45550C214yesmaximal, complemented
12#45538C214yesmaximal, complemented
13#45536C214yesmaximal, complemented
14#45473C214yesmaximal, complemented
15#35463C211yesmaximal, characteristic, complemented
16#35448C211yesmaximal, characteristic, complemented
17#35370C212yesmaximal, complemented
18#35358C212yesmaximal, complemented
19#35088C212yesmaximal, complemented
20#35000C212yesmaximal, complemented
21#34984C212yesmaximal, complemented
22C2×#2430C211yesmaximal, characteristic, complemented
23C2×#2419C212yesmaximal, complemented
24C23×#41C2211yescharacteristic
25C2×#534C2212yes—
26C2×#534C2212yes—
27C2×#534C2212yes—
28C2×#534C2211yescharacteristic
29C22×#123C2212yes—
30C22×#123C2211yescharacteristic
31C22×#121C2212yes—
32C2×#518C2211yescharacteristic
33C22×C4×D4C2212yes—
34#2854C2214yescomplemented
35#2854C2214yescomplemented
36#2849C2214yescomplemented
37#2849C2214yescomplemented
38#2847C2214yescomplemented
39#2847C2214yescomplemented
40#2843C2212yescomplemented
41#2841C2212yescomplemented
42#2841C2214yescomplemented
43#2838C2214yescomplemented
44#2838C2214yescomplemented
45#2838C2214yescomplemented
46#2830C2214yescomplemented
47#2830C2212yescomplemented
48#2829C2214yescomplemented
49#2829C2214yescomplemented
50#2829C2214yescomplemented
51#2828C2214yescomplemented
52#2828C2212yescomplemented
53#2827C2214yescomplemented
54#2827C2214yescomplemented
55#2827C2214yescomplemented
56#2826C2212yescomplemented
57#2826C2214yescomplemented
58#2825C2214yescomplemented
59#2824C2212yescomplemented
60#2824C2214yescomplemented
61#2823C2212yescomplemented
62#2815C2212yescomplemented
63#2815C2214yescomplemented
64#2797C2214yescomplemented
65#2797C2214yescomplemented
66#2797C2214yescomplemented
67#2796C2214yescomplemented
68#2796C2214yescomplemented
69#2796C2214yescomplemented
70#2795C2214yescomplemented
71#2795C2212yescomplemented
72#2792C2214yescomplemented
73#2792C2212yescomplemented
74#2790C2214yescomplemented
75#2790C2214yescomplemented
76#2790C2214yescomplemented
77#2784C2214yescomplemented
78#2784C2212yescomplemented
79#2780C2214yescomplemented
80#2780C2214yescomplemented
81#2780C2214yescomplemented
82#2760C2212yescomplemented
83#2752C2212yescomplemented
84#2752C2214yescomplemented
85#2749C2214yescomplemented
86#2749C2214yescomplemented
87#2749C2214yescomplemented
88#2746C2214yescomplemented
89#2746C2214yescomplemented
90#2746C2214yescomplemented
91#2742C2214yescomplemented
92#2742C2212yescomplemented
93#2737C2214yescomplemented
94#2737C2214yescomplemented
95#2737C2214yescomplemented
96#2714C2214yescomplemented
97#2714C2214yescomplemented
98#2714C2214yescomplemented
99#2699C2214yescomplemented
100#2699C2212yescomplemented
101#2691C2214yescomplemented
102#2691C2214yescomplemented
103#2691C2214yescomplemented
104#2688C2214yescomplemented
105#2688C2214yescomplemented
106#2688C2214yescomplemented
107#2675C2212yescomplemented
108#2618C2214yescomplemented
109#2618C2214yescomplemented
110#2617C2214yescomplemented
111#2617C2214yescomplemented
112#2614C2214yescomplemented
113#2613C2214yescomplemented
114#2543C2214yescomplemented
115#2543C2214yescomplemented
116#2543C2214yescomplemented
117#2543C2214yescomplemented
118#2539C2212yes—
119#2539C2212yes—
120#2539C2214yescomplemented
121#2539C2214yescomplemented
122#2534C2214yescomplemented
123#2534C2214yescomplemented
124#2510C2214yescomplemented
125#2510C2214yescomplemented
126#2510C2214yescomplemented
127#2510C2214yescomplemented
128#2501C2212yes—
129#2501C2212yes—
130#2501C2214yescomplemented
131#2501C2214yescomplemented
132#2493C2214yescomplemented
133#2493C2214yescomplemented
134#2486C2214yescomplemented
135#2484C2212yescomplemented
136#2484C2212yescomplemented
137#2483C2212yescomplemented
138#2483C2212yescomplemented
139#2481C2214yescomplemented
140#2481C2214yescomplemented
141#2481C2214yescomplemented
142#2481C2214yescomplemented
143#2480C2214yescomplemented
144#2480C2214yescomplemented
145#2430C2214yescomplemented
146#2430C2214yescomplemented
147#2430C2214yescomplemented
148#2430C2214yescomplemented
149#2430C2214yescomplemented
150#2430C2214yescomplemented
151#2430C2214yescomplemented
152#2430C2214yescomplemented
153#2425C2214yes—
154#2425C2214yes—
155#2425C2214yescomplemented
156#2425C2214yescomplemented
157#2425C2214yescomplemented
158#2425C2214yescomplemented
159#2424C2214yes—
160#2424C2214yes—
161#2424C2214yescomplemented
162#2424C2214yescomplemented
163#2424C2214yescomplemented
164#2424C2214yescomplemented
165#2419C2214yescomplemented
166#2419C2214yescomplemented
167#2419C2214yescomplemented
168#2419C2214yescomplemented
169#2419C2214yescomplemented
170#2419C2214yescomplemented
171#2419C2214yescomplemented
172#2419C2214yescomplemented
173#2419C2214yescomplemented
174#2419C2214yescomplemented
175#2419C2214yescomplemented
176#2419C2214yescomplemented
177#2416C2214yescomplemented
178#2416C2214yescomplemented
179#2416C2214yescomplemented
180#2416C2214yescomplemented
181#2413C2214yescomplemented
182#2412C2214yescomplemented
183#2411C2214yescomplemented
184#2410C2214yescomplemented
185#2408C2214yescomplemented
186#2406C2214yescomplemented
187#2406C2214yescomplemented
188#2404C2214yescomplemented
189#2404C2214yescomplemented
190C2×#400C2212yescomplemented
191C2×#398C2212yescomplemented
192C2×#397C2212yescomplemented
193C2×#397C2212yescomplemented
194C2×#395C2211yescharacteristic, complemented
195C2×#394C2211yescharacteristic, complemented
196C2×#393C2211yescharacteristic, complemented
197C2×#392C2211yescharacteristic, complemented
198#2383C2214yescomplemented
199#2377C2214yescomplemented
200#2377C2214yescomplemented
201#2377C2214yescomplemented
202#2315C2212yes—
203#2308C2212yes—
204#2308C2212yes—
205#2308C2211yescharacteristic
206C2×#387C2212yescomplemented
207C2×#387C2212yescomplemented
208C2×#386C2212yes—
209C2×#386C2212yes—
210C2×#386C2212yescomplemented
211C2×#385C2212yes—
212C2×#385C2212yescomplemented
213C2×#385C2212yescomplemented
214C2×#381C2212yes—
215C2×#381C2212yescomplemented
216C2×#380C2212yes—
217#2273C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C22×#41—48no—
220C22×#41—44no—
221C22×#41C2314yes—
222C22×#41C2314yes—
223C23×Q8C2311yescharacteristic
224C23×D4C2312yes—
225C23×D4C2311yescharacteristic
226C23×D4C2312yes—
227C23×D4C2311yescharacteristic
228C23×D4C2312yes—
229C24×C4C2311yescharacteristic
230C24×C4C2312yes—
231C24×C4C2312yes—
232C24×C4C2312yes—
233#534—48no—
234#534—48no—
235#534—48no—
236#534—44no—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#123—48no—
240C2×#123—44no—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#121—48no—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259C2×#121C2314yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#120C2314yes—
274C2×#120C2314yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277C2×#120C2314yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280#518—44no—
281C2×C4×D4—48no—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×#117C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2312yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2312yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2311yescharacteristic
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2312yes—
315C22×C42C2312yes—
316#401C2314yes—
317#401C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2312yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#399C2314yes—
332#399C2312yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2312yes—
337#399C2314yes—
338#398C2314yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2312yes—
396#394C2312yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2312yes—
421#393C2312yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2312yes—
428#392C2312yes—
429#392C2312yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2312yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2312yes—
443#392C2314yes—
444#390C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
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#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#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#385C2314yes—
542#385C2312yes—
543#385C2312yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
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#384C2312yes—
569#384C2312yes—
570#384C2314yes—
571#383C2314yes—
572#383C2314yes—
573#381C2314yes—
574#381C2314yes—
575#381C2312yes—
576#381C2312yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2312yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#379C2314yes—
600#379C2314yes—
601#379C2312yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C2×#95C2311yescharacteristic
607C2×#95C2311yescharacteristic
608C2×#95C2312yes—
609C2×#95C2312yes—
610C2×#95C2312yes—
611C2×#95C2312yes—
612C2×#95C2312yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C2×#95C2312yes—
624C2×#95C2312yes—
625C25C2411yescharacteristic
626C25C2412yes—
627C25C2412yes—
628C25C2411yescharacteristic
629C2×#41—48no—
630C2×#41—48no—
631C2×#41—48no—
632C2×#41—48no—
633C2×#41—48no—
634C2×#41—48no—
635C2×#41—464no—
636C22×Q8—42no—
637C22×Q8—44no—
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×D4—28no—
641C22×D4—24no—
642C22×D4—28no—
643C22×D4—28no—
644C22×D4—28no—
645C22×D4—28no—
646C22×D4—28no—
647C22×D4—28no—
648C22×D4—44no—
649C22×D4—42no—
650C22×D4—44no—
651C22×D4—44no—
652C22×D4—82no—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C22×D4C2414yes—
663C22×D4C2412yes—
664C22×D4C2412yes—
665C22×D4C2414yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C22×D4C2412yes—
669C22×D4C2412yes—
670C23×C4—24no—
671C23×C4—28no—
672C23×C4—28no—
673C23×C4—44no—
674C23×C4—44no—
675C23×C4—44no—
676C23×C4—44no—
677C23×C4—44no—
678C23×C4—44no—
679C23×C4—82no—
680C23×C4—82no—
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2414yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2414yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708#126—48no—
709#126—84no—
710#123—48no—
711#123—48no—
712#123—48no—
713#123—48no—
714#123—48no—
715#123—48no—
716#123—48no—
717#123—48no—
718#123—48no—
719#123—48no—
720#123—48no—
721#123—48no—
722#123—48no—
723#121—48no—
724#121—48no—
725#121—48no—
726#121—48no—
727#121—48no—
728#121—48no—
729#121—48no—
730#121—48no—
731#121—44no—
732#121—44no—
733#121—48no—
734#121—48no—
735#121—48no—
736#121—48no—
737#121—48no—
738#121—84no—
739#121—84no—
740#121—84no—
741#120—48no—
742#120—48no—
743#120—48no—
744#120—48no—
745#120—48no—
746#120—48no—
747#120—48no—
748C4×D4—48no—
749C4×D4—48no—
750C4×D4—48no—
751C4×D4—48no—
752C4×D4—48no—
753C4×D4—48no—
754#117—44no—
755C2×C4⋊C4—44no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4—44no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4—44no—
761C2×C4⋊C4—42no—
762C2×C4⋊C4—42no—
763C2×C4⋊C4—82no—
764C2×C4⋊C4—82no—
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⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C22⋊C4—28no—
799C2×C22⋊C4—28no—
800C2×C22⋊C4—24no—
801C2×C22⋊C4—28no—
802C2×C22⋊C4—44no—
803C2×C22⋊C4—44no—
804C2×C22⋊C4—44no—
805C2×C22⋊C4—44no—
806C2×C22⋊C4—44no—
807C2×C22⋊C4—44no—
808C2×C22⋊C4—42no—
809C2×C22⋊C4—42no—
810C2×C22⋊C4—44no—
811C2×C22⋊C4—44no—
812C2×C22⋊C4—82no—
813C2×C22⋊C4—82no—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C42—44no—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2412yes—
875#95C2411yescharacteristic
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2411yescharacteristic
881#95C2412yes—
882#95C2412yes—
883#95C2411yescharacteristic
884#95C2411yescharacteristic
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#95C2412yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
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#95C2412yes—
927C24—24no—
928C24—24no—
929C24—22no—
930C24—24no—
931C24—24no—
932C24—24no—
933C24—24no—
934C24—24no—
935C24—42no—
936C24—41no—
937C24—41no—
938C24—42no—
939C24—42no—
940C24—42no—
941C24—42no—
942C24—42no—
943C24—42no—
944C24—42no—
945C24—42no—
946C24—42no—
947C24—41no—
948C24—41no—
949C24H(5,𝔽2)14yes—
950C24H(5,𝔽2)18yes—
951C24C2514yes—
952C24C2512yes—
953C24C2514yes—
954C24C2511yescharacteristic
955C24C2512yes—
956#41—464no—
957#41—464no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—416no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—28no—
968C2×D4—28no—
969C2×D4—28no—
970C2×D4—28no—
971C2×D4—28no—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—28no—
978C2×D4—28no—
979C2×D4—42no—
980C2×D4—42no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—42no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—42no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—416no—
1012C2×D4—432no—
1013C2×D4—416no—
1014C2×D4—432no—
1015C2×D4—816no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—22no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—41no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—41no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—44no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—432no—
1093C22×C4—416no—
1094C22×C4—816no—
1095C22×C4—816no—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C42—44no—
1202C42—44no—
1203C42—42no—
1204C42—44no—
1205C42—44no—
1206C42—42no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—21no—
1212C23—22no—
1213C23—21no—
1214C23—22no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—22no—
1230C23—24no—
1231C23—22no—
1232C23—24no—
1233C23—48no—
1234C23—44no—
1235C23—44no—
1236C23—48no—
1237C23—48no—
1238C23—48no—
1239C23—48no—
1240C23—48no—
1241C23—48no—
1242C23—48no—
1243C23—44no—
1244C23—84no—
1245C23—84no—
1246C23—84no—
1247C23—84no—
1248C23—84no—
1249C23—84no—
1250C23—84no—
1251C23—84no—
1252C23—84no—
1253C23—82no—
1254C23—82no—
1255C23—84no—
1256C23#560116yes—
1257C23C2×H(5,𝔽2)12yes—
1258C23C2×H(5,𝔽2)14yes—
1259C23C2×H(5,𝔽2)14yes—
1260C23C2×H(5,𝔽2)14yes—
1261C23C2×H(5,𝔽2)14yes—
1262C23C2611yescharacteristic
1263Q8—48no—
1264Q8—48no—
1265D4—48no—
1266D4—48no—
1267D4—416no—
1268D4—416no—
1269D4—416no—
1270D4—416no—
1271D4—416no—
1272D4—88no—
1273D4—88no—
1274D4—164no—
1275D4—162no—
1276D4—164no—
1277D4—162no—
1278D4—164no—
1279D4—164no—
1280D4—164no—
1281D4—164no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—48no—
1332C2×C4—48no—
1333C2×C4—48no—
1334C2×C4—416no—
1335C2×C4—416no—
1336C2×C4—44no—
1337C2×C4—44no—
1338C2×C4—48no—
1339C2×C4—48no—
1340C2×C4—48no—
1341C2×C4—44no—
1342C2×C4—48no—
1343C2×C4—88no—
1344C2×C4—84no—
1345C2×C4—82no—
1346C2×C4—84no—
1347C2×C4—82no—
1348C2×C4—84no—
1349C2×C4—84no—
1350C2×C4—84no—
1351C2×C4—84no—
1352C2×C4—84no—
1353C2×C4—84no—
1354C2×C4—84no—
1355C2×C4—88no—
1356C2×C4—162no—
1357C2×C4—162no—
1358C2×C4#58514yes—
1359C22—22no—
1360C22—24no—
1361C22—22no—
1362C22—24no—
1363C22—24no—
1364C22—24no—
1365C22—24no—
1366C22—24no—
1367C22—24no—
1368C22—24no—
1369C22—416no—
1370C22—42no—
1371C22—44no—
1372C22—44no—
1373C22—42no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22—44no—
1381C22—44no—
1382C22—44no—
1383C22—44no—
1384C22—44no—
1385C22—44no—
1386C22—44no—
1387C22—44no—
1388C22—42no—
1389C22—816no—
1390C22—816no—
1391C22—164no—
1392C22C2×#56014yes—
1393C22C2×#56018yes—
1394C22C22×H(5,𝔽2)11yescharacteristic
1395C22C22×H(5,𝔽2)12yes—
1396C22C2×#58512yes—
1397C22H(7,𝔽2)11yescharacteristic
1398C222−1+611yescharacteristic
1399C4—24no—
1400C4—44no—
1401C4—42no—
1402C4—44no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—44no—
1409C4—44no—
1410C4—44no—
1411C4—42no—
1412C4—41no—
1413C4—41no—
1414C4—44no—
1415C4—42no—
1416C4—44no—
1417C2—24no—
1418C2—28no—
1419C2—84no—
1420C2—84no—
1421C2—82no—
1422C2C22×#56011yescharacteristic
1423C2#6282211yescharacteristic
1424C2#6286611yescharacteristic
1425C2#6290012yes—
1426C2#6290112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52913C2semidirect
2. #52912C2semidirect
3. #52799C2semidirect
4. #52549C2semidirect
5. #52369C2semidirect
6. #52369C2semidirect
7. #52339C2semidirect
8. #52309C2semidirect
9. #45743C2semidirect
10. #45550C2semidirect
11. #45550C2semidirect
12. #45538C2semidirect
13. #45536C2semidirect
14. #45473C2semidirect
15. #35463C2semidirect
16. #35448C2semidirect
17. #35370C2semidirect
18. #35358C2semidirect
19. #35088C2semidirect
20. #35000C2semidirect
21. #34984C2semidirect
22. C2×#2430C2semidirect
23. C2×#2419C2semidirect
34. #2854C22semidirect
35. #2854C22semidirect
36. #2849C22semidirect
37. #2849C22semidirect
38. #2847C22semidirect
39. #2847C22semidirect
40. #2843C22semidirect
41. #2841C22semidirect
42. #2841C22semidirect
43. #2838C22semidirect
44. #2838C22semidirect
45. #2838C22semidirect
46. #2830C22semidirect
47. #2830C22semidirect
48. #2829C22semidirect
49. #2829C22semidirect
50. #2829C22semidirect
51. #2828C22semidirect
52. #2828C22semidirect
53. #2827C22semidirect
54. #2827C22semidirect
55. #2827C22semidirect
56. #2826C22semidirect
57. #2826C22semidirect
58. #2825C22semidirect
59. #2824C22semidirect
60. #2824C22semidirect
61. #2823C22semidirect
62. #2815C22semidirect
63. #2815C22semidirect
64. #2797C22semidirect
65. #2797C22semidirect
66. #2797C22semidirect
67. #2796C22semidirect
68. #2796C22semidirect
69. #2796C22semidirect
70. #2795C22semidirect
71. #2795C22semidirect
72. #2792C22semidirect
73. #2792C22semidirect
74. #2790C22semidirect
75. #2790C22semidirect
76. #2790C22semidirect
77. #2784C22semidirect
78. #2784C22semidirect
79. #2780C22semidirect
80. #2780C22semidirect
81. #2780C22semidirect
82. #2760C22semidirect
83. #2752C22semidirect
84. #2752C22semidirect
85. #2749C22semidirect
86. #2749C22semidirect
87. #2749C22semidirect
88. #2746C22semidirect
89. #2746C22semidirect
90. #2746C22semidirect
91. #2742C22semidirect
92. #2742C22semidirect
93. #2737C22semidirect
94. #2737C22semidirect
95. #2737C22semidirect
96. #2714C22semidirect
97. #2714C22semidirect
98. #2714C22semidirect
99. #2699C22semidirect
100. #2699C22semidirect
101. #2691C22semidirect
102. #2691C22semidirect
103. #2691C22semidirect
104. #2688C22semidirect
105. #2688C22semidirect
106. #2688C22semidirect
107. #2675C22semidirect
108. #2618C22semidirect
109. #2618C22semidirect
110. #2617C22semidirect
111. #2617C22semidirect
112. #2614C22semidirect
113. #2613C22semidirect
114. #2543C22semidirect
115. #2543C22semidirect
116. #2543C22semidirect
117. #2543C22semidirect
120. #2539C22semidirect
121. #2539C22semidirect
122. #2534C22semidirect
123. #2534C22semidirect
124. #2510C22semidirect
125. #2510C22semidirect
126. #2510C22semidirect
127. #2510C22semidirect
130. #2501C22semidirect
131. #2501C22semidirect
132. #2493C22semidirect
133. #2493C22semidirect
134. #2486C22semidirect
135. #2484C22semidirect
136. #2484C22semidirect
137. #2483C22semidirect
138. #2483C22semidirect
139. #2481C22semidirect
140. #2481C22semidirect
141. #2481C22semidirect
142. #2481C22semidirect
143. #2480C22semidirect
144. #2480C22semidirect
145. #2430C22semidirect
146. #2430C22semidirect
147. #2430C22semidirect
148. #2430C22semidirect
149. #2430C22semidirect
150. #2430C22semidirect
151. #2430C22semidirect
152. #2430C22semidirect
155. #2425C22semidirect
156. #2425C22semidirect
157. #2425C22semidirect
158. #2425C22semidirect
161. #2424C22semidirect
162. #2424C22semidirect
163. #2424C22semidirect
164. #2424C22semidirect
165. #2419C22semidirect
166. #2419C22semidirect
167. #2419C22semidirect
168. #2419C22semidirect
169. #2419C22semidirect
170. #2419C22semidirect
171. #2419C22semidirect
172. #2419C22semidirect
173. #2419C22semidirect
174. #2419C22semidirect
175. #2419C22semidirect
176. #2419C22semidirect
177. #2416C22semidirect
178. #2416C22semidirect
179. #2416C22semidirect
180. #2416C22semidirect
181. #2413C22semidirect
182. #2412C22semidirect
183. #2411C22semidirect
184. #2410C22semidirect
185. #2408C22semidirect
186. #2406C22semidirect
187. #2406C22semidirect
188. #2404C22semidirect
189. #2404C22semidirect
190. C2×#400C22semidirect
191. C2×#398C22semidirect
192. C2×#397C22semidirect
193. C2×#397C22semidirect
194. C2×#395C22semidirect
195. C2×#394C22semidirect
196. C2×#393C22semidirect
197. C2×#392C22semidirect
198. #2383C22semidirect
199. #2377C22semidirect
200. #2377C22semidirect
201. #2377C22semidirect
206. C2×#387C22semidirect
207. C2×#387C22semidirect
210. C2×#386C22semidirect
212. C2×#385C22semidirect
213. C2×#385C22semidirect
215. C2×#381C22semidirect

Maximal subgroups

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

subgroupindex
#529132
#529122
#527992
#525492
#523692
#523392
#523092
#457432
#455502
#455382
#455362
#454732
#354632
#354482
#353702
#353582
#350882
#350002
#349842
C2×#24302
C2×#24192