Finite Group Databasebeta

← #8935526

Subgroups — #8935526

Order 512.

5434 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58590C212yesmaximal, complemented
2#58588C212yesmaximal, complemented
3#55126C214yesmaximal, complemented
4#55122C214yesmaximal, complemented
5#51927C214yesmaximal, complemented
6#51348C212yesmaximal, complemented
7#49594C212yesmaximal, complemented
8#48670C214yesmaximal, complemented
9#47841C214yesmaximal, complemented
10#47833C212yesmaximal, complemented
11#47006C214yesmaximal, complemented
12#44879C214yesmaximal, complemented
13#43135C214yesmaximal, complemented
14#42041C214yesmaximal, complemented
15#40953C214yesmaximal, complemented
16#40503C212yesmaximal, complemented
17#37768C212yesmaximal, complemented
18#37753C212yesmaximal, complemented
19#36719C211yesmaximal, characteristic, complemented
20#35932C212yesmaximal, complemented
21#35687C212yesmaximal, complemented
22#35659C211yesmaximal, characteristic, complemented
23#35391C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C2×D4×Q8C2214yescomplemented
26C2×#548C2212yes—
27C2×#544C2212yes—
28C2×#543C2211yescharacteristic
29C2×#539C2211yescharacteristic
30C2×#539C2212yes—
31C2×#525C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33#2848C2211yescharacteristic
34#2847C2211yescharacteristic
35#2837C2214yescomplemented
36#2832C2212yescomplemented
37#2829C2214yescomplemented
38#2823C2212yescomplemented
39#2820C2212yescomplemented
40#2816C2212yescomplemented
41#2813C2214yes—
42#2806C2214yescomplemented
43#2803C2214yescomplemented
44#2800C2214yescomplemented
45#2799C2212yescomplemented
46#2798C2214yescomplemented
47#2795C2212yescomplemented
48#2780C2214yes—
49#2771C2214yes—
50#2768C2214yescomplemented
51#2761C2214yes—
52#2755C2214yescomplemented
53#2753C2214yes—
54#2742C2214yescomplemented
55#2733C2212yescomplemented
56#2732C2214yes—
57#2732C2214yes—
58#2730C2214yes—
59#2729C2214yes—
60#2729C2214yescomplemented
61#2729C2214yescomplemented
62#2727C2214yescomplemented
63#2727C2214yescomplemented
64#2722C2214yescomplemented
65#2722C2214yescomplemented
66#2720C2214yescomplemented
67#2716C2214yescomplemented
68#2715C2214yescomplemented
69#2714C2214yes—
70#2714C2214yes—
71#2713C2214yescomplemented
72#2711C2214yes—
73#2710C2214yes—
74#2707C2214yes—
75#2705C2214yes—
76#2704C2214yes—
77#2704C2214yescomplemented
78#2704C2214yescomplemented
79#2704C2214yescomplemented
80#2702C2214yes—
81#2702C2214yescomplemented
82#2701C2214yes—
83#2700C2214yes—
84#2696C2214yes—
85#2695C2214yes—
86#2694C2214yes—
87#2692C2214yes—
88#2689C2214yescomplemented
89#2687C2214yes—
90#2683C2214yes—
91#2683C2214yes—
92#2682C2214yes—
93#2681C2214yes—
94#2680C2212yescomplemented
95#2676C2214yes—
96#2674C2214yes—
97#2672C2214yes—
98#2667C2212yes—
99#2662C2212yescomplemented
100#2662C2214yescomplemented
101#2661C2214yes—
102#2661C2212yescomplemented
103#2656C2212yes—
104#2652C2214yescomplemented
105#2651C2214yescomplemented
106#2639C2212yes—
107#2638C2212yes—
108#2637C2212yescomplemented
109#2630C2214yescomplemented
110#2627C2211yescharacteristic
111#2618C2212yes—
112#2618C2211yescharacteristic
113#2618C2212yes—
114#2616C2212yes—
115#2616C2214yescomplemented
116#2614C2212yescomplemented
117#2601C2214yes—
118#2600C2214yes—
119#2589C2214yes—
120#2589C2214yescomplemented
121#2588C2214yescomplemented
122#2586C2212yescomplemented
123#2584C2214yescomplemented
124#2584C2212yescomplemented
125#2583C2212yes—
126#2583C2212yes—
127#2566C2214yescomplemented
128#2559C2214yes—
129#2556C2214yescomplemented
130#2556C2214yescomplemented
131#2556C2214yescomplemented
132#2554C2214yes—
133#2554C2214yes—
134#2553C2214yes—
135#2551C2212yescomplemented
136#2550C2214yescomplemented
137#2549C2214yes—
138#2549C2214yes—
139#2539C2214yes—
140#2534C2212yes—
141#2522C2214yescomplemented
142#2522C2214yescomplemented
143#2521C2214yescomplemented
144#2520C2214yescomplemented
145#2516C2214yes—
146#2502C2212yes—
147#2479C2214yes—
148#2479C2214yes—
149#2475C2214yes—
150#2472C2214yes—
151#2468C2214yescomplemented
152#2466C2214yescomplemented
153#2465C2214yes—
154#2463C2214yes—
155#2462C2214yescomplemented
156#2460C2214yes—
157#2458C2214yes—
158#2457C2214yes—
159#2456C2214yes—
160#2455C2214yescomplemented
161#2454C2214yes—
162#2454C2214yescomplemented
163#2452C2214yes—
164#2452C2214yes—
165#2452C2214yescomplemented
166#2449C2214yes—
167#2440C2214yes—
168#2440C2214yes—
169#2439C2214yes—
170#2434C2212yes—
171#2434C2212yescomplemented
172#2434C2214yescomplemented
173#2432C2214yes—
174#2432C2214yes—
175#2432C2214yescomplemented
176#2427C2214yes—
177#2425C2214yes—
178#2424C2214yes—
179#2413C2212yes—
180#2411C2214yes—
181#2411C2212yes—
182#2409C2214yes—
183#2409C2214yes—
184#2409C2214yes—
185#2409C2212yes—
186#2409C2214yescomplemented
187#2407C2214yes—
188#2407C2214yes—
189#2407C2214yes—
190#2407C2214yes—
191#2407C2214yescomplemented
192#2406C2212yes—
193#2406C2212yes—
194#2404C2212yes—
195#2404C2212yes—
196#2396C2214yes—
197#2388C2212yes—
198#2388C2214yescomplemented
199#2378C2212yes—
200#2378C2214yescomplemented
201#2374C2214yes—
202#2369C2214yescomplemented
203#2363C2214yes—
204#2361C2214yes—
205#2359C2214yes—
206#2357C2212yes—
207#2341C2212yes—
208Q8×C22⋊C4C2214yescomplemented
209#2335C2214yes—
210#2329C2212yes—
211#2329C2212yes—
212#2324C2214yes—
213#2316C2211yescharacteristic
214#2315C2212yes—
215#2311C2212yes—
216#2310C2211yescharacteristic
217C2×#385C2212yes—
218#2273C2211yescharacteristic
219C2×2−1+4—48no—
220C2×2−1+4—44no—
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2314yes—
224C22×#41C2312yes—
225C23×Q8C2311yescharacteristic
226C23×Q8C2314yes—
227C23×Q8C2312yes—
228C24×C4C2311yescharacteristic
229D4×Q8—416no—
230#548—48no—
231#544—48no—
232#543—44no—
233#539—44no—
234#539—48no—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×#126C2312yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#125C2312yes—
245C2×#125C2314yes—
246C2×#125C2314yes—
247C2×#125C2314yes—
248C2×#124C2312yes—
249C2×#124C2314yes—
250C2×#124C2314yes—
251#525—48no—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2312yes—
257C2×#123C2314yes—
258C2×#123C2312yes—
259C2×#123C2314yes—
260C2×C22⋊Q8—44no—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2311yescharacteristic
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2312yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#120C2314yes—
289C2×#120C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×#117C2312yes—
301C2×#117C2314yes—
302C2×#117C2312yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2312yes—
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2314yes—
318#400C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#398C2312yes—
328#398C2312yes—
329#398C2312yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
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#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2312yes—
355#397C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#395C2312yes—
375#395C2312yes—
376#395C2312yes—
377#395C2312yes—
378#395C2314yes—
379#395C2312yes—
380#395C2312yes—
381#395C2314yes—
382#395C2312yes—
383#395C2312yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2312yes—
390#395C2314yes—
391#394C2312yes—
392#394C2314yes—
393#394C2312yes—
394#394C2314yes—
395#394C2312yes—
396#394C2314yes—
397#394C2312yes—
398#394C2312yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2312yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2312yes—
422#393C2312yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2312yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2312yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2312yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
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#385C2312yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2312yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#384C2312yes—
580#384C2312yes—
581#382C2312yes—
582#382C2314yes—
583#381C2312yes—
584#381C2312yes—
585#381C2312yes—
586#381C2314yes—
587#381C2312yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2311yescharacteristic
593#380C2311yescharacteristic
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#379C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C2×#95C2312yes—
623C2×#95C2312yes—
624C25C2411yescharacteristic
6252−1+4—464no—
626C2×#41—28no—
627C2×#41—28no—
628C2×#41—44no—
629C2×#41—48no—
630C2×#41—44no—
631C2×#41—44no—
632C2×#41—48no—
633C2×#41—48no—
634C2×#41—48no—
635C2×#41—48no—
636C22×Q8—216no—
637C22×Q8—24no—
638C22×Q8—44no—
639C22×Q8—48no—
640C22×Q8—48no—
641C22×Q8—44no—
642C22×Q8—48no—
643C22×Q8C2412yes—
644C22×Q8C2414yes—
645C22×Q8C2412yes—
646C22×Q8C2412yes—
647C22×Q8C2414yes—
648C22×Q8C2411yescharacteristic
649C22×Q8C2412yes—
650C22×Q8C2412yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2412yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2412yes—
658C22×D4C2412yes—
659C22×D4C2414yes—
660C22×D4C2411yescharacteristic
661C22×D4C2412yes—
662C23×C4—44no—
663C23×C4—42no—
664C23×C4C2411yescharacteristic
665C23×C4C2414yes—
666C23×C4C2414yes—
667C23×C4C2411yescharacteristic
668C23×C4C2411yescharacteristic
669C23×C4C2412yes—
670C23×C4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2414yes—
675C23×C4C2412yes—
676C23×C4C2414yes—
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2411yescharacteristic
680C23×C4C2412yes—
681C4⋊Q8—216no—
682C4⋊Q8—48no—
683C4⋊Q8—48no—
684C4⋊Q8—48no—
685#126—44no—
686#126—48no—
687#126—84no—
688#126—84no—
689#126—84no—
690#125—44no—
691#125—48no—
692#125—48no—
693#125—48no—
694#124—44no—
695#124—48no—
696#124—84no—
697#123—216no—
698#123—48no—
699#123—44no—
700#123—48no—
701#123—44no—
702#123—48no—
703#123—82no—
704#123—84no—
705C22⋊Q8—28no—
706C22⋊Q8—28no—
707C22⋊Q8—216no—
708C22⋊Q8—28no—
709C22⋊Q8—42no—
710C22⋊Q8—44no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—48no—
715C22⋊Q8—48no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718C22⋊Q8—44no—
719C22⋊Q8—44no—
720C22⋊Q8—48no—
721C22⋊Q8—48no—
722C22⋊Q8—48no—
723C22⋊Q8—48no—
724#121—216no—
725#121—44no—
726#121—48no—
727#121—44no—
728#121—44no—
729#121—44no—
730#121—42no—
731#121—84no—
732#120—48no—
733#120—82no—
734C4×Q8—44no—
735C4×Q8—48no—
736C4×D4—28no—
737C4×D4—48no—
738C4×D4—48no—
739C4×D4—48no—
740C4×D4—48no—
741C4×D4—48no—
742C4×D4—48no—
743C4×D4—48no—
744#117—48no—
745#117—44no—
746#117—82no—
747C2×C4⋊C4—24no—
748C2×C4⋊C4—44no—
749C2×C4⋊C4—44no—
750C2×C4⋊C4—42no—
751C2×C4⋊C4—42no—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C22⋊C4—24no—
805C2×C22⋊C4—28no—
806C2×C22⋊C4—44no—
807C2×C22⋊C4—42no—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
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×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2412yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914C24—22no—
915C24—24no—
916C24—42no—
917C24—41no—
918C24—41no—
919C24C2512yes—
920C24C2514yes—
921C24C2511yescharacteristic
922C24C2512yes—
923#41—432no—
924#41—432no—
925#41—464no—
926#41—432no—
927C2×Q8—28no—
928C2×Q8—24no—
929C2×Q8—28no—
930C2×Q8—28no—
931C2×Q8—28no—
932C2×Q8—24no—
933C2×Q8—28no—
934C2×Q8—42no—
935C2×Q8—44no—
936C2×Q8—42no—
937C2×Q8—42no—
938C2×Q8—44no—
939C2×Q8—44no—
940C2×Q8—44no—
941C2×Q8—42no—
942C2×Q8—41no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—416no—
947C2×Q8—464no—
948C2×Q8—816no—
949C2×Q8H(5,𝔽2)18yes—
950C2×D4—28no—
951C2×D4—24no—
952C2×D4—28no—
953C2×D4—28no—
954C2×D4—28no—
955C2×D4—28no—
956C2×D4—24no—
957C2×D4—24no—
958C2×D4—28no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—42no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—42no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—42no—
979C2×D4—41no—
980C22×C4—22no—
981C22×C4—24no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—24no—
987C22×C4—28no—
988C22×C4—28no—
989C22×C4—28no—
990C22×C4—28no—
991C22×C4—28no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—28no—
996C22×C4—42no—
997C22×C4—41no—
998C22×C4—42no—
999C22×C4—41no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—41no—
1016C22×C4—42no—
1017C22×C4—41no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—88no—
1025C22×C4H(5,𝔽2)14yes—
1026C22×C42−1+418yescomplemented
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—41no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—41no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C22⋊C4—28no—
1099C22⋊C4—24no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—24no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—42no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C42—28no—
1146C42—24no—
1147C42—42no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—42no—
1158C23—28no—
1159C23—22no—
1160C23—22no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—21no—
1166C23—22no—
1167C23—21no—
1168C23—22no—
1169C23—24no—
1170C23—22no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—22no—
1181C23—82no—
1182C23—82no—
1183C23—84no—
1184C23—84no—
1185C23C2×H(5,𝔽2)12yes—
1186C23C2×2−1+414yes—
1187C23C2611yescharacteristic
1188Q8—216no—
1189Q8—48no—
1190Q8—416no—
1191Q8—48no—
1192Q8—84no—
1193Q8—88no—
1194Q8—161no—
1195Q8—162no—
1196D4—416no—
1197D4—416no—
1198D4—48no—
1199D4—48no—
1200D4—48no—
1201D4—84no—
1202D4—88no—
1203D4—88no—
1204D4—88no—
1205D4—88no—
1206D4—161no—
1207C2×C4—28no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—21no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—44no—
1256C2×C4—48no—
1257C2×C4—416no—
1258C2×C4—416no—
1259C2×C4—416no—
1260C2×C4—44no—
1261C2×C4—44no—
1262C2×C4—84no—
1263C2×C4—84no—
1264C2×C4—88no—
1265C2×C4—84no—
1266C2×C4—82no—
1267C2×C4—84no—
1268C2×C4—82no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4C2×H(5,𝔽2)18yes—
1272C2×C4C2×H(5,𝔽2)14yes—
1273C2×C4C2×H(5,𝔽2)14yes—
1274C2×C4C2×2−1+418yes—
1275C22—22no—
1276C22—22no—
1277C22—24no—
1278C22—22no—
1279C22—24no—
1280C22—24no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—44no—
1288C22—42no—
1289C22—42no—
1290C22—44no—
1291C22—42no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—88no—
1300C22C22×H(5,𝔽2)11yescharacteristic
1301C22C22×H(5,𝔽2)12yes—
1302C22C22×2−1+412yes—
1303C22H(7,𝔽2)11yescharacteristic
1304C222−1+611yescharacteristic
1305C4—24no—
1306C4—28no—
1307C4—24no—
1308C4—28no—
1309C4—42no—
1310C4—41no—
1311C4—41no—
1312C4—44no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—44no—
1318C4—42no—
1319C4—44no—
1320C4—44no—
1321C4—44no—
1322C4—44no—
1323C4—44no—
1324C2—42no—
1325C2—44no—
1326C2—84no—
1327C2—82no—
1328C2#6281711yescharacteristic
1329C2#6283311yescharacteristic
1330C2#6287511yescharacteristic
1331C2#6289312yes—
1332C2#6291712yes—
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. #58590C2semidirect
2. #58588C2semidirect
3. #55126C2semidirect
4. #55122C2semidirect
5. #51927C2semidirect
6. #51348C2semidirect
7. #49594C2semidirect
8. #48670C2semidirect
9. #47841C2semidirect
10. #47833C2semidirect
11. #47006C2semidirect
12. #44879C2semidirect
13. #43135C2semidirect
14. #42041C2semidirect
15. #40953C2semidirect
16. #40503C2semidirect
17. #37768C2semidirect
18. #37753C2semidirect
19. #36719C2semidirect
20. #35932C2semidirect
21. #35687C2semidirect
22. #35659C2semidirect
23. #35391C2semidirect
25. C2×D4×Q8C22semidirect
35. #2837C22semidirect
36. #2832C22semidirect
37. #2829C22semidirect
38. #2823C22semidirect
39. #2820C22semidirect
40. #2816C22semidirect
42. #2806C22semidirect
43. #2803C22semidirect
44. #2800C22semidirect
45. #2799C22semidirect
46. #2798C22semidirect
47. #2795C22semidirect
50. #2768C22semidirect
52. #2755C22semidirect
54. #2742C22semidirect
55. #2733C22semidirect
60. #2729C22semidirect
61. #2729C22semidirect
62. #2727C22semidirect
63. #2727C22semidirect
64. #2722C22semidirect
65. #2722C22semidirect
66. #2720C22semidirect
67. #2716C22semidirect
68. #2715C22semidirect
71. #2713C22semidirect
77. #2704C22semidirect
78. #2704C22semidirect
79. #2704C22semidirect
81. #2702C22semidirect
88. #2689C22semidirect
94. #2680C22semidirect
99. #2662C22semidirect
100. #2662C22semidirect
102. #2661C22semidirect
104. #2652C22semidirect
105. #2651C22semidirect
108. #2637C22semidirect
109. #2630C22semidirect
115. #2616C22semidirect
116. #2614C22semidirect
120. #2589C22semidirect
121. #2588C22semidirect
122. #2586C22semidirect
123. #2584C22semidirect
124. #2584C22semidirect
127. #2566C22semidirect
129. #2556C22semidirect
130. #2556C22semidirect
131. #2556C22semidirect
135. #2551C22semidirect
136. #2550C22semidirect
141. #2522C22semidirect
142. #2522C22semidirect
143. #2521C22semidirect
144. #2520C22semidirect
151. #2468C22semidirect
152. #2466C22semidirect
155. #2462C22semidirect
160. #2455C22semidirect
162. #2454C22semidirect
165. #2452C22semidirect
171. #2434C22semidirect
172. #2434C22semidirect
175. #2432C22semidirect
186. #2409C22semidirect
191. #2407C22semidirect
198. #2388C22semidirect
200. #2378C22semidirect
202. #2369C22semidirect
208. Q8×C22⋊C4C22semidirect
1026. C22×C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#585902
#585882
#551262
#551222
#519272
#513482
#495942
#486702
#478412
#478332
#470062
#448792
#431352
#420412
#409532
#405032
#377682
#377532
#367192
#359322
#356872
#356592
#353912