Finite Group Databasebeta

← #7710149

Subgroups — #7710149

Order 512.

5148 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59346C214yesmaximal, complemented
2#59345C214yesmaximal, complemented
3#45983C214yesmaximal, complemented
4#45982C214yesmaximal, complemented
5#39141C212yesmaximal, complemented
6#38935C212yesmaximal, complemented
7#38059C214yesmaximal, complemented
8#37915C214yesmaximal, complemented
9#37913C214yesmaximal, complemented
10#37912C214yesmaximal, complemented
11#37912C214yesmaximal, complemented
12#37562C211yesmaximal, characteristic, complemented
13#37556C211yesmaximal, characteristic, complemented
14#36980C212yesmaximal, complemented
15#36978C212yesmaximal, complemented
16#36624C211yesmaximal, characteristic, complemented
17#36621C211yesmaximal, characteristic, complemented
18#36607C212yesmaximal, complemented
19#36146C212yesmaximal, complemented
20#36146C214yesmaximal, complemented
21#35051C212yesmaximal, complemented
22#34997C212yesmaximal, complemented
23#34401C211yesmaximal, characteristic, complemented
24#34388C211yesmaximal, characteristic, complemented
25C22×#383C211yesmaximal, characteristic, complemented
26C2×#532C2211yescharacteristic
27C2×#529C2211yescharacteristic
28C2×#525C2212yes—
29C2×#525C2214yes—
30C23×C42C2211yescharacteristic
31#2857C2212yes—
32#2856C2212yes—
33#2855C2211yescharacteristic
34#2854C2211yescharacteristic
35#2854C2212yes—
36#2854C2212yes—
37#2853C2212yes—
38#2852C2214yes—
39#2851C2212yes—
40#2850C2212yes—
41#2850C2214yes—
42#2849C2212yes—
43#2849C2214yes—
44#2848C2211yescharacteristic
45#2847C2211yescharacteristic
46#2847C2212yes—
47#2847C2212yes—
48#2847C2214yes—
49#2843C2214yescomplemented
50#2821C2212yescomplemented
51#2818C2212yescomplemented
52#2777C2214yescomplemented
53#2777C2214yescomplemented
54#2776C2214yescomplemented
55#2775C2214yescomplemented
56#2775C2214yescomplemented
57#2770C2214yescomplemented
58#2770C2214yescomplemented
59#2769C2214yescomplemented
60#2766C2214yescomplemented
61#2764C2214yescomplemented
62#2764C2214yescomplemented
63#2762C2214yescomplemented
64#2759C2214yescomplemented
65#2759C2214yescomplemented
66#2758C2214yescomplemented
67#2758C2214yescomplemented
68#2757C2214yescomplemented
69#2757C2214yescomplemented
70#2757C2214yescomplemented
71#2756C2214yescomplemented
72#2756C2214yescomplemented
73#2756C2214yescomplemented
74#2756C2214yescomplemented
75#2749C2214yescomplemented
76#2749C2214yescomplemented
77#2749C2214yescomplemented
78#2749C2214yescomplemented
79#2738C2214yescomplemented
80#2738C2214yescomplemented
81#2737C2214yescomplemented
82#2737C2214yescomplemented
83#2737C2214yescomplemented
84#2666C2214yescomplemented
85#2666C2214yescomplemented
86#2659C2212yes—
87#2656C2212yes—
88#2646C2212yes—
89#2643C2214yes—
90#2639C2214yes—
91#2639C2212yes—
92#2633C2212yescomplemented
93#2632C2212yescomplemented
94#2631C2212yescomplemented
95#2631C2212yescomplemented
96#2606C2212yescomplemented
97#2605C2212yescomplemented
98#2598C2214yescomplemented
99#2578C2214yescomplemented
100#2578C2214yescomplemented
101#2577C2214yescomplemented
102#2573C2214yescomplemented
103#2572C2214yescomplemented
104#2572C2214yescomplemented
105#2569C2214yes—
106#2569C2212yes—
107#2564C2214yes—
108#2564C2214yes—
109#2549C2212yes—
110#2549C2214yes—
111#2543C2212yes—
112#2543C2214yes—
113#2543C2214yes—
114#2543C2214yes—
115#2543C2214yes—
116#2543C2212yes—
117#2532C2214yescomplemented
118#2525C2214yescomplemented
119#2523C2214yescomplemented
120#2518C2214yescomplemented
121#2518C2214yescomplemented
122#2515C2214yescomplemented
123#2510C2214yes—
124#2510C2214yes—
125#2510C2214yes—
126#2510C2214yes—
127#2510C2214yescomplemented
128#2510C2214yescomplemented
129#2505C2214yes—
130#2498C2214yes—
131#2498C2214yes—
132#2495C2214yescomplemented
133#2493C2214yes—
134#2493C2214yescomplemented
135#2488C2214yes—
136#2488C2214yes—
137#2488C2214yes—
138#2488C2214yes—
139#2450C2214yes—
140#2450C2214yes—
141#2450C2214yes—
142#2450C2214yes—
143#2444C2214yes—
144#2444C2214yes—
145#2444C2214yes—
146#2444C2214yes—
147#2444C2214yes—
148#2444C2214yes—
149#2444C2214yes—
150#2438C2214yes—
151#2438C2214yes—
152#2438C2214yes—
153#2430C2214yes—
154#2430C2214yes—
155#2430C2214yes—
156#2430C2214yes—
157#2430C2214yes—
158#2425C2214yes—
159#2425C2214yes—
160#2425C2214yes—
161#2425C2214yes—
162#2425C2214yes—
163#2425C2214yes—
164#2425C2214yes—
165#2419C2214yes—
166#2419C2214yes—
167#2419C2214yes—
168#2419C2214yes—
169#2383C2214yescomplemented
170#2381C2212yescomplemented
171#2380C2212yescomplemented
172#2364C2212yes—
173#2364C2214yes—
174#2364C2214yes—
175#2364C2212yes—
176#2359C2214yes—
177#2359C2214yes—
178#2359C2214yes—
179#2353C2212yes—
180#2353C2214yes—
181#2353C2214yescomplemented
182#2349C2214yes—
183#2349C2212yes—
184#2347C2212yescomplemented
185#2343C2212yescomplemented
186#2339C2214yes—
187#2339C2214yes—
188#2339C2214yes—
189#2337C2212yescomplemented
190#2337C2214yescomplemented
191#2336C2212yescomplemented
192#2329C2212yes—
193#2325C2212yes—
194#2325C2212yes—
195#2325C2212yes—
196#2325C2214yes—
197#2320C2212yescomplemented
198#2318C2214yes—
199#2318C2212yescomplemented
200#2318C2214yescomplemented
201C4×C22⋊Q8C2212yes—
202C4×#123C2212yes—
203C4×#121C2212yes—
204C4×#121C2214yes—
205C4×#121C2212yes—
206C4×#121C2212yes—
207C4×#120C2212yes—
208C4×#120C2214yes—
209#2297C2212yes—
210#2290C2214yes—
211#2285C2211yescharacteristic
212#2283C2211yescharacteristic
213C2×#383C2211yescharacteristic
214C2×#383C2214yes—
215C2×#383C2214yes—
216C2×#383C2211yescharacteristic
217C2×#383C2212yes—
218C2×#383C2214yes—
219C2×#383C2212yes—
220C2×#383C2211yescharacteristic
221C2×#383C2214yes—
222C2×#383C2211yescharacteristic
223C22×#95C2212yes—
224C22×#95C2211yescharacteristic
225C22×#95C2212yes—
226C22×#95C2211yescharacteristic
227C22×#41C2312yes—
228C22×#41C2314yes—
229C24×C4C2311yescharacteristic
230C24×C4C2311yescharacteristic
231C24×C4C2311yescharacteristic
232C24×C4C2312yes—
233C24×C4C2312yes—
234#532—28no—
235C2×C4⋊Q8C2311yescharacteristic
236C2×#127C2311yescharacteristic
237#529—28no—
238C2×#126C2312yes—
239C2×#125C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2312yes—
242#525—48no—
243#525—416no—
244C2×#123C2312yes—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×#121C2312yes—
257C2×#121C2311yescharacteristic
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2314yes—
263C2×#121C2312yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#120C2312yes—
270C2×#120C2314yes—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×#117C2312yes—
287C2×#117C2314yes—
288C2×#117C2312yes—
289C22×C42—28no—
290C22×C42C2312yes—
291C22×C42C2312yes—
292C22×C42C2312yes—
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2312yes—
297C22×C42C2311yescharacteristic
298#401C2314yes—
299#401C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2314yes—
318#399C2314yes—
319#398C2312yes—
320#398C2312yes—
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#397C2312yes—
334#397C2312yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2312yes—
364#394C2312yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#393C2314yes—
372#393C2314yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#392C2314yes—
378#392C2314yes—
379#392C2312yes—
380#392C2312yes—
381#392C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2312yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#390C2312yes—
392#390C2314yes—
393#390C2312yes—
394#390C2314yes—
395#390C2312yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#386C2314yes—
467#386C2314yes—
468#386C2314yes—
469#386C2314yes—
470#386C2314yes—
471#386C2314yes—
472#386C2314yes—
473#386C2314yes—
474#386C2314yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2312yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2312yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2312yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2312yes—
530#385C2314yes—
531#385C2314yes—
532#384C2312yes—
533#383C2312yes—
534#383C2314yes—
535#383C2314yes—
536#383C2314yes—
537#383C2314yes—
538#383C2314yes—
539#383C2312yes—
540#383C2312yes—
541#383C2312yes—
542#383C2314yes—
543#383C2312yes—
544#383C2312yes—
545#383C2312yes—
546#383C2312yes—
547#383C2312yes—
548#383C2312yes—
549#383C2314yes—
550#383C2314yes—
551#383C2314yes—
552#383C2314yes—
553#383C2314yes—
554#383C2314yes—
555#383C2314yes—
556#383C2314yes—
557#382C2314yes—
558#382C2312yes—
559#382C2312yes—
560#382C2312yes—
561#382C2314yes—
562#381C2312yes—
563#381C2314yes—
564#381C2314yes—
565#381C2314yes—
566#381C2312yes—
567#381C2314yes—
568#381C2314yes—
569#381C2312yes—
570#381C2314yes—
571#381C2314yes—
572#380C2314yes—
573#380C2312yes—
574#380C2312yes—
575#380C2314yes—
576#380C2312yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2312yes—
582#380C2311yescharacteristic
583#380C2311yescharacteristic
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#379C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2311yescharacteristic
596C4×C4⋊C4C2311yescharacteristic
597C4×C4⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611#376C2312yes—
612#376C2312yes—
613C2×#95C2314yes—
614C2×#95C2314yes—
615C2×#95C2311yescharacteristic
616C2×#95C2314yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C2×#95C2314yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C2×#95C2314yes—
624C2×#95C2314yes—
625C2×#95C2311yescharacteristic
626C2×#95C2314yes—
627C2×#95C2311yescharacteristic
628C2×#95C2314yes—
629C2×#95C2312yes—
630C2×#95C2312yes—
631C2×#95C2314yes—
632C2×#95C2314yes—
633C2×#95C2312yes—
634C2×#95C2314yes—
635C2×#95C2314yes—
636C2×#95C2312yes—
637C2×#95C2312yes—
638C2×#95C2312yes—
639C2×#95C2314yes—
640C2×#95C2311yescharacteristic
641C25C2411yescharacteristic
642C2×#41—28no—
643C2×#41—44no—
644C2×#41—48no—
645C2×#41—44no—
646C2×#41—48no—
647C2×#41—48no—
648C22×Q8C2411yescharacteristic
649C22×Q8C2412yes—
650C22×Q8C2414yes—
651C22×D4C2412yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2411yescharacteristic
657C22×D4C2412yes—
658C22×D4C2412yes—
659C22×D4C2412yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C23×C4—24no—
663C23×C4—28no—
664C23×C4—24no—
665C23×C4—24no—
666C23×C4—24no—
667C23×C4—42no—
668C23×C4—44no—
669C23×C4—44no—
670C23×C4—44no—
671C23×C4—44no—
672C23×C4—44no—
673C23×C4—44no—
674C23×C4—44no—
675C23×C4C2414yes—
676C23×C4C2411yescharacteristic
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2412yes—
682C23×C4C2412yes—
683C23×C4C2411yescharacteristic
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2414yes—
687C23×C4C2414yes—
688C23×C4C2412yes—
689C23×C4C2414yes—
690C23×C4C2414yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2411yescharacteristic
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C4⋊Q8—24no—
701#127—24no—
702#126—28no—
703#125—24no—
704#124—24no—
705#124—28no—
706#123—28no—
707#123—44no—
708#123—48no—
709#123—48no—
710#123—48no—
711#123—48no—
712#123—48no—
713C22⋊Q8—24no—
714C22⋊Q8—44no—
715C22⋊Q8—48no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718#121—24no—
719#121—28no—
720#121—28no—
721#121—48no—
722#121—44no—
723#121—44no—
724#121—44no—
725#121—48no—
726#121—48no—
727#121—48no—
728#121—48no—
729#121—48no—
730#121—48no—
731#120—216no—
732#120—28no—
733C4×Q8—24no—
734C4×D4—28no—
735C4×D4—24no—
736C4×D4—28no—
737C4×D4—28no—
738C4×D4—48no—
739C4×D4—48no—
740C4×D4—48no—
741C4×D4—48no—
742C4×D4—48no—
743C4×D4—48no—
744C4×D4—48no—
745C4×D4—48no—
746C4×D4—48no—
747C4×D4—48no—
748#117—28no—
749#117—44no—
750#117—48no—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
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×C42—24no—
828C2×C42—24no—
829C2×C42—24no—
830C2×C42—28no—
831C2×C42—28no—
832C2×C42—28no—
833C2×C42—28no—
834C2×C42#4118yescomplemented
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853C2×C42C2411yescharacteristic
854#95C2414yes—
855#95C2412yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2412yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
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#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920C24—22no—
921C24—24no—
922C24—24no—
923C24—22no—
924C24H(5,𝔽2)14yes—
925C24C2512yes—
926C24C2514yes—
927C24C2511yescharacteristic
928C24C2512yes—
929#41—816no—
930#41—832no—
931C2×Q8—22no—
932C2×Q8—24no—
933C2×Q8—42no—
934C2×Q8—44no—
935C2×Q8—42no—
936C2×Q8—42no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×D4—24no—
940C2×D4—28no—
941C2×D4—24no—
942C2×D4—28no—
943C2×D4—28no—
944C2×D4—28no—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—28no—
949C2×D4—28no—
950C2×D4—24no—
951C2×D4—28no—
952C2×D4—28no—
953C2×D4—28no—
954C2×D4—22no—
955C2×D4—24no—
956C2×D4—24no—
957C2×D4—24no—
958C2×D4—42no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—22no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—28no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—22no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—22no—
984C22×C4—28no—
985C22×C4—28no—
986C22×C4—24no—
987C22×C4—28no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—28no—
991C22×C4—28no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—28no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—416no—
1038C22×C4—416no—
1039C22×C4—416no—
1040C22×C4—816no—
1041C22×C4—816no—
1042C22×C4C2×#4114yes—
1043C22×C4C2×#4114yes—
1044C22×C4C2×#4114yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—22no—
1071C4⋊C4—24no—
1072C4⋊C4—22no—
1073C4⋊C4—24no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—24no—
1106C22⋊C4—28no—
1107C22⋊C4—24no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
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—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C42—24no—
1143C42—24no—
1144C42—24no—
1145C42—24no—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—42no—
1150C42—42no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42C2×#4114yes—
1158C42C2×#4114yes—
1159C42C2×#4114yes—
1160C42C2×#4114yes—
1161C23—28no—
1162C23—28no—
1163C23—216no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—28no—
1171C23—216no—
1172C23—22no—
1173C23—24no—
1174C23—22no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—24no—
1184C23C22×#4112yes—
1185C23C2×H(5,𝔽2)12yes—
1186C23C2×H(5,𝔽2)14yes—
1187C23#58512yes—
1188C23#58514yes—
1189C23#58514yes—
1190C23C2611yescharacteristic
1191Q8—82no—
1192Q8—84no—
1193Q8—88no—
1194D4—48no—
1195D4—416no—
1196D4—416no—
1197D4—416no—
1198D4—416no—
1199D4—84no—
1200D4—84no—
1201D4—82no—
1202D4—84no—
1203D4—88no—
1204D4—164no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—28no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—44no—
1258C2×C4—44no—
1259C2×C4—48no—
1260C2×C4—48no—
1261C2×C4—48no—
1262C2×C4—48no—
1263C2×C4—48no—
1264C2×C4—48no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—44no—
1268C2×C4—416no—
1269C2×C4—84no—
1270C2×C4—88no—
1271C2×C4—84no—
1272C2×C4—88no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—88no—
1276C2×C4—88no—
1277C2×C4—84no—
1278C2×C4—88no—
1279C2×C4—88no—
1280C2×C4—164no—
1281C2×C4C22×#4112yes—
1282C2×C4C22×#4112yes—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4112yes—
1285C2×C4C22×#4112yes—
1286C2×C4C22×#4112yes—
1287C22—232no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—22no—
1292C22—22no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22#349414yes—
1311C22#356018yes—
1312C22C23×#4111yescharacteristic
1313C22C22×H(5,𝔽2)11yescharacteristic
1314C22C2×#58512yes—
1315C22C2×#58512yes—
1316C22C2×#58511yescharacteristic
1317C4—22no—
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—44no—
1324C4—44no—
1325C4—44no—
1326C4—44no—
1327C4—44no—
1328C4—42no—
1329C4—44no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4—44no—
1337C4—44no—
1338C2—24no—
1339C2—28no—
1340C2—82no—
1341C2—84no—
1342C2C2×#356012yes—
1343C2C2×#349411yescharacteristic
1344C2#6281411yescharacteristic
1345C2#6281411yescharacteristic
1346C2#6282612yes—
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. #59346C2semidirect
2. #59345C2semidirect
3. #45983C2semidirect
4. #45982C2semidirect
5. #39141C2semidirect
6. #38935C2semidirect
7. #38059C2semidirect
8. #37915C2semidirect
9. #37913C2semidirect
10. #37912C2semidirect
11. #37912C2semidirect
12. #37562C2semidirect
13. #37556C2semidirect
14. #36980C2semidirect
15. #36978C2semidirect
16. #36624C2semidirect
17. #36621C2semidirect
18. #36607C2semidirect
19. #36146C2semidirect
20. #36146C2semidirect
21. #35051C2semidirect
22. #34997C2semidirect
23. #34401C2semidirect
24. #34388C2semidirect
25. C22×#383C2semidirect
49. #2843C22semidirect
50. #2821C22semidirect
51. #2818C22semidirect
52. #2777C22semidirect
53. #2777C22semidirect
54. #2776C22semidirect
55. #2775C22semidirect
56. #2775C22semidirect
57. #2770C22semidirect
58. #2770C22semidirect
59. #2769C22semidirect
60. #2766C22semidirect
61. #2764C22semidirect
62. #2764C22semidirect
63. #2762C22semidirect
64. #2759C22semidirect
65. #2759C22semidirect
66. #2758C22semidirect
67. #2758C22semidirect
68. #2757C22semidirect
69. #2757C22semidirect
70. #2757C22semidirect
71. #2756C22semidirect
72. #2756C22semidirect
73. #2756C22semidirect
74. #2756C22semidirect
75. #2749C22semidirect
76. #2749C22semidirect
77. #2749C22semidirect
78. #2749C22semidirect
79. #2738C22semidirect
80. #2738C22semidirect
81. #2737C22semidirect
82. #2737C22semidirect
83. #2737C22semidirect
84. #2666C22semidirect
85. #2666C22semidirect
92. #2633C22semidirect
93. #2632C22semidirect
94. #2631C22semidirect
95. #2631C22semidirect
96. #2606C22semidirect
97. #2605C22semidirect
98. #2598C22semidirect
99. #2578C22semidirect
100. #2578C22semidirect
101. #2577C22semidirect
102. #2573C22semidirect
103. #2572C22semidirect
104. #2572C22semidirect
117. #2532C22semidirect
118. #2525C22semidirect
119. #2523C22semidirect
120. #2518C22semidirect
121. #2518C22semidirect
122. #2515C22semidirect
127. #2510C22semidirect
128. #2510C22semidirect
132. #2495C22semidirect
134. #2493C22semidirect
169. #2383C22semidirect
170. #2381C22semidirect
171. #2380C22semidirect
181. #2353C22semidirect
184. #2347C22semidirect
185. #2343C22semidirect
189. #2337C22semidirect
190. #2337C22semidirect
191. #2336C22semidirect
197. #2320C22semidirect
199. #2318C22semidirect
200. #2318C22semidirect
834. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#593462
#593452
#459832
#459822
#391412
#389352
#380592
#379152
#379132
#379122
#375622
#375562
#369802
#369782
#366242
#366212
#366072
#361462
#350512
#349972
#344012
#343882
C22×#3832