Finite Group Databasebeta

← #8096789

Subgroups — #8096789

Order 512.

5582 conjugacy classes of subgroups.

The subgroup lattice has 1472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53136C213yesmaximal, complemented
2#53128C213yesmaximal, complemented
3#53073C213yesmaximal, complemented
4#53064C213yesmaximal, complemented
5#52966C213yesmaximal, complemented
6#52956C213yesmaximal, complemented
7#52297C213yesmaximal, complemented
8#46339C213yesmaximal, complemented
9#46050C213yesmaximal, complemented
10#46048C213yesmaximal, complemented
11#45708C213yesmaximal, complemented
12#45687C213yesmaximal, complemented
13#45687C213yesmaximal, complemented
14#45616C213yesmaximal, complemented
15#45604C213yesmaximal, complemented
16#45518C213yesmaximal, complemented
17#36585C211yesmaximal, characteristic, complemented
18#36576C211yesmaximal, characteristic, complemented
19#36482C211yesmaximal, characteristic, complemented
20#36465C211yesmaximal, characteristic, complemented
21#36448C211yesmaximal, characteristic, complemented
22#36434C211yesmaximal, characteristic, complemented
23#36432C211yesmaximal, characteristic, complemented
24#36430C211yesmaximal, characteristic, complemented
25#36430C211yesmaximal, characteristic, complemented
26#36029C211yesmaximal, characteristic, complemented
27#35983C211yesmaximal, characteristic, complemented
28#35757C211yesmaximal, characteristic, complemented
29#35757C211yesmaximal, characteristic, complemented
30#35737C211yesmaximal, characteristic, complemented
31#35687C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#548C2211yescharacteristic
42C2×#548C2211yescharacteristic
43C2×#548C2211yescharacteristic
44C2×#548C2211yescharacteristic
45C2×#520C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47C22×C4×Q8C2211yescharacteristic
48#2863C2213yes—
49#2860C2213yes—
50#2858C2213yes—
51#2856C2213yes—
52#2855C2213yes—
53#2855C2213yes—
54#2850C2213yes—
55#2850C2213yes—
56#2850C2213yes—
57#2838C2216yes—
58#2838C2216yes—
59#2830C2216yes—
60#2829C2216yes—
61#2828C2216yes—
62#2828C2216yes—
63#2827C2216yes—
64#2826C2216yes—
65#2825C2216yes—
66#2825C2216yes—
67#2815C2216yes—
68#2803C2213yes—
69#2803C2213yes—
70#2797C2216yes—
71#2797C2216yes—
72#2796C2216yes—
73#2795C2213yes—
74#2792C2213yes—
75#2790C2216yes—
76#2784C2213yes—
77#2784C2216yes—
78#2760C2216yes—
79#2756C2216yes—
80#2756C2211yescharacteristic
81#2756C2213yes—
82#2752C2216yes—
83#2749C2216yes—
84#2749C2216yes—
85#2749C2216yes—
86#2746C2216yes—
87#2746C2216yes—
88#2737C2216yes—
89#2737C2213yes—
90#2737C2213yes—
91#2714C2213yes—
92#2714C2213yes—
93#2714C2216yes—
94#2705C2213yes—
95#2705C2213yes—
96#2703C2216yes—
97#2699C2216yes—
98#2699C2213yes—
99#2691C2216yes—
100#2688C2216yes—
101#2688C2216yes—
102#2673C2216yes—
103#2673C2213yes—
104#2673C2213yes—
105#2625C2213yes—
106#2621C2213yes—
107#2619C2213yes—
108#2616C2213yes—
109#2615C2213yes—
110#2615C2213yes—
111#2548C2213yes—
112#2547C2213yes—
113#2545C2213yes—
114#2544C2213yes—
115#2544C2213yes—
116#2542C2213yes—
117#2541C2213yes—
118#2541C2213yes—
119#2540C2213yes—
120#2540C2213yes—
121#2540C2213yes—
122#2540C2213yes—
123#2538C2213yes—
124#2536C2213yes—
125#2535C2213yes—
126#2535C2213yes—
127#2535C2213yes—
128#2535C2213yes—
129#2514C2213yes—
130#2514C2213yes—
131#2513C2213yes—
132#2513C2213yes—
133#2513C2213yes—
134#2511C2213yes—
135#2503C2213yes—
136#2503C2213yes—
137#2499C2213yes—
138#2496C2213yes—
139#2495C2213yes—
140#2494C2213yes—
141#2494C2213yes—
142#2494C2213yes—
143#2494C2213yes—
144#2487C2213yes—
145#2486C2213yes—
146#2485C2213yes—
147#2447C2213yes—
148#2447C2213yes—
149#2447C2213yes—
150#2447C2213yes—
151#2446C2213yes—
152#2446C2213yes—
153#2436C2213yes—
154#2436C2213yes—
155#2434C2213yes—
156#2432C2213yes—
157#2432C2213yes—
158#2431C2213yes—
159#2431C2213yes—
160#2431C2213yes—
161#2431C2213yes—
162#2429C2213yes—
163#2428C2213yes—
164#2428C2213yes—
165#2428C2213yes—
166#2428C2213yes—
167#2427C2213yes—
168#2427C2213yes—
169#2427C2213yes—
170#2427C2213yes—
171#2426C2213yes—
172#2426C2213yes—
173#2426C2213yes—
174#2422C2213yes—
175#2421C2213yes—
176#2421C2213yes—
177#2420C2213yes—
178#2420C2213yes—
179#2420C2213yes—
180#2417C2213yes—
181#2417C2213yes—
182#2417C2213yes—
183#2416C2213yes—
184#2416C2213yes—
185#2416C2213yes—
186#2416C2213yes—
187#2416C2213yes—
188#2415C2213yes—
189#2415C2213yes—
190#2414C2213yes—
191#2414C2213yes—
192#2409C2213yes—
193#2409C2213yes—
194#2409C2213yes—
195#2407C2213yes—
196#2407C2213yes—
197#2407C2213yes—
198#2407C2213yes—
199#2407C2213yes—
200#2407C2213yes—
201#2395C2213yes—
202#2392C2213yes—
203#2392C2213yes—
204#2388C2213yes—
205#2388C2213yes—
206#2388C2213yes—
207#2377C2216yes—
208#2377C2216yes—
209#2377C2216yes—
210#2351C2211yescharacteristic
211#2351C2211yescharacteristic
212#2351C2211yescharacteristic
213#2351C2211yescharacteristic
214#2351C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226Q8×C22⋊C4C2211yescharacteristic
227Q8×C22⋊C4C2211yescharacteristic
228C4×#127C2213yes—
229C4×#126C2213yes—
230C4×#126C2213yes—
231C4×#123C2213yes—
232C4×#123C2213yes—
233C4×#121C2213yes—
234C4×#121C2213yes—
235C4×#121C2213yes—
236C4×#121C2213yes—
237C42×Q8C2211yescharacteristic
238C2×2−1+4—44no—
239C2×2−1+4—44no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2313yes—
245C22×#41C2313yes—
246C22×#41C2313yes—
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249C23×Q8C2311yescharacteristic
250C23×Q8C2313yes—
251#550—44no—
252#550—44no—
253#550—44no—
254D4×Q8—44no—
255D4×Q8—44no—
256#548—44no—
257#548—44no—
258#548—44no—
259#548—44no—
260#548—44no—
261#548—44no—
262#548—44no—
263C2×C4⋊Q8C2313yes—
264C2×C4⋊Q8C2313yes—
265C2×#127C2313yes—
266C2×#127C2313yes—
267C2×#127C2313yes—
268C2×#127C2313yes—
269C2×#126C2313yes—
270C2×#126C2313yes—
271C2×#124C2313yes—
272C2×#124C2313yes—
273C2×#124C2313yes—
274C2×#124C2313yes—
275C2×#124C2313yes—
276C2×#124C2313yes—
277C2×#124C2313yes—
278C2×#123C2313yes—
279C2×#123C2313yes—
280C2×C22⋊Q8C2313yes—
281C2×C22⋊Q8C2313yes—
282C2×C22⋊Q8C2313yes—
283C2×C22⋊Q8C2313yes—
284C2×C22⋊Q8C2313yes—
285C2×C22⋊Q8C2313yes—
286C2×C22⋊Q8C2313yes—
287C2×C22⋊Q8C2313yes—
288C2×C22⋊Q8C2313yes—
289C2×C22⋊Q8C2313yes—
290C2×C22⋊Q8C2313yes—
291C2×#121C2313yes—
292C2×#121C2313yes—
293C2×#121C2313yes—
294C2×#121C2313yes—
295C2×#121C2316yes—
296C2×#121C2313yes—
297C2×#121C2313yes—
298C2×#121C2313yes—
299C2×#121C2313yes—
300C2×#121C2313yes—
301C2×#121C2313yes—
302C2×#121C2313yes—
303C2×#121C2313yes—
304C2×#121C2313yes—
305C2×#121C2313yes—
306C2×#121C2316yes—
307C2×#121C2316yes—
308C2×#121C2313yes—
309C2×#121C2313yes—
310C2×#121C2313yes—
311#520—44no—
312C4×#41—44no—
313C2×C4×Q8—44no—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2313yes—
324C2×C4×Q8C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×C4×D4C2313yes—
330C2×C4×D4C2313yes—
331C2×C4×D4C2313yes—
332C2×C4×D4C2313yes—
333C2×C4×D4C2313yes—
334C2×C4×D4C2313yes—
335C2×C4×D4C2313yes—
336C2×C4×D4C2313yes—
337C2×C4×D4C2313yes—
338C2×C4×D4C2313yes—
339C2×C4×D4C2313yes—
340C2×C4×D4C2313yes—
341C2×#117C2313yes—
342C2×#117C2313yes—
343C22×C4⋊C4C2313yes—
344C22×C4⋊C4C2313yes—
345C22×C42C2313yes—
346C22×C42C2313yes—
347#401C2316yes—
348#401C2316yes—
349#400C2316yes—
350#400C2316yes—
351#400C2316yes—
352#400C2316yes—
353#400C2316yes—
354#400C2313yes—
355#399C2316yes—
356#399C2313yes—
357#399C2316yes—
358#398C2313yes—
359#398C2313yes—
360#398C2316yes—
361#398C2316yes—
362#398C2316yes—
363#398C2311yescharacteristic
364#397C2316yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#397C2316yes—
369#397C2316yes—
370#397C2316yes—
371#397C2316yes—
372#397C2316yes—
373#397C2316yes—
374#397C2316yes—
375#397C2316yes—
376#397C2316yes—
377#397C2313yes—
378#397C2316yes—
379#397C2313yes—
380#397C2311yescharacteristic
381#397C2313yes—
382#397C2313yes—
383#396C2316yes—
384#396C2316yes—
385#396C2313yes—
386#396C2316yes—
387#396C2316yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#395C2313yes—
392#395C2316yes—
393#395C2313yes—
394#395C2313yes—
395#394C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2316yes—
399#394C2316yes—
400#394C2316yes—
401#394C2313yes—
402#394C2316yes—
403#394C2316yes—
404#394C2313yes—
405#394C2316yes—
406#394C2313yes—
407#394C2313yes—
408#394C2316yes—
409#394C2316yes—
410#394C2316yes—
411#394C2313yes—
412#394C2316yes—
413#394C2313yes—
414#394C2316yes—
415#394C2311yescharacteristic
416#394C2311yescharacteristic
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2311yescharacteristic
421#394C2313yes—
422#394C2313yes—
423#393C2316yes—
424#393C2316yes—
425#393C2313yes—
426#393C2313yes—
427#393C2313yes—
428#392C2316yes—
429#392C2313yes—
430#392C2313yes—
431#392C2316yes—
432#392C2316yes—
433#392C2316yes—
434#392C2316yes—
435#392C2316yes—
436#392C2316yes—
437#392C2313yes—
438#392C2313yes—
439#392C2316yes—
440#392C2311yescharacteristic
441#392C2313yes—
442#392C2313yes—
443#392C2313yes—
444#392C2313yes—
445#392C2313yes—
446#392C2313yes—
447#392C2316yes—
448#392C2316yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#390C2311yescharacteristic
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2316yes—
470#390C2316yes—
471#390C2316yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2316yes—
483#390C2316yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#388C2311yescharacteristic
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2316yes—
512#388C2316yes—
513#388C2316yes—
514#388C2316yes—
515#388C2316yes—
516#388C2313yes—
517#388C2313yes—
518#388C2316yes—
519#388C2316yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2311yescharacteristic
525#388C2313yes—
526#388C2313yes—
527#388C2311yescharacteristic
528#388C2311yescharacteristic
529#387C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2316yes—
536#387C2316yes—
537#387C2316yes—
538#387C2316yes—
539#387C2313yes—
540#387C2316yes—
541#387C2313yes—
542#387C2313yes—
543#387C2313yes—
544#386C2313yes—
545#386C2316yes—
546#386C2316yes—
547#386C2316yes—
548#386C2316yes—
549#386C2316yes—
550#386C2313yes—
551#386C2316yes—
552#386C2316yes—
553#386C2313yes—
554#386C2316yes—
555#386C2316yes—
556#386C2313yes—
557#386C2316yes—
558#386C2316yes—
559#386C2316yes—
560#386C2316yes—
561#386C2316yes—
562#386C2316yes—
563#386C2316yes—
564#386C2316yes—
565#386C2313yes—
566#386C2313yes—
567#386C2311yescharacteristic
568#386C2313yes—
569#386C2311yescharacteristic
570#386C2313yes—
571#385C2316yes—
572#385C2316yes—
573#385C2316yes—
574#385C2313yes—
575#385C2313yes—
576#385C2316yes—
577#385C2316yes—
578#385C2316yes—
579#385C2316yes—
580#384C2313yes—
581#384C2313yes—
582#383C2311yescharacteristic
583#383C2313yes—
584#383C2316yes—
585#382C2313yes—
586#382C2313yes—
587#382C2313yes—
588#382C2313yes—
589#382C2313yes—
590#381C2316yes—
591#381C2316yes—
592#381C2316yes—
593#381C2316yes—
594#381C2313yes—
595#381C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2313yes—
601#380C2313yes—
602#380C2313yes—
603#380C2313yes—
604#380C2313yes—
605#380C2313yes—
606#380C2313yes—
607#380C2313yes—
608#380C2313yes—
609#380C2316yes—
610#380C2316yes—
611#380C2313yes—
612#380C2313yes—
613#380C2311yescharacteristic
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C4⋊C4C2313yes—
619C4×C4⋊C4C2313yes—
620C4×C4⋊C4C2313yes—
621C4×C4⋊C4C2313yes—
622C4×C4⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631C4×C22⋊C4C2313yes—
632C4×C22⋊C4C2313yes—
633C4×C22⋊C4C2313yes—
634C4×C22⋊C4C2313yes—
635C43C2313yes—
6362−1+4—464no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—24no—
642C2×#41—24no—
643C2×#41—24no—
644C2×#41—24no—
645C2×#41—24no—
646C2×#41—46no—
647C2×#41—46no—
648C2×#41—46no—
649C2×#41—46no—
650C2×#41—46no—
651C2×#41—46no—
652C2×#41—46no—
653C2×#41—46no—
654C2×#41—46no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8—24no—
658C22×Q8—24no—
659C22×Q8—24no—
660C22×Q8—24no—
661C22×Q8—24no—
662C22×Q8—24no—
663C22×Q8—24no—
664C22×Q8—46no—
665C22×Q8—46no—
666C22×Q8—46no—
667C22×Q8C2413yes—
668C22×Q8C2413yes—
669C22×Q8C2413yes—
670C22×Q8C2413yes—
671C22×Q8C2411yescharacteristic
672C22×D4C2413yes—
673C22×D4C2413yes—
674C22×D4C2413yes—
675C22×D4C2411yescharacteristic
676C22×D4C2411yescharacteristic
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2413yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2413yes—
685C22×D4C2413yes—
686C22×D4C2413yes—
687C22×D4C2416yes—
688C22×D4C2416yes—
689C22×D4C2416yes—
690C22×D4C2411yescharacteristic
691C22×D4C2413yes—
692C22×D4C2413yes—
693C23×C4C2413yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2413yes—
697C23×C4C2413yes—
698C23×C4C2413yes—
699C23×C4C2413yes—
700C23×C4C2411yescharacteristic
701C23×C4C2416yes—
702C23×C4C2413yes—
703C23×C4C2413yes—
704C23×C4C2416yes—
705C4⋊Q8—46no—
706C4⋊Q8—46no—
707#127—46no—
708#127—46no—
709#127—46no—
710#127—46no—
711#126—46no—
712#126—46no—
713#124—46no—
714#124—46no—
715#124—46no—
716#124—46no—
717#124—46no—
718#124—46no—
719#124—46no—
720#123—46no—
721#123—46no—
722C22⋊Q8—46no—
723C22⋊Q8—46no—
724C22⋊Q8—46no—
725C22⋊Q8—46no—
726C22⋊Q8—46no—
727C22⋊Q8—46no—
728C22⋊Q8—46no—
729C22⋊Q8—46no—
730C22⋊Q8—46no—
731C22⋊Q8—46no—
732C22⋊Q8—46no—
733#121—46no—
734#121—412no—
735#121—412no—
736#121—46no—
737#121—46no—
738#121—46no—
739#121—46no—
740#121—46no—
741#121—46no—
742#121—46no—
743#121—46no—
744#121—46no—
745#121—46no—
746#121—46no—
747#121—46no—
748#121—46no—
749#121—46no—
750#121—46no—
751#121—46no—
752#121—412no—
753C4×Q8—24no—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—24no—
757C4×Q8—24no—
758C4×Q8—24no—
759C4×Q8—24no—
760C4×Q8—24no—
761C4×Q8—24no—
762C4×Q8—46no—
763C4×Q8—46no—
764C4×D4—46no—
765C4×D4—46no—
766C4×D4—46no—
767C4×D4—46no—
768C4×D4—46no—
769C4×D4—46no—
770C4×D4—46no—
771C4×D4—46no—
772C4×D4—46no—
773C4×D4—46no—
774C4×D4—46no—
775C4×D4—46no—
776C4×D4—46no—
777C4×D4—46no—
778C4×D4—46no—
779C4×D4—46no—
780#117—46no—
781#117—46no—
782C2×C4⋊C4—46no—
783C2×C4⋊C4—46no—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2416yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2416yes—
815C2×C4⋊C4C2416yes—
816C2×C4⋊C4C2416yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2413yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2411yescharacteristic
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2416yes—
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2411yescharacteristic
835C2×C22⋊C4C2411yescharacteristic
836C2×C22⋊C4C2411yescharacteristic
837C2×C22⋊C4C2411yescharacteristic
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2416yes—
857C2×C22⋊C4C2416yes—
858C2×C22⋊C4C2416yes—
859C2×C22⋊C4C2416yes—
860C2×C22⋊C4C2416yes—
861C2×C22⋊C4C2416yes—
862C2×C22⋊C4C2416yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2416yes—
870C2×C22⋊C4C2416yes—
871C2×C22⋊C4C2416yes—
872C2×C22⋊C4C2416yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2411yescharacteristic
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2416yes—
886C2×C42—46no—
887C2×C42—46no—
888C2×C42C2413yes—
889C2×C42C2413yes—
890C2×C42C2413yes—
891C2×C42C2413yes—
892C2×C42C2413yes—
893C2×C42C2413yes—
894C2×C42C2413yes—
895C2×C42C2413yes—
896C2×C42C2413yes—
897C2×C42C2411yescharacteristic
898C2×C42C2413yes—
899C2×C42C2413yes—
900C2×C42C2413yes—
901C2×C42C2413yes—
902C2×C42C2413yes—
903C2×C42C2413yes—
904C2×C42C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2411yescharacteristic
907#95C2411yescharacteristic
908#95C2411yescharacteristic
909#95C2411yescharacteristic
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2411yescharacteristic
930#95C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2411yescharacteristic
933#95C2411yescharacteristic
934#95C2416yes—
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2416yes—
943#95C2416yes—
944#95C2416yes—
945#95C2416yes—
946#95C2416yes—
947#95C2416yes—
948#95C2416yes—
949#95C2416yes—
950#95C2416yes—
951#95C2416yes—
952#95C2416yes—
953#95C2416yes—
954C24C2513yes—
955C24C2513yes—
956C24C2511yescharacteristic
957C24C2511yescharacteristic
958C24C2513yes—
959C24C2511yescharacteristic
960#41—448no—
961#41—448no—
962#41—448no—
963#41—416no—
964#41—416no—
965#41—416no—
966C2×Q8—26no—
967C2×Q8—26no—
968C2×Q8—26no—
969C2×Q8—26no—
970C2×Q8—26no—
971C2×Q8—26no—
972C2×Q8—26no—
973C2×Q8—26no—
974C2×Q8—26no—
975C2×Q8—43no—
976C2×Q8—43no—
977C2×Q8—43no—
978C2×Q8—448no—
979C2×Q8—416no—
980C2×Q8—416no—
981C2×Q8—416no—
982C2×Q8H(5,𝔽2)14yes—
983C2×Q8H(5,𝔽2)14yes—
984C2×Q8H(5,𝔽2)14yes—
985C2×D4—22no—
986C2×D4—22no—
987C2×D4—26no—
988C2×D4—26no—
989C2×D4—26no—
990C2×D4—26no—
991C2×D4—26no—
992C2×D4—26no—
993C2×D4—26no—
994C2×D4—26no—
995C2×D4—26no—
996C2×D4—26no—
997C2×D4—26no—
998C2×D4—26no—
999C2×D4—22no—
1000C2×D4—26no—
1001C2×D4—26no—
1002C2×D4—41no—
1003C2×D4—41no—
1004C2×D4—41no—
1005C2×D4—41no—
1006C2×D4—41no—
1007C2×D4—43no—
1008C2×D4—43no—
1009C2×D4—43no—
1010C2×D4—43no—
1011C2×D4—41no—
1012C2×D4—43no—
1013C2×D4—43no—
1014C2×D4—43no—
1015C2×D4—43no—
1016C2×D4—43no—
1017C2×D4—43no—
1018C2×D4—43no—
1019C2×D4—43no—
1020C2×D4—43no—
1021C2×D4—43no—
1022C2×D4—43no—
1023C2×D4—43no—
1024C2×D4—43no—
1025C2×D4—43no—
1026C2×D4—43no—
1027C2×D4—43no—
1028C2×D4—43no—
1029C2×D4—43no—
1030C2×D4—43no—
1031C2×D4—43no—
1032C2×D4—43no—
1033C2×D4—43no—
1034C2×D4—43no—
1035C2×D4—43no—
1036C2×D4—43no—
1037C2×D4—43no—
1038C2×D4—43no—
1039C2×D4—46no—
1040C2×D4—46no—
1041C2×D4—46no—
1042C2×D4—46no—
1043C2×D4—46no—
1044C2×D4—46no—
1045C2×D4—46no—
1046C2×D4—46no—
1047C2×D4—46no—
1048C22×C4—26no—
1049C22×C4—26no—
1050C22×C4—26no—
1051C22×C4—26no—
1052C22×C4—26no—
1053C22×C4—26no—
1054C22×C4—26no—
1055C22×C4—26no—
1056C22×C4—26no—
1057C22×C4—26no—
1058C22×C4—26no—
1059C22×C4—26no—
1060C22×C4—26no—
1061C22×C4—26no—
1062C22×C4—26no—
1063C22×C4—26no—
1064C22×C4—26no—
1065C22×C4—26no—
1066C22×C4—26no—
1067C22×C4—22no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—46no—
1071C22×C4—46no—
1072C22×C4—46no—
1073C22×C4—43no—
1074C22×C4—43no—
1075C22×C4—43no—
1076C22×C4—43no—
1077C22×C4—43no—
1078C22×C4—43no—
1079C22×C4—43no—
1080C22×C4—43no—
1081C22×C4—46no—
1082C22×C4—46no—
1083C22×C4—46no—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2513yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2513yes—
1089C22×C4C2513yes—
1090C22×C4C2513yes—
1091C22×C4C2513yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2513yes—
1094C22×C4C2513yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2513yes—
1098C22×C4C2513yes—
1099C22×C4C2513yes—
1100C22×C4C2513yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2513yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2513yes—
1109C4⋊C4—26no—
1110C4⋊C4—26no—
1111C4⋊C4—26no—
1112C4⋊C4—26no—
1113C4⋊C4—26no—
1114C4⋊C4—26no—
1115C4⋊C4—26no—
1116C4⋊C4—26no—
1117C4⋊C4—26no—
1118C4⋊C4—26no—
1119C4⋊C4—26no—
1120C4⋊C4—26no—
1121C4⋊C4—26no—
1122C4⋊C4—43no—
1123C4⋊C4—46no—
1124C4⋊C4—41no—
1125C4⋊C4—43no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—43no—
1133C4⋊C4—43no—
1134C4⋊C4—43no—
1135C4⋊C4—43no—
1136C4⋊C4—43no—
1137C4⋊C4—43no—
1138C4⋊C4—43no—
1139C4⋊C4—43no—
1140C4⋊C4—43no—
1141C4⋊C4—46no—
1142C4⋊C4—46no—
1143C4⋊C4—46no—
1144C4⋊C4—43no—
1145C4⋊C4—43no—
1146C4⋊C4—43no—
1147C4⋊C4—43no—
1148C22⋊C4—22no—
1149C22⋊C4—22no—
1150C22⋊C4—26no—
1151C22⋊C4—26no—
1152C22⋊C4—22no—
1153C22⋊C4—22no—
1154C22⋊C4—41no—
1155C22⋊C4—46no—
1156C22⋊C4—43no—
1157C22⋊C4—41no—
1158C22⋊C4—41no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4—46no—
1162C22⋊C4—41no—
1163C22⋊C4—41no—
1164C22⋊C4—41no—
1165C22⋊C4—41no—
1166C22⋊C4—41no—
1167C22⋊C4—41no—
1168C22⋊C4—41no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—43no—
1178C22⋊C4—43no—
1179C22⋊C4—43no—
1180C22⋊C4—43no—
1181C22⋊C4—43no—
1182C22⋊C4—43no—
1183C22⋊C4—43no—
1184C22⋊C4—43no—
1185C22⋊C4—43no—
1186C22⋊C4—46no—
1187C22⋊C4—43no—
1188C22⋊C4—43no—
1189C22⋊C4—46no—
1190C22⋊C4—43no—
1191C22⋊C4—43no—
1192C22⋊C4—46no—
1193C22⋊C4—43no—
1194C22⋊C4—46no—
1195C22⋊C4—43no—
1196C22⋊C4—46no—
1197C22⋊C4—46no—
1198C22⋊C4—46no—
1199C22⋊C4—46no—
1200C22⋊C4—46no—
1201C22⋊C4—46no—
1202C22⋊C4—46no—
1203C22⋊C4—43no—
1204C22⋊C4—43no—
1205C22⋊C4—43no—
1206C22⋊C4—43no—
1207C22⋊C4—43no—
1208C22⋊C4—43no—
1209C22⋊C4—43no—
1210C22⋊C4—43no—
1211C42—26no—
1212C42—26no—
1213C42—26no—
1214C42—26no—
1215C42—26no—
1216C42—26no—
1217C42—26no—
1218C42—26no—
1219C42—26no—
1220C42—22no—
1221C42—41no—
1222C42—43no—
1223C42—43no—
1224C42—43no—
1225C42—43no—
1226C42—43no—
1227C42—43no—
1228C23—21no—
1229C23—21no—
1230C23—21no—
1231C23—21no—
1232C23—21no—
1233C23—21no—
1234C23—23no—
1235C23—23no—
1236C23—23no—
1237C23—23no—
1238C23—23no—
1239C23—21no—
1240C23—21no—
1241C23—23no—
1242C23—23no—
1243C23—21no—
1244C23—21no—
1245C23—21no—
1246C23—21no—
1247C23—23no—
1248C23—23no—
1249C23—21no—
1250C23—21no—
1251C23—23no—
1252C23—23no—
1253C23—21no—
1254C23—21no—
1255C23—23no—
1256C23—23no—
1257C23—21no—
1258C23—23no—
1259C23—23no—
1260C23—23no—
1261C23—23no—
1262C23—23no—
1263C23—21no—
1264C23—23no—
1265C23—21no—
1266C23—21no—
1267C23—23no—
1268C23—23no—
1269C23#58512yes—
1270C23C2611yescharacteristic
1271Q8—412no—
1272Q8—412no—
1273Q8—412no—
1274Q8—412no—
1275Q8#560116yes—
1276D4—44no—
1277D4—44no—
1278D4—44no—
1279D4—412no—
1280D4—412no—
1281D4—412no—
1282D4—412no—
1283D4—412no—
1284D4—86no—
1285D4—86no—
1286D4—86no—
1287D4—86no—
1288D4—86no—
1289D4—86no—
1290D4—86no—
1291D4—86no—
1292D4—86no—
1293D4—86no—
1294D4—166no—
1295D4—166no—
1296D4—166no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—23no—
1317C2×C4—21no—
1318C2×C4—23no—
1319C2×C4—21no—
1320C2×C4—23no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—23no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—23no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—23no—
1334C2×C4—23no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—23no—
1339C2×C4—23no—
1340C2×C4—23no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—23no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—23no—
1350C2×C4—23no—
1351C2×C4—23no—
1352C2×C4—23no—
1353C2×C4—23no—
1354C2×C4—21no—
1355C2×C4—23no—
1356C2×C4—23no—
1357C2×C4—23no—
1358C2×C4—23no—
1359C2×C4—21no—
1360C2×C4—23no—
1361C2×C4—23no—
1362C2×C4—21no—
1363C2×C4—23no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—44no—
1368C2×C4—424no—
1369C2×C4—412no—
1370C2×C4—412no—
1371C2×C4—412no—
1372C2×C4—412no—
1373C2×C4—412no—
1374C2×C4—412no—
1375C2×C4—86no—
1376C2×C4—86no—
1377C2×C4—86no—
1378C2×C4—166no—
1379C2×C4C2×H(5,𝔽2)16yes—
1380C2×C4C2×H(5,𝔽2)16yes—
1381C2×C4C2×H(5,𝔽2)16yes—
1382C2×C4#58512yes—
1383C2×C4#58512yes—
1384C22—22no—
1385C22—22no—
1386C22—22no—
1387C22—41no—
1388C22—41no—
1389C22—41no—
1390C22—41no—
1391C22—43no—
1392C22—41no—
1393C22—43no—
1394C22—43no—
1395C22—41no—
1396C22—41no—
1397C22—41no—
1398C22—43no—
1399C22—43no—
1400C22—43no—
1401C22—43no—
1402C22—43no—
1403C22—43no—
1404C22—41no—
1405C22—41no—
1406C22—41no—
1407C22—41no—
1408C22—43no—
1409C22—43no—
1410C22—43no—
1411C22—43no—
1412C22—43no—
1413C22—43no—
1414C22—41no—
1415C22—41no—
1416C22—43no—
1417C22—41no—
1418C22—43no—
1419C22—43no—
1420C22—41no—
1421C22—43no—
1422C22—41no—
1423C22—41no—
1424C22—43no—
1425C22—43no—
1426C22C22×H(5,𝔽2)11yescharacteristic
1427C22C22×H(5,𝔽2)11yescharacteristic
1428C22C22×H(5,𝔽2)11yescharacteristic
1429C22C2×#58511yescharacteristic
1430C22C2×#58511yescharacteristic
1431C22C2×#58511yescharacteristic
1432C222−1+611yescharacteristic
1433C4—22no—
1434C4—22no—
1435C4—41no—
1436C4—43no—
1437C4—43no—
1438C4—43no—
1439C4—43no—
1440C4—41no—
1441C4—43no—
1442C4—43no—
1443C4—41no—
1444C4—43no—
1445C4—41no—
1446C4—41no—
1447C4—43no—
1448C4—41no—
1449C4—41no—
1450C4—43no—
1451C4—41no—
1452C4—41no—
1453C4—41no—
1454C4—43no—
1455C4—43no—
1456C4—43no—
1457C4C2×#560112yes—
1458C2—42no—
1459C2—83no—
1460C2—81no—
1461C2—83no—
1462C2—83no—
1463C2—81no—
1464C2C22×#56011yescharacteristic
1465C2#6289711yescharacteristic
1466C2#6291911yescharacteristic
1467C2#6292211yescharacteristic
1468C2#6301911yescharacteristic
1469C2#6302011yescharacteristic
1470C2#6303511yescharacteristic
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. #53136C2semidirect
2. #53128C2semidirect
3. #53073C2semidirect
4. #53064C2semidirect
5. #52966C2semidirect
6. #52956C2semidirect
7. #52297C2semidirect
8. #46339C2semidirect
9. #46050C2semidirect
10. #46048C2semidirect
11. #45708C2semidirect
12. #45687C2semidirect
13. #45687C2semidirect
14. #45616C2semidirect
15. #45604C2semidirect
16. #45518C2semidirect
17. #36585C2semidirect
18. #36576C2semidirect
19. #36482C2semidirect
20. #36465C2semidirect
21. #36448C2semidirect
22. #36434C2semidirect
23. #36432C2semidirect
24. #36430C2semidirect
25. #36430C2semidirect
26. #36029C2semidirect
27. #35983C2semidirect
28. #35757C2semidirect
29. #35757C2semidirect
30. #35737C2semidirect
31. #35687C2semidirect

Maximal subgroups

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

subgroupindex
#531362
#531282
#530732
#530642
#529662
#529562
#522972
#463392
#460502
#460482
#457082
#456872
#456162
#456042
#455182
#365852
#365762
#364822
#364652
#364482
#364342
#364322
#364302
#360292
#359832
#357572
#357372
#356872