Finite Group Databasebeta

← #8260852

Subgroups — #8260852

Order 512.

4522 conjugacy classes of subgroups.

The subgroup lattice has 1499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59549C212yesmaximal, complemented
2#58876C214yesmaximal, complemented
3#58309C214yesmaximal, complemented
4#57355C214yesmaximal, complemented
5#55809C214yesmaximal, complemented
6#53347C212yesmaximal, complemented
7#53096C212yesmaximal, complemented
8#52169C211yesmaximal, characteristic, complemented
9#50837C214yesmaximal, complemented
10#46545C214yesmaximal, complemented
11#45956C212yesmaximal, complemented
12#45499C212yesmaximal, complemented
13#45396C212yesmaximal, complemented
14#45385C212yesmaximal, complemented
15#44974C212yesmaximal, complemented
16#42939C212yesmaximal, complemented
17#42542C212yesmaximal, complemented
18#40068C212yesmaximal, complemented
19#40006C212yesmaximal, complemented
20#39743C211yesmaximal, characteristic, complemented
21#39632C211yesmaximal, characteristic, complemented
22#38922C212yesmaximal, complemented
23#38452C212yesmaximal, complemented
24#38035C212yesmaximal, complemented
25#37315C211yesmaximal, characteristic, complemented
26#37145C212yesmaximal, complemented
27#36315C211yesmaximal, characteristic, complemented
28#36273C211yesmaximal, characteristic, complemented
29#35313C211yesmaximal, characteristic, complemented
30C2×#555C2212yes—
31C2×#548C2212yes—
32C2×#529C2212yes—
33#2863C2212yes—
34#2863C2212yes—
35#2861C2212yes—
36#2858C2212yes—
37#2857C2212yes—
38#2857C2211yescharacteristic
39#2856C2211yescharacteristic
40#2855C2212yes—
41#2841C2214yes—
42#2838C2214yes—
43#2836C2214yes—
44#2829C2214yes—
45#2826C2214yes—
46#2813C2214yes—
47#2813C2214yes—
48#2808C2212yes—
49#2806C2212yes—
50#2805C2214yes—
51#2804C2212yes—
52#2801C2214yes—
53#2801C2214yes—
54#2799C2214yes—
55#2795C2214yes—
56#2791C2214yes—
57#2788C2214yes—
58#2783C2214yes—
59#2779C2214yes—
60#2778C2214yes—
61#2778C2214yes—
62#2759C2214yes—
63#2756C2214yes—
64#2756C2214yes—
65#2751C2214yes—
66#2750C2214yes—
67#2749C2214yes—
68#2748C2214yes—
69#2746C2214yes—
70#2745C2214yes—
71#2741C2214yes—
72#2733C2212yes—
73#2732C2212yes—
74#2732C2212yes—
75#2730C2214yes—
76#2729C2214yes—
77#2727C2211yescharacteristic
78#2727C2212yes—
79#2726C2211yescharacteristic
80#2724C2212yes—
81#2720C2214yes—
82#2715C2214yes—
83#2715C2214yes—
84#2715C2212yes—
85#2713C2214yes—
86#2712C2214yes—
87#2711C2214yes—
88#2710C2214yes—
89#2709C2214yes—
90#2707C2214yes—
91#2707C2212yes—
92#2702C2214yes—
93#2702C2212yes—
94#2701C2214yes—
95#2701C2214yes—
96#2700C2214yes—
97#2700C2214yes—
98#2700C2214yes—
99#2699C2214yes—
100#2699C2214yes—
101#2695C2212yes—
102#2695C2214yes—
103#2694C2214yes—
104#2693C2214yes—
105#2691C2214yes—
106#2687C2214yes—
107#2686C2214yes—
108#2683C2211yescharacteristic
109#2682C2211yescharacteristic
110#2681C2214yes—
111#2676C2214yes—
112#2676C2214yes—
113#2676C2212yes—
114#2673C2214yes—
115#2672C2214yes—
116#2672C2214yes—
117#2671C2212yes—
118#2667C2214yes—
119#2664C2214yes—
120#2656C2212yes—
121#2653C2214yes—
122#2653C2214yes—
123#2648C2214yes—
124#2646C2212yes—
125#2645C2212yes—
126#2645C2212yes—
127#2632C2214yes—
128#2624C2212yes—
129#2624C2212yes—
130#2620C2212yes—
131#2610C2214yes—
132#2606C2214yes—
133#2602C2214yes—
134#2594C2214yes—
135#2592C2212yes—
136#2587C2214yes—
137#2582C2212yes—
138#2576C2214yes—
139#2567C2212yes—
140#2560C2214yes—
141#2559C2214yes—
142#2558C2214yes—
143#2556C2214yes—
144#2556C2214yes—
145#2555C2214yes—
146#2552C2212yes—
147#2552C2211yescharacteristic
148#2551C2211yescharacteristic
149#2547C2211yescharacteristic
150#2543C2214yes—
151#2541C2211yescharacteristic
152#2538C2212yes—
153#2537C2214yes—
154#2537C2212yes—
155#2531C2214yes—
156#2531C2214yes—
157#2529C2214yes—
158#2526C2214yes—
159#2522C2214yes—
160#2514C2212yes—
161#2514C2212yes—
162#2512C2212yes—
163#2511C2212yes—
164#2511C2212yes—
165#2511C2212yes—
166#2507C2212yes—
167#2502C2212yes—
168#2501C2212yes—
169#2500C2212yes—
170#2497C2212yes—
171#2497C2212yes—
172#2494C2212yes—
173#2494C2214yes—
174#2493C2214yes—
175#2493C2214yes—
176#2492C2212yes—
177#2492C2212yes—
178#2491C2212yes—
179#2491C2212yes—
180#2489C2212yes—
181#2488C2214yes—
182#2485C2212yes—
183#2485C2212yes—
184#2474C2214yes—
185#2466C2214yes—
186#2464C2214yes—
187#2463C2214yes—
188#2459C2214yes—
189#2459C2214yes—
190#2457C2214yes—
191#2452C2212yes—
192#2451C2212yes—
193#2450C2214yes—
194#2448C2212yes—
195#2447C2214yes—
196#2447C2212yes—
197#2445C2212yes—
198#2444C2214yes—
199#2444C2214yes—
200#2441C2214yes—
201#2438C2214yes—
202#2431C2212yes—
203#2428C2212yes—
204#2427C2214yes—
205#2427C2212yes—
206#2426C2212yes—
207#2423C2214yes—
208#2423C2212yes—
209#2417C2212yes—
210#2416C2212yes—
211#2416C2212yes—
212#2415C2214yes—
213#2415C2212yes—
214#2415C2212yes—
215#2414C2212yes—
216#2409C2212yes—
217#2407C2212yes—
218#2407C2212yes—
219#2407C2212yes—
220#2396C2212yes—
221#2392C2212yes—
222#2392C2212yes—
223#2378C2214yes—
224#2366C2211yescharacteristic
225#2365C2211yescharacteristic
226#2363C2212yes—
227#2362C2212yes—
228#2357C2212yes—
229#2354C2211yescharacteristic
230#2354C2211yescharacteristic
231#2354C2212yes—
232#2353C2214yes—
233#2352C2212yes—
234D4×C4⋊C4C2212yes—
235#2346C2212yes—
236#2339C2212yes—
237#2337C2214yes—
238#2329C2214yes—
239#2325C2212yes—
240#2325C2212yes—
241#2324C2212yes—
242#2323C2212yes—
243#2317C2211yescharacteristic
244#2316C2211yescharacteristic
245#2316C2212yes—
246#2310C2211yescharacteristic
247#2310C2211yescharacteristic
248C4×C22⋊Q8C2212yes—
249C4×#121C2212yes—
250C4×#121C2211yescharacteristic
251C4×#121C2212yes—
252C4×#121C2211yescharacteristic
253#2297C2212yes—
254#2296C2211yescharacteristic
255#2295C2212yes—
256C2×#391C2211yescharacteristic
257#2293C2212yes—
258C4×#117C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2311yescharacteristic
261#555—48no—
262#548—48no—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×#127C2311yescharacteristic
267C2×#127C2312yes—
268#529—48no—
269C2×#126C2312yes—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2312yes—
276C2×#124C2314yes—
277C2×#124C2314yes—
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#124C2314yes—
281C2×#124C2312yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×#121C2312yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2311yescharacteristic
303C2×#121C2314yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C2×#117C2312yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2314yes—
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2312yes—
337C22×C42C2312yes—
338C22×C42C2311yescharacteristic
339#401C2314yes—
340#401C2314yes—
341#401C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2312yes—
361#399C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#397C2314yes—
379#397C2312yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2312yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2312yes—
407#396C2312yes—
408#396C2312yes—
409#396C2312yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2312yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2312yes—
434#394C2312yes—
435#394C2312yes—
436#394C2312yes—
437#394C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2312yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#392C2312yes—
458#392C2312yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2314yes—
486#391C2312yes—
487#390C2314yes—
488#390C2312yes—
489#390C2314yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2311yescharacteristic
497#390C2312yes—
498#390C2314yes—
499#390C2312yes—
500#390C2311yescharacteristic
501#390C2312yes—
502#390C2314yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2311yescharacteristic
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2311yescharacteristic
535#389C2311yescharacteristic
536#389C2312yes—
537#389C2314yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2311yescharacteristic
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2312yes—
622#386C2312yes—
623#386C2314yes—
624#386C2312yes—
625#386C2312yes—
626#386C2314yes—
627#386C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2312yes—
642#385C2312yes—
643#385C2312yes—
644#385C2312yes—
645#384C2314yes—
646#384C2312yes—
647#384C2312yes—
648#384C2311yescharacteristic
649#384C2312yes—
650#384C2311yescharacteristic
651#383C2314yes—
652#383C2314yes—
653#382C2312yes—
654#382C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2311yescharacteristic
667#380C2312yes—
668#380C2314yes—
669#380C2312yes—
670#380C2314yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2311yescharacteristic
678#380C2314yes—
679#380C2314yes—
680#380C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2314yes—
710#376C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2314yes—
714C43C2312yes—
715C2×#41—44no—
716C2×#41—44no—
717C2×#41—44no—
718C22×Q8—24no—
719C22×Q8—42no—
720C22×Q8—42no—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2414yes—
737C22×D4C2414yes—
738C22×D4C2412yes—
739C22×D4C2414yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C4⋊Q8—42no—
754C4⋊Q8—44no—
755C4⋊Q8—82no—
756#127—42no—
757#127—82no—
758#126—44no—
759#126—44no—
760#126—84no—
761#125—44no—
762#125—82no—
763#125—84no—
764#124—48no—
765#124—48no—
766#124—44no—
767#124—44no—
768#124—48no—
769#124—48no—
770#124—82no—
771#123—44no—
772#123—44no—
773#123—84no—
774#123—84no—
775#123—84no—
776C22⋊Q8—28no—
777C22⋊Q8—44no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—82no—
784C22⋊Q8—84no—
785C22⋊Q8—84no—
786#121—28no—
787#121—24no—
788#121—44no—
789#121—44no—
790#121—44no—
791#121—48no—
792#121—44no—
793#121—44no—
794#121—42no—
795#121—44no—
796#121—48no—
797#121—84no—
798#121—84no—
799#121—84no—
800#121—82no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×D4—28no—
805C4×D4—28no—
806C4×D4—28no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—42no—
810C4×D4—42no—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4—48no—
814C4×D4—84no—
815C4×D4—84no—
816#117—24no—
817#117—24no—
818#117—42no—
819#117—44no—
820#117—48no—
821#117—44no—
822#117—42no—
823#117—44no—
824C2×C4⋊C4—42no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C42—44no—
944C2×C42—42no—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2412yes—
964C2×C42C2412yes—
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24C2512yes—
1026C24C2514yes—
1027C24C2512yes—
1028C24C2511yescharacteristic
1029#41—816no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—88no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—28no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—22no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—41no—
1059C2×D4—41no—
1060C2×D4—42no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—42no—
1064C2×D4—44no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—44no—
1073C2×D4—42no—
1074C2×D4—41no—
1075C2×D4—42no—
1076C2×D4—41no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—42no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C2×D4—42no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—42no—
1088C22×C4—22no—
1089C22×C4—22no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—28no—
1098C22×C4—22no—
1099C22×C4—24no—
1100C22×C4—22no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—42no—
1108C22×C4—44no—
1109C22×C4—42no—
1110C22×C4—41no—
1111C22×C4—41no—
1112C22×C4—42no—
1113C22×C4—42no—
1114C22×C4—42no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—42no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—42no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4H(5,𝔽2)14yes—
1127C22×C4C2514yes—
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2514yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2512yes—
1144C22×C4C2514yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—22no—
1155C4⋊C4—22no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—24no—
1166C4⋊C4—22no—
1167C4⋊C4—24no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—41no—
1171C4⋊C4—41no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—41no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—41no—
1212C4⋊C42−1+414yes—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—28no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—28no—
1225C22⋊C4—24no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—42no—
1264C22⋊C4—44no—
1265C22⋊C4—42no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C42—24no—
1270C42—24no—
1271C42—24no—
1272C42—24no—
1273C42—24no—
1274C42—22no—
1275C42—22no—
1276C42—24no—
1277C42—24no—
1278C42—41no—
1279C42—41no—
1280C42—42no—
1281C42—42no—
1282C42—42no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42—44no—
1287C42—44no—
1288C42—42no—
1289C42—44no—
1290C42—42no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—22no—
1298C23—24no—
1299C23—22no—
1300C23—22no—
1301C23—24no—
1302C23—22no—
1303C23—24no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—24no—
1310C23—22no—
1311C23—24no—
1312C23—24no—
1313C23—22no—
1314C23—22no—
1315C23—24no—
1316C23—22no—
1317C23—22no—
1318C23C2×H(5,𝔽2)12yes—
1319C23C2611yescharacteristic
1320Q8—48no—
1321Q8—84no—
1322Q8—84no—
1323Q8—84no—
1324Q8—164no—
1325D4—48no—
1326D4—48no—
1327D4—82no—
1328D4—84no—
1329D4—82no—
1330D4—84no—
1331D4—88no—
1332D4—88no—
1333D4—84no—
1334D4—84no—
1335D4—88no—
1336D4—164no—
1337D4—162no—
1338D4—164no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—22no—
1347C2×C4—28no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—21no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—21no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—48no—
1409C2×C4—48no—
1410C2×C4—82no—
1411C2×C4—82no—
1412C2×C4—88no—
1413C2×C4—84no—
1414C2×C4—84no—
1415C2×C4—84no—
1416C2×C4—88no—
1417C2×C4—164no—
1418C2×C4—162no—
1419C2×C4—164no—
1420C2×C4C2×H(5,𝔽2)12yes—
1421C2×C4C2×H(5,𝔽2)12yes—
1422C2×C4C2×2−1+412yes—
1423C2×C4C2×2−1+414yes—
1424C2×C4#58512yes—
1425C2×C4#58512yes—
1426C2×C4#58512yes—
1427C22—22no—
1428C22—22no—
1429C22—22no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—42no—
1435C22—42no—
1436C22—44no—
1437C22—42no—
1438C22—44no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—44no—
1443C22—44no—
1444C22—42no—
1445C22—42no—
1446C22—44no—
1447C22—42no—
1448C22—42no—
1449C22—44no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—44no—
1455C22C22×H(5,𝔽2)11yescharacteristic
1456C22C22×2−1+411yescharacteristic
1457C22C2×#58511yescharacteristic
1458C22C2×#58511yescharacteristic
1459C22C2×#58511yescharacteristic
1460C22H(7,𝔽2)11yescharacteristic
1461C22H(7,𝔽2)11yescharacteristic
1462C4—22no—
1463C4—22no—
1464C4—22no—
1465C4—24no—
1466C4—42no—
1467C4—42no—
1468C4—44no—
1469C4—42no—
1470C4—44no—
1471C4—44no—
1472C4—42no—
1473C4—41no—
1474C4—42no—
1475C4—44no—
1476C4—42no—
1477C4—41no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—42no—
1483C4—42no—
1484C4—44no—
1485C4—42no—
1486C4#356014yes—
1487C2—42no—
1488C2—82no—
1489C2—82no—
1490C2—84no—
1491C2C2×#356011yescharacteristic
1492C2#6291011yescharacteristic
1493C2#6292911yescharacteristic
1494C2#6294411yescharacteristic
1495C2#6295511yescharacteristic
1496C2#6303411yescharacteristic
1497C2#6306011yescharacteristic
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. #59549C2semidirect
2. #58876C2semidirect
3. #58309C2semidirect
4. #57355C2semidirect
5. #55809C2semidirect
6. #53347C2semidirect
7. #53096C2semidirect
8. #52169C2semidirect
9. #50837C2semidirect
10. #46545C2semidirect
11. #45956C2semidirect
12. #45499C2semidirect
13. #45396C2semidirect
14. #45385C2semidirect
15. #44974C2semidirect
16. #42939C2semidirect
17. #42542C2semidirect
18. #40068C2semidirect
19. #40006C2semidirect
20. #39743C2semidirect
21. #39632C2semidirect
22. #38922C2semidirect
23. #38452C2semidirect
24. #38035C2semidirect
25. #37315C2semidirect
26. #37145C2semidirect
27. #36315C2semidirect
28. #36273C2semidirect
29. #35313C2semidirect

Maximal subgroups

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

subgroupindex
#595492
#588762
#583092
#573552
#558092
#533472
#530962
#521692
#508372
#465452
#459562
#454992
#453962
#453852
#449742
#429392
#425422
#400682
#400062
#397432
#396322
#389222
#384522
#380352
#373152
#371452
#363152
#362732
#353132