Finite Group Databasebeta

← #8260857

Subgroups — #8260857

Order 512.

4292 conjugacy classes of subgroups.

The subgroup lattice has 1435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59712C212yesmaximal, complemented
2#58870C214yesmaximal, complemented
3#58282C214yesmaximal, complemented
4#57571C214yesmaximal, complemented
5#55067C214yesmaximal, complemented
6#53357C212yesmaximal, complemented
7#53019C212yesmaximal, complemented
8#52280C211yesmaximal, characteristic
9#50795C214yesmaximal, complemented
10#47386C214yesmaximal, complemented
11#46079C212yesmaximal, complemented
12#46007C212yesmaximal, complemented
13#45325C212yesmaximal, complemented
14#45098C212yesmaximal, complemented
15#44916C212yesmaximal, complemented
16#42918C212yesmaximal, complemented
17#42534C212yesmaximal, complemented
18#40212C212yesmaximal, complemented
19#40000C212yesmaximal, complemented
20#39752C211yesmaximal, characteristic, complemented
21#39632C211yesmaximal, characteristic, complemented
22#39370C212yesmaximal, complemented
23#38828C212yesmaximal, complemented
24#38203C212yesmaximal, complemented
25#37307C211yesmaximal, characteristic, complemented
26#37142C212yesmaximal, complemented
27#36459C211yesmaximal, characteristic, complemented
28#36288C211yesmaximal, characteristic, complemented
29#35312C211yesmaximal, characteristic, complemented
30C2×#556C2212yes—
31C2×#544C2212yes—
32C2×#544C2211yescharacteristic
33C2×#536C2211yescharacteristic
34#2863C2212yes—
35#2862C2212yes—
36#2862C2212yes—
37#2861C2212yes—
38#2860C2212yes—
39#2859C2212yes—
40#2857C2211yescharacteristic
41#2857C2211yescharacteristic
42#2845C2214yes—
43#2841C2214yes—
44#2839C2214yes—
45#2836C2214yes—
46#2831C2214yes—
47#2821C2214yes—
48#2814C2214yes—
49#2809C2212yes—
50#2808C2211yescharacteristic
51#2806C2212yes—
52#2806C2211yescharacteristic
53#2806C2212yes—
54#2806C2212yes—
55#2806C2212yes—
56#2805C2214yes—
57#2804C2212yes—
58#2803C2212yes—
59#2799C2214yes—
60#2796C2214yes—
61#2793C2214yes—
62#2791C2214yes—
63#2788C2214yes—
64#2788C2214yes—
65#2786C2214yes—
66#2781C2212yes—
67#2777C2214yes—
68#2776C2214yes—
69#2775C2212yes—
70#2773C2214yes—
71#2767C2214yes—
72#2766C2214yes—
73#2766C2214yes—
74#2764C2214yes—
75#2761C2214yes—
76#2759C2214yes—
77#2756C2212yes—
78#2755C2214yes—
79#2755C2214yes—
80#2755C2214yes—
81#2755C2214yes—
82#2754C2214yes—
83#2748C2214yes—
84#2747C2214yes—
85#2746C2214yes—
86#2744C2214yes—
87#2740C2214yes—
88#2739C2214yes—
89#2733C2211yescharacteristic
90#2732C2212yes—
91#2732C2212yes—
92#2731C2214yes—
93#2730C2214yes—
94#2730C2212yes—
95#2729C2214yes—
96#2729C2214yes—
97#2727C2211yescharacteristic
98#2725C2214yes—
99#2721C2214yes—
100#2716C2214yes—
101#2715C2214yes—
102#2714C2212yes—
103#2712C2214yes—
104#2706C2214yes—
105#2706C2214yes—
106#2705C2214yes—
107#2704C2214yes—
108#2704C2214yes—
109#2702C2214yes—
110#2702C2214yes—
111#2695C2214yes—
112#2689C2214yes—
113#2689C2214yes—
114#2687C2214yes—
115#2683C2214yes—
116#2674C2214yes—
117#2674C2214yes—
118#2674C2214yes—
119#2664C2214yes—
120#2659C2212yes—
121#2654C2214yes—
122#2654C2214yes—
123#2649C2214yes—
124#2646C2212yes—
125#2642C2212yes—
126#2640C2212yes—
127#2637C2214yes—
128#2634C2214yes—
129#2629C2212yes—
130#2629C2212yes—
131#2625C2212yes—
132#2612C2214yes—
133#2612C2214yes—
134#2605C2214yes—
135#2602C2214yes—
136#2588C2214yes—
137#2581C2212yes—
138#2574C2214yes—
139#2569C2214yes—
140#2565C2212yes—
141#2563C2211yescharacteristic
142#2562C2212yes—
143#2560C2214yes—
144#2560C2214yes—
145#2557C2214yes—
146#2552C2212yes—
147#2552C2211yescharacteristic
148#2551C2212yes—
149#2551C2211yescharacteristic
150#2546C2211yescharacteristic
151#2546C2214yes—
152#2546C2214yes—
153#2538C2214yes—
154#2536C2212yes—
155#2532C2214yes—
156#2532C2214yes—
157#2530C2214yes—
158#2529C2214yes—
159#2527C2214yes—
160#2526C2214yes—
161#2526C2214yes—
162#2521C2214yes—
163#2519C2214yes—
164#2515C2214yes—
165#2511C2212yes—
166#2511C2212yes—
167#2508C2212yes—
168#2506C2214yes—
169#2502C2212yes—
170#2499C2212yes—
171#2497C2212yes—
172#2496C2212yes—
173#2495C2212yes—
174#2494C2212yes—
175#2492C2212yes—
176#2492C2212yes—
177#2492C2212yes—
178#2492C2212yes—
179#2492C2214yes—
180#2492C2212yes—
181#2490C2212yes—
182#2489C2212yes—
183#2489C2212yes—
184#2489C2212yes—
185#2488C2214yes—
186#2488C2214yes—
187#2486C2212yes—
188#2486C2212yes—
189#2485C2212yes—
190#2465C2214yes—
191#2458C2214yes—
192#2458C2214yes—
193#2457C2214yes—
194#2453C2212yes—
195#2453C2212yes—
196#2452C2214yes—
197#2451C2214yes—
198#2451C2214yes—
199#2451C2212yes—
200#2450C2214yes—
201#2446C2214yes—
202#2446C2214yes—
203#2442C2212yes—
204#2442C2212yes—
205#2441C2212yes—
206#2441C2212yes—
207#2441C2212yes—
208#2440C2212yes—
209#2440C2212yes—
210#2439C2212yes—
211#2439C2212yes—
212#2429C2212yes—
213#2423C2212yes—
214#2423C2212yes—
215#2423C2214yes—
216#2421C2214yes—
217#2417C2212yes—
218#2417C2212yes—
219#2415C2212yes—
220#2409C2212yes—
221#2395C2212yes—
222#2392C2212yes—
223#2388C2212yes—
224#2382C2214yes—
225#2373C2214yes—
226#2369C2212yes—
227#2369C2211yescharacteristic
228#2365C2211yescharacteristic
229#2360C2212yes—
230#2355C2211yescharacteristic
231#2354C2212yes—
232#2354C2211yescharacteristic
233#2352C2212yes—
234D4×C4⋊C4C2212yes—
235#2347C2212yes—
236#2346C2212yes—
237#2345C2212yes—
238Q8×C22⋊C4C2212yes—
239#2334C2214yes—
240#2332C2214yes—
241#2329C2212yes—
242#2325C2212yes—
243#2323C2212yes—
244#2311C2212yes—
245#2311C2211yescharacteristic
246#2310C2211yescharacteristic
247C4×C4⋊Q8C2212yes—
248C4×#125C2212yes—
249C4×#126C2212yes—
250C4×#124C2212yes—
251C4×C22⋊Q8C2211yescharacteristic
252C4×#121C2211yescharacteristic
253#2297C2211yescharacteristic
254#2295C2212yes—
255#2295C2212yes—
256C2×#391C2211yescharacteristic
257#2293C2212yes—
258C4×#117C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#556—48no—
262#544—44no—
263#544—48no—
264#536—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2314yes—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#124C2312yes—
286C2×#124C2314yes—
287C2×#124C2312yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2311yescharacteristic
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×#121C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2311yescharacteristic
318C2×#117C2311yescharacteristic
319C2×#117C2312yes—
320C2×#117C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2312yes—
324C22×C42C2311yescharacteristic
325#401C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2312yes—
353#399C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2312yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2312yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2312yes—
428#394C2312yes—
429#394C2312yes—
430#394C2312yes—
431#394C2312yes—
432#394C2312yes—
433#394C2312yes—
434#394C2314yes—
435#394C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2312yes—
444#393C2314yes—
445#392C2312yes—
446#392C2312yes—
447#392C2312yes—
448#392C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2312yes—
473#391C2311yescharacteristic
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2314yes—
477#391C2312yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2311yescharacteristic
482#391C2312yes—
483#391C2314yes—
484#391C2312yes—
485#390C2312yes—
486#390C2314yes—
487#390C2312yes—
488#390C2314yes—
489#390C2312yes—
490#390C2311yescharacteristic
491#390C2311yescharacteristic
492#390C2311yescharacteristic
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#389C2311yescharacteristic
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2314yes—
531#389C2314yes—
532#389C2311yescharacteristic
533#389C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2312yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
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#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#386C2312yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2312yes—
623#386C2312yes—
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#384C2312yes—
636#384C2311yescharacteristic
637#384C2311yescharacteristic
638#384C2312yes—
639#384C2312yes—
640#384C2314yes—
641#383C2312yes—
642#383C2314yes—
643#383C2314yes—
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#382C2314yes—
649#382C2314yes—
650#382C2312yes—
651#382C2314yes—
652#382C2312yes—
653#381C2314yes—
654#381C2314yes—
655#381C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2311yescharacteristic
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2311yescharacteristic
675#380C2314yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2314yes—
710#376C2314yes—
711#376C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C43C2312yes—
716C2×#41—24no—
717C2×#41—42no—
718C2×#41—42no—
719C22×Q8—24no—
720C22×Q8—42no—
721C22×Q8—42no—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C4⋊Q8—28no—
746C4⋊Q8—28no—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—48no—
751C4⋊Q8—44no—
752C4⋊Q8—84no—
753C4⋊Q8—82no—
754C4⋊Q8—82no—
755#126—28no—
756#126—48no—
757#126—48no—
758#126—48no—
759#125—28no—
760#125—48no—
761#125—44no—
762#125—44no—
763#125—44no—
764#125—44no—
765#124—44no—
766#124—44no—
767#124—48no—
768#123—48no—
769#123—84no—
770#123—84no—
771C22⋊Q8—28no—
772C22⋊Q8—48no—
773C22⋊Q8—48no—
774C22⋊Q8—48no—
775C22⋊Q8—48no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—42no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—82no—
782C22⋊Q8—84no—
783#121—24no—
784C4×Q8—42no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×Q8—48no—
788C4×Q8—44no—
789C4×Q8—84no—
790C4×D4—28no—
791C4×D4—42no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—84no—
795#117—24no—
796#117—24no—
797#117—28no—
798#117—42no—
799#117—44no—
800#117—44no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4—42no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C42—42no—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2411yescharacteristic
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011C24C2512yes—
1012C24C2512yes—
1013C24C2511yescharacteristic
1014#41—88no—
1015C2×Q8—24no—
1016C2×Q8—28no—
1017C2×Q8—28no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—22no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—22no—
1024C2×Q8—41no—
1025C2×Q8—44no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—41no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—41no—
1032C2×Q8—42no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—41no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—88no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—22no—
1044C2×D4—22no—
1045C2×D4—42no—
1046C2×D4—42no—
1047C2×D4—41no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—41no—
1053C2×D4—42no—
1054C2×D4—41no—
1055C2×D4—42no—
1056C2×D4—41no—
1057C2×D4—42no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—42no—
1073C22×C4—41no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—42no—
1084C22×C42−1+414yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—22no—
1129C4⋊C4—28no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—41no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—41no—
1137C4⋊C4—42no—
1138C4⋊C4—41no—
1139C4⋊C4—42no—
1140C4⋊C4—41no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—41no—
1177C4⋊C4H(5,𝔽2)14yes—
1178C4⋊C42−1+414yes—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C42—28no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—24no—
1228C42—24no—
1229C42—22no—
1230C42—22no—
1231C42—24no—
1232C42—24no—
1233C42—41no—
1234C42—41no—
1235C42—42no—
1236C42—44no—
1237C42—42no—
1238C42—44no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—42no—
1244C42—44no—
1245C42—42no—
1246C42—42no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—21no—
1251C23—21no—
1252C23—21no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23C2×2−1+412yes—
1268C23C2611yescharacteristic
1269Q8—48no—
1270Q8—88no—
1271Q8—88no—
1272Q8—84no—
1273Q8—82no—
1274Q8—84no—
1275Q8—82no—
1276Q8—162no—
1277D4—48no—
1278D4—82no—
1279D4—82no—
1280D4—84no—
1281D4—84no—
1282D4—84no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—22no—
1293C2×C4—28no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—48no—
1355C2×C4—48no—
1356C2×C4—82no—
1357C2×C4—82no—
1358C2×C4—84no—
1359C2×C4—162no—
1360C2×C4—164no—
1361C2×C4—164no—
1362C2×C4C2×H(5,𝔽2)14yes—
1363C2×C4C2×H(5,𝔽2)12yes—
1364C2×C4C2×2−1+412yes—
1365C2×C4C2×2−1+412yes—
1366C2×C4C2×2−1+414yes—
1367C2×C4C2×2−1+412yes—
1368C2×C4#58512yes—
1369C2×C4#58512yes—
1370C22—22no—
1371C22—22no—
1372C22—22no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—41no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22C22×H(5,𝔽2)11yescharacteristic
1392C22C22×2−1+411yescharacteristic
1393C22C22×2−1+411yescharacteristic
1394C22C2×#58511yescharacteristic
1395C22C2×#58511yescharacteristic
1396C22H(7,𝔽2)11yescharacteristic
1397C222−1+611yescharacteristic
1398C4—22no—
1399C4—24no—
1400C4—22no—
1401C4—22no—
1402C4—24no—
1403C4—42no—
1404C4—42no—
1405C4—44no—
1406C4—44no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—44no—
1411C4—44no—
1412C4—42no—
1413C4—42no—
1414C4—41no—
1415C4—44no—
1416C4—44no—
1417C4—42no—
1418C4—42no—
1419C4—41no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4#356114yes—
1424C2—42no—
1425C2—82no—
1426C2—82no—
1427C2C2×#356111yescharacteristic
1428C2#6291011yescharacteristic
1429C2#6293211yescharacteristic
1430C2#6294511yescharacteristic
1431C2#6295611yescharacteristic
1432C2#6303911yescharacteristic
1433C2#6304911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52280C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59712C2semidirect
2. #58870C2semidirect
3. #58282C2semidirect
4. #57571C2semidirect
5. #55067C2semidirect
6. #53357C2semidirect
7. #53019C2semidirect
9. #50795C2semidirect
10. #47386C2semidirect
11. #46079C2semidirect
12. #46007C2semidirect
13. #45325C2semidirect
14. #45098C2semidirect
15. #44916C2semidirect
16. #42918C2semidirect
17. #42534C2semidirect
18. #40212C2semidirect
19. #40000C2semidirect
20. #39752C2semidirect
21. #39632C2semidirect
22. #39370C2semidirect
23. #38828C2semidirect
24. #38203C2semidirect
25. #37307C2semidirect
26. #37142C2semidirect
27. #36459C2semidirect
28. #36288C2semidirect
29. #35312C2semidirect

Maximal subgroups

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

subgroupindex
#597122
#588702
#582822
#575712
#550672
#533572
#530192
#522802
#507952
#473862
#460792
#460072
#453252
#450982
#449162
#429182
#425342
#402122
#400002
#397522
#396322
#393702
#388282
#382032
#373072
#371422
#364592
#362882
#353122