Finite Group Databasebeta

← #8701626

Subgroups — #8701626

Order 512.

4353 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59933C212yesmaximal, complemented
2#59878C212yesmaximal, complemented
3#59752C212yesmaximal, complemented
4#59564C212yesmaximal, complemented
5#54813C214yesmaximal, complemented
6#54800C214yesmaximal, complemented
7#53986C214yesmaximal, complemented
8#52307C211yesmaximal, characteristic
9#51830C214yesmaximal, complemented
10#51248C214yesmaximal, complemented
11#50603C214yesmaximal, complemented
12#46158C211yesmaximal, characteristic, complemented
13#46023C211yesmaximal, characteristic, complemented
14#46005C211yesmaximal, characteristic, complemented
15#45237C212yesmaximal, complemented
16#45113C212yesmaximal, complemented
17#44898C212yesmaximal, complemented
18#42993C212yesmaximal, complemented
19#42786C212yesmaximal, complemented
20#42449C212yesmaximal, complemented
21#40000C212yesmaximal, complemented
22#39955C212yesmaximal, complemented
23#38978C212yesmaximal, complemented
24#37207C212yesmaximal, complemented
25#37199C212yesmaximal, complemented
26#37195C212yesmaximal, complemented
27#36446C211yesmaximal, characteristic, complemented
28#36312C211yesmaximal, characteristic, complemented
29#36299C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×#552C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×#536C2212yes—
34#2863C2212yes—
35#2862C2212yes—
36#2862C2211yescharacteristic
37#2860C2212yes—
38#2859C2212yes—
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2845C2212yes—
42#2829C2214yes—
43#2827C2214yes—
44#2820C2212yes—
45#2820C2212yes—
46#2814C2214yes—
47#2811C2211yescharacteristic
48#2808C2212yes—
49#2806C2212yes—
50#2806C2212yes—
51#2805C2212yes—
52#2799C2214yes—
53#2798C2214yes—
54#2797C2214yes—
55#2796C2214yes—
56#2788C2214yes—
57#2785C2212yes—
58#2785C2212yes—
59#2785C2212yes—
60#2783C2214yes—
61#2779C2214yes—
62#2777C2214yes—
63#2777C2214yes—
64#2774C2214yes—
65#2773C2214yes—
66#2772C2214yes—
67#2772C2214yes—
68#2772C2214yes—
69#2768C2214yes—
70#2767C2214yes—
71#2761C2214yes—
72#2756C2214yes—
73#2755C2214yes—
74#2754C2214yes—
75#2754C2214yes—
76#2753C2214yes—
77#2749C2214yes—
78#2748C2214yes—
79#2747C2214yes—
80#2744C2214yes—
81#2741C2214yes—
82#2734C2214yes—
83#2733C2212yes—
84#2733C2211yescharacteristic
85#2733C2211yescharacteristic
86#2733C2212yes—
87#2733C2212yes—
88#2733C2211yescharacteristic
89#2732C2212yes—
90#2731C2214yes—
91#2730C2214yes—
92#2730C2214yes—
93#2729C2214yes—
94#2727C2214yes—
95#2727C2212yes—
96#2725C2214yes—
97#2719C2214yes—
98#2716C2214yes—
99#2715C2214yes—
100#2715C2214yes—
101#2713C2214yes—
102#2713C2214yes—
103#2710C2214yes—
104#2707C2214yes—
105#2706C2214yes—
106#2704C2214yes—
107#2694C2214yes—
108#2694C2214yes—
109#2693C2214yes—
110#2674C2214yes—
111#2666C2214yes—
112#2664C2214yes—
113#2663C2214yes—
114#2654C2214yes—
115#2650C2214yes—
116#2649C2214yes—
117#2644C2214yes—
118#2636C2214yes—
119#2630C2214yes—
120#2616C2212yes—
121#2612C2214yes—
122#2612C2214yes—
123#2611C2214yes—
124#2610C2214yes—
125#2605C2214yes—
126#2605C2214yes—
127#2604C2214yes—
128#2602C2214yes—
129#2595C2214yes—
130#2593C2214yes—
131#2589C2214yes—
132#2589C2214yes—
133#2584C2212yes—
134#2582C2211yescharacteristic
135#2582C2212yes—
136#2582C2211yescharacteristic
137#2581C2212yes—
138#2568C2212yes—
139#2568C2211yescharacteristic
140#2562C2212yes—
141#2557C2214yes—
142#2554C2214yes—
143#2553C2214yes—
144#2550C2214yes—
145#2547C2211yescharacteristic
146#2547C2212yes—
147#2538C2212yes—
148#2538C2211yescharacteristic
149#2538C2211yescharacteristic
150#2536C2212yes—
151#2532C2214yes—
152#2531C2214yes—
153#2530C2214yes—
154#2529C2214yes—
155#2529C2214yes—
156#2529C2214yes—
157#2526C2214yes—
158#2522C2214yes—
159#2522C2214yes—
160#2521C2214yes—
161#2520C2214yes—
162#2519C2214yes—
163#2515C2214yes—
164#2509C2212yes—
165#2509C2214yes—
166#2508C2212yes—
167#2508C2214yes—
168#2502C2212yes—
169#2499C2212yes—
170#2499C2212yes—
171#2497C2212yes—
172#2497C2212yes—
173#2496C2212yes—
174#2496C2212yes—
175#2495C2212yes—
176#2495C2212yes—
177#2489C2214yes—
178#2489C2214yes—
179#2489C2212yes—
180#2489C2212yes—
181#2489C2212yes—
182#2489C2212yes—
183#2487C2212yes—
184#2485C2212yes—
185#2485C2212yes—
186#2477C2214yes—
187#2475C2214yes—
188#2474C2214yes—
189#2474C2214yes—
190#2471C2214yes—
191#2470C2214yes—
192#2467C2214yes—
193#2448C2214yes—
194#2448C2212yes—
195#2447C2212yes—
196#2442C2212yes—
197#2441C2212yes—
198#2441C2212yes—
199#2441C2212yes—
200#2440C2212yes—
201#2439C2212yes—
202#2439C2214yes—
203#2429C2212yes—
204#2429C2212yes—
205#2423C2212yes—
206#2423C2212yes—
207#2423C2212yes—
208#2423C2212yes—
209#2421C2212yes—
210#2421C2212yes—
211#2417C2212yes—
212#2417C2212yes—
213#2415C2212yes—
214#2415C2212yes—
215#2409C2212yes—
216#2409C2212yes—
217#2388C2212yes—
218#2388C2212yes—
219#2388C2212yes—
220#2382C2212yes—
221#2382C2212yes—
222#2379C2212yes—
223#2373C2214yes—
224#2372C2214yes—
225#2362C2212yes—
226#2362C2212yes—
227#2360C2212yes—
228#2360C2212yes—
229#2355C2211yescharacteristic
230#2354C2212yes—
231#2354C2211yescharacteristic
232#2352C2212yes—
233Q8×C4⋊C4C2211yescharacteristic
234D4×C4⋊C4C2211yescharacteristic
235#2346C2212yes—
236#2346C2214yes—
237#2344C2212yes—
238Q8×C22⋊C4C2212yes—
239Q8×C22⋊C4C2212yes—
240Q8×C22⋊C4C2212yes—
241#2334C2214yes—
242#2323C2214yes—
243#2320C2214yes—
244#2311C2212yes—
245#2311C2212yes—
246C4×#124C2212yes—
247C4×#124C2212yes—
248C4×#124C2212yes—
249C4×#124C2211yescharacteristic
250C4×#124C2211yescharacteristic
251C4×#124C2211yescharacteristic
252C4×#124C2212yes—
253#2295C2212yes—
254#2295C2212yes—
255#2295C2212yes—
256#2295C2212yes—
257#2293C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2312yes—
261#557—44no—
262#552—48no—
263D4×Q8—44no—
264#536—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#124C2312yes—
280C2×#124C2311yescharacteristic
281C2×#124C2311yescharacteristic
282C2×#124C2311yescharacteristic
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2314yes—
321C2×#117C2314yes—
322C2×#117C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
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#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2312yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2312yes—
409#395C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2312yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2312yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#393C2314yes—
429#393C2314yes—
430#393C2312yes—
431#393C2312yes—
432#393C2312yes—
433#393C2314yes—
434#392C2312yes—
435#392C2312yes—
436#392C2312yes—
437#392C2312yes—
438#392C2312yes—
439#392C2312yes—
440#392C2312yes—
441#392C2312yes—
442#392C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2312yes—
468#391C2312yes—
469#391C2311yescharacteristic
470#391C2311yescharacteristic
471#391C2312yes—
472#391C2312yes—
473#391C2311yescharacteristic
474#390C2314yes—
475#390C2314yes—
476#390C2314yes—
477#390C2311yescharacteristic
478#390C2312yes—
479#390C2312yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2311yescharacteristic
485#390C2312yes—
486#390C2311yescharacteristic
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2312yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2312yes—
562#388C2314yes—
563#388C2314yes—
564#388C2312yes—
565#388C2312yes—
566#388C2314yes—
567#388C2312yes—
568#388C2314yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2312yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
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#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#384C2311yescharacteristic
634#384C2311yescharacteristic
635#384C2312yes—
636#384C2312yes—
637#384C2311yescharacteristic
638#384C2311yescharacteristic
639#383C2314yes—
640#383C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2311yescharacteristic
645#382C2314yes—
646#382C2314yes—
647#382C2312yes—
648#382C2311yescharacteristic
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#382C2312yes—
655#382C2312yes—
656#382C2311yescharacteristic
657#382C2312yes—
658#382C2312yes—
659#381C2314yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2314yes—
671#380C2312yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2314yes—
710#376C2314yes—
711#376C2314yes—
712#376C2314yes—
713C43C2311yescharacteristic
714C43C2312yes—
715C43C2312yes—
716C2×#41—44no—
717C2×#41—44no—
718C2×#41—44no—
719C22×Q8—28no—
720C22×Q8—44no—
721C22×Q8—44no—
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×Q8C2414yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C4⋊Q8—42no—
746C4⋊Q8—44no—
747C4⋊Q8—42no—
748C4⋊Q8—44no—
749C4⋊Q8—48no—
750#126—48no—
751#126—48no—
752#126—48no—
753#125—44no—
754#125—44no—
755#125—44no—
756#125—48no—
757#125—44no—
758#125—48no—
759#124—28no—
760#124—24no—
761#124—44no—
762#124—42no—
763#124—42no—
764#124—44no—
765#124—44no—
766#124—48no—
767#123—48no—
768#123—48no—
769#123—48no—
770C22⋊Q8—28no—
771C22⋊Q8—28no—
772C22⋊Q8—48no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—48no—
779C4×Q8—24no—
780C4×Q8—28no—
781C4×Q8—28no—
782C4×Q8—42no—
783C4×Q8—42no—
784C4×Q8—44no—
785C4×Q8—42no—
786C4×Q8—42no—
787C4×Q8—44no—
788C4×Q8—42no—
789C4×Q8—44no—
790C4×D4—44no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—42no—
794C4×D4—42no—
795C4×D4—42no—
796C4×D4—44no—
797C4×D4—44no—
798#117—48no—
799#117—48no—
800#117—44no—
801#117—44no—
802#117—44no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
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—
1013C24C2512yes—
1014#41—816no—
1015C2×Q8—24no—
1016C2×Q8—28no—
1017C2×Q8—22no—
1018C2×Q8—22no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—22no—
1023C2×Q8—22no—
1024C2×Q8—41no—
1025C2×Q8—41no—
1026C2×Q8—42no—
1027C2×Q8—41no—
1028C2×Q8—41no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—41no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—816no—
1038C2×Q8H(5,𝔽2)14yes—
1039C2×Q82−1+414yes—
1040C2×D4—24no—
1041C2×D4—22no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—41no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C2×D4—42no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—41no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—28no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—22no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—41no—
1138C4⋊C4—41no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—41no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C42—28no—
1224C42—24no—
1225C42—24no—
1226C42—22no—
1227C42—24no—
1228C42—28no—
1229C42—24no—
1230C42—22no—
1231C42—24no—
1232C42—24no—
1233C42—22no—
1234C42—22no—
1235C42—24no—
1236C42—24no—
1237C42—22no—
1238C42—22no—
1239C42—41no—
1240C42—42no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—42no—
1246C42—42no—
1247C42—44no—
1248C42—44no—
1249C42—42no—
1250C42—42no—
1251C42—44no—
1252C23—22no—
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—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23C2611yescharacteristic
1274Q8—28no—
1275Q8—44no—
1276Q8—48no—
1277Q8—84no—
1278Q8—82no—
1279Q8—82no—
1280Q8—88no—
1281Q8—84no—
1282D4—44no—
1283D4—44no—
1284D4—82no—
1285D4—84no—
1286D4—84no—
1287D4—84no—
1288D4—84no—
1289D4—84no—
1290D4—84no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—21no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—48no—
1362C2×C4—48no—
1363C2×C4—48no—
1364C2×C4—88no—
1365C2×C4—88no—
1366C2×C4—88no—
1367C2×C4C2×H(5,𝔽2)14yes—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4C2×2−1+412yes—
1370C2×C4C2×2−1+414yes—
1371C2×C4#58512yes—
1372C2×C4#58512yes—
1373C2×C4#58512yes—
1374C2×C4#58512yes—
1375C22—42no—
1376C22—42no—
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—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22C22×H(5,𝔽2)11yescharacteristic
1397C22C22×2−1+411yescharacteristic
1398C22C2×#58511yescharacteristic
1399C22C2×#58511yescharacteristic
1400C22C2×#58511yescharacteristic
1401C22C2×#58511yescharacteristic
1402C222−1+611yescharacteristic
1403C4—24no—
1404C4—22no—
1405C4—22no—
1406C4—24no—
1407C4—22no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—44no—
1412C4—41no—
1413C4—42no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—41no—
1419C4—42no—
1420C4—41no—
1421C4—42no—
1422C4—44no—
1423C4—44no—
1424C4—44no—
1425C4—42no—
1426C4—44no—
1427C4—42no—
1428C4#354514yes—
1429C2—82no—
1430C2—82no—
1431C2—82no—
1432C2C2×#354511yescharacteristic
1433C2#6289711yescharacteristic
1434C2#6290411yescharacteristic
1435C2#6290711yescharacteristic
1436C2#6303111yescharacteristic
1437C2#6303411yescharacteristic
1438C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52307C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59933C2semidirect
2. #59878C2semidirect
3. #59752C2semidirect
4. #59564C2semidirect
5. #54813C2semidirect
6. #54800C2semidirect
7. #53986C2semidirect
9. #51830C2semidirect
10. #51248C2semidirect
11. #50603C2semidirect
12. #46158C2semidirect
13. #46023C2semidirect
14. #46005C2semidirect
15. #45237C2semidirect
16. #45113C2semidirect
17. #44898C2semidirect
18. #42993C2semidirect
19. #42786C2semidirect
20. #42449C2semidirect
21. #40000C2semidirect
22. #39955C2semidirect
23. #38978C2semidirect
24. #37207C2semidirect
25. #37199C2semidirect
26. #37195C2semidirect
27. #36446C2semidirect
28. #36312C2semidirect
29. #36299C2semidirect

Maximal subgroups

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

subgroupindex
#599332
#598782
#597522
#595642
#548132
#548002
#539862
#523072
#518302
#512482
#506032
#461582
#460232
#460052
#452372
#451132
#448982
#429932
#427862
#424492
#400002
#399552
#389782
#372072
#371992
#371952
#364462
#363122
#362992