Finite Group Databasebeta

← #8071498

Subgroups — #8071498

Order 512.

4405 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59897C213yesmaximal, complemented
2#59736C213yesmaximal, complemented
3#59455C213yesmaximal, complemented
4#51214C213yesmaximal, complemented
5#50901C213yesmaximal, complemented
6#48853C213yesmaximal, complemented
7#48848C213yesmaximal, complemented
8#47977C213yesmaximal, complemented
9#47977C213yesmaximal, complemented
10#47815C211yesmaximal, characteristic, complemented
11#47776C211yesmaximal, characteristic, complemented
12#47733C211yesmaximal, characteristic, complemented
13#46431C213yesmaximal, complemented
14#44951C213yesmaximal, complemented
15#44625C213yesmaximal, complemented
16#44611C213yesmaximal, complemented
17#43512C213yesmaximal, complemented
18#43123C213yesmaximal, complemented
19#43122C213yesmaximal, complemented
20#39710C213yesmaximal, complemented
21#39687C213yesmaximal, complemented
22#39664C213yesmaximal, complemented
23#34518C213yesmaximal
24C2×#560C2211yescharacteristic
25#2855C2213yescomplemented
26#2845C2211yescharacteristic, complemented
27#2842C2211yescharacteristic
28#2807C2213yes—
29#2807C2213yes—
30#2807C2213yes—
31#2807C2213yescomplemented
32#2806C2213yescomplemented
33#2805C2213yescomplemented
34#2802C2213yescomplemented
35#2802C2213yescomplemented
36#2792C2213yescomplemented
37#2791C2213yescomplemented
38#2791C2213yescomplemented
39#2791C2213yescomplemented
40#2790C2213yes—
41#2790C2213yes—
42#2788C2213yes—
43#2788C2213yes—
44#2788C2213yes—
45#2788C2213yes—
46#2788C2213yescomplemented
47#2784C2213yes—
48#2780C2213yes—
49#2780C2213yes—
50#2780C2213yes—
51#2780C2213yes—
52#2780C2213yes—
53#2780C2213yescomplemented
54#2780C2213yescomplemented
55#2780C2213yescomplemented
56#2768C2213yes—
57#2768C2213yes—
58#2768C2213yes—
59#2768C2213yes—
60#2768C2213yes—
61#2768C2213yes—
62#2768C2213yescomplemented
63#2768C2213yescomplemented
64#2748C2213yes—
65#2748C2213yes—
66#2748C2213yes—
67#2748C2213yes—
68#2748C2213yes—
69#2748C2213yes—
70#2748C2213yescomplemented
71#2732C2213yes—
72#2732C2213yes—
73#2732C2213yes—
74#2732C2213yes—
75#2732C2213yes—
76#2732C2213yescomplemented
77#2729C2213yescomplemented
78#2726C2213yescomplemented
79#2726C2213yescomplemented
80#2726C2213yescomplemented
81#2713C2213yescomplemented
82#2704C2213yes—
83#2704C2213yes—
84#2704C2213yescomplemented
85#2692C2213yes—
86#2692C2213yescomplemented
87#2677C2213yes—
88#2667C2213yescomplemented
89#2667C2213yescomplemented
90#2667C2213yescomplemented
91#2667C2213yescomplemented
92#2627C2213yescomplemented
93#2627C2213yescomplemented
94#2612C2213yescomplemented
95#2608C2213yescomplemented
96#2607C2213yescomplemented
97#2590C2213yescomplemented
98#2590C2213yescomplemented
99#2590C2213yescomplemented
100#2589C2213yes—
101#2589C2213yes—
102#2588C2213yescomplemented
103#2588C2213yescomplemented
104#2587C2213yes—
105#2587C2213yes—
106#2587C2213yes—
107#2587C2213yes—
108#2587C2213yescomplemented
109#2585C2213yescomplemented
110#2585C2213yescomplemented
111#2585C2213yescomplemented
112#2584C2213yescomplemented
113#2584C2213yescomplemented
114#2583C2213yes—
115#2580C2213yes—
116#2579C2213yes—
117#2579C2213yes—
118#2579C2213yescomplemented
119#2574C2213yes—
120#2570C2213yescomplemented
121#2566C2213yes—
122#2564C2213yes—
123#2564C2213yes—
124#2564C2213yescomplemented
125#2556C2213yes—
126#2556C2213yes—
127#2556C2213yes—
128#2556C2213yescomplemented
129#2550C2213yescomplemented
130#2549C2213yes—
131#2549C2213yescomplemented
132#2542C2213yescomplemented
133#2538C2213yes—
134#2522C2213yes—
135#2522C2213yes—
136#2522C2213yes—
137#2522C2213yescomplemented
138#2522C2213yescomplemented
139#2522C2213yescomplemented
140#2520C2213yescomplemented
141#2509C2213yescomplemented
142#2508C2213yescomplemented
143#2508C2213yescomplemented
144#2507C2213yescomplemented
145#2507C2213yescomplemented
146#2505C2213yes—
147#2505C2213yescomplemented
148#2502C2213yes—
149#2497C2213yes—
150#2497C2213yes—
151#2487C2213yes—
152#2487C2213yes—
153#2487C2213yes—
154#2487C2213yescomplemented
155#2473C2213yes—
156#2473C2213yes—
157#2473C2213yes—
158#2473C2213yes—
159#2473C2213yes—
160#2473C2213yescomplemented
161#2465C2213yes—
162#2454C2213yes—
163#2454C2213yes—
164#2454C2213yes—
165#2454C2213yes—
166#2454C2213yescomplemented
167#2454C2213yescomplemented
168#2452C2213yes—
169#2452C2213yes—
170#2451C2213yescomplemented
171#2450C2213yes—
172#2450C2213yes—
173#2450C2213yes—
174#2450C2213yescomplemented
175#2449C2213yes—
176#2449C2213yes—
177#2449C2213yes—
178#2449C2213yes—
179#2449C2213yes—
180#2449C2213yescomplemented
181#2446C2213yescomplemented
182#2442C2213yescomplemented
183#2442C2213yescomplemented
184#2442C2213yescomplemented
185#2440C2213yescomplemented
186#2437C2213yes—
187#2437C2213yes—
188#2437C2213yes—
189#2429C2213yes—
190#2429C2213yes—
191#2423C2213yescomplemented
192#2417C2213yes—
193#2417C2213yes—
194#2417C2213yes—
195#2417C2213yescomplemented
196#2402C2213yescomplemented
197C2×#399C2211yescharacteristic
198C2×#396C2211yescharacteristic
199C2×#396C2211yescharacteristic
200#2377C2213yes—
201#2377C2213yes—
202#2376C2213yes—
203#2374C2213yes—
204#2374C2213yes—
205#2373C2213yes—
206#2373C2213yes—
207#2370C2213yescomplemented
208#2369C2213yescomplemented
209#2368C2213yes—
210#2366C2213yes—
211#2361C2213yes—
212#2361C2213yes—
213#2361C2213yes—
214#2361C2213yes—
215#2360C2213yes—
216#2360C2213yescomplemented
217#2358C2213yes—
218#2358C2213yes—
219#2358C2213yes—
220#2349C2213yes—
221#2349C2213yes—
222#2349C2213yescomplemented
223D4×C4⋊C4C2213yes—
224#2345C2213yes—
225#2334C2213yes—
226#2334C2213yes—
227#2333C2213yes—
228#2333C2213yes—
229#2333C2213yes—
230#2333C2213yes—
231#2330C2213yescomplemented
232#2328C2213yes—
233#2322C2213yes—
234#2322C2213yes—
235#2321C2213yes—
236#2321C2213yes—
237#2321C2213yes—
238#2315C2213yes—
239C4×C22⋊Q8C2213yescomplemented
240C4×C22⋊Q8C2213yescomplemented
241C4×#123C2213yes—
242C4×#121C2213yes—
243C4×#121C2213yes—
244C2×#389C2213yescomplemented
245#560Q8116yescomplemented
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×#127C2311yescharacteristic
249C2×#126C2311yescharacteristic
250C2×#126C2311yescharacteristic
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#123C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#120C2313yes—
273C2×C4×Q8C2313yes—
274C2×C4×Q8C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×C4×D4C2313yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×C4×D4C2313yes—
287C22×C4⋊C4C2313yes—
288C22×C4⋊C4C2313yes—
289C22×C4⋊C4C2313yes—
290C22×C4⋊C4C2313yes—
291C22×C4⋊C4C2313yes—
292C22×C4⋊C4C2313yes—
293C22×C4⋊C4C2313yes—
294C22×C22⋊C4C2313yes—
295C22×C22⋊C4C2313yes—
296C22×C22⋊C4C2313yes—
297C22×C42C2313yes—
298#400C2313yes—
299#400C2313yes—
300#400C2313yes—
301#400C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#399C2313yes—
316#399C2313yes—
317#399C2313yes—
318#399C2313yes—
319#399C2313yes—
320#399C2311yescharacteristic
321#399C2313yes—
322#399C2313yes—
323#399C2311yescharacteristic
324#399C2311yescharacteristic
325#399C2313yes—
326#399C2313yes—
327#399C2313yes—
328#399C2313yes—
329#399C2313yes—
330#399C2313yes—
331#399C2313yes—
332#399C2313yes—
333#399C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#398C2313yes—
363#398C2313yes—
364#398C2313yes—
365#398C2313yes—
366#398C2313yes—
367#398C2313yes—
368#398C2313yes—
369#398C2313yes—
370#398C2313yes—
371#398C2313yes—
372#398C2313yes—
373#398C2313yes—
374#398C2313yes—
375#398C2313yes—
376#398C2313yes—
377#398C2313yes—
378#398C2313yes—
379#398C2313yes—
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2311yescharacteristic
394#396C2311yescharacteristic
395#396C2313yes—
396#396C2313yes—
397#396C2313yes—
398#396C2313yes—
399#396C2313yes—
400#396C2311yescharacteristic
401#396C2311yescharacteristic
402#396C2311yescharacteristic
403#396C2311yescharacteristic
404#396C2313yes—
405#396C2313yes—
406#396C2313yes—
407#396C2313yes—
408#396C2313yes—
409#396C2313yes—
410#395C2313yes—
411#395C2313yes—
412#395C2313yes—
413#395C2313yes—
414#395C2313yes—
415#395C2313yes—
416#395C2313yes—
417#395C2313yes—
418#395C2313yes—
419#393C2313yes—
420#393C2313yes—
421#393C2313yes—
422#393C2313yes—
423#393C2313yes—
424#391C2313yes—
425#391C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2313yes—
446#390C2313yes—
447#390C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
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#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2313yes—
528#387C2313yes—
529#387C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#387C2313yes—
538#387C2313yes—
539#387C2313yes—
540#387C2313yes—
541#387C2313yes—
542#387C2313yes—
543#387C2313yes—
544#387C2313yes—
545#387C2313yes—
546#387C2313yes—
547#387C2313yes—
548#387C2313yes—
549#387C2313yes—
550#387C2313yes—
551#387C2313yes—
552#387C2313yes—
553#387C2313yes—
554#387C2313yes—
555#387C2313yes—
556#387C2313yes—
557#387C2313yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2313yes—
563#387C2313yes—
564#387C2313yes—
565#387C2313yes—
566#387C2313yes—
567#387C2313yes—
568#387C2313yes—
569#387C2313yes—
570#387C2313yes—
571#387C2313yes—
572#386C2313yes—
573#386C2313yes—
574#386C2313yes—
575#386C2313yes—
576#386C2313yes—
577#386C2313yes—
578#386C2313yes—
579#386C2313yes—
580#386C2313yes—
581#386C2313yes—
582#386C2313yes—
583#386C2313yes—
584#386C2313yes—
585#386C2313yes—
586#386C2313yes—
587#386C2313yes—
588#386C2313yes—
589#386C2313yes—
590#386C2313yes—
591#386C2313yes—
592#386C2313yes—
593#386C2313yes—
594#386C2313yes—
595#386C2313yes—
596#385C2313yes—
597#385C2313yes—
598#385C2313yes—
599#385C2313yes—
600#385C2313yes—
601#385C2313yes—
602#385C2313yes—
603#385C2313yes—
604#385C2313yes—
605#385C2313yes—
606#385C2313yes—
607#385C2313yes—
608#385C2313yes—
609#385C2313yes—
610#385C2313yes—
611#385C2313yes—
612#385C2313yes—
613#385C2313yes—
614#385C2313yes—
615#385C2313yes—
616#385C2313yes—
617#385C2313yes—
618#385C2313yes—
619#385C2313yes—
620#385C2313yes—
621#385C2313yes—
622#385C2313yes—
623#385C2313yes—
624#385C2313yes—
625#385C2313yes—
626#385C2313yes—
627#385C2313yes—
628#385C2313yes—
629#385C2313yes—
630#385C2313yes—
631#385C2313yes—
632#385C2313yes—
633#385C2313yes—
634#385C2313yes—
635#385C2313yes—
636#385C2313yes—
637#385C2313yes—
638#385C2313yes—
639#385C2313yes—
640#385C2313yes—
641#385C2313yes—
642#385C2313yes—
643#385C2313yes—
644#385C2313yes—
645#385C2313yes—
646#384C2313yes—
647#384C2313yes—
648#384C2313yes—
649#382C2313yes—
650#382C2313yes—
651#382C2313yes—
652#382C2313yes—
653#382C2313yes—
654#381C2313yes—
655#381C2313yes—
656#381C2313yes—
657#380C2313yes—
658#380C2313yes—
659#380C2313yes—
660#380C2313yes—
661#380C2313yes—
662#380C2313yes—
663#380C2313yes—
664#380C2313yes—
665#380C2313yes—
666#380C2313yes—
667#380C2313yes—
668#380C2313yes—
669#380C2313yes—
670#380C2313yes—
671#380C2313yes—
672#380C2313yes—
673#380C2313yes—
674#380C2313yes—
675#380C2313yes—
676#380C2313yes—
677#380C2313yes—
678#380C2313yes—
679#380C2313yes—
680#379C2313yes—
681C4×C4⋊C4C2313yes—
682C4×C4⋊C4C2313yes—
683C4×C4⋊C4C2313yes—
684C4×C4⋊C4C2313yes—
685C4×C4⋊C4C2313yes—
686C4×C4⋊C4C2313yes—
687C4×C4⋊C4C2313yes—
688C4×C4⋊C4C2313yes—
689C4×C4⋊C4C2313yes—
690C4×C4⋊C4C2313yes—
691C4×C4⋊C4C2313yes—
692C4×C4⋊C4C2313yes—
693C4×C4⋊C4C2313yes—
694C4×C4⋊C4C2313yes—
695C4×C4⋊C4C2313yes—
696C4×C4⋊C4C2313yes—
697C4×C4⋊C4C2313yes—
698C4×C4⋊C4C2313yes—
699C4×C22⋊C4C2313yes—
700C4×C22⋊C4C2313yes—
701C4×C22⋊C4C2313yes—
702C4×C22⋊C4C2313yes—
703C4×C22⋊C4C2313yes—
704C4×C22⋊C4C2313yes—
705C4×C22⋊C4C2313yes—
706C4×C22⋊C4C2313yes—
707C4×C22⋊C4C2313yes—
708C4×C22⋊C4C2313yes—
709C4×C22⋊C4C2313yes—
710C4×C22⋊C4C2313yes—
711C4×C22⋊C4C2313yes—
712C4×C22⋊C4C2313yes—
713C4×C22⋊C4C2313yes—
714C4×C22⋊C4C2313yes—
715#376C2313yes—
716C2×#95C2313yes—
717C2×#95C2313yes—
718C2×#95C2311yescharacteristic
719C2×#95C2311yescharacteristic
720C2×#95C2311yescharacteristic
721C25C2411yescharacteristic
722C22×Q8C2413yes—
723C22×Q8C2413yes—
724C22×Q8C2413yes—
725C22×D4C2413yes—
726C22×D4C2413yes—
727C22×D4C2413yes—
728C22×D4C2413yes—
729C23×C4C2413yes—
730C23×C4C2413yes—
731C23×C4C2413yes—
732C23×C4C2413yes—
733C23×C4C2413yes—
734C23×C4C2413yes—
735C23×C4C2413yes—
736C23×C4C2413yes—
737C23×C4C2413yes—
738C23×C4C2413yes—
739C23×C4C2413yes—
740C23×C4C2413yes—
741C23×C4C2413yes—
742C4⋊Q8—46no—
743C4⋊Q8—83no—
744#127C2×Q818yes—
745#126C2×Q818yes—
746#126C2×Q818yes—
747#125—46no—
748#125—46no—
749#125—83no—
750#125—83no—
751#125—83no—
752#123C2×Q8124yes—
753C22⋊Q8—46no—
754C22⋊Q8—46no—
755C22⋊Q8—46no—
756C22⋊Q8—46no—
757C22⋊Q8—46no—
758C22⋊Q8—83no—
759C22⋊Q8—83no—
760C22⋊Q8—83no—
761C22⋊Q8—83no—
762C22⋊Q8—83no—
763C22⋊Q8—83no—
764C22⋊Q8—83no—
765C22⋊Q8—83no—
766#121C2×Q8124yes—
767#121C2×Q8124yes—
768#120C2×Q8124yes—
769C4×Q8—83no—
770C4×Q8—83no—
771C4×D4—46no—
772C4×D4—46no—
773C4×D4—46no—
774C4×D4—46no—
775C4×D4—83no—
776C4×D4—83no—
777C4×D4—83no—
778C4×D4—83no—
779C4×D4—83no—
780C4×D4—83no—
781C4×D4—83no—
782C4×D4—83no—
783C2×C4⋊C4—46no—
784C2×C4⋊C4—46no—
785C2×C4⋊C4—83no—
786C2×C4⋊C4—83no—
787C2×C4⋊C4—83no—
788C2×C4⋊C4—83no—
789C2×C4⋊C4—83no—
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⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C22⋊C4—46no—
862C2×C22⋊C4—83no—
863C2×C22⋊C4—83no—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2413yes—
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⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C42—83no—
905C2×C42C2413yes—
906C2×C42C2413yes—
907C2×C42C2413yes—
908C2×C42C2413yes—
909C2×C42C2413yes—
910C2×C42C2413yes—
911C2×C42C2413yes—
912C2×C42C2413yes—
913C2×C42C2413yes—
914C2×C42C2413yes—
915C2×C42C2413yes—
916C2×C42C2413yes—
917C2×C42C2413yes—
918C2×C42C2413yes—
919C2×C42C2413yes—
920C2×C42C2413yes—
921C2×C42C2413yes—
922C2×C42C2413yes—
923C2×C42C2411yescharacteristic
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2411yescharacteristic
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2413yes—
933#95C2411yescharacteristic
934#95C2411yescharacteristic
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2413yes—
947#95C2413yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2411yescharacteristic
994C24—43no—
995C24—43no—
996C24C22×Q814yes—
997C24C2511yescharacteristic
998C24C2511yescharacteristic
999C24C2511yescharacteristic
1000C24C2513yes—
1001C2×Q8—26no—
1002C2×Q8—26no—
1003C2×Q8—43no—
1004C2×Q8—43no—
1005C2×Q8—43no—
1006C2×Q8—43no—
1007C2×Q8—43no—
1008C2×Q8—43no—
1009C2×Q8—43no—
1010C2×D4—43no—
1011C2×D4—43no—
1012C2×D4—43no—
1013C2×D4—43no—
1014C2×D4—43no—
1015C2×D4—43no—
1016C2×D4—43no—
1017C2×D4—43no—
1018C2×D4C22×Q8112yes—
1019C2×D4C22×Q8112yes—
1020C2×D4C22×Q8112yes—
1021C2×D4C22×Q8112yes—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—43no—
1026C22×C4—43no—
1027C22×C4—43no—
1028C22×C4—43no—
1029C22×C4—43no—
1030C22×C4—43no—
1031C22×C4—43no—
1032C22×C4—43no—
1033C22×C4—43no—
1034C22×C4—43no—
1035C22×C4—43no—
1036C22×C4—43no—
1037C22×C4—43no—
1038C22×C4—43no—
1039C22×C4—43no—
1040C22×C4—43no—
1041C22×C4—43no—
1042C22×C4—43no—
1043C22×C4—43no—
1044C22×C4—43no—
1045C22×C4—43no—
1046C22×C4—43no—
1047C22×C4—43no—
1048C22×C4—43no—
1049C22×C4—43no—
1050C22×C4—43no—
1051C22×C4—43no—
1052C22×C4—43no—
1053C22×C4—43no—
1054C22×C4—43no—
1055C22×C4—43no—
1056C22×C4—43no—
1057C22×C4—43no—
1058C22×C4—43no—
1059C22×C4—43no—
1060C22×C4C22×Q8112yes—
1061C22×C4C2513yes—
1062C22×C4C2513yes—
1063C22×C4C2513yes—
1064C22×C4C2513yes—
1065C22×C4C2513yes—
1066C22×C4C2513yes—
1067C22×C4C2513yes—
1068C22×C4C2513yes—
1069C22×C4C2513yes—
1070C22×C4C2513yes—
1071C22×C4C2513yes—
1072C22×C4C2513yes—
1073C22×C4C2513yes—
1074C22×C4C2513yes—
1075C22×C4C2513yes—
1076C22×C4C2513yes—
1077C22×C4C2513yes—
1078C22×C4C2513yes—
1079C22×C4C2513yes—
1080C4⋊C4—26no—
1081C4⋊C4—26no—
1082C4⋊C4—26no—
1083C4⋊C4—26no—
1084C4⋊C4—26no—
1085C4⋊C4—26no—
1086C4⋊C4—26no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—43no—
1100C4⋊C4—43no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—43no—
1104C4⋊C4—43no—
1105C4⋊C4—43no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—43no—
1110C4⋊C4—43no—
1111C4⋊C4—43no—
1112C4⋊C4—43no—
1113C4⋊C4—43no—
1114C4⋊C4—43no—
1115C4⋊C4—43no—
1116C4⋊C4—43no—
1117C4⋊C4—43no—
1118C4⋊C4—43no—
1119C4⋊C4—43no—
1120C4⋊C4—43no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4—43no—
1124C4⋊C4—43no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—43no—
1129C4⋊C4—43no—
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—43no—
1142C4⋊C4—43no—
1143C4⋊C4—43no—
1144C4⋊C4—43no—
1145C4⋊C4—43no—
1146C4⋊C4—43no—
1147C4⋊C4—43no—
1148C4⋊C4—43no—
1149C4⋊C4C22×Q8112yes—
1150C4⋊C4C22×Q8112yes—
1151C22⋊C4—26no—
1152C22⋊C4—26no—
1153C22⋊C4—26no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
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—43no—
1187C22⋊C4C22×Q8112yes—
1188C22⋊C4C22×Q8112yes—
1189C22⋊C4C22×Q8112yes—
1190C22⋊C4C22×Q8112yes—
1191C42—43no—
1192C42—43no—
1193C42—43no—
1194C42—43no—
1195C42—43no—
1196C42—43no—
1197C42—43no—
1198C42—43no—
1199C42—43no—
1200C42—43no—
1201C42—43no—
1202C42—43no—
1203C42—43no—
1204C42—43no—
1205C42—43no—
1206C42—43no—
1207C42—43no—
1208C42—43no—
1209C42C22×Q814yes—
1210C23—23no—
1211C23—23no—
1212C23—23no—
1213C23—23no—
1214C23—23no—
1215C23—23no—
1216C23—23no—
1217C23—23no—
1218C23—23no—
1219C23—23no—
1220C23—23no—
1221C23—23no—
1222C23—412no—
1223C23—161no—
1224C23—163no—
1225C23C23×Q812yes—
1226C23C23×Q812yes—
1227C23C23×Q812yes—
1228C23C23×Q816yes—
1229C23C2611yescharacteristic
1230Q8—86no—
1231Q8—86no—
1232Q8—163no—
1233D4—412no—
1234D4—412no—
1235D4—412no—
1236D4—412no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—23no—
1290C2×C4—412no—
1291C2×C4—86no—
1292C2×C4—86no—
1293C2×C4—86no—
1294C2×C4—86no—
1295C2×C4—86no—
1296C2×C4—86no—
1297C2×C4—86no—
1298C2×C4—163no—
1299C2×C4—163no—
1300C2×C4—163no—
1301C2×C4—163no—
1302C2×C4—163no—
1303C2×C4C23×Q816yes—
1304C2×C4C23×Q816yes—
1305C2×C4C23×Q816yes—
1306C2×C4#58516yes—
1307C22—26no—
1308C22—26no—
1309C22—26no—
1310C22—26no—
1311C22—26no—
1312C22—26no—
1313C22—41no—
1314C22—43no—
1315C22—41no—
1316C22—41no—
1317C22—43no—
1318C22—43no—
1319C22—43no—
1320C22—43no—
1321C22—43no—
1322C22—43no—
1323C22—164no—
1324C22C24×Q811yescharacteristic
1325C22C2×#58513yes—
1326C22H(7,𝔽2)13yes—
1327C4—26no—
1328C4—26no—
1329C4—26no—
1330C4—26no—
1331C4—43no—
1332C4—43no—
1333C4—43no—
1334C4—43no—
1335C4—43no—
1336C4—43no—
1337C4—43no—
1338C4—43no—
1339C4—43no—
1340C4—43no—
1341C4—43no—
1342C4—43no—
1343C4—43no—
1344C4—43no—
1345C4—43no—
1346C2—46no—
1347C2—42no—
1348C2—42no—
1349C2—42no—
1350C2#6287013yes—
1351C2#6298913yes—
1352C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#560C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59897C2semidirect
2. #59736C2semidirect
3. #59455C2semidirect
4. #51214C2semidirect
5. #50901C2semidirect
6. #48853C2semidirect
7. #48848C2semidirect
8. #47977C2semidirect
9. #47977C2semidirect
10. #47815C2semidirect
11. #47776C2semidirect
12. #47733C2semidirect
13. #46431C2semidirect
14. #44951C2semidirect
15. #44625C2semidirect
16. #44611C2semidirect
17. #43512C2semidirect
18. #43123C2semidirect
19. #43122C2semidirect
20. #39710C2semidirect
21. #39687C2semidirect
22. #39664C2semidirect
25. #2855C22semidirect
26. #2845C22semidirect
31. #2807C22semidirect
32. #2806C22semidirect
33. #2805C22semidirect
34. #2802C22semidirect
35. #2802C22semidirect
36. #2792C22semidirect
37. #2791C22semidirect
38. #2791C22semidirect
39. #2791C22semidirect
46. #2788C22semidirect
53. #2780C22semidirect
54. #2780C22semidirect
55. #2780C22semidirect
62. #2768C22semidirect
63. #2768C22semidirect
70. #2748C22semidirect
76. #2732C22semidirect
77. #2729C22semidirect
78. #2726C22semidirect
79. #2726C22semidirect
80. #2726C22semidirect
81. #2713C22semidirect
84. #2704C22semidirect
86. #2692C22semidirect
88. #2667C22semidirect
89. #2667C22semidirect
90. #2667C22semidirect
91. #2667C22semidirect
92. #2627C22semidirect
93. #2627C22semidirect
94. #2612C22semidirect
95. #2608C22semidirect
96. #2607C22semidirect
97. #2590C22semidirect
98. #2590C22semidirect
99. #2590C22semidirect
102. #2588C22semidirect
103. #2588C22semidirect
108. #2587C22semidirect
109. #2585C22semidirect
110. #2585C22semidirect
111. #2585C22semidirect
112. #2584C22semidirect
113. #2584C22semidirect
118. #2579C22semidirect
120. #2570C22semidirect
124. #2564C22semidirect
128. #2556C22semidirect
129. #2550C22semidirect
131. #2549C22semidirect
132. #2542C22semidirect
137. #2522C22semidirect
138. #2522C22semidirect
139. #2522C22semidirect
140. #2520C22semidirect
141. #2509C22semidirect
142. #2508C22semidirect
143. #2508C22semidirect
144. #2507C22semidirect
145. #2507C22semidirect
147. #2505C22semidirect
154. #2487C22semidirect
160. #2473C22semidirect
166. #2454C22semidirect
167. #2454C22semidirect
170. #2451C22semidirect
174. #2450C22semidirect
180. #2449C22semidirect
181. #2446C22semidirect
182. #2442C22semidirect
183. #2442C22semidirect
184. #2442C22semidirect
185. #2440C22semidirect
191. #2423C22semidirect
195. #2417C22semidirect
196. #2402C22semidirect
207. #2370C22semidirect
208. #2369C22semidirect
216. #2360C22semidirect
222. #2349C22semidirect
231. #2330C22semidirect
239. C4×C22⋊Q8C22semidirect
240. C4×C22⋊Q8C22semidirect
244. C2×#389C22semidirect
245. #560Q8semidirect

Maximal subgroups

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

subgroupindex
#598972
#597362
#594552
#512142
#509012
#488532
#488482
#479772
#478152
#477762
#477332
#464312
#449512
#446252
#446112
#435122
#431232
#431222
#397102
#396872
#396642
#345182