Finite Group Databasebeta

← #8926660

Subgroups — #8926660

Order 512.

4088 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58666C214yesmaximal, complemented
2#58529C214yesmaximal, complemented
3#56637C214yesmaximal, complemented
4#55880C214yesmaximal, complemented
5#55611C212yesmaximal, complemented
6#54291C214yesmaximal, complemented
7#53974C212yesmaximal, complemented
8#47657C212yesmaximal, complemented
9#47247C214yesmaximal, complemented
10#47226C212yesmaximal, complemented
11#47216C212yesmaximal, complemented
12#47214C212yesmaximal
13#47173C212yesmaximal, complemented
14#46873C214yesmaximal, complemented
15#37423C212yesmaximal, complemented
16#37159C214yesmaximal, complemented
17#37052C214yesmaximal, complemented
18#37019C212yesmaximal, complemented
19#36959C211yesmaximal, characteristic, complemented
20#36959C211yesmaximal, characteristic, complemented
21#36813C214yesmaximal, complemented
22#35649C211yesmaximal, characteristic
23#35496C212yesmaximal, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C2×#542C2212yes—
27C2×#537C2211yescharacteristic
28C22×#125C2211yescharacteristic
29#2866C2214yes—
30#2862C2212yes—
31#2861C2212yes—
32#2855C2212yes—
33#2855C2212yes—
34#2844C2212yes—
35#2839C2214yes—
36#2836C2214yes—
37#2835C2214yes—
38#2833C2212yes—
39#2832C2212yes—
40#2831C2214yes—
41#2830C2212yes—
42#2827C2214yes—
43#2816C2212yes—
44#2809C2212yes—
45#2800C2214yes—
46#2799C2212yes—
47#2799C2212yes—
48#2799C2214yes—
49#2799C2214yes—
50#2798C2214yes—
51#2796C2214yes—
52#2796C2214yes—
53#2794C2214yes—
54#2785C2212yes—
55#2784C2212yes—
56#2782C2212yes—
57#2780C2214yes—
58#2775C2214yes—
59#2774C2214yes—
60#2774C2214yes—
61#2773C2214yes—
62#2770C2214yes—
63#2768C2214yes—
64#2767C2214yes—
65#2767C2214yes—
66#2767C2214yes—
67#2762C2214yes—
68#2761C2214yes—
69#2754C2214yes—
70#2754C2214yes—
71#2751C2214yes—
72#2751C2214yes—
73#2750C2214yes—
74#2747C2214yes—
75#2745C2214yes—
76#2745C2214yes—
77#2744C2214yes—
78#2743C2214yes—
79#2743C2214yes—
80#2741C2214yes—
81#2740C2214yes—
82#2740C2214yes—
83#2740C2214yes—
84#2739C2214yes—
85#2737C2214yes—
86#2734C2212yes—
87#2731C2214yes—
88#2724C2212yes—
89#2720C2214yes—
90#2719C2214yes—
91#2719C2214yes—
92#2719C2214yes—
93#2719C2214yes—
94#2716C2214yes—
95#2716C2214yes—
96#2716C2214yes—
97#2713C2214yes—
98#2713C2214yes—
99#2713C2214yes—
100#2713C2214yes—
101#2713C2214yes—
102#2713C2214yes—
103#2713C2214yes—
104#2704C2214yes—
105#2701C2214yes—
106#2700C2214yes—
107#2700C2214yes—
108#2700C2214yes—
109#2698C2214yes—
110#2694C2214yes—
111#2694C2214yes—
112#2690C2214yes—
113#2690C2214yes—
114#2690C2214yes—
115#2687C2214yes—
116#2687C2214yes—
117#2687C2214yes—
118#2686C2214yes—
119#2686C2214yes—
120#2681C2214yes—
121#2677C2214yes—
122#2666C2214yes—
123#2660C2212yes—
124#2654C2214yes—
125#2652C2214yes—
126#2652C2214yes—
127#2651C2214yes—
128#2650C2214yes—
129#2650C2214yes—
130#2640C2212yes—
131#2627C2212yes—
132#2627C2212yes—
133#2612C2212yes—
134#2608C2212yes—
135#2607C2214yes—
136#2597C2214yes—
137#2593C2212yes—
138#2591C2212yes—
139#2591C2212yes—
140#2590C2214yes—
141#2589C2214yes—
142#2589C2214yes—
143#2588C2214yes—
144#2586C2212yes—
145#2583C2214yes—
146#2583C2211yescharacteristic
147#2583C2211yescharacteristic
148#2583C2212yes—
149#2577C2214yes—
150#2576C2214yes—
151#2575C2214yes—
152#2574C2214yes—
153#2574C2214yes—
154#2573C2214yes—
155#2572C2212yes—
156#2568C2212yes—
157#2566C2212yes—
158#2565C2212yes—
159#2563C2212yes—
160#2559C2214yes—
161#2533C2214yes—
162#2532C2214yes—
163#2530C2214yes—
164#2530C2214yes—
165#2528C2214yes—
166#2527C2214yes—
167#2526C2214yes—
168#2524C2214yes—
169#2520C2214yes—
170#2520C2214yes—
171#2519C2214yes—
172#2517C2214yes—
173#2516C2214yes—
174#2515C2214yes—
175#2506C2214yes—
176#2504C2212yes—
177#2504C2212yes—
178#2503C2212yes—
179#2503C2211yescharacteristic
180#2503C2211yescharacteristic
181#2500C2212yes—
182#2499C2212yes—
183#2492C2214yes—
184#2490C2214yes—
185#2490C2214yes—
186#2489C2214yes—
187#2489C2214yes—
188#2484C2212yes—
189#2484C2212yes—
190#2484C2212yes—
191#2484C2212yes—
192#2475C2214yes—
193#2475C2214yes—
194#2474C2214yes—
195#2473C2214yes—
196#2470C2214yes—
197#2465C2214yes—
198#2460C2214yes—
199#2446C2214yes—
200#2443C2214yes—
201#2442C2214yes—
202#2440C2214yes—
203#2432C2214yes—
204#2406C2214yes—
205#2336C2214yes—
206#2335C2214yes—
207#2333C2212yes—
208#2332C2214yes—
209#2332C2212yes—
210#2331C2214yes—
211#2313C2214yes—
212#2313C2211yescharacteristic
213#2313C2211yescharacteristic
214#2311C2212yes—
215C4×#125C2214yes—
216#2298C2212yes—
217#2297C2212yes—
218#2274C2211yescharacteristic
219C22×#41C2312yes—
220#544—44no—
221#544—44no—
222#542—48no—
223#537—44no—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2314yes—
229C2×#126C2314yes—
230C2×#125—44no—
231C2×#125C2314yes—
232C2×#125C2312yes—
233C2×#125C2314yes—
234C2×#125C2312yes—
235C2×#125C2314yes—
236C2×#125C2314yes—
237C2×#125C2314yes—
238C2×#124C2312yes—
239C2×#124C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×C4×Q8C2312yes—
254C2×C4×D4C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C42C2311yescharacteristic
266#401C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2312yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2312yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2312yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2312yes—
292#400C2314yes—
293#400C2312yes—
294#400C2312yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#399C2314yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2312yes—
314#398C2314yes—
315#398C2314yes—
316#398C2312yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2312yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2312yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2312yes—
362#395C2314yes—
363#395C2314yes—
364#395C2312yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2312yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2312yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2312yes—
378#394C2314yes—
379#394C2312yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2314yes—
404#391C2312yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2312yes—
550#385C2314yes—
551#385C2312yes—
552#385C2312yes—
553#385C2312yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#384C2312yes—
560#384C2312yes—
561#383C2314yes—
562#383C2314yes—
563#382C2314yes—
564#382C2312yes—
565#382C2312yes—
566#382C2312yes—
567#382C2312yes—
568#382C2312yes—
569#382C2312yes—
570#382C2312yes—
571#382C2314yes—
572#382C2314yes—
573#382C2312yes—
574#382C2314yes—
575#381C2312yes—
576#381C2314yes—
577#381C2314yes—
578#381C2312yes—
579#381C2312yes—
580#381C2314yes—
581#381C2314yes—
582#381C2312yes—
583#381C2314yes—
584#381C2312yes—
585#381C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2312yes—
591#380C2312yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2311yescharacteristic
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2311yescharacteristic
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2312yes—
616#376C2314yes—
617#376C2312yes—
618C43C2312yes—
619C2×#41—44no—
620C2×#41—44no—
621C2×#41—44no—
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2414yes—
625C22×Q8C2411yescharacteristic
626C22×Q8C2411yescharacteristic
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×D4C2412yes—
630C22×D4C2412yes—
631C22×D4C2414yes—
632C22×D4C2412yes—
633C23×C4C2411yescharacteristic
634C23×C4C2411yescharacteristic
635C23×C4C2411yescharacteristic
636C23×C4C2411yescharacteristic
637C23×C4C2411yescharacteristic
638C23×C4C2411yescharacteristic
639C23×C4C2414yes—
640C23×C4C2414yes—
641C23×C4C2414yes—
642C23×C4C2411yescharacteristic
643C4⋊Q8—44no—
644C4⋊Q8—44no—
645C4⋊Q8—44no—
646C4⋊Q8—48no—
647C4⋊Q8—48no—
648#126—48no—
649#125—44no—
650#125—44no—
651#125—48no—
652#125—48no—
653#125—48no—
654#125—48no—
655#125—48no—
656#124—44no—
657#124—48no—
658#123—48no—
659#123—48no—
660C22⋊Q8—28no—
661C22⋊Q8—42no—
662C22⋊Q8—44no—
663C22⋊Q8—42no—
664C22⋊Q8—44no—
665C22⋊Q8—48no—
666C22⋊Q8—48no—
667C22⋊Q8—48no—
668#121—28no—
669#121—48no—
670#121—44no—
671C4×Q8—44no—
672C4×D4—44no—
673#117—28no—
674#117—44no—
675#117—44no—
676C2×C4⋊C4—24no—
677C2×C4⋊C4—24no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—48no—
680C2×C4⋊C4—42no—
681C2×C4⋊C4—42no—
682C2×C4⋊C4—42no—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C22⋊C4C2412yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C42—42no—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2414yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2414yes—
784C2×C42C2412yes—
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2414yes—
788C2×C42C2412yes—
789C2×C42C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2412yes—
797#95C2414yes—
798#95C2412yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2412yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2412yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2412yes—
829#95C2412yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2412yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2412yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858C24C2514yes—
859C24C2511yescharacteristic
860#41—816no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—44no—
868C2×Q8—41no—
869C2×Q8—42no—
870C2×Q8—41no—
871C2×Q8—42no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—44no—
877C2×Q8—44no—
878C2×D4—28no—
879C2×D4—24no—
880C2×D4—24no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—42no—
888C2×D4—44no—
889C22×C4—22no—
890C22×C4—24no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—28no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—42no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4H(5,𝔽2)14yes—
912C22×C4C2514yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2514yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2512yes—
919C22×C4C2512yes—
920C22×C4C2514yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—44no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—44no—
969C4⋊C4—42no—
970C4⋊C4—44no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—41no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—42no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—42no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C42—24no—
1021C42—24no—
1022C42—44no—
1023C42—42no—
1024C42—42no—
1025C42—42no—
1026C42—42no—
1027C42—44no—
1028C42—44no—
1029C42—44no—
1030C42—42no—
1031C42—42no—
1032C42—42no—
1033C42—42no—
1034C42—44no—
1035C42—44no—
1036C42—44no—
1037C42—44no—
1038C42—44no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23C2×H(5,𝔽2)12yes—
1050C23C2611yescharacteristic
1051Q8—84no—
1052Q8—84no—
1053Q8—164no—
1054Q8—162no—
1055Q8—162no—
1056Q8—161no—
1057Q8—161no—
1058D4—84no—
1059D4—84no—
1060D4—88no—
1061D4—162no—
1062C2×C4—28no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—88no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4—82no—
1121C2×C4—88no—
1122C2×C4—164no—
1123C2×C4C2×H(5,𝔽2)14yes—
1124C2×C4#58514yes—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22C22×H(5,𝔽2)11yescharacteristic
1137C22C2×#58512yes—
1138C222−1+612yes—
1139C222−1+612yes—
1140C4—24no—
1141C4—24no—
1142C4—44no—
1143C4—42no—
1144C4—44no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4—42no—
1150C4—42no—
1151C4—41no—
1152C4—41no—
1153C4—42no—
1154C4—42no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C2—42no—
1162C2—84no—
1163C2#6282411yescharacteristic
1164C2#6287111yescharacteristic
1165C2#6288711yescharacteristic
1166C2#6289014yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58666C2semidirect
2. #58529C2semidirect
3. #56637C2semidirect
4. #55880C2semidirect
5. #55611C2semidirect
6. #54291C2semidirect
7. #53974C2semidirect
8. #47657C2semidirect
9. #47247C2semidirect
10. #47226C2semidirect
11. #47216C2semidirect
13. #47173C2semidirect
14. #46873C2semidirect
15. #37423C2semidirect
16. #37159C2semidirect
17. #37052C2semidirect
18. #37019C2semidirect
19. #36959C2semidirect
20. #36959C2semidirect
21. #36813C2semidirect
23. #35496C2semidirect

Maximal subgroups

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

subgroupindex
#586662
#585292
#566372
#558802
#556112
#542912
#539742
#476572
#472472
#472262
#472162
#472142
#471732
#468732
#374232
#371592
#370522
#370192
#369592
#368132
#356492
#354962