Finite Group Databasebeta

← #8824378

Subgroups — #8824378

Order 512.

4548 conjugacy classes of subgroups.

The subgroup lattice has 1265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59923C211yesmaximal, characteristic, complemented
2#58211C214yesmaximal, complemented
3#55151C214yesmaximal, complemented
4#53299C212yesmaximal, complemented
5#51667C214yesmaximal, complemented
6#51531C212yesmaximal, complemented
7#51278C214yesmaximal, complemented
8#49933C214yesmaximal, complemented
9#49591C212yesmaximal, complemented
10#48305C214yesmaximal, complemented
11#47971C214yesmaximal, complemented
12#47663C212yesmaximal, complemented
13#46455C212yesmaximal, complemented
14#46315C212yesmaximal, complemented
15#46099C211yesmaximal, characteristic, complemented
16#45385C214yesmaximal, complemented
17#43369C214yesmaximal, complemented
18#41336C214yesmaximal, complemented
19#38821C212yesmaximal, complemented
20#38444C212yesmaximal, complemented
21#37194C212yesmaximal, complemented
22#36374C212yesmaximal, complemented
23#35307C211yesmaximal, characteristic, complemented
24C2×#555C2212yes—
25C2×#548C2212yes—
26C2×#536C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28#2855C2212yes—
29#2855C2212yes—
30#2855C2212yes—
31#2854C2212yes—
32#2850C2212yes—
33#2837C2214yes—
34#2832C2212yes—
35#2832C2212yes—
36#2829C2214yes—
37#2816C2212yes—
38#2811C2211yescharacteristic
39#2811C2211yescharacteristic
40#2809C2212yes—
41#2809C2214yes—
42#2806C2212yes—
43#2806C2212yes—
44#2806C2214yes—
45#2806C2214yes—
46#2805C2214yes—
47#2804C2212yes—
48#2799C2214yes—
49#2799C2214yes—
50#2799C2214yes—
51#2799C2214yes—
52#2798C2214yes—
53#2798C2214yes—
54#2798C2214yes—
55#2788C2214yes—
56#2781C2214yes—
57#2774C2214yes—
58#2774C2214yes—
59#2768C2214yes—
60#2763C2214yes—
61#2755C2214yes—
62#2751C2214yes—
63#2750C2214yes—
64#2744C2214yes—
65#2743C2214yes—
66#2743C2214yes—
67#2743C2214yes—
68#2742C2214yes—
69#2740C2214yes—
70#2740C2214yes—
71#2739C2214yes—
72#2739C2214yes—
73#2734C2211yescharacteristic
74#2734C2212yes—
75#2733C2211yescharacteristic
76#2732C2212yes—
77#2732C2214yes—
78#2731C2212yes—
79#2728C2214yes—
80#2727C2212yes—
81#2725C2214yes—
82#2723C2214yes—
83#2716C2214yes—
84#2712C2214yes—
85#2712C2214yes—
86#2705C2214yes—
87#2702C2214yes—
88#2700C2214yes—
89#2700C2214yes—
90#2699C2212yes—
91#2699C2214yes—
92#2698C2214yes—
93#2695C2214yes—
94#2695C2214yes—
95#2692C2214yes—
96#2690C2214yes—
97#2687C2214yes—
98#2686C2214yes—
99#2686C2214yes—
100#2683C2212yes—
101#2681C2214yes—
102#2674C2214yes—
103#2672C2214yes—
104#2672C2214yes—
105#2671C2214yes—
106#2665C2214yes—
107#2665C2214yes—
108#2665C2212yes—
109#2664C2214yes—
110#2652C2214yes—
111#2650C2214yes—
112#2628C2214yes—
113#2627C2214yes—
114#2625C2212yes—
115#2625C2212yes—
116#2616C2212yes—
117#2609C2214yes—
118#2607C2214yes—
119#2607C2212yes—
120#2601C2214yes—
121#2592C2212yes—
122#2589C2214yes—
123#2588C2214yes—
124#2588C2214yes—
125#2586C2214yes—
126#2586C2212yes—
127#2586C2212yes—
128#2583C2212yes—
129#2581C2212yes—
130#2569C2214yes—
131#2564C2214yes—
132#2560C2214yes—
133#2559C2214yes—
134#2556C2214yes—
135#2549C2214yes—
136#2549C2214yes—
137#2522C2214yes—
138#2521C2214yes—
139#2519C2214yes—
140#2509C2214yes—
141#2508C2214yes—
142#2492C2214yes—
143#2489C2214yes—
144#2488C2214yes—
145#2485C2214yes—
146#2479C2214yes—
147#2477C2214yes—
148#2475C2214yes—
149#2474C2214yes—
150#2474C2214yes—
151#2474C2214yes—
152#2471C2214yes—
153#2470C2214yes—
154#2468C2214yes—
155#2467C2214yes—
156#2466C2214yes—
157#2466C2214yes—
158#2465C2214yes—
159#2459C2214yes—
160#2457C2214yes—
161#2451C2214yes—
162#2450C2214yes—
163#2449C2214yes—
164#2447C2214yes—
165#2447C2214yes—
166#2447C2214yes—
167#2446C2214yes—
168#2444C2214yes—
169#2444C2214yes—
170#2438C2214yes—
171#2438C2214yes—
172#2438C2214yes—
173#2438C2214yes—
174#2438C2214yes—
175#2438C2214yes—
176#2436C2212yes—
177#2434C2212yes—
178#2430C2214yes—
179#2430C2214yes—
180#2427C2214yes—
181#2419C2214yes—
182#2419C2214yes—
183#2416C2212yes—
184#2415C2212yes—
185#2415C2214yes—
186#2409C2212yes—
187#2409C2214yes—
188#2407C2212yes—
189#2407C2214yes—
190#2407C2214yes—
191#2406C2212yes—
192#2392C2214yes—
193#2379C2212yes—
194#2379C2212yes—
195#2378C2212yes—
196#2378C2214yes—
197#2369C2212yes—
198#2368C2214yes—
199#2364C2214yes—
200#2362C2214yes—
201#2359C2214yes—
202#2352C2212yes—
203#2339C2214yes—
204#2339C2212yes—
205#2334C2214yes—
206#2333C2212yes—
207#2332C2212yes—
208#2329C2214yes—
209#2324C2214yes—
210#2316C2211yescharacteristic
211#2311C2211yescharacteristic
212#2310C2214yes—
213#2310C2211yescharacteristic
214C4×C22⋊Q8C2212yes—
215#2297C2212yes—
216#2296C2211yescharacteristic
217C2×#391C2211yescharacteristic
218C2×#391C2212yes—
219C22×#41C2311yescharacteristic
220C22×#41C2312yes—
221C22×#41C2312yes—
222C23×Q8C2312yes—
223C23×Q8C2311yescharacteristic
224#555—48no—
225#548—48no—
226#536—44no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#125C2314yes—
234C2×#124C2312yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238C2×#124C2314yes—
239C2×#124C2312yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#121C2314yes—
260C2×#121C2314yes—
261C2×#121C2312yes—
262C4×#41—44no—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2314yes—
275C2×#117C2311yescharacteristic
276C2×#117C2314yes—
277C2×#117C2312yes—
278C2×#117C2314yes—
279C2×#117C2312yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2312yes—
282C22×C42C2311yescharacteristic
283C22×C42C2312yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2312yes—
316#398C2312yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#395C2312yes—
353#395C2312yes—
354#395C2312yes—
355#395C2314yes—
356#395C2314yes—
357#395C2312yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2312yes—
377#394C2312yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2311yescharacteristic
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2311yescharacteristic
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#390C2314yes—
434#390C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2314yes—
438#390C2312yes—
439#390C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
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#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#382C2312yes—
568#382C2314yes—
569#382C2314yes—
570#382C2314yes—
571#381C2312yes—
572#381C2312yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2312yes—
581#381C2314yes—
582#380C2312yes—
583#380C2314yes—
584#380C2312yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C2×#95C2314yes—
615C2×#95C2314yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C2×#41—28no—
619C2×#41—24no—
620C2×#41—42no—
621C2×#41—42no—
622C2×#41—44no—
623C2×#41—44no—
624C2×#41—82no—
625C2×#41—84no—
626C22×Q8—28no—
627C22×Q8—44no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8—82no—
632C22×Q8C2411yescharacteristic
633C22×Q8C2411yescharacteristic
634C22×Q8C2412yes—
635C22×Q8C2414yes—
636C22×Q8C2411yescharacteristic
637C22×Q8C2412yes—
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×Q8C2412yes—
641C22×Q8C2412yes—
642C22×D4C2412yes—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2412yes—
648C22×D4C2412yes—
649C22×D4C2411yescharacteristic
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2414yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C4⋊Q8—44no—
663C4⋊Q8—44no—
664C4⋊Q8—44no—
665#126—48no—
666#126—84no—
667#126—84no—
668#125—84no—
669#124—28no—
670#124—44no—
671#124—48no—
672#124—48no—
673#124—44no—
674#124—44no—
675#123—48no—
676#123—48no—
677#123—84no—
678C22⋊Q8—216no—
679C22⋊Q8—28no—
680C22⋊Q8—44no—
681C22⋊Q8—44no—
682C22⋊Q8—44no—
683C22⋊Q8—44no—
684C22⋊Q8—44no—
685C22⋊Q8—48no—
686C22⋊Q8—84no—
687C22⋊Q8—84no—
688C22⋊Q8—84no—
689C22⋊Q8—84no—
690C22⋊Q8—82no—
691#121—216no—
692#121—48no—
693#121—48no—
694#121—44no—
695#121—44no—
696#121—82no—
697C4×Q8—44no—
698C4×Q8—44no—
699C4×D4—28no—
700C4×D4—44no—
701C4×D4—44no—
702C4×D4—48no—
703C4×D4—48no—
704C4×D4—84no—
705C4×D4—84no—
706#117—42no—
707#117—48no—
708#117—44no—
709#117—48no—
710#117—42no—
711#117—42no—
712#117—84no—
713#117—82no—
714C2×C4⋊C4—42no—
715C2×C4⋊C4—82no—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C42—42no—
805C2×C42—44no—
806C2×C42C2412yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2411yescharacteristic
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824C2×C42C2411yescharacteristic
825#95C2412yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
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—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883C24C2514yes—
884C24C2512yes—
885C24C2511yescharacteristic
886#41—416no—
887#41—816no—
888#41—816no—
889C2×Q8—22no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—28no—
893C2×Q8—22no—
894C2×Q8—22no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—41no—
898C2×Q8—41no—
899C2×Q8—41no—
900C2×Q8—41no—
901C2×Q8—42no—
902C2×Q8—44no—
903C2×Q8—44no—
904C2×Q8—42no—
905C2×Q8—44no—
906C2×Q8—42no—
907C2×Q8—41no—
908C2×Q8—41no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—44no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—88no—
917C2×Q8—816no—
918C2×Q82−1+418yes—
919C2×D4—24no—
920C2×D4—28no—
921C2×D4—24no—
922C2×D4—28no—
923C2×D4—28no—
924C2×D4—28no—
925C2×D4—24no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—41no—
929C2×D4—41no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—44no—
934C2×D4—42no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4H(5,𝔽2)14yes—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—28no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—28no—
958C22×C4—42no—
959C22×C4—44no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—42no—
969C22×C4—44no—
970C22×C4—42no—
971C22×C4—44no—
972C22×C4—42no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2511yescharacteristic
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2511yescharacteristic
997C4⋊C4—24no—
998C4⋊C4—28no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C22⋊C4—24no—
1047C22⋊C4—24no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—42no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—44no—
1061C22⋊C4—42no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C42—24no—
1086C42—24no—
1087C42—41no—
1088C42—41no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—44no—
1094C42—42no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—42no—
1099C42—44no—
1100C42—42no—
1101C42—44no—
1102C42—44no—
1103C42—42no—
1104C23—21no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—21no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23C2×H(5,𝔽2)14yes—
1122C23#58512yes—
1123C23C2611yescharacteristic
1124Q8—48no—
1125Q8—44no—
1126Q8—82no—
1127Q8—82no—
1128Q8—84no—
1129Q8—84no—
1130Q8—88no—
1131Q8—84no—
1132Q8—162no—
1133Q8—162no—
1134D4—44no—
1135D4—416no—
1136D4—48no—
1137D4—48no—
1138D4—84no—
1139D4—88no—
1140D4—88no—
1141D4—162no—
1142C2×C4—28no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—24no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—48no—
1198C2×C4—416no—
1199C2×C4—48no—
1200C2×C4—48no—
1201C2×C4—84no—
1202C2×C4—88no—
1203C2×C4—88no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—88no—
1207C2×C4—164no—
1208C2×C4C2×H(5,𝔽2)12yes—
1209C2×C4C2×2−1+414yes—
1210C2×C4C2×2−1+418yes—
1211C2×C4#58512yes—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22C22×H(5,𝔽2)11yescharacteristic
1232C22C22×2−1+412yes—
1233C22C2×#58511yescharacteristic
1234C22C2×#58511yescharacteristic
1235C22H(7,𝔽2)12yes—
1236C4—22no—
1237C4—22no—
1238C4—24no—
1239C4—28no—
1240C4—42no—
1241C4—44no—
1242C4—42no—
1243C4—44no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—44no—
1248C4—42no—
1249C4—44no—
1250C4—42no—
1251C4—42no—
1252C4—44no—
1253C4—44no—
1254C4—44no—
1255C4—44no—
1256C2—42no—
1257C2—44no—
1258C2—84no—
1259C2#6282011yescharacteristic
1260C2#6289412yes—
1261C2#6295212yes—
1262C2#6303811yescharacteristic
1263C2#6304611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59923C2semidirect
2. #58211C2semidirect
3. #55151C2semidirect
4. #53299C2semidirect
5. #51667C2semidirect
6. #51531C2semidirect
7. #51278C2semidirect
8. #49933C2semidirect
9. #49591C2semidirect
10. #48305C2semidirect
11. #47971C2semidirect
12. #47663C2semidirect
13. #46455C2semidirect
14. #46315C2semidirect
15. #46099C2semidirect
16. #45385C2semidirect
17. #43369C2semidirect
18. #41336C2semidirect
19. #38821C2semidirect
20. #38444C2semidirect
21. #37194C2semidirect
22. #36374C2semidirect
23. #35307C2semidirect

Maximal subgroups

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

subgroupindex
#599232
#582112
#551512
#532992
#516672
#515312
#512782
#499332
#495912
#483052
#479712
#476632
#464552
#463152
#460992
#453852
#433692
#413362
#388212
#384442
#371942
#363742
#353072