Finite Group Databasebeta

← #8757221

Subgroups — #8757221

Order 512.

4316 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58740C214yesmaximal, complemented
2#58689C214yesmaximal, complemented
3#57999C214yesmaximal, complemented
4#57442C214yesmaximal, complemented
5#55986C214yesmaximal, complemented
6#55544C214yesmaximal, complemented
7#50807C214yesmaximal, complemented
8#49609C214yesmaximal, complemented
9#48342C214yesmaximal, complemented
10#47655C214yesmaximal, complemented
11#47020C214yesmaximal, complemented
12#46790C214yesmaximal, complemented
13#46229C211yesmaximal, characteristic, complemented
14#46226C211yesmaximal, characteristic, complemented
15#46144C212yesmaximal, complemented
16#46135C212yesmaximal, complemented
17#45990C212yesmaximal, complemented
18#45990C212yesmaximal, complemented
19#45972C212yesmaximal, complemented
20#35334C211yesmaximal, characteristic, complemented
21#35130C212yesmaximal, complemented
22C2×#564C2211yescharacteristic
23C2×#562C2211yescharacteristic
24C2×#533C2211yescharacteristic
25C2×#529C2212yes—
26C2×C4×#41C2211yescharacteristic
27#2851C2212yes—
28#2851C2212yes—
29#2851C2212yes—
30#2851C2212yes—
31#2850C2212yes—
32#2850C2212yes—
33#2845C2212yes—
34#2841C2214yes—
35#2839C2214yes—
36#2836C2214yes—
37#2831C2214yes—
38#2831C2214yes—
39#2826C2214yes—
40#2822C2212yes—
41#2820C2212yes—
42#2820C2212yes—
43#2820C2214yes—
44#2802C2214yes—
45#2790C2214yes—
46#2784C2214yes—
47#2784C2214yes—
48#2783C2214yes—
49#2783C2214yes—
50#2783C2214yes—
51#2780C2214yes—
52#2780C2214yes—
53#2779C2214yes—
54#2774C2214yes—
55#2774C2214yes—
56#2774C2214yes—
57#2772C2214yes—
58#2772C2214yes—
59#2768C2214yes—
60#2768C2214yes—
61#2767C2214yes—
62#2767C2214yes—
63#2767C2214yes—
64#2767C2214yes—
65#2767C2214yes—
66#2761C2214yes—
67#2761C2214yes—
68#2755C2214yes—
69#2755C2214yes—
70#2751C2214yes—
71#2748C2214yes—
72#2744C2214yes—
73#2744C2214yes—
74#2743C2214yes—
75#2743C2214yes—
76#2743C2214yes—
77#2743C2214yes—
78#2742C2214yes—
79#2739C2214yes—
80#2739C2214yes—
81#2732C2214yes—
82#2725C2214yes—
83#2721C2214yes—
84#2720C2214yes—
85#2720C2214yes—
86#2719C2214yes—
87#2719C2214yes—
88#2717C2214yes—
89#2713C2214yes—
90#2711C2214yes—
91#2708C2214yes—
92#2707C2214yes—
93#2707C2214yes—
94#2706C2214yes—
95#2706C2214yes—
96#2704C2214yes—
97#2703C2214yes—
98#2698C2214yes—
99#2694C2214yes—
100#2694C2214yes—
101#2693C2214yes—
102#2693C2214yes—
103#2693C2214yes—
104#2691C2214yes—
105#2690C2214yes—
106#2688C2214yes—
107#2687C2214yes—
108#2683C2214yes—
109#2682C2214yes—
110#2676C2214yes—
111#2674C2214yes—
112#2652C2214yes—
113#2652C2214yes—
114#2650C2214yes—
115#2637C2214yes—
116#2636C2214yes—
117#2630C2214yes—
118#2629C2214yes—
119#2628C2212yes—
120#2628C2212yes—
121#2627C2214yes—
122#2609C2214yes—
123#2609C2214yes—
124#2609C2214yes—
125#2608C2214yes—
126#2585C2214yes—
127#2581C2214yes—
128#2581C2212yes—
129#2580C2214yes—
130#2580C2212yes—
131#2579C2214yes—
132#2579C2214yes—
133#2574C2214yes—
134#2569C2214yes—
135#2569C2214yes—
136#2564C2214yes—
137#2564C2214yes—
138#2558C2214yes—
139#2557C2214yes—
140#2536C2212yes—
141#2535C2212yes—
142#2522C2214yes—
143#2505C2214yes—
144#2505C2214yes—
145#2498C2214yes—
146#2498C2214yes—
147#2498C2214yes—
148#2487C2214yes—
149#2477C2214yes—
150#2475C2214yes—
151#2475C2214yes—
152#2473C2214yes—
153#2473C2214yes—
154#2473C2214yes—
155#2471C2214yes—
156#2471C2214yes—
157#2470C2214yes—
158#2465C2214yes—
159#2464C2214yes—
160#2462C2214yes—
161#2462C2214yes—
162#2460C2214yes—
163#2460C2214yes—
164#2459C2214yes—
165#2456C2214yes—
166#2454C2214yes—
167#2453C2214yes—
168#2449C2214yes—
169#2443C2214yes—
170#2441C2214yes—
171#2441C2214yes—
172#2438C2214yes—
173#2438C2214yes—
174#2430C2214yes—
175#2426C2214yes—
176#2425C2214yes—
177#2425C2214yes—
178#2421C2214yes—
179#2420C2214yes—
180#2419C2214yes—
181#2419C2214yes—
182#2417C2212yes—
183#2417C2212yes—
184#2416C2212yes—
185#2416C2212yes—
186#2413C2214yes—
187#2413C2214yes—
188#2413C2214yes—
189#2382C2212yes—
190#2382C2211yescharacteristic
191#2382C2211yescharacteristic
192#2379C2212yes—
193#2376C2214yes—
194#2352C2214yes—
195#2333C2214yes—
196#2325C2214yes—
197#2325C2214yes—
198#2324C2214yes—
199#2316C2212yes—
200#2311C2212yes—
201C2×#382C2211yescharacteristic
202C2×#382C2212yes—
203C22×#41C2311yescharacteristic
204#564—44no—
205#562—44no—
206#533—44no—
207C2×C4⋊Q8C2312yes—
208#529—48no—
209C2×#126C2314yes—
210C2×#125C2311yescharacteristic
211C2×#125C2312yes—
212C2×#125C2311yescharacteristic
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C4×#41—44no—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×#117C2312yes—
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2314yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2312yes—
260C22×C42C2311yescharacteristic
261C22×C42C2312yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#399C2314yes—
287#399C2314yes—
288#399C2314yes—
289#399C2314yes—
290#399C2314yes—
291#399C2314yes—
292#399C2314yes—
293#399C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#392C2314yes—
379#392C2314yes—
380#392C2314yes—
381#392C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2312yes—
385#391C2312yes—
386#391C2314yes—
387#391C2314yes—
388#390C2314yes—
389#390C2314yes—
390#390C2314yes—
391#390C2312yes—
392#390C2312yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2312yes—
404#389C2312yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
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#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#384C2314yes—
537#382C2314yes—
538#382C2312yes—
539#382C2312yes—
540#382C2312yes—
541#382C2314yes—
542#382C2312yes—
543#382C2312yes—
544#382C2314yes—
545#382C2314yes—
546#382C2314yes—
547#382C2311yescharacteristic
548#382C2311yescharacteristic
549#382C2314yes—
550#381C2314yes—
551#381C2314yes—
552#381C2314yes—
553#381C2314yes—
554#381C2314yes—
555#380C2314yes—
556#380C2314yes—
557#380C2312yes—
558#380C2312yes—
559#380C2312yes—
560#380C2312yes—
561#380C2314yes—
562#380C2312yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2314yes—
567#380C2314yes—
568#380C2314yes—
569#380C2312yes—
570#380C2312yes—
571#380C2312yes—
572#380C2314yes—
573#380C2314yes—
574#380C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2314yes—
577C4×C22⋊C4C2314yes—
578C4×C22⋊C4C2314yes—
579C4×C22⋊C4C2314yes—
580C4×C22⋊C4C2314yes—
581C4×C22⋊C4C2314yes—
582C2×#95C2314yes—
583C2×#95C2314yes—
584C2×#95C2314yes—
585C2×#41—24no—
586C2×#41—42no—
587C2×#41—42no—
588C22×Q8C2411yescharacteristic
589C22×Q8C2412yes—
590C22×Q8C2414yes—
591C22×D4C2412yes—
592C22×D4C2412yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C22×D4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2412yes—
604C23×C4C2412yes—
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2414yes—
608C23×C4C2414yes—
609C4⋊Q8—44no—
610#126—48no—
611#125—28no—
612#125—24no—
613#125—24no—
614#125—48no—
615#125—48no—
616#125—48no—
617#125—84no—
618#125—84no—
619#124—28no—
620#124—84no—
621#123—48no—
622#123—48no—
623#123—48no—
624#123—84no—
625#123—84no—
626#123—84no—
627#123—84no—
628C22⋊Q8—48no—
629C22⋊Q8—48no—
630C22⋊Q8—44no—
631C22⋊Q8—82no—
632C22⋊Q8—82no—
633C22⋊Q8—84no—
634#121—216no—
635#121—48no—
636#121—48no—
637#121—44no—
638#121—82no—
639#121—82no—
640C4×Q8—44no—
641C4×Q8—48no—
642C4×Q8—44no—
643C4×D4—44no—
644C4×D4—44no—
645C4×D4—44no—
646C4×D4—44no—
647C4×D4—48no—
648C4×D4—48no—
649C4×D4—84no—
650#117—42no—
651#117—44no—
652#117—48no—
653#117—44no—
654#117—84no—
655#117—84no—
656C2×C4⋊C4—44no—
657C2×C4⋊C4—84no—
658C2×C4⋊C4—82no—
659C2×C4⋊C4—82no—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2411yescharacteristic
720C2×C22⋊C4C2411yescharacteristic
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2412yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
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×C42—28no—
753C2×C42—24no—
754C2×C42C2412yes—
755C2×C42C2411yescharacteristic
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2411yescharacteristic
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822C24C2514yes—
823C24C2512yes—
824C24C2511yescharacteristic
825#41—416no—
826C2×Q8—24no—
827C2×Q8—22no—
828C2×Q8—41no—
829C2×Q8—41no—
830C2×Q8—44no—
831C2×Q8—42no—
832C2×Q8—44no—
833C2×Q8—42no—
834C2×Q8—44no—
835C2×D4—24no—
836C2×D4—24no—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—28no—
840C2×D4—24no—
841C2×D4—41no—
842C2×D4—42no—
843C2×D4—41no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—42no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—42no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D42−1+414yes—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—24no—
860C22×C4—28no—
861C22×C4—28no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4C2512yes—
890C22×C4C2514yes—
891C22×C4C2514yes—
892C22×C4C2514yes—
893C22×C4C2514yes—
894C22×C4C2512yes—
895C22×C4C2514yes—
896C22×C4C2514yes—
897C22×C4C2514yes—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2511yescharacteristic
905C22×C4C2512yes—
906C22×C4C2511yescharacteristic
907C4⋊C4—24no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—41no—
973C22⋊C4—42no—
974C22⋊C4—41no—
975C22⋊C4—42no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C42—24no—
1000C42—22no—
1001C42—24no—
1002C42—24no—
1003C42—24no—
1004C42—44no—
1005C42—44no—
1006C42—44no—
1007C42—44no—
1008C42—44no—
1009C42—44no—
1010C42—44no—
1011C42—44no—
1012C42H(5,𝔽2)14yes—
1013C23—21no—
1014C23—22no—
1015C23—21no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23C2×2−1+414yes—
1031C23#58512yes—
1032C23C2611yescharacteristic
1033Q8—44no—
1034Q8—84no—
1035Q8—88no—
1036D4—44no—
1037D4—48no—
1038D4—84no—
1039D4—88no—
1040D4—88no—
1041D4—88no—
1042D4—164no—
1043C2×C4—28no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—48no—
1096C2×C4—48no—
1097C2×C4—84no—
1098C2×C4—84no—
1099C2×C4—88no—
1100C2×C4—88no—
1101C2×C4—88no—
1102C2×C4—88no—
1103C2×C4—164no—
1104C2×C4—164no—
1105C2×C4C2×H(5,𝔽2)12yes—
1106C2×C4C2×H(5,𝔽2)14yes—
1107C2×C4C2×2−1+412yes—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—22no—
1112C22—24no—
1113C22—42no—
1114C22—42no—
1115C22—41no—
1116C22—41no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—44no—
1121C22—44no—
1122C22—44no—
1123C22—44no—
1124C22—44no—
1125C22—44no—
1126C22—44no—
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22C22×2−1+411yescharacteristic
1129C22C2×#58511yescharacteristic
1130C22H(7,𝔽2)12yes—
1131C222−1+612yes—
1132C4—22no—
1133C4—22no—
1134C4—24no—
1135C4—44no—
1136C4—44no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—42no—
1142C4—44no—
1143C4—42no—
1144C4—44no—
1145C4—42no—
1146C4—42no—
1147C4—44no—
1148C4—44no—
1149C4—44no—
1150C2—42no—
1151C2—44no—
1152C2—84no—
1153C2#6281911yescharacteristic
1154C2#6287512yes—
1155C2#6305012yes—
1156C2#6305411yescharacteristic
1157C2#6306711yescharacteristic
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. #58740C2semidirect
2. #58689C2semidirect
3. #57999C2semidirect
4. #57442C2semidirect
5. #55986C2semidirect
6. #55544C2semidirect
7. #50807C2semidirect
8. #49609C2semidirect
9. #48342C2semidirect
10. #47655C2semidirect
11. #47020C2semidirect
12. #46790C2semidirect
13. #46229C2semidirect
14. #46226C2semidirect
15. #46144C2semidirect
16. #46135C2semidirect
17. #45990C2semidirect
18. #45990C2semidirect
19. #45972C2semidirect
20. #35334C2semidirect
21. #35130C2semidirect

Maximal subgroups

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

subgroupindex
#587402
#586892
#579992
#574422
#559862
#555442
#508072
#496092
#483422
#476552
#470202
#467902
#462292
#462262
#461442
#461352
#459902
#459722
#353342
#351302