Finite Group Databasebeta

← #8824389

Subgroups — #8824389

Order 512.

4092 conjugacy classes of subgroups.

The subgroup lattice has 1185 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59923C211yesmaximal, characteristic, complemented
2#56020C214yesmaximal, complemented
3#55512C214yesmaximal, complemented
4#53366C212yesmaximal, complemented
5#51681C212yesmaximal, complemented
6#50461C214yesmaximal, complemented
7#50449C214yesmaximal, complemented
8#50262C214yesmaximal, complemented
9#49591C212yesmaximal, complemented
10#49223C214yesmaximal, complemented
11#48842C214yesmaximal, complemented
12#47750C212yesmaximal, complemented
13#47032C212yesmaximal, complemented
14#46099C211yesmaximal, characteristic
15#45956C212yesmaximal, complemented
16#44031C214yesmaximal, complemented
17#43869C214yesmaximal, complemented
18#42785C214yesmaximal, complemented
19#38763C212yesmaximal, complemented
20#38453C212yesmaximal, complemented
21#37195C212yesmaximal, complemented
22#36385C212yesmaximal, complemented
23#35313C211yesmaximal, characteristic, complemented
24#2863C2212yes—
25#2863C2212yes—
26#2862C2212yes—
27#2861C2212yes—
28#2850C2212yes—
29#2832C2212yes—
30#2832C2214yes—
31#2829C2214yes—
32#2823C2212yes—
33#2816C2212yes—
34#2811C2211yescharacteristic
35#2811C2211yescharacteristic
36#2811C2212yes—
37#2808C2212yes—
38#2806C2212yes—
39#2806C2214yes—
40#2806C2212yes—
41#2805C2212yes—
42#2804C2212yes—
43#2801C2214yes—
44#2801C2214yes—
45#2799C2214yes—
46#2789C2212yes—
47#2785C2212yes—
48#2784C2214yes—
49#2783C2214yes—
50#2779C2214yes—
51#2774C2214yes—
52#2774C2214yes—
53#2774C2214yes—
54#2770C2214yes—
55#2769C2214yes—
56#2765C2214yes—
57#2764C2214yes—
58#2763C2214yes—
59#2762C2214yes—
60#2761C2214yes—
61#2759C2214yes—
62#2759C2214yes—
63#2759C2214yes—
64#2759C2214yes—
65#2759C2214yes—
66#2756C2214yes—
67#2755C2214yes—
68#2755C2214yes—
69#2754C2214yes—
70#2754C2214yes—
71#2750C2214yes—
72#2743C2214yes—
73#2739C2214yes—
74#2739C2214yes—
75#2734C2211yescharacteristic
76#2734C2214yes—
77#2733C2211yescharacteristic
78#2731C2212yes—
79#2729C2214yes—
80#2729C2214yes—
81#2723C2214yes—
82#2720C2214yes—
83#2716C2214yes—
84#2716C2214yes—
85#2715C2214yes—
86#2713C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2712C2214yes—
90#2702C2214yes—
91#2700C2214yes—
92#2700C2214yes—
93#2700C2214yes—
94#2698C2214yes—
95#2695C2214yes—
96#2692C2214yes—
97#2687C2214yes—
98#2686C2214yes—
99#2683C2212yes—
100#2677C2214yes—
101#2674C2214yes—
102#2666C2214yes—
103#2665C2214yes—
104#2665C2212yes—
105#2665C2214yes—
106#2654C2214yes—
107#2654C2214yes—
108#2645C2212yes—
109#2645C2214yes—
110#2645C2212yes—
111#2628C2214yes—
112#2616C2212yes—
113#2612C2214yes—
114#2609C2214yes—
115#2608C2212yes—
116#2605C2214yes—
117#2605C2214yes—
118#2605C2214yes—
119#2604C2214yes—
120#2601C2214yes—
121#2594C2214yes—
122#2589C2214yes—
123#2587C2214yes—
124#2586C2212yes—
125#2586C2214yes—
126#2583C2212yes—
127#2574C2214yes—
128#2574C2214yes—
129#2572C2214yes—
130#2568C2214yes—
131#2562C2214yes—
132#2558C2214yes—
133#2556C2214yes—
134#2551C2212yes—
135#2550C2212yes—
136#2550C2214yes—
137#2549C2214yes—
138#2549C2214yes—
139#2545C2212yes—
140#2532C2214yes—
141#2532C2214yes—
142#2529C2214yes—
143#2528C2214yes—
144#2527C2214yes—
145#2527C2214yes—
146#2527C2214yes—
147#2521C2214yes—
148#2520C2214yes—
149#2520C2214yes—
150#2518C2214yes—
151#2514C2214yes—
152#2514C2214yes—
153#2511C2214yes—
154#2510C2214yes—
155#2494C2214yes—
156#2493C2214yes—
157#2493C2214yes—
158#2492C2214yes—
159#2492C2214yes—
160#2491C2212yes—
161#2489C2212yes—
162#2488C2214yes—
163#2477C2214yes—
164#2477C2214yes—
165#2476C2214yes—
166#2474C2214yes—
167#2474C2214yes—
168#2469C2214yes—
169#2466C2214yes—
170#2465C2214yes—
171#2465C2214yes—
172#2463C2214yes—
173#2459C2214yes—
174#2453C2214yes—
175#2451C2214yes—
176#2439C2214yes—
177#2438C2214yes—
178#2438C2214yes—
179#2436C2212yes—
180#2434C2212yes—
181#2432C2214yes—
182#2430C2214yes—
183#2429C2212yes—
184#2427C2212yes—
185#2421C2214yes—
186#2415C2214yes—
187#2406C2212yes—
188#2395C2214yes—
189#2381C2212yes—
190#2379C2212yes—
191#2378C2212yes—
192#2378C2214yes—
193#2372C2214yes—
194#2372C2212yes—
195#2369C2212yes—
196#2368C2214yes—
197#2367C2212yes—
198#2362C2214yes—
199#2356C2212yes—
200#2353C2214yes—
201#2346C2214yes—
202#2339C2212yes—
203#2334C2214yes—
204#2333C2212yes—
205#2332C2212yes—
206#2329C2214yes—
207#2323C2214yes—
208#2320C2214yes—
209#2317C2211yescharacteristic
210#2316C2211yescharacteristic
211#2310C2211yescharacteristic
212#2310C2211yescharacteristic
213C4×C22⋊Q8C2212yes—
214#2296C2211yescharacteristic
215#2295C2212yes—
216C2×#391C2211yescharacteristic
217#2293C2212yes—
218C4×#117C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#125C2314yes—
230C2×#125C2312yes—
231C2×#124C2312yes—
232C2×#124C2314yes—
233C2×#124C2312yes—
234C2×#124C2312yes—
235C2×#124C2312yes—
236C2×#123C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2314yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C42C2311yescharacteristic
261#401C2314yes—
262#401C2314yes—
263#401C2314yes—
264#401C2314yes—
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#400C2314yes—
287#399C2314yes—
288#399C2314yes—
289#399C2314yes—
290#398C2314yes—
291#398C2312yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2312yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#396C2314yes—
320#396C2314yes—
321#396C2314yes—
322#396C2314yes—
323#396C2314yes—
324#396C2314yes—
325#396C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#395C2314yes—
330#395C2314yes—
331#395C2312yes—
332#395C2314yes—
333#395C2312yes—
334#395C2312yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2312yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2312yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2312yes—
358#394C2314yes—
359#394C2314yes—
360#393C2314yes—
361#393C2314yes—
362#393C2314yes—
363#393C2314yes—
364#393C2314yes—
365#393C2314yes—
366#393C2314yes—
367#393C2314yes—
368#393C2314yes—
369#393C2314yes—
370#393C2314yes—
371#393C2314yes—
372#392C2314yes—
373#391C2314yes—
374#391C2312yes—
375#391C2312yes—
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2311yescharacteristic
392#391C2314yes—
393#391C2314yes—
394#391C2312yes—
395#391C2311yescharacteristic
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2314yes—
415#391C2312yes—
416#391C2312yes—
417#390C2312yes—
418#390C2314yes—
419#390C2312yes—
420#390C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2314yes—
446#389C2312yes—
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#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
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#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#384C2312yes—
553#383C2314yes—
554#383C2314yes—
555#383C2314yes—
556#383C2314yes—
557#383C2314yes—
558#382C2314yes—
559#382C2314yes—
560#382C2312yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2312yes—
565#382C2314yes—
566#381C2312yes—
567#381C2314yes—
568#381C2312yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#381C2312yes—
573#380C2314yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2312yes—
578#380C2312yes—
579#380C2314yes—
580#380C2314yes—
581#380C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C22⋊C4C2312yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607#376C2314yes—
608#376C2312yes—
609#376C2314yes—
610#376C2314yes—
611C2×#95C2314yes—
612C2×#95C2314yes—
613C43C2312yes—
614C2×#41—44no—
615C2×#41—84no—
616C22×Q8—42no—
617C22×Q8—42no—
618C22×Q8—42no—
619C22×Q8C2414yes—
620C22×Q8C2412yes—
621C22×Q8C2412yes—
622C22×Q8C2411yescharacteristic
623C22×Q8C2412yes—
624C22×Q8C2411yescharacteristic
625C22×Q8C2412yes—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×D4C2412yes—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C22×D4C2412yes—
633C23×C4C2411yescharacteristic
634C23×C4C2412yes—
635C23×C4C2414yes—
636C23×C4C2414yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2414yes—
640C4⋊Q8—44no—
641C4⋊Q8—44no—
642C4⋊Q8—84no—
643C4⋊Q8—84no—
644C4⋊Q8—82no—
645C4⋊Q8—82no—
646#126—48no—
647#126—84no—
648#125—84no—
649#125—82no—
650#124—44no—
651#124—48no—
652#124—44no—
653#124—44no—
654#124—82no—
655#123—84no—
656C22⋊Q8—216no—
657C22⋊Q8—28no—
658C22⋊Q8—44no—
659C22⋊Q8—44no—
660C22⋊Q8—48no—
661C22⋊Q8—84no—
662C22⋊Q8—84no—
663C22⋊Q8—84no—
664C22⋊Q8—82no—
665#121—44no—
666#121—82no—
667C4×Q8—28no—
668C4×Q8—44no—
669C4×Q8—84no—
670C4×D4—28no—
671C4×D4—84no—
672#117—42no—
673#117—42no—
674#117—48no—
675#117—42no—
676#117—42no—
677#117—84no—
678C2×C4⋊C4—42no—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2412yes—
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⋊C4C2411yescharacteristic
740C2×C22⋊C4C2411yescharacteristic
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C42—42no—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2412yes—
765C2×C42C2412yes—
766C2×C42C2412yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2412yes—
771C2×C42C2414yes—
772C2×C42C2412yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2412yes—
778C2×C42C2414yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786#95C2412yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2412yes—
795#95C2414yes—
796#95C2414yes—
797#95C2412yes—
798#95C2412yes—
799#95C2412yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2412yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
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#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2412yes—
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—
854C24C2514yes—
855C24C2511yescharacteristic
856#41—816no—
857C2×Q8—24no—
858C2×Q8—24no—
859C2×Q8—28no—
860C2×Q8—22no—
861C2×Q8—24no—
862C2×Q8—22no—
863C2×Q8—42no—
864C2×Q8—44no—
865C2×Q8—44no—
866C2×Q8—42no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—42no—
871C2×Q8—41no—
872C2×Q8—41no—
873C2×Q8—41no—
874C2×Q8—41no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—44no—
880C2×Q8—44no—
881C2×Q8—44no—
882C2×Q8—42no—
883C2×Q8—42no—
884C2×Q8—44no—
885C2×Q8—88no—
886C2×D4—28no—
887C2×D4—24no—
888C2×D4—44no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—28no—
903C22×C4—24no—
904C22×C4—28no—
905C22×C4—42no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—42no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—44no—
917C22×C4C2512yes—
918C22×C4C2512yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2514yes—
922C22×C4C2512yes—
923C22×C4C2514yes—
924C22×C4C2514yes—
925C22×C4C2514yes—
926C22×C4C2514yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2514yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2512yes—
935C22×C4C2514yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C4⋊C4—28no—
939C4⋊C4—28no—
940C4⋊C4—28no—
941C4⋊C4—28no—
942C4⋊C4—24no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—44no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—42no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—44no—
962C4⋊C4—42no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—42no—
978C4⋊C4—44no—
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⋊C42−1+418yes—
988C22⋊C4—24no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—28no—
994C22⋊C4—28no—
995C22⋊C4—28no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—42no—
999C22⋊C4—44no—
1000C22⋊C4—42no—
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—44no—
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—28no—
1023C42—24no—
1024C42—24no—
1025C42—24no—
1026C42—41no—
1027C42—41no—
1028C42—42no—
1029C42—42no—
1030C42—44no—
1031C42—44no—
1032C42—44no—
1033C42—44no—
1034C42—44no—
1035C42—44no—
1036C42—44no—
1037C42—44no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C23—22no—
1045C23—21no—
1046C23—21no—
1047C23—22no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23#58512yes—
1056C23C2611yescharacteristic
1057Q8—84no—
1058Q8—84no—
1059Q8—88no—
1060Q8—82no—
1061Q8—84no—
1062Q8—82no—
1063Q8—84no—
1064Q8—162no—
1065Q8—164no—
1066Q8—162no—
1067D4—48no—
1068D4—84no—
1069D4—88no—
1070D4—162no—
1071C2×C4—28no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—24no—
1077C2×C4—21no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—84no—
1130C2×C4—88no—
1131C2×C4—88no—
1132C2×C4—84no—
1133C2×C4—84no—
1134C2×C4—88no—
1135C2×C4C2×2−1+414yes—
1136C2×C4C2×2−1+418yes—
1137C2×C4#58512yes—
1138C2×C4#58512yes—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—42no—
1143C22—42no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22—44no—
1148C22—44no—
1149C22—44no—
1150C22—44no—
1151C22C22×2−1+412yes—
1152C22C2×#58511yescharacteristic
1153C22C2×#58511yescharacteristic
1154C22C2×#58511yescharacteristic
1155C22H(7,𝔽2)12yes—
1156C4—22no—
1157C4—22no—
1158C4—24no—
1159C4—28no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—44no—
1164C4—42no—
1165C4—44no—
1166C4—42no—
1167C4—42no—
1168C4—44no—
1169C4—44no—
1170C4—42no—
1171C4—44no—
1172C4—44no—
1173C4—42no—
1174C4—42no—
1175C4—44no—
1176C4—44no—
1177C2—42no—
1178C2—84no—
1179C2#6282611yescharacteristic
1180C2#6292912yes—
1181C2#6295112yes—
1182C2#6303811yescharacteristic
1183C2#6304611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#46099C2
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. #56020C2semidirect
3. #55512C2semidirect
4. #53366C2semidirect
5. #51681C2semidirect
6. #50461C2semidirect
7. #50449C2semidirect
8. #50262C2semidirect
9. #49591C2semidirect
10. #49223C2semidirect
11. #48842C2semidirect
12. #47750C2semidirect
13. #47032C2semidirect
15. #45956C2semidirect
16. #44031C2semidirect
17. #43869C2semidirect
18. #42785C2semidirect
19. #38763C2semidirect
20. #38453C2semidirect
21. #37195C2semidirect
22. #36385C2semidirect
23. #35313C2semidirect

Maximal subgroups

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

subgroupindex
#599232
#560202
#555122
#533662
#516812
#504612
#504492
#502622
#495912
#492232
#488422
#477502
#470322
#460992
#459562
#440312
#438692
#427852
#387632
#384532
#371952
#363852
#353132