Finite Group Databasebeta

← #9040122

Subgroups — #9040122

Order 512.

4089 conjugacy classes of subgroups.

The subgroup lattice has 1085 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58098C214yesmaximal, complemented
2#57944C214yesmaximal, complemented
3#57850C214yesmaximal, complemented
4#56407C214yesmaximal, complemented
5#55804C214yesmaximal, complemented
6#55778C214yesmaximal, complemented
7#52074C211yesmaximal, characteristic, complemented
8#51754C211yesmaximal, characteristic
9#51469C214yesmaximal, complemented
10#50896C212yesmaximal, complemented
11#50716C212yesmaximal, complemented
12#48645C214yesmaximal, complemented
13#48353C214yesmaximal, complemented
14#42809C212yesmaximal, complemented
15#42330C212yesmaximal, complemented
16#40970C214yesmaximal, complemented
17#40798C214yesmaximal, complemented
18#37244C214yesmaximal, complemented
19#37031C212yesmaximal, complemented
20#36030C212yesmaximal, complemented
21#35670C211yesmaximal, characteristic, complemented
22C2×#562C2211yescharacteristic
23C2×Q82C2211yescharacteristic
24C2×#556C2212yes—
25C2×#541C2211yescharacteristic
26C2×#519C2211yescharacteristic
27#2866C2214yes—
28#2836C2214yes—
29#2833C2214yes—
30#2833C2214yes—
31#2832C2214yes—
32#2829C2214yes—
33#2827C2214yes—
34#2821C2214yes—
35#2817C2214yes—
36#2808C2214yes—
37#2808C2214yes—
38#2801C2214yes—
39#2799C2214yes—
40#2799C2214yes—
41#2796C2214yes—
42#2793C2214yes—
43#2791C2214yes—
44#2791C2214yes—
45#2790C2214yes—
46#2789C2214yes—
47#2789C2214yes—
48#2788C2214yes—
49#2787C2214yes—
50#2787C2214yes—
51#2778C2214yes—
52#2777C2214yes—
53#2776C2214yes—
54#2775C2214yes—
55#2773C2214yes—
56#2771C2214yes—
57#2763C2214yes—
58#2762C2214yes—
59#2762C2214yes—
60#2759C2214yes—
61#2759C2214yes—
62#2759C2214yes—
63#2759C2214yes—
64#2755C2214yes—
65#2755C2214yes—
66#2754C2214yes—
67#2754C2214yes—
68#2753C2214yes—
69#2751C2214yes—
70#2747C2214yes—
71#2747C2214yes—
72#2746C2214yes—
73#2745C2214yes—
74#2743C2214yes—
75#2740C2214yes—
76#2740C2214yes—
77#2739C2214yes—
78#2737C2214yes—
79#2737C2214yes—
80#2729C2214yes—
81#2729C2214yes—
82#2723C2214yes—
83#2718C2214yes—
84#2716C2214yes—
85#2716C2214yes—
86#2716C2214yes—
87#2716C2214yes—
88#2714C2214yes—
89#2713C2214yes—
90#2702C2214yes—
91#2698C2214yes—
92#2698C2214yes—
93#2696C2214yes—
94#2692C2214yes—
95#2692C2214yes—
96#2691C2214yes—
97#2690C2214yes—
98#2687C2214yes—
99#2686C2214yes—
100#2677C2214yes—
101#2677C2214yes—
102#2666C2214yes—
103#2666C2214yes—
104#2659C2214yes—
105#2655C2214yes—
106#2655C2214yes—
107#2655C2214yes—
108#2653C2214yes—
109#2653C2214yes—
110#2653C2214yes—
111#2651C2214yes—
112#2648C2214yes—
113#2640C2212yes—
114#2637C2214yes—
115#2634C2212yes—
116#2632C2212yes—
117#2632C2212yes—
118#2628C2212yes—
119#2621C2214yes—
120#2610C2212yes—
121#2610C2212yes—
122#2607C2214yes—
123#2607C2214yes—
124#2605C2212yes—
125#2599C2214yes—
126#2599C2212yes—
127#2599C2212yes—
128#2596C2214yes—
129#2595C2214yes—
130#2594C2214yes—
131#2592C2212yes—
132#2588C2214yes—
133#2586C2214yes—
134#2585C2214yes—
135#2578C2214yes—
136#2577C2214yes—
137#2574C2214yes—
138#2567C2212yes—
139#2565C2212yes—
140#2560C2214yes—
141#2560C2214yes—
142#2553C2214yes—
143#2546C2212yes—
144#2536C2212yes—
145#2530C2214yes—
146#2528C2214yes—
147#2527C2214yes—
148#2524C2214yes—
149#2520C2214yes—
150#2520C2214yes—
151#2516C2214yes—
152#2514C2214yes—
153#2511C2214yes—
154#2499C2212yes—
155#2494C2214yes—
156#2493C2214yes—
157#2492C2214yes—
158#2490C2214yes—
159#2488C2214yes—
160#2479C2214yes—
161#2479C2214yes—
162#2478C2214yes—
163#2478C2214yes—
164#2476C2214yes—
165#2469C2214yes—
166#2469C2214yes—
167#2469C2214yes—
168#2468C2214yes—
169#2463C2214yes—
170#2462C2214yes—
171#2462C2214yes—
172#2462C2214yes—
173#2458C2214yes—
174#2452C2214yes—
175#2451C2214yes—
176#2450C2214yes—
177#2448C2214yes—
178#2446C2214yes—
179#2446C2214yes—
180#2444C2214yes—
181#2438C2214yes—
182#2434C2212yes—
183#2423C2214yes—
184#2421C2214yes—
185#2409C2214yes—
186#2399C2212yes—
187#2399C2212yes—
188#2392C2212yes—
189#2381C2211yescharacteristic
190#2378C2214yes—
191#2371C2211yescharacteristic
192#2368C2214yes—
193#2362C2214yes—
194#2356C2212yes—
195#2354C2214yes—
196#2337C2212yes—
197#2334C2214yes—
198#2332C2214yes—
199#2327C2212yes—
200#2320C2212yes—
201C4×C4⋊Q8C2212yes—
202#2298C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204#562—44no—
205Q82—44no—
206#556—48no—
207#541—44no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×#126C2314yes—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#126C2314yes—
218C2×#125C2311yescharacteristic
219C2×#125C2314yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#123C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×#121C2314yes—
231#519—44no—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×#117C2311yescharacteristic
243C2×#117C2314yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247#401C2314yes—
248#401C2314yes—
249#401C2314yes—
250#401C2314yes—
251#401C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
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#399C2314yes—
276#399C2314yes—
277#399C2314yes—
278#399C2314yes—
279#399C2314yes—
280#399C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2312yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2312yes—
300#398C2312yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2312yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#395C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2312yes—
340#395C2312yes—
341#395C2312yes—
342#395C2312yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2312yes—
347#395C2314yes—
348#395C2312yes—
349#395C2314yes—
350#394C2312yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2312yes—
360#394C2312yes—
361#394C2314yes—
362#394C2314yes—
363#393C2312yes—
364#393C2314yes—
365#393C2314yes—
366#393C2314yes—
367#393C2314yes—
368#393C2314yes—
369#393C2314yes—
370#393C2312yes—
371#393C2314yes—
372#393C2314yes—
373#393C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#392C2314yes—
378#392C2312yes—
379#391C2314yes—
380#391C2314yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2312yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#390C2314yes—
403#390C2314yes—
404#390C2314yes—
405#390C2314yes—
406#390C2314yes—
407#390C2314yes—
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#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#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#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#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#384C2312yes—
539#384C2314yes—
540#383C2314yes—
541#383C2314yes—
542#383C2312yes—
543#383C2312yes—
544#383C2314yes—
545#382C2312yes—
546#382C2314yes—
547#382C2314yes—
548#382C2314yes—
549#382C2312yes—
550#382C2314yes—
551#381C2314yes—
552#381C2314yes—
553#381C2314yes—
554#381C2314yes—
555#380C2314yes—
556#380C2314yes—
557#380C2314yes—
558#380C2314yes—
559#380C2314yes—
560#380C2314yes—
561#380C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2312yes—
567C4×C4⋊C4C2312yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576C4×C22⋊C4C2314yes—
577C4×C22⋊C4C2312yes—
578C4×C22⋊C4C2314yes—
579C4×C22⋊C4C2314yes—
580#376C2312yes—
581#376C2311yescharacteristic
582#376C2312yes—
583C2×#95C2314yes—
584C43C2311yescharacteristic
585C22×Q8—42no—
586C22×Q8—44no—
587C22×Q8C2412yes—
588C22×Q8C2412yes—
589C22×Q8C2412yes—
590C22×Q8C2412yes—
591C22×Q8C2412yes—
592C22×Q8C2414yes—
593C22×Q8C2414yes—
594C22×D4C2412yes—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2414yes—
600C23×C4C2411yescharacteristic
601C23×C4C2414yes—
602C23×C4C2414yes—
603C4⋊Q8—24no—
604C4⋊Q8—48no—
605C4⋊Q8—44no—
606C4⋊Q8—44no—
607C4⋊Q8—44no—
608C4⋊Q8—48no—
609#126—48no—
610#126—48no—
611#126—48no—
612#126—48no—
613#125—24no—
614#125—48no—
615#124—28no—
616#124—44no—
617#123—48no—
618C22⋊Q8—48no—
619C22⋊Q8—48no—
620C22⋊Q8—48no—
621C22⋊Q8—48no—
622C22⋊Q8—48no—
623C22⋊Q8—48no—
624C22⋊Q8—44no—
625#121—48no—
626C4×Q8—28no—
627C4×Q8—28no—
628C4×Q8—44no—
629C4×Q8—44no—
630C4×Q8—44no—
631C4×Q8—44no—
632C4×Q8—44no—
633C4×Q8—48no—
634C4×D4—44no—
635C4×D4—48no—
636#117—24no—
637#117—44no—
638#117—44no—
639#117—48no—
640#117—42no—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2412yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2414yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2414yes—
739C2×C42C2411yescharacteristic
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2412yes—
745#95C2412yes—
746#95C2414yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2412yes—
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—
806C24C2511yescharacteristic
807C24C2514yes—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—42no—
815C2×Q8—42no—
816C2×Q8—42no—
817C2×Q8—44no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—44no—
821C2×Q8—44no—
822C2×Q8—44no—
823C2×Q8—44no—
824C2×Q8—44no—
825C2×Q8—44no—
826C2×Q8—44no—
827C2×Q8—416no—
828C2×D4—24no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C22×C4—22no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2511yescharacteristic
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2511yescharacteristic
869C22×C4C2512yes—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—42no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C42—22no—
949C42—24no—
950C42—24no—
951C42—28no—
952C42—44no—
953C42—44no—
954C42—44no—
955C42—44no—
956C42—44no—
957C42—42no—
958C42—42no—
959C42—41no—
960C42—41no—
961C42—44no—
962C42—44no—
963C42—44no—
964C42—44no—
965C42—44no—
966C42—42no—
967C42—42no—
968C42H(5,𝔽2)14yes—
969C23—21no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23C2611yescharacteristic
980Q8—48no—
981Q8—48no—
982Q8—48no—
983Q8—84no—
984Q8—84no—
985Q8—164no—
986Q8—164no—
987D4—84no—
988D4—88no—
989D4—164no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—21no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—88no—
1042C2×C4—164no—
1043C2×C4—164no—
1044C2×C4C2×H(5,𝔽2)14yes—
1045C2×C4C2×H(5,𝔽2)12yes—
1046C2×C4#58514yes—
1047C22—41no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—42no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22C22×H(5,𝔽2)11yescharacteristic
1058C22C2×#58512yes—
1059C222−1+614yes—
1060C4—24no—
1061C4—22no—
1062C4—24no—
1063C4—42no—
1064C4—41no—
1065C4—44no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4—44no—
1071C4—44no—
1072C4—44no—
1073C4—44no—
1074C4—44no—
1075C4—44no—
1076C4—44no—
1077C4—44no—
1078C4—44no—
1079C2—81no—
1080C2—84no—
1081C2#6282111yescharacteristic
1082C2#6288712yes—
1083C2#6289114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#51754C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58098C2semidirect
2. #57944C2semidirect
3. #57850C2semidirect
4. #56407C2semidirect
5. #55804C2semidirect
6. #55778C2semidirect
7. #52074C2semidirect
9. #51469C2semidirect
10. #50896C2semidirect
11. #50716C2semidirect
12. #48645C2semidirect
13. #48353C2semidirect
14. #42809C2semidirect
15. #42330C2semidirect
16. #40970C2semidirect
17. #40798C2semidirect
18. #37244C2semidirect
19. #37031C2semidirect
20. #36030C2semidirect
21. #35670C2semidirect

Maximal subgroups

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

subgroupindex
#580982
#579442
#578502
#564072
#558042
#557782
#520742
#517542
#514692
#508962
#507162
#486452
#483532
#428092
#423302
#409702
#407982
#372442
#370312
#360302
#356702