Finite Group Databasebeta

← #8926245

Subgroups — #8926245

Order 512.

4434 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58571C214yesmaximal, complemented
2#58415C214yesmaximal, complemented
3#58257C212yesmaximal, complemented
4#58048C214yesmaximal, complemented
5#57963C212yesmaximal, complemented
6#55929C214yesmaximal, complemented
7#54354C214yesmaximal, complemented
8#46931C214yesmaximal, complemented
9#46857C212yesmaximal, complemented
10#46816C212yesmaximal, complemented
11#46814C212yesmaximal, complemented
12#46599C214yesmaximal, complemented
13#46570C214yesmaximal, complemented
14#37423C212yesmaximal, complemented
15#37158C214yesmaximal, complemented
16#37050C214yesmaximal, complemented
17#37020C212yesmaximal, complemented
18#36730C212yesmaximal, complemented
19#36730C212yesmaximal, complemented
20#36721C211yesmaximal, characteristic
21#36711C211yesmaximal, characteristic, complemented
22#35474C212yesmaximal, complemented
23#35455C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic, complemented
25C2×#543C2211yescharacteristic, complemented
26C2×#542C2212yes—
27C2×#534C2211yescharacteristic
28C22×#123C2211yescharacteristic
29#2866C2214yescomplemented
30#2862C2212yescomplemented
31#2861C2212yescomplemented
32#2848C2211yescharacteristic, complemented
33#2848C2211yescharacteristic, complemented
34#2847C2212yes—
35#2843C2214yescomplemented
36#2840C2212yescomplemented
37#2836C2214yescomplemented
38#2834C2212yescomplemented
39#2832C2214yescomplemented
40#2830C2214yescomplemented
41#2826C2214yes—
42#2816C2212yes—
43#2814C2214yescomplemented
44#2808C2214yescomplemented
45#2798C2214yescomplemented
46#2793C2214yescomplemented
47#2790C2214yescomplemented
48#2788C2214yescomplemented
49#2781C2214yescomplemented
50#2775C2214yescomplemented
51#2775C2214yescomplemented
52#2766C2214yescomplemented
53#2763C2212yescomplemented
54#2762C2214yescomplemented
55#2759C2214yescomplemented
56#2759C2214yescomplemented
57#2756C2214yes—
58#2756C2214yes—
59#2755C2214yescomplemented
60#2754C2214yescomplemented
61#2754C2214yescomplemented
62#2751C2214yescomplemented
63#2746C2214yescomplemented
64#2746C2214yescomplemented
65#2746C2214yescomplemented
66#2745C2214yescomplemented
67#2745C2214yescomplemented
68#2738C2214yescomplemented
69#2738C2214yescomplemented
70#2737C2214yescomplemented
71#2737C2214yescomplemented
72#2736C2214yes—
73#2736C2212yescomplemented
74#2735C2214yes—
75#2735C2212yescomplemented
76#2735C2214yescomplemented
77#2731C2214yescomplemented
78#2730C2214yescomplemented
79#2729C2214yescomplemented
80#2728C2214yescomplemented
81#2723C2214yescomplemented
82#2718C2214yescomplemented
83#2716C2214yescomplemented
84#2716C2214yescomplemented
85#2712C2214yes—
86#2706C2214yes—
87#2706C2214yes—
88#2702C2214yescomplemented
89#2701C2214yes—
90#2701C2214yescomplemented
91#2700C2214yescomplemented
92#2700C2214yescomplemented
93#2700C2214yescomplemented
94#2696C2214yes—
95#2694C2214yescomplemented
96#2694C2214yescomplemented
97#2692C2214yescomplemented
98#2692C2214yescomplemented
99#2690C2214yescomplemented
100#2690C2214yescomplemented
101#2687C2214yescomplemented
102#2687C2214yescomplemented
103#2687C2214yescomplemented
104#2686C2214yes—
105#2686C2214yescomplemented
106#2685C2214yescomplemented
107#2684C2214yescomplemented
108#2684C2214yescomplemented
109#2684C2214yescomplemented
110#2680C2214yescomplemented
111#2680C2214yescomplemented
112#2678C2214yes—
113#2678C2214yes—
114#2677C2212yescomplemented
115#2677C2214yescomplemented
116#2674C2214yescomplemented
117#2674C2214yescomplemented
118#2674C2214yescomplemented
119#2674C2214yescomplemented
120#2665C2214yescomplemented
121#2660C2212yescomplemented
122#2659C2212yescomplemented
123#2659C2212yescomplemented
124#2653C2214yescomplemented
125#2650C2214yescomplemented
126#2640C2212yescomplemented
127#2639C2212yescomplemented
128#2639C2212yescomplemented
129#2637C2214yescomplemented
130#2632C2214yescomplemented
131#2626C2211yescharacteristic
132#2626C2211yescharacteristic
133#2618C2212yes—
134#2607C2212yescomplemented
135#2595C2214yescomplemented
136#2594C2214yescomplemented
137#2583C2212yescomplemented
138#2578C2214yescomplemented
139#2575C2214yescomplemented
140#2572C2214yescomplemented
141#2568C2212yescomplemented
142#2566C2212yescomplemented
143#2565C2212yescomplemented
144#2563C2212yescomplemented
145#2561C2212yes—
146#2561C2212yes—
147#2560C2214yescomplemented
148#2560C2214yescomplemented
149#2557C2214yes—
150#2557C2214yescomplemented
151#2553C2214yescomplemented
152#2553C2214yescomplemented
153#2542C2214yescomplemented
154#2539C2212yes—
155#2534C2214yescomplemented
156#2532C2214yescomplemented
157#2531C2214yescomplemented
158#2524C2214yescomplemented
159#2523C2214yescomplemented
160#2523C2212yescomplemented
161#2518C2214yescomplemented
162#2517C2214yescomplemented
163#2516C2214yescomplemented
164#2510C2214yescomplemented
165#2510C2214yescomplemented
166#2504C2212yes—
167#2503C2212yescomplemented
168#2503C2212yescomplemented
169#2500C2212yes—
170#2499C2212yescomplemented
171#2497C2214yescomplemented
172#2488C2214yescomplemented
173#2488C2214yescomplemented
174#2488C2214yescomplemented
175#2488C2214yescomplemented
176#2482C2212yes—
177#2482C2212yescomplemented
178#2480C2214yescomplemented
179#2472C2214yescomplemented
180#2472C2214yescomplemented
181#2472C2214yescomplemented
182#2467C2214yescomplemented
183#2465C2214yescomplemented
184#2463C2214yescomplemented
185#2461C2214yes—
186#2459C2214yes—
187#2458C2214yescomplemented
188#2458C2214yescomplemented
189#2451C2214yescomplemented
190#2450C2214yescomplemented
191#2450C2214yescomplemented
192#2437C2212yescomplemented
193#2435C2212yes—
194#2435C2214yes—
195#2423C2214yescomplemented
196#2423C2214yescomplemented
197#2418C2214yescomplemented
198#2418C2214yescomplemented
199#2418C2214yescomplemented
200#2405C2214yes—
201#2405C2212yes—
202#2403C2212yes—
203#2337C2214yescomplemented
204#2335C2214yescomplemented
205#2333C2212yes—
206#2332C2212yescomplemented
207#2329C2212yescomplemented
208#2329C2212yescomplemented
209#2325C2212yescomplemented
210#2325C2212yescomplemented
211#2321C2214yescomplemented
212#2313C2211yescharacteristic, complemented
213#2312C2211yescharacteristic
214#2308C2212yes—
215C4×#124C2214yescomplemented
216#2298C2212yescomplemented
217C2×#381C2212yescomplemented
218#2273C2211yescharacteristic, complemented
219C23×D4C2311yescharacteristic
220C23×D4C2312yes—
221C24×C4C2311yescharacteristic
222#544—44no—
223#543—44no—
224#542—48no—
225#534—44no—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#125C2312yes—
233C2×#125C2312yes—
234C2×#124C2314yes—
235C2×#124C2312yes—
236C2×#124C2314yes—
237C2×#124C2314yes—
238C2×#124C2314yes—
239C2×#123—44no—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#120C2314yes—
266C2×#120C2314yes—
267C2×#120C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×#117C2312yes—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2314yes—
282#401C2314yes—
283#401C2314yes—
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#399C2314yes—
298#399C2314yes—
299#399C2312yes—
300#399C2314yes—
301#399C2314yes—
302#399C2312yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
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#398C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2312yes—
324#397C2314yes—
325#397C2312yes—
326#397C2314yes—
327#397C2314yes—
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#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
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#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2312yes—
387#393C2314yes—
388#393C2312yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2312yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2312yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#391C2312yes—
407#391C2314yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2312yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
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#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#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#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2312yes—
539#385C2314yes—
540#385C2312yes—
541#385C2312yes—
542#385C2312yes—
543#385C2312yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2312yes—
549#385C2314yes—
550#385C2314yes—
551#384C2312yes—
552#384C2312yes—
553#384C2314yes—
554#383C2314yes—
555#383C2314yes—
556#383C2314yes—
557#383C2314yes—
558#382C2312yes—
559#382C2312yes—
560#382C2312yes—
561#382C2312yes—
562#382C2312yes—
563#382C2312yes—
564#382C2314yes—
565#382C2314yes—
566#381C2312yes—
567#381C2314yes—
568#381C2314yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#381C2314yes—
573#380C2314yes—
574#380C2314yes—
575#380C2312yes—
576#380C2311yescharacteristic
577#380C2311yescharacteristic
578#380C2314yes—
579#380C2312yes—
580#380C2312yes—
581#380C2312yes—
582#380C2312yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#379C2314yes—
587#379C2312yes—
588#379C2314yes—
589#379C2312yes—
590#379C2314yes—
591#379C2312yes—
592#379C2312yes—
593#379C2312yes—
594#379C2312yes—
595#379C2312yes—
596#379C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613#376C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C43C2312yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C25C2412yes—
622C22×Q8C2412yes—
623C22×Q8C2414yes—
624C22×Q8C2412yes—
625C22×Q8C2414yes—
626C22×Q8C2411yescharacteristic
627C22×Q8C2411yescharacteristic
628C22×Q8C2412yes—
629C22×D4—42no—
630C22×D4—44no—
631C22×D4—44no—
632C22×D4—84no—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C23×C4—42no—
641C23×C4—44no—
642C23×C4C2411yescharacteristic
643C23×C4C2411yescharacteristic
644C23×C4C2411yescharacteristic
645C23×C4C2411yescharacteristic
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2412yes—
651C23×C4C2414yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2411yescharacteristic
656C4⋊Q8—44no—
657C4⋊Q8—44no—
658C4⋊Q8—44no—
659C4⋊Q8—84no—
660#126—48no—
661#126—84no—
662#125—44no—
663#125—44no—
664#124—44no—
665#124—48no—
666#124—48no—
667#124—48no—
668#124—84no—
669#123—48no—
670#123—48no—
671#123—48no—
672#123—48no—
673#123—48no—
674#123—84no—
675#123—84no—
676C22⋊Q8—28no—
677C22⋊Q8—44no—
678C22⋊Q8—44no—
679C22⋊Q8—44no—
680C22⋊Q8—42no—
681C22⋊Q8—44no—
682C22⋊Q8—42no—
683C22⋊Q8—48no—
684C22⋊Q8—48no—
685C22⋊Q8—48no—
686C22⋊Q8—84no—
687C22⋊Q8—84no—
688C22⋊Q8—84no—
689C22⋊Q8—84no—
690#121—28no—
691#121—44no—
692#121—44no—
693#121—44no—
694#120—48no—
695#120—48no—
696#120—84no—
697C4×Q8—44no—
698C4×Q8—84no—
699C4×D4—44no—
700C4×D4—84no—
701C4×D4—84no—
702#117—28no—
703C2×C4⋊C4—24no—
704C2×C4⋊C4—42no—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C22⋊C4—24no—
750C2×C22⋊C4—24no—
751C2×C22⋊C4—44no—
752C2×C22⋊C4—44no—
753C2×C22⋊C4—42no—
754C2×C22⋊C4—84no—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2412yes—
832#95C2414yes—
833#95C2412yes—
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#95C2414yes—
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#95C2412yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875C24—22no—
876C24—24no—
877C24—22no—
878C24—42no—
879C24—42no—
880C24—41no—
881C24—41no—
882C24—44no—
883C24—42no—
884C24—42no—
885C24—44no—
886C24—42no—
887C24—41no—
888C24—41no—
889C24—42no—
890C24C2512yes—
891C24C2514yes—
892C24C2511yescharacteristic
893C24C2512yes—
894C2×Q8—24no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—44no—
900C2×Q8—42no—
901C2×Q8—44no—
902C2×Q8—41no—
903C2×Q8—42no—
904C2×Q8—41no—
905C2×Q8—42no—
906C2×Q8—42no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—44no—
910C2×Q8—44no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—24no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—88no—
933C2×D4—816no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—44no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—88no—
971C22×C4H(5,𝔽2)14yes—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2512yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—44no—
1014C4⋊C4—42no—
1015C4⋊C4—44no—
1016C4⋊C4—41no—
1017C4⋊C4—42no—
1018C4⋊C4—41no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C22⋊C4—28no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
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—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C42—24no—
1088C42—24no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42—44no—
1100C42—44no—
1101C23—28no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—22no—
1121C23—22no—
1122C23—24no—
1123C23—24no—
1124C23—44no—
1125C23—84no—
1126C23—82no—
1127C23—84no—
1128C23—82no—
1129C23—82no—
1130C23—82no—
1131C23—84no—
1132C23—88no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23—162no—
1137C23—164no—
1138C23C2×H(5,𝔽2)12yes—
1139C23#58514yes—
1140C23C2611yescharacteristic
1141Q8—84no—
1142Q8—88no—
1143Q8—161no—
1144Q8—161no—
1145Q8—162no—
1146Q8—164no—
1147Q8—162no—
1148D4—84no—
1149D4—88no—
1150D4—88no—
1151D4—88no—
1152D4—88no—
1153D4—88no—
1154D4—162no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—44no—
1204C2×C4—82no—
1205C2×C4—82no—
1206C2×C4—84no—
1207C2×C4—84no—
1208C2×C4—82no—
1209C2×C4—82no—
1210C2×C4—84no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4—164no—
1214C2×C4—162no—
1215C2×C4—164no—
1216C2×C4—162no—
1217C2×C4C2×H(5,𝔽2)14yes—
1218C22—22no—
1219C22—24no—
1220C22—24no—
1221C22—22no—
1222C22—24no—
1223C22—22no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—88no—
1243C22—164no—
1244C22—168no—
1245C22C22×H(5,𝔽2)11yescharacteristic
1246C22C2×#58512yes—
1247C22H(7,𝔽2)12yes—
1248C222−1+611yescharacteristic
1249C222−1+611yescharacteristic
1250C4—24no—
1251C4—42no—
1252C4—41no—
1253C4—41no—
1254C4—42no—
1255C4—42no—
1256C4—42no—
1257C4—44no—
1258C4—44no—
1259C4—44no—
1260C4—44no—
1261C4—44no—
1262C4—44no—
1263C4—44no—
1264C4—44no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—42no—
1269C2—44no—
1270C2—42no—
1271C2—84no—
1272C2—82no—
1273C2#6282411yescharacteristic
1274C2#6286912yes—
1275C2#6287111yescharacteristic
1276C2#6287212yes—
1277C2#6287611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36721C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58571C2semidirect
2. #58415C2semidirect
3. #58257C2semidirect
4. #58048C2semidirect
5. #57963C2semidirect
6. #55929C2semidirect
7. #54354C2semidirect
8. #46931C2semidirect
9. #46857C2semidirect
10. #46816C2semidirect
11. #46814C2semidirect
12. #46599C2semidirect
13. #46570C2semidirect
14. #37423C2semidirect
15. #37158C2semidirect
16. #37050C2semidirect
17. #37020C2semidirect
18. #36730C2semidirect
19. #36730C2semidirect
21. #36711C2semidirect
22. #35474C2semidirect
23. #35455C2semidirect
24. C2×#544C22semidirect
25. C2×#543C22semidirect
29. #2866C22semidirect
30. #2862C22semidirect
31. #2861C22semidirect
32. #2848C22semidirect
33. #2848C22semidirect
35. #2843C22semidirect
36. #2840C22semidirect
37. #2836C22semidirect
38. #2834C22semidirect
39. #2832C22semidirect
40. #2830C22semidirect
43. #2814C22semidirect
44. #2808C22semidirect
45. #2798C22semidirect
46. #2793C22semidirect
47. #2790C22semidirect
48. #2788C22semidirect
49. #2781C22semidirect
50. #2775C22semidirect
51. #2775C22semidirect
52. #2766C22semidirect
53. #2763C22semidirect
54. #2762C22semidirect
55. #2759C22semidirect
56. #2759C22semidirect
59. #2755C22semidirect
60. #2754C22semidirect
61. #2754C22semidirect
62. #2751C22semidirect
63. #2746C22semidirect
64. #2746C22semidirect
65. #2746C22semidirect
66. #2745C22semidirect
67. #2745C22semidirect
68. #2738C22semidirect
69. #2738C22semidirect
70. #2737C22semidirect
71. #2737C22semidirect
73. #2736C22semidirect
75. #2735C22semidirect
76. #2735C22semidirect
77. #2731C22semidirect
78. #2730C22semidirect
79. #2729C22semidirect
80. #2728C22semidirect
81. #2723C22semidirect
82. #2718C22semidirect
83. #2716C22semidirect
84. #2716C22semidirect
88. #2702C22semidirect
90. #2701C22semidirect
91. #2700C22semidirect
92. #2700C22semidirect
93. #2700C22semidirect
95. #2694C22semidirect
96. #2694C22semidirect
97. #2692C22semidirect
98. #2692C22semidirect
99. #2690C22semidirect
100. #2690C22semidirect
101. #2687C22semidirect
102. #2687C22semidirect
103. #2687C22semidirect
105. #2686C22semidirect
106. #2685C22semidirect
107. #2684C22semidirect
108. #2684C22semidirect
109. #2684C22semidirect
110. #2680C22semidirect
111. #2680C22semidirect
114. #2677C22semidirect
115. #2677C22semidirect
116. #2674C22semidirect
117. #2674C22semidirect
118. #2674C22semidirect
119. #2674C22semidirect
120. #2665C22semidirect
121. #2660C22semidirect
122. #2659C22semidirect
123. #2659C22semidirect
124. #2653C22semidirect
125. #2650C22semidirect
126. #2640C22semidirect
127. #2639C22semidirect
128. #2639C22semidirect
129. #2637C22semidirect
130. #2632C22semidirect
134. #2607C22semidirect
135. #2595C22semidirect
136. #2594C22semidirect
137. #2583C22semidirect
138. #2578C22semidirect
139. #2575C22semidirect
140. #2572C22semidirect
141. #2568C22semidirect
142. #2566C22semidirect
143. #2565C22semidirect
144. #2563C22semidirect
147. #2560C22semidirect
148. #2560C22semidirect
150. #2557C22semidirect
151. #2553C22semidirect
152. #2553C22semidirect
153. #2542C22semidirect
155. #2534C22semidirect
156. #2532C22semidirect
157. #2531C22semidirect
158. #2524C22semidirect
159. #2523C22semidirect
160. #2523C22semidirect
161. #2518C22semidirect
162. #2517C22semidirect
163. #2516C22semidirect
164. #2510C22semidirect
165. #2510C22semidirect
167. #2503C22semidirect
168. #2503C22semidirect
170. #2499C22semidirect
171. #2497C22semidirect
172. #2488C22semidirect
173. #2488C22semidirect
174. #2488C22semidirect
175. #2488C22semidirect
177. #2482C22semidirect
178. #2480C22semidirect
179. #2472C22semidirect
180. #2472C22semidirect
181. #2472C22semidirect
182. #2467C22semidirect
183. #2465C22semidirect
184. #2463C22semidirect
187. #2458C22semidirect
188. #2458C22semidirect
189. #2451C22semidirect
190. #2450C22semidirect
191. #2450C22semidirect
192. #2437C22semidirect
195. #2423C22semidirect
196. #2423C22semidirect
197. #2418C22semidirect
198. #2418C22semidirect
199. #2418C22semidirect
203. #2337C22semidirect
204. #2335C22semidirect
206. #2332C22semidirect
207. #2329C22semidirect
208. #2329C22semidirect
209. #2325C22semidirect
210. #2325C22semidirect
211. #2321C22semidirect
212. #2313C22semidirect
215. C4×#124C22semidirect
216. #2298C22semidirect
217. C2×#381C22semidirect
218. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#585712
#584152
#582572
#580482
#579632
#559292
#543542
#469312
#468572
#468162
#468142
#465992
#465702
#374232
#371582
#370502
#370202
#367302
#367212
#367112
#354742
#354552