Finite Group Databasebeta

← #7722428

Subgroups — #7722428

Order 512.

5524 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51473C212yesmaximal, complemented
2#51427C212yesmaximal, complemented
3#51338C212yesmaximal, complemented
4#51337C212yesmaximal, complemented
5#47036C212yesmaximal, complemented
6#47032C212yesmaximal, complemented
7#46456C212yesmaximal, complemented
8#46455C212yesmaximal, complemented
9#44786C214yesmaximal, complemented
10#44759C214yesmaximal, complemented
11#39804C214yesmaximal, complemented
12#39559C214yesmaximal, complemented
13#39461C214yesmaximal, complemented
14#38233C214yesmaximal, complemented
15#38053C214yesmaximal, complemented
16#37446C211yesmaximal, characteristic
17#36809C214yesmaximal, complemented
18#36222C214yesmaximal, complemented
19#35387C214yesmaximal, complemented
20#35242C211yesmaximal, characteristic, complemented
21#35065C211yesmaximal, characteristic, complemented
22C2×#2436C211yesmaximal, characteristic, complemented
23#34358C211yesmaximal, characteristic, complemented
24#34228C211yesmaximal, characteristic, complemented
25C2×#2310C211yesmaximal, characteristic, complemented
26C24×Q8C2211yescharacteristic
27C2×#551C2214yes—
28C2×#536C2212yes—
29C22×#124C2212yes—
30C2×#525C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×#117C2212yes—
33#2855C2214yes—
34#2852C2214yescomplemented
35#2850C2214yescomplemented
36#2849C2212yes—
37#2849C2212yes—
38#2816C2212yes—
39#2815C2212yes—
40#2799C2214yescomplemented
41#2798C2214yescomplemented
42#2798C2214yescomplemented
43#2798C2214yescomplemented
44#2798C2214yescomplemented
45#2789C2214yescomplemented
46#2764C2214yescomplemented
47#2763C2214yescomplemented
48#2761C2214yescomplemented
49#2760C2214yescomplemented
50#2759C2214yescomplemented
51#2759C2214yescomplemented
52#2759C2214yescomplemented
53#2758C2214yescomplemented
54#2755C2214yescomplemented
55#2754C2214yescomplemented
56#2754C2214yescomplemented
57#2754C2214yescomplemented
58#2752C2214yescomplemented
59#2751C2214yescomplemented
60#2750C2214yescomplemented
61#2749C2214yescomplemented
62#2749C2214yescomplemented
63#2743C2214yescomplemented
64#2716C2214yescomplemented
65#2716C2214yescomplemented
66#2715C2214yescomplemented
67#2715C2214yescomplemented
68#2712C2214yescomplemented
69#2712C2214yescomplemented
70#2712C2214yescomplemented
71#2710C2214yescomplemented
72#2710C2214yescomplemented
73#2710C2214yescomplemented
74#2702C2214yescomplemented
75#2700C2214yescomplemented
76#2700C2214yescomplemented
77#2700C2214yescomplemented
78#2692C2214yescomplemented
79#2687C2214yescomplemented
80#2667C2212yescomplemented
81#2665C2212yescomplemented
82#2656C2212yes—
83#2643C2214yescomplemented
84#2639C2212yes—
85#2639C2214yescomplemented
86#2635C2212yes—
87#2635C2212yes—
88#2623C2212yes—
89#2614C2214yes—
90#2613C2212yes—
91#2610C2214yescomplemented
92#2609C2214yescomplemented
93#2608C2212yescomplemented
94#2607C2214yescomplemented
95#2607C2212yescomplemented
96#2607C2214yescomplemented
97#2605C2214yescomplemented
98#2601C2214yescomplemented
99#2598C2214yescomplemented
100#2589C2214yescomplemented
101#2589C2214yescomplemented
102#2589C2214yescomplemented
103#2588C2214yescomplemented
104#2588C2214yescomplemented
105#2569C2212yescomplemented
106#2561C2214yes—
107#2560C2214yescomplemented
108#2557C2214yescomplemented
109#2557C2214yescomplemented
110#2557C2214yescomplemented
111#2549C2212yescomplemented
112#2543C2214yes—
113#2534C2214yes—
114#2532C2214yescomplemented
115#2532C2214yescomplemented
116#2527C2214yescomplemented
117#2527C2214yescomplemented
118#2527C2214yescomplemented
119#2523C2214yescomplemented
120#2523C2214yescomplemented
121#2521C2214yescomplemented
122#2521C2214yescomplemented
123#2520C2214yescomplemented
124#2510C2214yescomplemented
125#2498C2214yes—
126#2493C2214yes—
127#2493C2214yes—
128#2492C2214yescomplemented
129#2488C2214yes—
130#2488C2214yescomplemented
131#2483C2214yes—
132#2482C2214yes—
133#2482C2212yes—
134#2481C2214yescomplemented
135#2479C2214yescomplemented
136#2477C2214yescomplemented
137#2477C2214yescomplemented
138#2474C2214yescomplemented
139#2474C2214yescomplemented
140#2471C2214yescomplemented
141#2471C2214yescomplemented
142#2459C2214yescomplemented
143#2459C2214yescomplemented
144#2459C2214yescomplemented
145#2450C2214yescomplemented
146#2450C2214yescomplemented
147#2449C2214yescomplemented
148#2444C2214yescomplemented
149#2444C2214yescomplemented
150#2443C2214yescomplemented
151#2443C2214yescomplemented
152#2439C2214yescomplemented
153#2438C2214yes—
154#2438C2214yes—
155#2437C2214yes—
156#2436C2212yes—
157#2436C2212yes—
158#2436C2214yes—
159#2436C2212yes—
160#2436C2212yes—
161#2436C2212yes—
162#2436C2212yes—
163#2436C2211yescharacteristic, complemented
164#2436C2212yescomplemented
165#2436C2211yescharacteristic, complemented
166#2434C2212yescomplemented
167#2434C2211yescharacteristic, complemented
168#2434C2211yescharacteristic, complemented
169#2419C2214yes—
170#2412C2214yes—
171#2411C2214yes—
172#2410C2214yes—
173#2409C2212yescomplemented
174#2409C2214yescomplemented
175#2409C2212yescomplemented
176#2404C2212yes—
177C2×#393C2214yes—
178#2377C2212yes—
179#2377C2212yes—
180#2368C2212yescomplemented
181#2364C2214yes—
182#2364C2212yescomplemented
183#2359C2214yes—
184#2358C2214yes—
185#2357C2212yescomplemented
186#2353C2212yescomplemented
187#2343C2214yes—
188#2343C2212yes—
189#2342C2214yes—
190#2342C2214yes—
191#2339C2212yes—
192D4×C22⋊C4C2214yes—
193#2333C2212yes—
194#2333C2212yes—
195#2333C2212yescomplemented
196#2332C2212yescomplemented
197#2329C2214yescomplemented
198#2325C2214yes—
199#2325C2214yescomplemented
200#2318C2214yescomplemented
201#2318C2212yescomplemented
202#2313C2212yes—
203#2310C2214yes—
204#2310C2212yes—
205#2310C2214yes—
206#2310C2211yescharacteristic, complemented
207#2310C2212yescomplemented
208#2310C2211yescharacteristic, complemented
209#2310C2211yescharacteristic, complemented
210#2310C2212yescomplemented
211#2310C2211yescharacteristic, complemented
212#2308C2212yes—
213C4×#123C2214yes—
214C4×#121C2214yescomplemented
215C2×#391C2212yes—
216C2×#391C2214yescomplemented
217C2×#391C2214yescomplemented
218#2290C2214yescomplemented
219C2×#386C2212yes—
220C2×#386C2212yes—
221#2280C2211yescharacteristic
222C2×#381C2211yescharacteristic
223C2×#381C2211yescharacteristic
224C2×#381C2212yes—
225#2275C2212yescomplemented
226C2×C4×C22⋊C4C2211yescharacteristic
227C22×#41C2311yescharacteristic
228C23×Q8—28no—
229C23×Q8—48no—
230C23×Q8C2312yes—
231C23×Q8C2312yes—
232C23×Q8C2311yescharacteristic
233C23×Q8C2311yescharacteristic
234C23×Q8C2311yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×Q8C2312yes—
237C23×Q8C2312yes—
238C23×D4C2311yescharacteristic
239C23×D4C2312yes—
240C24×C4C2311yescharacteristic
241C24×C4C2311yescharacteristic
242C24×C4C2311yescharacteristic
243#551—416no—
244#536—48no—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#124—48no—
250C2×#124C2314yes—
251C2×#124C2312yes—
252C2×#124C2314yes—
253C2×#124C2312yes—
254C2×#124C2314yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259#525—28no—
260C2×#123C2314yes—
261C2×#123C2312yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2311yescharacteristic
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×#121—28no—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2311yescharacteristic
276C2×#121C2312yes—
277C2×#121C2311yescharacteristic
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#120C2312yes—
282C2×#120C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×#117—48no—
291C2×#117C2311yescharacteristic
292C2×#117C2314yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2312yes—
299C2×#117C2314yes—
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2314yes—
302C22×C22⋊C4C2312yes—
303C22×C22⋊C4C2314yes—
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2314yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2312yes—
309C22×C42C2314yes—
310C22×C42C2312yes—
311#401C2314yes—
312#401C2314yes—
313#400C2314yes—
314#400C2312yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#399C2314yes—
328#399C2312yes—
329#399C2314yes—
330#399C2314yes—
331#399C2312yes—
332#399C2314yes—
333#399C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2312yes—
376#394C2312yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#392C2314yes—
398#392C2314yes—
399#392C2312yes—
400#392C2312yes—
401#392C2314yes—
402#392C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
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#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#386C2314yes—
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#386C2312yes—
530#386C2312yes—
531#386C2312yes—
532#386C2312yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2312yes—
558#385C2312yes—
559#385C2312yes—
560#385C2312yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#383C2312yes—
568#383C2314yes—
569#383C2314yes—
570#383C2314yes—
571#382C2312yes—
572#382C2314yes—
573#382C2314yes—
574#381C2312yes—
575#381C2314yes—
576#381C2314yes—
577#381C2312yes—
578#381C2312yes—
579#381C2312yes—
580#381C2312yes—
581#381C2312yes—
582#381C2314yes—
583#381C2314yes—
584#381C2312yes—
585#381C2311yescharacteristic
586#381C2311yescharacteristic
587#381C2311yescharacteristic
588#381C2311yescharacteristic
589#381C2312yes—
590#381C2312yes—
591#381C2312yes—
592#381C2312yes—
593#381C2312yes—
594#381C2314yes—
595#381C2314yes—
596#381C2314yes—
597#380C2314yes—
598#380C2312yes—
599#380C2314yes—
600#380C2312yes—
601#380C2314yes—
602#380C2314yes—
603#380C2312yes—
604#380C2314yes—
605#379C2314yes—
606#379C2314yes—
607#379C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2311yescharacteristic
617C4×C22⋊C4C2311yescharacteristic
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2312yes—
622C4×C22⋊C4C2311yescharacteristic
623C4×C22⋊C4C2311yescharacteristic
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2312yes—
632#376C2314yes—
633#376C2312yes—
634C2×#95C2312yes—
635C2×#95C2312yes—
636C2×#95C2314yes—
637C2×#95C2312yes—
638C2×#95C2312yes—
639C2×#95C2312yes—
640C2×#95C2314yes—
641C2×#95C2312yes—
642C2×#95C2314yes—
643C2×#95C2314yes—
644C25C2411yescharacteristic
645C25C2412yes—
646C2×#41—24no—
647C2×#41—44no—
648C22×Q8—28no—
649C22×Q8—28no—
650C22×Q8—24no—
651C22×Q8—24no—
652C22×Q8—28no—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—28no—
656C22×Q8—28no—
657C22×Q8—28no—
658C22×Q8—44no—
659C22×Q8—44no—
660C22×Q8—44no—
661C22×Q8—44no—
662C22×Q8—44no—
663C22×Q8—44no—
664C22×Q8—44no—
665C22×Q8—44no—
666C22×Q8—44no—
667C22×Q8—44no—
668C22×Q8—464no—
669C22×Q8C2412yes—
670C22×Q8C2412yes—
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2411yescharacteristic
678C22×Q8C2414yes—
679C22×D4—28no—
680C22×D4—24no—
681C22×D4—44no—
682C22×D4—44no—
683C22×D4—44no—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2414yes—
687C22×D4C2412yes—
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2411yescharacteristic
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C23×C4—24no—
695C23×C4—28no—
696C23×C4—24no—
697C23×C4—44no—
698C23×C4—44no—
699C23×C4#4118yes—
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2412yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2412yes—
713C23×C4C2411yescharacteristic
714C23×C4C2411yescharacteristic
715C23×C4C2414yes—
716C23×C4C2414yes—
717C23×C4C2414yes—
718C23×C4C2411yescharacteristic
719C23×C4C2411yescharacteristic
720C23×C4C2411yescharacteristic
721C23×C4C2411yescharacteristic
722C4⋊Q8—44no—
723C4⋊Q8—44no—
724#126—48no—
725#126—48no—
726#124—48no—
727#124—44no—
728#124—48no—
729#124—44no—
730#124—48no—
731#124—44no—
732#124—44no—
733#124—44no—
734#124—44no—
735#123—28no—
736#123—216no—
737#123—48no—
738#123—48no—
739#123—48no—
740C22⋊Q8—24no—
741C22⋊Q8—24no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—48no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747#121—28no—
748#121—28no—
749#121—28no—
750#121—28no—
751#121—24no—
752#121—24no—
753#121—48no—
754#121—48no—
755#120—28no—
756#120—48no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—48no—
760C4×D4—48no—
761C4×D4—48no—
762C4×D4—48no—
763C4×D4—48no—
764#117—24no—
765#117—216no—
766#117—44no—
767#117—44no—
768#117—48no—
769#117—48no—
770#117—44no—
771#117—44no—
772#117—44no—
773C2×C4⋊C4—24no—
774C2×C4⋊C4—48no—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C22⋊C4—28no—
807C2×C22⋊C4—216no—
808C2×C22⋊C4—44no—
809C2×C22⋊C4—44no—
810C2×C22⋊C4—44no—
811C2×C22⋊C4—48no—
812C2×C22⋊C4—48no—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C42—48no—
863C2×C42—44no—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879#95C2412yes—
880#95C2412yes—
881#95C2414yes—
882#95C2412yes—
883#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2412yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941C24—24no—
942C24—24no—
943C24—24no—
944C24—28no—
945C24—42no—
946C24—42no—
947C24—42no—
948C24—44no—
949C24C2×#4114yes—
950C24C2514yes—
951C24C2512yes—
952C24C2511yescharacteristic
953C24C2511yescharacteristic
954C24C2511yescharacteristic
955#41—88no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—22no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—42no—
976C2×Q8—42no—
977C2×Q8—42no—
978C2×Q8—42no—
979C2×Q8—42no—
980C2×Q8—42no—
981C2×Q8—42no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—432no—
986C2×Q8—432no—
987C2×Q8—432no—
988C2×Q8—432no—
989C2×Q8—416no—
990C2×Q8—416no—
991C2×Q8—416no—
992C2×Q8—416no—
993C2×D4—24no—
994C2×D4—24no—
995C2×D4—28no—
996C2×D4—28no—
997C2×D4—28no—
998C2×D4—28no—
999C2×D4—28no—
1000C2×D4—24no—
1001C2×D4—28no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—22no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—42no—
1008C2×D4—44no—
1009C2×D4—42no—
1010C2×D4—42no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—88no—
1020C2×D4—816no—
1021C22×C4—232no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—28no—
1041C22×C4—28no—
1042C22×C4—28no—
1043C22×C4—24no—
1044C22×C4—416no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—416no—
1072C22×C4C2×#4114yes—
1073C22×C4C2×#4114yes—
1074C22×C4C2×#4114yes—
1075C22×C4C2×#4114yes—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4114yes—
1078C22×C4H(5,𝔽2)18yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—42no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C42—24no—
1180C42—28no—
1181C42—28no—
1182C42—44no—
1183C42—44no—
1184C42—42no—
1185C42—44no—
1186C42—42no—
1187C42—44no—
1188C42—44no—
1189C42—42no—
1190C42—42no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—28no—
1202C23—28no—
1203C23—22no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—22no—
1213C23—24no—
1214C23—22no—
1215C23—44no—
1216C23—416no—
1217C23—48no—
1218C23—84no—
1219C23—84no—
1220C23—88no—
1221C23—88no—
1222C23C22×#4112yes—
1223C23C22×#4112yes—
1224C23C22×#4112yes—
1225C23C2×H(5,𝔽2)14yes—
1226C23#58514yes—
1227C23C2611yescharacteristic
1228Q8—48no—
1229Q8—48no—
1230Q8—48no—
1231Q8—48no—
1232Q8—48no—
1233Q8—48no—
1234Q8—48no—
1235Q8—48no—
1236Q8—82no—
1237Q8—164no—
1238D4—48no—
1239D4—48no—
1240D4—416no—
1241D4—84no—
1242D4—84no—
1243D4—82no—
1244D4—84no—
1245D4—88no—
1246D4—88no—
1247D4—164no—
1248C2×C4—216no—
1249C2×C4—28no—
1250C2×C4—28no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—216no—
1260C2×C4—28no—
1261C2×C4—28no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—44no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—44no—
1306C2×C4—48no—
1307C2×C4—44no—
1308C2×C4—44no—
1309C2×C4—48no—
1310C2×C4—84no—
1311C2×C4—88no—
1312C2×C4—88no—
1313C2×C4—88no—
1314C2×C4—84no—
1315C2×C4—88no—
1316C2×C4—164no—
1317C2×C4—164no—
1318C2×C4C22×#4112yes—
1319C2×C4C22×#4112yes—
1320C2×C4C22×#4112yes—
1321C2×C4C22×#4112yes—
1322C2×C4C2×H(5,𝔽2)14yes—
1323C2×C4C2×H(5,𝔽2)14yes—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—28no—
1329C22—28no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—416no—
1334C22—44no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—168no—
1348C22#349014yes—
1349C22#351014yes—
1350C22C23×#4111yescharacteristic
1351C22C22×H(5,𝔽2)12yes—
1352C22C2×#58512yes—
1353C222−1+612yes—
1354C4—24no—
1355C4—24no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4—42no—
1366C4—44no—
1367C4—44no—
1368C4—44no—
1369C4—44no—
1370C4—44no—
1371C4—44no—
1372C4—44no—
1373C4—44no—
1374C2—24no—
1375C2—24no—
1376C2—42no—
1377C2—82no—
1378C2—84no—
1379C2C2×#349011yescharacteristic
1380C2C2×#351011yescharacteristic
1381C2#6286011yescharacteristic
1382C2#6295414yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37446C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51473C2semidirect
2. #51427C2semidirect
3. #51338C2semidirect
4. #51337C2semidirect
5. #47036C2semidirect
6. #47032C2semidirect
7. #46456C2semidirect
8. #46455C2semidirect
9. #44786C2semidirect
10. #44759C2semidirect
11. #39804C2semidirect
12. #39559C2semidirect
13. #39461C2semidirect
14. #38233C2semidirect
15. #38053C2semidirect
17. #36809C2semidirect
18. #36222C2semidirect
19. #35387C2semidirect
20. #35242C2semidirect
21. #35065C2semidirect
22. C2×#2436C2semidirect
23. #34358C2semidirect
24. #34228C2semidirect
25. C2×#2310C2semidirect
34. #2852C22semidirect
35. #2850C22semidirect
40. #2799C22semidirect
41. #2798C22semidirect
42. #2798C22semidirect
43. #2798C22semidirect
44. #2798C22semidirect
45. #2789C22semidirect
46. #2764C22semidirect
47. #2763C22semidirect
48. #2761C22semidirect
49. #2760C22semidirect
50. #2759C22semidirect
51. #2759C22semidirect
52. #2759C22semidirect
53. #2758C22semidirect
54. #2755C22semidirect
55. #2754C22semidirect
56. #2754C22semidirect
57. #2754C22semidirect
58. #2752C22semidirect
59. #2751C22semidirect
60. #2750C22semidirect
61. #2749C22semidirect
62. #2749C22semidirect
63. #2743C22semidirect
64. #2716C22semidirect
65. #2716C22semidirect
66. #2715C22semidirect
67. #2715C22semidirect
68. #2712C22semidirect
69. #2712C22semidirect
70. #2712C22semidirect
71. #2710C22semidirect
72. #2710C22semidirect
73. #2710C22semidirect
74. #2702C22semidirect
75. #2700C22semidirect
76. #2700C22semidirect
77. #2700C22semidirect
78. #2692C22semidirect
79. #2687C22semidirect
80. #2667C22semidirect
81. #2665C22semidirect
83. #2643C22semidirect
85. #2639C22semidirect
91. #2610C22semidirect
92. #2609C22semidirect
93. #2608C22semidirect
94. #2607C22semidirect
95. #2607C22semidirect
96. #2607C22semidirect
97. #2605C22semidirect
98. #2601C22semidirect
99. #2598C22semidirect
100. #2589C22semidirect
101. #2589C22semidirect
102. #2589C22semidirect
103. #2588C22semidirect
104. #2588C22semidirect
105. #2569C22semidirect
107. #2560C22semidirect
108. #2557C22semidirect
109. #2557C22semidirect
110. #2557C22semidirect
111. #2549C22semidirect
114. #2532C22semidirect
115. #2532C22semidirect
116. #2527C22semidirect
117. #2527C22semidirect
118. #2527C22semidirect
119. #2523C22semidirect
120. #2523C22semidirect
121. #2521C22semidirect
122. #2521C22semidirect
123. #2520C22semidirect
124. #2510C22semidirect
128. #2492C22semidirect
130. #2488C22semidirect
134. #2481C22semidirect
135. #2479C22semidirect
136. #2477C22semidirect
137. #2477C22semidirect
138. #2474C22semidirect
139. #2474C22semidirect
140. #2471C22semidirect
141. #2471C22semidirect
142. #2459C22semidirect
143. #2459C22semidirect
144. #2459C22semidirect
145. #2450C22semidirect
146. #2450C22semidirect
147. #2449C22semidirect
148. #2444C22semidirect
149. #2444C22semidirect
150. #2443C22semidirect
151. #2443C22semidirect
152. #2439C22semidirect
163. #2436C22semidirect
164. #2436C22semidirect
165. #2436C22semidirect
166. #2434C22semidirect
167. #2434C22semidirect
168. #2434C22semidirect
173. #2409C22semidirect
174. #2409C22semidirect
175. #2409C22semidirect
180. #2368C22semidirect
182. #2364C22semidirect
185. #2357C22semidirect
186. #2353C22semidirect
195. #2333C22semidirect
196. #2332C22semidirect
197. #2329C22semidirect
199. #2325C22semidirect
200. #2318C22semidirect
201. #2318C22semidirect
206. #2310C22semidirect
207. #2310C22semidirect
208. #2310C22semidirect
209. #2310C22semidirect
210. #2310C22semidirect
211. #2310C22semidirect
214. C4×#121C22semidirect
216. C2×#391C22semidirect
217. C2×#391C22semidirect
218. #2290C22semidirect
225. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#514732
#514272
#513382
#513372
#470362
#470322
#464562
#464552
#447862
#447592
#398042
#395592
#394612
#382332
#380532
#374462
#368092
#362222
#353872
#352422
#350652
C2×#24362
#343582
#342282
C2×#23102