Finite Group Databasebeta

← #7726944

Subgroups — #7726944

Order 512.

4288 conjugacy classes of subgroups.

The subgroup lattice has 1277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51564C214yesmaximal, complemented
2#51563C214yesmaximal, complemented
3#47825C214yesmaximal, complemented
4#47811C214yesmaximal, complemented
5#44464C212yesmaximal, complemented
6#44081C212yesmaximal, complemented
7#43516C212yesmaximal, complemented
8#43515C212yesmaximal, complemented
9#40266C214yesmaximal, complemented
10#39551C212yesmaximal
11#39541C212yesmaximal, complemented
12#39508C212yesmaximal, complemented
13#39504C212yesmaximal, complemented
14#38667C214yesmaximal, complemented
15#38399C214yesmaximal, complemented
16#37549C211yesmaximal, characteristic, complemented
17#37028C212yesmaximal, complemented
18#37025C212yesmaximal, complemented
19#36343C214yesmaximal, complemented
20#35502C212yesmaximal, complemented
21#35494C212yesmaximal, complemented
22#35304C211yesmaximal, characteristic, complemented
23#35118C211yesmaximal, characteristic
24C2×#2611C211yesmaximal, characteristic, complemented
25#34378C211yesmaximal, characteristic, complemented
26#34220C211yesmaximal, characteristic, complemented
27#34048C211yesmaximal, characteristic, complemented
28C2×#529C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2865C2214yescomplemented
32#2863C2214yescomplemented
33#2857C2212yes—
34#2853C2212yes—
35#2851C2212yes—
36#2849C2212yes—
37#2822C2212yescomplemented
38#2820C2212yescomplemented
39#2810C2214yescomplemented
40#2809C2214yescomplemented
41#2808C2214yes—
42#2808C2214yescomplemented
43#2803C2214yes—
44#2802C2214yescomplemented
45#2801C2214yes—
46#2800C2214yes—
47#2798C2214yes—
48#2798C2214yescomplemented
49#2793C2214yes—
50#2788C2214yes—
51#2787C2214yes—
52#2787C2214yescomplemented
53#2786C2214yes—
54#2784C2214yes—
55#2783C2214yes—
56#2783C2214yescomplemented
57#2783C2214yescomplemented
58#2779C2214yes—
59#2777C2214yes—
60#2776C2214yescomplemented
61#2775C2214yes—
62#2774C2214yescomplemented
63#2773C2214yes—
64#2773C2214yes—
65#2770C2214yes—
66#2768C2214yes—
67#2766C2214yescomplemented
68#2766C2214yescomplemented
69#2759C2214yes—
70#2758C2214yescomplemented
71#2747C2214yescomplemented
72#2745C2214yescomplemented
73#2741C2214yes—
74#2737C2214yes—
75#2719C2214yescomplemented
76#2716C2214yes—
77#2695C2214yes—
78#2694C2214yes—
79#2664C2212yescomplemented
80#2664C2212yescomplemented
81#2660C2212yescomplemented
82#2653C2214yes—
83#2652C2214yes—
84#2647C2212yescomplemented
85#2629C2214yescomplemented
86#2627C2211yescharacteristic
87#2627C2212yes—
88#2626C2211yescharacteristic
89#2618C2211yescharacteristic
90#2618C2212yes—
91#2617C2211yescharacteristic
92#2612C2214yescomplemented
93#2611C2214yes—
94#2611C2212yes—
95#2611C2212yes—
96#2611C2212yes—
97#2611C2212yes—
98#2611C2212yes—
99#2611C2214yes—
100#2610C2212yes—
101#2609C2214yes—
102#2606C2214yescomplemented
103#2606C2212yescomplemented
104#2605C2212yescomplemented
105#2602C2214yes—
106#2601C2214yes—
107#2599C2212yes—
108#2598C2212yes—
109#2596C2214yes—
110#2596C2214yes—
111#2596C2214yescomplemented
112#2595C2214yes—
113#2594C2214yes—
114#2594C2214yes—
115#2594C2214yescomplemented
116#2590C2214yescomplemented
117#2590C2214yescomplemented
118#2589C2214yes—
119#2588C2214yescomplemented
120#2587C2214yes—
121#2585C2214yescomplemented
122#2585C2214yescomplemented
123#2584C2212yescomplemented
124#2578C2214yes—
125#2577C2214yescomplemented
126#2577C2214yescomplemented
127#2574C2214yescomplemented
128#2569C2212yes—
129#2569C2214yescomplemented
130#2562C2212yescomplemented
131#2561C2214yes—
132#2558C2214yes—
133#2549C2212yes—
134#2533C2214yescomplemented
135#2532C2214yes—
136#2532C2214yescomplemented
137#2531C2214yes—
138#2530C2214yescomplemented
139#2529C2214yes—
140#2528C2214yescomplemented
141#2528C2214yescomplemented
142#2528C2214yescomplemented
143#2528C2214yescomplemented
144#2525C2214yes—
145#2525C2214yescomplemented
146#2524C2214yescomplemented
147#2519C2214yes—
148#2518C2214yes—
149#2514C2214yescomplemented
150#2513C2214yes—
151#2510C2214yes—
152#2508C2214yescomplemented
153#2498C2214yes—
154#2497C2214yescomplemented
155#2493C2214yes—
156#2493C2214yes—
157#2488C2214yes—
158#2488C2214yes—
159#2487C2212yes—
160#2486C2214yes—
161#2486C2212yes—
162#2485C2214yescomplemented
163#2484C2214yes—
164#2480C2214yes—
165#2479C2214yes—
166#2475C2214yescomplemented
167#2473C2214yes—
168#2469C2214yes—
169#2462C2214yescomplemented
170#2439C2214yescomplemented
171#2438C2214yes—
172#2418C2214yes—
173#2413C2214yes—
174#2411C2214yes—
175C2×#400C2211yescharacteristic
176C2×#399C2211yescharacteristic
177C2×#398C2211yescharacteristic
178C2×#397C2211yescharacteristic
179#2382C2214yescomplemented
180#2373C2214yescomplemented
181#2370C2214yescomplemented
182#2368C2214yes—
183#2359C2214yes—
184#2359C2214yes—
185#2353C2212yes—
186#2352C2214yes—
187#2349C2212yes—
188#2346C2212yescomplemented
189#2345C2212yes—
190#2344C2212yes—
191#2344C2214yes—
192#2343C2214yes—
193#2343C2212yescomplemented
194#2336C2212yescomplemented
195#2336C2212yescomplemented
196#2335C2214yes—
197#2334C2214yes—
198#2331C2212yescomplemented
199#2330C2214yescomplemented
200#2330C2212yescomplemented
201#2330C2212yescomplemented
202#2326C2212yescomplemented
203#2322C2212yes—
204#2321C2212yes—
205#2320C2211yescharacteristic, complemented
206#2319C2211yescharacteristic, complemented
207#2316C2212yes—
208#2314C2214yes—
209#2314C2214yes—
210#2313C2212yes—
211#2313C2212yes—
212#2313C2212yes—
213#2312C2212yes—
214#2312C2212yes—
215C4×#125C2214yescomplemented
216C4×C22⋊Q8C2212yes—
217C4×#121C2212yes—
218#2298C2212yes—
219#2298C2212yes—
220#2298C2212yes—
221#2298C2212yes—
222#2298C2214yescomplemented
223C2×#389C2212yes—
224C2×#388C2212yes—
225C2×#387C2212yes—
226C2×#385C2212yes—
227#2285C2211yescharacteristic
228#2285C2211yescharacteristic
229#2283C2211yescharacteristic
230#2280C2212yes—
231#2276C2211yescharacteristic, complemented
232#2275C2211yescharacteristic, complemented
233C4×#117C2212yes—
234C2×#376C2211yescharacteristic
235C24×C4C2311yescharacteristic
236C2×C4⋊Q8C2312yes—
237#529—28no—
238C2×#126C2312yes—
239C2×#126C2314yes—
240C2×#125—28no—
241C2×#125C2312yes—
242C2×#125C2312yes—
243C2×#125C2311yescharacteristic
244C2×#125C2312yes—
245C2×#125C2312yes—
246C2×#125C2314yes—
247C2×#125C2312yes—
248C2×#124C2311yescharacteristic
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2314yes—
255C2×#121C2311yescharacteristic
256C2×#120C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2314yes—
263C2×#117—28no—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2314yes—
270C2×#117C2312yes—
271C2×#117C2314yes—
272C2×#117C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2312yes—
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C42C2311yescharacteristic
286C22×C42C2312yes—
287C22×C42C2311yescharacteristic
288#401C2314yes—
289#401C2314yes—
290#401C2314yes—
291#400C2314yes—
292#400C2312yes—
293#400C2312yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2312yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#399C2312yes—
315#399C2312yes—
316#399C2314yes—
317#399C2312yes—
318#399C2314yes—
319#399C2312yes—
320#399C2312yes—
321#398C2314yes—
322#398C2314yes—
323#398C2312yes—
324#398C2314yes—
325#398C2312yes—
326#398C2314yes—
327#398C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2312yes—
347#397C2312yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2312yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2312yes—
357#397C2314yes—
358#397C2312yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2312yes—
374#395C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2312yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2312yes—
386#393C2314yes—
387#392C2312yes—
388#391C2314yes—
389#391C2312yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#390C2312yes—
397#390C2314yes—
398#390C2314yes—
399#390C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2312yes—
419#389C2314yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
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#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#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#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#386C2312yes—
539#386C2314yes—
540#386C2312yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2312yes—
551#385C2314yes—
552#385C2312yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#384C2312yes—
563#384C2312yes—
564#384C2312yes—
565#383C2312yes—
566#383C2314yes—
567#383C2314yes—
568#383C2312yes—
569#383C2314yes—
570#383C2314yes—
571#382C2314yes—
572#382C2312yes—
573#382C2312yes—
574#382C2314yes—
575#382C2312yes—
576#382C2312yes—
577#382C2314yes—
578#382C2314yes—
579#382C2312yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2312yes—
584#381C2312yes—
585#381C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2311yescharacteristic
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2311yescharacteristic
599#380C2314yes—
600#380C2314yes—
601#380C2312yes—
602#379C2312yes—
603#379C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2311yescharacteristic
614C4×C4⋊C4C2311yescharacteristic
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2311yescharacteristic
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2311yescharacteristic
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2312yes—
634C4×C22⋊C4C2312yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2314yes—
640#376C2311yescharacteristic
641#376C2312yes—
642#376C2312yes—
643#376C2312yes—
644#376C2314yes—
645#376C2311yescharacteristic
646#376C2311yescharacteristic
647#376C2312yes—
648#376C2311yescharacteristic
649#376C2312yes—
650#376C2312yes—
651C2×#95C2311yescharacteristic
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2311yescharacteristic
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C43C2312yes—
660C43C2312yes—
661C25C2411yescharacteristic
662C22×Q8C2411yescharacteristic
663C22×Q8C2414yes—
664C22×D4C2412yes—
665C22×D4C2411yescharacteristic
666C22×D4C2414yes—
667C23×C4—24no—
668C23×C4—42no—
669C23×C4—42no—
670C23×C4C2412yes—
671C23×C4C2411yescharacteristic
672C23×C4C2412yes—
673C23×C4C2411yescharacteristic
674C23×C4C2412yes—
675C23×C4C2411yescharacteristic
676C23×C4C2411yescharacteristic
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2414yes—
681C23×C4C2412yes—
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C4⋊Q8—44no—
685#126—28no—
686#126—48no—
687#125—28no—
688#125—28no—
689#125—28no—
690#125—28no—
691#125—24no—
692#125—44no—
693#125—48no—
694#124—24no—
695#123—28no—
696#123—48no—
697#123—48no—
698#123—44no—
699C22⋊Q8—24no—
700C22⋊Q8—48no—
701#121—24no—
702#120—44no—
703C4×Q8—24no—
704C4×Q8—44no—
705C4×D4—28no—
706C4×D4—24no—
707C4×D4—44no—
708C4×D4—48no—
709#117—28no—
710#117—28no—
711#117—28no—
712#117—28no—
713#117—28no—
714#117—44no—
715#117—48no—
716#117—44no—
717#117—48no—
718C2×C4⋊C4—24no—
719C2×C4⋊C4—24no—
720C2×C4⋊C4—24no—
721C2×C4⋊C4—28no—
722C2×C4⋊C4—28no—
723C2×C4⋊C4—24no—
724C2×C4⋊C4—44no—
725C2×C4⋊C4—44no—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C22⋊C4—24no—
782C2×C22⋊C4—24no—
783C2×C22⋊C4—44no—
784C2×C22⋊C4—44no—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C42—24no—
820C2×C42—44no—
821C2×C42#4118yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2411yescharacteristic
846C2×C42C2411yescharacteristic
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2411yescharacteristic
851#95C2412yes—
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2412yes—
855#95C2412yes—
856#95C2412yes—
857#95C2412yes—
858#95C2412yes—
859#95C2414yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2412yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2412yes—
897#95C2414yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920C24—22no—
921C24—22no—
922C24—22no—
923C24—42no—
924C24—42no—
925C24C2512yes—
926C24C2512yes—
927C24C2511yescharacteristic
928C2×Q8—22no—
929C2×Q8—42no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×D4—24no—
934C2×D4—24no—
935C2×D4—24no—
936C2×D4—22no—
937C2×D4—42no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—24no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—22no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—28no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—416no—
976C22×C4C2×#4114yes—
977C22×C4C2×#4114yes—
978C22×C4C2×#4114yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2512yes—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—22no—
1018C4⋊C4—24no—
1019C4⋊C4—22no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
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—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—44no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—24no—
1061C22⋊C4—28no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—28no—
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—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C42—24no—
1093C42—24no—
1094C42—24no—
1095C42—24no—
1096C42—24no—
1097C42—42no—
1098C42—42no—
1099C42—44no—
1100C42—44no—
1101C42—44no—
1102C42—44no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—44no—
1108C42—44no—
1109C42—44no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42C2×#4114yes—
1116C42C2×#4114yes—
1117C42C2×#4114yes—
1118C42C2×#4114yes—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—24no—
1124C23—22no—
1125C23—24no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—24no—
1130C23—24no—
1131C23—48no—
1132C23—44no—
1133C23—82no—
1134C23—82no—
1135C23—84no—
1136C23C22×#4112yes—
1137C23#58512yes—
1138C23#58512yes—
1139C23C2611yescharacteristic
1140Q8—44no—
1141Q8—164no—
1142D4—44no—
1143D4—48no—
1144D4—164no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—28no—
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—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—44no—
1204C2×C4—44no—
1205C2×C4—48no—
1206C2×C4—48no—
1207C2×C4—48no—
1208C2×C4—48no—
1209C2×C4—44no—
1210C2×C4—84no—
1211C2×C4—88no—
1212C2×C4—82no—
1213C2×C4—84no—
1214C2×C4—82no—
1215C2×C4—84no—
1216C2×C4C22×#4112yes—
1217C2×C4C22×#4112yes—
1218C2×C4C22×#4112yes—
1219C2×C4C22×#4112yes—
1220C2×C4C22×#4112yes—
1221C2×C4C22×#4112yes—
1222C2×C4#58514yes—
1223C22—22no—
1224C22—22no—
1225C22—24no—
1226C22—24no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—88no—
1238C22#349314yes—
1239C22C23×#4111yescharacteristic
1240C22C2×#58511yescharacteristic
1241C22C2×#58511yescharacteristic
1242C22C2×#58512yes—
1243C222−1+612yes—
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—24no—
1251C4—44no—
1252C4—42no—
1253C4—42no—
1254C4—42no—
1255C4—44no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—44no—
1260C4—42no—
1261C4—44no—
1262C4—44no—
1263C4—44no—
1264C4—42no—
1265C4—42no—
1266C4—44no—
1267C4—44no—
1268C2—24no—
1269C2—82no—
1270C2—82no—
1271C2C2×#349311yescharacteristic
1272C2#6281511yescharacteristic
1273C2#6286011yescharacteristic
1274C2#6290912yes—
1275C2#6293412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2617C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51564C2semidirect
2. #51563C2semidirect
3. #47825C2semidirect
4. #47811C2semidirect
5. #44464C2semidirect
6. #44081C2semidirect
7. #43516C2semidirect
8. #43515C2semidirect
9. #40266C2semidirect
11. #39541C2semidirect
12. #39508C2semidirect
13. #39504C2semidirect
14. #38667C2semidirect
15. #38399C2semidirect
16. #37549C2semidirect
17. #37028C2semidirect
18. #37025C2semidirect
19. #36343C2semidirect
20. #35502C2semidirect
21. #35494C2semidirect
22. #35304C2semidirect
24. C2×#2611C2semidirect
25. #34378C2semidirect
26. #34220C2semidirect
27. #34048C2semidirect
31. #2865C22semidirect
32. #2863C22semidirect
37. #2822C22semidirect
38. #2820C22semidirect
39. #2810C22semidirect
40. #2809C22semidirect
42. #2808C22semidirect
44. #2802C22semidirect
48. #2798C22semidirect
52. #2787C22semidirect
56. #2783C22semidirect
57. #2783C22semidirect
60. #2776C22semidirect
62. #2774C22semidirect
67. #2766C22semidirect
68. #2766C22semidirect
70. #2758C22semidirect
71. #2747C22semidirect
72. #2745C22semidirect
75. #2719C22semidirect
79. #2664C22semidirect
80. #2664C22semidirect
81. #2660C22semidirect
84. #2647C22semidirect
85. #2629C22semidirect
92. #2612C22semidirect
102. #2606C22semidirect
103. #2606C22semidirect
104. #2605C22semidirect
111. #2596C22semidirect
115. #2594C22semidirect
116. #2590C22semidirect
117. #2590C22semidirect
119. #2588C22semidirect
121. #2585C22semidirect
122. #2585C22semidirect
123. #2584C22semidirect
125. #2577C22semidirect
126. #2577C22semidirect
127. #2574C22semidirect
129. #2569C22semidirect
130. #2562C22semidirect
134. #2533C22semidirect
136. #2532C22semidirect
138. #2530C22semidirect
140. #2528C22semidirect
141. #2528C22semidirect
142. #2528C22semidirect
143. #2528C22semidirect
145. #2525C22semidirect
146. #2524C22semidirect
149. #2514C22semidirect
152. #2508C22semidirect
154. #2497C22semidirect
162. #2485C22semidirect
166. #2475C22semidirect
169. #2462C22semidirect
170. #2439C22semidirect
179. #2382C22semidirect
180. #2373C22semidirect
181. #2370C22semidirect
188. #2346C22semidirect
193. #2343C22semidirect
194. #2336C22semidirect
195. #2336C22semidirect
198. #2331C22semidirect
199. #2330C22semidirect
200. #2330C22semidirect
201. #2330C22semidirect
202. #2326C22semidirect
205. #2320C22semidirect
206. #2319C22semidirect
215. C4×#125C22semidirect
222. #2298C22semidirect
231. #2276C22semidirect
232. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#515642
#515632
#478252
#478112
#444642
#440812
#435162
#435152
#402662
#395512
#395412
#395082
#395042
#386672
#383992
#375492
#370282
#370252
#363432
#355022
#354942
#353042
#351182
C2×#26112
#343782
#342202
#340482