Finite Group Databasebeta

← #7715982

Subgroups — #7715982

Order 512.

4298 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50442C214yesmaximal, complemented
2#50421C214yesmaximal, complemented
3#49260C214yesmaximal, complemented
4#49239C214yesmaximal, complemented
5#44865C214yesmaximal, complemented
6#44850C214yesmaximal, complemented
7#44614C214yesmaximal, complemented
8#44499C214yesmaximal, complemented
9#39679C212yesmaximal, complemented
10#39542C212yesmaximal
11#39542C212yesmaximal
12#39512C212yesmaximal, complemented
13#37959C212yesmaximal, complemented
14#37880C212yesmaximal
15#36970C212yesmaximal
16#36762C212yesmaximal, complemented
17#36571C212yesmaximal, complemented
18#36167C212yesmaximal
19#35315C212yesmaximal, complemented
20#35013C211yesmaximal, characteristic, complemented
21#35013C211yesmaximal, characteristic, complemented
22#35013C211yesmaximal, characteristic, complemented
23#35012C211yesmaximal, characteristic
24#35002C211yesmaximal, characteristic
25#34595C211yesmaximal, characteristic, complemented
26#34433C212yesmaximal
27C2×#2373C211yesmaximal, characteristic
28C2×#543C2212yes—
29C22×#126C2211yescharacteristic
30#2857C2212yes—
31#2857C2212yes—
32#2855C2212yes—
33#2855C2212yes—
34#2855C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2848C2212yes—
40#2810C2214yescomplemented
41#2809C2214yescomplemented
42#2805C2214yescomplemented
43#2805C2214yescomplemented
44#2802C2214yescomplemented
45#2802C2214yescomplemented
46#2794C2214yescomplemented
47#2789C2214yescomplemented
48#2789C2214yescomplemented
49#2787C2214yes—
50#2776C2214yescomplemented
51#2776C2214yescomplemented
52#2776C2214yescomplemented
53#2774C2214yescomplemented
54#2771C2214yes—
55#2771C2214yes—
56#2770C2214yes—
57#2767C2214yescomplemented
58#2766C2214yescomplemented
59#2765C2214yes—
60#2765C2214yes—
61#2762C2214yescomplemented
62#2758C2214yescomplemented
63#2758C2214yescomplemented
64#2747C2214yes—
65#2745C2214yes—
66#2745C2214yes—
67#2739C2214yes—
68#2739C2214yes—
69#2719C2214yescomplemented
70#2713C2214yescomplemented
71#2698C2214yes—
72#2698C2214yes—
73#2698C2214yes—
74#2698C2214yes—
75#2690C2214yes—
76#2689C2214yes—
77#2689C2214yes—
78#2689C2214yes—
79#2689C2214yes—
80#2666C2214yescomplemented
81#2666C2214yescomplemented
82#2659C2211yescharacteristic
83#2659C2211yescharacteristic
84#2659C2212yes—
85#2659C2211yescharacteristic
86#2659C2211yescharacteristic
87#2647C2212yescomplemented
88#2646C2212yes—
89#2645C2212yescomplemented
90#2645C2212yescomplemented
91#2642C2212yescomplemented
92#2627C2212yes—
93#2627C2212yes—
94#2627C2212yes—
95#2627C2212yes—
96#2627C2212yes—
97#2626C2212yes—
98#2605C2214yescomplemented
99#2599C2214yes—
100#2599C2214yes—
101#2590C2214yescomplemented
102#2588C2214yescomplemented
103#2588C2214yescomplemented
104#2586C2214yescomplemented
105#2586C2214yescomplemented
106#2586C2214yescomplemented
107#2585C2214yescomplemented
108#2585C2214yescomplemented
109#2585C2214yescomplemented
110#2585C2214yescomplemented
111#2583C2214yes—
112#2581C2214yescomplemented
113#2581C2214yescomplemented
114#2577C2214yes—
115#2575C2214yes—
116#2575C2214yes—
117#2574C2214yes—
118#2570C2214yescomplemented
119#2565C2212yescomplemented
120#2556C2214yes—
121#2550C2212yescomplemented
122#2549C2214yes—
123#2549C2214yes—
124#2533C2214yescomplemented
125#2533C2214yescomplemented
126#2530C2214yes—
127#2528C2214yescomplemented
128#2528C2214yescomplemented
129#2528C2214yescomplemented
130#2524C2214yescomplemented
131#2522C2214yes—
132#2520C2214yescomplemented
133#2520C2214yescomplemented
134#2520C2214yescomplemented
135#2520C2214yescomplemented
136#2515C2214yes—
137#2515C2214yes—
138#2514C2214yescomplemented
139#2509C2212yescomplemented
140#2508C2214yescomplemented
141#2506C2212yescomplemented
142#2505C2214yes—
143#2505C2214yes—
144#2505C2214yes—
145#2503C2212yes—
146#2503C2214yes—
147#2495C2212yes—
148#2494C2212yes—
149#2493C2214yes—
150#2493C2214yes—
151#2493C2214yes—
152#2493C2214yes—
153#2493C2214yes—
154#2493C2214yes—
155#2489C2212yes—
156#2484C2214yes—
157#2483C2214yes—
158#2483C2214yes—
159#2475C2214yes—
160#2475C2214yes—
161#2473C2214yes—
162#2473C2214yes—
163#2465C2214yes—
164#2462C2214yescomplemented
165#2462C2214yescomplemented
166#2462C2214yescomplemented
167#2462C2214yescomplemented
168#2453C2212yescomplemented
169#2451C2212yescomplemented
170#2446C2214yescomplemented
171#2442C2212yes—
172#2440C2214yes—
173#2440C2214yes—
174#2438C2214yes—
175#2421C2212yes—
176#2402C2214yescomplemented
177#2399C2214yescomplemented
178#2378C2214yes—
179#2378C2214yes—
180#2373C2214yes—
181#2373C2214yes—
182#2373C2214yes—
183#2373C2214yes—
184#2370C2214yescomplemented
185#2370C2212yescomplemented
186#2368C2214yes—
187#2362C2214yes—
188#2362C2214yes—
189#2360C2212yes—
190#2360C2214yes—
191#2351C2212yescomplemented
192#2344C2212yes—
193#2343C2214yes—
194#2342C2214yes—
195#2342C2214yes—
196#2332C2214yes—
197#2332C2214yes—
198#2330C2212yescomplemented
199#2329C2212yes—
200#2329C2212yes—
201#2329C2212yes—
202#2329C2212yes—
203#2327C2212yescomplemented
204#2323C2214yes—
205#2323C2214yes—
206#2320C2212yescomplemented
207#2320C2212yescomplemented
208#2315C2212yes—
209#2313C2212yes—
210#2313C2212yes—
211#2313C2212yes—
212#2312C2212yes—
213C4×C22⋊Q8C2212yes—
214C4×C22⋊Q8C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C4×C22⋊Q8C2212yes—
218C4×C22⋊Q8C2212yes—
219C2×#389C2211yescharacteristic
220C2×#388C2211yescharacteristic
221C2×#388C2211yescharacteristic
222C2×#388C2211yescharacteristic
223C2×#387C2211yescharacteristic
224C2×#387C2211yescharacteristic
225C2×#387C2211yescharacteristic
226C2×#385C2211yescharacteristic
227#2283C2212yes—
228C2×#380C2212yes—
229C2×C4×C4⋊C4C2211yescharacteristic
230C2×C4×C4⋊C4C2211yescharacteristic
231C2×C4×C4⋊C4C2211yescharacteristic
232C2×C4×C22⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C24×C4C2311yescharacteristic
236#543—216no—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×#126—28no—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2312yes—
243C2×#125C2312yes—
244C2×#125C2314yes—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2312yes—
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2314yes—
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2311yescharacteristic
284C22×C42C2311yescharacteristic
285C22×C42C2311yescharacteristic
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292#401C2314yes—
293#401C2314yes—
294#401C2314yes—
295#401C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#399C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#396C2314yes—
365#396C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#393C2314yes—
380#391C2312yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2312yes—
393#391C2312yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2312yes—
403#391C2312yes—
404#389C2314yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2314yes—
411#389C2312yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2314yes—
432#389C2312yes—
433#389C2314yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
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#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#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#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#384C2312yes—
559#384C2312yes—
560#383C2314yes—
561#383C2314yes—
562#383C2314yes—
563#383C2314yes—
564#383C2314yes—
565#382C2312yes—
566#382C2314yes—
567#382C2314yes—
568#382C2312yes—
569#382C2314yes—
570#382C2314yes—
571#382C2314yes—
572#382C2312yes—
573#382C2312yes—
574#382C2312yes—
575#382C2312yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#380C2312yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2314yes—
594#380C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2312yes—
599#380C2314yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#379C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2314yes—
642#376C2312yes—
643#376C2312yes—
644#376C2314yes—
645#376C2312yes—
646#376C2312yes—
647C2×#95C2311yescharacteristic
648C2×#95C2311yescharacteristic
649C2×#95C2311yescharacteristic
650C2×#95C2314yes—
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2311yescharacteristic
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C25C2411yescharacteristic
661C22×Q8C2412yes—
662C22×Q8C2412yes—
663C22×Q8C2412yes—
664C22×Q8C2414yes—
665C22×Q8C2412yes—
666C23×C4—24no—
667C23×C4—42no—
668C23×C4—81no—
669C23×C4C2411yescharacteristic
670C23×C4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C23×C4C2412yes—
673C23×C4C2411yescharacteristic
674C23×C4C2411yescharacteristic
675C23×C4C2411yescharacteristic
676C23×C4C2411yescharacteristic
677C23×C4C2411yescharacteristic
678C23×C4C2414yes—
679C23×C4C2414yes—
680C23×C4C2411yescharacteristic
681C23×C4C2411yescharacteristic
682C23×C4C2412yes—
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C4⋊Q8—44no—
688C4⋊Q8—82no—
689#126—216no—
690#126—216no—
691#125—44no—
692#125—44no—
693#125—48no—
694#125—82no—
695#125—82no—
696C22⋊Q8—28no—
697C22⋊Q8—28no—
698C22⋊Q8—216no—
699C22⋊Q8—28no—
700C22⋊Q8—28no—
701C22⋊Q8—216no—
702C22⋊Q8—216no—
703C22⋊Q8—216no—
704C22⋊Q8—216no—
705C22⋊Q8—44no—
706C22⋊Q8—82no—
707C4×Q8—44no—
708C4×Q8—44no—
709C4×Q8—44no—
710C4×Q8—82no—
711C4×Q8—82no—
712C4×Q8—82no—
713C4×Q8—84no—
714#117—48no—
715#117—84no—
716C2×C4⋊C4—24no—
717C2×C4⋊C4—24no—
718C2×C4⋊C4—24no—
719C2×C4⋊C4—24no—
720C2×C4⋊C4—24no—
721C2×C4⋊C4—24no—
722C2×C4⋊C4—42no—
723C2×C4⋊C4—44no—
724C2×C4⋊C4—81no—
725C2×C4⋊C4—82no—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C22⋊C4—24no—
788C2×C22⋊C4—24no—
789C2×C22⋊C4—216no—
790C2×C22⋊C4—24no—
791C2×C22⋊C4—42no—
792C2×C22⋊C4—81no—
793C2×C22⋊C4#4118yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C42—24no—
813C2×C42—24no—
814C2×C42—42no—
815C2×C42—42no—
816C2×C42—42no—
817C2×C42—81no—
818C2×C42—81no—
819C2×C42—81no—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2412yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858#95C2412yes—
859#95C2412yes—
860#95C2414yes—
861#95C2412yes—
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—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
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#95C2414yes—
897#95C2414yes—
898#95C2414yes—
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—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924C24—22no—
925C24—22no—
926C24—41no—
927C24—41no—
928C24—41no—
929C24—41no—
930C24C2×#4114yes—
931C24C2512yes—
932C24C2511yescharacteristic
933C2×Q8—24no—
934C2×Q8—24no—
935C2×Q8—28no—
936C2×Q8—24no—
937C2×Q8—24no—
938C2×Q8—42no—
939C2×Q8—42no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—42no—
943C2×Q8—44no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—42no—
947C2×Q8—44no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—28no—
959C22×C4—28no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—24no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—41no—
977C22×C4—41no—
978C22×C4—41no—
979C22×C4—42no—
980C22×C4—41no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—41no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—41no—
988C22×C4—41no—
989C22×C4—41no—
990C22×C4—41no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—44no—
997C22×C4—41no—
998C22×C4—88no—
999C22×C4C2×#4114yes—
1000C22×C4C2×#4114yes—
1001C22×C42−1+414yes—
1002C22×C42−1+414yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2514yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—24no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—24no—
1094C22⋊C4—24no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—24no—
1100C22⋊C4—42no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4C2×#41116yes—
1107C42—24no—
1108C42—24no—
1109C42—24no—
1110C42—24no—
1111C42—24no—
1112C42—24no—
1113C42—24no—
1114C42—28no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C42—44no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—22no—
1142C23—22no—
1143C23—28no—
1144C23—44no—
1145C23—44no—
1146C23—82no—
1147C23—82no—
1148C23—82no—
1149C23—82no—
1150C23C22×#4114yes—
1151C23C22×#4112yes—
1152C23C2×2−1+412yes—
1153C23C2×2−1+412yes—
1154C23C2611yescharacteristic
1155Q8—48no—
1156Q8—84no—
1157Q8—84no—
1158Q8—88no—
1159Q8—84no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—21no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—44no—
1230C2×C4—44no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—48no—
1234C2×C4—44no—
1235C2×C4—44no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—44no—
1239C2×C4—44no—
1240C2×C4—84no—
1241C2×C4—88no—
1242C2×C4—88no—
1243C2×C4—82no—
1244C2×C4—82no—
1245C2×C4—82no—
1246C2×C4—82no—
1247C2×C4C22×#4114yes—
1248C2×C4C22×#4114yes—
1249C2×C4C2×2−1+414yes—
1250C2×C4C2×2−1+414yes—
1251C2×C4#58512yes—
1252C2×C4#58512yes—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—88no—
1267C22#350914yes—
1268C22C23×#4111yescharacteristic
1269C22C22×2−1+411yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22C2×#58511yescharacteristic
1272C22C2×#58511yescharacteristic
1273C22H(7,𝔽2)11yescharacteristic
1274C222−1+611yescharacteristic
1275C4—24no—
1276C4—24no—
1277C4—24no—
1278C4—22no—
1279C4—24no—
1280C4—22no—
1281C4—42no—
1282C4—44no—
1283C4—44no—
1284C4—42no—
1285C4—42no—
1286C4—41no—
1287C4—41no—
1288C4—44no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—44no—
1293C4—41no—
1294C4—42no—
1295C4—44no—
1296C4—44no—
1297C4—41no—
1298C4—44no—
1299C4—42no—
1300C2—24no—
1301C2—44no—
1302C2#6278111yescharacteristic
1303C2C2×#350911yescharacteristic
1304C2#6284711yescharacteristic
1305C2#6290211yescharacteristic
1306C2#6290311yescharacteristic
1307C2#6292811yescharacteristic
1308C2#6293211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50442C2semidirect
2. #50421C2semidirect
3. #49260C2semidirect
4. #49239C2semidirect
5. #44865C2semidirect
6. #44850C2semidirect
7. #44614C2semidirect
8. #44499C2semidirect
9. #39679C2semidirect
12. #39512C2semidirect
13. #37959C2semidirect
16. #36762C2semidirect
17. #36571C2semidirect
19. #35315C2semidirect
20. #35013C2semidirect
21. #35013C2semidirect
22. #35013C2semidirect
25. #34595C2semidirect
40. #2810C22semidirect
41. #2809C22semidirect
42. #2805C22semidirect
43. #2805C22semidirect
44. #2802C22semidirect
45. #2802C22semidirect
46. #2794C22semidirect
47. #2789C22semidirect
48. #2789C22semidirect
50. #2776C22semidirect
51. #2776C22semidirect
52. #2776C22semidirect
53. #2774C22semidirect
57. #2767C22semidirect
58. #2766C22semidirect
61. #2762C22semidirect
62. #2758C22semidirect
63. #2758C22semidirect
69. #2719C22semidirect
70. #2713C22semidirect
80. #2666C22semidirect
81. #2666C22semidirect
87. #2647C22semidirect
89. #2645C22semidirect
90. #2645C22semidirect
91. #2642C22semidirect
98. #2605C22semidirect
101. #2590C22semidirect
102. #2588C22semidirect
103. #2588C22semidirect
104. #2586C22semidirect
105. #2586C22semidirect
106. #2586C22semidirect
107. #2585C22semidirect
108. #2585C22semidirect
109. #2585C22semidirect
110. #2585C22semidirect
112. #2581C22semidirect
113. #2581C22semidirect
118. #2570C22semidirect
119. #2565C22semidirect
121. #2550C22semidirect
124. #2533C22semidirect
125. #2533C22semidirect
127. #2528C22semidirect
128. #2528C22semidirect
129. #2528C22semidirect
130. #2524C22semidirect
132. #2520C22semidirect
133. #2520C22semidirect
134. #2520C22semidirect
135. #2520C22semidirect
138. #2514C22semidirect
139. #2509C22semidirect
140. #2508C22semidirect
141. #2506C22semidirect
164. #2462C22semidirect
165. #2462C22semidirect
166. #2462C22semidirect
167. #2462C22semidirect
168. #2453C22semidirect
169. #2451C22semidirect
170. #2446C22semidirect
176. #2402C22semidirect
177. #2399C22semidirect
184. #2370C22semidirect
185. #2370C22semidirect
191. #2351C22semidirect
198. #2330C22semidirect
203. #2327C22semidirect
206. #2320C22semidirect
207. #2320C22semidirect

Maximal subgroups

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

subgroupindex
#504422
#504212
#492602
#492392
#448652
#448502
#446142
#444992
#396792
#395422
#395122
#379592
#378802
#369702
#367622
#365712
#361672
#353152
#350132
#350122
#350022
#345952
#344332
C2×#23732