Finite Group Databasebeta

← #7658890

Subgroups — #7658890

Order 512.

4714 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42408C214yesmaximal, complemented
2#42397C212yesmaximal, complemented
3#42071C214yesmaximal, complemented
4#41980C212yesmaximal, complemented
5#41967C214yesmaximal, complemented
6#41059C214yesmaximal, complemented
7#41038C214yesmaximal, complemented
8#41020C214yesmaximal, complemented
9#41009C214yesmaximal, complemented
10#40657C212yesmaximal, complemented
11#40650C212yesmaximal, complemented
12#37611C212yesmaximal, complemented
13#37606C211yesmaximal, characteristic, complemented
14#37599C212yesmaximal, complemented
15#37599C212yesmaximal, complemented
16#37563C211yesmaximal, characteristic, complemented
17#37536C211yesmaximal, characteristic, complemented
18#36694C212yesmaximal, complemented
19#36687C211yesmaximal, characteristic, complemented
20#36084C212yesmaximal, complemented
21#35944C212yesmaximal, complemented
22#35924C212yesmaximal, complemented
23#35769C214yesmaximal, complemented
24#35684C212yesmaximal, complemented
25#34240C211yesmaximal, characteristic, complemented
26#34232C211yesmaximal, characteristic, complemented
27#34227C211yesmaximal, characteristic, complemented
28C2×#532C2211yescharacteristic
29C2×#529C2211yescharacteristic
30C22×#124C2211yescharacteristic
31#2844C2212yescomplemented
32#2844C2212yescomplemented
33#2832C2214yescomplemented
34#2832C2214yescomplemented
35#2832C2214yescomplemented
36#2828C2214yes—
37#2828C2214yescomplemented
38#2828C2214yescomplemented
39#2821C2212yescomplemented
40#2820C2212yes—
41#2820C2211yescharacteristic, complemented
42#2820C2211yescharacteristic, complemented
43#2819C2212yes—
44#2819C2212yes—
45#2819C2212yes—
46#2819C2211yescharacteristic, complemented
47#2819C2211yescharacteristic, complemented
48#2818C2212yescomplemented
49#2816C2212yes—
50#2815C2212yes—
51#2813C2214yes—
52#2808C2214yescomplemented
53#2803C2214yescomplemented
54#2798C2214yescomplemented
55#2796C2214yescomplemented
56#2777C2214yescomplemented
57#2758C2214yescomplemented
58#2751C2214yes—
59#2743C2214yes—
60#2737C2214yes—
61#2733C2214yescomplemented
62#2730C2214yes—
63#2714C2214yescomplemented
64#2712C2214yescomplemented
65#2710C2214yescomplemented
66#2709C2214yes—
67#2705C2214yes—
68#2700C2214yescomplemented
69#2696C2214yes—
70#2689C2214yescomplemented
71#2685C2214yes—
72#2684C2214yes—
73#2678C2214yes—
74#2673C2214yes—
75#2670C2214yes—
76#2665C2214yes—
77#2665C2212yes—
78#2665C2214yes—
79#2665C2212yes—
80#2665C2214yescomplemented
81#2665C2214yescomplemented
82#2663C2214yescomplemented
83#2663C2214yescomplemented
84#2662C2214yes—
85#2662C2214yes—
86#2662C2214yescomplemented
87#2657C2212yes—
88#2650C2214yescomplemented
89#2650C2214yescomplemented
90#2649C2214yescomplemented
91#2649C2214yescomplemented
92#2648C2214yes—
93#2648C2214yescomplemented
94#2640C2212yes—
95#2635C2214yes—
96#2635C2214yescomplemented
97#2635C2214yescomplemented
98#2632C2212yes—
99#2632C2214yescomplemented
100#2632C2214yescomplemented
101#2632C2214yescomplemented
102#2631C2212yes—
103#2631C2214yes—
104#2617C2214yes—
105#2614C2212yes—
106#2613C2212yes—
107#2610C2214yes—
108#2607C2214yescomplemented
109#2605C2214yescomplemented
110#2605C2214yescomplemented
111#2605C2212yescomplemented
112#2605C2214yescomplemented
113#2605C2212yescomplemented
114#2600C2214yescomplemented
115#2597C2214yescomplemented
116#2578C2214yescomplemented
117#2577C2214yescomplemented
118#2572C2214yes—
119#2572C2214yescomplemented
120#2572C2214yescomplemented
121#2572C2214yescomplemented
122#2572C2214yescomplemented
123#2561C2212yes—
124#2557C2214yes—
125#2555C2214yes—
126#2555C2214yescomplemented
127#2555C2214yescomplemented
128#2544C2214yes—
129#2544C2212yes—
130#2544C2212yes—
131#2539C2212yes—
132#2534C2214yes—
133#2534C2212yes—
134#2534C2212yes—
135#2532C2214yescomplemented
136#2526C2214yes—
137#2521C2214yescomplemented
138#2521C2214yescomplemented
139#2521C2214yescomplemented
140#2521C2214yescomplemented
141#2518C2214yescomplemented
142#2516C2214yes—
143#2516C2214yescomplemented
144#2516C2214yescomplemented
145#2516C2214yescomplemented
146#2488C2214yescomplemented
147#2472C2214yes—
148#2469C2214yescomplemented
149#2469C2214yescomplemented
150#2467C2214yes—
151#2467C2214yescomplemented
152#2465C2214yescomplemented
153#2465C2214yescomplemented
154#2461C2214yes—
155#2461C2214yescomplemented
156#2459C2214yescomplemented
157#2459C2214yescomplemented
158#2459C2214yescomplemented
159#2459C2214yescomplemented
160#2457C2214yes—
161#2457C2214yes—
162#2457C2214yescomplemented
163#2457C2214yescomplemented
164#2456C2214yescomplemented
165#2447C2214yescomplemented
166#2444C2214yescomplemented
167#2436C2212yes—
168#2433C2212yes—
169#2431C2214yes—
170#2427C2214yescomplemented
171#2424C2214yes—
172#2407C2214yescomplemented
173#2404C2214yes—
174#2404C2212yes—
175#2404C2212yes—
176#2398C2214yescomplemented
177#2398C2212yescomplemented
178#2398C2214yescomplemented
179#2398C2214yescomplemented
180#2397C2212yescomplemented
181#2392C2214yescomplemented
182#2388C2214yes—
183#2388C2212yes—
184#2388C2212yes—
185#2388C2214yescomplemented
186#2388C2214yescomplemented
187#2374C2214yes—
188#2373C2214yescomplemented
189#2372C2212yes—
190#2372C2212yes—
191#2372C2214yescomplemented
192#2367C2212yes—
193#2367C2212yes—
194#2366C2212yescomplemented
195#2365C2212yescomplemented
196#2364C2214yescomplemented
197#2363C2214yes—
198#2357C2212yes—
199#2353C2212yes—
200#2353C2214yescomplemented
201#2353C2212yescomplemented
202#2353C2212yescomplemented
203#2347C2212yescomplemented
204#2343C2212yescomplemented
205#2342C2214yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208Q8×C22⋊C4C2212yes—
209#2339C2211yescharacteristic
210#2339C2211yescharacteristic
211#2339C2214yescomplemented
212D4×C22⋊C4C2212yes—
213#2337C2214yes—
214#2333C2214yes—
215#2324C2212yes—
216#2323C2212yes—
217#2320C2211yescharacteristic, complemented
218#2319C2211yescharacteristic, complemented
219#2319C2212yescomplemented
220#2312C2212yes—
221C4×#125C2212yescomplemented
222C4×#124C2212yes—
223C4×#124C2212yes—
224C4×#124C2212yescomplemented
225C4×#124C2212yescomplemented
226C4×#124C2212yescomplemented
227#2283C2211yescharacteristic
228#2283C2211yescharacteristic
229#2283C2211yescharacteristic
230#2276C2211yescharacteristic, complemented
231#2275C2211yescharacteristic, complemented
232#2275C2212yescomplemented
233#2273C2212yes—
234C4×#117C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2311yescharacteristic
237C22×#41C2314yes—
238C23×Q8C2311yescharacteristic
239C23×D4C2311yescharacteristic
240#532—28no—
241C2×C4⋊Q8C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#127C2312yes—
244C2×#127C2312yes—
245#529—28no—
246C2×#126C2312yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2311yescharacteristic
250C2×#124—28no—
251C2×#124C2312yes—
252C2×#124C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2314yes—
264C2×#124C2314yes—
265C2×#123C2312yes—
266C2×#123C2312yes—
267C2×#123C2312yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2311yescharacteristic
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×#121C2312yes—
274C2×#121C2311yescharacteristic
275C2×#121C2312yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#120C2312yes—
280C2×#120C2312yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2314yes—
309C22×C42C2311yescharacteristic
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#399C2312yes—
325#399C2312yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#398C2314yes—
332#397C2314yes—
333#397C2312yes—
334#397C2312yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#395C2314yes—
357#395C2312yes—
358#395C2312yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2312yes—
371#394C2312yes—
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#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#393C2312yes—
400#393C2312yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2312yes—
408#393C2312yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#392C2312yes—
418#392C2312yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2312yes—
428#392C2312yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
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#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#383C2312yes—
571#383C2314yes—
572#383C2314yes—
573#383C2312yes—
574#383C2314yes—
575#383C2312yes—
576#383C2312yes—
577#382C2312yes—
578#382C2312yes—
579#382C2311yescharacteristic
580#382C2311yescharacteristic
581#382C2312yes—
582#381C2312yes—
583#381C2312yes—
584#381C2312yes—
585#381C2314yes—
586#381C2314yes—
587#381C2312yes—
588#381C2314yes—
589#381C2314yes—
590#381C2312yes—
591#381C2312yes—
592#381C2312yes—
593#381C2312yes—
594#381C2314yes—
595#380C2314yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2314yes—
600#380C2312yes—
601#380C2312yes—
602#380C2311yescharacteristic
603#380C2311yescharacteristic
604#380C2314yes—
605#379C2312yes—
606#379C2312yes—
607#379C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2311yescharacteristic
613C4×C4⋊C4C2311yescharacteristic
614C4×C4⋊C4C2311yescharacteristic
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2311yescharacteristic
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C22⋊C4C2312yes—
623C4×C22⋊C4C2311yescharacteristic
624C4×C22⋊C4C2312yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2311yescharacteristic
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2312yes—
650#376C2311yescharacteristic
651#376C2312yes—
652#376C2312yes—
653#376C2312yes—
654#376C2312yes—
655#376C2314yes—
656#376C2311yescharacteristic
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C43C2312yes—
661C25C2412yes—
662C2×#41—24no—
663C2×#41—24no—
664C2×#41—48no—
665C2×#41—82no—
666C2×#41—82no—
667C2×#41—84no—
668C2×#41—84no—
669C22×Q8—24no—
670C22×Q8—81no—
671C22×Q8—81no—
672C22×Q8C2411yescharacteristic
673C22×Q8C2412yes—
674C22×Q8C2411yescharacteristic
675C22×Q8C2411yescharacteristic
676C22×Q8C2412yes—
677C22×Q8C2414yes—
678C22×Q8C2414yes—
679C22×D4—24no—
680C22×D4—81no—
681C22×D4—81no—
682C22×D4C2411yescharacteristic
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2411yescharacteristic
686C22×D4C2411yescharacteristic
687C22×D4C2412yes—
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2412yes—
691C22×D4C2412yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C23×C4C2412yes—
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2414yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2411yescharacteristic
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C4⋊Q8—24no—
713#127—24no—
714#127—82no—
715#127—82no—
716#126—28no—
717#126—84no—
718#126—84no—
719#125—24no—
720#124—28no—
721#124—28no—
722#124—28no—
723#124—28no—
724#124—24no—
725#124—24no—
726#124—24no—
727#124—48no—
728#124—84no—
729#124—84no—
730#124—84no—
731#124—84no—
732#124—82no—
733#124—82no—
734#123—28no—
735#123—82no—
736#123—84no—
737#123—84no—
738#123—82no—
739C22⋊Q8—24no—
740C22⋊Q8—84no—
741C22⋊Q8—84no—
742#121—24no—
743#121—28no—
744#121—28no—
745#121—48no—
746#121—84no—
747#121—84no—
748#120—84no—
749#120—84no—
750#120—82no—
751#120—82no—
752C4×Q8—24no—
753C4×Q8—44no—
754C4×Q8—82no—
755C4×Q8—82no—
756C4×Q8—82no—
757C4×Q8—82no—
758C4×D4—28no—
759C4×D4—24no—
760C4×D4—28no—
761C4×D4—28no—
762C4×D4—44no—
763C4×D4—48no—
764C4×D4—48no—
765C4×D4—84no—
766C4×D4—84no—
767C4×D4—84no—
768C4×D4—82no—
769C4×D4—82no—
770C4×D4—84no—
771C4×D4—82no—
772C4×D4—82no—
773#117—28no—
774#117—44no—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C22⋊C4—28no—
809C2×C22⋊C4—28no—
810C2×C22⋊C4—48no—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C42#4118yescomplemented
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2411yescharacteristic
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2412yes—
898#95C2414yes—
899#95C2411yescharacteristic
900#95C2411yescharacteristic
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
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—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948C24—24no—
949C24—44no—
950C24—44no—
951C24—42no—
952C24—42no—
953C24C2514yes—
954C24C2512yes—
955C24C2512yes—
956C24C2512yes—
957C24C2511yescharacteristic
958#41—88no—
959#41—88no—
960#41—832no—
961C2×Q8—22no—
962C2×Q8—24no—
963C2×Q8—22no—
964C2×Q8—22no—
965C2×Q8—24no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—44no—
972C2×Q8—42no—
973C2×Q8—42no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×Q8—44no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—88no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—22no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—22no—
987C2×D4—22no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—42no—
991C2×D4—44no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—42no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—42no—
1015C2×D4—42no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—88no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—28no—
1036C22×C4—42no—
1037C22×C4—41no—
1038C22×C4—41no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4C2×#4114yes—
1058C22×C4C2×#4114yes—
1059C22×C4C2×#4114yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C22⋊C4—24no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—42no—
1152C22⋊C4—44no—
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—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C42—24no—
1174C42—24no—
1175C42—28no—
1176C42—42no—
1177C42—44no—
1178C42—44no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42—42no—
1184C42—42no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—42no—
1190C42—42no—
1191C42C2×#4114yes—
1192C42C2×#4114yes—
1193C42C2×#4114yes—
1194C42C2×#4114yes—
1195C23—22no—
1196C23—21no—
1197C23—21no—
1198C23—22no—
1199C23—22no—
1200C23—24no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—22no—
1209C23—24no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—24no—
1214C23—24no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—48no—
1222C23—84no—
1223C23—84no—
1224C23—164no—
1225C23—164no—
1226C23C22×#4112yes—
1227C23C2611yescharacteristic
1228Q8—44no—
1229Q8—48no—
1230Q8—44no—
1231Q8—44no—
1232Q8—84no—
1233Q8—88no—
1234Q8—164no—
1235D4—48no—
1236D4—44no—
1237D4—48no—
1238D4—44no—
1239D4—44no—
1240D4—416no—
1241D4—84no—
1242D4—84no—
1243D4—84no—
1244D4—84no—
1245D4—84no—
1246D4—88no—
1247D4—88no—
1248D4—88no—
1249D4—88no—
1250D4—88no—
1251D4—164no—
1252D4—164no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
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—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—44no—
1305C2×C4—44no—
1306C2×C4—44no—
1307C2×C4—84no—
1308C2×C4—88no—
1309C2×C4—88no—
1310C2×C4—88no—
1311C2×C4—84no—
1312C2×C4—84no—
1313C2×C4—84no—
1314C2×C4—164no—
1315C2×C4—164no—
1316C2×C4C22×#4112yes—
1317C2×C4C22×#4112yes—
1318C2×C4C22×#4112yes—
1319C2×C4C22×#4112yes—
1320C2×C4C22×#4112yes—
1321C2×C4C22×#4112yes—
1322C2×C4#58514yes—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—42no—
1327C22—42no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—44no—
1334C22—44no—
1335C22—44no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—44no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—44no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—44no—
1350C22—168no—
1351C22C23×#4111yescharacteristic
1352C22C2×#58512yes—
1353C22H(7,𝔽2)11yescharacteristic
1354C22H(7,𝔽2)12yes—
1355C22H(7,𝔽2)11yescharacteristic
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—44no—
1364C4—44no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—44no—
1370C4—44no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—44no—
1376C4—42no—
1377C4—42no—
1378C2—42no—
1379C2—82no—
1380C2—82no—
1381C2—82no—
1382C2—84no—
1383C2#6268611yescharacteristic
1384C2#6285511yescharacteristic
1385C2#6285511yescharacteristic
1386C2#6304612yes—
1387C2#6305112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42408C2semidirect
2. #42397C2semidirect
3. #42071C2semidirect
4. #41980C2semidirect
5. #41967C2semidirect
6. #41059C2semidirect
7. #41038C2semidirect
8. #41020C2semidirect
9. #41009C2semidirect
10. #40657C2semidirect
11. #40650C2semidirect
12. #37611C2semidirect
13. #37606C2semidirect
14. #37599C2semidirect
15. #37599C2semidirect
16. #37563C2semidirect
17. #37536C2semidirect
18. #36694C2semidirect
19. #36687C2semidirect
20. #36084C2semidirect
21. #35944C2semidirect
22. #35924C2semidirect
23. #35769C2semidirect
24. #35684C2semidirect
25. #34240C2semidirect
26. #34232C2semidirect
27. #34227C2semidirect
31. #2844C22semidirect
32. #2844C22semidirect
33. #2832C22semidirect
34. #2832C22semidirect
35. #2832C22semidirect
37. #2828C22semidirect
38. #2828C22semidirect
39. #2821C22semidirect
41. #2820C22semidirect
42. #2820C22semidirect
46. #2819C22semidirect
47. #2819C22semidirect
48. #2818C22semidirect
52. #2808C22semidirect
53. #2803C22semidirect
54. #2798C22semidirect
55. #2796C22semidirect
56. #2777C22semidirect
57. #2758C22semidirect
61. #2733C22semidirect
63. #2714C22semidirect
64. #2712C22semidirect
65. #2710C22semidirect
68. #2700C22semidirect
70. #2689C22semidirect
80. #2665C22semidirect
81. #2665C22semidirect
82. #2663C22semidirect
83. #2663C22semidirect
86. #2662C22semidirect
88. #2650C22semidirect
89. #2650C22semidirect
90. #2649C22semidirect
91. #2649C22semidirect
93. #2648C22semidirect
96. #2635C22semidirect
97. #2635C22semidirect
99. #2632C22semidirect
100. #2632C22semidirect
101. #2632C22semidirect
108. #2607C22semidirect
109. #2605C22semidirect
110. #2605C22semidirect
111. #2605C22semidirect
112. #2605C22semidirect
113. #2605C22semidirect
114. #2600C22semidirect
115. #2597C22semidirect
116. #2578C22semidirect
117. #2577C22semidirect
119. #2572C22semidirect
120. #2572C22semidirect
121. #2572C22semidirect
122. #2572C22semidirect
126. #2555C22semidirect
127. #2555C22semidirect
135. #2532C22semidirect
137. #2521C22semidirect
138. #2521C22semidirect
139. #2521C22semidirect
140. #2521C22semidirect
141. #2518C22semidirect
143. #2516C22semidirect
144. #2516C22semidirect
145. #2516C22semidirect
146. #2488C22semidirect
148. #2469C22semidirect
149. #2469C22semidirect
151. #2467C22semidirect
152. #2465C22semidirect
153. #2465C22semidirect
155. #2461C22semidirect
156. #2459C22semidirect
157. #2459C22semidirect
158. #2459C22semidirect
159. #2459C22semidirect
162. #2457C22semidirect
163. #2457C22semidirect
164. #2456C22semidirect
165. #2447C22semidirect
166. #2444C22semidirect
170. #2427C22semidirect
172. #2407C22semidirect
176. #2398C22semidirect
177. #2398C22semidirect
178. #2398C22semidirect
179. #2398C22semidirect
180. #2397C22semidirect
181. #2392C22semidirect
185. #2388C22semidirect
186. #2388C22semidirect
188. #2373C22semidirect
191. #2372C22semidirect
194. #2366C22semidirect
195. #2365C22semidirect
196. #2364C22semidirect
200. #2353C22semidirect
201. #2353C22semidirect
202. #2353C22semidirect
203. #2347C22semidirect
204. #2343C22semidirect
211. #2339C22semidirect
217. #2320C22semidirect
218. #2319C22semidirect
219. #2319C22semidirect
221. C4×#125C22semidirect
224. C4×#124C22semidirect
225. C4×#124C22semidirect
226. C4×#124C22semidirect
230. #2276C22semidirect
231. #2275C22semidirect
232. #2275C22semidirect
869. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#424082
#423972
#420712
#419802
#419672
#410592
#410382
#410202
#410092
#406572
#406502
#376112
#376062
#375992
#375632
#375362
#366942
#366872
#360842
#359442
#359242
#357692
#356842
#342402
#342322
#342272