Finite Group Databasebeta

← #7658906

Subgroups — #7658906

Order 512.

4786 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42404C212yesmaximal, complemented
2#42344C212yesmaximal, complemented
3#42222C212yesmaximal, complemented
4#42201C212yesmaximal, complemented
5#42050C212yesmaximal, complemented
6#42023C212yesmaximal, complemented
7#41668C214yesmaximal, complemented
8#41656C214yesmaximal, complemented
9#40996C214yesmaximal, complemented
10#40980C214yesmaximal, complemented
11#40670C214yesmaximal, complemented
12#40664C214yesmaximal, complemented
13#37612C211yesmaximal, characteristic, complemented
14#37611C211yesmaximal, characteristic, complemented
15#37608C211yesmaximal, characteristic, complemented
16#37599C212yesmaximal, complemented
17#37599C212yesmaximal, complemented
18#37554C212yesmaximal, complemented
19#36698C211yesmaximal, characteristic, complemented
20#36694C211yesmaximal, characteristic, complemented
21C2×#2844C211yesmaximal, characteristic, complemented
22#36032C212yesmaximal, complemented
23#35965C214yesmaximal, complemented
24#35929C214yesmaximal, complemented
25#35740C212yesmaximal, complemented
26#34229C212yesmaximal, complemented
27#34208C211yesmaximal, characteristic, complemented
28C2×#553C2212yes—
29C2×#548C2212yes—
30C2×#532C2211yescharacteristic
31C2×#529C2212yes—
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34#2844C2214yes—
35#2844C2214yes—
36#2844C2212yes—
37#2844C2211yescharacteristic
38#2844C2212yes—
39#2844C2212yes—
40#2844C2211yescharacteristic
41#2838C2214yes—
42#2836C2214yes—
43#2833C2212yes—
44#2832C2212yes—
45#2832C2214yes—
46#2830C2212yes—
47#2828C2214yes—
48#2828C2212yes—
49#2822C2211yescharacteristic
50#2820C2212yes—
51#2820C2212yes—
52#2820C2212yes—
53#2819C2212yes—
54#2819C2211yescharacteristic
55#2819C2212yes—
56#2788C2214yes—
57#2784C2214yes—
58#2779C2214yes—
59#2778C2214yes—
60#2774C2214yes—
61#2773C2214yes—
62#2770C2214yes—
63#2758C2214yes—
64#2753C2214yes—
65#2750C2214yes—
66#2749C2214yes—
67#2745C2214yes—
68#2743C2214yes—
69#2742C2214yes—
70#2741C2214yes—
71#2738C2214yes—
72#2737C2214yes—
73#2723C2214yes—
74#2715C2214yes—
75#2703C2214yes—
76#2688C2214yes—
77#2686C2214yes—
78#2686C2214yes—
79#2672C2214yes—
80#2665C2214yes—
81#2665C2214yes—
82#2663C2214yes—
83#2663C2214yes—
84#2662C2214yes—
85#2662C2214yes—
86#2656C2214yes—
87#2654C2214yes—
88#2650C2214yes—
89#2650C2214yes—
90#2650C2214yes—
91#2649C2214yes—
92#2649C2214yes—
93#2648C2214yes—
94#2648C2214yes—
95#2639C2214yes—
96#2638C2212yes—
97#2637C2214yes—
98#2636C2214yes—
99#2636C2214yes—
100#2636C2214yes—
101#2635C2214yes—
102#2635C2212yes—
103#2634C2212yes—
104#2632C2214yes—
105#2632C2212yes—
106#2628C2214yes—
107#2619C2214yes—
108#2618C2212yes—
109#2618C2212yes—
110#2611C2212yes—
111#2610C2214yes—
112#2610C2212yes—
113#2609C2212yes—
114#2609C2212yes—
115#2604C2214yes—
116#2599C2212yes—
117#2598C2212yes—
118#2597C2214yes—
119#2593C2212yes—
120#2591C2214yes—
121#2591C2212yes—
122#2586C2212yes—
123#2583C2212yes—
124#2580C2214yes—
125#2573C2214yes—
126#2572C2214yes—
127#2572C2212yes—
128#2564C2214yes—
129#2564C2214yes—
130#2559C2214yes—
131#2556C2214yes—
132#2556C2214yes—
133#2555C2212yes—
134#2555C2214yes—
135#2555C2214yes—
136#2543C2214yes—
137#2543C2214yes—
138#2543C2212yes—
139#2543C2212yes—
140#2535C2214yes—
141#2533C2214yes—
142#2533C2214yes—
143#2530C2214yes—
144#2526C2214yes—
145#2521C2214yes—
146#2521C2214yes—
147#2521C2214yes—
148#2516C2214yes—
149#2516C2214yes—
150#2510C2214yes—
151#2493C2214yes—
152#2487C2212yes—
153#2484C2212yes—
154#2481C2214yes—
155#2481C2214yes—
156#2474C2214yes—
157#2470C2214yes—
158#2469C2214yes—
159#2469C2214yes—
160#2465C2214yes—
161#2465C2214yes—
162#2461C2214yes—
163#2461C2214yes—
164#2461C2214yes—
165#2457C2214yes—
166#2457C2214yes—
167#2449C2214yes—
168#2444C2214yes—
169#2444C2214yes—
170#2444C2214yes—
171#2444C2214yes—
172#2443C2214yes—
173#2436C2214yes—
174#2430C2214yes—
175#2430C2214yes—
176#2430C2214yes—
177#2416C2214yes—
178#2416C2214yes—
179#2416C2214yes—
180#2409C2212yes—
181#2406C2212yes—
182#2401C2214yes—
183#2399C2212yes—
184#2398C2214yes—
185#2398C2212yes—
186#2396C2214yes—
187#2395C2212yes—
188C2×#400C2214yes—
189C2×#400C2212yes—
190#2388C2214yes—
191#2388C2212yes—
192C2×#395C2212yes—
193C2×#395C2214yes—
194#2364C2214yes—
195#2364C2214yes—
196#2364C2214yes—
197#2361C2212yes—
198#2361C2214yes—
199#2361C2212yes—
200#2360C2212yes—
201#2360C2212yes—
202#2359C2214yes—
203#2359C2214yes—
204#2357C2212yes—
205#2356C2212yes—
206#2353C2212yes—
207#2353C2212yes—
208#2352C2214yes—
209#2352C2214yes—
210#2351C2212yes—
211#2349C2212yes—
212#2346C2214yes—
213#2343C2214yes—
214#2334C2214yes—
215#2334C2214yes—
216#2328C2211yescharacteristic
217#2328C2211yescharacteristic
218#2327C2211yescharacteristic
219#2327C2211yescharacteristic
220#2318C2214yes—
221#2311C2211yescharacteristic
222#2311C2211yescharacteristic
223C4×#125C2212yes—
224C4×#125C2212yes—
225C4×#124C2211yescharacteristic
226C4×#124C2212yes—
227C4×#124C2211yescharacteristic
228C4×#124C2211yescharacteristic
229C4×#124C2211yescharacteristic
230C4×#124C2212yes—
231C2×#382C2211yescharacteristic
232C2×#382C2212yes—
233#2275C2214yes—
234C4×#117C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2311yescharacteristic
237C22×#41C2312yes—
238C23×Q8C2312yes—
239#553—48no—
240#548—48no—
241#532—28no—
242C2×C4⋊Q8C2311yescharacteristic
243C2×#127C2311yescharacteristic
244#529—216no—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#124C2312yes—
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2312yes—
254C2×#124C2314yes—
255C2×#124C2314yes—
256C2×#124C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×#121C2312yes—
265C2×#121C2314yes—
266C2×#121C2312yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276#520—44no—
277#520—44no—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×#117C2314yes—
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2314yes—
317C22×C42C2311yescharacteristic
318#401C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2312yes—
351#399C2312yes—
352#399C2314yes—
353#399C2314yes—
354#398C2312yes—
355#398C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2312yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2312yes—
395#395C2314yes—
396#395C2312yes—
397#395C2312yes—
398#395C2312yes—
399#395C2312yes—
400#395C2312yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#394C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2312yes—
424#394C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2314yes—
428#394C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2312yes—
441#393C2314yes—
442#393C2312yes—
443#393C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2312yes—
450#392C2314yes—
451#392C2312yes—
452#392C2314yes—
453#392C2314yes—
454#391C2311yescharacteristic
455#391C2311yescharacteristic
456#391C2311yescharacteristic
457#391C2311yescharacteristic
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#390C2311yescharacteristic
464#390C2311yescharacteristic
465#390C2311yescharacteristic
466#390C2311yescharacteristic
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
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#388C2314yes—
519#388C2314yes—
520#388C2314yes—
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#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
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#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#383C2312yes—
591#383C2314yes—
592#383C2312yes—
593#383C2314yes—
594#382C2312yes—
595#382C2312yes—
596#382C2311yescharacteristic
597#382C2311yescharacteristic
598#382C2314yes—
599#382C2314yes—
600#382C2311yescharacteristic
601#382C2311yescharacteristic
602#382C2314yes—
603#382C2312yes—
604#382C2312yes—
605#382C2314yes—
606#381C2312yes—
607#381C2314yes—
608#381C2312yes—
609#381C2314yes—
610#381C2314yes—
611#381C2314yes—
612#380C2312yes—
613#380C2312yes—
614#380C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650#376C2311yescharacteristic
651#376C2311yescharacteristic
652#376C2314yes—
653#376C2312yes—
654#376C2312yes—
655C2×#95C2314yes—
656C2×#95C2314yes—
657C2×#95C2314yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2314yes—
661C2×#95C2314yes—
662C43C2311yescharacteristic
663C43C2311yescharacteristic
664C2×#41—24no—
665C2×#41—24no—
666C2×#41—44no—
667C2×#41—42no—
668C2×#41—42no—
669C2×#41—42no—
670C2×#41—42no—
671C2×#41—84no—
672C22×Q8—44no—
673C22×Q8—84no—
674C22×Q8C2412yes—
675C22×Q8C2411yescharacteristic
676C22×Q8C2411yescharacteristic
677C22×Q8C2412yes—
678C22×Q8C2414yes—
679C22×Q8C2412yes—
680C22×D4C2414yes—
681C22×D4C2412yes—
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2411yescharacteristic
685C22×D4C2411yescharacteristic
686C22×D4C2414yes—
687C22×D4C2412yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2412yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2412yes—
697C23×C4C2414yes—
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2412yes—
708C4⋊Q8—24no—
709#127—24no—
710#126—216no—
711#126—48no—
712#126—84no—
713#125—28no—
714#125—44no—
715#124—28no—
716#124—24no—
717#124—24no—
718#124—44no—
719#124—48no—
720#124—84no—
721#124—84no—
722#123—216no—
723#123—48no—
724#123—84no—
725C22⋊Q8—28no—
726C22⋊Q8—48no—
727C22⋊Q8—44no—
728C22⋊Q8—84no—
729#121—28no—
730#121—216no—
731#121—44no—
732#121—48no—
733#121—48no—
734#121—44no—
735#121—48no—
736#121—48no—
737#121—44no—
738#121—84no—
739#121—84no—
740#121—84no—
741C4×Q8—28no—
742C4×Q8—42no—
743C4×Q8—42no—
744C4×Q8—44no—
745C4×Q8—42no—
746C4×Q8—42no—
747C4×Q8—82no—
748C4×Q8—82no—
749C4×D4—216no—
750C4×D4—28no—
751C4×D4—28no—
752C4×D4—216no—
753C4×D4—28no—
754C4×D4—216no—
755C4×D4—42no—
756C4×D4—42no—
757C4×D4—42no—
758C4×D4—42no—
759C4×D4—44no—
760C4×D4—48no—
761C4×D4—44no—
762C4×D4—44no—
763C4×D4—84no—
764C4×D4—82no—
765C4×D4—82no—
766#117—24no—
767#117—216no—
768#117—44no—
769#117—44no—
770#117—44no—
771#117—42no—
772C2×C4⋊C4—44no—
773C2×C4⋊C4—44no—
774C2×C4⋊C4—42no—
775C2×C4⋊C4—42no—
776C2×C4⋊C4—44no—
777C2×C4⋊C4—82no—
778C2×C4⋊C4—82no—
779C2×C4⋊C4—84no—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
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⋊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×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C42#4118yescomplemented
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2411yescharacteristic
883C2×C42C2411yescharacteristic
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896#95C2412yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
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—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954C24C2514yes—
955C24C2512yes—
956C24C2512yes—
957C24C2511yescharacteristic
958#41—416no—
959#41—416no—
960#41—816no—
961C2×Q8—24no—
962C2×Q8—22no—
963C2×Q8—22no—
964C2×Q8—41no—
965C2×Q8—41no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—44no—
969C2×Q8—42no—
970C2×Q8—41no—
971C2×Q8—41no—
972C2×Q8—44no—
973C2×Q8—42no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×Q8—44no—
977C2×Q8—816no—
978C2×D4—28no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—28no—
984C2×D4—28no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—24no—
988C2×D4—22no—
989C2×D4—22no—
990C2×D4—28no—
991C2×D4—41no—
992C2×D4—41no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—41no—
996C2×D4—41no—
997C2×D4—42no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—42no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
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—44no—
1015C22×C4—22no—
1016C22×C4—22no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—28no—
1020C22×C4—28no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—28no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4C2×#4114yes—
1053C22×C4C2×#4118yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—41no—
1093C4⋊C4—41no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C22⋊C4—28no—
1125C22⋊C4—22no—
1126C22⋊C4—24no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—28no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
1144C22⋊C4—42no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
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⋊C4H(5,𝔽2)14yes—
1170C42—28no—
1171C42—22no—
1172C42—22no—
1173C42—24no—
1174C42—24no—
1175C42—28no—
1176C42—42no—
1177C42—44no—
1178C42—42no—
1179C42—41no—
1180C42—41no—
1181C42—42no—
1182C42—42no—
1183C42—44no—
1184C42—42no—
1185C42—44no—
1186C42—42no—
1187C42—44no—
1188C42—44no—
1189C42C2×#4114yes—
1190C42C2×#4118yes—
1191C42C2×#4114yes—
1192C23—22no—
1193C23—22no—
1194C23—24no—
1195C23—22no—
1196C23—22no—
1197C23—24no—
1198C23—22no—
1199C23—22no—
1200C23—24no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23C22×#4112yes—
1212C23C2×H(5,𝔽2)12yes—
1213C23#58512yes—
1214C23C2611yescharacteristic
1215Q8—48no—
1216Q8—44no—
1217Q8—44no—
1218Q8—48no—
1219Q8—88no—
1220Q8—84no—
1221D4—48no—
1222D4—44no—
1223D4—44no—
1224D4—416no—
1225D4—48no—
1226D4—48no—
1227D4—88no—
1228D4—88no—
1229D4—84no—
1230D4—88no—
1231D4—84no—
1232D4—164no—
1233D4—164no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—28no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
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—48no—
1291C2×C4—48no—
1292C2×C4—48no—
1293C2×C4—84no—
1294C2×C4—88no—
1295C2×C4—84no—
1296C2×C4—88no—
1297C2×C4—88no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—88no—
1301C2×C4—162no—
1302C2×C4—164no—
1303C2×C4—162no—
1304C2×C4C22×#4114yes—
1305C2×C4C22×#4114yes—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4112yes—
1308C2×C4C2×H(5,𝔽2)12yes—
1309C2×C4C2×H(5,𝔽2)12yes—
1310C22—22no—
1311C22—24no—
1312C22—22no—
1313C22—24no—
1314C22—42no—
1315C22—44no—
1316C22—42no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—42no—
1322C22—44no—
1323C22—42no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—42no—
1329C22—42no—
1330C22—44no—
1331C22#346014yes—
1332C22C23×#4111yescharacteristic
1333C22C22×H(5,𝔽2)11yescharacteristic
1334C22C2×#58511yescharacteristic
1335C22H(7,𝔽2)12yes—
1336C222−1+612yes—
1337C4—22no—
1338C4—22no—
1339C4—24no—
1340C4—24no—
1341C4—22no—
1342C4—22no—
1343C4—44no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—41no—
1348C4—42no—
1349C4—44no—
1350C4—44no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—41no—
1355C4—44no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4—44no—
1360C2—24no—
1361C2—82no—
1362C2—84no—
1363C2—82no—
1364C2C2×#346011yescharacteristic
1365C2#6285612yes—
1366C2#6304511yescharacteristic
1367C2#6305912yes—
1368C2#6306311yescharacteristic
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. #42404C2semidirect
2. #42344C2semidirect
3. #42222C2semidirect
4. #42201C2semidirect
5. #42050C2semidirect
6. #42023C2semidirect
7. #41668C2semidirect
8. #41656C2semidirect
9. #40996C2semidirect
10. #40980C2semidirect
11. #40670C2semidirect
12. #40664C2semidirect
13. #37612C2semidirect
14. #37611C2semidirect
15. #37608C2semidirect
16. #37599C2semidirect
17. #37599C2semidirect
18. #37554C2semidirect
19. #36698C2semidirect
20. #36694C2semidirect
21. C2×#2844C2semidirect
22. #36032C2semidirect
23. #35965C2semidirect
24. #35929C2semidirect
25. #35740C2semidirect
26. #34229C2semidirect
27. #34208C2semidirect
873. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#424042
#423442
#422222
#422012
#420502
#420232
#416682
#416562
#409962
#409802
#406702
#406642
#376122
#376112
#376082
#375992
#375542
#366982
#366942
C2×#28442
#360322
#359652
#359292
#357402
#342292
#342082