Finite Group Databasebeta

← #7715095

Subgroups — #7715095

Order 512.

4572 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51791C214yesmaximal, complemented
2#51788C214yesmaximal, complemented
3#51597C214yesmaximal, complemented
4#51594C214yesmaximal, complemented
5#47024C214yesmaximal, complemented
6#46848C214yesmaximal, complemented
7#46433C214yesmaximal, complemented
8#46433C214yesmaximal, complemented
9#38966C212yesmaximal, complemented
10#38965C212yesmaximal, complemented
11#38961C212yesmaximal, complemented
12#38960C212yesmaximal, complemented
13#37878C212yesmaximal, complemented
14#37874C212yesmaximal, complemented
15#37691C212yesmaximal, complemented
16#37687C212yesmaximal, complemented
17#37481C211yesmaximal, characteristic, complemented
18#37477C211yesmaximal, characteristic, complemented
19#37427C211yesmaximal, characteristic, complemented
20#37310C212yesmaximal, complemented
21#37309C211yesmaximal, characteristic, complemented
22#35333C211yesmaximal, characteristic, complemented
23#35282C212yesmaximal, complemented
24#35280C211yesmaximal, characteristic, complemented
25#35253C212yesmaximal, complemented
26#34362C212yesmaximal
27#34065C211yesmaximal, characteristic
28C2×#544C2212yes—
29C2×#533C2211yescharacteristic, complemented
30C22×#125C2211yescharacteristic, complemented
31C2×#525C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33C22×#117C2211yescharacteristic
34#2864C2212yescomplemented
35#2859C2212yescomplemented
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yescomplemented
39#2851C2212yes—
40#2851C2212yes—
41#2851C2212yescomplemented
42#2842C2214yes—
43#2841C2214yes—
44#2806C2214yescomplemented
45#2806C2214yescomplemented
46#2799C2214yescomplemented
47#2792C2214yescomplemented
48#2792C2214yescomplemented
49#2791C2214yescomplemented
50#2791C2214yescomplemented
51#2791C2214yescomplemented
52#2791C2214yescomplemented
53#2790C2214yes—
54#2790C2214yes—
55#2790C2214yes—
56#2790C2214yes—
57#2790C2214yescomplemented
58#2784C2214yes—
59#2784C2214yes—
60#2780C2214yes—
61#2780C2214yes—
62#2780C2214yescomplemented
63#2774C2214yescomplemented
64#2768C2214yes—
65#2768C2214yes—
66#2768C2214yescomplemented
67#2768C2214yescomplemented
68#2755C2214yescomplemented
69#2748C2214yes—
70#2748C2214yes—
71#2742C2214yescomplemented
72#2732C2214yes—
73#2732C2214yes—
74#2729C2214yescomplemented
75#2726C2214yescomplemented
76#2726C2214yescomplemented
77#2720C2214yes—
78#2720C2214yes—
79#2720C2214yescomplemented
80#2713C2214yescomplemented
81#2704C2214yes—
82#2704C2214yes—
83#2704C2214yes—
84#2704C2214yes—
85#2704C2214yescomplemented
86#2704C2214yescomplemented
87#2692C2214yes—
88#2692C2214yes—
89#2692C2214yes—
90#2692C2214yes—
91#2692C2214yescomplemented
92#2667C2214yes—
93#2667C2214yes—
94#2660C2212yescomplemented
95#2660C2212yescomplemented
96#2659C2214yes—
97#2646C2214yes—
98#2629C2211yescharacteristic
99#2629C2211yescharacteristic
100#2629C2211yescharacteristic
101#2629C2212yes—
102#2629C2212yes—
103#2629C2211yescharacteristic
104#2629C2212yes—
105#2629C2211yescharacteristic, complemented
106#2629C2211yescharacteristic, complemented
107#2629C2211yescharacteristic, complemented
108#2629C2211yescharacteristic, complemented
109#2628C2212yes—
110#2628C2212yes—
111#2628C2212yes—
112#2608C2214yes—
113#2590C2214yescomplemented
114#2589C2214yes—
115#2589C2214yes—
116#2587C2214yescomplemented
117#2586C2214yescomplemented
118#2586C2214yescomplemented
119#2585C2214yescomplemented
120#2584C2214yescomplemented
121#2583C2214yescomplemented
122#2582C2214yescomplemented
123#2579C2214yes—
124#2579C2214yes—
125#2579C2214yescomplemented
126#2574C2214yes—
127#2574C2214yes—
128#2574C2214yescomplemented
129#2570C2212yescomplemented
130#2570C2212yescomplemented
131#2566C2214yes—
132#2566C2214yes—
133#2565C2214yescomplemented
134#2556C2214yes—
135#2556C2214yes—
136#2552C2214yescomplemented
137#2552C2212yescomplemented
138#2552C2212yescomplemented
139#2552C2212yescomplemented
140#2552C2212yescomplemented
141#2550C2212yescomplemented
142#2550C2212yescomplemented
143#2538C2214yes—
144#2538C2214yes—
145#2522C2214yes—
146#2522C2214yes—
147#2520C2214yescomplemented
148#2508C2214yescomplemented
149#2507C2214yescomplemented
150#2497C2214yescomplemented
151#2473C2214yescomplemented
152#2473C2214yescomplemented
153#2465C2214yes—
154#2465C2214yes—
155#2465C2214yescomplemented
156#2462C2214yescomplemented
157#2462C2214yescomplemented
158#2454C2214yes—
159#2454C2214yes—
160#2449C2214yes—
161#2449C2214yes—
162#2446C2214yescomplemented
163#2442C2214yes—
164#2442C2212yes—
165#2442C2212yes—
166#2442C2212yescomplemented
167#2442C2212yescomplemented
168#2441C2212yes—
169#2441C2212yes—
170#2441C2212yes—
171#2441C2212yes—
172#2441C2214yes—
173#2441C2212yescomplemented
174#2441C2212yescomplemented
175#2440C2214yes—
176#2440C2212yes—
177#2440C2212yes—
178#2440C2212yescomplemented
179#2440C2212yescomplemented
180#2440C2214yescomplemented
181#2439C2214yes—
182#2439C2212yescomplemented
183#2439C2212yescomplemented
184#2438C2214yes—
185#2438C2214yes—
186#2437C2214yes—
187#2437C2214yes—
188#2437C2214yes—
189#2423C2214yes—
190#2423C2214yes—
191#2417C2214yes—
192#2417C2214yes—
193#2417C2214yescomplemented
194#2378C2214yes—
195#2377C2214yes—
196#2368C2214yes—
197#2364C2214yes—
198#2354C2212yes—
199#2354C2212yes—
200#2352C2212yes—
201#2352C2212yes—
202#2352C2212yes—
203#2352C2212yes—
204D4×C4⋊C4C2212yes—
205D4×C4⋊C4C2212yes—
206#2335C2214yes—
207#2335C2214yes—
208#2331C2212yescomplemented
209#2330C2212yescomplemented
210#2324C2212yes—
211#2324C2212yes—
212#2323C2212yes—
213#2323C2212yes—
214#2322C2212yes—
215#2322C2212yes—
216#2321C2212yes—
217#2321C2212yes—
218#2321C2214yes—
219#2321C2214yes—
220#2317C2212yes—
221#2317C2212yes—
222#2317C2212yescomplemented
223#2316C2212yes—
224#2316C2212yescomplemented
225#2314C2212yes—
226#2314C2212yes—
227#2311C2212yes—
228#2311C2212yes—
229C4×C4⋊Q8C2212yescomplemented
230C4×#125C2212yescomplemented
231#2297C2211yescharacteristic
232#2296C2211yescharacteristic
233#2293C2212yes—
234#2293C2212yes—
235#2290C2212yes—
236#2290C2212yes—
237#2285C2211yescharacteristic, complemented
238C2×#384C2211yescharacteristic, complemented
239#2280C2211yescharacteristic
240#2280C2212yes—
241C2×#380C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C24×C4C2311yescharacteristic
245#544—48no—
246#533—44no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2314yes—
251C2×#125—44no—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#125C2311yescharacteristic
259C2×#125C2311yescharacteristic
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264#525Q8116yescomplemented
265C2×#123C2311yescharacteristic
266C2×#123C2311yescharacteristic
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×#121C2312yes—
279C2×#120C2311yescharacteristic
280C2×#120C2311yescharacteristic
281C4×#41—44no—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×#117—44no—
293C2×#117C2312yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C2×#117C2312yes—
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2314yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
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#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2311yescharacteristic
421#391C2311yescharacteristic
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#390C2314yes—
430#390C2312yes—
431#390C2314yes—
432#390C2314yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2312yes—
494#388C2314yes—
495#388C2312yes—
496#388C2314yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
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#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2312yes—
558#386C2312yes—
559#386C2312yes—
560#386C2314yes—
561#386C2312yes—
562#386C2312yes—
563#386C2312yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2312yes—
582#385C2312yes—
583#385C2314yes—
584#385C2314yes—
585#385C2312yes—
586#385C2312yes—
587#385C2312yes—
588#385C2312yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2312yes—
598#384C2314yes—
599#384C2314yes—
600#384C2312yes—
601#384C2312yes—
602#384C2311yescharacteristic
603#384C2311yescharacteristic
604#384C2312yes—
605#384C2312yes—
606#384C2314yes—
607#384C2314yes—
608#384C2311yescharacteristic
609#384C2311yescharacteristic
610#384C2314yes—
611#382C2312yes—
612#382C2314yes—
613#382C2314yes—
614#382C2312yes—
615#382C2312yes—
616#382C2312yes—
617#382C2314yes—
618#382C2312yes—
619#381C2312yes—
620#381C2314yes—
621#380C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2314yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#379C2312yes—
650#379C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677#376C2312yes—
678C2×#95C2314yes—
679C43C2312yes—
680C25C2411yescharacteristic
681C2×#41—42no—
682C2×#41—42no—
683C2×#41C2×Q818yes—
684C22×Q8C2414yes—
685C22×Q8C2414yes—
686C22×Q8C2414yes—
687C22×Q8C2411yescharacteristic
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2411yescharacteristic
691C22×D4C2411yescharacteristic
692C22×D4C2411yescharacteristic
693C23×C4—42no—
694C23×C4—42no—
695C23×C4C2×Q818yes—
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2412yes—
703C23×C4C2414yes—
704C23×C4C2414yes—
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2411yescharacteristic
709C23×C4C2412yes—
710C4⋊Q8—28no—
711C4⋊Q8—44no—
712C4⋊Q8—44no—
713C4⋊Q8—48no—
714#125—28no—
715#125—42no—
716#125—42no—
717#125—48no—
718#125—44no—
719#125—42no—
720#125—42no—
721#125—44no—
722#125—48no—
723#125—84no—
724#125—84no—
725#125—84no—
726#123C2×Q818yes—
727#123C2×Q818yes—
728C22⋊Q8—48no—
729C22⋊Q8—48no—
730C22⋊Q8—48no—
731C22⋊Q8—84no—
732C22⋊Q8—84no—
733C22⋊Q8—84no—
734C22⋊Q8—84no—
735C22⋊Q8—84no—
736C22⋊Q8—84no—
737C22⋊Q8—84no—
738C22⋊Q8C2×Q8116yes—
739#121C2×Q8116yes—
740#120C2×Q818yes—
741#120C2×Q818yes—
742C4×Q8—44no—
743C4×Q8—48no—
744C4×Q8—84no—
745C4×D4—44no—
746C4×D4—44no—
747C4×D4—44no—
748C4×D4—84no—
749C4×D4—84no—
750C4×D4C2×Q8116yes—
751C4×D4C2×Q8116yes—
752#117—28no—
753#117—44no—
754#117—42no—
755#117—42no—
756#117—42no—
757#117—42no—
758#117—44no—
759#117—44no—
760#117—44no—
761#117—44no—
762#117—44no—
763#117—44no—
764#117C2×Q818yes—
765C2×C4⋊C4—44no—
766C2×C4⋊C4—44no—
767C2×C4⋊C4—44no—
768C2×C4⋊C4—44no—
769C2×C4⋊C4—48no—
770C2×C4⋊C4—44no—
771C2×C4⋊C4—84no—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C22⋊C4—44no—
844C2×C22⋊C4—84no—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C42—24no—
884C2×C42—24no—
885C2×C42—24no—
886C2×C42—42no—
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
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#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969C24—41no—
970C24—42no—
971C24—41no—
972C24—42no—
973C24C22×Q814yes—
974C24C2512yes—
975C24C2511yescharacteristic
976C24C2511yescharacteristic
977C24C2511yescharacteristic
978#41—416no—
979C2×Q8—28no—
980C2×Q8—41no—
981C2×Q8—41no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—44no—
986C2×Q8—44no—
987C2×Q8—44no—
988C2×Q8—44no—
989C2×Q8—44no—
990C2×Q8C22×Q814yes—
991C2×D4—41no—
992C2×D4—41no—
993C2×D4—41no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—41no—
999C2×D4—41no—
1000C2×D4—41no—
1001C2×D4C22×Q818yes—
1002C2×D4C22×Q818yes—
1003C2×D4C22×Q814yes—
1004C2×D4C22×Q814yes—
1005C2×D4C22×Q814yes—
1006C22×C4—22no—
1007C22×C4—22no—
1008C22×C4—22no—
1009C22×C4—24no—
1010C22×C4—22no—
1011C22×C4—24no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—24no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—416no—
1018C22×C4—41no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—41no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
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×C4C22×Q814yes—
1044C22×C4C22×Q818yes—
1045C22×C4C22×Q814yes—
1046C22×C4C22×Q814yes—
1047C22×C4C22×Q818yes—
1048C22×C4C22×Q814yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—41no—
1107C4⋊C4—41no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4C22×Q818yes—
1141C4⋊C4C22×Q818yes—
1142C4⋊C4C22×Q818yes—
1143C22⋊C4—24no—
1144C22⋊C4—24no—
1145C22⋊C4—42no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—42no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4C22×Q814yes—
1176C22⋊C4C22×Q814yes—
1177C22⋊C4C22×Q818yes—
1178C22⋊C4C22×Q818yes—
1179C22⋊C4C22×Q818yes—
1180C22⋊C4C22×Q818yes—
1181C42—22no—
1182C42—24no—
1183C42—22no—
1184C42—22no—
1185C42—24no—
1186C42—24no—
1187C42—24no—
1188C42—24no—
1189C42—41no—
1190C42—41no—
1191C42—42no—
1192C42—44no—
1193C42—42no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—42no—
1201C42—44no—
1202C42—42no—
1203C42C22×Q818yes—
1204C42H(5,𝔽2)14yes—
1205C23—22no—
1206C23—21no—
1207C23—21no—
1208C23—21no—
1209C23—21no—
1210C23—22no—
1211C23—21no—
1212C23—21no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—44no—
1224C23—48no—
1225C23—84no—
1226C23—82no—
1227C23—82no—
1228C23C23×Q812yes—
1229C23C23×Q814yes—
1230C23C23×Q812yes—
1231C23C23×Q812yes—
1232C23C2611yescharacteristic
1233Q8—44no—
1234Q8—88no—
1235Q8—88no—
1236Q8—164no—
1237D4—48no—
1238D4—48no—
1239D4—44no—
1240D4—44no—
1241D4—44no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—216no—
1257C2×C4—28no—
1258C2×C4—28no—
1259C2×C4—28no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—44no—
1306C2×C4—48no—
1307C2×C4—48no—
1308C2×C4—84no—
1309C2×C4—84no—
1310C2×C4—88no—
1311C2×C4—84no—
1312C2×C4—164no—
1313C2×C4—164no—
1314C2×C4—164no—
1315C2×C4C23×Q814yes—
1316C2×C4C23×Q814yes—
1317C2×C4C23×Q814yes—
1318C2×C4C23×Q812yes—
1319C2×C4C23×Q812yes—
1320C2×C4C23×Q812yes—
1321C2×C4C23×Q812yes—
1322C2×C4C2×H(5,𝔽2)14yes—
1323C2×C4C2×H(5,𝔽2)12yes—
1324C2×C4#58512yes—
1325C22—22no—
1326C22—24no—
1327C22—22no—
1328C22—22no—
1329C22—24no—
1330C22—24no—
1331C22—24no—
1332C22—24no—
1333C22—24no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—42no—
1346C22—41no—
1347C22—88no—
1348C22C24×Q811yescharacteristic
1349C22C22×H(5,𝔽2)11yescharacteristic
1350C22C2×#58511yescharacteristic
1351C22H(7,𝔽2)12yes—
1352C222−1+612yes—
1353C4—24no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—24no—
1358C4—24no—
1359C4—24no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—44no—
1366C4—42no—
1367C4—44no—
1368C4—44no—
1369C4—44no—
1370C4—44no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—44no—
1375C4#350114yes—
1376C2—42no—
1377C2—42no—
1378C2—42no—
1379C2—44no—
1380C2C2×#350111yescharacteristic
1381C2#6285412yes—
1382C2#6287512yes—
1383C2#6288311yescharacteristic
1384C2#6289011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51791C2semidirect
2. #51788C2semidirect
3. #51597C2semidirect
4. #51594C2semidirect
5. #47024C2semidirect
6. #46848C2semidirect
7. #46433C2semidirect
8. #46433C2semidirect
9. #38966C2semidirect
10. #38965C2semidirect
11. #38961C2semidirect
12. #38960C2semidirect
13. #37878C2semidirect
14. #37874C2semidirect
15. #37691C2semidirect
16. #37687C2semidirect
17. #37481C2semidirect
18. #37477C2semidirect
19. #37427C2semidirect
20. #37310C2semidirect
21. #37309C2semidirect
22. #35333C2semidirect
23. #35282C2semidirect
24. #35280C2semidirect
25. #35253C2semidirect
29. C2×#533C22semidirect
30. C22×#125C22semidirect
34. #2864C22semidirect
35. #2859C22semidirect
38. #2857C22semidirect
41. #2851C22semidirect
44. #2806C22semidirect
45. #2806C22semidirect
46. #2799C22semidirect
47. #2792C22semidirect
48. #2792C22semidirect
49. #2791C22semidirect
50. #2791C22semidirect
51. #2791C22semidirect
52. #2791C22semidirect
57. #2790C22semidirect
62. #2780C22semidirect
63. #2774C22semidirect
66. #2768C22semidirect
67. #2768C22semidirect
68. #2755C22semidirect
71. #2742C22semidirect
74. #2729C22semidirect
75. #2726C22semidirect
76. #2726C22semidirect
79. #2720C22semidirect
80. #2713C22semidirect
85. #2704C22semidirect
86. #2704C22semidirect
91. #2692C22semidirect
94. #2660C22semidirect
95. #2660C22semidirect
105. #2629C22semidirect
106. #2629C22semidirect
107. #2629C22semidirect
108. #2629C22semidirect
113. #2590C22semidirect
116. #2587C22semidirect
117. #2586C22semidirect
118. #2586C22semidirect
119. #2585C22semidirect
120. #2584C22semidirect
121. #2583C22semidirect
122. #2582C22semidirect
125. #2579C22semidirect
128. #2574C22semidirect
129. #2570C22semidirect
130. #2570C22semidirect
133. #2565C22semidirect
136. #2552C22semidirect
137. #2552C22semidirect
138. #2552C22semidirect
139. #2552C22semidirect
140. #2552C22semidirect
141. #2550C22semidirect
142. #2550C22semidirect
147. #2520C22semidirect
148. #2508C22semidirect
149. #2507C22semidirect
150. #2497C22semidirect
151. #2473C22semidirect
152. #2473C22semidirect
155. #2465C22semidirect
156. #2462C22semidirect
157. #2462C22semidirect
162. #2446C22semidirect
166. #2442C22semidirect
167. #2442C22semidirect
173. #2441C22semidirect
174. #2441C22semidirect
178. #2440C22semidirect
179. #2440C22semidirect
180. #2440C22semidirect
182. #2439C22semidirect
183. #2439C22semidirect
193. #2417C22semidirect
208. #2331C22semidirect
209. #2330C22semidirect
222. #2317C22semidirect
224. #2316C22semidirect
229. C4×C4⋊Q8C22semidirect
230. C4×#125C22semidirect
237. #2285C22semidirect
238. C2×#384C22semidirect
264. #525Q8semidirect

Maximal subgroups

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

subgroupindex
#517912
#517882
#515972
#515942
#470242
#468482
#464332
#389662
#389652
#389612
#389602
#378782
#378742
#376912
#376872
#374812
#374772
#374272
#373102
#373092
#353332
#352822
#352802
#352532
#343622
#340652