Finite Group Databasebeta

← #7895473

Subgroups — #7895473

Order 512.

4257 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic, complemented
2#59871C212yesmaximal, complemented
3#52287C211yesmaximal, characteristic, complemented
4#51598C214yesmaximal, complemented
5#48850C214yesmaximal, complemented
6#47972C214yesmaximal, complemented
7#46846C214yesmaximal, complemented
8#45795C212yesmaximal, complemented
9#45363C212yesmaximal, complemented
10#44950C212yesmaximal, complemented
11#44949C212yesmaximal, complemented
12#43146C214yesmaximal, complemented
13#42816C214yesmaximal, complemented
14#42496C212yesmaximal
15#42494C212yesmaximal
16#39973C212yesmaximal
17#39749C211yesmaximal, characteristic, complemented
18#39711C212yesmaximal, complemented
19#39680C212yesmaximal, complemented
20#39637C211yesmaximal, characteristic, complemented
21#39624C212yesmaximal, complemented
22#39176C212yesmaximal, complemented
23#37194C212yesmaximal, complemented
24#36477C211yesmaximal, characteristic
25#35934C212yesmaximal
26#35581C212yesmaximal
27#35176C211yesmaximal, characteristic
28#34487C212yesmaximal
29#34334C211yesmaximal, characteristic
30C2×D4×Q8C2211yescharacteristic
31#2864C2212yes—
32#2859C2211yescharacteristic
33#2857C2212yes—
34#2855C2212yes—
35#2855C2212yes—
36#2841C2214yes—
37#2841C2214yes—
38#2811C2212yes—
39#2811C2212yes—
40#2811C2211yescharacteristic
41#2809C2214yes—
42#2809C2212yes—
43#2809C2214yes—
44#2809C2212yes—
45#2806C2214yes—
46#2806C2214yes—
47#2806C2212yes—
48#2806C2211yescharacteristic
49#2806C2212yes—
50#2806C2211yescharacteristic
51#2806C2214yes—
52#2806C2214yes—
53#2806C2212yes—
54#2806C2214yes—
55#2806C2214yes—
56#2806C2212yes—
57#2805C2212yes—
58#2805C2212yes—
59#2802C2214yes—
60#2802C2214yes—
61#2802C2214yes—
62#2799C2214yes—
63#2799C2214yes—
64#2799C2214yes—
65#2799C2214yes—
66#2792C2212yes—
67#2792C2212yes—
68#2792C2212yes—
69#2792C2214yes—
70#2791C2214yes—
71#2790C2214yes—
72#2790C2214yes—
73#2788C2214yes—
74#2788C2214yes—
75#2774C2214yes—
76#2742C2214yes—
77#2734C2211yescharacteristic
78#2734C2212yes—
79#2734C2214yes—
80#2729C2214yes—
81#2729C2214yes—
82#2726C2212yes—
83#2726C2212yes—
84#2720C2214yes—
85#2720C2214yes—
86#2713C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2704C2214yes—
90#2704C2214yes—
91#2677C2214yes—
92#2667C2214yes—
93#2667C2214yes—
94#2665C2214yes—
95#2665C2214yes—
96#2660C2212yes—
97#2659C2214yes—
98#2647C2212yes—
99#2647C2212yes—
100#2629C2214yes—
101#2627C2214yes—
102#2608C2214yes—
103#2608C2214yes—
104#2590C2214yes—
105#2590C2214yes—
106#2590C2214yes—
107#2588C2214yes—
108#2588C2214yes—
109#2588C2214yes—
110#2587C2214yes—
111#2587C2214yes—
112#2586C2214yes—
113#2585C2214yes—
114#2585C2214yes—
115#2584C2212yes—
116#2584C2212yes—
117#2584C2212yes—
118#2584C2214yes—
119#2584C2214yes—
120#2582C2214yes—
121#2582C2214yes—
122#2581C2214yes—
123#2580C2212yes—
124#2574C2214yes—
125#2570C2212yes—
126#2570C2212yes—
127#2570C2212yes—
128#2570C2212yes—
129#2567C2212yes—
130#2567C2212yes—
131#2567C2214yes—
132#2567C2214yes—
133#2567C2212yes—
134#2567C2214yes—
135#2566C2212yes—
136#2565C2214yes—
137#2556C2214yes—
138#2556C2214yes—
139#2552C2212yes—
140#2552C2212yes—
141#2552C2211yescharacteristic
142#2552C2214yes—
143#2551C2212yes—
144#2551C2212yes—
145#2551C2212yes—
146#2550C2212yes—
147#2550C2212yes—
148#2549C2214yes—
149#2549C2214yes—
150#2546C2211yescharacteristic
151#2546C2212yes—
152#2542C2211yescharacteristic
153#2538C2212yes—
154#2538C2211yescharacteristic
155#2538C2211yescharacteristic
156#2538C2211yescharacteristic
157#2522C2214yes—
158#2522C2214yes—
159#2520C2214yes—
160#2509C2212yes—
161#2509C2212yes—
162#2508C2212yes—
163#2507C2212yes—
164#2507C2212yes—
165#2507C2212yes—
166#2507C2214yes—
167#2507C2212yes—
168#2506C2212yes—
169#2506C2212yes—
170#2497C2212yes—
171#2465C2214yes—
172#2465C2214yes—
173#2462C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2454C2212yes—
177#2453C2214yes—
178#2453C2214yes—
179#2453C2214yes—
180#2452C2212yes—
181#2452C2212yes—
182#2451C2214yes—
183#2451C2214yes—
184#2451C2214yes—
185#2446C2214yes—
186#2441C2214yes—
187#2440C2214yes—
188#2439C2214yes—
189#2438C2214yes—
190#2438C2214yes—
191#2438C2214yes—
192#2438C2214yes—
193#2429C2212yes—
194#2429C2212yes—
195#2429C2214yes—
196#2423C2212yes—
197#2399C2212yes—
198#2399C2212yes—
199#2399C2212yes—
200#2396C2214yes—
201#2378C2214yes—
202#2378C2214yes—
203#2370C2212yes—
204#2370C2212yes—
205#2369C2212yes—
206#2369C2212yes—
207#2369C2212yes—
208#2369C2212yes—
209#2369C2212yes—
210#2368C2214yes—
211#2365C2211yescharacteristic
212#2365C2214yes—
213#2365C2212yes—
214#2362C2214yes—
215#2360C2212yes—
216#2357C2212yes—
217#2357C2212yes—
218#2355C2211yescharacteristic
219#2355C2212yes—
220#2355C2212yes—
221#2355C2211yescharacteristic
222#2354C2212yes—
223Q8×C4⋊C4C2212yes—
224Q8×C4⋊C4C2211yescharacteristic
225#2349C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227Q8×C22⋊C4C2212yes—
228Q8×C22⋊C4C2214yes—
229#2332C2214yes—
230#2332C2214yes—
231#2331C2212yes—
232#2331C2212yes—
233#2331C2212yes—
234#2331C2212yes—
235#2330C2212yes—
236#2330C2212yes—
237#2329C2214yes—
238#2329C2214yes—
239#2323C2214yes—
240#2319C2212yes—
241#2319C2212yes—
242#2310C2214yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2211yescharacteristic
248C4×C4⋊Q8C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251#2295C2212yes—
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2295C2211yescharacteristic
255C2×#391C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C23×Q8C2312yes—
260D4×Q8Q8116yescomplemented
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×#117C2314yes—
308C2×#117C2314yes—
309C22×C4⋊C4C2312yes—
310C22×C42C2312yes—
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#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#398C2312yes—
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#398C2312yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
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#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2312yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2312yes—
402#395C2312yes—
403#395C2314yes—
404#395C2312yes—
405#395C2312yes—
406#395C2312yes—
407#395C2312yes—
408#395C2312yes—
409#395C2312yes—
410#395C2312yes—
411#395C2312yes—
412#395C2314yes—
413#395C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2311yescharacteristic
421#391C2312yes—
422#391C2314yes—
423#391C2311yescharacteristic
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2311yescharacteristic
453#391C2312yes—
454#391C2311yescharacteristic
455#391C2314yes—
456#391C2312yes—
457#391C2314yes—
458#391C2311yescharacteristic
459#391C2312yes—
460#391C2312yes—
461#391C2311yescharacteristic
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2311yescharacteristic
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2311yescharacteristic
541#389C2312yes—
542#389C2314yes—
543#389C2311yescharacteristic
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#384C2312yes—
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2312yes—
628#384C2312yes—
629#384C2311yescharacteristic
630#384C2314yes—
631#384C2314yes—
632#384C2314yes—
633#384C2312yes—
634#384C2311yescharacteristic
635#384C2312yes—
636#384C2312yes—
637#384C2311yescharacteristic
638#382C2314yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2312yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C43C2311yescharacteristic
712C43C2312yes—
713C22×Q8—82no—
714C22×Q8—82no—
715C22×Q8C2×Q8116yes—
716C22×Q8C2412yes—
717C22×Q8C2411yescharacteristic
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2411yescharacteristic
727C22×D4C2411yescharacteristic
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2414yes—
731C23×C4C2412yes—
732C23×C4C2414yes—
733C4⋊Q8—28no—
734C4⋊Q8—24no—
735C4⋊Q8—24no—
736C4⋊Q8—44no—
737C4⋊Q8—44no—
738C4⋊Q8—82no—
739C4⋊Q8—84no—
740C4⋊Q8—84no—
741C4⋊Q8—84no—
742C4⋊Q8C2×Q8116yes—
743C4⋊Q8C2×Q818yes—
744#125—28no—
745#125—44no—
746#125—84no—
747#125—84no—
748#125—84no—
749#125—84no—
750C22⋊Q8—28no—
751C22⋊Q8—82no—
752C22⋊Q8—82no—
753C22⋊Q8—84no—
754C22⋊Q8—82no—
755C22⋊Q8—84no—
756C22⋊Q8—82no—
757C22⋊Q8—84no—
758C22⋊Q8C2×Q8132yes—
759C22⋊Q8C2×Q8116yes—
760C4×Q8—24no—
761C4×Q8—44no—
762C4×Q8—44no—
763C4×Q8—42no—
764C4×Q8—42no—
765C4×Q8—82no—
766C4×Q8—82no—
767C4×Q8—84no—
768C4×Q8—84no—
769C4×Q8—84no—
770C4×Q8—84no—
771C4×Q8—82no—
772C4×Q8—82no—
773C4×Q8C2×Q818yes—
774C4×D4—24no—
775C4×D4—42no—
776C4×D4—44no—
777C4×D4C2×Q818yes—
778C4×D4C2×Q8116yes—
779#117—84no—
780#117—84no—
781C2×C4⋊C4—82no—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C42—82no—
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2411yescharacteristic
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995C24C2512yes—
996C2×Q8—24no—
997C2×Q8—22no—
998C2×Q8—22no—
999C2×Q8—24no—
1000C2×Q8—41no—
1001C2×Q8—42no—
1002C2×Q8—41no—
1003C2×Q8—42no—
1004C2×Q8—42no—
1005C2×Q8—44no—
1006C2×Q8—44no—
1007C2×Q8—42no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—42no—
1012C2×Q8—42no—
1013C2×Q8—44no—
1014C2×Q8—41no—
1015C2×Q8—41no—
1016C2×Q8—42no—
1017C2×Q8—42no—
1018C2×Q8—44no—
1019C2×Q8—44no—
1020C2×Q8—41no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—816no—
1026C2×Q8C22×Q814yes—
1027C2×Q8C22×Q8116yes—
1028C2×Q8C22×Q818yes—
1029C2×Q82−1+414yes—
1030C2×D4—22no—
1031C2×D4—22no—
1032C2×D4C22×Q814yes—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4C22×Q818yes—
1047C22×C4C22×Q8116yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2511yescharacteristic
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—41no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—41no—
1106C4⋊C4—41no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—41no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
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—41no—
1131C4⋊C4—41no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4C22×Q814yes—
1161C4⋊C4C22×Q818yes—
1162C4⋊C4C22×Q818yes—
1163C4⋊C4C22×Q814yes—
1164C4⋊C4C22×Q818yes—
1165C4⋊C4C22×Q8116yes—
1166C22⋊C4—24no—
1167C22⋊C4—28no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4C22×Q818yes—
1178C22⋊C4C22×Q8116yes—
1179C42—24no—
1180C42—22no—
1181C42—24no—
1182C42—22no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—41no—
1188C42—42no—
1189C42—42no—
1190C42—42no—
1191C42—42no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—41no—
1196C42—41no—
1197C42—42no—
1198C42—44no—
1199C42—44no—
1200C42—42no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42C22×Q814yes—
1209C42C22×Q818yes—
1210C422−1+414yes—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23C23×Q814yes—
1218C23C2611yescharacteristic
1219Q8—44no—
1220Q8—48no—
1221Q8—416no—
1222Q8—44no—
1223Q8—48no—
1224Q8—82no—
1225Q8—84no—
1226Q8—82no—
1227Q8—84no—
1228Q8—88no—
1229Q8—164no—
1230D4—28no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—48no—
1303C2×C4—416no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—164no—
1307C2×C4C23×Q814yes—
1308C2×C4C23×Q812yes—
1309C2×C4C23×Q812yes—
1310C2×C4C23×Q814yes—
1311C2×C4C23×Q814yes—
1312C2×C4C23×Q818yes—
1313C2×C4C23×Q812yes—
1314C2×C4C2×2−1+414yes—
1315C2×C4C2×2−1+412yes—
1316C2×C4C2×2−1+412yes—
1317C2×C4C2×2−1+412yes—
1318C2×C4C2×2−1+412yes—
1319C2×C4#58512yes—
1320C22—24no—
1321C22—24no—
1322C22—24no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22C24×Q811yescharacteristic
1328C22C22×2−1+411yescharacteristic
1329C22C22×2−1+411yescharacteristic
1330C22C2×#58511yescharacteristic
1331C22H(7,𝔽2)11yescharacteristic
1332C22H(7,𝔽2)11yescharacteristic
1333C22H(7,𝔽2)11yescharacteristic
1334C4—24no—
1335C4—22no—
1336C4—24no—
1337C4—22no—
1338C4—24no—
1339C4—28no—
1340C4—22no—
1341C4—22no—
1342C4—24no—
1343C4—22no—
1344C4—41no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4—44no—
1355C4—42no—
1356C4—42no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4#350214yes—
1362C2—44no—
1363C2C2×#350211yescharacteristic
1364C2#6284311yescharacteristic
1365C2#6288111yescharacteristic
1366C2#6290211yescharacteristic
1367C2#6294311yescharacteristic
1368C2Q8×2−1+411yescharacteristic
1369C2#6305111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59924C2semidirect
2. #59871C2semidirect
3. #52287C2semidirect
4. #51598C2semidirect
5. #48850C2semidirect
6. #47972C2semidirect
7. #46846C2semidirect
8. #45795C2semidirect
9. #45363C2semidirect
10. #44950C2semidirect
11. #44949C2semidirect
12. #43146C2semidirect
13. #42816C2semidirect
17. #39749C2semidirect
18. #39711C2semidirect
19. #39680C2semidirect
20. #39637C2semidirect
21. #39624C2semidirect
22. #39176C2semidirect
23. #37194C2semidirect
260. D4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#599242
#598712
#522872
#515982
#488502
#479722
#468462
#457952
#453632
#449502
#449492
#431462
#428162
#424962
#424942
#399732
#397492
#397112
#396802
#396372
#396242
#391762
#371942
#364772
#359342
#355812
#351762
#344872
#343342