Finite Group Databasebeta

← #7898065

Subgroups — #7898065

Order 512.

4253 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59668C212yesmaximal, complemented
3#52274C211yesmaximal, characteristic, complemented
4#51594C214yesmaximal, complemented
5#48846C214yesmaximal, complemented
6#47976C214yesmaximal, complemented
7#46437C214yesmaximal, complemented
8#45795C212yesmaximal, complemented
9#45280C212yesmaximal, complemented
10#44953C212yesmaximal, complemented
11#44949C212yesmaximal, complemented
12#43142C214yesmaximal, complemented
13#42818C214yesmaximal, complemented
14#42499C212yesmaximal
15#42497C212yesmaximal
16#39976C212yesmaximal
17#39749C212yesmaximal, complemented
18#39709C212yesmaximal, complemented
19#39626C212yesmaximal, complemented
20#39624C212yesmaximal, complemented
21#39621C211yesmaximal, characteristic, complemented
22#39621C211yesmaximal, characteristic, complemented
23#37194C212yesmaximal, complemented
24#36476C211yesmaximal, characteristic
25#35934C212yesmaximal
26#35580C212yesmaximal
27#35176C211yesmaximal, characteristic
28#34487C212yesmaximal
29#34334C211yesmaximal, characteristic
30C2×D4×Q8C2211yescharacteristic
31#2862C2211yescharacteristic
32#2859C2212yes—
33#2857C2212yes—
34#2855C2212yes—
35#2855C2212yes—
36#2841C2214yes—
37#2841C2214yes—
38#2811C2212yes—
39#2811C2212yes—
40#2809C2211yescharacteristic
41#2809C2214yes—
42#2809C2214yes—
43#2807C2214yes—
44#2807C2214yes—
45#2806C2214yes—
46#2806C2214yes—
47#2806C2212yes—
48#2806C2212yes—
49#2806C2212yes—
50#2806C2211yescharacteristic
51#2806C2212yes—
52#2806C2214yes—
53#2806C2214yes—
54#2806C2214yes—
55#2806C2212yes—
56#2806C2212yes—
57#2806C2214yes—
58#2805C2211yescharacteristic
59#2805C2214yes—
60#2802C2212yes—
61#2802C2214yes—
62#2799C2212yes—
63#2799C2214yes—
64#2799C2214yes—
65#2799C2214yes—
66#2799C2214yes—
67#2792C2214yes—
68#2792C2214yes—
69#2791C2212yes—
70#2791C2214yes—
71#2791C2214yes—
72#2774C2212yes—
73#2768C2214yes—
74#2768C2214yes—
75#2755C2212yes—
76#2755C2214yes—
77#2742C2214yes—
78#2734C2212yes—
79#2734C2212yes—
80#2729C2214yes—
81#2729C2214yes—
82#2726C2211yescharacteristic
83#2726C2214yes—
84#2726C2214yes—
85#2720C2214yes—
86#2720C2214yes—
87#2713C2212yes—
88#2713C2214yes—
89#2704C2214yes—
90#2704C2214yes—
91#2677C2214yes—
92#2667C2214yes—
93#2667C2214yes—
94#2667C2214yes—
95#2667C2214yes—
96#2660C2212yes—
97#2660C2212yes—
98#2660C2212yes—
99#2659C2214yes—
100#2628C2214yes—
101#2627C2214yes—
102#2607C2214yes—
103#2607C2214yes—
104#2590C2214yes—
105#2590C2214yes—
106#2589C2214yes—
107#2589C2214yes—
108#2588C2214yes—
109#2588C2214yes—
110#2586C2214yes—
111#2586C2214yes—
112#2585C2214yes—
113#2584C2214yes—
114#2584C2214yes—
115#2582C2214yes—
116#2582C2214yes—
117#2582C2214yes—
118#2580C2212yes—
119#2570C2212yes—
120#2570C2212yes—
121#2570C2212yes—
122#2570C2212yes—
123#2567C2212yes—
124#2567C2214yes—
125#2566C2212yes—
126#2565C2214yes—
127#2565C2214yes—
128#2563C2211yescharacteristic
129#2556C2214yes—
130#2556C2214yes—
131#2556C2214yes—
132#2552C2212yes—
133#2552C2212yes—
134#2552C2212yes—
135#2552C2212yes—
136#2552C2211yescharacteristic
137#2552C2212yes—
138#2551C2212yes—
139#2551C2212yes—
140#2551C2212yes—
141#2550C2212yes—
142#2550C2212yes—
143#2550C2214yes—
144#2550C2212yes—
145#2550C2212yes—
146#2550C2212yes—
147#2549C2214yes—
148#2549C2214yes—
149#2546C2214yes—
150#2546C2211yescharacteristic
151#2542C2212yes—
152#2542C2211yescharacteristic
153#2542C2211yescharacteristic
154#2538C2211yescharacteristic
155#2522C2214yes—
156#2522C2214yes—
157#2520C2214yes—
158#2511C2214yes—
159#2509C2212yes—
160#2508C2212yes—
161#2507C2212yes—
162#2507C2212yes—
163#2507C2212yes—
164#2507C2212yes—
165#2507C2212yes—
166#2507C2214yes—
167#2506C2212yes—
168#2506C2212yes—
169#2492C2212yes—
170#2465C2214yes—
171#2465C2214yes—
172#2462C2214yes—
173#2462C2214yes—
174#2462C2214yes—
175#2454C2212yes—
176#2454C2212yes—
177#2453C2214yes—
178#2453C2214yes—
179#2452C2212yes—
180#2451C2214yes—
181#2451C2214yes—
182#2451C2214yes—
183#2451C2214yes—
184#2451C2214yes—
185#2451C2214yes—
186#2441C2214yes—
187#2441C2214yes—
188#2440C2214yes—
189#2438C2214yes—
190#2438C2214yes—
191#2438C2214yes—
192#2438C2214yes—
193#2429C2212yes—
194#2423C2212yes—
195#2423C2214yes—
196#2423C2212yes—
197#2402C2212yes—
198#2402C2212yes—
199#2399C2212yes—
200#2396C2214yes—
201#2378C2214yes—
202#2378C2214yes—
203#2370C2214yes—
204#2370C2212yes—
205#2369C2211yescharacteristic
206#2369C2212yes—
207#2369C2212yes—
208#2369C2212yes—
209#2369C2212yes—
210#2368C2214yes—
211#2365C2211yescharacteristic
212#2365C2211yescharacteristic
213#2365C2212yes—
214#2365C2212yes—
215#2362C2214yes—
216#2360C2212yes—
217#2357C2212yes—
218#2357C2212yes—
219#2355C2211yescharacteristic
220#2355C2212yes—
221#2355C2212yes—
222#2355C2212yes—
223#2354C2212yes—
224Q8×C4⋊C4C2212yes—
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×#125C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251#2295C2211yescharacteristic
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2295C2212yes—
255C2×#391C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C23×Q8C2312yes—
260D4×Q8Q8116yescomplemented
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×#117C2314yes—
308C2×#117C2314yes—
309C22×C4⋊C4C2312yes—
310C22×C42C2312yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2312yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2312yes—
325#400C2312yes—
326#400C2312yes—
327#400C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#398C2312yes—
336#398C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2312yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2312yes—
408#395C2314yes—
409#395C2314yes—
410#395C2312yes—
411#395C2312yes—
412#395C2312yes—
413#395C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2311yescharacteristic
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2311yescharacteristic
463#391C2314yes—
464#391C2311yescharacteristic
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2311yescharacteristic
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2311yescharacteristic
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2314yes—
531#389C2314yes—
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2311yescharacteristic
537#389C2314yes—
538#389C2312yes—
539#389C2311yescharacteristic
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2314yes—
626#384C2314yes—
627#384C2312yes—
628#384C2312yes—
629#384C2314yes—
630#384C2312yes—
631#384C2312yes—
632#384C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#380C2312yes—
646#380C2312yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
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—
711C43C2312yes—
712C43C2311yescharacteristic
713C22×Q8—82no—
714C22×Q8—82no—
715C22×Q8C2×Q8116yes—
716C22×Q8C2412yes—
717C22×Q8C2411yescharacteristic
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2414yes—
721C22×Q8C2414yes—
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×D4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2414yes—
730C23×C4C2412yes—
731C23×C4C2414yes—
732C4⋊Q8—24no—
733C4⋊Q8—24no—
734C4⋊Q8—44no—
735C4⋊Q8—42no—
736C4⋊Q8—42no—
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—44no—
747#125—44no—
748#125—84no—
749#125—84no—
750#125—84no—
751#125—84no—
752C22⋊Q8—28no—
753C22⋊Q8—84no—
754C22⋊Q8—82no—
755C22⋊Q8—82no—
756C22⋊Q8—82no—
757C22⋊Q8—82no—
758C22⋊Q8—84no—
759C22⋊Q8—84no—
760C22⋊Q8C2×Q8132yes—
761C22⋊Q8C2×Q8116yes—
762C4×Q8—28no—
763C4×Q8—24no—
764C4×Q8—82no—
765C4×Q8—82no—
766C4×Q8—84no—
767C4×Q8—84no—
768C4×Q8—82no—
769C4×Q8—84no—
770C4×Q8—82no—
771C4×Q8—84no—
772C4×Q8C2×Q818yes—
773C4×D4—24no—
774C4×D4—44no—
775C4×D4—42no—
776C4×D4C2×Q818yes—
777C4×D4C2×Q8116yes—
778#117—84no—
779#117—84no—
780C2×C4⋊C4—82no—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C42—82no—
884C2×C42C2412yes—
885C2×C42C2411yescharacteristic
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2411yescharacteristic
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2411yescharacteristic
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
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#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995C24C2512yes—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—22no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—42no—
1002C2×Q8—42no—
1003C2×Q8—44no—
1004C2×Q8—44no—
1005C2×Q8—42no—
1006C2×Q8—41no—
1007C2×Q8—41no—
1008C2×Q8—42no—
1009C2×Q8—42no—
1010C2×Q8—44no—
1011C2×Q8—41no—
1012C2×Q8—42no—
1013C2×Q8—42no—
1014C2×Q8—44no—
1015C2×Q8—41no—
1016C2×Q8—44no—
1017C2×Q8—44no—
1018C2×Q8—44no—
1019C2×Q8—42no—
1020C2×Q8—44no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—816no—
1024C2×Q8C22×Q814yes—
1025C2×Q8C22×Q8116yes—
1026C2×Q8C22×Q818yes—
1027C2×D4—22no—
1028C2×D4—22no—
1029C2×D4C22×Q814yes—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4C22×Q818yes—
1044C22×C4C22×Q8116yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C4⋊C4—22no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—41no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
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—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—41no—
1120C4⋊C4—41no—
1121C4⋊C4—41no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
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—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4C22×Q814yes—
1156C4⋊C4C22×Q818yes—
1157C4⋊C4C22×Q818yes—
1158C4⋊C4C22×Q814yes—
1159C4⋊C4C22×Q818yes—
1160C4⋊C4C22×Q8116yes—
1161C4⋊C42−1+414yes—
1162C22⋊C4—24no—
1163C22⋊C4—28no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4C22×Q818yes—
1174C22⋊C4C22×Q8116yes—
1175C42—24no—
1176C42—24no—
1177C42—24no—
1178C42—24no—
1179C42—22no—
1180C42—24no—
1181C42—22no—
1182C42—24no—
1183C42—41no—
1184C42—42no—
1185C42—42no—
1186C42—42no—
1187C42—42no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—41no—
1192C42—42no—
1193C42—44no—
1194C42—42no—
1195C42—44no—
1196C42—41no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—44no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42C22×Q814yes—
1205C42C22×Q818yes—
1206C422−1+414yes—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23C23×Q814yes—
1214C23C2611yescharacteristic
1215Q8—44no—
1216Q8—48no—
1217Q8—416no—
1218Q8—48no—
1219Q8—82no—
1220Q8—84no—
1221Q8—84no—
1222Q8—88no—
1223Q8—164no—
1224Q8—162no—
1225D4—28no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—21no—
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—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
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—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—48no—
1298C2×C4—416no—
1299C2×C4—84no—
1300C2×C4—84no—
1301C2×C4—164no—
1302C2×C4C23×Q814yes—
1303C2×C4C23×Q812yes—
1304C2×C4C23×Q812yes—
1305C2×C4C23×Q814yes—
1306C2×C4C23×Q814yes—
1307C2×C4C23×Q818yes—
1308C2×C4C23×Q812yes—
1309C2×C4C2×2−1+414yes—
1310C2×C4C2×2−1+412yes—
1311C2×C4C2×2−1+412yes—
1312C2×C4C2×2−1+412yes—
1313C2×C4C2×2−1+412yes—
1314C2×C4#58512yes—
1315C22—24no—
1316C22—24no—
1317C22—24no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22C24×Q811yescharacteristic
1323C22C22×2−1+411yescharacteristic
1324C22C22×2−1+411yescharacteristic
1325C22C2×#58511yescharacteristic
1326C22H(7,𝔽2)11yescharacteristic
1327C22H(7,𝔽2)11yescharacteristic
1328C22H(7,𝔽2)11yescharacteristic
1329C4—24no—
1330C4—22no—
1331C4—22no—
1332C4—24no—
1333C4—28no—
1334C4—24no—
1335C4—22no—
1336C4—24no—
1337C4—22no—
1338C4—22no—
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—44no—
1343C4—44no—
1344C4—41no—
1345C4—42no—
1346C4—42no—
1347C4—42no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4#350214yes—
1357C2—44no—
1358C2C2×#350211yescharacteristic
1359C2#6284311yescharacteristic
1360C2#6288111yescharacteristic
1361C2#6294511yescharacteristic
1362C2#6296211yescharacteristic
1363C2Q8×2−1+411yescharacteristic
1364C2#6306011yescharacteristic
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. #59871C2semidirect
2. #59668C2semidirect
3. #52274C2semidirect
4. #51594C2semidirect
5. #48846C2semidirect
6. #47976C2semidirect
7. #46437C2semidirect
8. #45795C2semidirect
9. #45280C2semidirect
10. #44953C2semidirect
11. #44949C2semidirect
12. #43142C2semidirect
13. #42818C2semidirect
17. #39749C2semidirect
18. #39709C2semidirect
19. #39626C2semidirect
20. #39624C2semidirect
21. #39621C2semidirect
22. #39621C2semidirect
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
#598712
#596682
#522742
#515942
#488462
#479762
#464372
#457952
#452802
#449532
#449492
#431422
#428182
#424992
#424972
#399762
#397492
#397092
#396262
#396242
#396212
#371942
#364762
#359342
#355802
#351762
#344872
#343342