Finite Group Databasebeta

← #7710086

Subgroups — #7710086

Order 512.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59925C212yesmaximal, complemented
2#59872C212yesmaximal, complemented
3#59671C212yesmaximal, complemented
4#59587C212yesmaximal, complemented
5#46243C212yesmaximal, complemented
6#46242C212yesmaximal, complemented
7#46155C212yesmaximal, complemented
8#46009C212yesmaximal, complemented
9#39715C214yesmaximal, complemented
10#39683C212yesmaximal, complemented
11#39682C212yesmaximal, complemented
12#39647C214yesmaximal, complemented
13#39638C212yesmaximal, complemented
14#39622C212yesmaximal, complemented
15#39178C212yesmaximal
16#38963C212yesmaximal
17#38103C214yesmaximal
18#37561C211yesmaximal, characteristic
19#37561C211yesmaximal, characteristic
20#36752C212yesmaximal
21#36751C212yesmaximal
22#36640C211yesmaximal, characteristic
23#36635C211yesmaximal, characteristic
24#36519C212yesmaximal
25#36425C214yesmaximal
26#36425C212yesmaximal
27#35159C212yesmaximal
28#35013C212yesmaximal
29#34378C211yesmaximal, characteristic
30#34378C211yesmaximal, characteristic
31C2×C4×#125C211yesmaximal, characteristic
32C22×#125C2211yescharacteristic
33#2864C2211yescharacteristic
34#2864C2211yescharacteristic
35#2864C2212yes—
36#2864C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2855C2212yes—
48#2855C2212yes—
49#2855C2214yes—
50#2851C2212yes—
51#2851C2211yescharacteristic
52#2851C2211yescharacteristic
53#2851C2212yes—
54#2851C2212yes—
55#2851C2212yes—
56#2851C2214yes—
57#2845C2212yes—
58#2845C2212yes—
59#2844C2212yes—
60#2844C2212yes—
61#2806C2214yes—
62#2806C2214yes—
63#2805C2214yes—
64#2805C2214yes—
65#2802C2214yes—
66#2802C2214yes—
67#2802C2214yes—
68#2802C2214yes—
69#2802C2214yes—
70#2792C2214yes—
71#2792C2214yes—
72#2792C2214yes—
73#2792C2214yes—
74#2791C2214yes—
75#2791C2214yes—
76#2791C2214yes—
77#2791C2214yes—
78#2791C2214yes—
79#2774C2214yes—
80#2774C2214yes—
81#2774C2214yes—
82#2774C2214yes—
83#2774C2214yes—
84#2755C2214yes—
85#2755C2214yes—
86#2755C2214yes—
87#2755C2214yes—
88#2734C2214yes—
89#2726C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2713C2214yes—
93#2666C2214yes—
94#2666C2214yes—
95#2660C2212yes—
96#2660C2212yes—
97#2659C2212yes—
98#2659C2212yes—
99#2647C2212yes—
100#2647C2212yes—
101#2646C2214yes—
102#2646C2212yes—
103#2646C2212yes—
104#2627C2214yes—
105#2590C2214yes—
106#2590C2214yes—
107#2590C2214yes—
108#2590C2214yes—
109#2590C2214yes—
110#2588C2214yes—
111#2588C2214yes—
112#2588C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2586C2214yes—
116#2586C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2586C2214yes—
121#2585C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2585C2214yes—
125#2585C2214yes—
126#2585C2214yes—
127#2584C2212yes—
128#2584C2212yes—
129#2584C2214yes—
130#2584C2212yes—
131#2584C2212yes—
132#2570C2212yes—
133#2570C2212yes—
134#2569C2214yes—
135#2567C2212yes—
136#2552C2212yes—
137#2552C2212yes—
138#2550C2214yes—
139#2550C2212yes—
140#2550C2212yes—
141#2550C2212yes—
142#2550C2212yes—
143#2550C2212yes—
144#2550C2212yes—
145#2549C2214yes—
146#2546C2212yes—
147#2520C2214yes—
148#2520C2214yes—
149#2520C2214yes—
150#2520C2214yes—
151#2520C2214yes—
152#2511C2214yes—
153#2509C2212yes—
154#2509C2212yes—
155#2509C2212yes—
156#2509C2212yes—
157#2509C2214yes—
158#2509C2214yes—
159#2509C2214yes—
160#2508C2212yes—
161#2508C2214yes—
162#2508C2212yes—
163#2508C2212yes—
164#2508C2212yes—
165#2508C2214yes—
166#2507C2212yes—
167#2507C2212yes—
168#2507C2214yes—
169#2507C2214yes—
170#2507C2214yes—
171#2507C2214yes—
172#2506C2212yes—
173#2506C2212yes—
174#2506C2214yes—
175#2506C2214yes—
176#2462C2214yes—
177#2462C2214yes—
178#2462C2214yes—
179#2442C2214yes—
180#2442C2212yes—
181#2442C2212yes—
182#2440C2214yes—
183#2440C2212yes—
184#2440C2212yes—
185#2438C2214yes—
186#2438C2214yes—
187#2438C2214yes—
188#2438C2214yes—
189#2438C2214yes—
190#2438C2214yes—
191#2382C2212yes—
192#2382C2212yes—
193#2382C2212yes—
194#2382C2212yes—
195#2370C2212yes—
196#2370C2212yes—
197#2370C2212yes—
198#2370C2212yes—
199#2370C2212yes—
200#2370C2212yes—
201#2370C2214yes—
202#2370C2212yes—
203#2370C2214yes—
204#2370C2212yes—
205#2369C2212yes—
206#2369C2214yes—
207#2365C2212yes—
208#2355C2214yes—
209#2355C2212yes—
210#2355C2212yes—
211#2345C2212yes—
212#2345C2212yes—
213#2344C2212yes—
214#2344C2212yes—
215#2344C2214yes—
216#2344C2214yes—
217#2336C2214yes—
218#2336C2214yes—
219#2330C2212yes—
220#2330C2212yes—
221#2330C2212yes—
222#2330C2212yes—
223#2329C2214yes—
224#2317C2214yes—
225#2316C2212yes—
226#2316C2212yes—
227#2313C2212yes—
228#2313C2212yes—
229C4×C4⋊Q8C2211yescharacteristic
230C4×C4⋊Q8C2211yescharacteristic
231C4×#125C2212yes—
232C4×#125C2212yes—
233C4×#125C2212yes—
234C4×#125C2211yescharacteristic
235C4×#125C2212yes—
236C4×#125C2212yes—
237C4×#125C2211yescharacteristic
238C4×#125C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#125C2212yes—
242C4×#125C2212yes—
243C4×#125C2212yes—
244C4×#125C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×C22⋊Q8C2212yes—
247C4×C22⋊Q8C2214yes—
248#2296C2212yes—
249#2296C2212yes—
250#2296C2214yes—
251#2295C2212yes—
252#2295C2212yes—
253C2×#389C2211yescharacteristic
254C2×#389C2211yescharacteristic
255C2×#387C2212yes—
256C2×#387C2212yes—
257#2285C2211yescharacteristic
258#2285C2211yescharacteristic
259#2283C2211yescharacteristic
260#2283C2211yescharacteristic
261C2×#382C2211yescharacteristic
262C2×C4×C4⋊C4C2211yescharacteristic
263C2×C4×C4⋊C4C2212yes—
264C2×C4×C4⋊C4C2212yes—
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×C43C2211yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×#125Q8116yescomplemented
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2311yescharacteristic
276C2×#125C2312yes—
277C2×#125C2311yescharacteristic
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2314yes—
294C2×#117C2314yes—
295C2×#117C2314yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2312yes—
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314C22×C42C2311yescharacteristic
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
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#398C2314yes—
376#398C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2312yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#389C2312yes—
438#389C2311yescharacteristic
439#389C2312yes—
440#389C2311yescharacteristic
441#389C2311yescharacteristic
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2312yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
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#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
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#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#385C2314yes—
598#385C2314yes—
599#385C2312yes—
600#385C2314yes—
601#385C2314yes—
602#385C2312yes—
603#385C2312yes—
604#385C2314yes—
605#385C2314yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#384C2311yescharacteristic
610#384C2311yescharacteristic
611#384C2314yes—
612#384C2312yes—
613#384C2312yes—
614#384C2314yes—
615#384C2311yescharacteristic
616#384C2311yescharacteristic
617#384C2311yescharacteristic
618#384C2311yescharacteristic
619#384C2314yes—
620#383C2312yes—
621#383C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2311yescharacteristic
631#382C2311yescharacteristic
632#382C2312yes—
633#382C2312yes—
634#382C2314yes—
635#382C2314yes—
636#382C2311yescharacteristic
637#382C2311yescharacteristic
638#382C2312yes—
639#382C2312yes—
640#382C2311yescharacteristic
641#382C2311yescharacteristic
642#382C2314yes—
643#382C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2312yes—
647#381C2312yes—
648#380C2311yescharacteristic
649#380C2311yescharacteristic
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2314yes—
654#380C2314yes—
655#380C2311yescharacteristic
656#380C2311yescharacteristic
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719#376C2312yes—
720#376C2312yes—
721C2×#95C2312yes—
722C2×#95C2312yes—
723C2×#95C2312yes—
724C2×#95C2312yes—
725C2×#95C2312yes—
726C2×#95C2312yes—
727C43C2311yescharacteristic
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C22×Q8C2412yes—
736C22×Q8C2412yes—
737C22×Q8C2414yes—
738C22×Q8C2414yes—
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C4⋊Q8—42no—
751C4⋊Q8—44no—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754C4⋊Q8—48no—
755#125—28no—
756#125—48no—
757#125—42no—
758#125—44no—
759#125—42no—
760#125—44no—
761#125—44no—
762#125—44no—
763#125—44no—
764#125—48no—
765#125C2×Q8116yes—
766#125C2×Q8116yes—
767#125C2×Q8116yes—
768#125C2×Q8116yes—
769C22⋊Q8—44no—
770C22⋊Q8—44no—
771C22⋊Q8—48no—
772C22⋊Q8—48no—
773C4×Q8—28no—
774C4×Q8—44no—
775C4×Q8—48no—
776#117—48no—
777#117—44no—
778#117—44no—
779#117—48no—
780C2×C4⋊C4—42no—
781C2×C4⋊C4—42no—
782C2×C4⋊C4—44no—
783C2×C4⋊C4—44no—
784C2×C4⋊C4C2×Q818yes—
785C2×C4⋊C4C2×Q8116yes—
786C2×C4⋊C4C2×Q818yes—
787C2×C4⋊C4C2×Q8116yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C42—24no—
883C2×C42—42no—
884C2×C42—44no—
885C2×C42—42no—
886C2×C42—42no—
887C2×C42—42no—
888C2×C42—44no—
889C2×C42—42no—
890C2×C42C2×Q818yes—
891C2×C42C2411yescharacteristic
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
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#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017C24C2511yescharacteristic
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—42no—
1021C2×Q8—44no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—44no—
1025C2×Q8—42no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—42no—
1047C22×C4—41no—
1048C22×C4—41no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4C22×Q814yes—
1059C22×C4C22×Q814yes—
1060C22×C4C22×Q818yes—
1061C22×C4C22×Q814yes—
1062C22×C4C22×Q818yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2511yescharacteristic
1083C22×C4C2514yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2514yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—41no—
1165C4⋊C4—41no—
1166C4⋊C4—41no—
1167C4⋊C4—41no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4C22×Q8116yes—
1174C4⋊C4C22×Q818yes—
1175C4⋊C4C22×Q818yes—
1176C4⋊C4C22×Q8116yes—
1177C4⋊C4C22×Q8116yes—
1178C4⋊C4C22×Q8116yes—
1179C4⋊C4C22×Q818yes—
1180C4⋊C4C22×Q818yes—
1181C22⋊C4—24no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C42—22no—
1188C42—22no—
1189C42—22no—
1190C42—24no—
1191C42—24no—
1192C42—22no—
1193C42—28no—
1194C42—22no—
1195C42—22no—
1196C42—22no—
1197C42—22no—
1198C42—22no—
1199C42—24no—
1200C42—24no—
1201C42—44no—
1202C42—41no—
1203C42—41no—
1204C42—41no—
1205C42—41no—
1206C42—41no—
1207C42—41no—
1208C42—41no—
1209C42—44no—
1210C42—44no—
1211C42—41no—
1212C42—41no—
1213C42—41no—
1214C42—41no—
1215C42—41no—
1216C42—41no—
1217C42—41no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42C22×Q814yes—
1229C42C22×Q814yes—
1230C42C22×Q814yes—
1231C42C22×Q814yes—
1232C422−1+414yes—
1233C23—21no—
1234C23—21no—
1235C23—21no—
1236C23—21no—
1237C23C23×Q812yes—
1238C23#58512yes—
1239C23#58512yes—
1240C23C2611yescharacteristic
1241Q8—84no—
1242Q8—84no—
1243Q8—88no—
1244Q8—164no—
1245C2×C4—28no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—24no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—24no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—28no—
1269C2×C4—216no—
1270C2×C4—28no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—44no—
1326C2×C4—48no—
1327C2×C4—44no—
1328C2×C4—44no—
1329C2×C4—44no—
1330C2×C4—84no—
1331C2×C4—84no—
1332C2×C4C23×Q812yes—
1333C2×C4C23×Q812yes—
1334C2×C4C23×Q812yes—
1335C2×C4C23×Q812yes—
1336C2×C4C23×Q812yes—
1337C2×C4C23×Q818yes—
1338C2×C4C23×Q818yes—
1339C2×C4C23×Q812yes—
1340C2×C4C2×2−1+412yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4#58512yes—
1344C2×C4#58512yes—
1345C2×C4#58512yes—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22#350414yes—
1353C22C24×Q811yescharacteristic
1354C22C22×2−1+411yescharacteristic
1355C22C2×#58511yescharacteristic
1356C22C2×#58511yescharacteristic
1357C22C2×#58511yescharacteristic
1358C22C2×#58511yescharacteristic
1359C22C2×#58511yescharacteristic
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—28no—
1364C4—22no—
1365C4—28no—
1366C4—22no—
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—42no—
1372C4—41no—
1373C4—41no—
1374C4—44no—
1375C4—44no—
1376C4—42no—
1377C4—44no—
1378C4—41no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—44no—
1384C4—41no—
1385C4—44no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4#350214yes—
1390C2—24no—
1391C2#6274311yescharacteristic
1392C2#6275211yescharacteristic
1393C2C2×#350211yescharacteristic
1394C2C2×#350411yescharacteristic
1395C2#6281311yescharacteristic
1396C2#6282511yescharacteristic
1397C2#6282811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59925C2semidirect
2. #59872C2semidirect
3. #59671C2semidirect
4. #59587C2semidirect
5. #46243C2semidirect
6. #46242C2semidirect
7. #46155C2semidirect
8. #46009C2semidirect
9. #39715C2semidirect
10. #39683C2semidirect
11. #39682C2semidirect
12. #39647C2semidirect
13. #39638C2semidirect
14. #39622C2semidirect
272. C2×#125Q8semidirect

Maximal subgroups

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

subgroupindex
#599252
#598722
#596712
#595872
#462432
#462422
#461552
#460092
#397152
#396832
#396822
#396472
#396382
#396222
#391782
#389632
#381032
#375612
#367522
#367512
#366402
#366352
#365192
#364252
#351592
#350132
#343782
C2×C4×#1252