Finite Group Databasebeta

← #7709543

Subgroups — #7709543

Order 512.

4270 conjugacy classes of subgroups.

The subgroup lattice has 1416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59663C212yesmaximal
2#59425C212yesmaximal
3#59287C214yesmaximal
4#46346C212yesmaximal, complemented
5#46344C212yesmaximal, complemented
6#45959C212yesmaximal, complemented
7#45941C212yesmaximal, complemented
8#40215C212yesmaximal, complemented
9#40143C212yesmaximal, complemented
10#39752C211yesmaximal, characteristic
11#39703C212yesmaximal, complemented
12#39640C211yesmaximal, characteristic
13#39575C212yesmaximal, complemented
14#39512C211yesmaximal, characteristic
15#39368C211yesmaximal, characteristic
16#38719C214yesmaximal, complemented
17#37914C214yesmaximal
18#37886C212yesmaximal
19#37689C212yesmaximal
20#37466C212yesmaximal
21#37086C214yesmaximal, complemented
22#36635C211yesmaximal, characteristic
23C2×#2863C211yesmaximal, characteristic
24#36383C212yesmaximal, complemented
25#36313C212yesmaximal, complemented
26#36307C212yesmaximal
27#36279C212yesmaximal
28#35199C212yesmaximal, complemented
29#35115C212yesmaximal, complemented
30#34432C212yesmaximal
31C4×#533C211yesmaximal, characteristic
32C2×#544C2212yes—
33C2×#533C2211yescharacteristic
34#2864C2212yes—
35#2864C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2863C2212yes—
40#2863C2212yes—
41#2863C2212yes—
42#2863C2212yes—
43#2863C2212yes—
44#2863C2212yes—
45#2863C2212yes—
46#2863C2212yes—
47#2863C2212yes—
48#2862C2211yescharacteristic
49#2862C2212yes—
50#2859C2211yescharacteristic
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2855C2212yes—
54#2855C2212yes—
55#2851C2212yes—
56#2839C2214yes—
57#2833C2214yes—
58#2810C2212yes—
59#2809C2212yes—
60#2806C2212yes—
61#2806C2212yes—
62#2805C2212yes—
63#2805C2212yes—
64#2802C2214yes—
65#2799C2214yes—
66#2794C2214yes—
67#2791C2214yes—
68#2789C2214yes—
69#2776C2214yes—
70#2776C2214yes—
71#2776C2214yes—
72#2774C2214yes—
73#2769C2214yes—
74#2769C2214yes—
75#2767C2214yes—
76#2766C2214yes—
77#2766C2214yes—
78#2766C2214yes—
79#2762C2214yes—
80#2762C2214yes—
81#2758C2214yes—
82#2758C2214yes—
83#2758C2214yes—
84#2758C2214yes—
85#2758C2214yes—
86#2755C2214yes—
87#2734C2214yes—
88#2734C2212yes—
89#2726C2214yes—
90#2726C2212yes—
91#2713C2214yes—
92#2713C2214yes—
93#2713C2214yes—
94#2666C2214yes—
95#2666C2214yes—
96#2659C2212yes—
97#2655C2214yes—
98#2655C2214yes—
99#2646C2212yes—
100#2634C2214yes—
101#2634C2214yes—
102#2627C2212yes—
103#2627C2212yes—
104#2612C2214yes—
105#2605C2214yes—
106#2605C2214yes—
107#2590C2214yes—
108#2590C2214yes—
109#2588C2214yes—
110#2588C2214yes—
111#2586C2214yes—
112#2585C2214yes—
113#2584C2212yes—
114#2584C2214yes—
115#2582C2212yes—
116#2581C2212yes—
117#2581C2212yes—
118#2581C2212yes—
119#2570C2212yes—
120#2569C2214yes—
121#2568C2212yes—
122#2568C2212yes—
123#2565C2212yes—
124#2551C2212yes—
125#2549C2214yes—
126#2546C2212yes—
127#2546C2212yes—
128#2533C2214yes—
129#2533C2214yes—
130#2533C2214yes—
131#2533C2214yes—
132#2533C2214yes—
133#2533C2214yes—
134#2528C2214yes—
135#2528C2214yes—
136#2528C2214yes—
137#2528C2214yes—
138#2524C2214yes—
139#2524C2214yes—
140#2524C2214yes—
141#2524C2214yes—
142#2524C2214yes—
143#2520C2214yes—
144#2520C2214yes—
145#2520C2214yes—
146#2514C2212yes—
147#2514C2212yes—
148#2514C2212yes—
149#2514C2214yes—
150#2514C2212yes—
151#2511C2212yes—
152#2511C2212yes—
153#2509C2212yes—
154#2509C2212yes—
155#2508C2212yes—
156#2508C2214yes—
157#2506C2212yes—
158#2506C2212yes—
159#2506C2212yes—
160#2505C2214yes—
161#2505C2214yes—
162#2505C2214yes—
163#2503C2212yes—
164#2493C2214yes—
165#2493C2214yes—
166#2493C2214yes—
167#2493C2214yes—
168#2484C2214yes—
169#2473C2214yes—
170#2462C2214yes—
171#2462C2214yes—
172#2462C2214yes—
173#2462C2214yes—
174#2453C2212yes—
175#2453C2212yes—
176#2453C2212yes—
177#2451C2212yes—
178#2451C2212yes—
179#2451C2214yes—
180#2451C2212yes—
181#2446C2212yes—
182#2446C2212yes—
183#2446C2212yes—
184#2446C2212yes—
185#2446C2212yes—
186#2446C2212yes—
187#2446C2214yes—
188#2442C2212yes—
189#2440C2212yes—
190#2438C2214yes—
191#2438C2214yes—
192#2438C2214yes—
193#2434C2212yes—
194#2382C2214yes—
195#2381C2214yes—
196#2371C2214yes—
197#2371C2214yes—
198#2368C2214yes—
199#2365C2212yes—
200#2365C2214yes—
201#2365C2212yes—
202#2360C2212yes—
203#2360C2214yes—
204#2360C2212yes—
205#2356C2212yes—
206#2356C2214yes—
207#2351C2212yes—
208#2344C2212yes—
209#2344C2214yes—
210#2343C2214yes—
211#2343C2214yes—
212#2343C2214yes—
213Q8×C22⋊C4C2212yes—
214#2336C2214yes—
215#2336C2214yes—
216#2336C2214yes—
217#2331C2214yes—
218#2329C2212yes—
219#2329C2212yes—
220#2327C2214yes—
221#2320C2214yes—
222#2313C2212yes—
223C4×C4⋊Q8C2211yescharacteristic
224C4×C4⋊Q8C2211yescharacteristic
225C4×C4⋊Q8C2211yescharacteristic
226C4×C4⋊Q8C2211yescharacteristic
227C4×C4⋊Q8C2211yescharacteristic
228C4×C4⋊Q8C2212yes—
229C4×C4⋊Q8C2211yescharacteristic
230C4×#125C2212yes—
231C4×#125C2212yes—
232C4×#125C2212yes—
233C4×#125C2212yes—
234C4×C22⋊Q8C2212yes—
235C4×C22⋊Q8C2212yes—
236C4×C22⋊Q8C2212yes—
237C4×C22⋊Q8C2212yes—
238C4×C22⋊Q8C2211yescharacteristic
239C4×C22⋊Q8C2211yescharacteristic
240C4×C22⋊Q8C2211yescharacteristic
241C4×C22⋊Q8C2211yescharacteristic
242#2296C2212yes—
243#2295C2212yes—
244#2295C2212yes—
245#2295C2212yes—
246#2295C2212yes—
247#2295C2212yes—
248#2295C2211yescharacteristic
249#2295C2211yescharacteristic
250C2×#391C2211yescharacteristic
251C2×#391C2211yescharacteristic
252C2×#391C2211yescharacteristic
253C2×#389C2211yescharacteristic
254C2×#389C2211yescharacteristic
255C2×#389C2211yescharacteristic
256C2×#387C2212yes—
257C2×#387C2212yes—
258C2×#387C2212yes—
259#2285C2211yescharacteristic
260#2283C2212yes—
261C2×#383C2212yes—
262C42×Q8C2211yescharacteristic
263C42×Q8C2212yes—
264C42×Q8C2211yescharacteristic
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267C23×Q8C2311yescharacteristic
268#544—216no—
269#533—28no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2314yes—
307C2×#117C2314yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323#401C2314yes—
324#401C2314yes—
325#401C2314yes—
326#401C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
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#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
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#391C2311yescharacteristic
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2312yes—
412#391C2311yescharacteristic
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2311yescharacteristic
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2311yescharacteristic
466#389C2311yescharacteristic
467#389C2312yes—
468#389C2311yescharacteristic
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#387C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2312yes—
513#387C2314yes—
514#387C2312yes—
515#387C2314yes—
516#387C2312yes—
517#387C2312yes—
518#387C2312yes—
519#387C2312yes—
520#387C2312yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
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#387C2314yes—
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#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#385C2312yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2312yes—
617#384C2311yescharacteristic
618#384C2311yescharacteristic
619#384C2311yescharacteristic
620#384C2311yescharacteristic
621#384C2312yes—
622#383C2314yes—
623#383C2314yes—
624#383C2314yes—
625#383C2314yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#383C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2314yes—
640#382C2312yes—
641#382C2314yes—
642#382C2314yes—
643#382C2314yes—
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#381C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2314yes—
651#380C2311yescharacteristic
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2311yescharacteristic
659#380C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2311yescharacteristic
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2314yes—
712#376C2314yes—
713#376C2314yes—
714#376C2312yes—
715#376C2314yes—
716#376C2312yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C2×#95C2312yes—
720C2×#95C2312yes—
721C2×#95C2312yes—
722C2×#95C2312yes—
723C2×#95C2312yes—
724C2×#95C2312yes—
725C2×#95C2312yes—
726C43C2311yescharacteristic
727C43C2311yescharacteristic
728C43C2311yescharacteristic
729C43C2312yes—
730C43C2311yescharacteristic
731C43C2312yes—
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C22×Q8—24no—
737C22×Q8—42no—
738C22×Q8—42no—
739C22×Q8C2412yes—
740C22×Q8C2412yes—
741C22×Q8C2412yes—
742C22×Q8C2411yescharacteristic
743C22×Q8C2412yes—
744C22×Q8C2414yes—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2411yescharacteristic
758C4⋊Q8—24no—
759C4⋊Q8—216no—
760C4⋊Q8—24no—
761C4⋊Q8—216no—
762C4⋊Q8—42no—
763C4⋊Q8—44no—
764C4⋊Q8—42no—
765C4⋊Q8—44no—
766C4⋊Q8—44no—
767#125—28no—
768#125—216no—
769#125—216no—
770#125—28no—
771#125—44no—
772#125—48no—
773C22⋊Q8—24no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—28no—
777C22⋊Q8—216no—
778C22⋊Q8#4118yes—
779C4×Q8—24no—
780C4×Q8—24no—
781C4×Q8—28no—
782C4×Q8—28no—
783C4×Q8—42no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—42no—
787C4×Q8—42no—
788C4×Q8—42no—
789C4×Q8—48no—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795#117—28no—
796#117—28no—
797#117—216no—
798C2×C4⋊C4—28no—
799C2×C4⋊C4—24no—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—42no—
802C2×C4⋊C4—44no—
803C2×C4⋊C4—42no—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C42—24no—
885C2×C42—24no—
886C2×C42—24no—
887C2×C42—24no—
888C2×C42—42no—
889C2×C42—42no—
890C2×C42—42no—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027C24C2511yescharacteristic
1028C2×Q8—24no—
1029C2×Q8—22no—
1030C2×Q8—24no—
1031C2×Q8—28no—
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—42no—
1041C2×Q8—41no—
1042C2×Q8—41no—
1043C2×Q8—41no—
1044C2×Q8—41no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8—44no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—88no—
1052C2×Q8C2×#4114yes—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—24no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—22no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—41no—
1074C22×C4—41no—
1075C22×C4—41no—
1076C22×C4—41no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4C2×#4114yes—
1084C22×C42−1+414yes—
1085C22×C42−1+414yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—22no—
1127C4⋊C4—24no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—41no—
1162C4⋊C4—41no—
1163C4⋊C4—41no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4C2×#4114yes—
1189C4⋊C4C2×#4118yes—
1190C22⋊C4—28no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—28no—
1195C22⋊C4C2×#4118yes—
1196C42—22no—
1197C42—22no—
1198C42—22no—
1199C42—22no—
1200C42—24no—
1201C42—24no—
1202C42—28no—
1203C42—28no—
1204C42—22no—
1205C42—22no—
1206C42—22no—
1207C42—22no—
1208C42—22no—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—22no—
1220C42—22no—
1221C42—22no—
1222C42—22no—
1223C42—22no—
1224C42—22no—
1225C42—24no—
1226C42—24no—
1227C42—28no—
1228C42—24no—
1229C42—24no—
1230C42—41no—
1231C42—41no—
1232C42—41no—
1233C42—41no—
1234C42—41no—
1235C42—41no—
1236C42—42no—
1237C42—44no—
1238C42—42no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C422−1+414yes—
1246C23—21no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23C22×#4112yes—
1251C23C2×2−1+412yes—
1252C23C2×2−1+412yes—
1253C23C2611yescharacteristic
1254Q8—44no—
1255Q8—48no—
1256Q8—44no—
1257Q8—48no—
1258Q8—48no—
1259Q8—84no—
1260Q8—88no—
1261Q8—84no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—28no—
1285C2×C4—28no—
1286C2×C4—24no—
1287C2×C4—21no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—21no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—44no—
1341C2×C4—44no—
1342C2×C4—44no—
1343C2×C4—44no—
1344C2×C4—44no—
1345C2×C4—48no—
1346C2×C4—84no—
1347C2×C4—84no—
1348C2×C4—84no—
1349C2×C4C22×#4114yes—
1350C2×C4C22×#4114yes—
1351C2×C4C22×#4112yes—
1352C2×C4C22×#4112yes—
1353C2×C4C2×2−1+412yes—
1354C2×C4C2×2−1+412yes—
1355C2×C4C2×2−1+412yes—
1356C2×C4C2×2−1+412yes—
1357C2×C4C2×2−1+412yes—
1358C2×C4C2×2−1+412yes—
1359C2×C4C2×2−1+412yes—
1360C2×C4#58512yes—
1361C2×C4#58512yes—
1362C2×C4#58512yes—
1363C22—22no—
1364C22—22no—
1365C22—22no—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22#352314yes—
1370C22C23×#4111yescharacteristic
1371C22C22×2−1+411yescharacteristic
1372C22C22×2−1+411yescharacteristic
1373C22C22×2−1+411yescharacteristic
1374C22C2×#58511yescharacteristic
1375C22C2×#58511yescharacteristic
1376C22C2×#58511yescharacteristic
1377C4—22no—
1378C4—22no—
1379C4—22no—
1380C4—22no—
1381C4—24no—
1382C4—22no—
1383C4—22no—
1384C4—22no—
1385C4—24no—
1386C4—22no—
1387C4—22no—
1388C4—44no—
1389C4—44no—
1390C4—42no—
1391C4—42no—
1392C4—41no—
1393C4—44no—
1394C4—44no—
1395C4—42no—
1396C4—44no—
1397C4—44no—
1398C4—44no—
1399C4—41no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—41no—
1405C4—41no—
1406C4#356414yes—
1407C2—24no—
1408C2C2×#356411yescharacteristic
1409C2#6275211yescharacteristic
1410C2#6278111yescharacteristic
1411C2C2×#352311yescharacteristic
1412C2#6280511yescharacteristic
1413C2#6283711yescharacteristic
1414C2#6283711yescharacteristic
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
4. #46346C2semidirect
5. #46344C2semidirect
6. #45959C2semidirect
7. #45941C2semidirect
8. #40215C2semidirect
9. #40143C2semidirect
11. #39703C2semidirect
13. #39575C2semidirect
16. #38719C2semidirect
21. #37086C2semidirect
24. #36383C2semidirect
25. #36313C2semidirect
28. #35199C2semidirect
29. #35115C2semidirect

Maximal subgroups

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

subgroupindex
#596632
#594252
#592872
#463462
#463442
#459592
#459412
#402152
#401432
#397522
#397032
#396402
#395752
#395122
#393682
#387192
#379142
#378862
#376892
#374662
#370862
#366352
C2×#28632
#363832
#363132
#363072
#362792
#351992
#351152
#344322
C4×#5332