Finite Group Databasebeta

← #8157148

Subgroups — #8157148

Order 512.

3884 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59663C212yesmaximal
2#59333C212yesmaximal
3#58404C214yesmaximal, complemented
4#58039C214yesmaximal, complemented
5#56010C214yesmaximal, complemented
6#54322C214yesmaximal, complemented
7#53143C212yesmaximal, complemented
8#52996C212yesmaximal, complemented
9#52817C214yesmaximal
10#45414C212yesmaximal, complemented
11#45363C212yesmaximal, complemented
12#42821C212yesmaximal, complemented
13#42782C212yesmaximal, complemented
14#42600C212yesmaximal, complemented
15#42511C212yesmaximal, complemented
16#40841C214yesmaximal
17#39541C212yesmaximal
18#39512C211yesmaximal, characteristic
19#39512C212yesmaximal
20#39496C211yesmaximal, characteristic
21#38069C212yesmaximal
22#38066C212yesmaximal
23#37466C212yesmaximal
24#36751C212yesmaximal
25#36564C211yesmaximal, characteristic
26#36552C211yesmaximal, characteristic
27#35015C211yesmaximal, characteristic
28C2×#2509C211yesmaximal, characteristic
29#34595C211yesmaximal, characteristic
30#2857C2211yescharacteristic
31#2857C2212yes—
32#2857C2211yescharacteristic
33#2855C2212yes—
34#2851C2212yes—
35#2844C2214yes—
36#2839C2214yes—
37#2839C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2839C2214yes—
43#2833C2214yes—
44#2833C2214yes—
45#2833C2214yes—
46#2833C2214yes—
47#2810C2214yes—
48#2810C2212yes—
49#2809C2214yes—
50#2806C2212yes—
51#2806C2214yes—
52#2805C2214yes—
53#2805C2212yes—
54#2805C2212yes—
55#2802C2214yes—
56#2802C2214yes—
57#2802C2214yes—
58#2802C2214yes—
59#2792C2214yes—
60#2776C2214yes—
61#2776C2214yes—
62#2776C2214yes—
63#2776C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2774C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2769C2214yes—
73#2769C2214yes—
74#2767C2214yes—
75#2767C2214yes—
76#2766C2214yes—
77#2766C2214yes—
78#2766C2214yes—
79#2762C2214yes—
80#2762C2214yes—
81#2762C2214yes—
82#2762C2214yes—
83#2758C2214yes—
84#2758C2214yes—
85#2758C2214yes—
86#2758C2214yes—
87#2758C2214yes—
88#2755C2214yes—
89#2755C2214yes—
90#2755C2214yes—
91#2726C2214yes—
92#2719C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2719C2214yes—
96#2713C2214yes—
97#2666C2212yes—
98#2666C2212yes—
99#2666C2212yes—
100#2666C2212yes—
101#2666C2214yes—
102#2666C2214yes—
103#2659C2211yescharacteristic
104#2659C2211yescharacteristic
105#2655C2214yes—
106#2655C2214yes—
107#2655C2214yes—
108#2647C2212yes—
109#2647C2212yes—
110#2646C2212yes—
111#2646C2212yes—
112#2645C2214yes—
113#2645C2212yes—
114#2645C2212yes—
115#2634C2214yes—
116#2634C2214yes—
117#2627C2212yes—
118#2627C2211yescharacteristic
119#2627C2211yescharacteristic
120#2627C2212yes—
121#2627C2212yes—
122#2627C2212yes—
123#2606C2214yes—
124#2590C2214yes—
125#2590C2214yes—
126#2590C2214yes—
127#2588C2214yes—
128#2588C2214yes—
129#2586C2214yes—
130#2584C2214yes—
131#2584C2212yes—
132#2584C2212yes—
133#2582C2212yes—
134#2581C2212yes—
135#2581C2214yes—
136#2581C2212yes—
137#2571C2212yes—
138#2570C2212yes—
139#2570C2212yes—
140#2570C2212yes—
141#2570C2214yes—
142#2568C2211yescharacteristic
143#2567C2211yescharacteristic
144#2552C2211yescharacteristic
145#2551C2211yescharacteristic
146#2550C2212yes—
147#2549C2214yes—
148#2549C2214yes—
149#2533C2214yes—
150#2528C2214yes—
151#2528C2214yes—
152#2524C2214yes—
153#2524C2214yes—
154#2514C2212yes—
155#2514C2212yes—
156#2514C2212yes—
157#2514C2214yes—
158#2514C2212yes—
159#2511C2212yes—
160#2511C2212yes—
161#2511C2212yes—
162#2509C2212yes—
163#2509C2212yes—
164#2509C2212yes—
165#2509C2212yes—
166#2509C2212yes—
167#2509C2214yes—
168#2509C2214yes—
169#2509C2212yes—
170#2509C2212yes—
171#2508C2212yes—
172#2508C2212yes—
173#2507C2212yes—
174#2507C2212yes—
175#2507C2212yes—
176#2507C2212yes—
177#2506C2212yes—
178#2506C2212yes—
179#2506C2212yes—
180#2505C2214yes—
181#2505C2214yes—
182#2503C2214yes—
183#2503C2212yes—
184#2502C2212yes—
185#2493C2214yes—
186#2493C2214yes—
187#2493C2214yes—
188#2493C2214yes—
189#2493C2214yes—
190#2493C2214yes—
191#2484C2214yes—
192#2473C2214yes—
193#2473C2214yes—
194#2462C2214yes—
195#2462C2214yes—
196#2453C2212yes—
197#2453C2212yes—
198#2453C2214yes—
199#2453C2212yes—
200#2451C2212yes—
201#2451C2212yes—
202#2451C2212yes—
203#2451C2212yes—
204#2446C2212yes—
205#2446C2214yes—
206#2446C2212yes—
207#2442C2212yes—
208#2442C2214yes—
209#2440C2212yes—
210#2438C2214yes—
211#2438C2214yes—
212#2438C2214yes—
213#2402C2212yes—
214#2402C2212yes—
215#2399C2212yes—
216#2399C2212yes—
217C2×#400C2212yes—
218C2×#400C2212yes—
219#2369C2211yescharacteristic
220#2369C2212yes—
221#2365C2212yes—
222#2365C2211yescharacteristic
223#2360C2214yes—
224#2360C2212yes—
225#2360C2212yes—
226#2356C2212yes—
227#2355C2212yes—
228#2355C2212yes—
229#2351C2212yes—
230Q8×C4⋊C4C2211yescharacteristic
231Q8×C4⋊C4C2211yescharacteristic
232#2345C2212yes—
233#2344C2212yes—
234#2343C2214yes—
235#2331C2212yes—
236#2330C2212yes—
237#2329C2212yes—
238#2320C2212yes—
239#2320C2212yes—
240#2316C2212yes—
241#2313C2212yes—
242#2313C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2211yescharacteristic
246C4×C22⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C2×#389C2211yescharacteristic
250C2×#389C2211yescharacteristic
251C2×#389C2212yes—
252C2×#389C2211yescharacteristic
253C2×#389C2211yescharacteristic
254C2×#387C2212yes—
255#2283C2212yes—
256C2×#382C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×#125C2312yes—
264C2×#125C2314yes—
265C2×#125C2312yes—
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2311yescharacteristic
270C2×C22⋊Q8C2311yescharacteristic
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2312yes—
283C2×#117C2314yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2312yes—
298#401C2314yes—
299#401C2314yes—
300#401C2314yes—
301#401C2314yes—
302#401C2314yes—
303#401C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
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#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2312yes—
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#400C2312yes—
354#400C2312yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
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#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2312yes—
408#398C2312yes—
409#398C2312yes—
410#398C2312yes—
411#398C2314yes—
412#398C2312yes—
413#398C2312yes—
414#398C2314yes—
415#395C2314yes—
416#395C2312yes—
417#395C2312yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2312yes—
429#395C2312yes—
430#395C2312yes—
431#395C2314yes—
432#395C2312yes—
433#395C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2312yes—
450#391C2314yes—
451#391C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2311yescharacteristic
460#391C2311yescharacteristic
461#391C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#389C2311yescharacteristic
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
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#387C2312yes—
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#387C2312yes—
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#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2314yes—
611#385C2312yes—
612#385C2314yes—
613#385C2314yes—
614#384C2312yes—
615#384C2311yescharacteristic
616#384C2312yes—
617#384C2312yes—
618#384C2312yes—
619#384C2311yescharacteristic
620#383C2314yes—
621#383C2314yes—
622#383C2314yes—
623#383C2314yes—
624#383C2314yes—
625#383C2314yes—
626#383C2314yes—
627#383C2312yes—
628#383C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2314yes—
634#382C2314yes—
635#382C2312yes—
636#382C2314yes—
637#382C2314yes—
638#382C2314yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2312yes—
649#381C2312yes—
650#380C2312yes—
651#380C2311yescharacteristic
652#380C2312yes—
653#380C2311yescharacteristic
654#380C2314yes—
655#380C2312yes—
656#380C2312yes—
657#380C2314yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700#376C2312yes—
701#376C2312yes—
702#376C2314yes—
703C2×#95C2311yescharacteristic
704C2×#95C2312yes—
705C2×#95C2311yescharacteristic
706C2×#95C2312yes—
707C2×#95C2312yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C22×Q8C2412yes—
713C22×Q8C2411yescharacteristic
714C22×Q8C2411yescharacteristic
715C22×Q8C2414yes—
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C23×C4C2411yescharacteristic
719C23×C4C2412yes—
720C23×C4C2412yes—
721C23×C4C2411yescharacteristic
722C23×C4C2412yes—
723C23×C4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2411yescharacteristic
726C23×C4C2411yescharacteristic
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C4⋊Q8—28no—
730C4⋊Q8—42no—
731C4⋊Q8—42no—
732C4⋊Q8—82no—
733#125—44no—
734#125—82no—
735#125—84no—
736#125—84no—
737#125—84no—
738C22⋊Q8—28no—
739C22⋊Q8—24no—
740C22⋊Q8—24no—
741C22⋊Q8—44no—
742C22⋊Q8—44no—
743C22⋊Q8—48no—
744C4×Q8—28no—
745C4×Q8—44no—
746C4×Q8—42no—
747C4×Q8—42no—
748C4×Q8—44no—
749C4×Q8—44no—
750C4×Q8—82no—
751C4×Q8—82no—
752C4×Q8—84no—
753#117—48no—
754C2×C4⋊C4—24no—
755C2×C4⋊C4—24no—
756C2×C4⋊C4—28no—
757C2×C4⋊C4—24no—
758C2×C4⋊C4—24no—
759C2×C4⋊C4—42no—
760C2×C4⋊C4—44no—
761C2×C4⋊C4—42no—
762C2×C4⋊C4—82no—
763C2×C4⋊C4—82no—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C42—24no—
855C2×C42—42no—
856C2×C42—42no—
857C2×C42—82no—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2411yescharacteristic
883C2×C42C2411yescharacteristic
884#95C2414yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
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#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980C24C2511yescharacteristic
981C2×Q8—24no—
982C2×Q8—22no—
983C2×Q8—22no—
984C2×Q8—24no—
985C2×Q8—28no—
986C2×Q8—24no—
987C2×Q8—41no—
988C2×Q8—41no—
989C2×Q8—41no—
990C2×Q8—41no—
991C2×Q8—42no—
992C2×Q8—44no—
993C2×Q8—44no—
994C2×Q8—42no—
995C2×Q8—42no—
996C2×Q8—42no—
997C2×Q8—42no—
998C2×Q8—42no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—22no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—22no—
1009C22×C4—24no—
1010C22×C4—22no—
1011C22×C4—24no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—24no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—42no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—41no—
1024C22×C4—42no—
1025C22×C4—41no—
1026C22×C4—42no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C42−1+414yes—
1031C22×C42−1+414yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2512yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—24no—
1070C4⋊C4—22no—
1071C4⋊C4—28no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—41no—
1105C4⋊C4—41no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—41no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C42−1+414yes—
1144C22⋊C4—28no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C42—24no—
1151C42—24no—
1152C42—24no—
1153C42—28no—
1154C42—24no—
1155C42—24no—
1156C42—22no—
1157C42—22no—
1158C42—24no—
1159C42—24no—
1160C42—41no—
1161C42—41no—
1162C42—42no—
1163C42—42no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23C2×2−1+412yes—
1181C23C2×2−1+412yes—
1182C23#58512yes—
1183C23C2611yescharacteristic
1184Q8—44no—
1185Q8—44no—
1186Q8—48no—
1187Q8—88no—
1188Q8—84no—
1189Q8—162no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—28no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
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—21no—
1268C2×C4—44no—
1269C2×C4—48no—
1270C2×C4—44no—
1271C2×C4—48no—
1272C2×C4—82no—
1273C2×C4—84no—
1274C2×C4—82no—
1275C2×C4—84no—
1276C2×C4—82no—
1277C2×C4—82no—
1278C2×C4C2×2−1+412yes—
1279C2×C4C2×2−1+414yes—
1280C2×C4C2×2−1+412yes—
1281C2×C4C2×2−1+412yes—
1282C2×C4C2×2−1+412yes—
1283C2×C4C2×2−1+412yes—
1284C2×C4#58512yes—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22#355514yes—
1292C22C22×2−1+411yescharacteristic
1293C22C22×2−1+411yescharacteristic
1294C22C22×2−1+411yescharacteristic
1295C22C2×#58511yescharacteristic
1296C22C2×#58511yescharacteristic
1297C22H(7,𝔽2)11yescharacteristic
1298C222−1+611yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—24no—
1303C4—44no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—44no—
1312C4—42no—
1313C4—42no—
1314C4—41no—
1315C4—42no—
1316C4—41no—
1317C4—42no—
1318C4—42no—
1319C4—44no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—44no—
1325C4—42no—
1326C4#356314yes—
1327C2—24no—
1328C2C2×#356311yescharacteristic
1329C2C2×#355511yescharacteristic
1330C2#6287911yescharacteristic
1331C2#6290211yescharacteristic
1332C2#6291111yescharacteristic
1333C2#6294711yescharacteristic
1334C2#6294811yescharacteristic
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
3. #58404C2semidirect
4. #58039C2semidirect
5. #56010C2semidirect
6. #54322C2semidirect
7. #53143C2semidirect
8. #52996C2semidirect
10. #45414C2semidirect
11. #45363C2semidirect
12. #42821C2semidirect
13. #42782C2semidirect
14. #42600C2semidirect
15. #42511C2semidirect

Maximal subgroups

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

subgroupindex
#596632
#593332
#584042
#580392
#560102
#543222
#531432
#529962
#528172
#454142
#453632
#428212
#427822
#426002
#425112
#408412
#395412
#395122
#394962
#380692
#380662
#374662
#367512
#365642
#365522
#350152
C2×#25092
#345952