Finite Group Databasebeta

← #7657607

Subgroups — #7657607

Order 512.

4449 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41782C214yesmaximal, complemented
2#41775C214yesmaximal, complemented
3#41257C214yesmaximal, complemented
4#41203C214yesmaximal, complemented
5#40792C214yesmaximal, complemented
6#40775C214yesmaximal, complemented
7#39552C212yesmaximal, complemented
8#39547C212yesmaximal, complemented
9#39494C211yesmaximal, characteristic, complemented
10#39483C211yesmaximal, characteristic, complemented
11#38914C212yesmaximal, complemented
12#38266C212yesmaximal, complemented
13#38260C212yesmaximal, complemented
14#37571C212yesmaximal, complemented
15#37508C212yesmaximal, complemented
16#37502C212yesmaximal, complemented
17#36573C211yesmaximal, characteristic, complemented
18#36567C211yesmaximal, characteristic, complemented
19#36372C212yesmaximal, complemented
20#35775C214yesmaximal, complemented
21#35721C214yesmaximal, complemented
22#35336C211yesmaximal, characteristic, complemented
23#35265C212yesmaximal, complemented
24#34621C211yesmaximal, characteristic, complemented
25#34621C212yesmaximal, complemented
26#34323C212yesmaximal, complemented
27#34151C211yesmaximal, characteristic, complemented
28C2×#553C2212yes—
29C2×#529C2211yescharacteristic
30#2864C2212yes—
31#2864C2212yes—
32#2859C2211yescharacteristic
33#2859C2211yescharacteristic
34#2859C2212yes—
35#2859C2212yes—
36#2851C2212yes—
37#2837C2214yes—
38#2836C2214yes—
39#2836C2214yes—
40#2831C2214yes—
41#2827C2214yes—
42#2826C2214yes—
43#2803C2214yes—
44#2802C2214yes—
45#2800C2214yes—
46#2797C2214yes—
47#2780C2214yes—
48#2779C2214yes—
49#2773C2214yes—
50#2773C2214yes—
51#2772C2214yes—
52#2772C2214yes—
53#2741C2214yes—
54#2739C2214yes—
55#2727C2214yes—
56#2723C2214yes—
57#2721C2214yes—
58#2721C2214yes—
59#2719C2214yes—
60#2714C2214yes—
61#2707C2214yes—
62#2707C2214yes—
63#2694C2214yes—
64#2686C2214yes—
65#2682C2214yes—
66#2671C2214yes—
67#2667C2214yes—
68#2664C2214yes—
69#2654C2214yes—
70#2652C2214yes—
71#2652C2214yes—
72#2651C2214yes—
73#2651C2214yes—
74#2651C2214yes—
75#2651C2214yes—
76#2650C2214yes—
77#2649C2214yes—
78#2648C2214yes—
79#2648C2214yes—
80#2648C2214yes—
81#2647C2212yes—
82#2647C2211yescharacteristic
83#2647C2212yes—
84#2647C2212yes—
85#2644C2212yes—
86#2644C2212yes—
87#2644C2212yes—
88#2641C2211yescharacteristic
89#2633C2214yes—
90#2630C2214yes—
91#2629C2211yescharacteristic
92#2629C2211yescharacteristic
93#2629C2212yes—
94#2629C2211yescharacteristic
95#2624C2212yes—
96#2624C2212yes—
97#2624C2212yes—
98#2623C2214yes—
99#2619C2212yes—
100#2619C2211yescharacteristic
101#2618C2214yes—
102#2611C2214yes—
103#2609C2214yes—
104#2606C2214yes—
105#2602C2214yes—
106#2600C2214yes—
107#2590C2214yes—
108#2590C2214yes—
109#2590C2214yes—
110#2587C2214yes—
111#2587C2214yes—
112#2587C2214yes—
113#2585C2214yes—
114#2584C2212yes—
115#2580C2212yes—
116#2580C2214yes—
117#2577C2214yes—
118#2573C2214yes—
119#2570C2212yes—
120#2566C2212yes—
121#2558C2214yes—
122#2558C2214yes—
123#2553C2214yes—
124#2553C2214yes—
125#2530C2214yes—
126#2530C2214yes—
127#2529C2214yes—
128#2522C2214yes—
129#2517C2214yes—
130#2515C2214yes—
131#2513C2212yes—
132#2512C2212yes—
133#2509C2214yes—
134#2509C2212yes—
135#2508C2214yes—
136#2507C2214yes—
137#2507C2212yes—
138#2506C2214yes—
139#2506C2212yes—
140#2506C2212yes—
141#2505C2214yes—
142#2505C2214yes—
143#2501C2212yes—
144#2500C2212yes—
145#2497C2212yes—
146#2495C2212yes—
147#2486C2212yes—
148#2485C2212yes—
149#2485C2214yes—
150#2478C2214yes—
151#2475C2214yes—
152#2475C2214yes—
153#2473C2214yes—
154#2473C2214yes—
155#2470C2214yes—
156#2470C2214yes—
157#2466C2214yes—
158#2466C2214yes—
159#2462C2214yes—
160#2460C2214yes—
161#2460C2214yes—
162#2456C2214yes—
163#2455C2214yes—
164#2455C2214yes—
165#2455C2214yes—
166#2454C2214yes—
167#2454C2214yes—
168#2454C2212yes—
169#2454C2212yes—
170#2442C2212yes—
171#2441C2214yes—
172#2441C2212yes—
173#2425C2214yes—
174#2422C2214yes—
175#2422C2212yes—
176#2420C2212yes—
177#2419C2214yes—
178#2416C2212yes—
179#2414C2212yes—
180#2395C2214yes—
181#2395C2214yes—
182#2395C2214yes—
183#2392C2214yes—
184#2392C2214yes—
185#2392C2214yes—
186#2374C2212yes—
187#2374C2212yes—
188#2373C2214yes—
189#2373C2212yes—
190#2373C2212yes—
191#2370C2212yes—
192#2370C2212yes—
193#2370C2214yes—
194#2367C2212yes—
195#2363C2212yes—
196#2363C2212yes—
197#2362C2212yes—
198#2361C2214yes—
199#2361C2212yes—
200#2359C2214yes—
201#2359C2214yes—
202#2352C2212yes—
203#2352C2214yes—
204#2349C2212yes—
205#2349C2214yes—
206#2346C2212yes—
207#2345C2212yes—
208#2343C2214yes—
209#2335C2214yes—
210#2334C2214yes—
211#2330C2211yescharacteristic
212#2330C2211yescharacteristic
213#2325C2214yes—
214#2317C2212yes—
215#2317C2212yes—
216#2317C2212yes—
217#2316C2212yes—
218#2314C2212yes—
219C4×#127C2211yescharacteristic
220C4×#127C2212yes—
221C4×#125C2212yes—
222C4×#125C2211yescharacteristic
223C4×#125C2212yes—
224C4×#121C2212yes—
225C4×#121C2212yes—
226C4×#121C2212yes—
227#2298C2212yes—
228#2296C2212yes—
229#2295C2211yescharacteristic
230#2293C2212yes—
231#2293C2212yes—
232#2293C2212yes—
233#2293C2211yescharacteristic
234#2293C2212yes—
235C2×#389C2212yes—
236#2290C2212yes—
237#2275C2214yes—
238C42×Q8C2211yescharacteristic
239C42×D4C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C4×#117C2212yes—
243#553—216no—
244C2×#127C2311yescharacteristic
245#529—28no—
246C2×#126C2314yes—
247C2×#126C2312yes—
248C2×#126C2314yes—
249C2×#125C2311yescharacteristic
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#125C2311yescharacteristic
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#124C2311yescharacteristic
259C2×#123C2314yes—
260C2×#123C2312yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2311yescharacteristic
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2311yescharacteristic
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2311yescharacteristic
296C2×#117C2314yes—
297C2×#117C2314yes—
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C42C2311yescharacteristic
302C22×C42C2312yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#395C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#393C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#391C2312yes—
408#390C2312yes—
409#390C2312yes—
410#390C2314yes—
411#390C2314yes—
412#390C2312yes—
413#390C2314yes—
414#390C2312yes—
415#390C2312yes—
416#390C2314yes—
417#390C2314yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#389C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
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#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2312yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2312yes—
490#388C2314yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2312yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
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#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2314yes—
546#387C2312yes—
547#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#386C2312yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2312yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2312yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2312yes—
583#384C2312yes—
584#384C2311yescharacteristic
585#384C2312yes—
586#384C2312yes—
587#384C2314yes—
588#384C2311yescharacteristic
589#384C2311yescharacteristic
590#383C2314yes—
591#382C2312yes—
592#382C2312yes—
593#382C2311yescharacteristic
594#382C2312yes—
595#382C2312yes—
596#382C2314yes—
597#382C2314yes—
598#382C2314yes—
599#382C2314yes—
600#381C2314yes—
601#381C2314yes—
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2312yes—
610#380C2312yes—
611#380C2314yes—
612#380C2314yes—
613#380C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2311yescharacteristic
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2311yescharacteristic
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2311yescharacteristic
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2311yescharacteristic
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664#376C2311yescharacteristic
665#376C2311yescharacteristic
666#376C2314yes—
667#376C2311yescharacteristic
668#376C2311yescharacteristic
669#376C2312yes—
670C2×#95C2314yes—
671C2×#95C2314yes—
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C43C2312yes—
675C43C2312yes—
676C22×Q8C2411yescharacteristic
677C22×D4C2412yes—
678C22×D4C2414yes—
679C22×D4C2414yes—
680C22×D4C2414yes—
681C22×D4C2412yes—
682C22×D4C2414yes—
683C22×D4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2412yes—
686C23×C4C2414yes—
687C23×C4C2411yescharacteristic
688C23×C4C2414yes—
689C23×C4C2414yes—
690C23×C4C2414yes—
691C23×C4C2412yes—
692C23×C4C2411yescharacteristic
693C23×C4C2414yes—
694C23×C4C2412yes—
695#127—24no—
696#126—216no—
697#126—28no—
698#126—84no—
699#125—24no—
700#125—28no—
701#125—24no—
702#125—48no—
703#125—42no—
704#125—42no—
705#125—84no—
706#125—84no—
707#125—84no—
708#124—24no—
709#123—28no—
710#123—216no—
711#123—48no—
712#123—84no—
713#123—84no—
714#123—84no—
715C22⋊Q8—24no—
716#121—24no—
717#121—216no—
718#121—28no—
719#121—28no—
720#121—44no—
721#121—84no—
722C4×Q8—24no—
723C4×Q8—44no—
724C4×D4—28no—
725C4×D4—216no—
726C4×D4—28no—
727C4×D4—44no—
728C4×D4—44no—
729C4×D4—48no—
730C4×D4—48no—
731C4×D4—44no—
732C4×D4—48no—
733C4×D4—84no—
734C4×D4—84no—
735C4×D4—84no—
736C4×D4—84no—
737C4×D4#4118yes—
738#117—28no—
739#117—28no—
740#117—28no—
741#117—24no—
742#117—42no—
743#117—48no—
744#117—44no—
745#117—44no—
746#117—84no—
747#117—84no—
748C2×C4⋊C4—28no—
749C2×C4⋊C4—44no—
750C2×C4⋊C4—84no—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C42—24no—
855C2×C42—44no—
856C2×C42C2412yes—
857C2×C42C2411yescharacteristic
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2411yescharacteristic
897#95C2412yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949C24C2514yes—
950C24C2511yescharacteristic
951C24C2512yes—
952C2×Q8—22no—
953C2×Q8—42no—
954C2×D4—28no—
955C2×D4—24no—
956C2×D4—28no—
957C2×D4—24no—
958C2×D4—28no—
959C2×D4—24no—
960C2×D4—24no—
961C2×D4—44no—
962C2×D4—42no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—42no—
973C2×D4C2×#4114yes—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—28no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—28no—
983C22×C4—28no—
984C22×C4—24no—
985C22×C4—28no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4C2×#4118yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2512yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2512yes—
1017C22×C4C2514yes—
1018C22×C4C2514yes—
1019C22×C4C2514yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—24no—
1037C4⋊C4—22no—
1038C4⋊C4—24no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—24no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4C2×#4114yes—
1088C22⋊C4—28no—
1089C22⋊C4—24no—
1090C22⋊C4—24no—
1091C22⋊C4—24no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—24no—
1095C22⋊C4—28no—
1096C22⋊C4—24no—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—24no—
1100C22⋊C4—24no—
1101C22⋊C4—42no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—42no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—42no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—44no—
1131C22⋊C4C2×#4118yes—
1132C42—22no—
1133C42—22no—
1134C42—22no—
1135C42—24no—
1136C42—28no—
1137C42—22no—
1138C42—24no—
1139C42—22no—
1140C42—24no—
1141C42—24no—
1142C42—28no—
1143C42—22no—
1144C42—24no—
1145C42—42no—
1146C42—42no—
1147C42—44no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—44no—
1152C42—44no—
1153C42—42no—
1154C42—44no—
1155C42—42no—
1156C42—42no—
1157C42—42no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42—44no—
1162C42C2×#4114yes—
1163C422−1+414yes—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—24no—
1171C23—21no—
1172C23—21no—
1173C23—24no—
1174C23—22no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—21no—
1179C23—24no—
1180C23—24no—
1181C23—22no—
1182C23C22×#4114yes—
1183C23C2611yescharacteristic
1184Q8—44no—
1185D4—44no—
1186D4—416no—
1187D4—416no—
1188D4—48no—
1189D4—88no—
1190D4—84no—
1191D4—88no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—216no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—44no—
1254C2×C4—44no—
1255C2×C4—82no—
1256C2×C4—88no—
1257C2×C4—88no—
1258C2×C4—84no—
1259C2×C4—88no—
1260C2×C4—88no—
1261C2×C4—84no—
1262C2×C4—164no—
1263C2×C4C22×#4114yes—
1264C2×C4C22×#4112yes—
1265C2×C4C22×#4112yes—
1266C2×C4C22×#4112yes—
1267C2×C4C2×2−1+414yes—
1268C2×C4C2×2−1+412yes—
1269C2×C4#58514yes—
1270C2×C4#58512yes—
1271C22—24no—
1272C22—24no—
1273C22—24no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—41no—
1279C22—44no—
1280C22—41no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—44no—
1287C22—42no—
1288C22—41no—
1289C22—44no—
1290C22C23×#4111yescharacteristic
1291C22C22×2−1+411yescharacteristic
1292C22C2×#58511yescharacteristic
1293C22C2×#58512yes—
1294C22H(7,𝔽2)12yes—
1295C4—24no—
1296C4—22no—
1297C4—24no—
1298C4—24no—
1299C4—22no—
1300C4—41no—
1301C4—41no—
1302C4—44no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—42no—
1310C4—42no—
1311C4—44no—
1312C4—42no—
1313C4—44no—
1314C4—44no—
1315C4—41no—
1316C4—44no—
1317C4—42no—
1318C4#351514yes—
1319C2—44no—
1320C2—81no—
1321C2—84no—
1322C2#6268611yescharacteristic
1323C2C2×#351511yescharacteristic
1324C2#6285811yescharacteristic
1325C2#6292612yes—
1326C2#6294112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41782C2semidirect
2. #41775C2semidirect
3. #41257C2semidirect
4. #41203C2semidirect
5. #40792C2semidirect
6. #40775C2semidirect
7. #39552C2semidirect
8. #39547C2semidirect
9. #39494C2semidirect
10. #39483C2semidirect
11. #38914C2semidirect
12. #38266C2semidirect
13. #38260C2semidirect
14. #37571C2semidirect
15. #37508C2semidirect
16. #37502C2semidirect
17. #36573C2semidirect
18. #36567C2semidirect
19. #36372C2semidirect
20. #35775C2semidirect
21. #35721C2semidirect
22. #35336C2semidirect
23. #35265C2semidirect
24. #34621C2semidirect
25. #34621C2semidirect
26. #34323C2semidirect
27. #34151C2semidirect

Maximal subgroups

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

subgroupindex
#417822
#417752
#412572
#412032
#407922
#407752
#395522
#395472
#394942
#394832
#389142
#382662
#382602
#375712
#375082
#375022
#365732
#365672
#363722
#357752
#357212
#353362
#352652
#346212
#343232
#341512