Finite Group Databasebeta

← #7657402

Subgroups — #7657402

Order 512.

4856 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42130C214yesmaximal, complemented
2#42123C214yesmaximal, complemented
3#41251C214yesmaximal, complemented
4#41210C214yesmaximal, complemented
5#40801C214yesmaximal, complemented
6#40767C214yesmaximal, complemented
7#39808C212yesmaximal, complemented
8#39739C211yesmaximal, characteristic, complemented
9#39718C212yesmaximal, complemented
10#39675C212yesmaximal, complemented
11#39622C211yesmaximal, characteristic, complemented
12#37799C212yesmaximal, complemented
13#37792C212yesmaximal, complemented
14#37625C212yesmaximal, complemented
15#37581C212yesmaximal, complemented
16#37572C212yesmaximal, complemented
17#36602C211yesmaximal, characteristic, complemented
18#36573C211yesmaximal, characteristic, complemented
19#36139C212yesmaximal, complemented
20#35721C214yesmaximal, complemented
21#35696C214yesmaximal, complemented
22#35332C211yesmaximal, characteristic, complemented
23#35300C212yesmaximal, complemented
24#34624C212yesmaximal, complemented
25#34621C211yesmaximal, characteristic, complemented
26#34331C212yesmaximal, complemented
27#34145C211yesmaximal, characteristic, complemented
28C2×#559C2212yes—
29C2×#541C2211yescharacteristic
30C2×#540C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#532C2212yes—
33C2×#529C2212yes—
34#2861C2212yes—
35#2859C2211yescharacteristic
36#2859C2212yes—
37#2858C2211yescharacteristic
38#2855C2212yes—
39#2854C2212yes—
40#2850C2212yes—
41#2838C2214yes—
42#2837C2214yes—
43#2832C2214yes—
44#2831C2214yes—
45#2829C2214yes—
46#2829C2214yes—
47#2806C2214yes—
48#2803C2214yes—
49#2803C2214yes—
50#2797C2214yes—
51#2792C2214yes—
52#2790C2214yes—
53#2742C2214yes—
54#2733C2214yes—
55#2731C2214yes—
56#2730C2214yes—
57#2725C2214yes—
58#2721C2214yes—
59#2720C2214yes—
60#2718C2214yes—
61#2718C2214yes—
62#2710C2214yes—
63#2710C2214yes—
64#2704C2214yes—
65#2696C2214yes—
66#2682C2214yes—
67#2682C2214yes—
68#2674C2214yes—
69#2672C2214yes—
70#2671C2214yes—
71#2665C2214yes—
72#2663C2214yes—
73#2662C2214yes—
74#2662C2214yes—
75#2661C2214yes—
76#2661C2214yes—
77#2660C2212yes—
78#2657C2212yes—
79#2654C2214yes—
80#2653C2214yes—
81#2653C2214yes—
82#2652C2214yes—
83#2651C2214yes—
84#2650C2214yes—
85#2649C2214yes—
86#2648C2214yes—
87#2647C2211yescharacteristic
88#2645C2212yes—
89#2644C2212yes—
90#2644C2212yes—
91#2642C2211yescharacteristic
92#2641C2211yescharacteristic
93#2641C2211yescharacteristic
94#2641C2212yes—
95#2640C2212yes—
96#2630C2214yes—
97#2630C2214yes—
98#2629C2211yescharacteristic
99#2624C2212yes—
100#2624C2214yes—
101#2620C2212yes—
102#2620C2214yes—
103#2620C2212yes—
104#2619C2212yes—
105#2619C2211yescharacteristic
106#2602C2214yes—
107#2600C2214yes—
108#2597C2214yes—
109#2594C2214yes—
110#2593C2214yes—
111#2592C2212yes—
112#2592C2212yes—
113#2587C2214yes—
114#2587C2214yes—
115#2586C2214yes—
116#2581C2212yes—
117#2580C2212yes—
118#2580C2214yes—
119#2576C2214yes—
120#2574C2214yes—
121#2559C2214yes—
122#2559C2214yes—
123#2558C2214yes—
124#2558C2214yes—
125#2558C2214yes—
126#2558C2214yes—
127#2552C2212yes—
128#2550C2212yes—
129#2550C2212yes—
130#2549C2214yes—
131#2548C2212yes—
132#2545C2212yes—
133#2544C2212yes—
134#2541C2212yes—
135#2538C2212yes—
136#2530C2214yes—
137#2529C2214yes—
138#2527C2214yes—
139#2526C2214yes—
140#2521C2214yes—
141#2507C2214yes—
142#2505C2214yes—
143#2477C2214yes—
144#2475C2214yes—
145#2475C2214yes—
146#2474C2214yes—
147#2470C2214yes—
148#2470C2214yes—
149#2468C2214yes—
150#2468C2214yes—
151#2466C2214yes—
152#2463C2214yes—
153#2461C2214yes—
154#2460C2214yes—
155#2459C2214yes—
156#2458C2214yes—
157#2456C2214yes—
158#2456C2214yes—
159#2455C2214yes—
160#2455C2214yes—
161#2454C2214yes—
162#2454C2212yes—
163#2454C2214yes—
164#2454C2212yes—
165#2454C2212yes—
166#2453C2212yes—
167#2452C2212yes—
168#2451C2212yes—
169#2448C2212yes—
170#2447C2212yes—
171#2446C2212yes—
172#2445C2212yes—
173#2445C2212yes—
174#2445C2212yes—
175#2443C2214yes—
176#2441C2214yes—
177#2430C2214yes—
178#2427C2214yes—
179#2425C2214yes—
180#2425C2214yes—
181#2422C2214yes—
182#2407C2214yes—
183#2406C2214yes—
184#2395C2214yes—
185#2392C2214yes—
186#2392C2214yes—
187#2392C2214yes—
188#2388C2214yes—
189#2388C2214yes—
190#2374C2214yes—
191#2370C2212yes—
192#2370C2212yes—
193#2369C2212yes—
194#2368C2212yes—
195#2368C2212yes—
196#2367C2212yes—
197#2367C2212yes—
198#2367C2214yes—
199#2366C2212yes—
200#2365C2212yes—
201#2360C2212yes—
202#2360C2212yes—
203#2359C2214yes—
204#2359C2214yes—
205#2359C2214yes—
206#2355C2212yes—
207#2354C2214yes—
208Q8×C4⋊C4C2212yes—
209#2349C2212yes—
210#2349C2212yes—
211#2349C2214yes—
212#2339C2214yes—
213#2335C2214yes—
214#2335C2214yes—
215#2330C2212yes—
216#2326C2212yes—
217#2326C2214yes—
218#2326C2212yes—
219#2324C2212yes—
220#2323C2212yes—
221C4×#127C2212yes—
222C4×#127C2211yescharacteristic
223C4×#127C2212yes—
224C4×#125C2211yescharacteristic
225C4×#124C2212yes—
226C4×#124C2212yes—
227C4×#124C2212yes—
228C4×#121C2212yes—
229#2296C2212yes—
230#2295C2212yes—
231#2295C2211yescharacteristic
232#2295C2212yes—
233#2295C2211yescharacteristic
234#2295C2212yes—
235#2293C2212yes—
236#2293C2212yes—
237#2275C2214yes—
238C42×Q8C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2212yes—
242C2×C4×C4⋊C4C2211yescharacteristic
243C22×#41C2314yes—
244#559—216no—
245#541—44no—
246#540—44no—
247#533—28no—
248#532—48no—
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×#127C2311yescharacteristic
254C2×#127C2312yes—
255C2×#127C2311yescharacteristic
256C2×#127C2312yes—
257#529—48no—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2311yescharacteristic
261C2×#125C2312yes—
262C2×#125C2311yescharacteristic
263C2×#125C2311yescharacteristic
264C2×#125C2312yes—
265C2×#125C2314yes—
266C2×#125C2314yes—
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2314yes—
273C2×#124C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2311yescharacteristic
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×#117C2312yes—
319C2×#117C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C2×#117C2314yes—
322C2×#117C2314yes—
323C2×#117C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C42C2311yescharacteristic
326C22×C42C2312yes—
327#401C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
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#397C2314yes—
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#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
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#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#390C2314yes—
448#390C2312yes—
449#390C2312yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2312yes—
458#390C2314yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2314yes—
466#390C2312yes—
467#390C2314yes—
468#390C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#387C2314yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2312yes—
599#385C2312yes—
600#385C2312yes—
601#385C2312yes—
602#385C2314yes—
603#384C2311yescharacteristic
604#384C2312yes—
605#384C2312yes—
606#384C2314yes—
607#384C2314yes—
608#382C2311yescharacteristic
609#382C2314yes—
610#382C2312yes—
611#382C2312yes—
612#381C2314yes—
613#381C2314yes—
614#380C2314yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
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⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667#376C2311yescharacteristic
668#376C2312yes—
669#376C2314yes—
670#376C2312yes—
671#376C2311yescharacteristic
672C2×#95C2311yescharacteristic
673C2×#95C2314yes—
674C2×#95C2314yes—
675C2×#95C2311yescharacteristic
676C43C2311yescharacteristic
677C43C2312yes—
678C43C2312yes—
679C43C2311yescharacteristic
680C2×#41—48no—
681C2×#41—48no—
682C2×#41—84no—
683C22×Q8C2412yes—
684C22×Q8C2411yescharacteristic
685C22×Q8C2412yes—
686C22×Q8C2414yes—
687C22×Q8C2411yescharacteristic
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C23×C4C2412yes—
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2414yes—
705C23×C4C2414yes—
706C23×C4C2411yescharacteristic
707C23×C4C2414yes—
708C23×C4C2414yes—
709C4⋊Q8—24no—
710C4⋊Q8—24no—
711C4⋊Q8—44no—
712C4⋊Q8—42no—
713#127—28no—
714#127—24no—
715#127—44no—
716#127—42no—
717#126—48no—
718#126—48no—
719#125—28no—
720#125—24no—
721#125—44no—
722#125—42no—
723#125—42no—
724#125—48no—
725#125—84no—
726#124—216no—
727#124—28no—
728#124—28no—
729#124—28no—
730#124—48no—
731#124—44no—
732#124—84no—
733#123—216no—
734#123—216no—
735#123—48no—
736#123—48no—
737#123—48no—
738#123—48no—
739#123—84no—
740#123—84no—
741C22⋊Q8—24no—
742C22⋊Q8—28no—
743C22⋊Q8—24no—
744C22⋊Q8—28no—
745C22⋊Q8—84no—
746C22⋊Q8—84no—
747#121—28no—
748#121—28no—
749#121—48no—
750#121—48no—
751#121—84no—
752#121—84no—
753C4×Q8—28no—
754C4×Q8—24no—
755C4×Q8—28no—
756C4×Q8—44no—
757C4×Q8—44no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×Q8#4118yescomplemented
761C4×D4—216no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—48no—
765C4×D4—44no—
766C4×D4—44no—
767C4×D4—44no—
768C4×D4—44no—
769C4×D4—48no—
770C4×D4—48no—
771C4×D4—48no—
772C4×D4—48no—
773C4×D4—84no—
774C4×D4—84no—
775C4×D4—84no—
776C4×D4—84no—
777#117—24no—
778#117—28no—
779#117—24no—
780#117—48no—
781#117—84no—
782#117—84no—
783C2×C4⋊C4—44no—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C42—28no—
885C2×C42—24no—
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918#95C2411yescharacteristic
919#95C2414yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2411yescharacteristic
926#95C2412yes—
927#95C2411yescharacteristic
928#95C2411yescharacteristic
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975C24C2514yes—
976C24C2514yes—
977C24C2511yescharacteristic
978#41—832no—
979C2×Q8—22no—
980C2×Q8—24no—
981C2×Q8—24no—
982C2×Q8—24no—
983C2×Q8—24no—
984C2×Q8—42no—
985C2×Q8—42no—
986C2×Q8—42no—
987C2×Q8—44no—
988C2×Q8—44no—
989C2×Q8—42no—
990C2×Q8—44no—
991C2×Q8C2×#4114yes—
992C2×D4—28no—
993C2×D4—28no—
994C2×D4—28no—
995C2×D4—24no—
996C2×D4—24no—
997C2×D4—28no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—28no—
1002C2×D4—24no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—22no—
1027C22×C4—24no—
1028C22×C4—22no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4H(5,𝔽2)14yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2511yescharacteristic
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—22no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4C2×#4118yes—
1130C4⋊C4C2×#4114yes—
1131C22⋊C4—24no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—24no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C42—22no—
1178C42—22no—
1179C42—22no—
1180C42—24no—
1181C42—28no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—22no—
1187C42—22no—
1188C42—22no—
1189C42—24no—
1190C42—24no—
1191C42—44no—
1192C42—42no—
1193C42—42no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—42no—
1198C42—42no—
1199C42—42no—
1200C42—42no—
1201C42—42no—
1202C42—42no—
1203C42—42no—
1204C42—44no—
1205C42—42no—
1206C42C2×#4114yes—
1207C42C2×#4118yes—
1208C422−1+414yes—
1209C23—21no—
1210C23—21no—
1211C23—22no—
1212C23—22no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23C2×H(5,𝔽2)12yes—
1228C23C2611yescharacteristic
1229Q8—44no—
1230Q8—44no—
1231Q8—48no—
1232Q8—84no—
1233Q8—88no—
1234D4—416no—
1235D4—416no—
1236D4—416no—
1237D4—48no—
1238D4—48no—
1239D4—88no—
1240D4—88no—
1241D4—88no—
1242D4—88no—
1243D4—164no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—28no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—48no—
1304C2×C4—44no—
1305C2×C4—88no—
1306C2×C4—82no—
1307C2×C4—88no—
1308C2×C4—88no—
1309C2×C4—88no—
1310C2×C4—88no—
1311C2×C4—84no—
1312C2×C4—164no—
1313C2×C4C22×#4114yes—
1314C2×C4C22×#4112yes—
1315C2×C4C22×#4112yes—
1316C2×C4C22×#4114yes—
1317C2×C4C22×#4112yes—
1318C2×C4C2×H(5,𝔽2)12yes—
1319C2×C4C2×H(5,𝔽2)12yes—
1320C2×C4C2×2−1+414yes—
1321C2×C4C2×2−1+412yes—
1322C2×C4#58514yes—
1323C22—22no—
1324C22—24no—
1325C22—41no—
1326C22—42no—
1327C22—41no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—44no—
1333C22—44no—
1334C22—44no—
1335C22—44no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22C23×#4111yescharacteristic
1343C22C22×H(5,𝔽2)11yescharacteristic
1344C22C22×2−1+411yescharacteristic
1345C22C2×#58512yes—
1346C22H(7,𝔽2)12yes—
1347C4—22no—
1348C4—22no—
1349C4—24no—
1350C4—24no—
1351C4—24no—
1352C4—22no—
1353C4—24no—
1354C4—44no—
1355C4—44no—
1356C4—41no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—44no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—44no—
1368C4—41no—
1369C4—42no—
1370C4#352214yes—
1371C2—42no—
1372C2—84no—
1373C2—84no—
1374C2#6268611yescharacteristic
1375C2C2×#352211yescharacteristic
1376C2#6285811yescharacteristic
1377C2#6292412yes—
1378C2#6292612yes—
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. #42130C2semidirect
2. #42123C2semidirect
3. #41251C2semidirect
4. #41210C2semidirect
5. #40801C2semidirect
6. #40767C2semidirect
7. #39808C2semidirect
8. #39739C2semidirect
9. #39718C2semidirect
10. #39675C2semidirect
11. #39622C2semidirect
12. #37799C2semidirect
13. #37792C2semidirect
14. #37625C2semidirect
15. #37581C2semidirect
16. #37572C2semidirect
17. #36602C2semidirect
18. #36573C2semidirect
19. #36139C2semidirect
20. #35721C2semidirect
21. #35696C2semidirect
22. #35332C2semidirect
23. #35300C2semidirect
24. #34624C2semidirect
25. #34621C2semidirect
26. #34331C2semidirect
27. #34145C2semidirect
760. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#421302
#421232
#412512
#412102
#408012
#407672
#398082
#397392
#397182
#396752
#396222
#377992
#377922
#376252
#375812
#375722
#366022
#365732
#361392
#357212
#356962
#353322
#353002
#346242
#346212
#343312
#341452