Finite Group Databasebeta

← #7658047

Subgroups — #7658047

Order 512.

4645 conjugacy classes of subgroups.

The subgroup lattice has 1351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41876C214yesmaximal, complemented
2#41871C214yesmaximal, complemented
3#41866C214yesmaximal, complemented
4#41858C214yesmaximal, complemented
5#41602C214yesmaximal, complemented
6#41572C214yesmaximal, complemented
7#39425C212yesmaximal, complemented
8#39418C212yesmaximal, complemented
9#39366C211yesmaximal, characteristic, complemented
10#39356C211yesmaximal, characteristic, complemented
11#38903C212yesmaximal, complemented
12#38252C212yesmaximal, complemented
13#38251C212yesmaximal, complemented
14#37581C212yesmaximal, complemented
15#37501C212yesmaximal, complemented
16#37495C212yesmaximal, complemented
17#36608C211yesmaximal, characteristic, complemented
18#36602C211yesmaximal, characteristic, complemented
19#36385C212yesmaximal, complemented
20#36074C214yesmaximal, complemented
21#36025C214yesmaximal, complemented
22#35331C211yesmaximal, characteristic, complemented
23#35312C212yesmaximal, complemented
24#34629C211yesmaximal, characteristic, complemented
25#34619C212yesmaximal, complemented
26#34327C212yesmaximal, complemented
27#34151C211yesmaximal, characteristic, complemented
28C2×#548C2212yes—
29C2×#544C2212yes—
30C2×#542C2212yes—
31C2×#536C2212yes—
32C2×#529C2211yescharacteristic
33#2862C2211yescharacteristic
34#2862C2212yes—
35#2862C2212yes—
36#2861C2212yes—
37#2861C2212yes—
38#2858C2211yescharacteristic
39#2850C2212yes—
40#2838C2214yes—
41#2833C2214yes—
42#2831C2214yes—
43#2831C2214yes—
44#2825C2214yes—
45#2824C2214yes—
46#2799C2214yes—
47#2789C2214yes—
48#2778C2214yes—
49#2778C2214yes—
50#2746C2214yes—
51#2745C2214yes—
52#2744C2214yes—
53#2743C2214yes—
54#2730C2214yes—
55#2729C2214yes—
56#2713C2214yes—
57#2707C2214yes—
58#2706C2214yes—
59#2702C2214yes—
60#2700C2214yes—
61#2698C2214yes—
62#2692C2214yes—
63#2692C2214yes—
64#2690C2214yes—
65#2688C2214yes—
66#2687C2214yes—
67#2686C2214yes—
68#2683C2214yes—
69#2682C2214yes—
70#2666C2214yes—
71#2665C2214yes—
72#2655C2214yes—
73#2654C2214yes—
74#2654C2214yes—
75#2653C2214yes—
76#2653C2214yes—
77#2652C2214yes—
78#2652C2214yes—
79#2650C2214yes—
80#2650C2214yes—
81#2650C2214yes—
82#2649C2214yes—
83#2648C2214yes—
84#2647C2211yescharacteristic
85#2646C2214yes—
86#2645C2212yes—
87#2645C2212yes—
88#2644C2212yes—
89#2643C2214yes—
90#2642C2211yescharacteristic
91#2642C2212yes—
92#2640C2212yes—
93#2640C2212yes—
94#2631C2214yes—
95#2630C2214yes—
96#2629C2211yescharacteristic
97#2628C2212yes—
98#2625C2212yes—
99#2625C2212yes—
100#2624C2212yes—
101#2621C2211yescharacteristic
102#2621C2211yescharacteristic
103#2620C2212yes—
104#2619C2211yescharacteristic
105#2609C2214yes—
106#2605C2214yes—
107#2598C2214yes—
108#2597C2214yes—
109#2593C2214yes—
110#2592C2212yes—
111#2581C2214yes—
112#2581C2212yes—
113#2578C2214yes—
114#2574C2214yes—
115#2560C2214yes—
116#2560C2214yes—
117#2557C2214yes—
118#2557C2214yes—
119#2557C2214yes—
120#2557C2214yes—
121#2557C2214yes—
122#2556C2214yes—
123#2553C2214yes—
124#2550C2212yes—
125#2549C2214yes—
126#2545C2214yes—
127#2545C2212yes—
128#2536C2214yes—
129#2532C2214yes—
130#2530C2214yes—
131#2529C2214yes—
132#2527C2214yes—
133#2527C2214yes—
134#2521C2214yes—
135#2520C2214yes—
136#2519C2214yes—
137#2518C2214yes—
138#2515C2214yes—
139#2514C2214yes—
140#2514C2212yes—
141#2514C2212yes—
142#2514C2214yes—
143#2510C2214yes—
144#2510C2214yes—
145#2505C2214yes—
146#2498C2214yes—
147#2492C2214yes—
148#2492C2214yes—
149#2492C2214yes—
150#2491C2212yes—
151#2489C2212yes—
152#2489C2214yes—
153#2489C2214yes—
154#2488C2214yes—
155#2488C2214yes—
156#2488C2214yes—
157#2488C2214yes—
158#2488C2214yes—
159#2474C2214yes—
160#2468C2214yes—
161#2461C2214yes—
162#2461C2214yes—
163#2461C2214yes—
164#2458C2214yes—
165#2457C2214yes—
166#2457C2214yes—
167#2454C2212yes—
168#2451C2212yes—
169#2447C2212yes—
170#2446C2212yes—
171#2446C2212yes—
172#2445C2212yes—
173#2442C2212yes—
174#2439C2212yes—
175#2434C2212yes—
176#2431C2212yes—
177#2429C2212yes—
178#2427C2212yes—
179#2417C2212yes—
180#2414C2212yes—
181#2409C2212yes—
182#2407C2212yes—
183#2402C2214yes—
184#2401C2214yes—
185#2401C2214yes—
186#2398C2214yes—
187#2396C2214yes—
188#2395C2214yes—
189#2374C2212yes—
190#2374C2212yes—
191#2374C2214yes—
192#2373C2212yes—
193#2373C2212yes—
194#2372C2214yes—
195#2372C2214yes—
196#2370C2212yes—
197#2368C2214yes—
198#2367C2212yes—
199#2367C2212yes—
200#2364C2214yes—
201#2363C2212yes—
202#2362C2212yes—
203#2362C2212yes—
204#2361C2212yes—
205#2356C2212yes—
206#2356C2214yes—
207#2353C2214yes—
208#2352C2212yes—
209#2346C2214yes—
210Q8×C22⋊C4C2212yes—
211#2339C2212yes—
212#2337C2214yes—
213#2332C2214yes—
214#2328C2211yescharacteristic
215#2327C2211yescharacteristic
216#2325C2214yes—
217#2311C2212yes—
218#2310C2212yes—
219C4×C4⋊Q8C2212yes—
220C4×C4⋊Q8C2211yescharacteristic
221C4×#125C2211yescharacteristic
222C4×#124C2212yes—
223C4×#124C2212yes—
224C4×C22⋊Q8C2212yes—
225C4×C22⋊Q8C2212yes—
226C4×#121C2212yes—
227#2298C2212yes—
228#2297C2212yes—
229#2295C2212yes—
230#2295C2212yes—
231#2295C2211yescharacteristic
232C2×#391C2212yes—
233#2293C2212yes—
234#2293C2212yes—
235#2293C2211yescharacteristic
236#2290C2212yes—
237#2275C2214yes—
238C42×Q8C2211yescharacteristic
239C42×D4C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C4×#117C2212yes—
243C22×#41C2312yes—
244C23×Q8C2312yes—
245#548—216no—
246#544—48no—
247#542—48no—
248#536—48no—
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2314yes—
255C2×#127C2311yescharacteristic
256#529—28no—
257C2×#126C2312yes—
258C2×#126C2314yes—
259C2×#125C2311yescharacteristic
260C2×#125C2311yescharacteristic
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2312yes—
266C2×#124C2311yescharacteristic
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2314yes—
270C2×#123C2312yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×#121C2314yes—
286C2×#121C2312yes—
287C2×#121C2311yescharacteristic
288C2×#121C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2311yescharacteristic
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C2×#117C2314yes—
308C2×#117C2312yes—
309C2×#117C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C42C2311yescharacteristic
312C22×C42C2312yes—
313#401C2314yes—
314#401C2314yes—
315#401C2314yes—
316#401C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
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#398C2314yes—
355#398C2314yes—
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#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2312yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2312yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2312yes—
513#388C2314yes—
514#388C2314yes—
515#388C2312yes—
516#388C2312yes—
517#388C2314yes—
518#388C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2312yes—
528#387C2312yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2312yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2312yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#385C2312yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2312yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#384C2311yescharacteristic
586#383C2314yes—
587#383C2314yes—
588#383C2314yes—
589#382C2311yescharacteristic
590#382C2314yes—
591#382C2312yes—
592#382C2314yes—
593#382C2311yescharacteristic
594#382C2311yescharacteristic
595#382C2314yes—
596#382C2314yes—
597#382C2314yes—
598#381C2314yes—
599#381C2314yes—
600#381C2314yes—
601#381C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2312yes—
607#380C2312yes—
608#380C2312yes—
609#380C2314yes—
610#380C2314yes—
611#380C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2311yescharacteristic
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2311yescharacteristic
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2311yescharacteristic
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664#376C2311yescharacteristic
665#376C2311yescharacteristic
666#376C2314yes—
667#376C2314yes—
668#376C2314yes—
669#376C2311yescharacteristic
670#376C2311yescharacteristic
671#376C2312yes—
672C2×#95C2314yes—
673C2×#95C2314yes—
674C2×#95C2314yes—
675C43C2311yescharacteristic
676C43C2312yes—
677C43C2312yes—
678C43C2311yescharacteristic
679C2×#41—28no—
680C2×#41—44no—
681C2×#41—44no—
682C22×Q8—28no—
683C22×Q8—44no—
684C22×Q8—44no—
685C22×Q8C2412yes—
686C22×Q8C2412yes—
687C22×Q8C2411yescharacteristic
688C22×Q8C2414yes—
689C22×Q8C2414yes—
690C22×Q8C2414yes—
691C22×D4C2412yes—
692C22×D4C2414yes—
693C22×D4C2412yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2414yes—
704C23×C4C2414yes—
705C23×C4C2411yescharacteristic
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2412yes—
709C4⋊Q8—24no—
710C4⋊Q8—28no—
711C4⋊Q8—44no—
712C4⋊Q8—42no—
713C4⋊Q8—44no—
714C4⋊Q8—48no—
715#127—42no—
716#126—28no—
717#126—48no—
718#125—24no—
719#125—24no—
720#125—44no—
721#125—48no—
722#124—24no—
723#124—216no—
724#124—28no—
725#124—28no—
726#124—48no—
727#124—44no—
728#124—48no—
729#123—28no—
730#123—48no—
731#123—48no—
732#123—48no—
733#123—48no—
734C22⋊Q8—28no—
735C22⋊Q8—24no—
736C22⋊Q8—216no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739C22⋊Q8—48no—
740C22⋊Q8—48no—
741C22⋊Q8—48no—
742C22⋊Q8—44no—
743C22⋊Q8—44no—
744#121—24no—
745#121—216no—
746#121—28no—
747#121—44no—
748C4×Q8—24no—
749C4×Q8—28no—
750C4×Q8—48no—
751C4×Q8—44no—
752C4×Q8—44no—
753C4×Q8—44no—
754C4×D4—28no—
755C4×D4—216no—
756C4×D4—48no—
757C4×D4—44no—
758C4×D4—44no—
759C4×D4—48no—
760C4×D4—44no—
761C4×D4#4118yes—
762#117—28no—
763#117—28no—
764#117—24no—
765#117—42no—
766#117—48no—
767#117—44no—
768#117—44no—
769C2×C4⋊C4—44no—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C42—24no—
861C2×C42—44no—
862C2×C42C2412yes—
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2411yescharacteristic
906#95C2411yescharacteristic
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2411yescharacteristic
922#95C2411yescharacteristic
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
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#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963C24C2514yes—
964C24C2511yescharacteristic
965C24C2512yes—
966#41—816no—
967C2×Q8—22no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—28no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—28no—
974C2×Q8—24no—
975C2×Q8—24no—
976C2×Q8—42no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×Q8—44no—
981C2×Q8—44no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—816no—
985C2×D4—28no—
986C2×D4—24no—
987C2×D4—28no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—42no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4C2×#4114yes—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—22no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—28no—
1014C22×C4—28no—
1015C22×C4—24no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—42no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4C2×#4118yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—22no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4C2×#4114yes—
1106C22⋊C4—24no—
1107C22⋊C4—24no—
1108C22⋊C4—24no—
1109C22⋊C4—28no—
1110C22⋊C4—24no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
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—42no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4C2×#4118yes—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—24no—
1154C42—28no—
1155C42—22no—
1156C42—24no—
1157C42—22no—
1158C42—24no—
1159C42—24no—
1160C42—28no—
1161C42—22no—
1162C42—28no—
1163C42—24no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—44no—
1168C42—42no—
1169C42—42no—
1170C42—42no—
1171C42—42no—
1172C42—42no—
1173C42—42no—
1174C42—44no—
1175C42—42no—
1176C42—44no—
1177C42—42no—
1178C42—42no—
1179C42—44no—
1180C42C2×#4114yes—
1181C42H(5,𝔽2)14yes—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—24no—
1189C23—21no—
1190C23—21no—
1191C23—24no—
1192C23—22no—
1193C23—24no—
1194C23—21no—
1195C23—24no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—22no—
1200C23C22×#4114yes—
1201C23C2611yescharacteristic
1202Q8—44no—
1203Q8—48no—
1204Q8—48no—
1205Q8—88no—
1206Q8—88no—
1207Q8—164no—
1208D4—44no—
1209D4—416no—
1210D4—48no—
1211D4—84no—
1212D4—88no—
1213D4—164no—
1214D4—164no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—216no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—21no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—44no—
1277C2×C4—44no—
1278C2×C4—82no—
1279C2×C4—88no—
1280C2×C4—84no—
1281C2×C4—88no—
1282C2×C4—88no—
1283C2×C4—84no—
1284C2×C4—164no—
1285C2×C4—164no—
1286C2×C4C22×#4112yes—
1287C2×C4C22×#4112yes—
1288C2×C4C22×#4114yes—
1289C2×C4C22×#4112yes—
1290C2×C4C2×H(5,𝔽2)14yes—
1291C2×C4C2×H(5,𝔽2)12yes—
1292C2×C4#58514yes—
1293C2×C4#58512yes—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—41no—
1302C22—44no—
1303C22—41no—
1304C22—44no—
1305C22—44no—
1306C22—42no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—42no—
1311C22—41no—
1312C22—44no—
1313C22C23×#4111yescharacteristic
1314C22C22×H(5,𝔽2)11yescharacteristic
1315C22C2×#58511yescharacteristic
1316C22C2×#58512yes—
1317C222−1+612yes—
1318C4—24no—
1319C4—22no—
1320C4—24no—
1321C4—24no—
1322C4—22no—
1323C4—41no—
1324C4—44no—
1325C4—44no—
1326C4—41no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—44no—
1332C4—44no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4—42no—
1337C4—42no—
1338C4—41no—
1339C4—44no—
1340C4—42no—
1341C4#351414yes—
1342C2—44no—
1343C2—81no—
1344C2—84no—
1345C2#6268611yescharacteristic
1346C2C2×#351411yescharacteristic
1347C2#6286111yescharacteristic
1348C2#6293112yes—
1349C2#6294012yes—
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. #41876C2semidirect
2. #41871C2semidirect
3. #41866C2semidirect
4. #41858C2semidirect
5. #41602C2semidirect
6. #41572C2semidirect
7. #39425C2semidirect
8. #39418C2semidirect
9. #39366C2semidirect
10. #39356C2semidirect
11. #38903C2semidirect
12. #38252C2semidirect
13. #38251C2semidirect
14. #37581C2semidirect
15. #37501C2semidirect
16. #37495C2semidirect
17. #36608C2semidirect
18. #36602C2semidirect
19. #36385C2semidirect
20. #36074C2semidirect
21. #36025C2semidirect
22. #35331C2semidirect
23. #35312C2semidirect
24. #34629C2semidirect
25. #34619C2semidirect
26. #34327C2semidirect
27. #34151C2semidirect

Maximal subgroups

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

subgroupindex
#418762
#418712
#418662
#418582
#416022
#415722
#394252
#394182
#393662
#393562
#389032
#382522
#382512
#375812
#375012
#374952
#366082
#366022
#363852
#360742
#360252
#353312
#353122
#346292
#346192
#343272
#341512