Finite Group Databasebeta

← #8119205

Subgroups — #8119205

Order 512.

4425 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58794C212yesmaximal, complemented
2#58767C212yesmaximal, complemented
3#57873C214yesmaximal, complemented
4#57740C214yesmaximal, complemented
5#56586C212yesmaximal, complemented
6#56508C212yesmaximal, complemented
7#52914C212yesmaximal, complemented
8#52912C212yesmaximal, complemented
9#47806C212yesmaximal, complemented
10#47484C214yesmaximal, complemented
11#47174C212yesmaximal, complemented
12#47152C212yesmaximal, complemented
13#47039C214yesmaximal, complemented
14#47003C212yesmaximal, complemented
15#43342C212yesmaximal, complemented
16#43325C212yesmaximal, complemented
17#38177C214yesmaximal, complemented
18#38144C214yesmaximal, complemented
19#37959C212yesmaximal, complemented
20#37948C212yesmaximal, complemented
21#37702C212yesmaximal, complemented
22#37698C212yesmaximal, complemented
23#36980C212yesmaximal, complemented
24#35311C211yesmaximal, characteristic, complemented
25#35301C211yesmaximal, characteristic
26#35092C212yesmaximal, complemented
27C2×#2599C211yesmaximal, characteristic, complemented
28C2×#539C2212yes—
29C2×#532C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2855C2212yes—
34#2855C2212yes—
35#2854C2212yes—
36#2853C2214yes—
37#2847C2212yes—
38#2844C2214yescomplemented
39#2844C2212yescomplemented
40#2841C2212yes—
41#2838C2214yes—
42#2835C2214yescomplemented
43#2832C2212yescomplemented
44#2832C2214yescomplemented
45#2830C2214yes—
46#2824C2214yes—
47#2824C2212yes—
48#2811C2212yescomplemented
49#2798C2214yes—
50#2797C2214yes—
51#2795C2214yescomplemented
52#2793C2214yescomplemented
53#2789C2214yescomplemented
54#2789C2212yescomplemented
55#2785C2212yescomplemented
56#2784C2214yes—
57#2784C2214yes—
58#2781C2214yes—
59#2781C2214yes—
60#2778C2214yes—
61#2775C2214yescomplemented
62#2771C2212yes—
63#2770C2214yescomplemented
64#2767C2214yescomplemented
65#2767C2214yescomplemented
66#2766C2214yescomplemented
67#2764C2214yescomplemented
68#2763C2214yescomplemented
69#2763C2214yescomplemented
70#2763C2214yescomplemented
71#2762C2214yescomplemented
72#2762C2214yescomplemented
73#2760C2212yes—
74#2759C2214yes—
75#2759C2214yescomplemented
76#2759C2214yescomplemented
77#2758C2214yescomplemented
78#2758C2214yescomplemented
79#2757C2214yescomplemented
80#2755C2214yescomplemented
81#2754C2214yescomplemented
82#2753C2214yes—
83#2751C2214yes—
84#2751C2214yes—
85#2750C2214yes—
86#2750C2214yes—
87#2747C2214yescomplemented
88#2746C2214yescomplemented
89#2745C2214yes—
90#2744C2214yes—
91#2742C2212yes—
92#2741C2214yescomplemented
93#2738C2214yescomplemented
94#2737C2214yes—
95#2737C2214yes—
96#2737C2214yescomplemented
97#2728C2214yes—
98#2728C2212yescomplemented
99#2723C2214yes—
100#2715C2214yescomplemented
101#2713C2214yescomplemented
102#2712C2212yes—
103#2709C2214yescomplemented
104#2700C2214yescomplemented
105#2690C2214yes—
106#2686C2214yes—
107#2681C2214yes—
108#2659C2212yes—
109#2655C2214yescomplemented
110#2653C2214yescomplemented
111#2650C2214yes—
112#2648C2214yes—
113#2639C2212yes—
114#2628C2211yescharacteristic
115#2628C2211yescharacteristic
116#2627C2212yes—
117#2625C2212yes—
118#2625C2212yes—
119#2619C2211yescharacteristic
120#2619C2211yescharacteristic
121#2618C2212yes—
122#2614C2214yes—
123#2610C2212yes—
124#2610C2212yes—
125#2609C2214yes—
126#2609C2212yescomplemented
127#2605C2214yescomplemented
128#2600C2212yes—
129#2599C2212yes—
130#2599C2212yes—
131#2599C2212yes—
132#2599C2212yes—
133#2599C2212yes—
134#2599C2212yes—
135#2599C2212yes—
136#2599C2212yes—
137#2598C2212yes—
138#2598C2212yes—
139#2597C2214yes—
140#2595C2214yes—
141#2591C2212yes—
142#2588C2214yescomplemented
143#2586C2212yescomplemented
144#2574C2214yes—
145#2574C2214yes—
146#2539C2212yes—
147#2534C2214yes—
148#2528C2214yescomplemented
149#2525C2214yescomplemented
150#2524C2214yescomplemented
151#2517C2212yes—
152#2515C2214yescomplemented
153#2515C2214yescomplemented
154#2513C2214yes—
155#2511C2214yescomplemented
156#2510C2214yes—
157#2510C2214yes—
158#2505C2214yescomplemented
159#2503C2214yes—
160#2503C2212yes—
161#2502C2212yes—
162#2499C2212yes—
163#2499C2212yes—
164#2493C2214yes—
165#2493C2214yes—
166#2488C2214yes—
167#2488C2214yes—
168#2488C2214yes—
169#2484C2212yes—
170#2484C2212yes—
171#2483C2212yes—
172#2483C2212yes—
173#2481C2214yes—
174#2477C2214yescomplemented
175#2476C2214yes—
176#2474C2214yes—
177#2472C2214yes—
178#2469C2214yescomplemented
179#2469C2214yescomplemented
180#2466C2214yescomplemented
181#2465C2214yescomplemented
182#2465C2214yescomplemented
183#2462C2214yescomplemented
184#2462C2214yescomplemented
185#2460C2214yescomplemented
186#2459C2214yes—
187#2458C2214yescomplemented
188#2458C2214yescomplemented
189#2450C2214yes—
190#2450C2214yescomplemented
191#2449C2214yes—
192#2447C2214yes—
193#2444C2214yes—
194#2443C2214yes—
195#2442C2214yes—
196#2438C2214yescomplemented
197#2425C2214yes—
198#2419C2214yes—
199#2419C2214yescomplemented
200#2412C2214yes—
201#2409C2214yes—
202#2406C2214yes—
203#2406C2212yes—
204#2404C2212yes—
205C2×#398C2211yescharacteristic
206C2×#397C2211yescharacteristic
207C2×#395C2211yescharacteristic
208C2×#393C2211yescharacteristic
209#2368C2214yes—
210#2358C2214yes—
211#2352C2214yes—
212#2339C2214yes—
213#2337C2214yes—
214#2332C2214yescomplemented
215#2329C2212yes—
216#2325C2212yes—
217#2324C2212yes—
218#2324C2212yes—
219#2322C2214yes—
220#2318C2214yes—
221#2317C2211yescharacteristic
222#2317C2211yescharacteristic
223#2314C2214yescomplemented
224#2313C2212yes—
225#2310C2211yescharacteristic
226#2310C2211yescharacteristic
227C4×#123C2214yes—
228C2×#388C2212yes—
229C2×#387C2212yes—
230C2×#387C2212yes—
231C2×#385C2212yes—
232#2283C2211yescharacteristic
233C2×#383C2211yescharacteristic
234#2280C2211yescharacteristic
235C22×#41C2312yes—
236C23×Q8C2311yescharacteristic
237C23×Q8C2311yescharacteristic
238C24×C4C2311yescharacteristic
239#539—48no—
240#532—44no—
241C2×C4⋊Q8C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#126C2314yes—
244C2×#125C2314yes—
245C2×#124C2314yes—
246C2×#124C2312yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×C22⋊Q8—44no—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2312yes—
263C2×#120C2314yes—
264C2×C4×Q8—44no—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×#117—44no—
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2314yes—
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2312yes—
302#401C2314yes—
303#401C2314yes—
304#401C2314yes—
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#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#399C2312yes—
332#399C2312yes—
333#399C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2314yes—
340#398C2312yes—
341#398C2312yes—
342#398C2312yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2312yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2312yes—
364#397C2312yes—
365#397C2312yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2312yes—
382#395C2312yes—
383#395C2312yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2312yes—
388#395C2314yes—
389#395C2312yes—
390#395C2314yes—
391#395C2312yes—
392#395C2314yes—
393#395C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2312yes—
400#394C2314yes—
401#394C2312yes—
402#394C2314yes—
403#394C2312yes—
404#394C2312yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#393C2312yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2312yes—
415#393C2312yes—
416#393C2314yes—
417#393C2312yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2312yes—
423#393C2312yes—
424#393C2314yes—
425#393C2314yes—
426#392C2312yes—
427#392C2312yes—
428#392C2312yes—
429#392C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
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#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
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#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#385C2312yes—
568#385C2314yes—
569#385C2312yes—
570#385C2312yes—
571#385C2312yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
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#384C2312yes—
593#384C2312yes—
594#383C2314yes—
595#383C2314yes—
596#383C2312yes—
597#383C2312yes—
598#383C2312yes—
599#383C2312yes—
600#383C2312yes—
601#383C2314yes—
602#382C2314yes—
603#382C2312yes—
604#382C2312yes—
605#382C2314yes—
606#382C2314yes—
607#382C2314yes—
608#382C2314yes—
609#382C2314yes—
610#382C2311yescharacteristic
611#382C2311yescharacteristic
612#381C2312yes—
613#381C2312yes—
614#381C2312yes—
615#381C2312yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#381C2314yes—
620#381C2314yes—
621#381C2314yes—
622#381C2312yes—
623#381C2314yes—
624#381C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2312yes—
637#379C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2312yes—
653#376C2312yes—
654C2×#95C2314yes—
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2311yescharacteristic
659C2×#95C2312yes—
660C2×#95C2311yescharacteristic
661C2×#95C2312yes—
662C2×#95C2312yes—
663C25C2411yescharacteristic
664C2×#41—44no—
665C2×#41—48no—
666C22×Q8—42no—
667C22×Q8—44no—
668C22×Q8—42no—
669C22×Q8—42no—
670C22×Q8—42no—
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2412yes—
675C22×Q8C2414yes—
676C22×Q8C2412yes—
677C22×D4C2414yes—
678C22×D4C2414yes—
679C22×D4C2412yes—
680C22×D4C2412yes—
681C22×D4C2414yes—
682C22×D4C2412yes—
683C23×C4—24no—
684C23×C4—42no—
685C23×C4—42no—
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2411yescharacteristic
697C23×C4C2412yes—
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2412yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2411yescharacteristic
705C4⋊Q8—42no—
706#127—42no—
707#126—48no—
708#125—48no—
709#124—44no—
710#124—48no—
711#123—48no—
712#123—48no—
713#123—48no—
714#123—48no—
715C22⋊Q8—28no—
716C22⋊Q8—44no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—44no—
721C22⋊Q8—44no—
722#121—28no—
723#121—44no—
724#121—44no—
725#121—44no—
726#120—48no—
727C4×Q8—44no—
728C4×Q8—44no—
729C4×Q8—44no—
730C4×Q8—44no—
731C4×D4—44no—
732C4×D4—44no—
733C4×D4—48no—
734C4×D4—48no—
735C4×D4—48no—
736#117—42no—
737#117—42no—
738#117—42no—
739#117—42no—
740#117—42no—
741#117—42no—
742#117—42no—
743#117—42no—
744#117—42no—
745#117—48no—
746#117—42no—
747C2×C4⋊C4—28no—
748C2×C4⋊C4—44no—
749C2×C4⋊C4—44no—
750C2×C4⋊C4—42no—
751C2×C4⋊C4—44no—
752C2×C4⋊C4—42no—
753C2×C4⋊C4—42no—
754C2×C4⋊C4—42no—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C22⋊C4—44no—
803C2×C22⋊C4—44no—
804C2×C22⋊C4—44no—
805C2×C22⋊C4—42no—
806C2×C22⋊C4—42no—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
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×C42—24no—
851C2×C42—24no—
852C2×C42—44no—
853C2×C42C2412yes—
854C2×C42C2411yescharacteristic
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2412yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
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#95C2414yes—
937#95C2414yes—
938C24—22no—
939C24—22no—
940C24—24no—
941C24—41no—
942C24—42no—
943C24C2511yescharacteristic
944C24C2514yes—
945C24C2511yescharacteristic
946C24C2511yescharacteristic
947#41—816no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—42no—
951C2×Q8—42no—
952C2×Q8—44no—
953C2×Q8—44no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—42no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—416no—
964C2×Q8—88no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—28no—
968C2×D4—28no—
969C2×D4—24no—
970C2×D4—42no—
971C2×D4—44no—
972C2×D4—42no—
973C2×D4—42no—
974C2×D4—42no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—24no—
988C22×C4—22no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—22no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—22no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—41no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—44no—
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—416no—
1033C22×C4H(5,𝔽2)14yes—
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2514yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2514yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C4⋊C4—28no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
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—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—42no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C42—22no—
1148C42—22no—
1149C42—22no—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—24no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—42no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C23—21no—
1167C23—21no—
1168C23—22no—
1169C23—21no—
1170C23—22no—
1171C23—21no—
1172C23—22no—
1173C23—24no—
1174C23—21no—
1175C23—24no—
1176C23—21no—
1177C23—24no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—21no—
1182C23—24no—
1183C23—24no—
1184C23—22no—
1185C23—44no—
1186C23—48no—
1187C23—44no—
1188C23—82no—
1189C23—84no—
1190C23C2×H(5,𝔽2)12yes—
1191C23#58512yes—
1192C23#58514yes—
1193C23C2611yescharacteristic
1194Q8—48no—
1195Q8—48no—
1196Q8—84no—
1197Q8—84no—
1198Q8—84no—
1199Q8—164no—
1200D4—416no—
1201D4—84no—
1202D4—88no—
1203D4—84no—
1204D4—84no—
1205D4—164no—
1206C2×C4—28no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—21no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—21no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—44no—
1268C2×C4—44no—
1269C2×C4—44no—
1270C2×C4—44no—
1271C2×C4—44no—
1272C2×C4—48no—
1273C2×C4—44no—
1274C2×C4—84no—
1275C2×C4—82no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—88no—
1281C2×C4—88no—
1282C2×C4—164no—
1283C2×C4C2×H(5,𝔽2)12yes—
1284C2×C4C2×H(5,𝔽2)12yes—
1285C2×C4#58512yes—
1286C22—22no—
1287C22—22no—
1288C22—24no—
1289C22—24no—
1290C22—22no—
1291C22—24no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—44no—
1296C22—41no—
1297C22—41no—
1298C22—44no—
1299C22—44no—
1300C22—41no—
1301C22—44no—
1302C22—44no—
1303C22—42no—
1304C22—44no—
1305C22—42no—
1306C22—44no—
1307C22—88no—
1308C22#354014yes—
1309C22C22×H(5,𝔽2)11yescharacteristic
1310C22C2×#58512yes—
1311C22C2×#58511yescharacteristic
1312C22C2×#58511yescharacteristic
1313C222−1+612yes—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—44no—
1322C4—44no—
1323C4—41no—
1324C4—44no—
1325C4—44no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—44no—
1330C4—41no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—44no—
1337C2—24no—
1338C2—42no—
1339C2—84no—
1340C2—81no—
1341C2C2×#354011yescharacteristic
1342C2#6282011yescharacteristic
1343C2#6288611yescharacteristic
1344C2#6290912yes—
1345C2#6291112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35301C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58794C2semidirect
2. #58767C2semidirect
3. #57873C2semidirect
4. #57740C2semidirect
5. #56586C2semidirect
6. #56508C2semidirect
7. #52914C2semidirect
8. #52912C2semidirect
9. #47806C2semidirect
10. #47484C2semidirect
11. #47174C2semidirect
12. #47152C2semidirect
13. #47039C2semidirect
14. #47003C2semidirect
15. #43342C2semidirect
16. #43325C2semidirect
17. #38177C2semidirect
18. #38144C2semidirect
19. #37959C2semidirect
20. #37948C2semidirect
21. #37702C2semidirect
22. #37698C2semidirect
23. #36980C2semidirect
24. #35311C2semidirect
26. #35092C2semidirect
27. C2×#2599C2semidirect
38. #2844C22semidirect
39. #2844C22semidirect
42. #2835C22semidirect
43. #2832C22semidirect
44. #2832C22semidirect
48. #2811C22semidirect
51. #2795C22semidirect
52. #2793C22semidirect
53. #2789C22semidirect
54. #2789C22semidirect
55. #2785C22semidirect
61. #2775C22semidirect
63. #2770C22semidirect
64. #2767C22semidirect
65. #2767C22semidirect
66. #2766C22semidirect
67. #2764C22semidirect
68. #2763C22semidirect
69. #2763C22semidirect
70. #2763C22semidirect
71. #2762C22semidirect
72. #2762C22semidirect
75. #2759C22semidirect
76. #2759C22semidirect
77. #2758C22semidirect
78. #2758C22semidirect
79. #2757C22semidirect
80. #2755C22semidirect
81. #2754C22semidirect
87. #2747C22semidirect
88. #2746C22semidirect
92. #2741C22semidirect
93. #2738C22semidirect
96. #2737C22semidirect
98. #2728C22semidirect
100. #2715C22semidirect
101. #2713C22semidirect
103. #2709C22semidirect
104. #2700C22semidirect
109. #2655C22semidirect
110. #2653C22semidirect
126. #2609C22semidirect
127. #2605C22semidirect
142. #2588C22semidirect
143. #2586C22semidirect
148. #2528C22semidirect
149. #2525C22semidirect
150. #2524C22semidirect
152. #2515C22semidirect
153. #2515C22semidirect
155. #2511C22semidirect
158. #2505C22semidirect
174. #2477C22semidirect
178. #2469C22semidirect
179. #2469C22semidirect
180. #2466C22semidirect
181. #2465C22semidirect
182. #2465C22semidirect
183. #2462C22semidirect
184. #2462C22semidirect
185. #2460C22semidirect
187. #2458C22semidirect
188. #2458C22semidirect
190. #2450C22semidirect
196. #2438C22semidirect
199. #2419C22semidirect
214. #2332C22semidirect
223. #2314C22semidirect

Maximal subgroups

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

subgroupindex
#587942
#587672
#578732
#577402
#565862
#565082
#529142
#529122
#478062
#474842
#471742
#471522
#470392
#470032
#433422
#433252
#381772
#381442
#379592
#379482
#377022
#376982
#369802
#353112
#353012
#350922
C2×#25992