Finite Group Databasebeta

← #10069080

Subgroups — #10069080

Order 512.

4633 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59465C211yesmaximal, characteristic, complemented
2#58590C212yesmaximal, complemented
3#57759C214yesmaximal, complemented
4#57323C214yesmaximal, complemented
5#55614C212yesmaximal, complemented
6#54784C214yesmaximal, complemented
7#52673C214yesmaximal, complemented
8#50973C214yesmaximal, complemented
9#48105C214yesmaximal, complemented
10#47170C212yesmaximal, complemented
11#46434C212yesmaximal, complemented
12#46380C214yesmaximal, complemented
13#46163C212yesmaximal, complemented
14#44450C212yesmaximal, complemented
15#44227C214yesmaximal, complemented
16#43688C212yesmaximal, complemented
17#43420C214yesmaximal, complemented
18#42180C212yesmaximal, complemented
19#42149C212yesmaximal, complemented
20#40812C214yesmaximal, complemented
21#38951C211yesmaximal, characteristic, complemented
22#38770C212yesmaximal, complemented
23#37249C211yesmaximal, characteristic, complemented
24C2×#547C2211yescharacteristic
25C2×#547C2211yescharacteristic, complemented
26C2×#538C2212yescomplemented
27C2×#537C2212yes—
28#2862C2211yescharacteristic, complemented
29#2861C2212yes—
30#2842C2212yescomplemented
31#2841C2214yescomplemented
32#2837C2214yes—
33#2837C2214yescomplemented
34#2832C2212yes—
35#2827C2214yescomplemented
36#2822C2212yescomplemented
37#2820C2212yes—
38#2820C2214yescomplemented
39#2817C2212yescomplemented
40#2813C2214yes—
41#2813C2212yes—
42#2809C2212yescomplemented
43#2807C2212yescomplemented
44#2805C2212yescomplemented
45#2804C2211yescharacteristic
46#2799C2214yescomplemented
47#2799C2212yescomplemented
48#2798C2214yescomplemented
49#2795C2212yes—
50#2784C2212yes—
51#2784C2212yescomplemented
52#2782C2214yescomplemented
53#2781C2214yes—
54#2780C2214yes—
55#2780C2214yes—
56#2772C2214yescomplemented
57#2771C2214yescomplemented
58#2769C2214yescomplemented
59#2752C2214yes—
60#2751C2214yes—
61#2751C2214yescomplemented
62#2749C2214yes—
63#2749C2214yes—
64#2744C2214yescomplemented
65#2743C2214yes—
66#2743C2214yescomplemented
67#2742C2212yescomplemented
68#2740C2214yescomplemented
69#2740C2214yescomplemented
70#2738C2214yescomplemented
71#2738C2214yescomplemented
72#2737C2214yes—
73#2733C2212yes—
74#2732C2212yescomplemented
75#2729C2214yescomplemented
76#2729C2214yescomplemented
77#2728C2214yescomplemented
78#2724C2212yes—
79#2720C2214yescomplemented
80#2716C2214yescomplemented
81#2713C2214yescomplemented
82#2711C2214yes—
83#2710C2214yescomplemented
84#2708C2214yescomplemented
85#2706C2214yes—
86#2706C2214yescomplemented
87#2706C2214yescomplemented
88#2702C2214yescomplemented
89#2701C2214yescomplemented
90#2700C2214yescomplemented
91#2700C2214yescomplemented
92#2694C2214yescomplemented
93#2694C2214yescomplemented
94#2693C2214yes—
95#2691C2214yes—
96#2689C2214yescomplemented
97#2688C2214yes—
98#2688C2214yescomplemented
99#2686C2214yescomplemented
100#2683C2214yes—
101#2682C2212yes—
102#2679C2211yescharacteristic
103#2678C2214yes—
104#2678C2214yescomplemented
105#2676C2214yes—
106#2674C2214yescomplemented
107#2670C2214yes—
108#2669C2212yes—
109#2665C2214yescomplemented
110#2663C2212yescomplemented
111#2654C2214yescomplemented
112#2652C2214yescomplemented
113#2650C2214yescomplemented
114#2646C2214yescomplemented
115#2639C2212yes—
116#2635C2212yes—
117#2630C2214yes—
118#2630C2214yes—
119#2627C2212yescomplemented
120#2623C2212yescomplemented
121#2620C2212yescomplemented
122#2605C2214yescomplemented
123#2600C2214yescomplemented
124#2598C2214yescomplemented
125#2591C2212yes—
126#2589C2214yescomplemented
127#2587C2214yescomplemented
128#2579C2214yescomplemented
129#2572C2212yes—
130#2571C2211yescharacteristic, complemented
131#2569C2214yescomplemented
132#2564C2212yes—
133#2564C2212yescomplemented
134#2564C2214yescomplemented
135#2563C2214yescomplemented
136#2560C2214yes—
137#2557C2214yes—
138#2556C2214yescomplemented
139#2551C2211yescharacteristic, complemented
140#2547C2211yescharacteristic, complemented
141#2543C2214yescomplemented
142#2542C2211yescharacteristic
143#2534C2214yescomplemented
144#2532C2214yescomplemented
145#2529C2214yescomplemented
146#2529C2214yescomplemented
147#2526C2214yescomplemented
148#2516C2214yescomplemented
149#2515C2214yescomplemented
150#2503C2212yescomplemented
151#2502C2212yescomplemented
152#2497C2214yescomplemented
153#2488C2214yescomplemented
154#2481C2214yes—
155#2475C2214yescomplemented
156#2471C2214yes—
157#2464C2214yes—
158#2461C2214yes—
159#2461C2214yescomplemented
160#2460C2214yescomplemented
161#2459C2214yes—
162#2459C2214yescomplemented
163#2457C2214yes—
164#2456C2214yes—
165#2454C2214yes—
166#2454C2214yescomplemented
167#2452C2214yescomplemented
168#2450C2214yes—
169#2450C2214yescomplemented
170#2450C2214yescomplemented
171#2444C2214yes—
172#2444C2214yescomplemented
173#2438C2214yescomplemented
174#2437C2214yescomplemented
175#2437C2212yescomplemented
176#2432C2214yes—
177#2431C2212yes—
178#2430C2212yes—
179#2430C2214yescomplemented
180#2427C2214yescomplemented
181#2425C2214yes—
182#2425C2214yescomplemented
183#2424C2214yes—
184#2424C2214yescomplemented
185#2419C2214yescomplemented
186#2419C2214yescomplemented
187#2418C2214yes—
188#2418C2214yescomplemented
189#2417C2214yescomplemented
190#2414C2214yes—
191#2413C2214yescomplemented
192#2412C2214yes—
193#2407C2214yescomplemented
194#2406C2212yes—
195#2404C2214yes—
196#2404C2214yes—
197#2397C2214yes—
198C2×#400C2212yescomplemented
199C2×#397C2212yescomplemented
200#2382C2212yescomplemented
201#2379C2212yes—
202#2366C2212yes—
203#2364C2212yescomplemented
204#2359C2214yescomplemented
205#2358C2214yescomplemented
206#2349C2214yescomplemented
207#2343C2214yescomplemented
208#2339C2214yes—
209#2339C2212yescomplemented
210#2325C2214yes—
211#2324C2214yescomplemented
212#2321C2214yes—
213#2321C2212yes—
214#2318C2214yescomplemented
215#2311C2212yes—
216C4×#127C2211yescharacteristic
217C4×#125C2212yescomplemented
218#2293C2211yescharacteristic, complemented
219C22×#41C2312yes—
220C22×#41C2312yes—
221C22×#41C2312yes—
222#547—44no—
223#547—44no—
224#538—48no—
225#537—48no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2314yes—
229C2×#127C2311yescharacteristic
230C2×#126C2314yes—
231C2×#125C2312yes—
232C2×#125C2312yes—
233C2×#125C2314yes—
234C2×#124C2312yes—
235C2×#124C2314yes—
236C2×#124C2314yes—
237C2×#124C2312yes—
238C2×#123C2314yes—
239C2×#123C2312yes—
240C2×#123C2312yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×#121C2314yes—
256C2×#121C2312yes—
257C2×#121C2314yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#120C2312yes—
265C2×#120C2314yes—
266C2×#120C2314yes—
267C2×#120C2314yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×#117C2314yes—
281C2×#117C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2314yes—
287C22×C22⋊C4C2314yes—
288#400C2312yes—
289#400C2312yes—
290#400C2314yes—
291#400C2312yes—
292#400C2312yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2312yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#399C2312yes—
311#399C2312yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2312yes—
318#399C2314yes—
319#399C2312yes—
320#399C2312yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#395C2314yes—
370#395C2312yes—
371#395C2312yes—
372#395C2312yes—
373#395C2314yes—
374#395C2312yes—
375#395C2314yes—
376#395C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2312yes—
383#394C2314yes—
384#394C2312yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2312yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#393C2314yes—
399#393C2312yes—
400#393C2312yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2312yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#390C2312yes—
430#390C2314yes—
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2314yes—
434#390C2312yes—
435#390C2314yes—
436#390C2314yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2314yes—
442#390C2314yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
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#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2312yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2312yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#384C2311yescharacteristic
565#384C2312yes—
566#383C2314yes—
567#383C2314yes—
568#382C2312yes—
569#382C2314yes—
570#382C2312yes—
571#382C2314yes—
572#382C2312yes—
573#381C2312yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2312yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2312yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#379C2312yes—
596#379C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2311yescharacteristic
602C4×C4⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2312yes—
610#376C2314yes—
611C2×#95C2312yes—
612C2×#95C2312yes—
613C2×#95C2314yes—
614C2×#95C2314yes—
615C2×#95C2312yes—
616C2×#95C2314yes—
617C43C2311yescharacteristic
618C25C2412yes—
619C2×#41—28no—
620C2×#41—28no—
621C2×#41—44no—
622C2×#41—44no—
623C2×#41—82no—
624C2×#41—84no—
625C2×#41—84no—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2411yescharacteristic
637C22×D4C2414yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2411yescharacteristic
644C22×D4C2411yescharacteristic
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2414yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2412yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C4⋊Q8—42no—
659C4⋊Q8—42no—
660C4⋊Q8—84no—
661#127—24no—
662#126—48no—
663#125—44no—
664#125—44no—
665#125—84no—
666#124—44no—
667#124—48no—
668#124—82no—
669#124—84no—
670#123—48no—
671#123—48no—
672#123—48no—
673#123—44no—
674#123—44no—
675#123—84no—
676#123—84no—
677#123—84no—
678C22⋊Q8—44no—
679C22⋊Q8—44no—
680C22⋊Q8—48no—
681C22⋊Q8—44no—
682C22⋊Q8—44no—
683C22⋊Q8—44no—
684C22⋊Q8—84no—
685C22⋊Q8—84no—
686C22⋊Q8—84no—
687#121—216no—
688#121—28no—
689#121—44no—
690#121—48no—
691#121—48no—
692#121—44no—
693#121—48no—
694#121—44no—
695#121—84no—
696#120—28no—
697#120—48no—
698#120—48no—
699#120—84no—
700C4×D4—24no—
701C4×D4—48no—
702C4×D4—48no—
703C4×D4—42no—
704C4×D4—42no—
705C4×D4—48no—
706C4×D4—84no—
707C4×D4—84no—
708C4×D4—84no—
709C4×D4—84no—
710C4×D4—84no—
711C4×D4—84no—
712#117—48no—
713#117—82no—
714C2×C4⋊C4—44no—
715C2×C4⋊C4—44no—
716C2×C4⋊C4—44no—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C22⋊C4—44no—
765C2×C22⋊C4—84no—
766C2×C22⋊C4—84no—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C42C2414yes—
818C2×C42C2411yescharacteristic
819C2×C42C2412yes—
820C2×C42C2411yescharacteristic
821C2×C42C2411yescharacteristic
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830#95C2412yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2412yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
839#95C2414yes—
840#95C2412yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2412yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2412yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2412yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882C24—24no—
883C24—42no—
884C24—44no—
885C24—44no—
886C24—42no—
887C24C2514yes—
888C24C2512yes—
889C24C2512yes—
890C24C2512yes—
891#41—816no—
892#41—816no—
893#41—816no—
894C2×Q8—24no—
895C2×Q8—24no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—44no—
899C2×Q8—42no—
900C2×Q8—44no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—44no—
904C2×Q8—42no—
905C2×Q8—42no—
906C2×D4—28no—
907C2×D4—24no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—24no—
913C2×D4—28no—
914C2×D4—22no—
915C2×D4—28no—
916C2×D4—41no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—41no—
921C2×D4—42no—
922C2×D4—41no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—42no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—41no—
936C2×D4—44no—
937C2×D4—42no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4H(5,𝔽2)14yes—
943C2×D42−1+414yes—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—28no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2511yescharacteristic
993C22×C4C2512yes—
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2512yes—
997C4⋊C4—22no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—41no—
1004C4⋊C4—42no—
1005C4⋊C4—44no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—44no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—41no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—44no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C22⋊C4—24no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—24no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C42—22no—
1095C42—22no—
1096C42—28no—
1097C42—24no—
1098C42—44no—
1099C42—41no—
1100C42—42no—
1101C42—44no—
1102C42—42no—
1103C42—44no—
1104C42—44no—
1105C42—44no—
1106C42—44no—
1107C23—22no—
1108C23—22no—
1109C23—24no—
1110C23—24no—
1111C23—22no—
1112C23—24no—
1113C23—22no—
1114C23—24no—
1115C23—24no—
1116C23—22no—
1117C23—24no—
1118C23—22no—
1119C23—24no—
1120C23—24no—
1121C23—24no—
1122C23—24no—
1123C23—22no—
1124C23—24no—
1125C23—24no—
1126C23—24no—
1127C23—84no—
1128C23—88no—
1129C23—88no—
1130C23—162no—
1131C23—162no—
1132C23C2×H(5,𝔽2)14yes—
1133C23C2×2−1+414yes—
1134C23C2611yescharacteristic
1135Q8—84no—
1136Q8—84no—
1137Q8—84no—
1138Q8—162no—
1139Q8—162no—
1140D4—44no—
1141D4—44no—
1142D4—416no—
1143D4—416no—
1144D4—48no—
1145D4—82no—
1146D4—88no—
1147D4—88no—
1148D4—84no—
1149D4—88no—
1150D4—88no—
1151D4—84no—
1152D4—164no—
1153D4—162no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—48no—
1203C2×C4—48no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—88no—
1207C2×C4—84no—
1208C2×C4—88no—
1209C2×C4—88no—
1210C2×C4—162no—
1211C2×C4—164no—
1212C2×C4—164no—
1213C2×C4—164no—
1214C2×C4—164no—
1215C2×C4C2×H(5,𝔽2)12yes—
1216C2×C4C2×2−1+412yes—
1217C2×C4#58514yes—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—28no—
1223C22—42no—
1224C22—44no—
1225C22—44no—
1226C22—42no—
1227C22—44no—
1228C22—44no—
1229C22—42no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—42no—
1234C22—44no—
1235C22—42no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—168no—
1241C22C22×H(5,𝔽2)11yescharacteristic
1242C22C22×2−1+411yescharacteristic
1243C22C2×#58512yes—
1244C22H(7,𝔽2)11yescharacteristic
1245C22H(7,𝔽2)12yes—
1246C4—22no—
1247C4—22no—
1248C4—24no—
1249C4—41no—
1250C4—44no—
1251C4—44no—
1252C4—44no—
1253C4—44no—
1254C4—44no—
1255C4—44no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—42no—
1260C4—44no—
1261C4—42no—
1262C4—42no—
1263C4—44no—
1264C4—44no—
1265C2—44no—
1266C2—44no—
1267C2—82no—
1268C2—84no—
1269C2#6286211yescharacteristic
1270C2#6289411yescharacteristic
1271C2#6294812yes—
1272C2#6302411yescharacteristic
1273C2#6306012yes—
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. #59465C2semidirect
2. #58590C2semidirect
3. #57759C2semidirect
4. #57323C2semidirect
5. #55614C2semidirect
6. #54784C2semidirect
7. #52673C2semidirect
8. #50973C2semidirect
9. #48105C2semidirect
10. #47170C2semidirect
11. #46434C2semidirect
12. #46380C2semidirect
13. #46163C2semidirect
14. #44450C2semidirect
15. #44227C2semidirect
16. #43688C2semidirect
17. #43420C2semidirect
18. #42180C2semidirect
19. #42149C2semidirect
20. #40812C2semidirect
21. #38951C2semidirect
22. #38770C2semidirect
23. #37249C2semidirect
25. C2×#547C22semidirect
26. C2×#538C22semidirect
28. #2862C22semidirect
30. #2842C22semidirect
31. #2841C22semidirect
33. #2837C22semidirect
35. #2827C22semidirect
36. #2822C22semidirect
38. #2820C22semidirect
39. #2817C22semidirect
42. #2809C22semidirect
43. #2807C22semidirect
44. #2805C22semidirect
46. #2799C22semidirect
47. #2799C22semidirect
48. #2798C22semidirect
51. #2784C22semidirect
52. #2782C22semidirect
56. #2772C22semidirect
57. #2771C22semidirect
58. #2769C22semidirect
61. #2751C22semidirect
64. #2744C22semidirect
66. #2743C22semidirect
67. #2742C22semidirect
68. #2740C22semidirect
69. #2740C22semidirect
70. #2738C22semidirect
71. #2738C22semidirect
74. #2732C22semidirect
75. #2729C22semidirect
76. #2729C22semidirect
77. #2728C22semidirect
79. #2720C22semidirect
80. #2716C22semidirect
81. #2713C22semidirect
83. #2710C22semidirect
84. #2708C22semidirect
86. #2706C22semidirect
87. #2706C22semidirect
88. #2702C22semidirect
89. #2701C22semidirect
90. #2700C22semidirect
91. #2700C22semidirect
92. #2694C22semidirect
93. #2694C22semidirect
96. #2689C22semidirect
98. #2688C22semidirect
99. #2686C22semidirect
104. #2678C22semidirect
106. #2674C22semidirect
109. #2665C22semidirect
110. #2663C22semidirect
111. #2654C22semidirect
112. #2652C22semidirect
113. #2650C22semidirect
114. #2646C22semidirect
119. #2627C22semidirect
120. #2623C22semidirect
121. #2620C22semidirect
122. #2605C22semidirect
123. #2600C22semidirect
124. #2598C22semidirect
126. #2589C22semidirect
127. #2587C22semidirect
128. #2579C22semidirect
130. #2571C22semidirect
131. #2569C22semidirect
133. #2564C22semidirect
134. #2564C22semidirect
135. #2563C22semidirect
138. #2556C22semidirect
139. #2551C22semidirect
140. #2547C22semidirect
141. #2543C22semidirect
143. #2534C22semidirect
144. #2532C22semidirect
145. #2529C22semidirect
146. #2529C22semidirect
147. #2526C22semidirect
148. #2516C22semidirect
149. #2515C22semidirect
150. #2503C22semidirect
151. #2502C22semidirect
152. #2497C22semidirect
153. #2488C22semidirect
155. #2475C22semidirect
159. #2461C22semidirect
160. #2460C22semidirect
162. #2459C22semidirect
166. #2454C22semidirect
167. #2452C22semidirect
169. #2450C22semidirect
170. #2450C22semidirect
172. #2444C22semidirect
173. #2438C22semidirect
174. #2437C22semidirect
175. #2437C22semidirect
179. #2430C22semidirect
180. #2427C22semidirect
182. #2425C22semidirect
184. #2424C22semidirect
185. #2419C22semidirect
186. #2419C22semidirect
188. #2418C22semidirect
189. #2417C22semidirect
191. #2413C22semidirect
193. #2407C22semidirect
198. C2×#400C22semidirect
199. C2×#397C22semidirect
200. #2382C22semidirect
203. #2364C22semidirect
204. #2359C22semidirect
205. #2358C22semidirect
206. #2349C22semidirect
207. #2343C22semidirect
209. #2339C22semidirect
211. #2324C22semidirect
214. #2318C22semidirect
217. C4×#125C22semidirect
218. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#594652
#585902
#577592
#573232
#556142
#547842
#526732
#509732
#481052
#471702
#464342
#463802
#461632
#444502
#442272
#436882
#434202
#421802
#421492
#408122
#389512
#387702
#372492