Finite Group Databasebeta

← #9058629

Subgroups — #9058629

Order 512.

4207 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60027C211yesmaximal, characteristic, complemented
2#59578C213yesmaximal, complemented
3#58460C211yesmaximal, characteristic, complemented
4#57669C211yesmaximal, characteristic, complemented
5#54366C213yesmaximal, complemented
6#54216C213yesmaximal, complemented
7#49173C213yesmaximal, complemented
8#48719C213yesmaximal, complemented
9#47246C213yesmaximal, complemented
10#46994C213yesmaximal, complemented
11#46891C213yesmaximal, complemented
12#46626C213yesmaximal, complemented
13#44695C213yesmaximal, complemented
14#44232C213yesmaximal, complemented
15#43818C213yesmaximal, complemented
16#43626C213yesmaximal, complemented
17#43623C213yesmaximal, complemented
18#43187C213yesmaximal, complemented
19#43092C213yesmaximal, complemented
20#43074C213yesmaximal, complemented
21#36053C213yesmaximal, complemented
22#35696C213yesmaximal, complemented
23#35485C213yesmaximal, complemented
24#2838C2213yes—
25#2838C2213yes—
26#2835C2213yes—
27#2833C2213yescomplemented
28#2809C2213yescomplemented
29#2804C2213yes—
30#2798C2213yes—
31#2796C2213yes—
32#2794C2213yescomplemented
33#2793C2213yes—
34#2790C2213yes—
35#2790C2213yescomplemented
36#2789C2213yescomplemented
37#2789C2213yescomplemented
38#2789C2213yescomplemented
39#2787C2213yes—
40#2784C2213yes—
41#2781C2213yes—
42#2780C2213yes—
43#2779C2213yes—
44#2778C2213yes—
45#2778C2213yes—
46#2777C2213yes—
47#2776C2213yescomplemented
48#2770C2213yescomplemented
49#2764C2213yescomplemented
50#2762C2213yescomplemented
51#2762C2213yescomplemented
52#2762C2213yescomplemented
53#2761C2213yes—
54#2760C2213yes—
55#2759C2213yes—
56#2759C2213yes—
57#2759C2213yes—
58#2759C2213yes—
59#2759C2213yes—
60#2755C2213yescomplemented
61#2751C2213yes—
62#2751C2213yes—
63#2746C2213yes—
64#2746C2213yescomplemented
65#2745C2213yes—
66#2745C2213yescomplemented
67#2744C2213yes—
68#2744C2213yes—
69#2743C2213yes—
70#2739C2213yescomplemented
71#2736C2211yescharacteristic
72#2735C2213yes—
73#2729C2213yescomplemented
74#2723C2213yes—
75#2720C2213yescomplemented
76#2718C2213yes—
77#2716C2213yes—
78#2716C2213yes—
79#2715C2213yes—
80#2713C2213yescomplemented
81#2702C2213yes—
82#2700C2213yes—
83#2697C2213yes—
84#2695C2213yes—
85#2691C2213yes—
86#2689C2213yescomplemented
87#2684C2213yes—
88#2684C2213yes—
89#2668C2213yes—
90#2665C2213yescomplemented
91#2653C2213yes—
92#2645C2213yescomplemented
93#2643C2213yes—
94#2643C2213yes—
95#2630C2213yes—
96#2611C2213yes—
97#2607C2213yes—
98#2605C2213yescomplemented
99#2603C2213yes—
100#2601C2213yes—
101#2600C2213yes—
102#2600C2213yescomplemented
103#2598C2213yes—
104#2596C2213yes—
105#2596C2213yes—
106#2594C2213yes—
107#2594C2213yes—
108#2589C2213yescomplemented
109#2586C2213yescomplemented
110#2585C2213yescomplemented
111#2578C2213yes—
112#2578C2213yes—
113#2577C2213yes—
114#2577C2213yes—
115#2576C2213yes—
116#2576C2213yes—
117#2576C2213yescomplemented
118#2576C2213yescomplemented
119#2574C2213yes—
120#2574C2213yescomplemented
121#2574C2213yescomplemented
122#2572C2213yes—
123#2564C2213yescomplemented
124#2562C2213yescomplemented
125#2559C2213yes—
126#2559C2213yes—
127#2549C2213yescomplemented
128#2533C2213yescomplemented
129#2532C2213yes—
130#2528C2213yescomplemented
131#2527C2213yes—
132#2527C2213yes—
133#2527C2213yescomplemented
134#2527C2213yescomplemented
135#2527C2213yescomplemented
136#2526C2213yes—
137#2524C2213yescomplemented
138#2521C2213yes—
139#2521C2213yes—
140#2519C2213yes—
141#2516C2213yes—
142#2515C2213yes—
143#2514C2213yescomplemented
144#2514C2213yescomplemented
145#2514C2213yescomplemented
146#2514C2213yescomplemented
147#2514C2213yescomplemented
148#2511C2213yescomplemented
149#2510C2213yes—
150#2510C2213yes—
151#2510C2213yes—
152#2510C2213yes—
153#2510C2213yes—
154#2510C2213yes—
155#2510C2213yes—
156#2510C2213yes—
157#2496C2213yescomplemented
158#2494C2213yes—
159#2494C2213yes—
160#2494C2213yes—
161#2493C2213yescomplemented
162#2493C2213yescomplemented
163#2493C2213yescomplemented
164#2493C2213yescomplemented
165#2493C2213yescomplemented
166#2493C2213yescomplemented
167#2493C2213yescomplemented
168#2493C2213yescomplemented
169#2492C2213yescomplemented
170#2488C2213yes—
171#2488C2213yes—
172#2488C2213yes—
173#2480C2213yes—
174#2480C2213yes—
175#2478C2213yes—
176#2477C2213yes—
177#2477C2213yescomplemented
178#2468C2213yescomplemented
179#2468C2213yescomplemented
180#2468C2213yescomplemented
181#2467C2213yes—
182#2466C2213yes—
183#2466C2213yescomplemented
184#2466C2213yescomplemented
185#2463C2213yescomplemented
186#2461C2213yes—
187#2460C2213yes—
188#2459C2213yes—
189#2459C2213yes—
190#2459C2213yes—
191#2456C2213yes—
192#2450C2213yes—
193#2450C2213yescomplemented
194#2444C2213yes—
195#2444C2213yes—
196#2438C2213yescomplemented
197#2432C2213yes—
198#2430C2213yes—
199#2427C2213yes—
200#2419C2213yes—
201#2418C2213yes—
202#2407C2213yes—
203#2404C2213yes—
204#2401C2213yes—
205C2×#401C2213yescomplemented
206C2×#401C2211yescharacteristic, complemented
207#2392C2213yescomplemented
208#2388C2213yes—
209#2388C2211yescharacteristic, complemented
210#2383C2211yescharacteristic, complemented
211#2375C2211yescharacteristic
212#2374C2213yes—
213#2373C2213yes—
214#2373C2213yescomplemented
215#2368C2213yescomplemented
216#2368C2213yescomplemented
217#2364C2213yes—
218#2359C2213yes—
219#2354C2213yes—
220#2353C2213yescomplemented
221#2349C2213yescomplemented
222#2349C2213yescomplemented
223#2349C2213yescomplemented
224#2343C2213yescomplemented
225#2342C2213yes—
226#2339C2213yes—
227#2339C2213yes—
228#2339C2213yes—
229#2339C2213yescomplemented
230#2337C2213yes—
231#2337C2213yes—
232#2336C2213yescomplemented
233#2334C2213yes—
234#2332C2213yescomplemented
235#2331C2213yescomplemented
236#2329C2213yescomplemented
237#2325C2213yes—
238#2321C2213yes—
239#2318C2213yes—
240#2318C2213yescomplemented
241C4×#126C2211yescharacteristic, complemented
242C4×#126C2213yescomplemented
243#2298C2213yes—
244#2275C2213yescomplemented
245C22×#41C2313yes—
246C22×#41C2311yescharacteristic
247C2×C4⋊Q8C2313yes—
248C2×#126C2313yes—
249C2×#126C2311yescharacteristic
250C2×#126C2313yes—
251C2×#126C2313yes—
252C2×#126C2313yes—
253C2×#126C2311yescharacteristic
254C2×#125C2313yes—
255C2×#124C2313yes—
256C2×#124C2313yes—
257C2×#123C2313yes—
258C2×#123C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265C2×#120C2313yes—
266C2×#120C2311yescharacteristic
267C2×C4×D4C2313yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2313yes—
272C2×C4×D4C2313yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×#117C2313yes—
278C2×#117C2313yes—
279C22×C22⋊C4C2313yes—
280#401C2313yes—
281#401C2313yes—
282#401C2313yes—
283#401C2313yes—
284#401C2313yes—
285#401C2313yes—
286#401C2311yescharacteristic
287#401C2313yes—
288#401C2313yes—
289#401C2313yes—
290#401C2311yescharacteristic
291#401C2313yes—
292#401C2313yes—
293#401C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2313yes—
298#400C2313yes—
299#400C2313yes—
300#400C2313yes—
301#400C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#399C2313yes—
325#399C2313yes—
326#399C2313yes—
327#399C2313yes—
328#398C2313yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#397C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2313yes—
350#397C2313yes—
351#397C2313yes—
352#397C2313yes—
353#397C2313yes—
354#397C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#396C2313yes—
367#396C2313yes—
368#396C2313yes—
369#396C2313yes—
370#396C2313yes—
371#396C2313yes—
372#396C2313yes—
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#395C2313yes—
377#395C2311yescharacteristic
378#395C2313yes—
379#395C2313yes—
380#395C2313yes—
381#395C2313yes—
382#395C2313yes—
383#395C2313yes—
384#394C2313yes—
385#394C2313yes—
386#394C2313yes—
387#394C2313yes—
388#394C2313yes—
389#394C2313yes—
390#394C2313yes—
391#394C2313yes—
392#394C2313yes—
393#394C2313yes—
394#394C2313yes—
395#394C2313yes—
396#394C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#393C2313yes—
401#393C2313yes—
402#393C2313yes—
403#393C2313yes—
404#393C2313yes—
405#393C2313yes—
406#393C2313yes—
407#393C2313yes—
408#393C2311yescharacteristic
409#393C2313yes—
410#393C2313yes—
411#393C2313yes—
412#392C2313yes—
413#392C2313yes—
414#392C2313yes—
415#392C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2313yes—
425#391C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2313yes—
463#388C2313yes—
464#388C2313yes—
465#388C2313yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2313yes—
472#388C2313yes—
473#388C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2313yes—
528#387C2313yes—
529#387C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#387C2313yes—
538#387C2313yes—
539#387C2313yes—
540#387C2313yes—
541#387C2313yes—
542#387C2313yes—
543#387C2313yes—
544#387C2313yes—
545#387C2313yes—
546#387C2313yes—
547#387C2313yes—
548#387C2313yes—
549#387C2313yes—
550#387C2313yes—
551#387C2313yes—
552#387C2313yes—
553#387C2313yes—
554#387C2313yes—
555#387C2313yes—
556#387C2313yes—
557#387C2313yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2313yes—
563#387C2313yes—
564#386C2313yes—
565#386C2313yes—
566#386C2313yes—
567#386C2313yes—
568#386C2313yes—
569#386C2313yes—
570#386C2313yes—
571#386C2313yes—
572#386C2313yes—
573#386C2313yes—
574#386C2313yes—
575#386C2313yes—
576#386C2313yes—
577#386C2313yes—
578#386C2313yes—
579#386C2313yes—
580#386C2313yes—
581#386C2313yes—
582#386C2313yes—
583#386C2313yes—
584#386C2313yes—
585#386C2313yes—
586#386C2313yes—
587#386C2313yes—
588#386C2313yes—
589#386C2313yes—
590#386C2313yes—
591#386C2313yes—
592#386C2313yes—
593#386C2313yes—
594#385C2313yes—
595#385C2313yes—
596#385C2313yes—
597#385C2313yes—
598#385C2313yes—
599#385C2313yes—
600#385C2313yes—
601#385C2313yes—
602#385C2313yes—
603#385C2313yes—
604#385C2313yes—
605#385C2313yes—
606#385C2313yes—
607#385C2313yes—
608#385C2313yes—
609#385C2313yes—
610#385C2313yes—
611#385C2313yes—
612#385C2313yes—
613#385C2313yes—
614#385C2313yes—
615#385C2313yes—
616#385C2313yes—
617#385C2313yes—
618#385C2313yes—
619#385C2313yes—
620#385C2313yes—
621#385C2313yes—
622#385C2313yes—
623#385C2313yes—
624#384C2313yes—
625#384C2311yescharacteristic
626#383C2313yes—
627#383C2311yescharacteristic
628#383C2313yes—
629#383C2313yes—
630#383C2313yes—
631#383C2313yes—
632#383C2313yes—
633#383C2313yes—
634#383C2313yes—
635#383C2311yescharacteristic
636#382C2313yes—
637#382C2313yes—
638#382C2313yes—
639#382C2313yes—
640#382C2313yes—
641#382C2313yes—
642#381C2313yes—
643#381C2313yes—
644#381C2313yes—
645#381C2313yes—
646#381C2313yes—
647#381C2313yes—
648#381C2313yes—
649#381C2313yes—
650#381C2313yes—
651#381C2313yes—
652#381C2313yes—
653#381C2313yes—
654#380C2313yes—
655#380C2313yes—
656#380C2313yes—
657#380C2313yes—
658#380C2313yes—
659#380C2313yes—
660#380C2313yes—
661#380C2313yes—
662#380C2313yes—
663#380C2313yes—
664#380C2313yes—
665#380C2313yes—
666#380C2313yes—
667#380C2313yes—
668#379C2313yes—
669#379C2313yes—
670#379C2311yescharacteristic
671#379C2311yescharacteristic
672C4×C4⋊C4C2313yes—
673C4×C4⋊C4C2313yes—
674C4×C4⋊C4C2313yes—
675C4×C4⋊C4C2313yes—
676C4×C4⋊C4C2313yes—
677C4×C4⋊C4C2313yes—
678C4×C4⋊C4C2313yes—
679C4×C4⋊C4C2313yes—
680C4×C4⋊C4C2313yes—
681C4×C4⋊C4C2313yes—
682C4×C4⋊C4C2313yes—
683C4×C4⋊C4C2313yes—
684C4×C4⋊C4C2313yes—
685C4×C4⋊C4C2313yes—
686C4×C22⋊C4C2313yes—
687C4×C22⋊C4C2313yes—
688C4×C22⋊C4C2313yes—
689C4×C22⋊C4C2313yes—
690C4×C22⋊C4C2313yes—
691C4×C22⋊C4C2313yes—
692C4×C22⋊C4C2313yes—
693C4×C22⋊C4C2313yes—
694C4×C22⋊C4C2313yes—
695C4×C22⋊C4C2313yes—
696C4×C22⋊C4C2313yes—
697C4×C22⋊C4C2313yes—
698C4×C22⋊C4C2313yes—
699C4×C22⋊C4C2313yes—
700C4×C22⋊C4C2313yes—
701C4×C22⋊C4C2313yes—
702C4×C22⋊C4C2313yes—
703C4×C22⋊C4C2313yes—
704C4×C22⋊C4C2313yes—
705C4×C22⋊C4C2313yes—
706#376C2313yes—
707#376C2313yes—
708#376C2313yes—
709C2×#95C2313yes—
710C2×#95C2313yes—
711C2×#95C2313yes—
712C2×#95C2313yes—
713C2×#95C2313yes—
714C2×#95C2313yes—
715C2×#95C2313yes—
716C2×#95C2311yescharacteristic
717C2×#95C2313yes—
718C2×#95C2313yes—
719C43C2311yescharacteristic
720C25C2411yescharacteristic
721C2×#41—46no—
722C2×#41—46no—
723C2×#41—46no—
724C2×#41—46no—
725C22×Q8C2413yes—
726C22×Q8C2413yes—
727C22×Q8C2413yes—
728C22×Q8C2411yescharacteristic
729C22×D4C2413yes—
730C22×D4C2413yes—
731C22×D4C2413yes—
732C22×D4C2413yes—
733C22×D4C2413yes—
734C22×D4C2413yes—
735C23×C4C2413yes—
736C23×C4C2413yes—
737C23×C4C2413yes—
738C23×C4C2413yes—
739C23×C4C2413yes—
740C23×C4C2413yes—
741C23×C4C2411yescharacteristic
742C23×C4C2413yes—
743C23×C4C2413yes—
744C23×C4C2413yes—
745C23×C4C2413yes—
746C23×C4C2413yes—
747C4⋊Q8—46no—
748#126—46no—
749#126—46no—
750#126—46no—
751#126—42no—
752#126—42no—
753#126—46no—
754#125—46no—
755#124—46no—
756#124—46no—
757#123—46no—
758#123—46no—
759C22⋊Q8—46no—
760C22⋊Q8—46no—
761C22⋊Q8—46no—
762C22⋊Q8—46no—
763#121—46no—
764#121—46no—
765#120—46no—
766#120—42no—
767C4×D4—46no—
768C4×D4—46no—
769C4×D4—46no—
770C4×D4—46no—
771C4×D4—46no—
772C4×D4—46no—
773C4×D4—46no—
774C4×D4—46no—
775C4×D4—46no—
776C4×D4—46no—
777#117—46no—
778#117—46no—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C22⋊C4—46no—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2413yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2413yes—
879C2×C42C2413yes—
880C2×C42C2413yes—
881C2×C42C2413yes—
882C2×C42C2413yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2413yes—
886C2×C42C2413yes—
887C2×C42C2411yescharacteristic
888C2×C42C2413yes—
889C2×C42C2413yes—
890C2×C42C2411yescharacteristic
891C2×C42C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2411yescharacteristic
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2413yes—
933#95C2413yes—
934#95C2413yes—
935#95C2413yes—
936#95C2413yes—
937#95C2413yes—
938#95C2413yes—
939#95C2413yes—
940#95C2413yes—
941#95C2413yes—
942#95C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2413yes—
947#95C2413yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978C24—43no—
979C24—43no—
980C24—41no—
981C24C2513yes—
982C24C2513yes—
983C24C2511yescharacteristic
984#41—824no—
985#41—88no—
986C2×Q8—26no—
987C2×Q8—43no—
988C2×Q8—43no—
989C2×Q8—43no—
990C2×Q8—43no—
991C2×Q8—43no—
992C2×Q8—43no—
993C2×Q8—43no—
994C2×Q8—43no—
995C2×Q8—43no—
996C2×D4—26no—
997C2×D4—26no—
998C2×D4—26no—
999C2×D4—26no—
1000C2×D4—26no—
1001C2×D4—26no—
1002C2×D4—26no—
1003C2×D4—26no—
1004C2×D4—26no—
1005C2×D4—43no—
1006C2×D4—43no—
1007C2×D4—43no—
1008C2×D4—43no—
1009C2×D4—43no—
1010C2×D4—43no—
1011C2×D4—43no—
1012C2×D4—43no—
1013C2×D4—43no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—26no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—43no—
1020C22×C4—43no—
1021C22×C4—43no—
1022C22×C4—43no—
1023C22×C4—43no—
1024C22×C4—43no—
1025C22×C4—43no—
1026C22×C4—43no—
1027C22×C4—43no—
1028C22×C4—43no—
1029C22×C4—43no—
1030C22×C4—43no—
1031C22×C4—43no—
1032C22×C4—43no—
1033C22×C4—43no—
1034C22×C4—43no—
1035C22×C4—43no—
1036C22×C4—43no—
1037C22×C4—43no—
1038C22×C4—43no—
1039C22×C4—43no—
1040C22×C4—43no—
1041C22×C4—43no—
1042C22×C4—43no—
1043C22×C4—43no—
1044C22×C4—43no—
1045C22×C4—43no—
1046C22×C4—43no—
1047C22×C4—43no—
1048C22×C4C2513yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2513yes—
1051C22×C4C2513yes—
1052C22×C4C2513yes—
1053C22×C4C2513yes—
1054C22×C4C2513yes—
1055C22×C4C2513yes—
1056C22×C4C2513yes—
1057C22×C4C2513yes—
1058C22×C4C2513yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2513yes—
1061C22×C4C2513yes—
1062C22×C4C2513yes—
1063C22×C4C2513yes—
1064C22×C4C2513yes—
1065C22×C4C2513yes—
1066C22×C4C2513yes—
1067C22×C4C2513yes—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—43no—
1081C4⋊C4—43no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—43no—
1100C4⋊C4—43no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—43no—
1104C4⋊C4—43no—
1105C4⋊C4—43no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—43no—
1110C4⋊C4—43no—
1111C4⋊C4—43no—
1112C22⋊C4—26no—
1113C22⋊C4—26no—
1114C22⋊C4—26no—
1115C22⋊C4—26no—
1116C22⋊C4—26no—
1117C22⋊C4—26no—
1118C22⋊C4—26no—
1119C22⋊C4—26no—
1120C22⋊C4—26no—
1121C22⋊C4—26no—
1122C22⋊C4—26no—
1123C22⋊C4—26no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—43no—
1138C22⋊C4—43no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—43no—
1160C42—26no—
1161C42—26no—
1162C42—43no—
1163C42—43no—
1164C42—43no—
1165C42—43no—
1166C42—43no—
1167C42—43no—
1168C42—43no—
1169C42—43no—
1170C42—43no—
1171C42—43no—
1172C42—43no—
1173C42—43no—
1174C42—41no—
1175C42—43no—
1176C42—41no—
1177C42—43no—
1178C42—43no—
1179C42—43no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23—23no—
1195C23—86no—
1196C23—161no—
1197C23—163no—
1198C23#58516yes—
1199C23#58512yes—
1200C23C2611yescharacteristic
1201Q8—86no—
1202Q8—82no—
1203Q8—163no—
1204Q8—163no—
1205D4—224no—
1206D4—412no—
1207D4—86no—
1208D4—86no—
1209D4—86no—
1210D4—86no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—86no—
1267C2×C4—86no—
1268C2×C4—86no—
1269C2×C4—86no—
1270C2×C4—86no—
1271C2×C4—86no—
1272C2×C4—161no—
1273C2×C4—163no—
1274C2×C4—163no—
1275C2×C4—163no—
1276C2×C4—163no—
1277C2×C4—163no—
1278C2×C4#58516yes—
1279C22—26no—
1280C22—26no—
1281C22—26no—
1282C22—26no—
1283C22—41no—
1284C22—43no—
1285C22—43no—
1286C22—43no—
1287C22—43no—
1288C22—43no—
1289C22—43no—
1290C22—43no—
1291C22—43no—
1292C22—43no—
1293C22—43no—
1294C22—43no—
1295C22—43no—
1296C22—164no—
1297C22C2×#58513yes—
1298C22C2×#58513yes—
1299C22C2×#58511yescharacteristic
1300C4—26no—
1301C4—41no—
1302C4—43no—
1303C4—41no—
1304C4—43no—
1305C4—43no—
1306C4—43no—
1307C4—43no—
1308C4—43no—
1309C4—43no—
1310C4—43no—
1311C4—43no—
1312C4—43no—
1313C4—43no—
1314C4—43no—
1315C4—43no—
1316C4—43no—
1317C4—43no—
1318C4—43no—
1319C4—43no—
1320C2—46no—
1321C2—42no—
1322C2—83no—
1323C2#6282613yes—
1324C2#6302611yescharacteristic
1325C2#6302913yes—
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. #60027C2semidirect
2. #59578C2semidirect
3. #58460C2semidirect
4. #57669C2semidirect
5. #54366C2semidirect
6. #54216C2semidirect
7. #49173C2semidirect
8. #48719C2semidirect
9. #47246C2semidirect
10. #46994C2semidirect
11. #46891C2semidirect
12. #46626C2semidirect
13. #44695C2semidirect
14. #44232C2semidirect
15. #43818C2semidirect
16. #43626C2semidirect
17. #43623C2semidirect
18. #43187C2semidirect
19. #43092C2semidirect
20. #43074C2semidirect
21. #36053C2semidirect
22. #35696C2semidirect
23. #35485C2semidirect
27. #2833C22semidirect
28. #2809C22semidirect
32. #2794C22semidirect
35. #2790C22semidirect
36. #2789C22semidirect
37. #2789C22semidirect
38. #2789C22semidirect
47. #2776C22semidirect
48. #2770C22semidirect
49. #2764C22semidirect
50. #2762C22semidirect
51. #2762C22semidirect
52. #2762C22semidirect
60. #2755C22semidirect
64. #2746C22semidirect
66. #2745C22semidirect
70. #2739C22semidirect
73. #2729C22semidirect
75. #2720C22semidirect
80. #2713C22semidirect
86. #2689C22semidirect
90. #2665C22semidirect
92. #2645C22semidirect
98. #2605C22semidirect
102. #2600C22semidirect
108. #2589C22semidirect
109. #2586C22semidirect
110. #2585C22semidirect
117. #2576C22semidirect
118. #2576C22semidirect
120. #2574C22semidirect
121. #2574C22semidirect
123. #2564C22semidirect
124. #2562C22semidirect
127. #2549C22semidirect
128. #2533C22semidirect
130. #2528C22semidirect
133. #2527C22semidirect
134. #2527C22semidirect
135. #2527C22semidirect
137. #2524C22semidirect
143. #2514C22semidirect
144. #2514C22semidirect
145. #2514C22semidirect
146. #2514C22semidirect
147. #2514C22semidirect
148. #2511C22semidirect
157. #2496C22semidirect
161. #2493C22semidirect
162. #2493C22semidirect
163. #2493C22semidirect
164. #2493C22semidirect
165. #2493C22semidirect
166. #2493C22semidirect
167. #2493C22semidirect
168. #2493C22semidirect
169. #2492C22semidirect
177. #2477C22semidirect
178. #2468C22semidirect
179. #2468C22semidirect
180. #2468C22semidirect
183. #2466C22semidirect
184. #2466C22semidirect
185. #2463C22semidirect
193. #2450C22semidirect
196. #2438C22semidirect
205. C2×#401C22semidirect
206. C2×#401C22semidirect
207. #2392C22semidirect
209. #2388C22semidirect
210. #2383C22semidirect
214. #2373C22semidirect
215. #2368C22semidirect
216. #2368C22semidirect
220. #2353C22semidirect
221. #2349C22semidirect
222. #2349C22semidirect
223. #2349C22semidirect
224. #2343C22semidirect
229. #2339C22semidirect
232. #2336C22semidirect
234. #2332C22semidirect
235. #2331C22semidirect
236. #2329C22semidirect
240. #2318C22semidirect
241. C4×#126C22semidirect
242. C4×#126C22semidirect
244. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#600272
#595782
#584602
#576692
#543662
#542162
#491732
#487192
#472462
#469942
#468912
#466262
#446952
#442322
#438182
#436262
#436232
#431872
#430922
#430742
#360532
#356962
#354852