Finite Group Databasebeta

← #9712324

Subgroups — #9712324

Order 512.

4381 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#56998C213yesmaximal, complemented
2#56475C213yesmaximal, complemented
3#56344C211yesmaximal, characteristic, complemented
4#55937C213yesmaximal, complemented
5#54567C213yesmaximal, complemented
6#54056C213yesmaximal, complemented
7#54049C213yesmaximal, complemented
8#53389C211yesmaximal, characteristic, complemented
9#53307C211yesmaximal, characteristic, complemented
10#51138C213yesmaximal, complemented
11#50472C213yesmaximal, complemented
12#49258C213yesmaximal, complemented
13#48913C213yesmaximal, complemented
14#47042C213yesmaximal, complemented
15#46599C213yesmaximal, complemented
16#44083C213yesmaximal, complemented
17#43092C213yesmaximal, complemented
18#41468C213yesmaximal, complemented
19#41427C213yesmaximal, complemented
20#38656C213yesmaximal, complemented
21#38628C213yesmaximal, complemented
22#38304C213yesmaximal, complemented
23#38059C213yesmaximal, complemented
24#2865C2213yescomplemented
25#2853C2213yescomplemented
26#2838C2213yescomplemented
27#2831C2213yescomplemented
28#2831C2213yescomplemented
29#2827C2213yescomplemented
30#2827C2213yescomplemented
31#2826C2213yes—
32#2825C2211yescharacteristic, complemented
33#2824C2213yes—
34#2824C2213yes—
35#2808C2213yescomplemented
36#2804C2213yescomplemented
37#2800C2213yescomplemented
38#2800C2213yescomplemented
39#2798C2213yescomplemented
40#2793C2213yescomplemented
41#2793C2213yescomplemented
42#2788C2213yescomplemented
43#2784C2213yescomplemented
44#2783C2213yescomplemented
45#2781C2213yescomplemented
46#2780C2213yescomplemented
47#2778C2213yescomplemented
48#2771C2213yescomplemented
49#2766C2213yescomplemented
50#2765C2213yescomplemented
51#2765C2213yescomplemented
52#2764C2213yescomplemented
53#2762C2213yescomplemented
54#2761C2213yescomplemented
55#2760C2213yescomplemented
56#2759C2213yescomplemented
57#2759C2213yescomplemented
58#2759C2213yescomplemented
59#2759C2213yescomplemented
60#2759C2213yescomplemented
61#2759C2213yescomplemented
62#2759C2213yescomplemented
63#2758C2213yescomplemented
64#2758C2213yescomplemented
65#2758C2213yescomplemented
66#2757C2213yescomplemented
67#2757C2213yescomplemented
68#2756C2213yes—
69#2756C2213yes—
70#2754C2213yescomplemented
71#2752C2213yes—
72#2751C2213yescomplemented
73#2751C2213yescomplemented
74#2750C2213yescomplemented
75#2749C2213yes—
76#2749C2213yes—
77#2749C2213yes—
78#2749C2213yescomplemented
79#2745C2213yescomplemented
80#2743C2213yescomplemented
81#2743C2213yescomplemented
82#2740C2213yescomplemented
83#2737C2213yescomplemented
84#2737C2213yescomplemented
85#2736C2213yes—
86#2736C2211yescharacteristic
87#2736C2213yes—
88#2735C2213yes—
89#2735C2213yes—
90#2735C2213yescomplemented
91#2731C2213yescomplemented
92#2730C2213yescomplemented
93#2729C2213yescomplemented
94#2728C2213yescomplemented
95#2720C2213yescomplemented
96#2718C2213yescomplemented
97#2712C2213yes—
98#2711C2213yescomplemented
99#2703C2213yes—
100#2703C2213yes—
101#2700C2213yescomplemented
102#2697C2213yes—
103#2697C2213yescomplemented
104#2697C2213yescomplemented
105#2696C2213yes—
106#2694C2213yescomplemented
107#2693C2213yes—
108#2692C2213yescomplemented
109#2692C2213yescomplemented
110#2691C2213yescomplemented
111#2690C2213yescomplemented
112#2687C2213yescomplemented
113#2684C2213yescomplemented
114#2684C2213yescomplemented
115#2681C2213yescomplemented
116#2678C2213yes—
117#2678C2213yes—
118#2674C2213yescomplemented
119#2674C2213yescomplemented
120#2668C2213yescomplemented
121#2667C2213yescomplemented
122#2665C2213yescomplemented
123#2655C2213yescomplemented
124#2654C2213yescomplemented
125#2653C2213yescomplemented
126#2653C2213yescomplemented
127#2649C2213yescomplemented
128#2649C2213yescomplemented
129#2648C2213yescomplemented
130#2643C2213yescomplemented
131#2642C2213yescomplemented
132#2639C2213yescomplemented
133#2626C2213yescomplemented
134#2620C2213yescomplemented
135#2617C2213yes—
136#2610C2213yescomplemented
137#2609C2213yescomplemented
138#2607C2213yescomplemented
139#2600C2213yescomplemented
140#2598C2213yescomplemented
141#2598C2213yescomplemented
142#2593C2213yescomplemented
143#2578C2213yescomplemented
144#2577C2213yescomplemented
145#2576C2213yescomplemented
146#2576C2213yescomplemented
147#2573C2213yescomplemented
148#2572C2213yescomplemented
149#2572C2213yescomplemented
150#2561C2213yescomplemented
151#2558C2213yescomplemented
152#2557C2213yes—
153#2557C2213yescomplemented
154#2534C2213yescomplemented
155#2532C2213yescomplemented
156#2530C2213yescomplemented
157#2527C2213yescomplemented
158#2526C2213yescomplemented
159#2524C2213yescomplemented
160#2523C2213yescomplemented
161#2518C2213yescomplemented
162#2518C2213yescomplemented
163#2516C2213yescomplemented
164#2516C2213yescomplemented
165#2510C2213yescomplemented
166#2510C2213yescomplemented
167#2510C2213yescomplemented
168#2510C2213yescomplemented
169#2499C2213yescomplemented
170#2498C2213yescomplemented
171#2498C2213yescomplemented
172#2497C2213yescomplemented
173#2493C2213yescomplemented
174#2493C2213yescomplemented
175#2493C2213yescomplemented
176#2488C2213yescomplemented
177#2488C2213yescomplemented
178#2488C2213yescomplemented
179#2477C2213yescomplemented
180#2477C2213yescomplemented
181#2475C2213yescomplemented
182#2472C2213yescomplemented
183#2472C2213yescomplemented
184#2471C2213yes—
185#2471C2213yescomplemented
186#2471C2213yescomplemented
187#2470C2213yescomplemented
188#2461C2213yes—
189#2459C2213yes—
190#2459C2213yescomplemented
191#2457C2213yescomplemented
192#2456C2213yes—
193#2452C2213yescomplemented
194#2450C2213yescomplemented
195#2450C2213yescomplemented
196#2449C2213yescomplemented
197#2444C2213yescomplemented
198#2444C2213yescomplemented
199#2443C2213yescomplemented
200#2439C2213yescomplemented
201#2438C2213yescomplemented
202#2435C2213yes—
203#2430C2213yes—
204#2430C2213yescomplemented
205#2424C2213yescomplemented
206#2418C2213yescomplemented
207#2418C2213yescomplemented
208#2418C2213yescomplemented
209#2417C2213yescomplemented
210#2413C2213yescomplemented
211#2413C2213yescomplemented
212#2411C2213yescomplemented
213#2408C2213yes—
214#2407C2213yescomplemented
215#2405C2213yes—
216#2405C2213yes—
217#2404C2213yes—
218#2404C2213yescomplemented
219#2404C2213yescomplemented
220#2403C2213yes—
221C2×#397C2213yescomplemented
222#2388C2211yescharacteristic, complemented
223#2378C2213yescomplemented
224#2375C2211yescharacteristic
225#2364C2213yescomplemented
226#2359C2213yescomplemented
227#2353C2213yescomplemented
228#2352C2213yescomplemented
229#2342C2213yescomplemented
230#2342C2213yescomplemented
231#2339C2213yescomplemented
232#2339C2213yescomplemented
233#2337C2213yescomplemented
234#2333C2213yescomplemented
235#2325C2213yescomplemented
236#2321C2213yescomplemented
237#2321C2213yescomplemented
238#2321C2213yescomplemented
239#2318C2213yescomplemented
240#2308C2213yes—
241C4×#126C2211yescharacteristic, complemented
242#2297C2213yescomplemented
243#2293C2213yescomplemented
244C2×#383C2211yescharacteristic, complemented
245C22×#41C2311yescharacteristic
246C22×#41C2313yes—
247C23×D4C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×#126C2311yescharacteristic
250C2×#125C2313yes—
251C2×#124C2313yes—
252C2×#124C2313yes—
253C2×#124C2313yes—
254C2×#123C2313yes—
255C2×#123C2313yes—
256C2×#123C2313yes—
257C2×#123C2313yes—
258C2×#123C2313yes—
259C2×#123C2313yes—
260C2×#123C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#120C2313yes—
272C2×#120C2313yes—
273C2×#120C2313yes—
274C2×#120C2311yescharacteristic
275C2×#120C2313yes—
276C2×#120C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×#117C2313yes—
284C2×#117C2313yes—
285C2×#117C2313yes—
286C2×#117C2313yes—
287C22×C4⋊C4C2313yes—
288C22×C22⋊C4C2313yes—
289C22×C22⋊C4C2313yes—
290C22×C22⋊C4C2313yes—
291C22×C22⋊C4C2313yes—
292C22×C42C2311yescharacteristic
293#401C2311yescharacteristic
294#401C2313yes—
295#401C2313yes—
296#401C2313yes—
297#401C2313yes—
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#399C2313yes—
323#399C2313yes—
324#399C2313yes—
325#399C2313yes—
326#399C2313yes—
327#399C2313yes—
328#399C2313yes—
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#397C2313yes—
341#397C2313yes—
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#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#396C2311yescharacteristic
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#396C2313yes—
377#396C2313yes—
378#396C2313yes—
379#396C2313yes—
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#395C2313yes—
392#395C2313yes—
393#395C2313yes—
394#395C2313yes—
395#395C2311yescharacteristic
396#395C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2313yes—
406#394C2313yes—
407#394C2313yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2313yes—
421#394C2313yes—
422#394C2313yes—
423#393C2313yes—
424#393C2313yes—
425#393C2313yes—
426#393C2313yes—
427#393C2313yes—
428#393C2313yes—
429#393C2313yes—
430#393C2313yes—
431#393C2313yes—
432#393C2313yes—
433#393C2313yes—
434#393C2313yes—
435#393C2313yes—
436#393C2313yes—
437#393C2311yescharacteristic
438#393C2313yes—
439#393C2313yes—
440#393C2313yes—
441#392C2313yes—
442#392C2313yes—
443#392C2311yescharacteristic
444#392C2313yes—
445#392C2313yes—
446#392C2313yes—
447#392C2313yes—
448#392C2313yes—
449#392C2313yes—
450#392C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#391C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2313yes—
465#391C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2313yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
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#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2313yes—
523#388C2313yes—
524#388C2313yes—
525#388C2313yes—
526#388C2313yes—
527#388C2313yes—
528#388C2313yes—
529#388C2313yes—
530#388C2313yes—
531#388C2313yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#388C2313yes—
537#388C2313yes—
538#388C2313yes—
539#388C2313yes—
540#388C2313yes—
541#388C2313yes—
542#388C2313yes—
543#388C2313yes—
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#387C2313yes—
565#387C2313yes—
566#387C2313yes—
567#387C2313yes—
568#387C2313yes—
569#387C2313yes—
570#387C2313yes—
571#387C2313yes—
572#387C2313yes—
573#387C2313yes—
574#387C2313yes—
575#387C2313yes—
576#387C2313yes—
577#387C2313yes—
578#387C2313yes—
579#387C2313yes—
580#387C2313yes—
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#386C2313yes—
595#386C2313yes—
596#386C2313yes—
597#386C2313yes—
598#386C2313yes—
599#386C2313yes—
600#386C2313yes—
601#386C2313yes—
602#386C2313yes—
603#386C2313yes—
604#386C2313yes—
605#386C2313yes—
606#386C2313yes—
607#386C2313yes—
608#386C2313yes—
609#386C2313yes—
610#386C2313yes—
611#386C2313yes—
612#386C2313yes—
613#386C2313yes—
614#386C2313yes—
615#386C2313yes—
616#386C2313yes—
617#386C2313yes—
618#386C2313yes—
619#386C2313yes—
620#386C2313yes—
621#386C2313yes—
622#386C2313yes—
623#386C2313yes—
624#386C2313yes—
625#386C2313yes—
626#386C2313yes—
627#386C2313yes—
628#385C2313yes—
629#385C2313yes—
630#385C2313yes—
631#385C2313yes—
632#385C2313yes—
633#385C2313yes—
634#385C2313yes—
635#385C2313yes—
636#385C2313yes—
637#385C2313yes—
638#385C2313yes—
639#385C2313yes—
640#385C2313yes—
641#385C2313yes—
642#385C2313yes—
643#385C2313yes—
644#385C2313yes—
645#385C2313yes—
646#385C2313yes—
647#385C2313yes—
648#385C2313yes—
649#385C2313yes—
650#385C2313yes—
651#384C2313yes—
652#383C2311yescharacteristic
653#383C2313yes—
654#383C2313yes—
655#383C2313yes—
656#383C2313yes—
657#383C2313yes—
658#383C2313yes—
659#383C2313yes—
660#383C2311yescharacteristic
661#383C2311yescharacteristic
662#382C2313yes—
663#382C2313yes—
664#382C2313yes—
665#381C2313yes—
666#381C2313yes—
667#381C2313yes—
668#381C2313yes—
669#381C2313yes—
670#381C2313yes—
671#381C2313yes—
672#381C2313yes—
673#381C2313yes—
674#381C2313yes—
675#381C2313yes—
676#380C2313yes—
677#380C2313yes—
678#380C2313yes—
679#380C2313yes—
680#380C2313yes—
681#380C2313yes—
682#380C2313yes—
683#380C2313yes—
684#380C2313yes—
685#380C2313yes—
686#379C2313yes—
687#379C2313yes—
688#379C2313yes—
689#379C2313yes—
690#379C2313yes—
691#379C2313yes—
692#379C2313yes—
693#379C2311yescharacteristic
694#379C2311yescharacteristic
695#379C2313yes—
696C4×C4⋊C4C2313yes—
697C4×C4⋊C4C2313yes—
698C4×C4⋊C4C2313yes—
699C4×C22⋊C4C2313yes—
700C4×C22⋊C4C2313yes—
701C4×C22⋊C4C2313yes—
702C4×C22⋊C4C2313yes—
703C4×C22⋊C4C2313yes—
704C4×C22⋊C4C2313yes—
705C4×C22⋊C4C2313yes—
706C4×C22⋊C4C2313yes—
707C4×C22⋊C4C2313yes—
708C4×C22⋊C4C2313yes—
709C4×C22⋊C4C2313yes—
710C4×C22⋊C4C2313yes—
711C4×C22⋊C4C2313yes—
712C4×C22⋊C4C2313yes—
713#376C2313yes—
714C2×#95C2313yes—
715C2×#95C2313yes—
716C2×#95C2313yes—
717C2×#95C2313yes—
718C2×#95C2313yes—
719C43C2311yescharacteristic
720C25C2413yes—
721C25C2411yescharacteristic
722C2×#41—46no—
723C2×#41—46no—
724C2×#41—46no—
725C2×#41—83no—
726C22×Q8C2413yes—
727C22×Q8C2413yes—
728C22×Q8C2413yes—
729C22×Q8C2411yescharacteristic
730C22×D4—46no—
731C22×D4—83no—
732C22×D4—83no—
733C22×D4C2413yes—
734C22×D4C2413yes—
735C22×D4C2413yes—
736C22×D4C2413yes—
737C22×D4C2413yes—
738C22×D4C2413yes—
739C22×D4C2413yes—
740C22×D4C2413yes—
741C22×D4C2413yes—
742C22×D4C2413yes—
743C22×D4C2413yes—
744C23×C4C2413yes—
745C23×C4C2413yes—
746C23×C4C2413yes—
747C23×C4C2413yes—
748C23×C4C2413yes—
749C23×C4C2413yes—
750C23×C4C2413yes—
751C23×C4C2413yes—
752C23×C4C2413yes—
753C23×C4C2411yescharacteristic
754C23×C4C2413yes—
755C23×C4C2413yes—
756C4⋊Q8—83no—
757#126—42no—
758#125—83no—
759#124—46no—
760#124—83no—
761#124—83no—
762#123—46no—
763#123—83no—
764#123—83no—
765#123—83no—
766#123—83no—
767#123—83no—
768#123—83no—
769C22⋊Q8—46no—
770C22⋊Q8—83no—
771C22⋊Q8—83no—
772C22⋊Q8—83no—
773C22⋊Q8—83no—
774C22⋊Q8—83no—
775#121—46no—
776#121—46no—
777#121—46no—
778#121—83no—
779#120—46no—
780#120—46no—
781#120—46no—
782#120—42no—
783#120—83no—
784#120—83no—
785C4×D4—46no—
786C4×D4—46no—
787C4×D4—46no—
788C4×D4—46no—
789C4×D4—83no—
790C4×D4—83no—
791#117—83no—
792#117—83no—
793#117—83no—
794#117—83no—
795C2×C4⋊C4—83no—
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×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C22⋊C4—46no—
836C2×C22⋊C4—46no—
837C2×C22⋊C4—83no—
838C2×C22⋊C4—83no—
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×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2413yes—
905C2×C42—42no—
906C2×C42C2413yes—
907C2×C42C2413yes—
908C2×C42C2413yes—
909C2×C42C2413yes—
910C2×C42C2413yes—
911C2×C42C2413yes—
912C2×C42C2413yes—
913C2×C42C2413yes—
914C2×C42C2413yes—
915C2×C42C2413yes—
916C2×C42C2413yes—
917C2×C42C2413yes—
918C2×C42C2411yescharacteristic
919C2×C42C2413yes—
920C2×C42C2411yescharacteristic
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#95C2411yescharacteristic
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993C24—26no—
994C24—43no—
995C24—43no—
996C24—43no—
997C24—43no—
998C24—43no—
999C24—43no—
1000C24—43no—
1001C24—43no—
1002C24—41no—
1003C24C2513yes—
1004C24C2513yes—
1005C24C2513yes—
1006C24C2511yescharacteristic
1007#41—824no—
1008#41—88no—
1009C2×Q8—43no—
1010C2×Q8—43no—
1011C2×Q8—43no—
1012C2×Q8—43no—
1013C2×Q8—43no—
1014C2×Q8—43no—
1015C2×Q8—43no—
1016C2×Q8—43no—
1017C2×Q8—43no—
1018C2×Q8—43no—
1019C2×D4—26no—
1020C2×D4—26no—
1021C2×D4—26no—
1022C2×D4—26no—
1023C2×D4—26no—
1024C2×D4—26no—
1025C2×D4—26no—
1026C2×D4—26no—
1027C2×D4—26no—
1028C2×D4—26no—
1029C2×D4—43no—
1030C2×D4—43no—
1031C2×D4—43no—
1032C2×D4—43no—
1033C2×D4—43no—
1034C2×D4—43no—
1035C2×D4—43no—
1036C2×D4—43no—
1037C2×D4—43no—
1038C2×D4—43no—
1039C2×D4—43no—
1040C2×D4—43no—
1041C2×D4—43no—
1042C2×D4—43no—
1043C2×D4—43no—
1044C2×D4—43no—
1045C2×D4—43no—
1046C2×D4—43no—
1047C2×D4—43no—
1048C2×D4—43no—
1049C2×D4—43no—
1050C2×D4—43no—
1051C2×D4—43no—
1052C2×D4—824no—
1053C22×C4—26no—
1054C22×C4—26no—
1055C22×C4—26no—
1056C22×C4—26no—
1057C22×C4—26no—
1058C22×C4—43no—
1059C22×C4—43no—
1060C22×C4—43no—
1061C22×C4—43no—
1062C22×C4—43no—
1063C22×C4—43no—
1064C22×C4—43no—
1065C22×C4—43no—
1066C22×C4—43no—
1067C22×C4—43no—
1068C22×C4—43no—
1069C22×C4—43no—
1070C22×C4—43no—
1071C22×C4—43no—
1072C22×C4—43no—
1073C22×C4—43no—
1074C22×C4—43no—
1075C22×C4—43no—
1076C22×C4—43no—
1077C22×C4—43no—
1078C22×C4—43no—
1079C22×C4—43no—
1080C22×C4—43no—
1081C22×C4—43no—
1082C22×C4—43no—
1083C22×C4—43no—
1084C22×C4—43no—
1085C22×C4—43no—
1086C22×C4—43no—
1087C22×C4C2511yescharacteristic
1088C22×C4C2513yes—
1089C22×C4C2513yes—
1090C22×C4C2513yes—
1091C22×C4C2513yes—
1092C22×C4C2513yes—
1093C22×C4C2513yes—
1094C22×C4C2513yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2513yes—
1097C22×C4C2513yes—
1098C22×C4C2513yes—
1099C22×C4C2513yes—
1100C22×C4C2513yes—
1101C22×C4C2513yes—
1102C22×C4C2513yes—
1103C22×C4C2513yes—
1104C22×C4C2513yes—
1105C22×C4C2513yes—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—43no—
1110C4⋊C4—43no—
1111C4⋊C4—43no—
1112C4⋊C4—43no—
1113C4⋊C4—43no—
1114C4⋊C4—43no—
1115C4⋊C4—43no—
1116C4⋊C4—43no—
1117C4⋊C4—43no—
1118C4⋊C4—43no—
1119C4⋊C4—43no—
1120C4⋊C4—43no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4—43no—
1124C4⋊C4—43no—
1125C4⋊C4—43no—
1126C4⋊C4—43no—
1127C4⋊C4—43no—
1128C4⋊C4—43no—
1129C4⋊C4—43no—
1130C4⋊C4—43no—
1131C4⋊C4—43no—
1132C4⋊C4—43no—
1133C4⋊C4—43no—
1134C4⋊C4—43no—
1135C4⋊C4—43no—
1136C4⋊C4—43no—
1137C4⋊C4—43no—
1138C4⋊C4—43no—
1139C4⋊C4—43no—
1140C4⋊C4—43no—
1141C4⋊C4—43no—
1142C4⋊C4—43no—
1143C4⋊C4—43no—
1144C4⋊C4—43no—
1145C22⋊C4—26no—
1146C22⋊C4—26no—
1147C22⋊C4—26no—
1148C22⋊C4—26no—
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—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4—43no—
1165C22⋊C4—43no—
1166C22⋊C4—43no—
1167C22⋊C4—43no—
1168C22⋊C4—43no—
1169C22⋊C4—43no—
1170C22⋊C4—43no—
1171C22⋊C4—43no—
1172C22⋊C4—43no—
1173C22⋊C4—43no—
1174C22⋊C4—43no—
1175C22⋊C4—43no—
1176C22⋊C4—43no—
1177C22⋊C4—43no—
1178C22⋊C4—43no—
1179C22⋊C4—43no—
1180C22⋊C4—43no—
1181C22⋊C4—43no—
1182C22⋊C4—43no—
1183C22⋊C4—43no—
1184C22⋊C4—43no—
1185C22⋊C4—43no—
1186C22⋊C4—43no—
1187C22⋊C4—43no—
1188C22⋊C4—43no—
1189C22⋊C4—43no—
1190C22⋊C4—43no—
1191C22⋊C4—43no—
1192C22⋊C4—43no—
1193C22⋊C4—43no—
1194C22⋊C4—43no—
1195C22⋊C4—43no—
1196C22⋊C4—43no—
1197C22⋊C4—43no—
1198C22⋊C4—43no—
1199C22⋊C4—43no—
1200C22⋊C4—43no—
1201C22⋊C4—43no—
1202C22⋊C4—43no—
1203C22⋊C4—43no—
1204C22⋊C4—43no—
1205C22⋊C4—43no—
1206C22⋊C4—43no—
1207C22⋊C4—43no—
1208C22⋊C4—43no—
1209C22⋊C4—43no—
1210C22⋊C4—43no—
1211C42—43no—
1212C42—41no—
1213C42—43no—
1214C42—43no—
1215C42—43no—
1216C42—43no—
1217C42—43no—
1218C42—43no—
1219C42—43no—
1220C42—43no—
1221C42—43no—
1222C42—43no—
1223C42—43no—
1224C42—43no—
1225C42—41no—
1226C23—23no—
1227C23—23no—
1228C23—23no—
1229C23—23no—
1230C23—23no—
1231C23—23no—
1232C23—23no—
1233C23—23no—
1234C23—23no—
1235C23—23no—
1236C23—23no—
1237C23—23no—
1238C23—23no—
1239C23—23no—
1240C23—23no—
1241C23—23no—
1242C23—23no—
1243C23—23no—
1244C23—23no—
1245C23—23no—
1246C23—23no—
1247C23—23no—
1248C23—412no—
1249C23—86no—
1250C23—86no—
1251C23—86no—
1252C23—163no—
1253C23—163no—
1254C23—163no—
1255C23—163no—
1256C23—161no—
1257C23—163no—
1258C23#58516yes—
1259C23#58512yes—
1260C23C2611yescharacteristic
1261Q8—82no—
1262Q8—86no—
1263Q8—163no—
1264Q8—163no—
1265D4—412no—
1266D4—412no—
1267D4—86no—
1268D4—86no—
1269D4—86no—
1270D4—86no—
1271D4—86no—
1272D4—86no—
1273D4—86no—
1274D4—86no—
1275D4—163no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—23no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—23no—
1288C2×C4—23no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—23no—
1302C2×C4—23no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—23no—
1316C2×C4—23no—
1317C2×C4—23no—
1318C2×C4—23no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—23no—
1322C2×C4—23no—
1323C2×C4—23no—
1324C2×C4—23no—
1325C2×C4—23no—
1326C2×C4—23no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—412no—
1330C2×C4—86no—
1331C2×C4—86no—
1332C2×C4—86no—
1333C2×C4—86no—
1334C2×C4—86no—
1335C2×C4—86no—
1336C2×C4—86no—
1337C2×C4—86no—
1338C2×C4—161no—
1339C2×C4—163no—
1340C2×C4—163no—
1341C22—26no—
1342C22—26no—
1343C22—26no—
1344C22—26no—
1345C22—41no—
1346C22—43no—
1347C22—43no—
1348C22—43no—
1349C22—43no—
1350C22—43no—
1351C22—43no—
1352C22—43no—
1353C22—43no—
1354C22—43no—
1355C22—43no—
1356C22—43no—
1357C22—43no—
1358C22—43no—
1359C22—43no—
1360C22—43no—
1361C22—43no—
1362C22—43no—
1363C22—43no—
1364C22—43no—
1365C22—1612no—
1366C22—164no—
1367C22C2×#58513yes—
1368C22C2×#58511yescharacteristic
1369C22H(7,𝔽2)13yes—
1370C4—41no—
1371C4—43no—
1372C4—41no—
1373C4—43no—
1374C4—43no—
1375C4—43no—
1376C4—43no—
1377C4—43no—
1378C4—43no—
1379C4—43no—
1380C4—43no—
1381C4—43no—
1382C4—43no—
1383C4—43no—
1384C4—43no—
1385C4—43no—
1386C4—43no—
1387C4—43no—
1388C4—43no—
1389C2—42no—
1390C2—46no—
1391C2—83no—
1392C2—83no—
1393C2#6286713yes—
1394C2#6290613yes—
1395C2#6302611yescharacteristic
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. #56998C2semidirect
2. #56475C2semidirect
3. #56344C2semidirect
4. #55937C2semidirect
5. #54567C2semidirect
6. #54056C2semidirect
7. #54049C2semidirect
8. #53389C2semidirect
9. #53307C2semidirect
10. #51138C2semidirect
11. #50472C2semidirect
12. #49258C2semidirect
13. #48913C2semidirect
14. #47042C2semidirect
15. #46599C2semidirect
16. #44083C2semidirect
17. #43092C2semidirect
18. #41468C2semidirect
19. #41427C2semidirect
20. #38656C2semidirect
21. #38628C2semidirect
22. #38304C2semidirect
23. #38059C2semidirect
24. #2865C22semidirect
25. #2853C22semidirect
26. #2838C22semidirect
27. #2831C22semidirect
28. #2831C22semidirect
29. #2827C22semidirect
30. #2827C22semidirect
32. #2825C22semidirect
35. #2808C22semidirect
36. #2804C22semidirect
37. #2800C22semidirect
38. #2800C22semidirect
39. #2798C22semidirect
40. #2793C22semidirect
41. #2793C22semidirect
42. #2788C22semidirect
43. #2784C22semidirect
44. #2783C22semidirect
45. #2781C22semidirect
46. #2780C22semidirect
47. #2778C22semidirect
48. #2771C22semidirect
49. #2766C22semidirect
50. #2765C22semidirect
51. #2765C22semidirect
52. #2764C22semidirect
53. #2762C22semidirect
54. #2761C22semidirect
55. #2760C22semidirect
56. #2759C22semidirect
57. #2759C22semidirect
58. #2759C22semidirect
59. #2759C22semidirect
60. #2759C22semidirect
61. #2759C22semidirect
62. #2759C22semidirect
63. #2758C22semidirect
64. #2758C22semidirect
65. #2758C22semidirect
66. #2757C22semidirect
67. #2757C22semidirect
70. #2754C22semidirect
72. #2751C22semidirect
73. #2751C22semidirect
74. #2750C22semidirect
78. #2749C22semidirect
79. #2745C22semidirect
80. #2743C22semidirect
81. #2743C22semidirect
82. #2740C22semidirect
83. #2737C22semidirect
84. #2737C22semidirect
90. #2735C22semidirect
91. #2731C22semidirect
92. #2730C22semidirect
93. #2729C22semidirect
94. #2728C22semidirect
95. #2720C22semidirect
96. #2718C22semidirect
98. #2711C22semidirect
101. #2700C22semidirect
103. #2697C22semidirect
104. #2697C22semidirect
106. #2694C22semidirect
108. #2692C22semidirect
109. #2692C22semidirect
110. #2691C22semidirect
111. #2690C22semidirect
112. #2687C22semidirect
113. #2684C22semidirect
114. #2684C22semidirect
115. #2681C22semidirect
118. #2674C22semidirect
119. #2674C22semidirect
120. #2668C22semidirect
121. #2667C22semidirect
122. #2665C22semidirect
123. #2655C22semidirect
124. #2654C22semidirect
125. #2653C22semidirect
126. #2653C22semidirect
127. #2649C22semidirect
128. #2649C22semidirect
129. #2648C22semidirect
130. #2643C22semidirect
131. #2642C22semidirect
132. #2639C22semidirect
133. #2626C22semidirect
134. #2620C22semidirect
136. #2610C22semidirect
137. #2609C22semidirect
138. #2607C22semidirect
139. #2600C22semidirect
140. #2598C22semidirect
141. #2598C22semidirect
142. #2593C22semidirect
143. #2578C22semidirect
144. #2577C22semidirect
145. #2576C22semidirect
146. #2576C22semidirect
147. #2573C22semidirect
148. #2572C22semidirect
149. #2572C22semidirect
150. #2561C22semidirect
151. #2558C22semidirect
153. #2557C22semidirect
154. #2534C22semidirect
155. #2532C22semidirect
156. #2530C22semidirect
157. #2527C22semidirect
158. #2526C22semidirect
159. #2524C22semidirect
160. #2523C22semidirect
161. #2518C22semidirect
162. #2518C22semidirect
163. #2516C22semidirect
164. #2516C22semidirect
165. #2510C22semidirect
166. #2510C22semidirect
167. #2510C22semidirect
168. #2510C22semidirect
169. #2499C22semidirect
170. #2498C22semidirect
171. #2498C22semidirect
172. #2497C22semidirect
173. #2493C22semidirect
174. #2493C22semidirect
175. #2493C22semidirect
176. #2488C22semidirect
177. #2488C22semidirect
178. #2488C22semidirect
179. #2477C22semidirect
180. #2477C22semidirect
181. #2475C22semidirect
182. #2472C22semidirect
183. #2472C22semidirect
185. #2471C22semidirect
186. #2471C22semidirect
187. #2470C22semidirect
190. #2459C22semidirect
191. #2457C22semidirect
193. #2452C22semidirect
194. #2450C22semidirect
195. #2450C22semidirect
196. #2449C22semidirect
197. #2444C22semidirect
198. #2444C22semidirect
199. #2443C22semidirect
200. #2439C22semidirect
201. #2438C22semidirect
204. #2430C22semidirect
205. #2424C22semidirect
206. #2418C22semidirect
207. #2418C22semidirect
208. #2418C22semidirect
209. #2417C22semidirect
210. #2413C22semidirect
211. #2413C22semidirect
212. #2411C22semidirect
214. #2407C22semidirect
218. #2404C22semidirect
219. #2404C22semidirect
221. C2×#397C22semidirect
222. #2388C22semidirect
223. #2378C22semidirect
225. #2364C22semidirect
226. #2359C22semidirect
227. #2353C22semidirect
228. #2352C22semidirect
229. #2342C22semidirect
230. #2342C22semidirect
231. #2339C22semidirect
232. #2339C22semidirect
233. #2337C22semidirect
234. #2333C22semidirect
235. #2325C22semidirect
236. #2321C22semidirect
237. #2321C22semidirect
238. #2321C22semidirect
239. #2318C22semidirect
241. C4×#126C22semidirect
242. #2297C22semidirect
243. #2293C22semidirect
244. C2×#383C22semidirect

Maximal subgroups

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

subgroupindex
#569982
#564752
#563442
#559372
#545672
#540562
#540492
#533892
#533072
#511382
#504722
#492582
#489132
#470422
#465992
#440832
#430922
#414682
#414272
#386562
#386282
#383042
#380592