Finite Group Databasebeta

← #9712343

Subgroups — #9712343

Order 512.

4864 conjugacy classes of subgroups.

The subgroup lattice has 1445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58981C211yesmaximal, characteristic, complemented
2#57375C213yesmaximal, complemented
3#57310C213yesmaximal, complemented
4#57310C213yesmaximal, complemented
5#56913C213yesmaximal, complemented
6#55492C213yesmaximal, complemented
7#55162C213yesmaximal, complemented
8#53380C211yesmaximal, characteristic, complemented
9#53240C211yesmaximal, characteristic, complemented
10#51202C213yesmaximal, complemented
11#50657C213yesmaximal, complemented
12#50651C213yesmaximal, complemented
13#49922C213yesmaximal, complemented
14#47685C213yesmaximal, complemented
15#46824C213yesmaximal, complemented
16#44618C213yesmaximal, complemented
17#44206C213yesmaximal, complemented
18#42548C213yesmaximal, complemented
19#41386C213yesmaximal, complemented
20#40130C213yesmaximal, complemented
21#40109C213yesmaximal, complemented
22#39445C213yesmaximal, complemented
23#39348C213yesmaximal, complemented
24C2×#563C2213yescomplemented
25C2×#553C2213yes—
26C2×#539C2213yes—
27C2×#539C2213yes—
28C2×#539C2213yescomplemented
29C2×#538C2213yes—
30#2860C2213yes—
31#2854C2213yes—
32#2844C2213yescomplemented
33#2835C2213yes—
34#2835C2213yescomplemented
35#2835C2211yescharacteristic, complemented
36#2828C2213yescomplemented
37#2820C2213yes—
38#2820C2213yes—
39#2815C2213yes—
40#2813C2213yes—
41#2803C2213yes—
42#2803C2213yes—
43#2795C2213yescomplemented
44#2783C2213yes—
45#2783C2213yes—
46#2783C2213yescomplemented
47#2783C2213yescomplemented
48#2782C2213yes—
49#2782C2213yescomplemented
50#2782C2213yescomplemented
51#2781C2213yescomplemented
52#2781C2213yescomplemented
53#2753C2213yes—
54#2753C2213yes—
55#2753C2213yes—
56#2753C2213yes—
57#2744C2213yes—
58#2744C2213yes—
59#2744C2213yes—
60#2744C2213yescomplemented
61#2744C2213yescomplemented
62#2744C2213yescomplemented
63#2736C2211yescharacteristic
64#2727C2213yes—
65#2727C2213yescomplemented
66#2723C2213yes—
67#2723C2213yes—
68#2723C2213yescomplemented
69#2721C2213yes—
70#2721C2213yescomplemented
71#2721C2213yescomplemented
72#2720C2213yes—
73#2720C2213yes—
74#2720C2213yes—
75#2720C2213yescomplemented
76#2720C2213yescomplemented
77#2720C2213yescomplemented
78#2720C2213yescomplemented
79#2720C2213yescomplemented
80#2720C2213yescomplemented
81#2718C2213yes—
82#2718C2213yes—
83#2718C2213yes—
84#2718C2213yes—
85#2718C2213yescomplemented
86#2714C2213yes—
87#2714C2213yes—
88#2714C2213yes—
89#2711C2213yes—
90#2706C2213yes—
91#2706C2213yes—
92#2706C2213yescomplemented
93#2705C2213yescomplemented
94#2703C2213yescomplemented
95#2703C2213yescomplemented
96#2699C2213yes—
97#2696C2213yes—
98#2696C2213yes—
99#2694C2213yes—
100#2685C2213yes—
101#2683C2213yes—
102#2683C2213yescomplemented
103#2682C2213yes—
104#2682C2213yes—
105#2682C2213yes—
106#2681C2213yes—
107#2681C2213yes—
108#2681C2213yes—
109#2680C2213yes—
110#2680C2213yes—
111#2680C2213yescomplemented
112#2678C2213yes—
113#2678C2213yes—
114#2678C2213yes—
115#2678C2213yes—
116#2677C2213yes—
117#2676C2213yes—
118#2675C2213yes—
119#2674C2213yes—
120#2674C2213yes—
121#2673C2213yes—
122#2673C2213yescomplemented
123#2672C2213yes—
124#2672C2213yes—
125#2672C2213yes—
126#2671C2213yes—
127#2664C2213yes—
128#2664C2213yescomplemented
129#2664C2213yescomplemented
130#2662C2213yescomplemented
131#2661C2213yes—
132#2660C2213yescomplemented
133#2636C2213yes—
134#2636C2213yes—
135#2636C2213yescomplemented
136#2636C2213yescomplemented
137#2635C2213yes—
138#2628C2213yes—
139#2623C2213yes—
140#2623C2213yes—
141#2623C2213yescomplemented
142#2611C2213yes—
143#2603C2213yes—
144#2602C2213yes—
145#2601C2213yes—
146#2593C2213yes—
147#2571C2213yescomplemented
148#2566C2213yes—
149#2566C2213yes—
150#2566C2213yescomplemented
151#2559C2213yescomplemented
152#2558C2213yes—
153#2558C2213yescomplemented
154#2558C2213yescomplemented
155#2554C2213yes—
156#2554C2213yes—
157#2554C2213yes—
158#2554C2213yescomplemented
159#2553C2213yescomplemented
160#2552C2213yescomplemented
161#2542C2213yes—
162#2542C2213yescomplemented
163#2540C2213yes—
164#2540C2213yes—
165#2540C2213yes—
166#2539C2213yes—
167#2535C2213yes—
168#2529C2213yes—
169#2529C2213yescomplemented
170#2526C2213yes—
171#2526C2213yescomplemented
172#2519C2213yes—
173#2519C2213yescomplemented
174#2519C2213yescomplemented
175#2513C2213yes—
176#2512C2213yes—
177#2512C2213yes—
178#2512C2213yes—
179#2508C2213yescomplemented
180#2508C2213yescomplemented
181#2507C2213yescomplemented
182#2506C2213yescomplemented
183#2506C2213yescomplemented
184#2501C2213yes—
185#2501C2213yes—
186#2497C2213yescomplemented
187#2496C2213yes—
188#2496C2213yescomplemented
189#2487C2213yes—
190#2482C2213yes—
191#2467C2213yes—
192#2464C2213yes—
193#2464C2213yes—
194#2464C2213yescomplemented
195#2461C2213yes—
196#2461C2213yes—
197#2461C2213yes—
198#2461C2213yes—
199#2461C2213yescomplemented
200#2461C2213yescomplemented
201#2456C2213yes—
202#2456C2213yes—
203#2456C2213yes—
204#2456C2213yescomplemented
205#2455C2213yescomplemented
206#2454C2213yes—
207#2454C2213yes—
208#2452C2213yescomplemented
209#2449C2213yes—
210#2449C2213yescomplemented
211#2449C2213yescomplemented
212#2449C2213yescomplemented
213#2449C2213yescomplemented
214#2449C2213yescomplemented
215#2443C2213yes—
216#2443C2213yescomplemented
217#2440C2213yescomplemented
218#2440C2213yescomplemented
219#2440C2213yescomplemented
220#2437C2213yes—
221#2424C2213yes—
222#2422C2213yes—
223#2422C2213yes—
224#2420C2213yescomplemented
225#2418C2213yes—
226#2416C2213yes—
227#2397C2211yescharacteristic, complemented
228#2395C2213yes—
229#2375C2211yescharacteristic
230#2373C2213yescomplemented
231#2373C2213yescomplemented
232#2370C2213yescomplemented
233#2361C2213yes—
234#2361C2213yescomplemented
235#2357C2213yes—
236D4×C4⋊C4C2213yescomplemented
237#2335C2213yes—
238#2334C2213yes—
239#2334C2213yescomplemented
240#2324C2213yes—
241C4×#127C2211yescharacteristic, complemented
242C4×#125C2213yescomplemented
243C4×#123C2213yescomplemented
244C2×#384C2211yescharacteristic, complemented
245#563—412no—
246#553—412no—
247#539—412no—
248#539—412no—
249#539—412no—
250#538—412no—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×#127C2311yescharacteristic
254C2×#126C2313yes—
255C2×#126C2313yes—
256C2×#126C2313yes—
257C2×#126C2313yes—
258C2×#126C2313yes—
259C2×#126C2313yes—
260C2×#126C2313yes—
261C2×#126C2313yes—
262C2×#126C2313yes—
263C2×#126C2313yes—
264C2×#125C2313yes—
265C2×#125C2313yes—
266C2×#125C2313yes—
267C2×#125C2313yes—
268C2×#125C2313yes—
269C2×#125C2313yes—
270C2×#125C2313yes—
271C2×#124C2313yes—
272C2×#124C2313yes—
273C2×#124C2313yes—
274C2×#123C2313yes—
275C2×#123C2313yes—
276C2×#123C2313yes—
277C2×#123C2313yes—
278C2×#123C2313yes—
279C2×#123C2313yes—
280C2×#123C2313yes—
281C2×#123C2313yes—
282C2×#123C2313yes—
283C2×#123C2313yes—
284C2×#123C2313yes—
285C2×#123C2313yes—
286C2×#123C2313yes—
287C2×#123C2313yes—
288C2×#123C2313yes—
289C2×#123C2313yes—
290C2×C22⋊Q8C2313yes—
291C2×C22⋊Q8C2313yes—
292C2×C22⋊Q8C2313yes—
293C2×C22⋊Q8C2313yes—
294C2×C22⋊Q8C2313yes—
295C2×C22⋊Q8C2313yes—
296C2×C22⋊Q8C2313yes—
297C2×C22⋊Q8C2313yes—
298C2×C22⋊Q8C2313yes—
299C2×C22⋊Q8C2313yes—
300C2×C22⋊Q8C2313yes—
301C2×C22⋊Q8C2313yes—
302C2×C22⋊Q8C2313yes—
303C2×C22⋊Q8C2313yes—
304C2×#121C2313yes—
305C2×#121C2313yes—
306C2×#121C2313yes—
307C2×#121C2313yes—
308C2×#121C2313yes—
309C2×#121C2313yes—
310C2×#121C2313yes—
311C2×#121C2313yes—
312C2×#121C2313yes—
313C2×#121C2313yes—
314C2×#121C2313yes—
315C2×#121C2313yes—
316C2×#121C2313yes—
317C2×#120C2311yescharacteristic
318C2×#120C2313yes—
319C2×#120C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2313yes—
329C2×C4×D4C2313yes—
330C2×C4×D4C2313yes—
331C2×C4×D4C2313yes—
332C2×#117C2313yes—
333C22×C4⋊C4C2313yes—
334C22×C4⋊C4C2313yes—
335C22×C4⋊C4C2313yes—
336C22×C4⋊C4C2313yes—
337C22×C22⋊C4C2313yes—
338C22×C42C2311yescharacteristic
339#400C2313yes—
340#400C2313yes—
341#400C2313yes—
342#400C2313yes—
343#400C2313yes—
344#400C2313yes—
345#400C2313yes—
346#400C2313yes—
347#400C2313yes—
348#400C2313yes—
349#400C2313yes—
350#400C2313yes—
351#400C2313yes—
352#400C2313yes—
353#400C2313yes—
354#400C2313yes—
355#400C2313yes—
356#399C2313yes—
357#399C2313yes—
358#399C2313yes—
359#399C2313yes—
360#399C2313yes—
361#399C2313yes—
362#399C2313yes—
363#399C2313yes—
364#399C2313yes—
365#399C2313yes—
366#399C2311yescharacteristic
367#399C2313yes—
368#399C2313yes—
369#399C2313yes—
370#399C2313yes—
371#399C2313yes—
372#399C2313yes—
373#398C2313yes—
374#398C2313yes—
375#398C2313yes—
376#398C2313yes—
377#398C2313yes—
378#398C2313yes—
379#398C2313yes—
380#398C2313yes—
381#398C2313yes—
382#398C2313yes—
383#398C2313yes—
384#398C2313yes—
385#398C2313yes—
386#398C2313yes—
387#398C2313yes—
388#398C2313yes—
389#398C2313yes—
390#398C2313yes—
391#397C2313yes—
392#397C2313yes—
393#397C2313yes—
394#397C2313yes—
395#397C2313yes—
396#397C2313yes—
397#397C2313yes—
398#397C2313yes—
399#397C2313yes—
400#397C2313yes—
401#397C2313yes—
402#397C2313yes—
403#397C2313yes—
404#397C2313yes—
405#397C2313yes—
406#397C2313yes—
407#397C2313yes—
408#397C2313yes—
409#396C2313yes—
410#396C2313yes—
411#396C2313yes—
412#396C2313yes—
413#396C2313yes—
414#396C2313yes—
415#396C2313yes—
416#396C2313yes—
417#396C2313yes—
418#396C2313yes—
419#396C2313yes—
420#396C2313yes—
421#396C2313yes—
422#396C2313yes—
423#396C2313yes—
424#396C2313yes—
425#396C2313yes—
426#396C2313yes—
427#396C2313yes—
428#396C2313yes—
429#396C2313yes—
430#396C2313yes—
431#396C2313yes—
432#396C2313yes—
433#395C2313yes—
434#395C2313yes—
435#395C2313yes—
436#395C2313yes—
437#395C2313yes—
438#395C2313yes—
439#395C2311yescharacteristic
440#395C2313yes—
441#395C2313yes—
442#395C2311yescharacteristic
443#395C2313yes—
444#395C2313yes—
445#394C2313yes—
446#394C2313yes—
447#394C2313yes—
448#394C2313yes—
449#394C2313yes—
450#394C2313yes—
451#394C2313yes—
452#394C2313yes—
453#394C2313yes—
454#394C2313yes—
455#394C2313yes—
456#394C2313yes—
457#394C2313yes—
458#394C2313yes—
459#394C2313yes—
460#394C2313yes—
461#394C2313yes—
462#394C2313yes—
463#394C2313yes—
464#394C2313yes—
465#394C2313yes—
466#394C2313yes—
467#394C2313yes—
468#394C2313yes—
469#394C2313yes—
470#394C2313yes—
471#394C2313yes—
472#394C2313yes—
473#394C2313yes—
474#393C2313yes—
475#393C2313yes—
476#393C2311yescharacteristic
477#393C2313yes—
478#392C2313yes—
479#392C2313yes—
480#392C2313yes—
481#392C2313yes—
482#392C2313yes—
483#392C2313yes—
484#392C2313yes—
485#392C2313yes—
486#392C2313yes—
487#392C2313yes—
488#392C2313yes—
489#392C2313yes—
490#392C2311yescharacteristic
491#392C2313yes—
492#392C2313yes—
493#392C2313yes—
494#392C2313yes—
495#392C2313yes—
496#392C2313yes—
497#390C2313yes—
498#390C2313yes—
499#390C2313yes—
500#390C2313yes—
501#390C2313yes—
502#390C2313yes—
503#390C2313yes—
504#390C2313yes—
505#390C2313yes—
506#390C2313yes—
507#390C2313yes—
508#390C2313yes—
509#390C2313yes—
510#390C2313yes—
511#390C2313yes—
512#390C2313yes—
513#390C2313yes—
514#390C2313yes—
515#390C2313yes—
516#390C2313yes—
517#390C2313yes—
518#390C2313yes—
519#390C2313yes—
520#390C2313yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2313yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#389C2313yes—
529#389C2313yes—
530#389C2313yes—
531#389C2313yes—
532#389C2313yes—
533#389C2313yes—
534#389C2313yes—
535#389C2313yes—
536#389C2313yes—
537#389C2313yes—
538#389C2313yes—
539#389C2313yes—
540#389C2313yes—
541#389C2313yes—
542#389C2313yes—
543#389C2313yes—
544#389C2313yes—
545#388C2313yes—
546#388C2313yes—
547#388C2313yes—
548#388C2313yes—
549#388C2313yes—
550#388C2313yes—
551#388C2313yes—
552#388C2313yes—
553#388C2313yes—
554#388C2313yes—
555#388C2313yes—
556#388C2313yes—
557#388C2313yes—
558#388C2313yes—
559#388C2313yes—
560#388C2313yes—
561#388C2313yes—
562#388C2313yes—
563#388C2313yes—
564#388C2313yes—
565#388C2313yes—
566#388C2313yes—
567#388C2313yes—
568#388C2313yes—
569#388C2313yes—
570#388C2313yes—
571#388C2313yes—
572#388C2313yes—
573#388C2313yes—
574#388C2313yes—
575#388C2313yes—
576#388C2313yes—
577#388C2313yes—
578#388C2313yes—
579#388C2313yes—
580#388C2313yes—
581#388C2313yes—
582#388C2313yes—
583#388C2313yes—
584#388C2313yes—
585#388C2313yes—
586#388C2313yes—
587#388C2313yes—
588#388C2313yes—
589#388C2313yes—
590#388C2313yes—
591#388C2313yes—
592#388C2313yes—
593#388C2313yes—
594#388C2313yes—
595#387C2313yes—
596#387C2313yes—
597#387C2313yes—
598#387C2313yes—
599#387C2313yes—
600#387C2313yes—
601#387C2313yes—
602#387C2313yes—
603#387C2313yes—
604#387C2313yes—
605#387C2313yes—
606#387C2313yes—
607#387C2313yes—
608#387C2313yes—
609#387C2313yes—
610#387C2313yes—
611#387C2313yes—
612#387C2313yes—
613#387C2313yes—
614#387C2313yes—
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#386C2313yes—
629#386C2313yes—
630#386C2313yes—
631#386C2313yes—
632#386C2313yes—
633#386C2313yes—
634#386C2313yes—
635#386C2313yes—
636#386C2313yes—
637#386C2313yes—
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#385C2313yes—
652#385C2313yes—
653#385C2313yes—
654#385C2313yes—
655#385C2313yes—
656#385C2313yes—
657#385C2313yes—
658#385C2313yes—
659#385C2313yes—
660#385C2313yes—
661#385C2313yes—
662#385C2313yes—
663#385C2313yes—
664#385C2313yes—
665#385C2313yes—
666#385C2313yes—
667#385C2313yes—
668#385C2313yes—
669#384C2311yescharacteristic
670#384C2313yes—
671#384C2313yes—
672#384C2313yes—
673#384C2313yes—
674#384C2313yes—
675#384C2313yes—
676#384C2313yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#382C2313yes—
680#382C2313yes—
681#382C2313yes—
682#382C2313yes—
683#382C2313yes—
684#382C2313yes—
685#382C2313yes—
686#382C2313yes—
687#382C2313yes—
688#381C2313yes—
689#381C2313yes—
690#381C2313yes—
691#380C2313yes—
692#380C2313yes—
693#380C2313yes—
694#380C2313yes—
695#380C2313yes—
696#380C2313yes—
697#380C2313yes—
698#380C2313yes—
699#379C2311yescharacteristic
700#379C2311yescharacteristic
701#379C2313yes—
702C4×C4⋊C4C2313yes—
703C4×C4⋊C4C2313yes—
704C4×C4⋊C4C2313yes—
705C4×C4⋊C4C2313yes—
706C4×C4⋊C4C2313yes—
707C4×C4⋊C4C2313yes—
708C4×C4⋊C4C2313yes—
709C4×C4⋊C4C2313yes—
710C4×C4⋊C4C2313yes—
711C4×C4⋊C4C2313yes—
712C4×C4⋊C4C2313yes—
713C4×C4⋊C4C2313yes—
714C4×C4⋊C4C2313yes—
715C4×C4⋊C4C2313yes—
716C4×C22⋊C4C2313yes—
717C4×C22⋊C4C2313yes—
718C4×C22⋊C4C2313yes—
719C4×C22⋊C4C2313yes—
720C4×C22⋊C4C2313yes—
721C4×C22⋊C4C2313yes—
722C4×C22⋊C4C2313yes—
723#376C2313yes—
724#376C2311yescharacteristic
725C43C2311yescharacteristic
726C25C2411yescharacteristic
727C22×Q8C2413yes—
728C22×Q8C2413yes—
729C22×Q8C2411yescharacteristic
730C22×D4C2413yes—
731C22×D4C2413yes—
732C22×D4C2413yes—
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×C4C2411yescharacteristic
750C23×C4C2413yes—
751C23×C4C2413yes—
752C23×C4C2413yes—
753C23×C4C2413yes—
754C23×C4C2413yes—
755C4⋊Q8—46no—
756C4⋊Q8—46no—
757#127—42no—
758#126—212no—
759#126—212no—
760#126—212no—
761#126—212no—
762#126—46no—
763#126—46no—
764#126—46no—
765#126—46no—
766#126—46no—
767#126—46no—
768#125—212no—
769#125—212no—
770#125—46no—
771#125—46no—
772#125—46no—
773#125—46no—
774#125—46no—
775#124—46no—
776#124—46no—
777#124—46no—
778#123—212no—
779#123—212no—
780#123—46no—
781#123—46no—
782#123—46no—
783#123—46no—
784#123—46no—
785#123—46no—
786#123—46no—
787#123—46no—
788#123—46no—
789#123—46no—
790#123—46no—
791#123—46no—
792#123—46no—
793#123—46no—
794C22⋊Q8—46no—
795C22⋊Q8—46no—
796C22⋊Q8—46no—
797C22⋊Q8—46no—
798C22⋊Q8—46no—
799C22⋊Q8—46no—
800C22⋊Q8—46no—
801C22⋊Q8—46no—
802C22⋊Q8—46no—
803C22⋊Q8—46no—
804C22⋊Q8—46no—
805C22⋊Q8—46no—
806C22⋊Q8—46no—
807C22⋊Q8—46no—
808#121—46no—
809#121—46no—
810#121—46no—
811#121—46no—
812#121—46no—
813#121—46no—
814#121—46no—
815#121—46no—
816#121—46no—
817#121—46no—
818#121—46no—
819#121—46no—
820#121—46no—
821#120—46no—
822#120—46no—
823#120—42no—
824C4×D4—212no—
825C4×D4—46no—
826C4×D4—46no—
827C4×D4—46no—
828C4×D4—46no—
829C4×D4—46no—
830C4×D4—46no—
831C4×D4—46no—
832C4×D4—46no—
833C4×D4—46no—
834C4×D4—46no—
835C4×D4—46no—
836#117—46no—
837C2×C4⋊C4—46no—
838C2×C4⋊C4—46no—
839C2×C4⋊C4—46no—
840C2×C4⋊C4—46no—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2413yes—
873C2×C4⋊C4C2413yes—
874C2×C4⋊C4C2413yes—
875C2×C4⋊C4C2413yes—
876C2×C4⋊C4C2413yes—
877C2×C4⋊C4C2413yes—
878C2×C4⋊C4C2413yes—
879C2×C4⋊C4C2413yes—
880C2×C4⋊C4C2413yes—
881C2×C4⋊C4C2413yes—
882C2×C4⋊C4C2413yes—
883C2×C4⋊C4C2413yes—
884C2×C4⋊C4C2413yes—
885C2×C4⋊C4C2413yes—
886C2×C4⋊C4C2413yes—
887C2×C4⋊C4C2413yes—
888C2×C4⋊C4C2413yes—
889C2×C4⋊C4C2413yes—
890C2×C4⋊C4C2413yes—
891C2×C4⋊C4C2413yes—
892C2×C4⋊C4C2413yes—
893C2×C4⋊C4C2413yes—
894C2×C4⋊C4C2413yes—
895C2×C4⋊C4C2413yes—
896C2×C4⋊C4C2413yes—
897C2×C4⋊C4C2413yes—
898C2×C4⋊C4C2413yes—
899C2×C4⋊C4C2413yes—
900C2×C22⋊C4—46no—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2413yes—
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2413yes—
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2413yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2413yes—
925C2×C22⋊C4C2413yes—
926C2×C22⋊C4C2413yes—
927C2×C22⋊C4C2413yes—
928C2×C22⋊C4C2413yes—
929C2×C22⋊C4C2413yes—
930C2×C22⋊C4C2413yes—
931C2×C22⋊C4C2413yes—
932C2×C22⋊C4C2413yes—
933C2×C22⋊C4C2413yes—
934C2×C22⋊C4C2413yes—
935C2×C22⋊C4C2413yes—
936C2×C22⋊C4C2413yes—
937C2×C22⋊C4C2413yes—
938C2×C22⋊C4C2413yes—
939C2×C22⋊C4C2413yes—
940C2×C22⋊C4C2413yes—
941C2×C22⋊C4C2413yes—
942C2×C22⋊C4C2413yes—
943C2×C22⋊C4C2413yes—
944C2×C22⋊C4C2413yes—
945C2×C22⋊C4C2413yes—
946C2×C22⋊C4C2413yes—
947C2×C22⋊C4C2413yes—
948C2×C22⋊C4C2413yes—
949C2×C22⋊C4C2413yes—
950C2×C22⋊C4C2413yes—
951C2×C22⋊C4C2413yes—
952C2×C22⋊C4C2413yes—
953C2×C22⋊C4C2413yes—
954C2×C22⋊C4C2413yes—
955C2×C22⋊C4C2413yes—
956C2×C22⋊C4C2413yes—
957C2×C22⋊C4C2413yes—
958C2×C22⋊C4C2413yes—
959C2×C22⋊C4C2413yes—
960C2×C22⋊C4C2413yes—
961C2×C22⋊C4C2413yes—
962C2×C22⋊C4C2413yes—
963C2×C22⋊C4C2413yes—
964C2×C22⋊C4C2413yes—
965C2×C42—42no—
966C2×C42C2413yes—
967C2×C42C2413yes—
968C2×C42C2413yes—
969C2×C42C2413yes—
970C2×C42C2413yes—
971C2×C42C2413yes—
972C2×C42C2413yes—
973C2×C42C2413yes—
974C2×C42C2411yescharacteristic
975C2×C42C2413yes—
976C2×C42C2413yes—
977C2×C42C2413yes—
978C2×C42C2413yes—
979C2×C42C2413yes—
980C2×C42C2413yes—
981C2×C42C2413yes—
982C2×C42C2411yescharacteristic
983#95C2413yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2411yescharacteristic
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2413yes—
994#95C2413yes—
995#95C2413yes—
996#95C2413yes—
997#95C2413yes—
998#95C2413yes—
999#95C2413yes—
1000#95C2413yes—
1001#95C2413yes—
1002#95C2413yes—
1003#95C2413yes—
1004#95C2413yes—
1005#95C2413yes—
1006#95C2413yes—
1007#95C2413yes—
1008#95C2413yes—
1009#95C2413yes—
1010#95C2413yes—
1011#95C2413yes—
1012#95C2413yes—
1013#95C2413yes—
1014#95C2413yes—
1015#95C2413yes—
1016#95C2413yes—
1017#95C2413yes—
1018#95C2413yes—
1019#95C2413yes—
1020#95C2413yes—
1021#95C2413yes—
1022#95C2413yes—
1023#95C2413yes—
1024#95C2413yes—
1025#95C2413yes—
1026#95C2413yes—
1027#95C2413yes—
1028#95C2413yes—
1029#95C2413yes—
1030#95C2413yes—
1031#95C2413yes—
1032#95C2413yes—
1033#95C2413yes—
1034#95C2413yes—
1035C24—43no—
1036C24—43no—
1037C24—41no—
1038C24C2513yes—
1039C24C2513yes—
1040C24C2513yes—
1041C24C2511yescharacteristic
1042C2×Q8—43no—
1043C2×Q8—43no—
1044C2×Q8—43no—
1045C2×Q8—43no—
1046C2×Q8—43no—
1047C2×Q8—43no—
1048C2×Q8—43no—
1049C2×D4—26no—
1050C2×D4—26no—
1051C2×D4—26no—
1052C2×D4—26no—
1053C2×D4—26no—
1054C2×D4—26no—
1055C2×D4—43no—
1056C2×D4—43no—
1057C2×D4—43no—
1058C2×D4—43no—
1059C2×D4—43no—
1060C2×D4—43no—
1061C2×D4—43no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—43no—
1065C2×D4—43no—
1066C2×D4—43no—
1067C2×D4—43no—
1068C2×D4—43no—
1069C2×D4—43no—
1070C2×D4—43no—
1071C2×D4—43no—
1072C2×D4—43no—
1073C2×D4—43no—
1074C2×D4—43no—
1075C2×D4—43no—
1076C2×D4—43no—
1077C2×D4—43no—
1078C2×D4—43no—
1079C2×D4—43no—
1080C2×D4—43no—
1081C2×D4—43no—
1082C2×D4—43no—
1083C2×D4—43no—
1084C2×D4—43no—
1085C2×D4—43no—
1086C2×D4—43no—
1087C2×D4—43no—
1088C2×D4—43no—
1089C2×D4—43no—
1090C2×D4—43no—
1091C22×C4—26no—
1092C22×C4—26no—
1093C22×C4—26no—
1094C22×C4—26no—
1095C22×C4—26no—
1096C22×C4—43no—
1097C22×C4—43no—
1098C22×C4—43no—
1099C22×C4—43no—
1100C22×C4—43no—
1101C22×C4—43no—
1102C22×C4—43no—
1103C22×C4—43no—
1104C22×C4—43no—
1105C22×C4—43no—
1106C22×C4—43no—
1107C22×C4—43no—
1108C22×C4—43no—
1109C22×C4—43no—
1110C22×C4—43no—
1111C22×C4—43no—
1112C22×C4—43no—
1113C22×C4—43no—
1114C22×C4—43no—
1115C22×C4—43no—
1116C22×C4—43no—
1117C22×C4—43no—
1118C22×C4—43no—
1119C22×C4—43no—
1120C22×C4—43no—
1121C22×C4—43no—
1122C22×C4C2513yes—
1123C22×C4C2513yes—
1124C22×C4C2513yes—
1125C22×C4C2513yes—
1126C22×C4C2513yes—
1127C22×C4C2513yes—
1128C22×C4C2513yes—
1129C22×C4C2513yes—
1130C22×C4C2513yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2513yes—
1134C22×C4C2513yes—
1135C22×C4C2513yes—
1136C22×C4C2513yes—
1137C22×C4C2513yes—
1138C22×C4C2513yes—
1139C22×C4C2513yes—
1140C22×C4C2513yes—
1141C4⋊C4—26no—
1142C4⋊C4—26no—
1143C4⋊C4—26no—
1144C4⋊C4—26no—
1145C4⋊C4—26no—
1146C4⋊C4—26no—
1147C4⋊C4—26no—
1148C4⋊C4—26no—
1149C4⋊C4—26no—
1150C4⋊C4—26no—
1151C4⋊C4—26no—
1152C4⋊C4—26no—
1153C4⋊C4—26no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—26no—
1158C4⋊C4—26no—
1159C4⋊C4—26no—
1160C4⋊C4—26no—
1161C4⋊C4—43no—
1162C4⋊C4—43no—
1163C4⋊C4—43no—
1164C4⋊C4—43no—
1165C4⋊C4—43no—
1166C4⋊C4—43no—
1167C4⋊C4—43no—
1168C4⋊C4—43no—
1169C4⋊C4—43no—
1170C4⋊C4—43no—
1171C4⋊C4—43no—
1172C4⋊C4—43no—
1173C4⋊C4—43no—
1174C4⋊C4—43no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4—43no—
1178C4⋊C4—43no—
1179C4⋊C4—43no—
1180C4⋊C4—43no—
1181C4⋊C4—43no—
1182C4⋊C4—43no—
1183C4⋊C4—43no—
1184C4⋊C4—43no—
1185C4⋊C4—43no—
1186C4⋊C4—43no—
1187C4⋊C4—43no—
1188C4⋊C4—43no—
1189C4⋊C4—43no—
1190C4⋊C4—43no—
1191C4⋊C4—43no—
1192C4⋊C4—43no—
1193C4⋊C4—43no—
1194C4⋊C4—43no—
1195C4⋊C4—43no—
1196C4⋊C4—43no—
1197C4⋊C4—43no—
1198C4⋊C4—43no—
1199C4⋊C4H(5,𝔽2)112yes—
1200C22⋊C4—26no—
1201C22⋊C4—26no—
1202C22⋊C4—26no—
1203C22⋊C4—26no—
1204C22⋊C4—26no—
1205C22⋊C4—26no—
1206C22⋊C4—26no—
1207C22⋊C4—26no—
1208C22⋊C4—26no—
1209C22⋊C4—26no—
1210C22⋊C4—26no—
1211C22⋊C4—26no—
1212C22⋊C4—26no—
1213C22⋊C4—26no—
1214C22⋊C4—26no—
1215C22⋊C4—26no—
1216C22⋊C4—26no—
1217C22⋊C4—26no—
1218C22⋊C4—26no—
1219C22⋊C4—26no—
1220C22⋊C4—26no—
1221C22⋊C4—43no—
1222C22⋊C4—43no—
1223C22⋊C4—43no—
1224C22⋊C4—43no—
1225C22⋊C4—43no—
1226C22⋊C4—43no—
1227C22⋊C4—43no—
1228C22⋊C4—43no—
1229C22⋊C4—43no—
1230C22⋊C4—43no—
1231C22⋊C4—43no—
1232C22⋊C4—43no—
1233C22⋊C4—43no—
1234C22⋊C4—43no—
1235C22⋊C4—43no—
1236C22⋊C4—43no—
1237C22⋊C4—43no—
1238C22⋊C4—43no—
1239C22⋊C4—43no—
1240C22⋊C4—43no—
1241C22⋊C4—43no—
1242C22⋊C4—43no—
1243C22⋊C4—43no—
1244C22⋊C4—43no—
1245C22⋊C4—43no—
1246C22⋊C4—43no—
1247C22⋊C4—43no—
1248C22⋊C4—43no—
1249C22⋊C4—43no—
1250C22⋊C4—43no—
1251C22⋊C4—43no—
1252C22⋊C4—43no—
1253C22⋊C4—43no—
1254C22⋊C4—43no—
1255C22⋊C4—43no—
1256C22⋊C4—43no—
1257C22⋊C4—43no—
1258C22⋊C4—43no—
1259C22⋊C4—43no—
1260C22⋊C4—43no—
1261C22⋊C4—43no—
1262C22⋊C4—43no—
1263C22⋊C4—43no—
1264C42—26no—
1265C42—26no—
1266C42—26no—
1267C42—26no—
1268C42—26no—
1269C42—26no—
1270C42—26no—
1271C42—43no—
1272C42—41no—
1273C42—43no—
1274C42—43no—
1275C42—43no—
1276C42—43no—
1277C42—43no—
1278C42—43no—
1279C42—43no—
1280C42—41no—
1281C23—23no—
1282C23—23no—
1283C23—23no—
1284C23—23no—
1285C23—23no—
1286C23—23no—
1287C23—23no—
1288C23—23no—
1289C23—23no—
1290C23—23no—
1291C23—23no—
1292C23—23no—
1293C23—23no—
1294C23—23no—
1295C23—23no—
1296C23—23no—
1297C23—23no—
1298C23—23no—
1299C23—23no—
1300C23—23no—
1301C23—23no—
1302C23—23no—
1303C23—23no—
1304C23—86no—
1305C23—161no—
1306C23—163no—
1307C23#58512yes—
1308C23C2611yescharacteristic
1309Q8—163no—
1310Q8—163no—
1311Q8—161no—
1312D4—412no—
1313D4—86no—
1314D4—86no—
1315D4—86no—
1316D4—86no—
1317D4—86no—
1318D4—86no—
1319D4—86no—
1320D4—86no—
1321D4—86no—
1322D4—163no—
1323D4—163no—
1324D4—163no—
1325D4—163no—
1326C2×C4—23no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—23no—
1334C2×C4—23no—
1335C2×C4—23no—
1336C2×C4—23no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—23no—
1340C2×C4—23no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—23no—
1345C2×C4—23no—
1346C2×C4—23no—
1347C2×C4—23no—
1348C2×C4—23no—
1349C2×C4—23no—
1350C2×C4—23no—
1351C2×C4—23no—
1352C2×C4—23no—
1353C2×C4—23no—
1354C2×C4—23no—
1355C2×C4—23no—
1356C2×C4—23no—
1357C2×C4—23no—
1358C2×C4—23no—
1359C2×C4—23no—
1360C2×C4—23no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—23no—
1364C2×C4—23no—
1365C2×C4—23no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—23no—
1371C2×C4—23no—
1372C2×C4—23no—
1373C2×C4—23no—
1374C2×C4—23no—
1375C2×C4—23no—
1376C2×C4—412no—
1377C2×C4—86no—
1378C2×C4—86no—
1379C2×C4—86no—
1380C2×C4—161no—
1381C2×C4—163no—
1382C2×C4—163no—
1383C2×C4—163no—
1384C2×C4—163no—
1385C2×C4—163no—
1386C2×C4—163no—
1387C2×C4C2×H(5,𝔽2)16yes—
1388C2×C4C2×H(5,𝔽2)16yes—
1389C2×C4C2×H(5,𝔽2)16yes—
1390C22—26no—
1391C22—41no—
1392C22—43no—
1393C22—43no—
1394C22—43no—
1395C22—43no—
1396C22—43no—
1397C22—43no—
1398C22—43no—
1399C22—43no—
1400C22—43no—
1401C22—43no—
1402C22—43no—
1403C22—43no—
1404C22—43no—
1405C22—43no—
1406C22—43no—
1407C22—43no—
1408C22—43no—
1409C22—43no—
1410C22—43no—
1411C22—43no—
1412C22—43no—
1413C22—43no—
1414C22—164no—
1415C22C22×H(5,𝔽2)13yes—
1416C22C2×#58511yescharacteristic
1417C222−1+613yes—
1418C4—26no—
1419C4—26no—
1420C4—26no—
1421C4—41no—
1422C4—41no—
1423C4—43no—
1424C4—43no—
1425C4—43no—
1426C4—43no—
1427C4—43no—
1428C4—43no—
1429C4—43no—
1430C4—43no—
1431C4—43no—
1432C4—43no—
1433C4—43no—
1434C4—43no—
1435C4—43no—
1436C4—43no—
1437C2—42no—
1438C2—83no—
1439C2—83no—
1440C2—83no—
1441C2#6288813yes—
1442C2#6289813yes—
1443C2#6304011yescharacteristic
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. #58981C2semidirect
2. #57375C2semidirect
3. #57310C2semidirect
4. #57310C2semidirect
5. #56913C2semidirect
6. #55492C2semidirect
7. #55162C2semidirect
8. #53380C2semidirect
9. #53240C2semidirect
10. #51202C2semidirect
11. #50657C2semidirect
12. #50651C2semidirect
13. #49922C2semidirect
14. #47685C2semidirect
15. #46824C2semidirect
16. #44618C2semidirect
17. #44206C2semidirect
18. #42548C2semidirect
19. #41386C2semidirect
20. #40130C2semidirect
21. #40109C2semidirect
22. #39445C2semidirect
23. #39348C2semidirect
24. C2×#563C22semidirect
28. C2×#539C22semidirect
32. #2844C22semidirect
34. #2835C22semidirect
35. #2835C22semidirect
36. #2828C22semidirect
43. #2795C22semidirect
46. #2783C22semidirect
47. #2783C22semidirect
49. #2782C22semidirect
50. #2782C22semidirect
51. #2781C22semidirect
52. #2781C22semidirect
60. #2744C22semidirect
61. #2744C22semidirect
62. #2744C22semidirect
65. #2727C22semidirect
68. #2723C22semidirect
70. #2721C22semidirect
71. #2721C22semidirect
75. #2720C22semidirect
76. #2720C22semidirect
77. #2720C22semidirect
78. #2720C22semidirect
79. #2720C22semidirect
80. #2720C22semidirect
85. #2718C22semidirect
92. #2706C22semidirect
93. #2705C22semidirect
94. #2703C22semidirect
95. #2703C22semidirect
102. #2683C22semidirect
111. #2680C22semidirect
122. #2673C22semidirect
128. #2664C22semidirect
129. #2664C22semidirect
130. #2662C22semidirect
132. #2660C22semidirect
135. #2636C22semidirect
136. #2636C22semidirect
141. #2623C22semidirect
147. #2571C22semidirect
150. #2566C22semidirect
151. #2559C22semidirect
153. #2558C22semidirect
154. #2558C22semidirect
158. #2554C22semidirect
159. #2553C22semidirect
160. #2552C22semidirect
162. #2542C22semidirect
169. #2529C22semidirect
171. #2526C22semidirect
173. #2519C22semidirect
174. #2519C22semidirect
179. #2508C22semidirect
180. #2508C22semidirect
181. #2507C22semidirect
182. #2506C22semidirect
183. #2506C22semidirect
186. #2497C22semidirect
188. #2496C22semidirect
194. #2464C22semidirect
199. #2461C22semidirect
200. #2461C22semidirect
204. #2456C22semidirect
205. #2455C22semidirect
208. #2452C22semidirect
210. #2449C22semidirect
211. #2449C22semidirect
212. #2449C22semidirect
213. #2449C22semidirect
214. #2449C22semidirect
216. #2443C22semidirect
217. #2440C22semidirect
218. #2440C22semidirect
219. #2440C22semidirect
224. #2420C22semidirect
227. #2397C22semidirect
230. #2373C22semidirect
231. #2373C22semidirect
232. #2370C22semidirect
234. #2361C22semidirect
236. D4×C4⋊C4C22semidirect
239. #2334C22semidirect
241. C4×#127C22semidirect
242. C4×#125C22semidirect
243. C4×#123C22semidirect
244. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#589812
#573752
#573102
#569132
#554922
#551622
#533802
#532402
#512022
#506572
#506512
#499222
#476852
#468242
#446182
#442062
#425482
#413862
#401302
#401092
#394452
#393482