Finite Group Databasebeta

← #7900920

Subgroups — #7900920

Order 512.

4611 conjugacy classes of subgroups.

The subgroup lattice has 1425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59827C211yesmaximal, characteristic, complemented
2#59638C212yesmaximal, complemented
3#52162C211yesmaximal, characteristic, complemented
4#51443C214yesmaximal, complemented
5#50507C214yesmaximal, complemented
6#49665C214yesmaximal, complemented
7#46741C214yesmaximal, complemented
8#45939C212yesmaximal, complemented
9#45392C212yesmaximal, complemented
10#44966C212yesmaximal, complemented
11#44956C212yesmaximal, complemented
12#43449C214yesmaximal, complemented
13#42939C212yesmaximal, complemented
14#42698C212yesmaximal, complemented
15#41190C214yesmaximal, complemented
16#40034C212yesmaximal, complemented
17#39829C212yesmaximal, complemented
18#39757C211yesmaximal, characteristic, complemented
19#39718C212yesmaximal, complemented
20#39483C211yesmaximal, characteristic
21#38770C212yesmaximal, complemented
22#38085C212yesmaximal, complemented
23#37256C212yesmaximal, complemented
24#36535C211yesmaximal, characteristic, complemented
25#36041C212yesmaximal, complemented
26#35662C212yesmaximal, complemented
27#35186C211yesmaximal, characteristic, complemented
28#34466C212yesmaximal, complemented
29#34311C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×#553C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×#533C2212yes—
34C2×#519C2212yes—
35#2864C2212yes—
36#2861C2212yes—
37#2860C2212yes—
38#2859C2211yescharacteristic
39#2850C2212yes—
40#2838C2214yes—
41#2836C2214yes—
42#2810C2212yes—
43#2810C2212yes—
44#2805C2212yes—
45#2805C2212yes—
46#2798C2214yes—
47#2796C2214yes—
48#2790C2214yes—
49#2788C2214yes—
50#2782C2214yes—
51#2768C2214yes—
52#2766C2214yes—
53#2765C2214yes—
54#2764C2214yes—
55#2763C2214yes—
56#2754C2214yes—
57#2754C2214yes—
58#2750C2214yes—
59#2747C2214yes—
60#2745C2214yes—
61#2743C2214yes—
62#2742C2214yes—
63#2738C2214yes—
64#2737C2214yes—
65#2734C2211yescharacteristic
66#2732C2211yescharacteristic
67#2731C2214yes—
68#2730C2214yes—
69#2729C2212yes—
70#2727C2212yes—
71#2727C2212yes—
72#2726C2211yescharacteristic
73#2724C2212yes—
74#2724C2212yes—
75#2723C2214yes—
76#2720C2214yes—
77#2720C2212yes—
78#2719C2214yes—
79#2716C2214yes—
80#2716C2214yes—
81#2713C2212yes—
82#2707C2214yes—
83#2704C2212yes—
84#2696C2214yes—
85#2695C2214yes—
86#2694C2214yes—
87#2692C2212yes—
88#2687C2214yes—
89#2687C2214yes—
90#2687C2214yes—
91#2683C2211yescharacteristic
92#2682C2212yes—
93#2682C2212yes—
94#2677C2212yes—
95#2674C2214yes—
96#2667C2214yes—
97#2664C2214yes—
98#2654C2214yes—
99#2651C2214yes—
100#2650C2214yes—
101#2650C2214yes—
102#2642C2212yes—
103#2632C2214yes—
104#2620C2212yes—
105#2619C2212yes—
106#2612C2214yes—
107#2611C2214yes—
108#2610C2214yes—
109#2607C2214yes—
110#2606C2214yes—
111#2598C2214yes—
112#2596C2214yes—
113#2592C2212yes—
114#2592C2212yes—
115#2590C2214yes—
116#2589C2214yes—
117#2588C2214yes—
118#2587C2214yes—
119#2583C2214yes—
120#2582C2211yescharacteristic
121#2582C2212yes—
122#2582C2212yes—
123#2582C2212yes—
124#2581C2212yes—
125#2581C2212yes—
126#2581C2212yes—
127#2581C2212yes—
128#2580C2212yes—
129#2576C2214yes—
130#2575C2214yes—
131#2574C2214yes—
132#2571C2211yescharacteristic
133#2571C2212yes—
134#2570C2212yes—
135#2566C2212yes—
136#2565C2212yes—
137#2558C2214yes—
138#2556C2214yes—
139#2552C2211yescharacteristic
140#2552C2212yes—
141#2552C2211yescharacteristic
142#2550C2212yes—
143#2548C2211yescharacteristic
144#2548C2211yescharacteristic
145#2547C2212yes—
146#2547C2212yes—
147#2538C2212yes—
148#2533C2214yes—
149#2533C2214yes—
150#2532C2214yes—
151#2527C2214yes—
152#2525C2214yes—
153#2516C2214yes—
154#2514C2212yes—
155#2512C2212yes—
156#2511C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2502C2212yes—
160#2501C2212yes—
161#2500C2212yes—
162#2499C2212yes—
163#2498C2214yes—
164#2488C2214yes—
165#2486C2214yes—
166#2475C2214yes—
167#2473C2214yes—
168#2471C2214yes—
169#2471C2214yes—
170#2468C2214yes—
171#2463C2214yes—
172#2461C2214yes—
173#2460C2214yes—
174#2458C2214yes—
175#2458C2214yes—
176#2455C2214yes—
177#2455C2214yes—
178#2454C2212yes—
179#2453C2214yes—
180#2453C2214yes—
181#2451C2214yes—
182#2451C2214yes—
183#2450C2214yes—
184#2450C2214yes—
185#2448C2212yes—
186#2448C2212yes—
187#2448C2212yes—
188#2447C2214yes—
189#2447C2212yes—
190#2447C2212yes—
191#2447C2212yes—
192#2444C2214yes—
193#2444C2214yes—
194#2438C2214yes—
195#2438C2214yes—
196#2438C2214yes—
197#2438C2214yes—
198#2436C2212yes—
199#2436C2212yes—
200#2419C2214yes—
201#2399C2212yes—
202#2398C2214yes—
203#2396C2212yes—
204#2396C2212yes—
205#2377C2214yes—
206#2376C2214yes—
207#2373C2214yes—
208#2370C2212yes—
209#2367C2212yes—
210#2367C2212yes—
211#2365C2211yescharacteristic
212#2365C2212yes—
213#2363C2212yes—
214#2363C2212yes—
215#2362C2214yes—
216#2362C2212yes—
217#2359C2214yes—
218#2356C2212yes—
219#2355C2212yes—
220#2355C2211yescharacteristic
221#2355C2211yescharacteristic
222#2354C2212yes—
223#2354C2211yescharacteristic
224#2352C2214yes—
225Q8×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2212yes—
227D4×C4⋊C4C2212yes—
228#2346C2212yes—
229#2344C2212yes—
230Q8×C22⋊C4C2212yes—
231#2334C2214yes—
232#2334C2214yes—
233#2330C2212yes—
234#2326C2212yes—
235#2324C2212yes—
236#2324C2214yes—
237#2323C2212yes—
238#2323C2214yes—
239#2322C2214yes—
240#2319C2214yes—
241#2319C2212yes—
242#2317C2212yes—
243#2316C2212yes—
244#2310C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2211yescharacteristic
248C4×#127C2211yescharacteristic
249C4×#125C2212yes—
250C4×C22⋊Q8C2212yes—
251C4×#121C2212yes—
252#2296C2212yes—
253#2295C2211yescharacteristic
254C2×#391C2212yes—
255#2293C2211yescharacteristic
256#2293C2212yes—
257#2290C2212yes—
258C42×Q8C2211yescharacteristic
259C23×Q8C2312yes—
260#559—48no—
261#553—216no—
262D4×Q8—28no—
263#533—48no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×#127C2311yescharacteristic
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#124C2312yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2312yes—
297C2×#121C2314yes—
298C2×#121C2312yes—
299#519—48no—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C2×#117C2314yes—
327C2×#117C2314yes—
328C2×#117C2314yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2314yes—
331C22×C42C2312yes—
332#401C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2312yes—
358#399C2314yes—
359#399C2314yes—
360#399C2312yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2312yes—
406#396C2312yes—
407#396C2312yes—
408#396C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#395C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2312yes—
433#393C2314yes—
434#393C2312yes—
435#393C2314yes—
436#392C2314yes—
437#392C2314yes—
438#391C2312yes—
439#391C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2314yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2311yescharacteristic
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2311yescharacteristic
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2314yes—
470#390C2312yes—
471#390C2314yes—
472#390C2312yes—
473#390C2312yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2311yescharacteristic
480#390C2311yescharacteristic
481#389C2311yescharacteristic
482#389C2312yes—
483#389C2312yes—
484#389C2311yescharacteristic
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2311yescharacteristic
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2311yescharacteristic
520#389C2312yes—
521#389C2311yescharacteristic
522#389C2311yescharacteristic
523#388C2314yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2312yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#388C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2312yes—
633#385C2314yes—
634#385C2312yes—
635#385C2314yes—
636#384C2311yescharacteristic
637#384C2311yescharacteristic
638#384C2311yescharacteristic
639#384C2312yes—
640#384C2312yes—
641#384C2312yes—
642#384C2312yes—
643#384C2311yescharacteristic
644#384C2311yescharacteristic
645#383C2314yes—
646#383C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2312yes—
653#382C2314yes—
654#382C2312yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711#376C2314yes—
712#376C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C22×Q8—28no—
718C22×Q8—28no—
719C22×Q8—44no—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C23×C4C2414yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C4⋊Q8—28no—
742C4⋊Q8—24no—
743C4⋊Q8—42no—
744C4⋊Q8—44no—
745C4⋊Q8—44no—
746#127—24no—
747#126—216no—
748#126—48no—
749#125—28no—
750#125—44no—
751#125—44no—
752#125—44no—
753#125—84no—
754#125—82no—
755#124—28no—
756#124—44no—
757#124—44no—
758#124—48no—
759#124—82no—
760#123—216no—
761#123—48no—
762#123—48no—
763#123—48no—
764#123—84no—
765C22⋊Q8—28no—
766C22⋊Q8—216no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769C22⋊Q8—44no—
770C22⋊Q8—44no—
771C22⋊Q8—44no—
772C22⋊Q8—84no—
773#121—216no—
774#121—28no—
775#121—28no—
776C4×Q8—24no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—28no—
780C4×Q8—24no—
781C4×Q8—28no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—48no—
785C4×Q8—48no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×D4—28no—
789C4×D4—216no—
790C4×D4—28no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—48no—
795C4×D4—84no—
796C4×D4—82no—
797C4×D4#4118yes—
798#117—28no—
799#117—28no—
800#117—44no—
801#117—48no—
802#117—48no—
803#117—44no—
804#117—84no—
805C2×C4⋊C4—28no—
806C2×C4⋊C4—84no—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C42—44no—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2514yes—
1017C24C2512yes—
1018C2×Q8—22no—
1019C2×Q8—28no—
1020C2×Q8—24no—
1021C2×Q8—22no—
1022C2×Q8—24no—
1023C2×Q8—22no—
1024C2×Q8—24no—
1025C2×Q8—28no—
1026C2×Q8—24no—
1027C2×Q8—44no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—41no—
1033C2×Q8—42no—
1034C2×Q8—41no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×Q8—432no—
1039C2×Q82−1+414yes—
1040C2×D4—28no—
1041C2×D4—28no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—42no—
1048C2×D4—41no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C2×D4—42no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4C2×#4114yes—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—28no—
1061C22×C4—28no—
1062C22×C4—28no—
1063C22×C4—28no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4C2×#4118yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—22no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—41no—
1142C4⋊C4—42no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—41no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4C2×#4114yes—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—24no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4C2×#4118yes—
1221C42—28no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—28no—
1228C42—24no—
1229C42—24no—
1230C42—22no—
1231C42—24no—
1232C42—22no—
1233C42—24no—
1234C42—42no—
1235C42—42no—
1236C42—41no—
1237C42—42no—
1238C42—41no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—44no—
1245C42—44no—
1246C42—41no—
1247C42—42no—
1248C42C2×#4114yes—
1249C42H(5,𝔽2)14yes—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—24no—
1257C23—24no—
1258C23—24no—
1259C23—24no—
1260C23—24no—
1261C23—24no—
1262C23—24no—
1263C23C22×#4114yes—
1264C23C2611yescharacteristic
1265Q8—28no—
1266Q8—416no—
1267Q8—48no—
1268Q8—82no—
1269Q8—84no—
1270Q8—84no—
1271Q8—84no—
1272D4—44no—
1273D4—48no—
1274D4—48no—
1275D4—84no—
1276D4—88no—
1277D4—88no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—216no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—21no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—416no—
1351C2×C4—88no—
1352C2×C4—88no—
1353C2×C4—84no—
1354C2×C4—84no—
1355C2×C4—164no—
1356C2×C4—164no—
1357C2×C4C22×#4112yes—
1358C2×C4C22×#4114yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C2×H(5,𝔽2)12yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4C2×H(5,𝔽2)12yes—
1364C2×C4C2×2−1+414yes—
1365C2×C4C2×2−1+412yes—
1366C2×C4#58512yes—
1367C22—24no—
1368C22—24no—
1369C22—24no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22—44no—
1381C22C23×#4111yescharacteristic
1382C22C22×H(5,𝔽2)11yescharacteristic
1383C22C22×2−1+411yescharacteristic
1384C22C2×#58511yescharacteristic
1385C22H(7,𝔽2)11yescharacteristic
1386C222−1+611yescharacteristic
1387C222−1+611yescharacteristic
1388C4—22no—
1389C4—24no—
1390C4—24no—
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—22no—
1395C4—42no—
1396C4—44no—
1397C4—44no—
1398C4—44no—
1399C4—42no—
1400C4—42no—
1401C4—41no—
1402C4—44no—
1403C4—42no—
1404C4—42no—
1405C4—44no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4#352014yes—
1415C2—44no—
1416C2—84no—
1417C2C2×#352011yescharacteristic
1418C2#6286011yescharacteristic
1419C2#6287811yescharacteristic
1420C2#6292511yescharacteristic
1421C2#6294911yescharacteristic
1422C2#6301011yescharacteristic
1423C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39483C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59827C2semidirect
2. #59638C2semidirect
3. #52162C2semidirect
4. #51443C2semidirect
5. #50507C2semidirect
6. #49665C2semidirect
7. #46741C2semidirect
8. #45939C2semidirect
9. #45392C2semidirect
10. #44966C2semidirect
11. #44956C2semidirect
12. #43449C2semidirect
13. #42939C2semidirect
14. #42698C2semidirect
15. #41190C2semidirect
16. #40034C2semidirect
17. #39829C2semidirect
18. #39757C2semidirect
19. #39718C2semidirect
21. #38770C2semidirect
22. #38085C2semidirect
23. #37256C2semidirect
24. #36535C2semidirect
25. #36041C2semidirect
26. #35662C2semidirect
27. #35186C2semidirect
28. #34466C2semidirect
29. #34311C2semidirect

Maximal subgroups

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

subgroupindex
#598272
#596382
#521622
#514432
#505072
#496652
#467412
#459392
#453922
#449662
#449562
#434492
#429392
#426982
#411902
#400342
#398292
#397572
#397182
#394832
#387702
#380852
#372562
#365352
#360412
#356622
#351862
#344662
#343112