Finite Group Databasebeta

← #7898426

Subgroups — #7898426

Order 512.

4431 conjugacy classes of subgroups.

The subgroup lattice has 1403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59446C212yesmaximal, complemented
3#52274C211yesmaximal, characteristic, complemented
4#48934C214yesmaximal, complemented
5#48674C214yesmaximal, complemented
6#48495C214yesmaximal, complemented
7#47052C214yesmaximal, complemented
8#46098C212yesmaximal, complemented
9#45430C212yesmaximal, complemented
10#45056C212yesmaximal, complemented
11#44968C212yesmaximal, complemented
12#44826C214yesmaximal, complemented
13#42704C212yesmaximal, complemented
14#42530C212yesmaximal, complemented
15#41215C214yesmaximal, complemented
16#39750C212yesmaximal, complemented
17#39749C211yesmaximal, characteristic, complemented
18#39618C212yesmaximal, complemented
19#39611C211yesmaximal, characteristic, complemented
20#39203C212yesmaximal, complemented
21#38763C212yesmaximal, complemented
22#38484C212yesmaximal, complemented
23#37157C212yesmaximal, complemented
24#36416C211yesmaximal, characteristic, complemented
25#35952C212yesmaximal, complemented
26#35562C212yesmaximal
27#35197C211yesmaximal, characteristic
28#34489C212yesmaximal, complemented
29#34334C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×D4×Q8C2211yescharacteristic
32#2862C2212yes—
33#2859C2211yescharacteristic
34#2854C2212yes—
35#2851C2212yes—
36#2850C2212yes—
37#2836C2214yes—
38#2831C2214yes—
39#2809C2211yescharacteristic
40#2809C2212yes—
41#2808C2212yes—
42#2808C2212yes—
43#2806C2211yescharacteristic
44#2806C2212yes—
45#2805C2212yes—
46#2805C2211yescharacteristic
47#2802C2212yes—
48#2799C2212yes—
49#2799C2214yes—
50#2799C2214yes—
51#2798C2214yes—
52#2798C2214yes—
53#2791C2212yes—
54#2781C2214yes—
55#2779C2214yes—
56#2774C2212yes—
57#2761C2214yes—
58#2755C2214yes—
59#2755C2214yes—
60#2755C2212yes—
61#2754C2214yes—
62#2754C2214yes—
63#2750C2214yes—
64#2747C2214yes—
65#2744C2214yes—
66#2741C2214yes—
67#2741C2214yes—
68#2740C2214yes—
69#2740C2214yes—
70#2739C2214yes—
71#2732C2212yes—
72#2732C2212yes—
73#2726C2211yescharacteristic
74#2726C2212yes—
75#2722C2214yes—
76#2713C2212yes—
77#2707C2214yes—
78#2704C2214yes—
79#2700C2214yes—
80#2700C2214yes—
81#2698C2214yes—
82#2695C2214yes—
83#2692C2214yes—
84#2692C2214yes—
85#2692C2214yes—
86#2692C2214yes—
87#2690C2214yes—
88#2689C2214yes—
89#2687C2214yes—
90#2687C2214yes—
91#2683C2212yes—
92#2683C2212yes—
93#2665C2214yes—
94#2664C2214yes—
95#2660C2212yes—
96#2660C2212yes—
97#2660C2212yes—
98#2654C2214yes—
99#2650C2214yes—
100#2648C2214yes—
101#2637C2214yes—
102#2625C2214yes—
103#2609C2214yes—
104#2601C2214yes—
105#2592C2214yes—
106#2590C2214yes—
107#2589C2214yes—
108#2588C2214yes—
109#2588C2214yes—
110#2587C2214yes—
111#2580C2212yes—
112#2574C2214yes—
113#2574C2214yes—
114#2571C2212yes—
115#2571C2211yescharacteristic
116#2571C2211yescharacteristic
117#2571C2212yes—
118#2570C2212yes—
119#2570C2212yes—
120#2570C2212yes—
121#2570C2212yes—
122#2570C2212yes—
123#2570C2212yes—
124#2569C2214yes—
125#2566C2212yes—
126#2566C2212yes—
127#2566C2212yes—
128#2566C2212yes—
129#2563C2212yes—
130#2563C2212yes—
131#2563C2212yes—
132#2560C2214yes—
133#2560C2214yes—
134#2559C2214yes—
135#2558C2214yes—
136#2557C2214yes—
137#2552C2212yes—
138#2552C2211yescharacteristic
139#2548C2211yescharacteristic
140#2548C2212yes—
141#2547C2212yes—
142#2542C2212yes—
143#2542C2212yes—
144#2541C2211yescharacteristic
145#2538C2211yescharacteristic
146#2522C2214yes—
147#2521C2214yes—
148#2521C2214yes—
149#2520C2214yes—
150#2520C2214yes—
151#2519C2214yes—
152#2513C2212yes—
153#2513C2212yes—
154#2513C2212yes—
155#2513C2212yes—
156#2513C2212yes—
157#2513C2212yes—
158#2512C2212yes—
159#2512C2212yes—
160#2512C2212yes—
161#2498C2214yes—
162#2498C2214yes—
163#2489C2214yes—
164#2485C2214yes—
165#2481C2214yes—
166#2477C2214yes—
167#2477C2214yes—
168#2476C2214yes—
169#2471C2214yes—
170#2470C2214yes—
171#2469C2214yes—
172#2468C2214yes—
173#2467C2214yes—
174#2465C2214yes—
175#2462C2214yes—
176#2460C2214yes—
177#2459C2214yes—
178#2457C2214yes—
179#2449C2214yes—
180#2449C2214yes—
181#2445C2212yes—
182#2445C2212yes—
183#2445C2212yes—
184#2444C2214yes—
185#2441C2212yes—
186#2439C2212yes—
187#2438C2214yes—
188#2427C2212yes—
189#2425C2214yes—
190#2421C2214yes—
191#2420C2212yes—
192#2419C2214yes—
193#2417C2214yes—
194#2417C2214yes—
195#2413C2214yes—
196#2409C2214yes—
197#2409C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2399C2212yes—
201#2396C2214yes—
202#2378C2214yes—
203#2378C2214yes—
204#2370C2212yes—
205#2370C2212yes—
206#2369C2212yes—
207#2368C2214yes—
208#2365C2211yescharacteristic
209#2365C2212yes—
210#2362C2214yes—
211#2360C2212yes—
212#2359C2214yes—
213#2357C2212yes—
214#2357C2212yes—
215#2357C2212yes—
216#2355C2211yescharacteristic
217#2355C2212yes—
218#2355C2212yes—
219#2355C2212yes—
220#2354C2211yescharacteristic
221#2354C2212yes—
222#2354C2212yes—
223#2354C2211yescharacteristic
224#2354C2212yes—
225#2349C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227#2344C2214yes—
228Q8×C22⋊C4C2212yes—
229#2332C2214yes—
230#2332C2214yes—
231#2331C2212yes—
232#2331C2212yes—
233#2330C2212yes—
234#2329C2214yes—
235#2328C2212yes—
236#2328C2212yes—
237#2328C2212yes—
238#2323C2214yes—
239#2323C2214yes—
240#2319C2212yes—
241#2319C2212yes—
242#2313C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×#127C2212yes—
246C4×#127C2211yescharacteristic
247C4×#125C2212yes—
248C4×#125C2212yes—
249C4×C22⋊Q8C2212yes—
250#2296C2212yes—
251#2295C2211yescharacteristic
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2212yes—
255C2×#391C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C23×Q8C2312yes—
260#554—216no—
261D4×Q8—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×#127C2312yes—
267C2×#127C2311yescharacteristic
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#124C2314yes—
277C2×#124C2312yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2312yes—
311C2×#117C2312yes—
312C2×#117C2314yes—
313C2×#117C2314yes—
314C2×#117C2312yes—
315C2×#117C2314yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2312yes—
318C22×C42C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#398C2312yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2314yes—
355#398C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2312yes—
405#395C2312yes—
406#395C2312yes—
407#395C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#392C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2311yescharacteristic
448#391C2312yes—
449#391C2312yes—
450#391C2311yescharacteristic
451#390C2312yes—
452#390C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2311yescharacteristic
478#389C2311yescharacteristic
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2311yescharacteristic
501#389C2311yescharacteristic
502#389C2312yes—
503#389C2312yes—
504#389C2311yescharacteristic
505#389C2312yes—
506#389C2311yescharacteristic
507#389C2312yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2314yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#384C2312yes—
620#384C2311yescharacteristic
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#384C2311yescharacteristic
624#384C2312yes—
625#384C2312yes—
626#384C2312yes—
627#384C2311yescharacteristic
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2312yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C22×Q8—28no—
715C22×Q8—82no—
716C22×Q8—82no—
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×D4C2412yes—
724C22×D4C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2412yes—
729C23×C4C2412yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2412yes—
737C4⋊Q8—24no—
738C4⋊Q8—28no—
739C4⋊Q8—28no—
740C4⋊Q8—42no—
741#127—28no—
742#127—24no—
743#126—84no—
744#126—84no—
745#126—84no—
746#125—28no—
747#125—28no—
748#125—44no—
749#125—82no—
750#125—84no—
751#124—82no—
752#124—84no—
753#123—48no—
754#123—84no—
755#123—84no—
756C22⋊Q8—216no—
757C22⋊Q8—216no—
758C22⋊Q8—28no—
759C22⋊Q8—216no—
760C22⋊Q8—216no—
761C22⋊Q8—48no—
762C22⋊Q8—82no—
763C22⋊Q8—84no—
764C22⋊Q8—84no—
765C22⋊Q8—84no—
766#121—82no—
767#121—82no—
768C4×Q8—28no—
769C4×Q8—24no—
770C4×Q8—82no—
771C4×Q8—84no—
772C4×Q8—82no—
773C4×Q8#4118yes—
774C4×D4—24no—
775C4×D4—28no—
776C4×D4—24no—
777C4×D4—28no—
778C4×D4—28no—
779C4×D4—28no—
780C4×D4—28no—
781C4×D4—24no—
782C4×D4—44no—
783C4×D4—84no—
784C4×D4—82no—
785C4×D4—84no—
786#117—44no—
787#117—84no—
788#117—84no—
789#117—84no—
790#117—82no—
791C2×C4⋊C4—216no—
792C2×C4⋊C4—82no—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C42—82no—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24C2514yes—
1004C24C2512yes—
1005C2×Q8—24no—
1006C2×Q8—28no—
1007C2×Q8—28no—
1008C2×Q8—24no—
1009C2×Q8—22no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—41no—
1013C2×Q8—41no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8—41no—
1017C2×Q8—44no—
1018C2×Q8—44no—
1019C2×Q8—42no—
1020C2×Q8—41no—
1021C2×Q8—42no—
1022C2×Q8—816no—
1023C2×Q8C2×#4114yes—
1024C2×D4—28no—
1025C2×D4—28no—
1026C2×D4—22no—
1027C2×D4—24no—
1028C2×D4—22no—
1029C2×D4—24no—
1030C2×D4—24no—
1031C2×D4—24no—
1032C2×D4—24no—
1033C2×D4—42no—
1034C2×D4—42no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—42no—
1039C2×D4—44no—
1040C2×D4—42no—
1041C2×D42−1+414yes—
1042C22×C4—24no—
1043C22×C4—28no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—28no—
1047C22×C4—28no—
1048C22×C4—28no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—22no—
1100C4⋊C4—24no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—22no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—22no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—41no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—41no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—41no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—41no—
1139C4⋊C4—41no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—41no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4C2×#4118yes—
1165C4⋊C4C2×#4114yes—
1166C22⋊C4—24no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—28no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C42—22no—
1201C42—24no—
1202C42—24no—
1203C42—24no—
1204C42—24no—
1205C42—24no—
1206C42—22no—
1207C42—41no—
1208C42—42no—
1209C42—42no—
1210C42—42no—
1211C42—44no—
1212C42—42no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—41no—
1219C42—42no—
1220C42—42no—
1221C42—41no—
1222C42—44no—
1223C42—44no—
1224C42—42no—
1225C42—44no—
1226C42C2×#4114yes—
1227C42C2×#4118yes—
1228C422−1+414yes—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—24no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23C2×2−1+414yes—
1243C23C2611yescharacteristic
1244Q8—44no—
1245Q8—48no—
1246Q8—88no—
1247Q8—82no—
1248Q8—84no—
1249Q8—88no—
1250D4—28no—
1251D4—48no—
1252D4—84no—
1253D4—84no—
1254D4—88no—
1255D4—88no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—48no—
1328C2×C4—48no—
1329C2×C4—88no—
1330C2×C4—88no—
1331C2×C4—88no—
1332C2×C4—84no—
1333C2×C4—88no—
1334C2×C4—88no—
1335C2×C4C22×#4114yes—
1336C2×C4C22×#4112yes—
1337C2×C4C22×#4112yes—
1338C2×C4C22×#4114yes—
1339C2×C4C22×#4112yes—
1340C2×C4C2×2−1+412yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4C2×2−1+412yes—
1344C2×C4#58512yes—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—42no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22C23×#4111yescharacteristic
1360C22C22×2−1+411yescharacteristic
1361C22C22×2−1+411yescharacteristic
1362C22C2×#58511yescharacteristic
1363C22H(7,𝔽2)11yescharacteristic
1364C22H(7,𝔽2)11yescharacteristic
1365C22H(7,𝔽2)11yescharacteristic
1366C4—22no—
1367C4—24no—
1368C4—22no—
1369C4—24no—
1370C4—22no—
1371C4—22no—
1372C4—22no—
1373C4—44no—
1374C4—44no—
1375C4—41no—
1376C4—44no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—44no—
1381C4—44no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4#352314yes—
1393C2—44no—
1394C2—84no—
1395C2C2×#352311yescharacteristic
1396C2#6285511yescharacteristic
1397C2#6288111yescharacteristic
1398C2#6292911yescharacteristic
1399C2#6294811yescharacteristic
1400C2#6301011yescharacteristic
1401C2#6305411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59863C2semidirect
2. #59446C2semidirect
3. #52274C2semidirect
4. #48934C2semidirect
5. #48674C2semidirect
6. #48495C2semidirect
7. #47052C2semidirect
8. #46098C2semidirect
9. #45430C2semidirect
10. #45056C2semidirect
11. #44968C2semidirect
12. #44826C2semidirect
13. #42704C2semidirect
14. #42530C2semidirect
15. #41215C2semidirect
16. #39750C2semidirect
17. #39749C2semidirect
18. #39618C2semidirect
19. #39611C2semidirect
20. #39203C2semidirect
21. #38763C2semidirect
22. #38484C2semidirect
23. #37157C2semidirect
24. #36416C2semidirect
25. #35952C2semidirect
28. #34489C2semidirect
29. #34334C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#594462
#522742
#489342
#486742
#484952
#470522
#460982
#454302
#450562
#449682
#448262
#427042
#425302
#412152
#397502
#397492
#396182
#396112
#392032
#387632
#384842
#371572
#364162
#359522
#355622
#351972
#344892
#343342