Finite Group Databasebeta

← #7763441

Subgroups — #7763441

Order 512.

4402 conjugacy classes of subgroups.

The subgroup lattice has 1419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59876C212yesmaximal, complemented
2#59644C212yesmaximal, complemented
3#59639C212yesmaximal, complemented
4#59584C212yesmaximal, complemented
5#51092C212yesmaximal, complemented
6#51090C212yesmaximal, complemented
7#50920C212yesmaximal, complemented
8#50918C212yesmaximal, complemented
9#45260C212yesmaximal, complemented
10#45259C212yesmaximal, complemented
11#45176C212yesmaximal, complemented
12#44988C212yesmaximal, complemented
13#42665C212yesmaximal, complemented
14#42472C212yesmaximal, complemented
15#42206C214yesmaximal, complemented
16#41647C214yesmaximal, complemented
17#40971C214yesmaximal, complemented
18#39833C214yesmaximal, complemented
19#39773C214yesmaximal, complemented
20#37559C211yesmaximal, characteristic
21#35818C212yesmaximal, complemented
22#35812C214yesmaximal, complemented
23#35785C212yesmaximal, complemented
24#35180C211yesmaximal, characteristic, complemented
25#34966C211yesmaximal, characteristic, complemented
26#34631C211yesmaximal, characteristic, complemented
27#34375C211yesmaximal, characteristic, complemented
28#34241C211yesmaximal, characteristic, complemented
29#34232C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#529C2211yescharacteristic
33#2850C2212yes—
34#2850C2212yes—
35#2839C2214yes—
36#2829C2214yes—
37#2816C2212yes—
38#2815C2212yes—
39#2799C2214yes—
40#2798C2214yes—
41#2798C2214yes—
42#2798C2214yes—
43#2797C2214yes—
44#2796C2214yes—
45#2793C2214yes—
46#2782C2214yes—
47#2767C2214yes—
48#2756C2214yes—
49#2754C2214yes—
50#2754C2214yes—
51#2754C2214yes—
52#2753C2214yes—
53#2752C2214yes—
54#2750C2214yes—
55#2747C2214yes—
56#2747C2214yes—
57#2746C2214yes—
58#2746C2214yes—
59#2743C2214yes—
60#2741C2214yes—
61#2741C2214yes—
62#2739C2214yes—
63#2738C2214yes—
64#2730C2214yes—
65#2730C2214yes—
66#2728C2214yes—
67#2716C2214yes—
68#2712C2214yes—
69#2710C2214yes—
70#2700C2214yes—
71#2664C2212yes—
72#2664C2212yes—
73#2663C2212yes—
74#2663C2212yes—
75#2661C2214yes—
76#2660C2211yescharacteristic
77#2658C2211yescharacteristic
78#2655C2214yes—
79#2654C2214yes—
80#2651C2214yes—
81#2650C2214yes—
82#2648C2214yes—
83#2642C2211yescharacteristic
84#2640C2211yescharacteristic
85#2639C2214yes—
86#2638C2214yes—
87#2633C2212yes—
88#2631C2212yes—
89#2621C2212yes—
90#2621C2212yes—
91#2620C2212yes—
92#2619C2212yes—
93#2606C2212yes—
94#2605C2212yes—
95#2603C2214yes—
96#2602C2214yes—
97#2600C2214yes—
98#2598C2214yes—
99#2597C2214yes—
100#2597C2214yes—
101#2596C2214yes—
102#2596C2214yes—
103#2595C2214yes—
104#2595C2214yes—
105#2595C2214yes—
106#2594C2214yes—
107#2593C2214yes—
108#2593C2214yes—
109#2593C2214yes—
110#2592C2212yes—
111#2592C2212yes—
112#2592C2211yescharacteristic
113#2592C2211yescharacteristic
114#2589C2214yes—
115#2577C2214yes—
116#2575C2214yes—
117#2575C2214yes—
118#2574C2214yes—
119#2573C2214yes—
120#2573C2214yes—
121#2570C2212yes—
122#2568C2211yescharacteristic
123#2568C2211yescharacteristic
124#2568C2212yes—
125#2566C2212yes—
126#2565C2212yes—
127#2564C2214yes—
128#2563C2212yes—
129#2562C2214yes—
130#2560C2214yes—
131#2550C2212yes—
132#2548C2211yescharacteristic
133#2548C2211yescharacteristic
134#2547C2212yes—
135#2542C2212yes—
136#2540C2211yescharacteristic
137#2540C2211yescharacteristic
138#2531C2214yes—
139#2531C2214yes—
140#2527C2214yes—
141#2527C2214yes—
142#2525C2214yes—
143#2524C2214yes—
144#2523C2214yes—
145#2521C2214yes—
146#2520C2214yes—
147#2520C2214yes—
148#2516C2214yes—
149#2515C2214yes—
150#2514C2212yes—
151#2513C2212yes—
152#2513C2212yes—
153#2513C2212yes—
154#2512C2212yes—
155#2511C2212yes—
156#2511C2212yes—
157#2511C2212yes—
158#2505C2214yes—
159#2503C2212yes—
160#2502C2212yes—
161#2500C2212yes—
162#2500C2212yes—
163#2499C2214yes—
164#2492C2212yes—
165#2492C2214yes—
166#2491C2212yes—
167#2490C2212yes—
168#2489C2212yes—
169#2474C2214yes—
170#2468C2214yes—
171#2467C2214yes—
172#2463C2214yes—
173#2461C2214yes—
174#2459C2214yes—
175#2459C2214yes—
176#2458C2214yes—
177#2457C2214yes—
178#2442C2212yes—
179#2440C2212yes—
180#2438C2214yes—
181#2438C2214yes—
182#2423C2212yes—
183#2422C2212yes—
184#2421C2214yes—
185#2421C2212yes—
186#2420C2212yes—
187#2419C2214yes—
188#2407C2212yes—
189#2407C2212yes—
190#2402C2212yes—
191#2402C2214yes—
192#2399C2212yes—
193#2396C2212yes—
194#2396C2212yes—
195#2395C2212yes—
196#2395C2212yes—
197#2392C2214yes—
198#2381C2212yes—
199#2381C2212yes—
200#2373C2214yes—
201#2373C2214yes—
202#2371C2214yes—
203#2368C2212yes—
204#2367C2214yes—
205#2366C2212yes—
206#2365C2212yes—
207#2364C2212yes—
208#2363C2214yes—
209#2362C2214yes—
210#2362C2212yes—
211#2362C2212yes—
212#2361C2212yes—
213#2361C2212yes—
214#2357C2214yes—
215#2357C2212yes—
216#2356C2212yes—
217#2355C2212yes—
218#2355C2212yes—
219#2355C2212yes—
220#2355C2212yes—
221#2355C2212yes—
222#2355C2212yes—
223#2354C2212yes—
224#2353C2212yes—
225#2353C2212yes—
226#2352C2212yes—
227#2352C2212yes—
228D4×C4⋊C4C2212yes—
229#2341C2211yescharacteristic
230#2341C2211yescharacteristic
231#2339C2211yescharacteristic
232#2339C2211yescharacteristic
233#2337C2212yes—
234#2336C2212yes—
235#2333C2214yes—
236#2332C2214yes—
237#2332C2212yes—
238#2332C2212yes—
239#2319C2212yes—
240#2314C2212yes—
241#2314C2212yes—
242#2314C2212yes—
243#2311C2212yes—
244#2311C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2212yes—
247C4×#125C2212yes—
248C4×#124C2212yes—
249C4×#124C2212yes—
250C4×#124C2212yes—
251C4×C22⋊Q8C2214yes—
252C4×#123C2214yes—
253#2283C2211yescharacteristic
254#2283C2211yescharacteristic
255#2275C2212yes—
256#2274C2212yes—
257C4×#117C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261#533—28no—
262#532—28no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×#127C2311yescharacteristic
269#529—28no—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#124C2311yescharacteristic
276C2×#124C2311yescharacteristic
277C2×#124C2311yescharacteristic
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#123C2312yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2311yescharacteristic
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2311yescharacteristic
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2314yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2314yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C42C2312yes—
323C22×C42C2311yescharacteristic
324#401C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#399C2312yes—
348#399C2312yes—
349#399C2312yes—
350#399C2314yes—
351#399C2312yes—
352#399C2314yes—
353#399C2312yes—
354#399C2312yes—
355#399C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2312yes—
384#397C2312yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2312yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2312yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2312yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2314yes—
426#393C2314yes—
427#393C2312yes—
428#393C2312yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2312yes—
433#393C2312yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2312yes—
438#392C2314yes—
439#392C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#390C2314yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2314yes—
472#390C2314yes—
473#390C2312yes—
474#390C2314yes—
475#390C2314yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2312yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2312yes—
540#388C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
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#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#384C2312yes—
611#384C2312yes—
612#384C2312yes—
613#384C2312yes—
614#384C2312yes—
615#383C2314yes—
616#383C2314yes—
617#383C2312yes—
618#383C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2314yes—
627#382C2312yes—
628#382C2312yes—
629#382C2314yes—
630#381C2312yes—
631#381C2314yes—
632#381C2314yes—
633#381C2312yes—
634#381C2312yes—
635#381C2314yes—
636#381C2312yes—
637#381C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2311yescharacteristic
644#380C2311yescharacteristic
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2311yescharacteristic
709#376C2311yescharacteristic
710#376C2314yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C2×#41—24no—
716C2×#41—24no—
717C2×#41—44no—
718C2×#41—44no—
719C22×Q8C2411yescharacteristic
720C22×Q8C2411yescharacteristic
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C4⋊Q8—24no—
747C4⋊Q8—24no—
748C4⋊Q8—24no—
749C4⋊Q8—44no—
750C4⋊Q8—44no—
751#127—24no—
752#126—28no—
753#126—48no—
754#125—24no—
755#125—28no—
756#125—44no—
757#124—24no—
758#124—24no—
759#124—24no—
760#124—44no—
761#124—48no—
762#124—82no—
763#124—82no—
764#123—28no—
765#123—84no—
766C22⋊Q8—24no—
767C22⋊Q8—28no—
768C22⋊Q8—24no—
769C22⋊Q8—24no—
770C22⋊Q8—48no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—48no—
774C22⋊Q8—84no—
775#121—24no—
776#121—28no—
777#121—28no—
778#121—44no—
779#121—44no—
780C4×Q8—24no—
781C4×Q8—24no—
782C4×Q8—24no—
783C4×Q8—28no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—84no—
787C4×D4—28no—
788C4×D4—24no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—48no—
794C4×D4—48no—
795C4×D4—84no—
796C4×D4—84no—
797#117—28no—
798#117—28no—
799#117—44no—
800#117—44no—
801#117—84no—
802C2×C4⋊C4—44no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C42—82no—
908C2×C42#4118yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937#95C2411yescharacteristic
938#95C2411yescharacteristic
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2411yescharacteristic
949#95C2411yescharacteristic
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2512yes—
1009C24C2512yes—
1010C24C2512yes—
1011C24C2511yescharacteristic
1012#41—88no—
1013#41—88no—
1014C2×Q8—22no—
1015C2×Q8—22no—
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—22no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—28no—
1023C2×Q8—44no—
1024C2×Q8—42no—
1025C2×Q8—41no—
1026C2×Q8—41no—
1027C2×Q8—44no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—41no—
1031C2×Q8—41no—
1032C2×D4—24no—
1033C2×D4—24no—
1034C2×D4—24no—
1035C2×D4—24no—
1036C2×D4—22no—
1037C2×D4—22no—
1038C2×D4—22no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—44no—
1043C2×D4—42no—
1044C2×D4—42no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—42no—
1050C2×D4—44no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—28no—
1063C22×C4—41no—
1064C22×C4—42no—
1065C22×C4—41no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4C2×#4114yes—
1080C22×C4C2×#4114yes—
1081C22×C4C2×#4114yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—22no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—22no—
1122C4⋊C4—22no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—44no—
1217C42—42no—
1218C42—42no—
1219C42—42no—
1220C42—42no—
1221C42—44no—
1222C42—42no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—42no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C42C2×#4114yes—
1235C42C2×#4114yes—
1236C42C2×#4114yes—
1237C42C2×#4114yes—
1238C23—22no—
1239C23—22no—
1240C23—21no—
1241C23—21no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—24no—
1250C23—22no—
1251C23—24no—
1252C23—24no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23C22×#4112yes—
1260C23C2611yescharacteristic
1261Q8—44no—
1262Q8—44no—
1263Q8—82no—
1264Q8—84no—
1265Q8—82no—
1266Q8—82no—
1267Q8—88no—
1268D4—48no—
1269D4—48no—
1270D4—44no—
1271D4—44no—
1272D4—82no—
1273D4—84no—
1274D4—84no—
1275D4—84no—
1276D4—88no—
1277D4—88no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—28no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
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—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—44no—
1341C2×C4—44no—
1342C2×C4—48no—
1343C2×C4—88no—
1344C2×C4—84no—
1345C2×C4—84no—
1346C2×C4—88no—
1347C2×C4—164no—
1348C2×C4—164no—
1349C2×C4C22×#4112yes—
1350C2×C4C22×#4112yes—
1351C2×C4C22×#4112yes—
1352C2×C4C22×#4112yes—
1353C2×C4C22×#4112yes—
1354C2×C4C22×#4112yes—
1355C2×C4#58514yes—
1356C2×C4#58514yes—
1357C22—22no—
1358C22—22no—
1359C22—22no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
1371C22—44no—
1372C22—42no—
1373C22—44no—
1374C22—42no—
1375C22—42no—
1376C22—44no—
1377C22—44no—
1378C22—42no—
1379C22C23×#4111yescharacteristic
1380C22C2×#58512yes—
1381C22C2×#58512yes—
1382C22H(7,𝔽2)11yescharacteristic
1383C222−1+611yescharacteristic
1384C4—22no—
1385C4—22no—
1386C4—22no—
1387C4—22no—
1388C4—22no—
1389C4—24no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4—44no—
1401C4—44no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—42no—
1406C4—44no—
1407C4—44no—
1408C4#351014yes—
1409C2—42no—
1410C2—82no—
1411C2—82no—
1412C2—82no—
1413C2C2×#351011yescharacteristic
1414C2#6281511yescharacteristic
1415C2#6285611yescharacteristic
1416C2#6296512yes—
1417C2#6296712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37559C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59876C2semidirect
2. #59644C2semidirect
3. #59639C2semidirect
4. #59584C2semidirect
5. #51092C2semidirect
6. #51090C2semidirect
7. #50920C2semidirect
8. #50918C2semidirect
9. #45260C2semidirect
10. #45259C2semidirect
11. #45176C2semidirect
12. #44988C2semidirect
13. #42665C2semidirect
14. #42472C2semidirect
15. #42206C2semidirect
16. #41647C2semidirect
17. #40971C2semidirect
18. #39833C2semidirect
19. #39773C2semidirect
21. #35818C2semidirect
22. #35812C2semidirect
23. #35785C2semidirect
24. #35180C2semidirect
25. #34966C2semidirect
26. #34631C2semidirect
27. #34375C2semidirect
28. #34241C2semidirect
29. #34232C2semidirect

Maximal subgroups

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

subgroupindex
#598762
#596442
#596392
#595842
#510922
#510902
#509202
#509182
#452602
#452592
#451762
#449882
#426652
#424722
#422062
#416472
#409712
#398332
#397732
#375592
#358182
#358122
#357852
#351802
#349662
#346312
#343752
#342412
#342322