Finite Group Databasebeta

← #7658969

Subgroups — #7658969

Order 512.

4088 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42948C212yesmaximal, complemented
2#42921C212yesmaximal, complemented
3#42667C212yesmaximal, complemented
4#42665C212yesmaximal, complemented
5#42512C212yesmaximal, complemented
6#42511C212yesmaximal, complemented
7#42242C214yesmaximal, complemented
8#42237C214yesmaximal, complemented
9#41704C214yesmaximal, complemented
10#41697C214yesmaximal, complemented
11#41647C214yesmaximal
12#41636C214yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37612C212yesmaximal, complemented
15#37603C212yesmaximal, complemented
16#37600C212yesmaximal, complemented
17#37561C211yesmaximal, characteristic, complemented
18#37555C211yesmaximal, characteristic
19#36701C212yesmaximal, complemented
20#36699C211yesmaximal, characteristic
21#36069C212yesmaximal, complemented
22#36050C212yesmaximal, complemented
23#36006C212yesmaximal, complemented
24#35958C212yesmaximal, complemented
25#35819C212yesmaximal, complemented
26#35818C212yesmaximal, complemented
27#34242C211yesmaximal, characteristic
28#34231C211yesmaximal, characteristic, complemented
29#34215C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#529C2211yescharacteristic
33#2845C2212yes—
34#2844C2212yes—
35#2839C2214yes—
36#2839C2214yes—
37#2839C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2822C2212yes—
42#2822C2212yes—
43#2822C2211yescharacteristic
44#2822C2211yescharacteristic
45#2822C2212yes—
46#2821C2212yes—
47#2821C2212yes—
48#2820C2211yescharacteristic
49#2820C2211yescharacteristic
50#2820C2212yes—
51#2817C2212yes—
52#2816C2212yes—
53#2814C2212yes—
54#2814C2212yes—
55#2799C2214yes—
56#2798C2214yes—
57#2782C2214yes—
58#2776C2214yes—
59#2770C2214yes—
60#2770C2214yes—
61#2770C2214yes—
62#2767C2214yes—
63#2764C2214yes—
64#2763C2214yes—
65#2758C2214yes—
66#2758C2214yes—
67#2755C2214yes—
68#2754C2214yes—
69#2754C2214yes—
70#2750C2214yes—
71#2747C2214yes—
72#2746C2214yes—
73#2728C2214yes—
74#2719C2214yes—
75#2716C2214yes—
76#2713C2214yes—
77#2698C2214yes—
78#2690C2214yes—
79#2667C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2664C2214yes—
86#2660C2212yes—
87#2659C2212yes—
88#2659C2212yes—
89#2655C2214yes—
90#2655C2214yes—
91#2655C2214yes—
92#2654C2214yes—
93#2654C2214yes—
94#2654C2214yes—
95#2652C2214yes—
96#2651C2214yes—
97#2650C2214yes—
98#2650C2214yes—
99#2647C2212yes—
100#2646C2212yes—
101#2639C2212yes—
102#2638C2214yes—
103#2637C2214yes—
104#2634C2214yes—
105#2628C2212yes—
106#2625C2212yes—
107#2625C2212yes—
108#2625C2214yes—
109#2621C2214yes—
110#2621C2212yes—
111#2612C2214yes—
112#2605C2214yes—
113#2605C2214yes—
114#2597C2214yes—
115#2596C2214yes—
116#2595C2214yes—
117#2593C2214yes—
118#2589C2214yes—
119#2586C2214yes—
120#2585C2214yes—
121#2582C2212yes—
122#2582C2212yes—
123#2581C2212yes—
124#2577C2214yes—
125#2575C2214yes—
126#2573C2214yes—
127#2573C2214yes—
128#2571C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2568C2212yes—
132#2568C2212yes—
133#2568C2212yes—
134#2565C2212yes—
135#2560C2214yes—
136#2556C2214yes—
137#2556C2214yes—
138#2550C2214yes—
139#2550C2212yes—
140#2546C2212yes—
141#2546C2212yes—
142#2536C2212yes—
143#2532C2214yes—
144#2532C2214yes—
145#2531C2214yes—
146#2530C2214yes—
147#2529C2214yes—
148#2527C2214yes—
149#2525C2214yes—
150#2524C2214yes—
151#2524C2214yes—
152#2524C2214yes—
153#2524C2214yes—
154#2522C2214yes—
155#2520C2214yes—
156#2520C2214yes—
157#2520C2214yes—
158#2520C2214yes—
159#2520C2214yes—
160#2519C2214yes—
161#2515C2214yes—
162#2514C2212yes—
163#2511C2212yes—
164#2511C2212yes—
165#2511C2212yes—
166#2509C2212yes—
167#2507C2212yes—
168#2506C2212yes—
169#2506C2212yes—
170#2503C2212yes—
171#2502C2212yes—
172#2498C2214yes—
173#2497C2212yes—
174#2496C2212yes—
175#2495C2212yes—
176#2495C2214yes—
177#2495C2212yes—
178#2492C2212yes—
179#2492C2214yes—
180#2489C2212yes—
181#2489C2214yes—
182#2468C2214yes—
183#2462C2214yes—
184#2442C2212yes—
185#2442C2212yes—
186#2440C2212yes—
187#2440C2212yes—
188#2438C2214yes—
189#2423C2212yes—
190#2421C2212yes—
191#2417C2212yes—
192#2417C2212yes—
193#2402C2214yes—
194#2402C2214yes—
195#2402C2214yes—
196#2402C2214yes—
197#2402C2214yes—
198#2402C2214yes—
199#2399C2212yes—
200#2398C2212yes—
201#2396C2212yes—
202#2396C2212yes—
203#2395C2212yes—
204#2395C2212yes—
205#2373C2214yes—
206#2370C2212yes—
207#2369C2212yes—
208#2369C2211yescharacteristic
209#2369C2211yescharacteristic
210#2368C2214yes—
211#2368C2214yes—
212#2365C2211yescharacteristic
213#2365C2211yescharacteristic
214#2363C2212yes—
215#2362C2212yes—
216#2362C2212yes—
217#2362C2212yes—
218#2362C2212yes—
219#2362C2212yes—
220#2356C2214yes—
221#2356C2212yes—
222#2355C2212yes—
223#2355C2211yescharacteristic
224#2355C2212yes—
225#2355C2212yes—
226#2355C2212yes—
227#2355C2212yes—
228#2354C2212yes—
229#2354C2211yescharacteristic
230#2352C2212yes—
231Q8×C4⋊C4C2211yescharacteristic
232D4×C4⋊C4C2211yescharacteristic
233#2347C2212yes—
234#2347C2212yes—
235#2346C2212yes—
236#2346C2212yes—
237#2335C2214yes—
238#2332C2214yes—
239#2331C2212yes—
240#2331C2212yes—
241#2320C2212yes—
242#2317C2211yescharacteristic
243#2317C2211yescharacteristic
244#2314C2212yes—
245C4×#125C2212yes—
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×#125C2212yes—
249C4×#125C2212yes—
250C4×#124C2212yes—
251#2285C2211yescharacteristic
252#2283C2211yescharacteristic
253C2×#382C2211yescharacteristic
254#2276C2212yes—
255#2274C2211yescharacteristic
256#2274C2211yescharacteristic
257#2274C2212yes—
258C4×#117C2211yescharacteristic
259#533—28no—
260#533—28no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267#529—28no—
268C2×#126C2312yes—
269C2×#126C2314yes—
270C2×#125C2311yescharacteristic
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#124C2311yescharacteristic
278C2×#123C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2311yescharacteristic
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×#117C2312yes—
301C2×#117C2311yescharacteristic
302C2×#117C2311yescharacteristic
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2312yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C42C2311yescharacteristic
312#401C2314yes—
313#400C2312yes—
314#400C2312yes—
315#400C2312yes—
316#400C2312yes—
317#400C2312yes—
318#400C2312yes—
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#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
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#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#399C2312yes—
356#399C2312yes—
357#399C2312yes—
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2312yes—
407#397C2312yes—
408#397C2312yes—
409#397C2312yes—
410#397C2312yes—
411#397C2314yes—
412#397C2312yes—
413#397C2312yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#396C2312yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#396C2312yes—
428#396C2312yes—
429#396C2314yes—
430#395C2312yes—
431#395C2312yes—
432#395C2312yes—
433#395C2312yes—
434#395C2314yes—
435#395C2312yes—
436#395C2312yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#394C2312yes—
444#394C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2314yes—
450#393C2314yes—
451#393C2312yes—
452#393C2312yes—
453#393C2312yes—
454#393C2312yes—
455#393C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#390C2314yes—
482#390C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
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#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#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#384C2312yes—
603#384C2312yes—
604#384C2312yes—
605#384C2312yes—
606#384C2311yescharacteristic
607#384C2311yescharacteristic
608#383C2312yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#383C2314yes—
614#383C2314yes—
615#382C2311yescharacteristic
616#382C2312yes—
617#382C2311yescharacteristic
618#382C2312yes—
619#382C2312yes—
620#382C2314yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2314yes—
625#382C2312yes—
626#382C2314yes—
627#382C2312yes—
628#382C2312yes—
629#382C2314yes—
630#382C2314yes—
631#382C2314yes—
632#381C2312yes—
633#381C2314yes—
634#381C2314yes—
635#380C2312yes—
636#380C2312yes—
637#380C2314yes—
638#380C2312yes—
639#380C2311yescharacteristic
640#380C2312yes—
641#380C2311yescharacteristic
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2314yes—
710#376C2314yes—
711#376C2314yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C22×Q8C2412yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2414yes—
721C22×D4C2411yescharacteristic
722C22×D4C2412yes—
723C23×C4C2412yes—
724C23×C4C2411yescharacteristic
725C23×C4C2414yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C4⋊Q8—24no—
731C4⋊Q8—24no—
732C4⋊Q8—24no—
733C4⋊Q8—24no—
734C4⋊Q8—44no—
735C4⋊Q8—84no—
736#126—28no—
737#126—84no—
738#125—24no—
739#125—24no—
740#125—28no—
741#125—24no—
742#125—44no—
743#125—84no—
744#125—84no—
745#124—24no—
746#123—28no—
747C22⋊Q8—24no—
748C22⋊Q8—28no—
749C22⋊Q8—28no—
750C22⋊Q8—28no—
751C22⋊Q8—28no—
752C22⋊Q8—44no—
753C22⋊Q8—44no—
754C22⋊Q8—84no—
755C22⋊Q8—84no—
756#121—24no—
757C4×Q8—28no—
758C4×Q8—24no—
759C4×Q8—28no—
760C4×Q8—28no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—44no—
764C4×Q8—82no—
765C4×D4—28no—
766C4×D4—24no—
767C4×D4—82no—
768#117—24no—
769#117—24no—
770#117—28no—
771#117—24no—
772#117—28no—
773#117—28no—
774#117—42no—
775#117—82no—
776C2×C4⋊C4—44no—
777C2×C4⋊C4—42no—
778C2×C4⋊C4—42no—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C42#4118yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994C24C2512yes—
995C24C2511yescharacteristic
996C2×Q8—22no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—41no—
1004C2×Q8—41no—
1005C2×Q8—42no—
1006C2×Q8—42no—
1007C2×Q8—42no—
1008C2×Q8—42no—
1009C2×Q8—42no—
1010C2×Q8—42no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×D4—24no—
1015C2×D4—22no—
1016C2×D4—41no—
1017C2×D4—41no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—44no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—44no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4C2×#4114yes—
1039C22×C4C2×#4114yes—
1040C22×C4C2×#4114yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—22no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—22no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—22no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—41no—
1102C4⋊C4—41no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C42−1+414yes—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—28no—
1147C22⋊C4—24no—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—28no—
1154C22⋊C4—42no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—42no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—42no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C42—24no—
1173C42—28no—
1174C42—24no—
1175C42—24no—
1176C42—24no—
1177C42—28no—
1178C42—24no—
1179C42—28no—
1180C42—24no—
1181C42—42no—
1182C42—42no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—42no—
1188C42—44no—
1189C42—44no—
1190C42—42no—
1191C42—44no—
1192C42—42no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42C2×#4114yes—
1197C42C2×#4114yes—
1198C42C2×#4114yes—
1199C42C2×#4114yes—
1200C23—21no—
1201C23—21no—
1202C23—21no—
1203C23—21no—
1204C23—21no—
1205C23—21no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23C22×#4112yes—
1214C23C2611yescharacteristic
1215Q8—44no—
1216Q8—48no—
1217Q8—84no—
1218Q8—84no—
1219Q8—84no—
1220Q8—164no—
1221D4—44no—
1222D4—84no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—28no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
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—44no—
1297C2×C4—44no—
1298C2×C4—48no—
1299C2×C4—162no—
1300C2×C4—164no—
1301C2×C4—162no—
1302C2×C4C22×#4112yes—
1303C2×C4C22×#4112yes—
1304C2×C4C22×#4112yes—
1305C2×C4C22×#4112yes—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4112yes—
1308C2×C4C2×2−1+414yes—
1309C2×C4C2×2−1+412yes—
1310C2×C4#58512yes—
1311C22—22no—
1312C22—22no—
1313C22—22no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22C23×#4111yescharacteristic
1326C22C22×2−1+411yescharacteristic
1327C22C2×#58511yescharacteristic
1328C22H(7,𝔽2)11yescharacteristic
1329C222−1+611yescharacteristic
1330C222−1+611yescharacteristic
1331C222−1+611yescharacteristic
1332C4—24no—
1333C4—22no—
1334C4—22no—
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—42no—
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—44no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—44no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—42no—
1357C4—44no—
1358C4#346114yes—
1359C2—42no—
1360C2—82no—
1361C2C2×#346111yescharacteristic
1362C2#6285611yescharacteristic
1363C2#6286011yescharacteristic
1364C2#6306111yescharacteristic
1365C2#6306211yescharacteristic
1366C2#6306711yescharacteristic
1367C2#6306911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42948C2semidirect
2. #42921C2semidirect
3. #42667C2semidirect
4. #42665C2semidirect
5. #42512C2semidirect
6. #42511C2semidirect
7. #42242C2semidirect
8. #42237C2semidirect
9. #41704C2semidirect
10. #41697C2semidirect
12. #41636C2semidirect
13. #37641C2semidirect
14. #37612C2semidirect
15. #37603C2semidirect
16. #37600C2semidirect
17. #37561C2semidirect
19. #36701C2semidirect
21. #36069C2semidirect
22. #36050C2semidirect
23. #36006C2semidirect
24. #35958C2semidirect
25. #35819C2semidirect
26. #35818C2semidirect
28. #34231C2semidirect
29. #34215C2semidirect

Maximal subgroups

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

subgroupindex
#429482
#429212
#426672
#426652
#425122
#425112
#422422
#422372
#417042
#416972
#416472
#416362
#376412
#376122
#376032
#376002
#375612
#375552
#367012
#366992
#360692
#360502
#360062
#359582
#358192
#358182
#342422
#342312
#342152