Finite Group Databasebeta

← #7658933

Subgroups — #7658933

Order 512.

4168 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42954C212yesmaximal
2#42930C212yesmaximal
3#42824C212yesmaximal, complemented
4#42820C212yesmaximal, complemented
5#42500C212yesmaximal, complemented
6#42496C212yesmaximal, complemented
7#42188C214yesmaximal, complemented
8#42184C214yesmaximal, complemented
9#42008C214yesmaximal, complemented
10#42001C214yesmaximal, complemented
11#40634C214yesmaximal, complemented
12#40630C214yesmaximal, complemented
13#37642C211yesmaximal, characteristic, complemented
14#37609C212yesmaximal, complemented
15#37563C212yesmaximal, complemented
16#37561C211yesmaximal, characteristic, complemented
17#37561C211yesmaximal, characteristic, complemented
18#37561C212yesmaximal, complemented
19#36691C212yesmaximal, complemented
20#36691C211yesmaximal, characteristic, complemented
21#35958C212yesmaximal, complemented
22#35952C212yesmaximal, complemented
23#35871C212yesmaximal, complemented
24#35867C212yesmaximal, complemented
25#35819C212yesmaximal, complemented
26#35815C212yesmaximal, complemented
27#34193C211yesmaximal, characteristic
28#34191C211yesmaximal, characteristic
29#34189C211yesmaximal, characteristic
30C2×C4×#41C2211yescharacteristic
31#2845C2211yescharacteristic
32#2845C2212yes—
33#2845C2211yescharacteristic
34#2845C2212yes—
35#2844C2212yes—
36#2844C2212yes—
37#2844C2211yescharacteristic
38#2844C2212yes—
39#2844C2211yescharacteristic
40#2844C2212yes—
41#2843C2212yes—
42#2843C2214yes—
43#2843C2214yes—
44#2843C2212yes—
45#2841C2214yes—
46#2841C2214yes—
47#2841C2212yes—
48#2841C2214yes—
49#2841C2212yes—
50#2841C2212yes—
51#2841C2212yes—
52#2841C2214yes—
53#2806C2214yes—
54#2804C2214yes—
55#2802C2214yes—
56#2791C2214yes—
57#2790C2214yes—
58#2788C2214yes—
59#2788C2214yes—
60#2784C2214yes—
61#2780C2214yes—
62#2774C2214yes—
63#2768C2214yes—
64#2763C2214yes—
65#2755C2214yes—
66#2755C2214yes—
67#2748C2214yes—
68#2734C2214yes—
69#2732C2214yes—
70#2729C2214yes—
71#2713C2214yes—
72#2704C2214yes—
73#2692C2214yes—
74#2692C2214yes—
75#2692C2214yes—
76#2677C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2665C2214yes—
86#2665C2214yes—
87#2665C2214yes—
88#2665C2214yes—
89#2665C2214yes—
90#2665C2214yes—
91#2660C2212yes—
92#2660C2214yes—
93#2660C2212yes—
94#2659C2212yes—
95#2659C2214yes—
96#2659C2212yes—
97#2647C2212yes—
98#2647C2212yes—
99#2647C2214yes—
100#2646C2214yes—
101#2646C2212yes—
102#2646C2212yes—
103#2628C2214yes—
104#2628C2212yes—
105#2628C2214yes—
106#2628C2212yes—
107#2627C2214yes—
108#2627C2214yes—
109#2612C2214yes—
110#2612C2214yes—
111#2605C2214yes—
112#2605C2214yes—
113#2605C2214yes—
114#2605C2214yes—
115#2605C2214yes—
116#2605C2214yes—
117#2590C2214yes—
118#2589C2214yes—
119#2589C2214yes—
120#2589C2214yes—
121#2588C2214yes—
122#2587C2214yes—
123#2586C2214yes—
124#2585C2214yes—
125#2582C2212yes—
126#2581C2212yes—
127#2580C2212yes—
128#2574C2214yes—
129#2574C2214yes—
130#2574C2214yes—
131#2571C2212yes—
132#2571C2212yes—
133#2571C2212yes—
134#2570C2212yes—
135#2570C2212yes—
136#2570C2214yes—
137#2569C2214yes—
138#2569C2214yes—
139#2568C2212yes—
140#2567C2212yes—
141#2566C2212yes—
142#2565C2212yes—
143#2563C2212yes—
144#2556C2214yes—
145#2551C2212yes—
146#2551C2212yes—
147#2551C2212yes—
148#2550C2212yes—
149#2550C2212yes—
150#2550C2212yes—
151#2550C2214yes—
152#2550C2212yes—
153#2549C2214yes—
154#2549C2214yes—
155#2546C2212yes—
156#2538C2212yes—
157#2522C2214yes—
158#2522C2214yes—
159#2520C2214yes—
160#2520C2214yes—
161#2509C2212yes—
162#2508C2212yes—
163#2507C2212yes—
164#2506C2212yes—
165#2492C2214yes—
166#2492C2214yes—
167#2465C2214yes—
168#2465C2214yes—
169#2454C2212yes—
170#2453C2212yes—
171#2452C2212yes—
172#2452C2212yes—
173#2452C2212yes—
174#2451C2214yes—
175#2451C2212yes—
176#2451C2212yes—
177#2451C2212yes—
178#2446C2214yes—
179#2442C2214yes—
180#2442C2212yes—
181#2442C2212yes—
182#2440C2214yes—
183#2440C2212yes—
184#2440C2212yes—
185#2438C2214yes—
186#2438C2214yes—
187#2438C2214yes—
188#2438C2214yes—
189#2429C2214yes—
190#2423C2214yes—
191#2402C2212yes—
192#2402C2212yes—
193#2402C2214yes—
194#2402C2214yes—
195#2399C2212yes—
196#2399C2214yes—
197#2399C2214yes—
198#2399C2212yes—
199#2396C2214yes—
200#2396C2214yes—
201#2396C2212yes—
202#2396C2212yes—
203#2370C2212yes—
204#2370C2212yes—
205#2369C2212yes—
206#2369C2212yes—
207#2365C2212yes—
208#2365C2212yes—
209#2357C2212yes—
210#2357C2212yes—
211#2356C2212yes—
212#2356C2212yes—
213#2355C2211yescharacteristic
214#2355C2212yes—
215#2355C2212yes—
216#2355C2211yescharacteristic
217#2354C2211yescharacteristic
218#2354C2211yescharacteristic
219#2354C2212yes—
220#2354C2212yes—
221#2353C2214yes—
222#2353C2214yes—
223#2352C2212yes—
224#2352C2212yes—
225Q8×C4⋊C4C2211yescharacteristic
226Q8×C4⋊C4C2211yescharacteristic
227D4×C4⋊C4C2211yescharacteristic
228D4×C4⋊C4C2211yescharacteristic
229#2347C2214yes—
230#2347C2212yes—
231#2346C2212yes—
232#2343C2214yes—
233#2341C2212yes—
234#2339C2212yes—
235#2320C2212yes—
236#2319C2212yes—
237#2319C2214yes—
238#2318C2214yes—
239#2314C2212yes—
240#2314C2212yes—
241#2311C2211yescharacteristic
242#2311C2211yescharacteristic
243#2285C2211yescharacteristic
244#2285C2211yescharacteristic
245#2285C2211yescharacteristic
246#2285C2212yes—
247#2283C2212yes—
248#2283C2211yescharacteristic
249#2283C2212yes—
250#2283C2211yescharacteristic
251#2283C2212yes—
252#2283C2212yes—
253C2×#382C2211yescharacteristic
254C2×#382C2212yes—
255#2276C2212yes—
256#2275C2212yes—
257#2274C2211yescharacteristic
258#2274C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2314yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C4×#41Q8116yescomplemented
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2314yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C2×#117C2312yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C42C2312yes—
304C22×C42C2311yescharacteristic
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2312yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2312yes—
323#400C2314yes—
324#400C2312yes—
325#400C2312yes—
326#400C2314yes—
327#400C2312yes—
328#400C2312yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#399C2314yes—
338#399C2312yes—
339#399C2314yes—
340#399C2312yes—
341#399C2314yes—
342#399C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2312yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2312yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2312yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2312yes—
413#395C2314yes—
414#395C2314yes—
415#395C2312yes—
416#395C2314yes—
417#395C2312yes—
418#395C2312yes—
419#395C2312yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2312yes—
426#395C2314yes—
427#395C2312yes—
428#395C2314yes—
429#395C2314yes—
430#395C2312yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2312yes—
444#393C2312yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2314yes—
477#390C2314yes—
478#390C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
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#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
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#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#384C2312yes—
580#384C2312yes—
581#384C2314yes—
582#384C2311yescharacteristic
583#384C2311yescharacteristic
584#384C2311yescharacteristic
585#384C2311yescharacteristic
586#384C2312yes—
587#384C2312yes—
588#384C2311yescharacteristic
589#384C2311yescharacteristic
590#383C2314yes—
591#383C2312yes—
592#383C2312yes—
593#383C2314yes—
594#383C2314yes—
595#383C2314yes—
596#382C2312yes—
597#382C2312yes—
598#382C2312yes—
599#382C2312yes—
600#382C2312yes—
601#382C2314yes—
602#382C2314yes—
603#382C2312yes—
604#382C2312yes—
605#382C2314yes—
606#382C2314yes—
607#382C2314yes—
608#382C2311yescharacteristic
609#382C2312yes—
610#382C2311yescharacteristic
611#382C2311yescharacteristic
612#382C2312yes—
613#382C2312yes—
614#382C2311yescharacteristic
615#382C2311yescharacteristic
616#382C2311yescharacteristic
617#382C2312yes—
618#382C2312yes—
619#381C2312yes—
620#381C2312yes—
621#381C2314yes—
622#381C2314yes—
623#381C2314yes—
624#381C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2314yes—
635#380C2314yes—
636#380C2312yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2311yescharacteristic
641#380C2311yescharacteristic
642#380C2312yes—
643#380C2312yes—
644#380C2311yescharacteristic
645#380C2311yescharacteristic
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703#376C2314yes—
704#376C2312yes—
705#376C2312yes—
706#376C2314yes—
707#376C2314yes—
708#376C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#41—42no—
714C2×#41—42no—
715C2×#41C2×Q818yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C23×C4C2411yescharacteristic
726C23×C4C2414yes—
727C23×C4C2414yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2412yes—
732C23×C4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2412yes—
735C4⋊Q8—44no—
736C4⋊Q8—44no—
737C4⋊Q8—44no—
738C4⋊Q8—44no—
739C4⋊Q8—84no—
740C4⋊Q8—84no—
741C4⋊Q8—84no—
742#125—44no—
743#125—44no—
744#125—84no—
745C22⋊Q8—84no—
746C22⋊Q8—84no—
747C22⋊Q8—84no—
748C22⋊Q8—84no—
749C22⋊Q8—84no—
750C22⋊Q8—84no—
751C4×Q8—44no—
752C4×Q8—44no—
753C4×Q8—44no—
754C4×Q8—44no—
755C4×Q8—84no—
756C4×Q8—84no—
757C4×Q8C2×Q818yes—
758C4×Q8C2×Q818yes—
759C4×D4—44no—
760C4×D4—44no—
761C4×D4C2×Q818yes—
762C4×D4C2×Q818yes—
763C4×D4C2×Q8116yes—
764C4×D4C2×Q8116yes—
765#117—42no—
766#117—42no—
767#117—82no—
768#117—82no—
769#117—82no—
770#117—82no—
771#117C2×Q818yes—
772#117C2×Q8116yes—
773C2×C4⋊C4—42no—
774C2×C4⋊C4—42no—
775C2×C4⋊C4—82no—
776C2×C4⋊C4—82no—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
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⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C42C2×Q818yes—
883C2×C42C2×Q8116yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989C24C2511yescharacteristic
990C24C2512yes—
991#41—416no—
992C2×Q8—22no—
993C2×Q8—22no—
994C2×Q8—42no—
995C2×Q8—42no—
996C2×Q8—44no—
997C2×Q8—44no—
998C2×Q8—42no—
999C2×Q8—44no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—42no—
1003C2×Q8—42no—
1004C2×Q8—42no—
1005C2×Q8—44no—
1006C2×Q8—44no—
1007C2×Q8—44no—
1008C2×Q8—44no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8C22×Q814yes—
1013C2×D4—22no—
1014C2×D4—22no—
1015C2×D4—42no—
1016C2×D4—42no—
1017C2×D4C22×Q814yes—
1018C2×D4C22×Q818yes—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4C22×Q814yes—
1044C22×C4C22×Q818yes—
1045C22×C4C22×Q818yes—
1046C22×C4C22×Q818yes—
1047C22×C4C22×Q814yes—
1048C22×C4C22×Q814yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2511yescharacteristic
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—41no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—41no—
1108C4⋊C4—41no—
1109C4⋊C4—41no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4C22×Q818yes—
1157C4⋊C4C22×Q818yes—
1158C4⋊C4C22×Q814yes—
1159C4⋊C4C22×Q814yes—
1160C22⋊C4—42no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—42no—
1164C22⋊C4—44no—
1165C22⋊C4—42no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4C22×Q818yes—
1179C22⋊C4C22×Q818yes—
1180C22⋊C4C22×Q818yes—
1181C42—24no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42C22×Q814yes—
1200C42C22×Q818yes—
1201C42C22×Q814yes—
1202C42C22×Q818yes—
1203C42C22×Q818yes—
1204C42C22×Q814yes—
1205C42C22×Q814yes—
1206C23—21no—
1207C23—22no—
1208C23—22no—
1209C23—21no—
1210C23—22no—
1211C23—21no—
1212C23—21no—
1213C23—22no—
1214C23—22no—
1215C23—21no—
1216C23—21no—
1217C23—22no—
1218C23C23×Q812yes—
1219C23C23×Q814yes—
1220C23C2611yescharacteristic
1221Q8—28no—
1222Q8—84no—
1223Q8—88no—
1224Q8—84no—
1225Q8—88no—
1226Q8—164no—
1227Q8—164no—
1228D4—28no—
1229D4—48no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—28no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—48no—
1302C2×C4—48no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—164no—
1307C2×C4—162no—
1308C2×C4—164no—
1309C2×C4—162no—
1310C2×C4C23×Q812yes—
1311C2×C4C23×Q812yes—
1312C2×C4C23×Q812yes—
1313C2×C4C23×Q814yes—
1314C2×C4C23×Q812yes—
1315C2×C4C23×Q812yes—
1316C2×C4C23×Q814yes—
1317C2×C4C23×Q814yes—
1318C2×C4C23×Q812yes—
1319C2×C4#58512yes—
1320C2×C4#58512yes—
1321C22—22no—
1322C22—22no—
1323C22—24no—
1324C22—24no—
1325C22—22no—
1326C22—24no—
1327C22—42no—
1328C22—41no—
1329C22—41no—
1330C22—42no—
1331C22—41no—
1332C22—42no—
1333C22—42no—
1334C22—41no—
1335C22C24×Q811yescharacteristic
1336C22C2×#58511yescharacteristic
1337C22C2×#58511yescharacteristic
1338C22H(7,𝔽2)11yescharacteristic
1339C22H(7,𝔽2)11yescharacteristic
1340C222−1+611yescharacteristic
1341C222−1+611yescharacteristic
1342C4—22no—
1343C4—22no—
1344C4—24no—
1345C4—22no—
1346C4—22no—
1347C4—24no—
1348C4—22no—
1349C4—24no—
1350C4—42no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4—44no—
1355C4—42no—
1356C4—42no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—44no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4—44no—
1367C4—42no—
1368C4#345814yes—
1369C2—42no—
1370C2—44no—
1371C2C2×#345811yescharacteristic
1372C2#6285411yescharacteristic
1373C2#6285411yescharacteristic
1374C2#6305111yescharacteristic
1375C2#6305311yescharacteristic
1376C2#6305611yescharacteristic
1377C2#6306911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #42824C2semidirect
4. #42820C2semidirect
5. #42500C2semidirect
6. #42496C2semidirect
7. #42188C2semidirect
8. #42184C2semidirect
9. #42008C2semidirect
10. #42001C2semidirect
11. #40634C2semidirect
12. #40630C2semidirect
13. #37642C2semidirect
14. #37609C2semidirect
15. #37563C2semidirect
16. #37561C2semidirect
17. #37561C2semidirect
18. #37561C2semidirect
19. #36691C2semidirect
20. #36691C2semidirect
21. #35958C2semidirect
22. #35952C2semidirect
23. #35871C2semidirect
24. #35867C2semidirect
25. #35819C2semidirect
26. #35815C2semidirect
276. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#429542
#429302
#428242
#428202
#425002
#424962
#421882
#421842
#420082
#420012
#406342
#406302
#376422
#376092
#375632
#375612
#366912
#359582
#359522
#358712
#358672
#358192
#358152
#341932
#341912
#341892