Finite Group Databasebeta

← #7660819

Subgroups — #7660819

Order 512.

4144 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52290C211yesmaximal, characteristic
2#52274C212yesmaximal, complemented
3#42825C212yesmaximal, complemented
4#42820C212yesmaximal, complemented
5#42817C212yesmaximal
6#42187C214yesmaximal
7#42183C214yesmaximal, complemented
8#42008C214yesmaximal
9#39978C212yesmaximal, complemented
10#39970C214yesmaximal
11#39752C211yesmaximal, characteristic
12#39624C211yesmaximal, characteristic
13#39621C212yesmaximal, complemented
14#39181C212yesmaximal, complemented
15#38456C214yesmaximal
16#38454C212yesmaximal, complemented
17#37314C212yesmaximal
18#37308C211yesmaximal, characteristic
19#37195C214yesmaximal, complemented
20#37195C212yesmaximal, complemented
21#36565C212yesmaximal, complemented
22#36480C211yesmaximal, characteristic
23#36288C211yesmaximal, characteristic
24#36286C212yesmaximal, complemented
25#35958C212yesmaximal, complemented
26#35867C212yesmaximal, complemented
27#35819C212yesmaximal
28#34262C212yesmaximal
29#34254C211yesmaximal, characteristic
30C2×#519C2211yescharacteristic
31#2863C2214yes—
32#2863C2212yes—
33#2862C2212yes—
34#2862C2214yes—
35#2862C2212yes—
36#2859C2212yes—
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2844C2214yes—
40#2843C2214yes—
41#2841C2214yes—
42#2811C2212yes—
43#2811C2214yes—
44#2809C2212yes—
45#2806C2214yes—
46#2806C2212yes—
47#2806C2211yescharacteristic
48#2806C2212yes—
49#2806C2214yes—
50#2806C2214yes—
51#2805C2214yes—
52#2805C2212yes—
53#2805C2211yescharacteristic
54#2805C2212yes—
55#2802C2214yes—
56#2799C2214yes—
57#2799C2214yes—
58#2799C2214yes—
59#2799C2214yes—
60#2791C2214yes—
61#2791C2212yes—
62#2788C2214yes—
63#2788C2212yes—
64#2774C2214yes—
65#2774C2214yes—
66#2774C2214yes—
67#2774C2214yes—
68#2774C2212yes—
69#2768C2212yes—
70#2763C2214yes—
71#2755C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2742C2214yes—
75#2734C2214yes—
76#2734C2212yes—
77#2734C2214yes—
78#2734C2211yescharacteristic
79#2734C2212yes—
80#2729C2212yes—
81#2729C2214yes—
82#2726C2211yescharacteristic
83#2720C2212yes—
84#2713C2214yes—
85#2713C2214yes—
86#2713C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2704C2214yes—
91#2677C2214yes—
92#2666C2214yes—
93#2666C2214yes—
94#2666C2214yes—
95#2666C2214yes—
96#2666C2214yes—
97#2666C2214yes—
98#2666C2214yes—
99#2665C2214yes—
100#2665C2214yes—
101#2660C2214yes—
102#2660C2212yes—
103#2659C2212yes—
104#2659C2212yes—
105#2647C2214yes—
106#2647C2212yes—
107#2628C2212yes—
108#2612C2214yes—
109#2612C2214yes—
110#2612C2214yes—
111#2612C2214yes—
112#2607C2214yes—
113#2605C2214yes—
114#2605C2214yes—
115#2605C2214yes—
116#2605C2214yes—
117#2605C2214yes—
118#2605C2214yes—
119#2605C2214yes—
120#2605C2214yes—
121#2590C2214yes—
122#2589C2214yes—
123#2588C2214yes—
124#2588C2214yes—
125#2588C2214yes—
126#2586C2214yes—
127#2586C2214yes—
128#2586C2214yes—
129#2586C2214yes—
130#2586C2214yes—
131#2585C2214yes—
132#2582C2212yes—
133#2581C2212yes—
134#2581C2212yes—
135#2581C2212yes—
136#2574C2214yes—
137#2571C2212yes—
138#2570C2214yes—
139#2570C2212yes—
140#2570C2212yes—
141#2570C2212yes—
142#2569C2214yes—
143#2568C2212yes—
144#2568C2212yes—
145#2567C2211yescharacteristic
146#2567C2212yes—
147#2565C2212yes—
148#2556C2214yes—
149#2551C2214yes—
150#2551C2212yes—
151#2551C2211yescharacteristic
152#2551C2212yes—
153#2551C2211yescharacteristic
154#2551C2212yes—
155#2550C2214yes—
156#2550C2212yes—
157#2550C2212yes—
158#2550C2214yes—
159#2550C2214yes—
160#2550C2214yes—
161#2549C2214yes—
162#2546C2211yescharacteristic
163#2546C2212yes—
164#2522C2214yes—
165#2520C2214yes—
166#2520C2214yes—
167#2511C2214yes—
168#2509C2212yes—
169#2509C2212yes—
170#2508C2212yes—
171#2506C2212yes—
172#2497C2212yes—
173#2492C2214yes—
174#2492C2212yes—
175#2492C2212yes—
176#2465C2214yes—
177#2453C2212yes—
178#2451C2212yes—
179#2451C2212yes—
180#2451C2214yes—
181#2451C2212yes—
182#2451C2214yes—
183#2451C2212yes—
184#2451C2212yes—
185#2451C2212yes—
186#2451C2212yes—
187#2446C2214yes—
188#2442C2212yes—
189#2440C2212yes—
190#2439C2212yes—
191#2439C2212yes—
192#2429C2212yes—
193#2402C2212yes—
194#2402C2214yes—
195#2402C2214yes—
196#2399C2214yes—
197#2399C2212yes—
198#2396C2212yes—
199#2370C2212yes—
200#2369C2212yes—
201#2369C2212yes—
202#2369C2211yescharacteristic
203#2369C2212yes—
204#2365C2211yescharacteristic
205#2365C2212yes—
206#2356C2212yes—
207#2356C2212yes—
208#2356C2214yes—
209#2356C2212yes—
210#2355C2212yes—
211#2355C2212yes—
212#2355C2211yescharacteristic
213#2355C2212yes—
214#2355C2212yes—
215#2355C2211yescharacteristic
216#2355C2214yes—
217#2351C2212yes—
218Q8×C4⋊C4C2212yes—
219#2347C2214yes—
220#2347C2212yes—
221#2346C2214yes—
222#2346C2212yes—
223#2343C2214yes—
224#2343C2214yes—
225Q8×C22⋊C4C2212yes—
226Q8×C22⋊C4C2212yes—
227#2331C2214yes—
228#2331C2214yes—
229#2329C2212yes—
230#2329C2212yes—
231#2320C2212yes—
232#2320C2212yes—
233#2320C2214yes—
234#2320C2212yes—
235#2317C2211yescharacteristic
236#2314C2214yes—
237#2314C2212yes—
238#2310C2211yescharacteristic
239C4×C4⋊Q8C2212yes—
240C4×C4⋊Q8C2212yes—
241C4×#125C2214yes—
242C4×#125C2212yes—
243C4×C22⋊Q8C2211yescharacteristic
244C4×C22⋊Q8C2211yescharacteristic
245#2298C2214yes—
246#2298C2212yes—
247#2296C2211yescharacteristic
248#2295C2212yes—
249#2295C2212yes—
250#2295C2214yes—
251#2295C2212yes—
252#2295C2214yes—
253#2295C2212yes—
254C2×#391C2211yescharacteristic
255#2276C2212yes—
256#2274C2211yescharacteristic
257C42×Q8C2212yes—
258C4×#117C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283#519Q8116yescomplemented
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2314yes—
301C2×#117C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C42C2311yescharacteristic
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2312yes—
322#400C2314yes—
323#400C2312yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#399C2314yes—
333#399C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2312yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2312yes—
375#396C2312yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2312yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2312yes—
396#395C2312yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2312yes—
405#395C2312yes—
406#395C2314yes—
407#395C2314yes—
408#393C2314yes—
409#393C2312yes—
410#393C2314yes—
411#393C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2314yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2311yescharacteristic
464#391C2314yes—
465#391C2312yes—
466#391C2314yes—
467#391C2311yescharacteristic
468#391C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2311yescharacteristic
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2311yescharacteristic
497#389C2311yescharacteristic
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2311yescharacteristic
524#389C2311yescharacteristic
525#389C2311yescharacteristic
526#388C2314yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2312yes—
534#388C2312yes—
535#388C2312yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
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#387C2312yes—
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#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2314yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#385C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2312yes—
607#385C2312yes—
608#384C2312yes—
609#384C2312yes—
610#384C2311yescharacteristic
611#384C2311yescharacteristic
612#384C2312yes—
613#384C2314yes—
614#384C2312yes—
615#384C2312yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#382C2314yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2314yes—
629#382C2314yes—
630#382C2312yes—
631#382C2314yes—
632#382C2314yes—
633#382C2314yes—
634#382C2314yes—
635#382C2314yes—
636#382C2314yes—
637#381C2314yes—
638#380C2312yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2311yescharacteristic
646#380C2311yescharacteristic
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700#376C2312yes—
701#376C2314yes—
702#376C2312yes—
703#376C2314yes—
704#376C2314yes—
705#376C2314yes—
706#376C2314yes—
707#376C2314yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C43C2312yes—
711C43C2314yes—
712C43C2312yes—
713C22×Q8—42no—
714C22×Q8—42no—
715C22×Q8C2×Q818yes—
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2414yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2412yes—
732C4⋊Q8—28no—
733C4⋊Q8—42no—
734C4⋊Q8—42no—
735C4⋊Q8—44no—
736C4⋊Q8—44no—
737C4⋊Q8—44no—
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—48no—
741C4⋊Q8—84no—
742C4⋊Q8—84no—
743C4⋊Q8—82no—
744C4⋊Q8—84no—
745C4⋊Q8—82no—
746#125—28no—
747#125—44no—
748#125—84no—
749#125—84no—
750C22⋊Q8—24no—
751C22⋊Q8—44no—
752C22⋊Q8—42no—
753C22⋊Q8—84no—
754C22⋊Q8—82no—
755C4×Q8—42no—
756C4×Q8—42no—
757C4×Q8—44no—
758C4×Q8—48no—
759C4×Q8—44no—
760C4×Q8—44no—
761C4×Q8—44no—
762C4×Q8—44no—
763C4×Q8—44no—
764C4×Q8C2×Q8116yes—
765C4×Q8C2×Q8116yes—
766C4×Q8C2×Q8116yes—
767C4×Q8C2×Q8116yes—
768#117—42no—
769#117—42no—
770#117C2×Q818yes—
771#117C2×Q818yes—
772#117C2×Q8132yes—
773C2×C4⋊C4—42no—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C42—42no—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2411yescharacteristic
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2412yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2412yes—
921#95C2414yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988C24C2511yescharacteristic
989C2×Q8—22no—
990C2×Q8—28no—
991C2×Q8—24no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—22no—
995C2×Q8—42no—
996C2×Q8—42no—
997C2×Q8—41no—
998C2×Q8—41no—
999C2×Q8—44no—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—44no—
1003C2×Q8—42no—
1004C2×Q8—42no—
1005C2×Q8—41no—
1006C2×Q8—42no—
1007C2×Q8—41no—
1008C2×Q8—42no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—42no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—42no—
1018C2×Q8—44no—
1019C2×Q8—44no—
1020C2×Q8—416no—
1021C2×Q8C22×Q818yes—
1022C2×Q8C22×Q818yes—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4C22×Q814yes—
1037C22×C4C22×Q818yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—42no—
1086C4⋊C4—41no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—41no—
1142C4⋊C4C22×Q8116yes—
1143C4⋊C4C22×Q814yes—
1144C4⋊C4C22×Q8116yes—
1145C4⋊C4C22×Q814yes—
1146C4⋊C4C22×Q814yes—
1147C4⋊C4C22×Q814yes—
1148C4⋊C42−1+414yes—
1149C22⋊C4—24no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—44no—
1157C22⋊C4C22×Q818yes—
1158C22⋊C4C22×Q818yes—
1159C42—24no—
1160C42—24no—
1161C42—22no—
1162C42—22no—
1163C42—24no—
1164C42—24no—
1165C42—24no—
1166C42—24no—
1167C42—24no—
1168C42—24no—
1169C42—41no—
1170C42—41no—
1171C42—42no—
1172C42—44no—
1173C42—44no—
1174C42—42no—
1175C42—42no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—44no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—42no—
1184C42—44no—
1185C42—42no—
1186C42—44no—
1187C42—42no—
1188C42—44no—
1189C42C22×Q818yes—
1190C42C22×Q8116yes—
1191C42C22×Q8116yes—
1192C42C22×Q818yes—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23C23×Q812yes—
1200C23C2611yescharacteristic
1201Q8—216no—
1202Q8—48no—
1203Q8—88no—
1204Q8—82no—
1205Q8—84no—
1206Q8—82no—
1207Q8—84no—
1208Q8—164no—
1209Q8—164no—
1210Q8—162no—
1211Q8—164no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—28no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—48no—
1286C2×C4—82no—
1287C2×C4—82no—
1288C2×C4—162no—
1289C2×C4C23×Q814yes—
1290C2×C4C23×Q814yes—
1291C2×C4C23×Q814yes—
1292C2×C4C23×Q814yes—
1293C2×C4C23×Q812yes—
1294C2×C4C23×Q818yes—
1295C2×C4C23×Q812yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4C2×2−1+414yes—
1298C2×C4#58512yes—
1299C2×C4#58512yes—
1300C2×C4#58512yes—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22C24×Q811yescharacteristic
1309C22C22×2−1+411yescharacteristic
1310C22C2×#58511yescharacteristic
1311C22C2×#58511yescharacteristic
1312C22C2×#58511yescharacteristic
1313C22H(7,𝔽2)11yescharacteristic
1314C222−1+611yescharacteristic
1315C4—24no—
1316C4—24no—
1317C4—24no—
1318C4—24no—
1319C4—24no—
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—28no—
1324C4—42no—
1325C4—44no—
1326C4—42no—
1327C4—44no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—44no—
1332C4—41no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4—42no—
1337C4—44no—
1338C4—42no—
1339C4—42no—
1340C4—41no—
1341C4—42no—
1342C4#345814yes—
1343C2—42no—
1344C2C2×#345811yescharacteristic
1345C2#6291011yescharacteristic
1346C2#6293211yescharacteristic
1347C2Q8×2−1+411yescharacteristic
1348C2#6300411yescharacteristic
1349C2#6302511yescharacteristic
1350C2#6306911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #52274C2semidirect
3. #42825C2semidirect
4. #42820C2semidirect
7. #42183C2semidirect
9. #39978C2semidirect
13. #39621C2semidirect
14. #39181C2semidirect
16. #38454C2semidirect
19. #37195C2semidirect
20. #37195C2semidirect
21. #36565C2semidirect
24. #36286C2semidirect
25. #35958C2semidirect
26. #35867C2semidirect
283. #519Q8semidirect

Maximal subgroups

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

subgroupindex
#522902
#522742
#428252
#428202
#428172
#421872
#421832
#420082
#399782
#399702
#397522
#396242
#396212
#391812
#384562
#384542
#373142
#373082
#371952
#365652
#364802
#362882
#362862
#359582
#358672
#358192
#342622
#342542