Finite Group Databasebeta

← #7901027

Subgroups — #7901027

Order 512.

4071 conjugacy classes of subgroups.

The subgroup lattice has 1325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic
2#59445C212yesmaximal
3#52287C211yesmaximal, characteristic
4#52040C214yesmaximal
5#51602C214yesmaximal
6#50706C214yesmaximal
7#47730C214yesmaximal
8#46313C212yesmaximal
9#45435C212yesmaximal
10#45426C212yesmaximal
11#44949C212yesmaximal
12#44639C214yesmaximal
13#42823C214yesmaximal
14#42820C212yesmaximal
15#42820C212yesmaximal
16#39749C211yesmaximal, characteristic
17#39682C212yesmaximal
18#39637C211yesmaximal, characteristic
19#39626C212yesmaximal
20#39621C212yesmaximal
21#39181C212yesmaximal
22#38454C212yesmaximal
23#37195C212yesmaximal
24#36285C211yesmaximal, characteristic
25#35958C212yesmaximal
26#35582C212yesmaximal
27#35199C211yesmaximal, characteristic
28#34490C212yesmaximal
29#34337C211yesmaximal, characteristic
30C2×#557C2211yescharacteristic
31#2863C2212yes—
32#2863C2212yes—
33#2862C2212yes—
34#2859C2212yes—
35#2859C2211yescharacteristic
36#2843C2214yes—
37#2843C2214yes—
38#2811C2212yes—
39#2811C2212yes—
40#2811C2211yescharacteristic
41#2809C2212yes—
42#2809C2212yes—
43#2806C2212yes—
44#2806C2211yescharacteristic
45#2806C2212yes—
46#2806C2211yescharacteristic
47#2806C2212yes—
48#2806C2214yes—
49#2806C2212yes—
50#2806C2214yes—
51#2805C2212yes—
52#2805C2212yes—
53#2802C2214yes—
54#2799C2214yes—
55#2799C2214yes—
56#2792C2212yes—
57#2792C2214yes—
58#2792C2212yes—
59#2792C2212yes—
60#2792C2214yes—
61#2792C2214yes—
62#2792C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2791C2214yes—
66#2791C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2755C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2755C2214yes—
75#2755C2214yes—
76#2734C2214yes—
77#2734C2214yes—
78#2734C2214yes—
79#2734C2211yescharacteristic
80#2734C2212yes—
81#2734C2214yes—
82#2726C2214yes—
83#2726C2212yes—
84#2726C2212yes—
85#2713C2214yes—
86#2713C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2666C2214yes—
93#2666C2214yes—
94#2666C2214yes—
95#2666C2214yes—
96#2660C2212yes—
97#2660C2214yes—
98#2660C2214yes—
99#2660C2214yes—
100#2647C2212yes—
101#2647C2212yes—
102#2612C2214yes—
103#2612C2214yes—
104#2606C2214yes—
105#2606C2214yes—
106#2605C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2605C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2586C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2585C2214yes—
121#2585C2214yes—
122#2584C2212yes—
123#2582C2211yescharacteristic
124#2582C2212yes—
125#2582C2211yescharacteristic
126#2582C2211yescharacteristic
127#2581C2214yes—
128#2581C2212yes—
129#2571C2212yes—
130#2570C2212yes—
131#2570C2212yes—
132#2570C2212yes—
133#2570C2212yes—
134#2568C2211yescharacteristic
135#2567C2212yes—
136#2567C2212yes—
137#2567C2214yes—
138#2567C2214yes—
139#2567C2212yes—
140#2567C2212yes—
141#2565C2214yes—
142#2565C2212yes—
143#2552C2214yes—
144#2552C2212yes—
145#2552C2214yes—
146#2551C2212yes—
147#2551C2212yes—
148#2551C2212yes—
149#2551C2212yes—
150#2551C2214yes—
151#2551C2212yes—
152#2551C2211yescharacteristic
153#2551C2214yes—
154#2550C2214yes—
155#2550C2214yes—
156#2550C2214yes—
157#2550C2214yes—
158#2546C2211yescharacteristic
159#2546C2214yes—
160#2546C2212yes—
161#2546C2212yes—
162#2520C2214yes—
163#2520C2214yes—
164#2520C2214yes—
165#2520C2214yes—
166#2520C2214yes—
167#2520C2214yes—
168#2511C2214yes—
169#2509C2214yes—
170#2509C2212yes—
171#2508C2212yes—
172#2508C2212yes—
173#2508C2214yes—
174#2508C2212yes—
175#2507C2212yes—
176#2507C2212yes—
177#2507C2212yes—
178#2506C2212yes—
179#2506C2212yes—
180#2506C2212yes—
181#2506C2214yes—
182#2462C2214yes—
183#2462C2214yes—
184#2462C2214yes—
185#2462C2214yes—
186#2453C2214yes—
187#2451C2214yes—
188#2451C2212yes—
189#2451C2212yes—
190#2451C2212yes—
191#2451C2214yes—
192#2451C2212yes—
193#2446C2214yes—
194#2446C2214yes—
195#2446C2212yes—
196#2446C2212yes—
197#2402C2214yes—
198#2399C2212yes—
199#2399C2212yes—
200#2399C2212yes—
201#2382C2214yes—
202#2381C2214yes—
203#2371C2214yes—
204#2370C2212yes—
205#2370C2214yes—
206#2370C2212yes—
207#2370C2212yes—
208#2370C2212yes—
209#2370C2212yes—
210#2369C2212yes—
211#2369C2212yes—
212#2369C2212yes—
213#2365C2212yes—
214#2365C2211yescharacteristic
215#2356C2214yes—
216#2356C2212yes—
217#2356C2212yes—
218#2355C2212yes—
219#2355C2214yes—
220#2355C2212yes—
221#2355C2211yescharacteristic
222#2355C2212yes—
223#2355C2212yes—
224Q8×C4⋊C4C2211yescharacteristic
225Q8×C4⋊C4C2211yescharacteristic
226Q8×C4⋊C4C2212yes—
227Q8×C4⋊C4C2212yes—
228Q8×C4⋊C4C2211yescharacteristic
229#2336C2214yes—
230#2336C2214yes—
231#2331C2212yes—
232#2331C2212yes—
233#2331C2214yes—
234#2331C2214yes—
235#2331C2212yes—
236#2330C2212yes—
237#2330C2212yes—
238#2330C2214yes—
239#2330C2212yes—
240#2320C2212yes—
241#2320C2212yes—
242#2320C2214yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2212yes—
248C4×C4⋊Q8C2212yes—
249C4×#125C2212yes—
250#2295C2212yes—
251#2295C2212yes—
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2295C2212yes—
255#2295C2211yescharacteristic
256#2295C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259#557Q8116yescomplemented
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
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×Q8C2314yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302#400C2314yes—
303#400C2314yes—
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#400C2314yes—
322#398C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2312yes—
388#395C2312yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2312yes—
397#395C2312yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2312yes—
402#395C2312yes—
403#395C2312yes—
404#395C2312yes—
405#395C2312yes—
406#395C2312yes—
407#395C2314yes—
408#391C2311yescharacteristic
409#391C2312yes—
410#391C2314yes—
411#391C2312yes—
412#391C2311yescharacteristic
413#391C2312yes—
414#391C2311yescharacteristic
415#391C2312yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2311yescharacteristic
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2311yescharacteristic
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2311yescharacteristic
531#389C2312yes—
532#389C2314yes—
533#389C2311yescharacteristic
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2314yes—
537#389C2312yes—
538#389C2311yescharacteristic
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#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
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#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2312yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2314yes—
612#387C2312yes—
613#387C2312yes—
614#387C2312yes—
615#387C2314yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#384C2312yes—
620#384C2311yescharacteristic
621#384C2312yes—
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2314yes—
626#384C2314yes—
627#384C2314yes—
628#384C2314yes—
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2312yes—
632#384C2311yescharacteristic
633#384C2314yes—
634#384C2312yes—
635#383C2314yes—
636#383C2314yes—
637#383C2314yes—
638#383C2314yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2314yes—
648#382C2314yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703#376C2312yes—
704#376C2312yes—
705#376C2314yes—
706#376C2312yes—
707#376C2314yes—
708#376C2314yes—
709#376C2314yes—
710C43C2312yes—
711C43C2311yescharacteristic
712C43C2312yes—
713C22×Q8C2411yescharacteristic
714C22×Q8C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2412yes—
717C22×Q8C2411yescharacteristic
718C22×Q8C2412yes—
719C22×Q8C2414yes—
720C22×Q8C2414yes—
721C22×Q8C2414yes—
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C4⋊Q8—28no—
726C4⋊Q8—24no—
727C4⋊Q8—24no—
728C4⋊Q8—44no—
729C4⋊Q8—44no—
730C4⋊Q8—44no—
731C4⋊Q8—84no—
732C4⋊Q8—84no—
733C4⋊Q8—84no—
734C4⋊Q8—84no—
735C4⋊Q8—84no—
736C4⋊Q8—84no—
737C4⋊Q8—82no—
738C4⋊Q8—82no—
739C4⋊Q8C2×Q818yes—
740C4⋊Q8C2×Q8116yes—
741#125—28no—
742#125—84no—
743#125—84no—
744#125—84no—
745#125—84no—
746#125—84no—
747#125C2×Q8116yes—
748#125C2×Q8132yes—
749C4×Q8—28no—
750C4×Q8—24no—
751C4×Q8—24no—
752C4×Q8—42no—
753C4×Q8—42no—
754C4×Q8—44no—
755C4×Q8—44no—
756C4×Q8—44no—
757C4×Q8—42no—
758C4×Q8—82no—
759C4×Q8—84no—
760C4×Q8—82no—
761C4×Q8—82no—
762C4×Q8—82no—
763C4×Q8C2×Q8116yes—
764C4×Q8C2×Q8116yes—
765C4×Q8C2×Q818yes—
766C4×Q8C2×Q818yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
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⋊C4C2411yescharacteristic
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2412yes—
872C2×C42C2411yescharacteristic
873C2×C42C2412yes—
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2411yescharacteristic
899#95C2412yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2414yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984C2×Q8—22no—
985C2×Q8—22no—
986C2×Q8—24no—
987C2×Q8—22no—
988C2×Q8—24no—
989C2×Q8—22no—
990C2×Q8—41no—
991C2×Q8—41no—
992C2×Q8—42no—
993C2×Q8—42no—
994C2×Q8—41no—
995C2×Q8—41no—
996C2×Q8—41no—
997C2×Q8—42no—
998C2×Q8—42no—
999C2×Q8—42no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—41no—
1003C2×Q8—42no—
1004C2×Q8—44no—
1005C2×Q8—42no—
1006C2×Q8—42no—
1007C2×Q8—41no—
1008C2×Q8—42no—
1009C2×Q8—41no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8C22×Q814yes—
1017C2×Q8C22×Q818yes—
1018C2×Q8C22×Q814yes—
1019C2×Q82−1+414yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2512yes—
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C4⋊C4—24no—
1050C4⋊C4—28no—
1051C4⋊C4—24no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—22no—
1069C4⋊C4—24no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—41no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—41no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4C22×Q814yes—
1136C4⋊C4C22×Q8116yes—
1137C4⋊C4C22×Q818yes—
1138C4⋊C4C22×Q818yes—
1139C4⋊C4C22×Q814yes—
1140C4⋊C4C22×Q8116yes—
1141C4⋊C4C22×Q818yes—
1142C4⋊C4C22×Q8116yes—
1143C4⋊C4C22×Q818yes—
1144C42—24no—
1145C42—28no—
1146C42—24no—
1147C42—24no—
1148C42—22no—
1149C42—24no—
1150C42—22no—
1151C42—24no—
1152C42—24no—
1153C42—24no—
1154C42—24no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—42no—
1159C42—41no—
1160C42—42no—
1161C42—44no—
1162C42—41no—
1163C42—41no—
1164C42—44no—
1165C42—42no—
1166C42—42no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—42no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—42no—
1176C42C22×Q8116yes—
1177C42C22×Q818yes—
1178C42C22×Q818yes—
1179C42C22×Q814yes—
1180C422−1+414yes—
1181C23C2611yescharacteristic
1182Q8—28no—
1183Q8—44no—
1184Q8—48no—
1185Q8—44no—
1186Q8—82no—
1187Q8—84no—
1188Q8—82no—
1189Q8—84no—
1190Q8—84no—
1191Q8—88no—
1192Q8—164no—
1193Q8—164no—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4C23×Q814yes—
1268C2×C4C23×Q814yes—
1269C2×C4C23×Q812yes—
1270C2×C4C23×Q814yes—
1271C2×C4C23×Q812yes—
1272C2×C4C23×Q814yes—
1273C2×C4C23×Q818yes—
1274C2×C4C23×Q812yes—
1275C2×C4C2×2−1+412yes—
1276C2×C4C2×2−1+414yes—
1277C2×C4C2×2−1+412yes—
1278C2×C4C2×2−1+412yes—
1279C2×C4C2×2−1+412yes—
1280C2×C4#58512yes—
1281C22C24×Q811yescharacteristic
1282C22C22×2−1+411yescharacteristic
1283C22C22×2−1+411yescharacteristic
1284C22C2×#58511yescharacteristic
1285C22H(7,𝔽2)11yescharacteristic
1286C22H(7,𝔽2)11yescharacteristic
1287C222−1+611yescharacteristic
1288C4—24no—
1289C4—22no—
1290C4—24no—
1291C4—24no—
1292C4—24no—
1293C4—28no—
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—24no—
1298C4—22no—
1299C4—41no—
1300C4—42no—
1301C4—42no—
1302C4—44no—
1303C4—42no—
1304C4—42no—
1305C4—44no—
1306C4—42no—
1307C4—44no—
1308C4—42no—
1309C4—44no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—44no—
1316C4#350214yes—
1317C2C2×#350211yescharacteristic
1318C2#6285411yescharacteristic
1319C2#6287911yescharacteristic
1320C2#6290411yescharacteristic
1321C2#6294311yescharacteristic
1322C2Q8×2−1+411yescharacteristic
1323C2#6305111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
259. #557Q8semidirect

Maximal subgroups

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

subgroupindex
#599242
#594452
#522872
#520402
#516022
#507062
#477302
#463132
#454352
#454262
#449492
#446392
#428232
#428202
#397492
#396822
#396372
#396262
#396212
#391812
#384542
#371952
#362852
#359582
#355822
#351992
#344902
#343372