Finite Group Databasebeta

← #8508897

Subgroups — #8508897

Order 512.

3741 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic
2#58606C214yesmaximal
3#57931C214yesmaximal
4#57693C214yesmaximal
5#57559C214yesmaximal
6#57381C214yesmaximal
7#53368C212yesmaximal
8#53358C212yesmaximal
9#53121C212yesmaximal
10#52274C211yesmaximal, characteristic
11#48734C214yesmaximal
12#46191C212yesmaximal
13#46022C212yesmaximal
14#45426C212yesmaximal
15#45202C212yesmaximal
16#42765C212yesmaximal
17#42689C212yesmaximal
18#42527C212yesmaximal
19#40189C212yesmaximal
20#39749C211yesmaximal, characteristic
21#39681C212yesmaximal
22#39637C211yesmaximal, characteristic
23#39176C212yesmaximal
24#37413C212yesmaximal
25#37404C212yesmaximal
26#37163C212yesmaximal
27#36535C211yesmaximal, characteristic
28#35208C211yesmaximal, characteristic
29#35199C211yesmaximal, characteristic
30#2864C2212yes—
31#2864C2212yes—
32#2864C2212yes—
33#2863C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2862C2212yes—
37#2859C2211yescharacteristic
38#2859C2212yes—
39#2839C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2833C2214yes—
43#2833C2214yes—
44#2833C2214yes—
45#2822C2214yes—
46#2822C2214yes—
47#2810C2214yes—
48#2809C2211yescharacteristic
49#2809C2212yes—
50#2809C2212yes—
51#2806C2214yes—
52#2806C2214yes—
53#2806C2212yes—
54#2806C2211yescharacteristic
55#2806C2212yes—
56#2805C2212yes—
57#2805C2211yescharacteristic
58#2805C2212yes—
59#2805C2212yes—
60#2805C2212yes—
61#2802C2214yes—
62#2802C2214yes—
63#2802C2212yes—
64#2802C2214yes—
65#2799C2214yes—
66#2799C2214yes—
67#2799C2212yes—
68#2794C2214yes—
69#2794C2214yes—
70#2791C2214yes—
71#2791C2212yes—
72#2791C2214yes—
73#2791C2214yes—
74#2789C2214yes—
75#2776C2214yes—
76#2776C2214yes—
77#2776C2214yes—
78#2774C2214yes—
79#2774C2212yes—
80#2774C2214yes—
81#2769C2214yes—
82#2769C2214yes—
83#2767C2214yes—
84#2767C2214yes—
85#2767C2214yes—
86#2767C2214yes—
87#2766C2214yes—
88#2766C2214yes—
89#2766C2214yes—
90#2766C2214yes—
91#2766C2214yes—
92#2766C2214yes—
93#2766C2214yes—
94#2762C2214yes—
95#2762C2214yes—
96#2762C2214yes—
97#2762C2214yes—
98#2762C2214yes—
99#2762C2214yes—
100#2758C2214yes—
101#2758C2214yes—
102#2758C2214yes—
103#2758C2214yes—
104#2758C2214yes—
105#2755C2214yes—
106#2755C2214yes—
107#2755C2214yes—
108#2755C2214yes—
109#2755C2212yes—
110#2755C2214yes—
111#2726C2212yes—
112#2726C2211yescharacteristic
113#2726C2214yes—
114#2726C2214yes—
115#2726C2212yes—
116#2719C2214yes—
117#2719C2214yes—
118#2719C2214yes—
119#2719C2214yes—
120#2719C2214yes—
121#2719C2214yes—
122#2713C2214yes—
123#2713C2212yes—
124#2713C2214yes—
125#2666C2214yes—
126#2666C2214yes—
127#2666C2214yes—
128#2666C2214yes—
129#2660C2212yes—
130#2655C2214yes—
131#2655C2214yes—
132#2655C2214yes—
133#2655C2214yes—
134#2647C2212yes—
135#2647C2212yes—
136#2647C2212yes—
137#2645C2212yes—
138#2634C2214yes—
139#2590C2214yes—
140#2590C2214yes—
141#2588C2214yes—
142#2588C2214yes—
143#2588C2214yes—
144#2588C2214yes—
145#2585C2214yes—
146#2585C2214yes—
147#2584C2212yes—
148#2582C2211yescharacteristic
149#2582C2211yescharacteristic
150#2581C2214yes—
151#2581C2212yes—
152#2581C2214yes—
153#2571C2212yes—
154#2571C2212yes—
155#2571C2211yescharacteristic
156#2570C2212yes—
157#2570C2212yes—
158#2570C2212yes—
159#2570C2212yes—
160#2568C2211yescharacteristic
161#2568C2212yes—
162#2567C2211yescharacteristic
163#2567C2212yes—
164#2567C2211yescharacteristic
165#2565C2214yes—
166#2565C2212yes—
167#2552C2212yes—
168#2552C2212yes—
169#2552C2212yes—
170#2552C2211yescharacteristic
171#2552C2211yescharacteristic
172#2551C2211yescharacteristic
173#2550C2212yes—
174#2550C2212yes—
175#2550C2212yes—
176#2550C2214yes—
177#2546C2211yescharacteristic
178#2524C2214yes—
179#2520C2214yes—
180#2520C2214yes—
181#2520C2214yes—
182#2514C2212yes—
183#2514C2212yes—
184#2514C2212yes—
185#2514C2214yes—
186#2514C2212yes—
187#2511C2212yes—
188#2511C2212yes—
189#2511C2212yes—
190#2511C2214yes—
191#2511C2214yes—
192#2509C2212yes—
193#2509C2212yes—
194#2509C2212yes—
195#2509C2214yes—
196#2509C2212yes—
197#2509C2212yes—
198#2508C2212yes—
199#2508C2212yes—
200#2508C2212yes—
201#2508C2214yes—
202#2508C2212yes—
203#2508C2212yes—
204#2507C2212yes—
205#2507C2212yes—
206#2507C2212yes—
207#2507C2212yes—
208#2506C2212yes—
209#2506C2214yes—
210#2506C2212yes—
211#2506C2212yes—
212#2462C2214yes—
213#2462C2214yes—
214#2462C2214yes—
215#2462C2214yes—
216#2462C2214yes—
217#2462C2214yes—
218#2453C2212yes—
219#2453C2214yes—
220#2453C2214yes—
221#2451C2212yes—
222#2451C2212yes—
223#2446C2214yes—
224#2446C2212yes—
225#2402C2212yes—
226#2402C2212yes—
227#2399C2212yes—
228#2382C2214yes—
229#2370C2212yes—
230#2370C2212yes—
231#2370C2212yes—
232#2370C2212yes—
233#2365C2212yes—
234#2355C2212yes—
235#2355C2212yes—
236#2355C2211yescharacteristic
237#2355C2212yes—
238#2355C2211yescharacteristic
239Q8×C4⋊C4C2212yes—
240#2336C2214yes—
241#2331C2212yes—
242#2331C2212yes—
243#2331C2212yes—
244#2330C2212yes—
245#2330C2212yes—
246#2320C2212yes—
247#2320C2212yes—
248C4×C4⋊Q8C2212yes—
249C4×C4⋊Q8C2211yescharacteristic
250C4×C4⋊Q8C2211yescharacteristic
251C4×C4⋊Q8C2211yescharacteristic
252C4×#125C2212yes—
253C4×#125C2212yes—
254#2295C2212yes—
255#2295C2212yes—
256#2295C2211yescharacteristic
257#2295C2211yescharacteristic
258C42×Q8C2211yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2314yes—
285#401C2314yes—
286#401C2314yes—
287#401C2314yes—
288#401C2314yes—
289#401C2314yes—
290#400C2312yes—
291#400C2312yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
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#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2312yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2314yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2311yescharacteristic
443#391C2314yes—
444#391C2311yescharacteristic
445#391C2314yes—
446#391C2311yescharacteristic
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2311yescharacteristic
453#389C2311yescharacteristic
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2311yescharacteristic
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2311yescharacteristic
512#389C2314yes—
513#389C2314yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2311yescharacteristic
529#389C2314yes—
530#389C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
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#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2312yes—
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#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2312yes—
618#387C2314yes—
619#387C2314yes—
620#387C2312yes—
621#387C2312yes—
622#387C2314yes—
623#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#384C2311yescharacteristic
627#384C2312yes—
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2312yes—
632#384C2312yes—
633#384C2314yes—
634#384C2311yescharacteristic
635#384C2311yescharacteristic
636#384C2312yes—
637#384C2312yes—
638#383C2314yes—
639#383C2314yes—
640#383C2314yes—
641#383C2314yes—
642#383C2314yes—
643#383C2314yes—
644#383C2314yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652#382C2312yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#382C2314yes—
660#382C2314yes—
661#382C2314yes—
662#382C2314yes—
663#382C2312yes—
664#382C2314yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2312yes—
709C43C2312yes—
710C43C2312yes—
711C43C2311yescharacteristic
712C22×Q8C2411yescharacteristic
713C22×Q8C2412yes—
714C22×Q8C2414yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C4⋊Q8—28no—
720C4⋊Q8—24no—
721C4⋊Q8—24no—
722C4⋊Q8—42no—
723C4⋊Q8—82no—
724C4⋊Q8—82no—
725#125—28no—
726#125—28no—
727#125—48no—
728#125—44no—
729#125—48no—
730#125—44no—
731#125—84no—
732#125—84no—
733#125—84no—
734#125—84no—
735C4×Q8—24no—
736C4×Q8—24no—
737C4×Q8—28no—
738C4×Q8—24no—
739C4×Q8—24no—
740C4×Q8—24no—
741C4×Q8—44no—
742C4×Q8—82no—
743C4×Q8—84no—
744C4×Q8—84no—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C42C2411yescharacteristic
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2411yescharacteristic
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2411yescharacteristic
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860C2×C42C2411yescharacteristic
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2412yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
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#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967C2×Q8—22no—
968C2×Q8—22no—
969C2×Q8—22no—
970C2×Q8—24no—
971C2×Q8—22no—
972C2×Q8—22no—
973C2×Q8—24no—
974C2×Q8—28no—
975C2×Q8—24no—
976C2×Q8—42no—
977C2×Q8—42no—
978C2×Q8—44no—
979C2×Q8—42no—
980C2×Q8—42no—
981C2×Q8—41no—
982C2×Q8—41no—
983C2×Q8—44no—
984C2×Q8—41no—
985C2×Q8—42no—
986C2×Q8—41no—
987C2×Q8—42no—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2512yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2511yescharacteristic
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—24no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—24no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—41no—
1049C4⋊C4—42no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—41no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—41no—
1108C4⋊C42−1+414yes—
1109C42—22no—
1110C42—24no—
1111C42—24no—
1112C42—24no—
1113C42—24no—
1114C42—24no—
1115C42—24no—
1116C42—24no—
1117C42—24no—
1118C42—24no—
1119C42—22no—
1120C42—24no—
1121C42—42no—
1122C42—41no—
1123C42—44no—
1124C42—41no—
1125C42—44no—
1126C42—44no—
1127C42—42no—
1128C42—42no—
1129C42—44no—
1130C42—41no—
1131C42—44no—
1132C42—44no—
1133C42—42no—
1134C42—44no—
1135C42—44no—
1136C42—44no—
1137C42—42no—
1138C42—44no—
1139C42—42no—
1140C422−1+414yes—
1141C422−1+414yes—
1142C23C2611yescharacteristic
1143Q8—48no—
1144Q8—44no—
1145Q8—88no—
1146Q8—82no—
1147Q8—84no—
1148Q8—82no—
1149Q8—84no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4C2×2−1+412yes—
1229C2×C4C2×2−1+412yes—
1230C2×C4C2×2−1+414yes—
1231C2×C4C2×2−1+412yes—
1232C2×C4C2×2−1+412yes—
1233C2×C4C2×2−1+412yes—
1234C2×C4C2×2−1+412yes—
1235C2×C4C2×2−1+412yes—
1236C2×C4#58512yes—
1237C22C22×2−1+411yescharacteristic
1238C22C22×2−1+411yescharacteristic
1239C22C22×2−1+411yescharacteristic
1240C22C2×#58511yescharacteristic
1241C22H(7,𝔽2)11yescharacteristic
1242C222−1+611yescharacteristic
1243C222−1+611yescharacteristic
1244C4—24no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—42no—
1251C4—42no—
1252C4—41no—
1253C4—44no—
1254C4—42no—
1255C4—42no—
1256C4—42no—
1257C4—42no—
1258C4—44no—
1259C4—44no—
1260C4—42no—
1261C4—42no—
1262C4—42no—
1263C4—44no—
1264C4—44no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—42no—
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4#355614yes—
1273C2C2×#355611yescharacteristic
1274C2#6287911yescharacteristic
1275C2#6288911yescharacteristic
1276C2#6292611yescharacteristic
1277C2#6294911yescharacteristic
1278C2#6295911yescharacteristic
1279C2#6305811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#598702
#586062
#579312
#576932
#575592
#573812
#533682
#533582
#531212
#522742
#487342
#461912
#460222
#454262
#452022
#427652
#426892
#425272
#401892
#397492
#396812
#396372
#391762
#374132
#374042
#371632
#365352
#352082
#351992