Finite Group Databasebeta

← #7898436

Subgroups — #7898436

Order 512.

3985 conjugacy classes of subgroups.

The subgroup lattice has 1289 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C211yesmaximal, characteristic
2#59447C212yesmaximal
3#52274C211yesmaximal, characteristic
4#50508C214yesmaximal
5#50381C214yesmaximal
6#49714C214yesmaximal
7#47490C214yesmaximal
8#45941C212yesmaximal
9#45431C212yesmaximal
10#45347C212yesmaximal
11#45154C212yesmaximal
12#44528C214yesmaximal
13#42703C212yesmaximal
14#42527C212yesmaximal
15#41920C214yesmaximal
16#39750C212yesmaximal
17#39749C211yesmaximal, characteristic
18#39619C212yesmaximal
19#39612C211yesmaximal, characteristic
20#39575C212yesmaximal
21#38986C212yesmaximal
22#38790C212yesmaximal
23#37255C212yesmaximal
24#36535C211yesmaximal, characteristic
25#35958C212yesmaximal
26#35656C212yesmaximal
27#35187C211yesmaximal, characteristic
28#34490C212yesmaximal
29#34335C211yesmaximal, characteristic
30C2×Q82C2211yescharacteristic
31C2×#557C2212yes—
32#2864C2212yes—
33#2864C2212yes—
34#2863C2212yes—
35#2862C2212yes—
36#2859C2211yescharacteristic
37#2839C2214yes—
38#2833C2214yes—
39#2810C2212yes—
40#2810C2212yes—
41#2809C2211yescharacteristic
42#2809C2212yes—
43#2806C2211yescharacteristic
44#2806C2212yes—
45#2805C2211yescharacteristic
46#2805C2212yes—
47#2802C2212yes—
48#2799C2214yes—
49#2799C2214yes—
50#2799C2212yes—
51#2794C2214yes—
52#2791C2212yes—
53#2791C2214yes—
54#2789C2214yes—
55#2789C2214yes—
56#2776C2214yes—
57#2774C2212yes—
58#2769C2214yes—
59#2769C2214yes—
60#2767C2214yes—
61#2766C2214yes—
62#2766C2214yes—
63#2766C2214yes—
64#2766C2214yes—
65#2762C2214yes—
66#2762C2214yes—
67#2762C2214yes—
68#2762C2214yes—
69#2762C2214yes—
70#2762C2214yes—
71#2758C2214yes—
72#2758C2214yes—
73#2758C2214yes—
74#2758C2214yes—
75#2758C2214yes—
76#2755C2214yes—
77#2755C2212yes—
78#2755C2214yes—
79#2755C2214yes—
80#2734C2212yes—
81#2734C2212yes—
82#2726C2211yescharacteristic
83#2726C2212yes—
84#2726C2212yes—
85#2726C2212yes—
86#2719C2214yes—
87#2719C2214yes—
88#2713C2212yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2713C2214yes—
93#2666C2214yes—
94#2666C2214yes—
95#2660C2212yes—
96#2660C2212yes—
97#2660C2212yes—
98#2655C2214yes—
99#2655C2214yes—
100#2655C2214yes—
101#2645C2214yes—
102#2634C2214yes—
103#2612C2214yes—
104#2606C2214yes—
105#2605C2214yes—
106#2605C2214yes—
107#2605C2214yes—
108#2590C2214yes—
109#2590C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2588C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2586C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2582C2211yescharacteristic
120#2581C2212yes—
121#2571C2212yes—
122#2571C2211yescharacteristic
123#2571C2211yescharacteristic
124#2571C2212yes—
125#2570C2212yes—
126#2570C2212yes—
127#2570C2212yes—
128#2570C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2570C2212yes—
132#2568C2212yes—
133#2568C2212yes—
134#2568C2212yes—
135#2568C2212yes—
136#2568C2211yescharacteristic
137#2568C2212yes—
138#2567C2212yes—
139#2567C2212yes—
140#2565C2212yes—
141#2565C2212yes—
142#2565C2212yes—
143#2565C2212yes—
144#2552C2211yescharacteristic
145#2552C2212yes—
146#2550C2212yes—
147#2546C2211yescharacteristic
148#2533C2214yes—
149#2533C2214yes—
150#2533C2214yes—
151#2533C2214yes—
152#2528C2214yes—
153#2528C2214yes—
154#2528C2214yes—
155#2528C2214yes—
156#2528C2214yes—
157#2528C2214yes—
158#2528C2214yes—
159#2524C2214yes—
160#2524C2214yes—
161#2524C2214yes—
162#2524C2214yes—
163#2524C2214yes—
164#2524C2214yes—
165#2520C2214yes—
166#2520C2214yes—
167#2520C2214yes—
168#2520C2214yes—
169#2520C2214yes—
170#2520C2214yes—
171#2520C2214yes—
172#2514C2212yes—
173#2514C2212yes—
174#2514C2212yes—
175#2514C2212yes—
176#2514C2212yes—
177#2514C2212yes—
178#2514C2214yes—
179#2514C2214yes—
180#2514C2212yes—
181#2514C2214yes—
182#2511C2212yes—
183#2511C2212yes—
184#2511C2212yes—
185#2508C2212yes—
186#2462C2214yes—
187#2462C2214yes—
188#2462C2214yes—
189#2462C2214yes—
190#2453C2214yes—
191#2451C2214yes—
192#2451C2214yes—
193#2446C2212yes—
194#2446C2212yes—
195#2446C2212yes—
196#2446C2214yes—
197#2446C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2402C2214yes—
201#2399C2212yes—
202#2382C2214yes—
203#2381C2214yes—
204#2371C2214yes—
205#2371C2214yes—
206#2370C2212yes—
207#2370C2212yes—
208#2369C2212yes—
209#2369C2211yescharacteristic
210#2369C2212yes—
211#2365C2212yes—
212#2365C2214yes—
213#2356C2212yes—
214#2356C2212yes—
215#2356C2212yes—
216#2356C2214yes—
217#2355C2212yes—
218#2355C2211yescharacteristic
219#2355C2211yescharacteristic
220#2355C2212yes—
221#2355C2211yescharacteristic
222#2355C2212yes—
223#2355C2212yes—
224#2355C2212yes—
225#2355C2212yes—
226#2355C2212yes—
227#2351C2212yes—
228Q8×C4⋊C4C2211yescharacteristic
229#2336C2214yes—
230#2336C2214yes—
231#2331C2212yes—
232#2331C2214yes—
233#2331C2212yes—
234#2331C2214yes—
235#2330C2212yes—
236#2327C2212yes—
237#2327C2212yes—
238#2327C2212yes—
239#2320C2212yes—
240#2320C2214yes—
241#2320C2214yes—
242#2320C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2211yescharacteristic
248C4×#125C2212yes—
249C4×#125C2212yes—
250C4×#125C2212yes—
251#2295C2211yescharacteristic
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2295C2212yes—
255#2295C2212yes—
256#2295C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259Q82—28no—
260#557—216no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2311yescharacteristic
292#401C2314yes—
293#401C2314yes—
294#401C2314yes—
295#401C2314yes—
296#401C2314yes—
297#401C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
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#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#398C2314yes—
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#398C2312yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2312yes—
393#395C2312yes—
394#395C2312yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2314yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2314yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2312yes—
443#391C2312yes—
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#389C2311yescharacteristic
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2311yescharacteristic
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2311yescharacteristic
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2311yescharacteristic
495#389C2311yescharacteristic
496#389C2312yes—
497#389C2312yes—
498#389C2311yescharacteristic
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2312yes—
503#387C2314yes—
504#387C2312yes—
505#387C2312yes—
506#387C2312yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2312yes—
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#387C2312yes—
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#387C2312yes—
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#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2312yes—
605#387C2312yes—
606#384C2311yescharacteristic
607#384C2312yes—
608#384C2311yescharacteristic
609#384C2311yescharacteristic
610#384C2312yes—
611#384C2311yescharacteristic
612#384C2312yes—
613#384C2312yes—
614#384C2312yes—
615#384C2311yescharacteristic
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#383C2314yes—
622#383C2314yes—
623#383C2314yes—
624#383C2314yes—
625#383C2314yes—
626#383C2314yes—
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2314yes—
636#382C2312yes—
637#382C2314yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2312yes—
644#382C2314yes—
645#382C2314yes—
646#382C2314yes—
647#382C2314yes—
648#382C2312yes—
649#382C2314yes—
650C4×C4⋊C4C2311yescharacteristic
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⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703#376C2312yes—
704#376C2312yes—
705#376C2314yes—
706#376C2314yes—
707#376C2312yes—
708#376C2314yes—
709#376C2314yes—
710#376C2314yes—
711C43C2312yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C22×Q8C2412yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C22×Q8C2414yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C4⋊Q8—216no—
723C4⋊Q8—28no—
724C4⋊Q8—216no—
725C4⋊Q8—28no—
726C4⋊Q8—28no—
727C4⋊Q8—24no—
728C4⋊Q8—28no—
729C4⋊Q8—24no—
730C4⋊Q8—42no—
731#125—216no—
732#125—216no—
733#125—28no—
734#125—28no—
735#125—44no—
736#125—48no—
737#125—44no—
738C4×Q8—28no—
739C4×Q8—28no—
740C4×Q8—24no—
741C4×Q8—216no—
742C4×Q8—28no—
743C4×Q8—28no—
744C4×Q8—28no—
745C4×Q8—24no—
746C4×Q8—28no—
747C4×Q8—24no—
748C4×Q8—28no—
749C4×Q8—24no—
750C4×Q8—48no—
751C4×Q8—44no—
752C4×Q8#4118yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C42C2412yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2411yescharacteristic
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2411yescharacteristic
873C2×C42C2412yes—
874C2×C42C2411yescharacteristic
875#95C2412yes—
876#95C2414yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2414yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974C2×Q8—22no—
975C2×Q8—24no—
976C2×Q8—28no—
977C2×Q8—24no—
978C2×Q8—28no—
979C2×Q8—22no—
980C2×Q8—24no—
981C2×Q8—24no—
982C2×Q8—22no—
983C2×Q8—24no—
984C2×Q8—41no—
985C2×Q8—41no—
986C2×Q8—42no—
987C2×Q8—44no—
988C2×Q8—42no—
989C2×Q8—41no—
990C2×Q8—41no—
991C2×Q8—42no—
992C2×Q8—44no—
993C2×Q8—42no—
994C2×Q8—44no—
995C2×Q8—44no—
996C2×Q8C2×#4114yes—
997C2×Q82−1+414yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C4⋊C4—28no—
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—28no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—22no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—22no—
1048C4⋊C4—24no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—28no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4C2×#4118yes—
1111C4⋊C4C2×#4114yes—
1112C42—28no—
1113C42—28no—
1114C42—28no—
1115C42—24no—
1116C42—28no—
1117C42—24no—
1118C42—22no—
1119C42—24no—
1120C42—28no—
1121C42—24no—
1122C42—24no—
1123C42—24no—
1124C42—24no—
1125C42—24no—
1126C42—24no—
1127C42—22no—
1128C42—41no—
1129C42—41no—
1130C42—42no—
1131C42—42no—
1132C42—41no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—44no—
1140C42—44no—
1141C42—44no—
1142C42—44no—
1143C42—44no—
1144C42—42no—
1145C42—44no—
1146C42C2×#4114yes—
1147C42C2×#4118yes—
1148C422−1+414yes—
1149C23C2611yescharacteristic
1150Q8—28no—
1151Q8—44no—
1152Q8—48no—
1153Q8—84no—
1154Q8—88no—
1155Q8—88no—
1156Q8—82no—
1157Q8—84no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4C22×#4112yes—
1235C2×C4C22×#4114yes—
1236C2×C4C22×#4112yes—
1237C2×C4C22×#4114yes—
1238C2×C4C22×#4112yes—
1239C2×C4C2×2−1+414yes—
1240C2×C4C2×2−1+412yes—
1241C2×C4C2×2−1+412yes—
1242C2×C4C2×2−1+412yes—
1243C2×C4C2×2−1+412yes—
1244C2×C4#58512yes—
1245C22C23×#4111yescharacteristic
1246C22C22×2−1+411yescharacteristic
1247C22C22×2−1+411yescharacteristic
1248C22C2×#58511yescharacteristic
1249C222−1+611yescharacteristic
1250C222−1+611yescharacteristic
1251C222−1+611yescharacteristic
1252C4—22no—
1253C4—24no—
1254C4—24no—
1255C4—22no—
1256C4—24no—
1257C4—22no—
1258C4—22no—
1259C4—22no—
1260C4—44no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—42no—
1265C4—42no—
1266C4—41no—
1267C4—42no—
1268C4—44no—
1269C4—44no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—44no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4#352314yes—
1281C2C2×#352311yescharacteristic
1282C2#6286011yescharacteristic
1283C2#6288911yescharacteristic
1284C2#6294911yescharacteristic
1285C2#6295911yescharacteristic
1286C2#6299511yescharacteristic
1287C2#6305711yescharacteristic
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
#598752
#594472
#522742
#505082
#503812
#497142
#474902
#459412
#454312
#453472
#451542
#445282
#427032
#425272
#419202
#397502
#397492
#396192
#396122
#395752
#389862
#387902
#372552
#365352
#359582
#356562
#351872
#344902
#343352