Finite Group Databasebeta

← #8757169

Subgroups — #8757169

Order 512.

4333 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58703C212yesmaximal, complemented
2#58371C212yesmaximal, complemented
3#58355C212yesmaximal, complemented
4#57984C214yesmaximal, complemented
5#55492C212yesmaximal, complemented
6#54458C214yesmaximal, complemented
7#54314C214yesmaximal, complemented
8#53929C214yesmaximal, complemented
9#52039C212yesmaximal, complemented
10#52002C212yesmaximal, complemented
11#50700C212yesmaximal, complemented
12#50219C212yesmaximal, complemented
13#49703C212yesmaximal, complemented
14#48184C212yesmaximal, complemented
15#47804C212yesmaximal, complemented
16#47783C212yesmaximal, complemented
17#47148C214yesmaximal, complemented
18#46658C214yesmaximal, complemented
19#46233C212yesmaximal, complemented
20#46228C212yesmaximal, complemented
21#46140C212yesmaximal, complemented
22#45987C212yesmaximal, complemented
23#45979C212yesmaximal, complemented
24#45979C212yesmaximal, complemented
25#35333C211yesmaximal, characteristic, complemented
26#35190C211yesmaximal, characteristic
27#35138C211yesmaximal, characteristic, complemented
28C2×#563C2212yes—
29C2×#532C2211yescharacteristic
30C22×#125C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2851C2212yes—
34#2851C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2850C2212yes—
38#2850C2212yes—
39#2845C2212yes—
40#2844C2212yes—
41#2839C2214yes—
42#2837C2214yes—
43#2834C2214yes—
44#2827C2214yes—
45#2827C2214yes—
46#2823C2212yes—
47#2822C2212yes—
48#2820C2214yes—
49#2820C2212yes—
50#2820C2212yes—
51#2800C2214yes—
52#2795C2214yes—
53#2795C2212yes—
54#2794C2212yes—
55#2792C2214yes—
56#2790C2214yes—
57#2790C2214yes—
58#2787C2214yes—
59#2782C2214yes—
60#2782C2212yes—
61#2781C2214yes—
62#2780C2214yes—
63#2780C2214yes—
64#2780C2214yes—
65#2778C2214yes—
66#2769C2212yes—
67#2769C2214yes—
68#2768C2214yes—
69#2767C2214yes—
70#2766C2214yes—
71#2765C2214yes—
72#2762C2214yes—
73#2762C2214yes—
74#2762C2214yes—
75#2757C2214yes—
76#2757C2214yes—
77#2753C2214yes—
78#2753C2214yes—
79#2749C2214yes—
80#2748C2212yes—
81#2748C2214yes—
82#2746C2214yes—
83#2744C2214yes—
84#2743C2214yes—
85#2741C2214yes—
86#2741C2214yes—
87#2740C2214yes—
88#2738C2214yes—
89#2734C2214yes—
90#2732C2214yes—
91#2730C2214yes—
92#2725C2214yes—
93#2725C2214yes—
94#2721C2214yes—
95#2721C2214yes—
96#2721C2214yes—
97#2720C2214yes—
98#2720C2214yes—
99#2720C2214yes—
100#2720C2214yes—
101#2720C2214yes—
102#2718C2214yes—
103#2715C2214yes—
104#2713C2214yes—
105#2713C2214yes—
106#2709C2212yes—
107#2709C2212yes—
108#2709C2214yes—
109#2707C2214yes—
110#2707C2214yes—
111#2705C2214yes—
112#2704C2214yes—
113#2698C2214yes—
114#2694C2214yes—
115#2691C2214yes—
116#2691C2214yes—
117#2691C2214yes—
118#2690C2214yes—
119#2690C2214yes—
120#2683C2212yes—
121#2672C2214yes—
122#2672C2214yes—
123#2667C2214yes—
124#2666C2214yes—
125#2651C2214yes—
126#2648C2214yes—
127#2636C2214yes—
128#2635C2212yes—
129#2635C2212yes—
130#2634C2212yes—
131#2633C2212yes—
132#2630C2214yes—
133#2629C2212yes—
134#2629C2212yes—
135#2611C2212yes—
136#2611C2214yes—
137#2611C2212yes—
138#2609C2212yes—
139#2609C2214yes—
140#2606C2214yes—
141#2601C2214yes—
142#2598C2214yes—
143#2598C2212yes—
144#2598C2212yes—
145#2594C2214yes—
146#2586C2214yes—
147#2585C2214yes—
148#2584C2212yes—
149#2579C2212yes—
150#2579C2212yes—
151#2579C2212yes—
152#2579C2212yes—
153#2579C2214yes—
154#2577C2214yes—
155#2576C2214yes—
156#2576C2214yes—
157#2571C2212yes—
158#2568C2211yescharacteristic
159#2566C2212yes—
160#2566C2212yes—
161#2565C2212yes—
162#2565C2212yes—
163#2562C2212yes—
164#2556C2214yes—
165#2552C2214yes—
166#2548C2211yescharacteristic
167#2542C2211yescharacteristic
168#2541C2211yescharacteristic
169#2529C2214yes—
170#2528C2214yes—
171#2524C2214yes—
172#2522C2214yes—
173#2522C2214yes—
174#2520C2214yes—
175#2519C2214yes—
176#2500C2212yes—
177#2487C2211yescharacteristic
178#2487C2211yescharacteristic
179#2486C2211yescharacteristic
180#2486C2211yescharacteristic
181#2484C2212yes—
182#2481C2214yes—
183#2481C2214yes—
184#2481C2214yes—
185#2481C2214yes—
186#2479C2214yes—
187#2479C2214yes—
188#2478C2214yes—
189#2476C2214yes—
190#2475C2214yes—
191#2474C2214yes—
192#2474C2214yes—
193#2473C2214yes—
194#2471C2214yes—
195#2466C2214yes—
196#2466C2214yes—
197#2461C2214yes—
198#2449C2214yes—
199#2449C2214yes—
200#2449C2214yes—
201#2449C2214yes—
202#2449C2214yes—
203#2443C2214yes—
204#2443C2214yes—
205#2440C2214yes—
206#2440C2214yes—
207#2432C2214yes—
208#2431C2212yes—
209#2417C2214yes—
210#2417C2214yes—
211#2407C2212yes—
212#2407C2212yes—
213#2406C2212yes—
214#2406C2214yes—
215#2382C2212yes—
216#2382C2212yes—
217#2380C2212yes—
218#2379C2212yes—
219#2376C2212yes—
220#2374C2212yes—
221#2366C2212yes—
222#2334C2214yes—
223#2328C2212yes—
224#2326C2212yes—
225#2322C2212yes—
226#2322C2212yes—
227#2317C2211yescharacteristic
228#2317C2211yescharacteristic
229#2317C2214yes—
230#2311C2211yescharacteristic
231#2311C2211yescharacteristic
232#2285C2211yescharacteristic
233#2283C2211yescharacteristic
234#2283C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237#563—48no—
238#532—44no—
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2314yes—
241C2×#127C2312yes—
242C2×#127C2311yescharacteristic
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#125—44no—
248C2×#125—44no—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#123C2312yes—
263C2×#123C2312yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C4×#41—44no—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C2×#117C2314yes—
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2314yes—
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2314yes—
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309#401C2314yes—
310#401C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2312yes—
315#400C2312yes—
316#400C2312yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#399C2312yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2312yes—
339#399C2312yes—
340#399C2312yes—
341#399C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
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#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2312yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2312yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2312yes—
420#394C2314yes—
421#394C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#392C2312yes—
434#392C2312yes—
435#392C2314yes—
436#392C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
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#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#386C2312yes—
548#386C2312yes—
549#386C2312yes—
550#386C2312yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2312yes—
558#386C2312yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2312yes—
582#385C2314yes—
583#385C2312yes—
584#385C2312yes—
585#385C2312yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2312yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#384C2312yes—
606#384C2312yes—
607#384C2314yes—
608#384C2312yes—
609#384C2312yes—
610#384C2314yes—
611#383C2314yes—
612#383C2312yes—
613#383C2314yes—
614#383C2312yes—
615#382C2314yes—
616#382C2312yes—
617#382C2312yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2314yes—
623#382C2314yes—
624#382C2314yes—
625#381C2312yes—
626#381C2314yes—
627#381C2312yes—
628#381C2312yes—
629#381C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2312yes—
644#380C2314yes—
645#380C2311yescharacteristic
646#380C2311yescharacteristic
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661#376C2312yes—
662#376C2312yes—
663C2×#41—24no—
664C2×#41—42no—
665C2×#41—42no—
666C2×#41—44no—
667C2×#41—82no—
668C2×#41—82no—
669C22×Q8C2411yescharacteristic
670C22×Q8C2412yes—
671C22×Q8C2414yes—
672C22×D4C2411yescharacteristic
673C22×D4C2411yescharacteristic
674C22×D4C2412yes—
675C22×D4C2414yes—
676C22×D4C2414yes—
677C22×D4C2412yes—
678C22×D4C2412yes—
679C22×D4C2414yes—
680C22×D4C2411yescharacteristic
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2412yes—
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2414yes—
695C23×C4C2414yes—
696C23×C4C2414yes—
697C4⋊Q8—42no—
698C4⋊Q8—48no—
699#127—28no—
700#127—42no—
701#126—48no—
702#126—48no—
703#126—48no—
704#126—84no—
705#125—28no—
706#125—28no—
707#125—44no—
708#125—44no—
709#125—44no—
710#125—44no—
711#125—44no—
712#125—44no—
713#125—84no—
714#125—84no—
715#124—28no—
716#124—44no—
717#124—84no—
718#123—28no—
719#123—44no—
720#123—48no—
721#123—84no—
722C22⋊Q8—48no—
723C22⋊Q8—48no—
724C22⋊Q8—84no—
725C22⋊Q8—84no—
726C22⋊Q8—84no—
727C22⋊Q8—82no—
728C22⋊Q8—82no—
729#121—44no—
730#121—44no—
731#121—82no—
732#121—82no—
733C4×Q8—42no—
734C4×Q8—42no—
735C4×D4—44no—
736C4×D4—44no—
737C4×D4—42no—
738C4×D4—42no—
739C4×D4—42no—
740C4×D4—42no—
741C4×D4—42no—
742C4×D4—42no—
743C4×D4—84no—
744C4×D4—84no—
745#117—42no—
746#117—42no—
747#117—42no—
748#117—42no—
749#117—42no—
750#117—48no—
751#117—84no—
752C2×C4⋊C4—42no—
753C2×C4⋊C4—42no—
754C2×C4⋊C4—44no—
755C2×C4⋊C4—44no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4—44no—
758C2×C4⋊C4—42no—
759C2×C4⋊C4—42no—
760C2×C4⋊C4—84no—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2411yescharacteristic
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C42—24no—
866C2×C42—24no—
867C2×C42—24no—
868C2×C42C2412yes—
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2412yes—
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2411yescharacteristic
889#95C2412yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
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#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943C24C2514yes—
944C24C2511yescharacteristic
945C24C2511yescharacteristic
946C24C2511yescharacteristic
947#41—416no—
948#41—816no—
949C2×Q8—24no—
950C2×Q8—22no—
951C2×Q8—22no—
952C2×Q8—41no—
953C2×Q8—42no—
954C2×Q8—42no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×D4—22no—
959C2×D4—22no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—24no—
963C2×D4—24no—
964C2×D4—22no—
965C2×D4—41no—
966C2×D4—41no—
967C2×D4—41no—
968C2×D4—41no—
969C2×D4—41no—
970C2×D4—42no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—42no—
977C2×D4—44no—
978C2×D4—42no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D42−1+414yes—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—24no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—44no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4C2514yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2514yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2514yes—
1038C22×C4C2514yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C22⋊C4—24no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4—42no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—22no—
1156C42—22no—
1157C42—22no—
1158C42—22no—
1159C42—24no—
1160C42—24no—
1161C42—24no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—42no—
1168C42—44no—
1169C42—44no—
1170C42H(5,𝔽2)14yes—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—21no—
1181C23—21no—
1182C23—24no—
1183C23—24no—
1184C23—21no—
1185C23—24no—
1186C23—22no—
1187C23—24no—
1188C23—22no—
1189C23—24no—
1190C23—24no—
1191C23C2×2−1+412yes—
1192C23C2×2−1+412yes—
1193C23C2611yescharacteristic
1194Q8—44no—
1195Q8—84no—
1196Q8—164no—
1197D4—44no—
1198D4—44no—
1199D4—44no—
1200D4—84no—
1201D4—84no—
1202D4—88no—
1203D4—88no—
1204D4—84no—
1205D4—88no—
1206C2×C4—28no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—21no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—21no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—44no—
1264C2×C4—44no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—416no—
1268C2×C4—82no—
1269C2×C4—82no—
1270C2×C4—82no—
1271C2×C4—82no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—88no—
1277C2×C4—164no—
1278C2×C4C2×H(5,𝔽2)12yes—
1279C2×C4C2×H(5,𝔽2)12yes—
1280C2×C4C2×H(5,𝔽2)12yes—
1281C2×C4C2×2−1+412yes—
1282C2×C4#58512yes—
1283C22—24no—
1284C22—24no—
1285C22—22no—
1286C22—22no—
1287C22—42no—
1288C22—42no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—44no—
1294C22—44no—
1295C22—42no—
1296C22—44no—
1297C22—44no—
1298C22—42no—
1299C22—41no—
1300C22—44no—
1301C22—41no—
1302C22—44no—
1303C22—41no—
1304C22—44no—
1305C22C22×H(5,𝔽2)11yescharacteristic
1306C22C22×2−1+411yescharacteristic
1307C22C2×#58511yescharacteristic
1308C22H(7,𝔽2)12yes—
1309C222−1+612yes—
1310C4—22no—
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—44no—
1316C4—44no—
1317C4—44no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—41no—
1322C4—44no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—44no—
1327C4—44no—
1328C4—44no—
1329C4—41no—
1330C4—41no—
1331C4—44no—
1332C4—41no—
1333C2—42no—
1334C2—42no—
1335C2—84no—
1336C2—81no—
1337C2#6281911yescharacteristic
1338C2#6287411yescharacteristic
1339C2#6288611yescharacteristic
1340C2#6304712yes—
1341C2#6305812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35190C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58703C2semidirect
2. #58371C2semidirect
3. #58355C2semidirect
4. #57984C2semidirect
5. #55492C2semidirect
6. #54458C2semidirect
7. #54314C2semidirect
8. #53929C2semidirect
9. #52039C2semidirect
10. #52002C2semidirect
11. #50700C2semidirect
12. #50219C2semidirect
13. #49703C2semidirect
14. #48184C2semidirect
15. #47804C2semidirect
16. #47783C2semidirect
17. #47148C2semidirect
18. #46658C2semidirect
19. #46233C2semidirect
20. #46228C2semidirect
21. #46140C2semidirect
22. #45987C2semidirect
23. #45979C2semidirect
24. #45979C2semidirect
25. #35333C2semidirect
27. #35138C2semidirect

Maximal subgroups

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

subgroupindex
#587032
#583712
#583552
#579842
#554922
#544582
#543142
#539292
#520392
#520022
#507002
#502192
#497032
#481842
#478042
#477832
#471482
#466582
#462332
#462282
#461402
#459872
#459792
#353332
#351902
#351382