Finite Group Databasebeta

← #8757567

Subgroups — #8757567

Order 512.

4326 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58942C212yesmaximal, complemented
2#58791C212yesmaximal, complemented
3#58587C214yesmaximal, complemented
4#58504C212yesmaximal, complemented
5#57108C214yesmaximal, complemented
6#55614C212yesmaximal, complemented
7#55190C212yesmaximal, complemented
8#54854C212yesmaximal, complemented
9#53980C212yesmaximal, complemented
10#53491C212yesmaximal, complemented
11#51497C214yesmaximal, complemented
12#49960C214yesmaximal, complemented
13#49612C214yesmaximal, complemented
14#47817C212yesmaximal, complemented
15#47726C212yesmaximal, complemented
16#47661C214yesmaximal, complemented
17#47546C212yesmaximal, complemented
18#47538C212yesmaximal, complemented
19#46228C212yesmaximal, complemented
20#46227C212yesmaximal, complemented
21#46227C212yesmaximal, complemented
22#46142C212yesmaximal, complemented
23#46140C212yesmaximal, complemented
24#45990C212yesmaximal, complemented
25#35334C211yesmaximal, characteristic, complemented
26#35200C211yesmaximal, characteristic, complemented
27#35190C211yesmaximal, characteristic
28C2×#563C2212yes—
29C2×#533C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2851C2212yes—
34#2851C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2850C2212yes—
38#2850C2212yes—
39#2845C2212yes—
40#2844C2212yes—
41#2843C2212yes—
42#2837C2214yes—
43#2832C2212yes—
44#2832C2214yes—
45#2830C2212yes—
46#2829C2214yes—
47#2829C2214yes—
48#2822C2212yes—
49#2821C2214yes—
50#2820C2212yes—
51#2820C2212yes—
52#2809C2212yes—
53#2806C2214yes—
54#2803C2214yes—
55#2802C2214yes—
56#2799C2212yes—
57#2794C2212yes—
58#2792C2212yes—
59#2790C2214yes—
60#2787C2214yes—
61#2786C2214yes—
62#2785C2212yes—
63#2784C2212yes—
64#2783C2214yes—
65#2782C2212yes—
66#2779C2214yes—
67#2777C2214yes—
68#2774C2214yes—
69#2773C2214yes—
70#2772C2214yes—
71#2770C2214yes—
72#2769C2214yes—
73#2768C2214yes—
74#2768C2214yes—
75#2766C2214yes—
76#2765C2214yes—
77#2763C2214yes—
78#2761C2214yes—
79#2755C2214yes—
80#2751C2214yes—
81#2751C2214yes—
82#2746C2214yes—
83#2744C2214yes—
84#2744C2214yes—
85#2741C2214yes—
86#2738C2214yes—
87#2738C2214yes—
88#2737C2214yes—
89#2737C2214yes—
90#2734C2214yes—
91#2731C2214yes—
92#2731C2214yes—
93#2729C2214yes—
94#2723C2214yes—
95#2716C2214yes—
96#2716C2214yes—
97#2710C2214yes—
98#2710C2214yes—
99#2709C2214yes—
100#2709C2214yes—
101#2706C2214yes—
102#2702C2214yes—
103#2702C2214yes—
104#2701C2214yes—
105#2696C2214yes—
106#2696C2214yes—
107#2695C2214yes—
108#2692C2214yes—
109#2692C2214yes—
110#2691C2214yes—
111#2691C2214yes—
112#2689C2214yes—
113#2687C2214yes—
114#2683C2212yes—
115#2681C2214yes—
116#2681C2214yes—
117#2677C2214yes—
118#2677C2214yes—
119#2677C2214yes—
120#2677C2214yes—
121#2674C2214yes—
122#2672C2214yes—
123#2672C2214yes—
124#2663C2214yes—
125#2653C2214yes—
126#2651C2214yes—
127#2638C2212yes—
128#2638C2212yes—
129#2635C2212yes—
130#2635C2212yes—
131#2630C2214yes—
132#2628C2211yescharacteristic
133#2628C2211yescharacteristic
134#2628C2211yescharacteristic
135#2628C2211yescharacteristic
136#2628C2214yes—
137#2623C2214yes—
138#2612C2214yes—
139#2612C2212yes—
140#2610C2214yes—
141#2606C2214yes—
142#2599C2212yes—
143#2599C2212yes—
144#2598C2212yes—
145#2598C2212yes—
146#2597C2214yes—
147#2593C2212yes—
148#2588C2214yes—
149#2587C2214yes—
150#2587C2214yes—
151#2585C2214yes—
152#2583C2214yes—
153#2581C2212yes—
154#2581C2212yes—
155#2580C2212yes—
156#2580C2212yes—
157#2579C2214yes—
158#2577C2214yes—
159#2572C2212yes—
160#2568C2211yescharacteristic
161#2567C2211yescharacteristic
162#2564C2212yes—
163#2564C2212yes—
164#2564C2212yes—
165#2564C2212yes—
166#2563C2211yescharacteristic
167#2554C2214yes—
168#2553C2214yes—
169#2551C2212yes—
170#2548C2211yescharacteristic
171#2547C2211yescharacteristic
172#2546C2211yescharacteristic
173#2542C2211yescharacteristic
174#2541C2211yescharacteristic
175#2531C2214yes—
176#2531C2214yes—
177#2529C2214yes—
178#2528C2214yes—
179#2527C2214yes—
180#2524C2214yes—
181#2522C2214yes—
182#2520C2214yes—
183#2518C2214yes—
184#2500C2212yes—
185#2499C2212yes—
186#2498C2214yes—
187#2485C2212yes—
188#2485C2212yes—
189#2479C2214yes—
190#2479C2214yes—
191#2479C2214yes—
192#2477C2214yes—
193#2477C2214yes—
194#2469C2214yes—
195#2469C2214yes—
196#2466C2214yes—
197#2466C2214yes—
198#2459C2214yes—
199#2458C2214yes—
200#2458C2214yes—
201#2451C2214yes—
202#2451C2214yes—
203#2449C2214yes—
204#2449C2214yes—
205#2445C2214yes—
206#2440C2214yes—
207#2438C2214yes—
208#2432C2214yes—
209#2432C2212yes—
210#2431C2212yes—
211#2429C2214yes—
212#2429C2214yes—
213#2425C2214yes—
214#2419C2214yes—
215#2413C2214yes—
216#2407C2212yes—
217#2407C2212yes—
218#2406C2214yes—
219#2382C2212yes—
220#2382C2212yes—
221#2379C2212yes—
222#2376C2214yes—
223#2352C2214yes—
224#2337C2214yes—
225#2331C2214yes—
226#2328C2212yes—
227#2327C2212yes—
228#2326C2212yes—
229#2326C2212yes—
230#2316C2212yes—
231#2311C2212yes—
232#2283C2211yescharacteristic
233#2283C2211yescharacteristic
234C2×#382C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237#563—48no—
238#533—44no—
239#533—44no—
240#532—44no—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2314yes—
250C2×#127C2312yes—
251C2×#127C2311yescharacteristic
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C4×#41—44no—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2314yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2314yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2314yes—
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308#401C2314yes—
309#400C2312yes—
310#400C2312yes—
311#400C2312yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#399C2312yes—
328#399C2312yes—
329#399C2312yes—
330#399C2312yes—
331#399C2314yes—
332#399C2314yes—
333#399C2312yes—
334#399C2314yes—
335#399C2314yes—
336#399C2312yes—
337#399C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2312yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2312yes—
377#397C2314yes—
378#397C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#395C2312yes—
391#395C2312yes—
392#395C2312yes—
393#395C2312yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2312yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2312yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#393C2312yes—
427#393C2312yes—
428#393C2312yes—
429#393C2312yes—
430#393C2312yes—
431#393C2312yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#392C2312yes—
441#392C2314yes—
442#392C2312yes—
443#392C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#390C2312yes—
459#390C2314yes—
460#390C2314yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
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#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
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#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#384C2312yes—
607#384C2312yes—
608#383C2314yes—
609#383C2314yes—
610#383C2312yes—
611#383C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2312yes—
619#382C2314yes—
620#382C2314yes—
621#382C2311yescharacteristic
622#382C2311yescharacteristic
623#382C2314yes—
624#381C2314yes—
625#381C2312yes—
626#381C2312yes—
627#381C2314yes—
628#381C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2312yes—
642#380C2314yes—
643#380C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2311yescharacteristic
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658#376C2312yes—
659#376C2312yes—
660#376C2314yes—
661C2×#95C2312yes—
662C2×#95C2312yes—
663C2×#41—24no—
664C2×#41—42no—
665C2×#41—42no—
666C2×#41—44no—
667C2×#41—82no—
668C2×#41—82no—
669C22×Q8C2412yes—
670C22×Q8C2412yes—
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2414yes—
675C22×Q8C2411yescharacteristic
676C22×D4C2411yescharacteristic
677C22×D4C2411yescharacteristic
678C22×D4C2411yescharacteristic
679C22×D4C2414yes—
680C22×D4C2412yes—
681C22×D4C2412yes—
682C22×D4C2412yes—
683C22×D4C2414yes—
684C22×D4C2414yes—
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2414yes—
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2411yescharacteristic
694C23×C4C2411yescharacteristic
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C4⋊Q8—28no—
699C4⋊Q8—42no—
700C4⋊Q8—42no—
701C4⋊Q8—42no—
702C4⋊Q8—42no—
703C4⋊Q8—42no—
704C4⋊Q8—48no—
705C4⋊Q8—84no—
706C4⋊Q8—84no—
707#127—42no—
708#127—44no—
709#126—48no—
710#126—48no—
711#126—84no—
712#125—28no—
713#125—28no—
714#124—28no—
715#124—28no—
716#124—44no—
717#124—84no—
718#123—48no—
719#123—48no—
720#123—84no—
721#123—84no—
722#123—84no—
723C22⋊Q8—48no—
724C22⋊Q8—48no—
725C22⋊Q8—44no—
726C22⋊Q8—44no—
727C22⋊Q8—44no—
728C22⋊Q8—44no—
729C22⋊Q8—82no—
730C22⋊Q8—84no—
731C22⋊Q8—84no—
732C22⋊Q8—84no—
733C22⋊Q8—82no—
734#121—44no—
735#121—44no—
736#121—82no—
737#121—82no—
738C4×Q8—42no—
739C4×Q8—42no—
740C4×Q8—44no—
741C4×Q8—44no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×D4—44no—
745C4×D4—44no—
746C4×D4—42no—
747C4×D4—42no—
748C4×D4—42no—
749C4×D4—42no—
750C4×D4—42no—
751C4×D4—42no—
752C4×D4—48no—
753#117—42no—
754#117—42no—
755#117—42no—
756#117—44no—
757#117—44no—
758#117—84no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4—84no—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2411yescharacteristic
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C42—24no—
860C2×C42—24no—
861C2×C42—24no—
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2411yescharacteristic
884#95C2412yes—
885#95C2412yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2412yes—
890#95C2414yes—
891#95C2414yes—
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#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
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—
942C24C2514yes—
943C24C2511yescharacteristic
944C24C2511yescharacteristic
945C24C2511yescharacteristic
946#41—416no—
947#41—816no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—41no—
951C2×Q8—41no—
952C2×Q8—42no—
953C2×Q8—42no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q82−1+414yes—
966C2×D4—22no—
967C2×D4—22no—
968C2×D4—28no—
969C2×D4—24no—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—22no—
973C2×D4—24no—
974C2×D4—41no—
975C2×D4—41no—
976C2×D4—41no—
977C2×D4—41no—
978C2×D4—42no—
979C2×D4—42no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—42no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—28no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—42no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—42no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—44no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2514yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
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—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—41no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
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—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C42—22no—
1147C42—22no—
1148C42—22no—
1149C42—22no—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—24no—
1156C42—24no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—42no—
1164C42—44no—
1165C42—44no—
1166C42—42no—
1167C42H(5,𝔽2)14yes—
1168C23—21no—
1169C23—21no—
1170C23—22no—
1171C23—22no—
1172C23—24no—
1173C23—21no—
1174C23—21no—
1175C23—24no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—24no—
1180C23—21no—
1181C23—22no—
1182C23—24no—
1183C23—22no—
1184C23—24no—
1185C23—22no—
1186C23—24no—
1187C23—24no—
1188C23—22no—
1189C23#58512yes—
1190C23C2611yescharacteristic
1191Q8—44no—
1192Q8—84no—
1193Q8—84no—
1194Q8—84no—
1195Q8—84no—
1196Q8—84no—
1197Q8—164no—
1198D4—44no—
1199D4—44no—
1200D4—44no—
1201D4—84no—
1202D4—84no—
1203D4—88no—
1204D4—84no—
1205D4—88no—
1206D4—164no—
1207C2×C4—28no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
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—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—44no—
1264C2×C4—44no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—82no—
1268C2×C4—82no—
1269C2×C4—82no—
1270C2×C4—82no—
1271C2×C4—88no—
1272C2×C4—88no—
1273C2×C4—88no—
1274C2×C4—164no—
1275C2×C4C2×H(5,𝔽2)12yes—
1276C2×C4C2×H(5,𝔽2)12yes—
1277C2×C4C2×H(5,𝔽2)12yes—
1278C2×C4C2×2−1+412yes—
1279C2×C4C2×2−1+412yes—
1280C2×C4C2×2−1+412yes—
1281C22—24no—
1282C22—22no—
1283C22—42no—
1284C22—41no—
1285C22—41no—
1286C22—44no—
1287C22—44no—
1288C22—42no—
1289C22—42no—
1290C22—44no—
1291C22—44no—
1292C22—42no—
1293C22—42no—
1294C22—41no—
1295C22—41no—
1296C22—44no—
1297C22—41no—
1298C22—44no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—44no—
1303C22C22×H(5,𝔽2)11yescharacteristic
1304C22C22×2−1+411yescharacteristic
1305C22C2×#58511yescharacteristic
1306C22H(7,𝔽2)12yes—
1307C222−1+612yes—
1308C4—22no—
1309C4—22no—
1310C4—22no—
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—44no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—41no—
1322C4—44no—
1323C4—41no—
1324C4—41no—
1325C4—44no—
1326C4—44no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—44no—
1331C2—42no—
1332C2—84no—
1333C2—81no—
1334C2—81no—
1335C2#6281911yescharacteristic
1336C2#6287411yescharacteristic
1337C2#6288611yescharacteristic
1338C2#6305012yes—
1339C2#6306112yes—
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. #58942C2semidirect
2. #58791C2semidirect
3. #58587C2semidirect
4. #58504C2semidirect
5. #57108C2semidirect
6. #55614C2semidirect
7. #55190C2semidirect
8. #54854C2semidirect
9. #53980C2semidirect
10. #53491C2semidirect
11. #51497C2semidirect
12. #49960C2semidirect
13. #49612C2semidirect
14. #47817C2semidirect
15. #47726C2semidirect
16. #47661C2semidirect
17. #47546C2semidirect
18. #47538C2semidirect
19. #46228C2semidirect
20. #46227C2semidirect
21. #46227C2semidirect
22. #46142C2semidirect
23. #46140C2semidirect
24. #45990C2semidirect
25. #35334C2semidirect
26. #35200C2semidirect

Maximal subgroups

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

subgroupindex
#589422
#587912
#585872
#585042
#571082
#556142
#551902
#548542
#539802
#534912
#514972
#499602
#496122
#478172
#477262
#476612
#475462
#475382
#462282
#462272
#461422
#461402
#459902
#353342
#352002
#351902