Finite Group Databasebeta

← #8095306

Subgroups — #8095306

Order 512.

3997 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53147C211yesmaximal, characteristic, complemented
2#53124C212yesmaximal, complemented
3#53121C211yesmaximal, characteristic, complemented
4#53030C211yesmaximal, characteristic, complemented
5#52987C211yesmaximal, characteristic, complemented
6#52982C212yesmaximal
7#52830C214yesmaximal, complemented
8#52818C214yesmaximal, complemented
9#52577C214yesmaximal, complemented
10#52574C214yesmaximal, complemented
11#46170C214yesmaximal, complemented
12#46165C214yesmaximal
13#46060C212yesmaximal, complemented
14#46001C212yesmaximal, complemented
15#45925C214yesmaximal, complemented
16#45794C214yesmaximal, complemented
17#45648C212yesmaximal, complemented
18#45501C212yesmaximal, complemented
19#35646C212yesmaximal, complemented
20#35609C212yesmaximal, complemented
21#35583C212yesmaximal, complemented
22#35323C211yesmaximal, characteristic, complemented
23#35283C211yesmaximal, characteristic, complemented
24#35239C212yesmaximal, complemented
25#35228C212yesmaximal, complemented
26#34879C211yesmaximal, characteristic
27#34772C212yesmaximal, complemented
28#2868C2211yescharacteristic
29#2863C2212yes—
30#2862C2211yescharacteristic
31#2857C2212yes—
32#2857C2214yes—
33#2857C2211yescharacteristic
34#2855C2214yes—
35#2853C2214yes—
36#2851C2211yescharacteristic
37#2851C2214yes—
38#2843C2214yes—
39#2841C2214yes—
40#2841C2214yes—
41#2841C2214yes—
42#2839C2214yes—
43#2839C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2838C2214yes—
49#2834C2214yes—
50#2833C2214yes—
51#2833C2214yes—
52#2833C2214yes—
53#2833C2214yes—
54#2831C2214yes—
55#2827C2214yes—
56#2822C2214yes—
57#2821C2214yes—
58#2809C2214yes—
59#2806C2214yes—
60#2802C2214yes—
61#2794C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2788C2214yes—
66#2787C2214yes—
67#2773C2214yes—
68#2765C2214yes—
69#2764C2214yes—
70#2762C2214yes—
71#2762C2214yes—
72#2758C2214yes—
73#2750C2214yes—
74#2745C2214yes—
75#2743C2214yes—
76#2739C2214yes—
77#2734C2214yes—
78#2734C2214yes—
79#2729C2214yes—
80#2728C2214yes—
81#2726C2214yes—
82#2720C2214yes—
83#2719C2214yes—
84#2716C2214yes—
85#2713C2214yes—
86#2704C2214yes—
87#2704C2214yes—
88#2704C2214yes—
89#2698C2214yes—
90#2698C2214yes—
91#2696C2214yes—
92#2695C2214yes—
93#2694C2214yes—
94#2692C2214yes—
95#2680C2214yes—
96#2677C2214yes—
97#2677C2214yes—
98#2666C2214yes—
99#2666C2214yes—
100#2655C2214yes—
101#2650C2214yes—
102#2647C2211yescharacteristic
103#2647C2211yescharacteristic
104#2647C2211yescharacteristic
105#2642C2211yescharacteristic
106#2628C2212yes—
107#2625C2212yes—
108#2612C2214yes—
109#2606C2214yes—
110#2605C2214yes—
111#2594C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2588C2214yes—
115#2585C2214yes—
116#2581C2212yes—
117#2577C2214yes—
118#2577C2214yes—
119#2574C2214yes—
120#2574C2212yes—
121#2573C2212yes—
122#2572C2212yes—
123#2571C2212yes—
124#2570C2214yes—
125#2567C2212yes—
126#2565C2212yes—
127#2562C2212yes—
128#2553C2212yes—
129#2552C2212yes—
130#2552C2212yes—
131#2552C2212yes—
132#2551C2212yes—
133#2550C2212yes—
134#2550C2214yes—
135#2550C2214yes—
136#2546C2212yes—
137#2538C2212yes—
138#2533C2214yes—
139#2531C2214yes—
140#2530C2214yes—
141#2528C2214yes—
142#2528C2214yes—
143#2527C2214yes—
144#2525C2214yes—
145#2524C2214yes—
146#2524C2212yes—
147#2522C2214yes—
148#2522C2214yes—
149#2520C2214yes—
150#2520C2214yes—
151#2520C2214yes—
152#2519C2214yes—
153#2515C2214yes—
154#2515C2212yes—
155#2514C2214yes—
156#2514C2212yes—
157#2511C2214yes—
158#2511C2212yes—
159#2511C2212yes—
160#2509C2212yes—
161#2508C2212yes—
162#2507C2212yes—
163#2507C2212yes—
164#2506C2212yes—
165#2505C2214yes—
166#2503C2212yes—
167#2502C2212yes—
168#2497C2212yes—
169#2496C2212yes—
170#2494C2212yes—
171#2494C2212yes—
172#2494C2212yes—
173#2493C2214yes—
174#2492C2212yes—
175#2492C2214yes—
176#2492C2212yes—
177#2492C2212yes—
178#2488C2214yes—
179#2487C2212yes—
180#2486C2212yes—
181#2479C2214yes—
182#2475C2214yes—
183#2468C2212yes—
184#2462C2214yes—
185#2457C2212yes—
186#2453C2212yes—
187#2451C2212yes—
188#2451C2214yes—
189#2451C2214yes—
190#2451C2212yes—
191#2450C2214yes—
192#2446C2212yes—
193#2442C2212yes—
194#2442C2212yes—
195#2440C2212yes—
196#2440C2212yes—
197#2440C2212yes—
198#2440C2212yes—
199#2438C2214yes—
200#2438C2214yes—
201#2429C2212yes—
202#2423C2212yes—
203#2423C2212yes—
204#2423C2214yes—
205#2421C2212yes—
206#2417C2212yes—
207#2417C2212yes—
208#2402C2211yescharacteristic
209#2402C2214yes—
210#2398C2211yescharacteristic
211#2396C2211yescharacteristic
212#2396C2214yes—
213#2392C2211yescharacteristic
214#2383C2214yes—
215#2378C2214yes—
216#2378C2214yes—
217#2376C2214yes—
218#2331C2212yes—
219#2331C2212yes—
220#2330C2212yes—
221#2330C2211yescharacteristic
222#2327C2211yescharacteristic
223#2323C2212yes—
224#2320C2212yes—
225#2314C2211yescharacteristic
226#2314C2211yescharacteristic
227C4×C4⋊Q8C2212yes—
228C4×#126C2212yes—
229C4×C22⋊Q8C2212yes—
230C4×C22⋊Q8C2212yes—
231C4×C22⋊Q8C2214yes—
232C4×#123C2212yes—
233#2295C2211yescharacteristic
234#2295C2212yes—
235#2290C2212yes—
236#2290C2214yes—
237#2285C2212yes—
238#2283C2212yes—
239#2276C2212yes—
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×C4×C4⋊C4C2212yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2314yes—
250C2×#126C2312yes—
251C2×#126C2314yes—
252C2×#125C2312yes—
253C2×#125C2311yescharacteristic
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#123C2312yes—
258C2×#123C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C42C2312yes—
281C22×C42C2311yescharacteristic
282C22×C42C2314yes—
283#401C2314yes—
284#401C2314yes—
285#401C2314yes—
286#401C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2312yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2311yescharacteristic
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
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#400C2312yes—
322#400C2314yes—
323#400C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2311yescharacteristic
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
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#398C2311yescharacteristic
357#398C2312yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#397C2311yescharacteristic
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2312yes—
385#396C2314yes—
386#396C2314yes—
387#396C2312yes—
388#396C2314yes—
389#396C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2311yescharacteristic
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#394C2314yes—
405#394C2312yes—
406#394C2311yescharacteristic
407#394C2312yes—
408#393C2311yescharacteristic
409#393C2314yes—
410#393C2312yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#392C2311yescharacteristic
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2314yes—
439#390C2314yes—
440#389C2312yes—
441#389C2314yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2312yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2312yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#387C2312yes—
503#387C2312yes—
504#387C2312yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2312yes—
514#387C2312yes—
515#387C2314yes—
516#387C2312yes—
517#387C2314yes—
518#387C2314yes—
519#387C2312yes—
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#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#386C2314yes—
561#386C2312yes—
562#386C2312yes—
563#386C2312yes—
564#386C2314yes—
565#386C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2312yes—
569#385C2314yes—
570#385C2312yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2312yes—
580#385C2314yes—
581#384C2312yes—
582#384C2312yes—
583#384C2312yes—
584#384C2311yescharacteristic
585#384C2311yescharacteristic
586#384C2314yes—
587#384C2311yescharacteristic
588#384C2314yes—
589#384C2312yes—
590#383C2312yes—
591#383C2314yes—
592#383C2312yes—
593#383C2312yes—
594#383C2314yes—
595#383C2314yes—
596#382C2311yescharacteristic
597#382C2314yes—
598#382C2311yescharacteristic
599#382C2312yes—
600#382C2314yes—
601#382C2312yes—
602#382C2312yes—
603#382C2314yes—
604#382C2312yes—
605#382C2311yescharacteristic
606#382C2314yes—
607#381C2312yes—
608#381C2312yes—
609#381C2312yes—
610#381C2314yes—
611#381C2314yes—
612#381C2314yes—
613#380C2312yes—
614#380C2312yes—
615#380C2312yes—
616#380C2312yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2312yes—
628#380C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666#376C2312yes—
667#376C2311yescharacteristic
668#376C2314yes—
669#376C2314yes—
670#376C2311yescharacteristic
671C2×#95C2314yes—
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C22×Q8C2412yes—
675C22×Q8C2414yes—
676C22×Q8C2411yescharacteristic
677C22×Q8C2414yes—
678C22×Q8C2414yes—
679C22×D4C2411yescharacteristic
680C22×D4C2412yes—
681C23×C4C2412yes—
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2414yes—
686C23×C4C2412yes—
687C23×C4C2414yes—
688C4⋊Q8—44no—
689C4⋊Q8—44no—
690C4⋊Q8—44no—
691C4⋊Q8—42no—
692C4⋊Q8—84no—
693C4⋊Q8—84no—
694C4⋊Q8—84no—
695#126—28no—
696#126—84no—
697#125—42no—
698#125—44no—
699#125—84no—
700#125—84no—
701#125—84no—
702#123—28no—
703#123—84no—
704C22⋊Q8—216no—
705C22⋊Q8—44no—
706C22⋊Q8—44no—
707C22⋊Q8—44no—
708C22⋊Q8—84no—
709C22⋊Q8—84no—
710C22⋊Q8—84no—
711C22⋊Q8—84no—
712C4×Q8—28no—
713C4×Q8—42no—
714C4×Q8—44no—
715C4×Q8—44no—
716C4×Q8—84no—
717C4×D4—28no—
718C4×D4—42no—
719C4×D4—44no—
720#117—24no—
721#117—42no—
722#117—84no—
723C2×C4⋊C4—44no—
724C2×C4⋊C4—44no—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C42—28no—
818C2×C42—42no—
819C2×C42—84no—
820C2×C42C2411yescharacteristic
821C2×C42C2411yescharacteristic
822C2×C42C2411yescharacteristic
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2414yes—
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2412yes—
845C2×C42C2411yescharacteristic
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2412yes—
855#95C2412yes—
856#95C2414yes—
857#95C2412yes—
858#95C2412yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2412yes—
866#95C2412yes—
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2412yes—
870#95C2412yes—
871#95C2414yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2414yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2411yescharacteristic
900#95C2411yescharacteristic
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
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—
929C24C2511yescharacteristic
930C24C2512yes—
931C2×Q8—24no—
932C2×Q8—28no—
933C2×Q8—24no—
934C2×Q8—24no—
935C2×Q8—41no—
936C2×Q8—44no—
937C2×Q8—44no—
938C2×Q8—42no—
939C2×Q8—44no—
940C2×Q8—44no—
941C2×Q8—44no—
942C2×Q8—44no—
943C2×Q8—44no—
944C2×Q8—44no—
945C2×D4—24no—
946C2×D4—24no—
947C2×D4—41no—
948C2×D4—42no—
949C2×D4—42no—
950C22×C4—24no—
951C22×C4—28no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—22no—
956C22×C4—24no—
957C22×C4—22no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—22no—
961C22×C4—24no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—42no—
970C22×C4—44no—
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2512yes—
979C22×C4C2511yescharacteristic
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2511yescharacteristic
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2514yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2511yescharacteristic
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2511yescharacteristic
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—42no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C22⋊C4—28no—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—42no—
1087C22⋊C42−1+418yes—
1088C42—24no—
1089C42—24no—
1090C42—24no—
1091C42—22no—
1092C42—24no—
1093C42—28no—
1094C42—24no—
1095C42—22no—
1096C42—22no—
1097C42—22no—
1098C42—22no—
1099C42—24no—
1100C42—24no—
1101C42—42no—
1102C42—44no—
1103C42—44no—
1104C42—44no—
1105C42—44no—
1106C42—44no—
1107C42—44no—
1108C42—44no—
1109C42—42no—
1110C42—44no—
1111C42—44no—
1112C42—42no—
1113C422−1+414yes—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—21no—
1121C23—22no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23C2×2−1+414yes—
1126C23C2611yescharacteristic
1127Q8—48no—
1128Q8—88no—
1129Q8—82no—
1130Q8—164no—
1131Q8—164no—
1132D4—44no—
1133D4—84no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—21no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—21no—
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—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—48no—
1200C2×C4—48no—
1201C2×C4—48no—
1202C2×C4—44no—
1203C2×C4—84no—
1204C2×C4—88no—
1205C2×C4—88no—
1206C2×C4C2×2−1+414yes—
1207C2×C4C2×2−1+414yes—
1208C2×C4C2×2−1+414yes—
1209C2×C4C2×2−1+412yes—
1210C2×C4#58512yes—
1211C2×C4#58512yes—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—41no—
1220C22—41no—
1221C22—42no—
1222C22—41no—
1223C22—42no—
1224C22C22×2−1+412yes—
1225C22C22×2−1+411yescharacteristic
1226C22C2×#58511yescharacteristic
1227C22C2×#58511yescharacteristic
1228C22H(7,𝔽2)12yes—
1229C4—24no—
1230C4—24no—
1231C4—24no—
1232C4—41no—
1233C4—42no—
1234C4—41no—
1235C4—44no—
1236C4—44no—
1237C4—41no—
1238C4—42no—
1239C4—44no—
1240C4—41no—
1241C4—42no—
1242C4—44no—
1243C4—42no—
1244C4—42no—
1245C4—41no—
1246C4—44no—
1247C4—42no—
1248C4—42no—
1249C4—44no—
1250C4—44no—
1251C4—42no—
1252C4—44no—
1253C4#353114yes—
1254C2—44no—
1255C2—81no—
1256C2C2×#353111yescharacteristic
1257C2#6283711yescharacteristic
1258C2#6288311yescharacteristic
1259C2#6294512yes—
1260C2#6295112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53147C2semidirect
2. #53124C2semidirect
3. #53121C2semidirect
4. #53030C2semidirect
5. #52987C2semidirect
7. #52830C2semidirect
8. #52818C2semidirect
9. #52577C2semidirect
10. #52574C2semidirect
11. #46170C2semidirect
13. #46060C2semidirect
14. #46001C2semidirect
15. #45925C2semidirect
16. #45794C2semidirect
17. #45648C2semidirect
18. #45501C2semidirect
19. #35646C2semidirect
20. #35609C2semidirect
21. #35583C2semidirect
22. #35323C2semidirect
23. #35283C2semidirect
24. #35239C2semidirect
25. #35228C2semidirect
27. #34772C2semidirect

Maximal subgroups

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

subgroupindex
#531472
#531242
#531212
#530302
#529872
#529822
#528302
#528182
#525772
#525742
#461702
#461652
#460602
#460012
#459252
#457942
#456482
#455012
#356462
#356092
#355832
#353232
#352832
#352392
#352282
#348792
#347722