Finite Group Databasebeta

← #8107633

Subgroups — #8107633

Order 512.

3940 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53143C212yesmaximal, complemented
2#53100C212yesmaximal, complemented
3#52818C214yesmaximal, complemented
4#52577C214yesmaximal
5#45149C212yesmaximal
6#45025C212yesmaximal
7#44582C214yesmaximal
8#44419C214yesmaximal, complemented
9#42941C211yesmaximal, characteristic
10#42933C211yesmaximal, characteristic
11#42850C212yesmaximal, complemented
12#42818C211yesmaximal, characteristic
13#42695C211yesmaximal, characteristic
14#42600C212yesmaximal, complemented
15#42330C214yesmaximal, complemented
16#42320C214yesmaximal
17#41739C214yesmaximal, complemented
18#41155C214yesmaximal
19#36400C212yesmaximal
20#36313C212yesmaximal, complemented
21#36285C212yesmaximal, complemented
22#36279C212yesmaximal
23#35324C211yesmaximal, characteristic
24#35313C211yesmaximal, characteristic
25#35199C212yesmaximal, complemented
26#35115C212yesmaximal, complemented
27#34552C211yesmaximal, characteristic
28#2864C2211yescharacteristic
29#2863C2212yes—
30#2863C2212yes—
31#2863C2212yes—
32#2863C2212yes—
33#2862C2211yescharacteristic
34#2862C2212yes—
35#2859C2212yes—
36#2855C2212yes—
37#2843C2212yes—
38#2841C2212yes—
39#2839C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2839C2214yes—
43#2839C2214yes—
44#2834C2212yes—
45#2833C2214yes—
46#2833C2212yes—
47#2833C2214yes—
48#2833C2214yes—
49#2833C2214yes—
50#2822C2214yes—
51#2810C2214yes—
52#2809C2212yes—
53#2807C2212yes—
54#2806C2214yes—
55#2805C2214yes—
56#2802C2214yes—
57#2802C2214yes—
58#2799C2214yes—
59#2799C2212yes—
60#2794C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2789C2214yes—
65#2789C2212yes—
66#2788C2214yes—
67#2776C2214yes—
68#2776C2214yes—
69#2774C2214yes—
70#2771C2212yes—
71#2769C2212yes—
72#2766C2214yes—
73#2765C2214yes—
74#2764C2212yes—
75#2762C2214yes—
76#2762C2214yes—
77#2762C2214yes—
78#2758C2214yes—
79#2745C2214yes—
80#2739C2214yes—
81#2729C2214yes—
82#2713C2214yes—
83#2713C2214yes—
84#2713C2214yes—
85#2704C2214yes—
86#2677C2212yes—
87#2667C2214yes—
88#2666C2214yes—
89#2666C2214yes—
90#2666C2214yes—
91#2666C2214yes—
92#2655C2214yes—
93#2655C2214yes—
94#2655C2214yes—
95#2655C2214yes—
96#2652C2214yes—
97#2645C2212yes—
98#2645C2212yes—
99#2645C2212yes—
100#2634C2214yes—
101#2634C2214yes—
102#2628C2211yescharacteristic
103#2621C2211yescharacteristic
104#2612C2214yes—
105#2611C2214yes—
106#2607C2212yes—
107#2606C2214yes—
108#2606C2214yes—
109#2605C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2588C2214yes—
114#2586C2214yes—
115#2586C2214yes—
116#2586C2214yes—
117#2586C2212yes—
118#2584C2214yes—
119#2584C2212yes—
120#2582C2212yes—
121#2582C2212yes—
122#2582C2212yes—
123#2581C2212yes—
124#2575C2214yes—
125#2575C2214yes—
126#2575C2214yes—
127#2573C2214yes—
128#2570C2212yes—
129#2570C2214yes—
130#2568C2212yes—
131#2568C2212yes—
132#2565C2214yes—
133#2565C2212yes—
134#2551C2212yes—
135#2551C2212yes—
136#2546C2212yes—
137#2546C2212yes—
138#2533C2214yes—
139#2533C2214yes—
140#2528C2214yes—
141#2528C2214yes—
142#2528C2214yes—
143#2528C2214yes—
144#2527C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2524C2214yes—
148#2524C2214yes—
149#2523C2212yes—
150#2522C2214yes—
151#2520C2214yes—
152#2520C2214yes—
153#2520C2214yes—
154#2520C2214yes—
155#2515C2214yes—
156#2514C2214yes—
157#2514C2212yes—
158#2514C2214yes—
159#2514C2212yes—
160#2514C2212yes—
161#2511C2212yes—
162#2511C2212yes—
163#2511C2214yes—
164#2511C2212yes—
165#2509C2212yes—
166#2509C2212yes—
167#2508C2214yes—
168#2507C2212yes—
169#2507C2212yes—
170#2506C2212yes—
171#2506C2212yes—
172#2505C2214yes—
173#2499C2212yes—
174#2493C2214yes—
175#2493C2214yes—
176#2475C2214yes—
177#2462C2214yes—
178#2453C2212yes—
179#2453C2212yes—
180#2453C2212yes—
181#2451C2212yes—
182#2451C2214yes—
183#2451C2212yes—
184#2451C2212yes—
185#2446C2214yes—
186#2446C2212yes—
187#2446C2212yes—
188#2446C2212yes—
189#2446C2212yes—
190#2446C2212yes—
191#2446C2214yes—
192#2446C2212yes—
193#2441C2212yes—
194#2440C2212yes—
195#2438C2214yes—
196#2434C2212yes—
197#2423C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2402C2212yes—
201#2399C2212yes—
202#2399C2211yescharacteristic
203#2399C2212yes—
204#2399C2211yescharacteristic
205#2396C2212yes—
206#2396C2211yescharacteristic
207#2396C2212yes—
208#2396C2212yes—
209#2396C2212yes—
210#2396C2211yescharacteristic
211#2396C2212yes—
212#2371C2214yes—
213#2370C2214yes—
214#2370C2214yes—
215#2368C2214yes—
216#2365C2212yes—
217#2365C2212yes—
218#2365C2214yes—
219#2362C2212yes—
220#2360C2212yes—
221#2356C2214yes—
222#2356C2214yes—
223#2355C2212yes—
224Q8×C4⋊C4C2212yes—
225#2347C2212yes—
226#2343C2214yes—
227Q8×C22⋊C4C2212yes—
228#2336C2214yes—
229#2336C2214yes—
230#2331C2214yes—
231#2331C2211yescharacteristic
232#2327C2211yescharacteristic
233#2323C2212yes—
234#2320C2214yes—
235#2317C2211yescharacteristic
236#2316C2211yescharacteristic
237#2310C2211yescharacteristic
238#2310C2211yescharacteristic
239C4×C4⋊Q8C2212yes—
240C4×#125C2212yes—
241#2296C2211yescharacteristic
242#2295C2212yes—
243#2295C2212yes—
244#2295C2212yes—
245C2×#391C2211yescharacteristic
246C42×Q8C2212yes—
247C42×Q8C2211yescharacteristic
248C42×Q8C2211yescharacteristic
249C4×#117C2212yes—
250C4×#117C2211yescharacteristic
251C23×Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2314yes—
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2314yes—
259C2×#125C2314yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×#117C2311yescharacteristic
279C2×#117C2312yes—
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C42C2311yescharacteristic
286#401C2314yes—
287#401C2314yes—
288#401C2314yes—
289#401C2314yes—
290#401C2314yes—
291#401C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2311yescharacteristic
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2311yescharacteristic
337#400C2312yes—
338#400C2314yes—
339#399C2312yes—
340#399C2312yes—
341#399C2314yes—
342#399C2311yescharacteristic
343#399C2311yescharacteristic
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2312yes—
395#396C2314yes—
396#396C2312yes—
397#396C2312yes—
398#396C2312yes—
399#396C2312yes—
400#395C2312yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2311yescharacteristic
412#395C2312yes—
413#395C2314yes—
414#395C2312yes—
415#395C2312yes—
416#395C2311yescharacteristic
417#395C2312yes—
418#393C2312yes—
419#393C2311yescharacteristic
420#393C2311yescharacteristic
421#393C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
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#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
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#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#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#385C2312yes—
589#385C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#384C2312yes—
597#384C2314yes—
598#384C2312yes—
599#384C2312yes—
600#384C2312yes—
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#382C2312yes—
610#382C2311yescharacteristic
611#382C2314yes—
612#382C2314yes—
613#382C2314yes—
614#382C2311yescharacteristic
615#382C2314yes—
616#382C2312yes—
617#382C2314yes—
618#382C2314yes—
619#382C2314yes—
620#381C2314yes—
621#381C2312yes—
622#381C2312yes—
623#381C2314yes—
624#380C2314yes—
625#380C2312yes—
626#380C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2311yescharacteristic
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678#376C2314yes—
679#376C2311yescharacteristic
680#376C2314yes—
681#376C2312yes—
682#376C2314yes—
683#376C2312yes—
684#376C2311yescharacteristic
685C2×#95C2314yes—
686C43C2312yes—
687C43C2312yes—
688C43C2311yescharacteristic
689C43C2311yescharacteristic
690C22×Q8—24no—
691C22×Q8—42no—
692C22×Q8—42no—
693C22×Q8C2412yes—
694C22×Q8C2412yes—
695C22×Q8C2411yescharacteristic
696C22×Q8C2411yescharacteristic
697C22×Q8C2412yes—
698C22×Q8C2414yes—
699C22×Q8C2412yes—
700C22×Q8C2412yes—
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2412yes—
705C4⋊Q8—42no—
706C4⋊Q8—44no—
707C4⋊Q8—42no—
708C4⋊Q8—44no—
709C4⋊Q8—44no—
710C4⋊Q8—48no—
711C4⋊Q8—48no—
712#125—216no—
713#125—44no—
714#125—48no—
715#125—48no—
716C22⋊Q8—28no—
717C22⋊Q8—48no—
718C4×Q8—28no—
719C4×Q8—28no—
720C4×Q8—42no—
721C4×Q8—44no—
722C4×Q8—42no—
723C4×Q8—44no—
724C4×Q8—44no—
725C4×Q8—44no—
726C4×Q8—44no—
727C4×Q8—44no—
728C4×Q8—44no—
729C4×Q8—44no—
730C4×Q8—48no—
731#117—24no—
732#117—28no—
733#117—42no—
734#117—42no—
735#117—44no—
736#117—42no—
737C2×C4⋊C4—42no—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C42—24no—
823C2×C42C2411yescharacteristic
824C2×C42C2412yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2411yescharacteristic
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2411yescharacteristic
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2411yescharacteristic
899#95C2412yes—
900#95C2411yescharacteristic
901#95C2412yes—
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—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950C24C2511yescharacteristic
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—28no—
962C2×Q8—41no—
963C2×Q8—42no—
964C2×Q8—41no—
965C2×Q8—42no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—44no—
972C2×Q8—88no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—24no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—44no—
983C22×C42−1+414yes—
984C22×C4C2511yescharacteristic
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2511yescharacteristic
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2511yescharacteristic
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
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—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C22⋊C4—24no—
1084C22⋊C4—28no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—24no—
1088C22⋊C4—42no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—44no—
1094C42—22no—
1095C42—24no—
1096C42—22no—
1097C42—24no—
1098C42—24no—
1099C42—24no—
1100C42—24no—
1101C42—24no—
1102C42—24no—
1103C42—24no—
1104C42—22no—
1105C42—22no—
1106C42—22no—
1107C42—22no—
1108C42—24no—
1109C42—24no—
1110C42—24no—
1111C42—28no—
1112C42—24no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C42—44no—
1123C42—44no—
1124C42—44no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C422−1+418yes—
1129C23—22no—
1130C23—22no—
1131C23—21no—
1132C23—21no—
1133C23C2×2−1+412yes—
1134C23C2611yescharacteristic
1135Q8—44no—
1136Q8—44no—
1137Q8—48no—
1138Q8—48no—
1139Q8—48no—
1140Q8—88no—
1141Q8—84no—
1142Q8—162no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—28no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—48no—
1211C2×C4—84no—
1212C2×C4—162no—
1213C2×C4C2×2−1+414yes—
1214C2×C4C2×2−1+412yes—
1215C2×C4C2×2−1+414yes—
1216C2×C4C2×2−1+414yes—
1217C2×C4C2×2−1+412yes—
1218C2×C4#58514yes—
1219C2×C4#58512yes—
1220C2×C4#58512yes—
1221C22—22no—
1222C22—24no—
1223C22—42no—
1224C22—41no—
1225C22—41no—
1226C22C22×2−1+411yescharacteristic
1227C22C22×2−1+412yes—
1228C22C2×#58511yescharacteristic
1229C22C2×#58511yescharacteristic
1230C22C2×#58512yes—
1231C4—22no—
1232C4—24no—
1233C4—24no—
1234C4—24no—
1235C4—24no—
1236C4—44no—
1237C4—44no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—44no—
1242C4—44no—
1243C4—42no—
1244C4—42no—
1245C4—42no—
1246C4—44no—
1247C4—41no—
1248C4—44no—
1249C4—41no—
1250C4—42no—
1251C4—41no—
1252C4—44no—
1253C4—44no—
1254C4—42no—
1255C4—41no—
1256C4#356414yes—
1257C2—42no—
1258C2C2×#356411yescharacteristic
1259C2#6276112yes—
1260C2#6282911yescharacteristic
1261C2#6283711yescharacteristic
1262C2#6283712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53143C2semidirect
2. #53100C2semidirect
3. #52818C2semidirect
8. #44419C2semidirect
11. #42850C2semidirect
14. #42600C2semidirect
15. #42330C2semidirect
17. #41739C2semidirect
20. #36313C2semidirect
21. #36285C2semidirect
25. #35199C2semidirect
26. #35115C2semidirect

Maximal subgroups

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

subgroupindex
#531432
#531002
#528182
#525772
#451492
#450252
#445822
#444192
#429412
#429332
#428502
#428182
#426952
#426002
#423302
#423202
#417392
#411552
#364002
#363132
#362852
#362792
#353242
#353132
#351992
#351152
#345522