Finite Group Databasebeta

← #8824388

Subgroups — #8824388

Order 512.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59923C211yesmaximal, characteristic
2#57927C214yesmaximal, complemented
3#55232C214yesmaximal
4#53349C212yesmaximal, complemented
5#52038C214yesmaximal, complemented
6#51671C214yesmaximal
7#51668C212yesmaximal
8#50949C214yesmaximal
9#50232C214yesmaximal, complemented
10#50183C212yesmaximal
11#49344C214yesmaximal, complemented
12#47791C212yesmaximal
13#47034C212yesmaximal
14#46205C211yesmaximal, characteristic
15#45941C212yesmaximal, complemented
16#45414C214yesmaximal, complemented
17#44588C214yesmaximal
18#41920C214yesmaximal, complemented
19#38801C212yesmaximal
20#38454C212yesmaximal, complemented
21#37196C212yesmaximal, complemented
22#36384C212yesmaximal
23#35313C211yesmaximal, characteristic
24#2864C2212yes—
25#2863C2212yes—
26#2863C2212yes—
27#2859C2212yes—
28#2851C2212yes—
29#2843C2212yes—
30#2839C2214yes—
31#2839C2214yes—
32#2833C2212yes—
33#2817C2212yes—
34#2811C2211yescharacteristic
35#2810C2212yes—
36#2809C2212yes—
37#2809C2214yes—
38#2809C2212yes—
39#2809C2211yescharacteristic
40#2806C2212yes—
41#2806C2214yes—
42#2805C2212yes—
43#2805C2214yes—
44#2802C2214yes—
45#2802C2214yes—
46#2799C2214yes—
47#2799C2214yes—
48#2799C2214yes—
49#2794C2214yes—
50#2792C2214yes—
51#2792C2214yes—
52#2791C2214yes—
53#2791C2214yes—
54#2789C2212yes—
55#2776C2214yes—
56#2774C2214yes—
57#2774C2214yes—
58#2774C2214yes—
59#2774C2214yes—
60#2771C2214yes—
61#2770C2214yes—
62#2769C2214yes—
63#2769C2212yes—
64#2769C2214yes—
65#2767C2214yes—
66#2767C2214yes—
67#2766C2214yes—
68#2766C2214yes—
69#2766C2214yes—
70#2766C2214yes—
71#2764C2214yes—
72#2764C2214yes—
73#2762C2214yes—
74#2762C2214yes—
75#2762C2214yes—
76#2758C2214yes—
77#2758C2214yes—
78#2758C2214yes—
79#2758C2214yes—
80#2758C2214yes—
81#2758C2214yes—
82#2758C2214yes—
83#2755C2214yes—
84#2755C2214yes—
85#2744C2214yes—
86#2738C2214yes—
87#2734C2211yescharacteristic
88#2734C2212yes—
89#2734C2212yes—
90#2734C2211yescharacteristic
91#2729C2214yes—
92#2726C2214yes—
93#2726C2212yes—
94#2719C2214yes—
95#2713C2214yes—
96#2713C2214yes—
97#2713C2214yes—
98#2713C2214yes—
99#2698C2214yes—
100#2698C2214yes—
101#2689C2214yes—
102#2667C2212yes—
103#2666C2214yes—
104#2666C2214yes—
105#2666C2214yes—
106#2666C2214yes—
107#2666C2214yes—
108#2655C2214yes—
109#2655C2214yes—
110#2645C2212yes—
111#2645C2212yes—
112#2625C2212yes—
113#2612C2214yes—
114#2612C2214yes—
115#2611C2214yes—
116#2607C2212yes—
117#2606C2214yes—
118#2606C2214yes—
119#2606C2214yes—
120#2605C2214yes—
121#2605C2214yes—
122#2605C2214yes—
123#2605C2214yes—
124#2599C2214yes—
125#2590C2214yes—
126#2588C2214yes—
127#2588C2214yes—
128#2588C2214yes—
129#2586C2214yes—
130#2586C2212yes—
131#2586C2214yes—
132#2585C2214yes—
133#2585C2214yes—
134#2583C2212yes—
135#2582C2212yes—
136#2577C2214yes—
137#2574C2214yes—
138#2573C2214yes—
139#2570C2212yes—
140#2565C2212yes—
141#2550C2214yes—
142#2549C2214yes—
143#2533C2214yes—
144#2528C2214yes—
145#2528C2214yes—
146#2528C2214yes—
147#2528C2214yes—
148#2527C2214yes—
149#2524C2214yes—
150#2524C2214yes—
151#2524C2214yes—
152#2524C2214yes—
153#2524C2214yes—
154#2524C2214yes—
155#2520C2214yes—
156#2520C2214yes—
157#2517C2214yes—
158#2515C2214yes—
159#2514C2214yes—
160#2514C2214yes—
161#2514C2214yes—
162#2514C2214yes—
163#2514C2214yes—
164#2514C2214yes—
165#2511C2214yes—
166#2509C2214yes—
167#2509C2214yes—
168#2496C2212yes—
169#2494C2212yes—
170#2493C2214yes—
171#2493C2214yes—
172#2493C2214yes—
173#2484C2212yes—
174#2478C2214yes—
175#2478C2214yes—
176#2475C2214yes—
177#2462C2214yes—
178#2451C2214yes—
179#2451C2214yes—
180#2451C2214yes—
181#2446C2214yes—
182#2446C2214yes—
183#2438C2214yes—
184#2434C2212yes—
185#2434C2212yes—
186#2423C2212yes—
187#2421C2212yes—
188#2402C2214yes—
189#2381C2212yes—
190#2381C2214yes—
191#2381C2212yes—
192#2378C2212yes—
193#2373C2214yes—
194#2371C2214yes—
195#2370C2212yes—
196#2369C2212yes—
197#2369C2212yes—
198#2368C2214yes—
199#2365C2214yes—
200#2356C2214yes—
201#2351C2212yes—
202#2346C2212yes—
203#2336C2214yes—
204#2332C2212yes—
205#2332C2212yes—
206#2331C2214yes—
207#2320C2214yes—
208#2320C2214yes—
209#2317C2211yescharacteristic
210#2316C2211yescharacteristic
211#2310C2211yescharacteristic
212#2310C2211yescharacteristic
213C4×C22⋊Q8C2212yes—
214#2296C2211yescharacteristic
215#2295C2212yes—
216#2295C2212yes—
217C2×#391C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C2×C4⋊Q8C2314yes—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2312yes—
225C2×#126C2314yes—
226C2×#125C2312yes—
227C2×#125C2314yes—
228C2×#125C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C22×C4⋊C4C2311yescharacteristic
243C22×C42C2311yescharacteristic
244#401C2314yes—
245#401C2314yes—
246#401C2314yes—
247#401C2314yes—
248#401C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2312yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2312yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#399C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2312yes—
300#398C2312yes—
301#398C2312yes—
302#398C2312yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#396C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2312yes—
343#395C2312yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#393C2314yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#391C2312yes—
361#391C2312yes—
362#391C2312yes—
363#391C2312yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2311yescharacteristic
371#391C2314yes—
372#391C2314yes—
373#391C2311yescharacteristic
374#391C2312yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2312yes—
385#391C2312yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2314yes—
428#389C2312yes—
429#389C2312yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#384C2312yes—
542#384C2312yes—
543#384C2312yes—
544#383C2314yes—
545#383C2314yes—
546#383C2314yes—
547#383C2314yes—
548#383C2314yes—
549#383C2314yes—
550#383C2314yes—
551#383C2314yes—
552#383C2314yes—
553#383C2314yes—
554#383C2314yes—
555#383C2314yes—
556#383C2314yes—
557#382C2312yes—
558#382C2312yes—
559#382C2312yes—
560#382C2312yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#382C2314yes—
568#382C2314yes—
569#381C2312yes—
570#381C2314yes—
571#381C2312yes—
572#381C2312yes—
573#381C2314yes—
574#380C2312yes—
575#380C2312yes—
576#380C2312yes—
577#380C2312yes—
578#380C2312yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2312yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607#376C2314yes—
608#376C2314yes—
609#376C2314yes—
610#376C2314yes—
611#376C2312yes—
612C2×#95C2314yes—
613C43C2312yes—
614C22×Q8—42no—
615C22×Q8—42no—
616C22×Q8—42no—
617C22×Q8C2414yes—
618C22×Q8C2412yes—
619C22×Q8C2411yescharacteristic
620C22×Q8C2411yescharacteristic
621C22×Q8C2412yes—
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C23×C4C2411yescharacteristic
626C23×C4C2412yes—
627C23×C4C2412yes—
628C23×C4C2412yes—
629C4⋊Q8—216no—
630C4⋊Q8—44no—
631C4⋊Q8—44no—
632C4⋊Q8—44no—
633C4⋊Q8—44no—
634#126—48no—
635#125—44no—
636#125—48no—
637#125—48no—
638C22⋊Q8—28no—
639C22⋊Q8—44no—
640C22⋊Q8—44no—
641C22⋊Q8—44no—
642C4×Q8—28no—
643C4×Q8—28no—
644C4×Q8—44no—
645C4×Q8—48no—
646#117—42no—
647#117—42no—
648#117—44no—
649#117—42no—
650#117—42no—
651C2×C4⋊C4—42no—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2412yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2411yescharacteristic
720C2×C22⋊C4C2411yescharacteristic
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2412yes—
723C2×C22⋊C4C2414yes—
724C2×C42—42no—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2412yes—
734C2×C42C2414yes—
735C2×C42C2412yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2414yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2411yescharacteristic
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2411yescharacteristic
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2412yes—
757#95C2414yes—
758#95C2412yes—
759#95C2412yes—
760#95C2412yes—
761#95C2414yes—
762#95C2412yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2412yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2412yes—
814#95C2414yes—
815#95C2414yes—
816#95C2412yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836C24C2511yescharacteristic
837C2×Q8—28no—
838C2×Q8—24no—
839C2×Q8—22no—
840C2×Q8—22no—
841C2×Q8—42no—
842C2×Q8—42no—
843C2×Q8—44no—
844C2×Q8—41no—
845C2×Q8—41no—
846C2×Q8—42no—
847C2×Q8—41no—
848C2×Q8—41no—
849C2×Q8—42no—
850C2×Q8—44no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—42no—
854C2×Q8—42no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—44no—
859C2×Q8—88no—
860C2×Q82−1+418yes—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—44no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2514yes—
889C22×C4C2514yes—
890C22×C4C2514yes—
891C22×C4C2512yes—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—24no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C22⋊C4—28no—
958C22⋊C4—24no—
959C22⋊C4—28no—
960C22⋊C4—28no—
961C22⋊C4—44no—
962C22⋊C4—42no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—42no—
966C42—28no—
967C42—28no—
968C42—24no—
969C42—24no—
970C42—28no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—41no—
975C42—41no—
976C42—42no—
977C42—42no—
978C42—44no—
979C42—44no—
980C42—44no—
981C42—42no—
982C42—42no—
983C42—44no—
984C42—44no—
985C42—44no—
986C42—44no—
987C42—44no—
988C42—44no—
989C42—42no—
990C42—42no—
991C42—42no—
992C42—42no—
993C23—22no—
994C23—21no—
995C23—21no—
996C23—22no—
997C23#58512yes—
998C23C2611yescharacteristic
999Q8—48no—
1000Q8—88no—
1001Q8—82no—
1002Q8—82no—
1003Q8—84no—
1004Q8—162no—
1005Q8—162no—
1006Q8—162no—
1007C2×C4—28no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—84no—
1069C2×C4—84no—
1070C2×C4—84no—
1071C2×C4C2×2−1+418yes—
1072C2×C4C2×2−1+414yes—
1073C2×C4#58512yes—
1074C2×C4#58512yes—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—42no—
1079C22—42no—
1080C22C22×2−1+412yes—
1081C22C2×#58511yescharacteristic
1082C22C2×#58511yescharacteristic
1083C22C2×#58511yescharacteristic
1084C222−1+612yes—
1085C4—22no—
1086C4—22no—
1087C4—24no—
1088C4—28no—
1089C4—42no—
1090C4—44no—
1091C4—42no—
1092C4—42no—
1093C4—42no—
1094C4—44no—
1095C4—42no—
1096C4—42no—
1097C4—44no—
1098C4—44no—
1099C4—42no—
1100C4—44no—
1101C4—44no—
1102C4—42no—
1103C4—42no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C2—42no—
1108C2#6282611yescharacteristic
1109C2#6290412yes—
1110C2#6295312yes—
1111C2#6303811yescharacteristic
1112C2#6306411yescharacteristic
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
2. #57927C2semidirect
4. #53349C2semidirect
5. #52038C2semidirect
9. #50232C2semidirect
11. #49344C2semidirect
15. #45941C2semidirect
16. #45414C2semidirect
18. #41920C2semidirect
20. #38454C2semidirect
21. #37196C2semidirect

Maximal subgroups

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

subgroupindex
#599232
#579272
#552322
#533492
#520382
#516712
#516682
#509492
#502322
#501832
#493442
#477912
#470342
#462052
#459412
#454142
#445882
#419202
#388012
#384542
#371962
#363842
#353132