Finite Group Databasebeta

← #8757433

Subgroups — #8757433

Order 512.

3652 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58541C214yesmaximal, complemented
2#58288C214yesmaximal, complemented
3#55769C214yesmaximal
4#54710C214yesmaximal, complemented
5#54651C214yesmaximal, complemented
6#54219C214yesmaximal
7#50994C214yesmaximal
8#50184C212yesmaximal
9#50183C212yesmaximal
10#49167C214yesmaximal
11#47821C212yesmaximal
12#47791C212yesmaximal
13#47474C214yesmaximal, complemented
14#47323C214yesmaximal, complemented
15#46243C212yesmaximal, complemented
16#46243C212yesmaximal, complemented
17#46235C212yesmaximal
18#46160C212yesmaximal, complemented
19#46160C212yesmaximal, complemented
20#46145C211yesmaximal, characteristic
21#46145C211yesmaximal, characteristic
22#35339C211yesmaximal, characteristic
23#35142C212yesmaximal
24#2864C2212yes—
25#2864C2212yes—
26#2864C2212yes—
27#2859C2212yes—
28#2851C2212yes—
29#2851C2212yes—
30#2844C2211yescharacteristic
31#2844C2211yescharacteristic
32#2844C2212yes—
33#2843C2212yes—
34#2839C2214yes—
35#2839C2214yes—
36#2839C2214yes—
37#2839C2214yes—
38#2833C2214yes—
39#2833C2214yes—
40#2822C2211yescharacteristic
41#2822C2211yescharacteristic
42#2822C2212yes—
43#2822C2212yes—
44#2809C2214yes—
45#2805C2214yes—
46#2805C2214yes—
47#2805C2214yes—
48#2805C2214yes—
49#2802C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2799C2214yes—
56#2794C2214yes—
57#2794C2214yes—
58#2794C2214yes—
59#2794C2212yes—
60#2792C2212yes—
61#2792C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2789C2214yes—
66#2789C2212yes—
67#2789C2212yes—
68#2789C2212yes—
69#2776C2214yes—
70#2776C2214yes—
71#2776C2214yes—
72#2776C2214yes—
73#2776C2214yes—
74#2776C2214yes—
75#2776C2214yes—
76#2774C2214yes—
77#2774C2214yes—
78#2774C2214yes—
79#2774C2214yes—
80#2774C2214yes—
81#2774C2214yes—
82#2774C2214yes—
83#2771C2214yes—
84#2769C2214yes—
85#2769C2212yes—
86#2769C2212yes—
87#2769C2212yes—
88#2767C2214yes—
89#2767C2214yes—
90#2767C2214yes—
91#2766C2214yes—
92#2766C2214yes—
93#2764C2214yes—
94#2762C2214yes—
95#2758C2214yes—
96#2758C2214yes—
97#2758C2214yes—
98#2758C2214yes—
99#2758C2214yes—
100#2755C2214yes—
101#2755C2214yes—
102#2755C2214yes—
103#2755C2214yes—
104#2747C2214yes—
105#2747C2214yes—
106#2745C2214yes—
107#2744C2214yes—
108#2742C2214yes—
109#2742C2214yes—
110#2739C2214yes—
111#2738C2214yes—
112#2726C2214yes—
113#2719C2214yes—
114#2698C2214yes—
115#2689C2214yes—
116#2667C2212yes—
117#2666C2214yes—
118#2665C2212yes—
119#2655C2214yes—
120#2655C2214yes—
121#2655C2214yes—
122#2652C2214yes—
123#2647C2212yes—
124#2647C2212yes—
125#2645C2214yes—
126#2625C2212yes—
127#2625C2212yes—
128#2612C2214yes—
129#2612C2212yes—
130#2611C2214yes—
131#2606C2214yes—
132#2606C2214yes—
133#2606C2214yes—
134#2599C2214yes—
135#2590C2214yes—
136#2590C2214yes—
137#2590C2214yes—
138#2590C2214yes—
139#2588C2214yes—
140#2588C2214yes—
141#2588C2214yes—
142#2588C2214yes—
143#2588C2214yes—
144#2586C2214yes—
145#2586C2214yes—
146#2586C2214yes—
147#2586C2214yes—
148#2583C2212yes—
149#2583C2212yes—
150#2582C2212yes—
151#2575C2214yes—
152#2570C2214yes—
153#2570C2214yes—
154#2569C2214yes—
155#2569C2214yes—
156#2533C2214yes—
157#2533C2214yes—
158#2533C2214yes—
159#2533C2214yes—
160#2533C2214yes—
161#2533C2214yes—
162#2533C2214yes—
163#2528C2214yes—
164#2528C2214yes—
165#2528C2214yes—
166#2528C2214yes—
167#2527C2214yes—
168#2524C2214yes—
169#2524C2214yes—
170#2524C2214yes—
171#2514C2214yes—
172#2509C2214yes—
173#2509C2214yes—
174#2509C2214yes—
175#2509C2212yes—
176#2509C2214yes—
177#2508C2212yes—
178#2507C2212yes—
179#2506C2212yes—
180#2497C2212yes—
181#2496C2212yes—
182#2495C2212yes—
183#2494C2212yes—
184#2493C2214yes—
185#2493C2214yes—
186#2484C2212yes—
187#2484C2212yes—
188#2478C2214yes—
189#2478C2214yes—
190#2478C2214yes—
191#2475C2214yes—
192#2462C2214yes—
193#2462C2214yes—
194#2462C2214yes—
195#2453C2214yes—
196#2438C2214yes—
197#2438C2214yes—
198#2382C2212yes—
199#2382C2212yes—
200#2382C2212yes—
201#2382C2212yes—
202#2378C2212yes—
203#2378C2212yes—
204#2347C2212yes—
205#2346C2212yes—
206#2336C2214yes—
207#2334C2214yes—
208#2330C2214yes—
209#2320C2214yes—
210#2317C2211yescharacteristic
211#2317C2211yescharacteristic
212#2316C2211yescharacteristic
213#2316C2211yescharacteristic
214C4×#125C2212yes—
215C4×#125C2212yes—
216#2285C2211yescharacteristic
217C2×#382C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C2×#126C2314yes—
220C2×#125C2312yes—
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2312yes—
232C2×#117C2312yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C42C2311yescharacteristic
236#401C2314yes—
237#401C2314yes—
238#401C2314yes—
239#401C2314yes—
240#401C2314yes—
241#400C2314yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2312yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2312yes—
287#400C2312yes—
288#400C2314yes—
289#400C2312yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#399C2314yes—
298#398C2314yes—
299#398C2312yes—
300#398C2312yes—
301#398C2312yes—
302#398C2314yes—
303#398C2312yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2312yes—
312#398C2312yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2312yes—
322#398C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
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#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#396C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2312yes—
352#395C2312yes—
353#395C2312yes—
354#395C2312yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#393C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2314yes—
383#389C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
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#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2312yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
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#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#384C2312yes—
545#384C2312yes—
546#384C2312yes—
547#384C2312yes—
548#384C2312yes—
549#383C2314yes—
550#383C2314yes—
551#383C2314yes—
552#383C2314yes—
553#383C2314yes—
554#383C2314yes—
555#383C2314yes—
556#383C2314yes—
557#382C2312yes—
558#382C2312yes—
559#382C2312yes—
560#382C2311yescharacteristic
561#382C2311yescharacteristic
562#382C2312yes—
563#382C2312yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#382C2314yes—
568#382C2314yes—
569#382C2312yes—
570#382C2312yes—
571#382C2314yes—
572#382C2311yescharacteristic
573#382C2311yescharacteristic
574#381C2314yes—
575#381C2312yes—
576#381C2312yes—
577#381C2314yes—
578#380C2312yes—
579#380C2312yes—
580#380C2312yes—
581#380C2312yes—
582#380C2314yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2312yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2312yes—
608#376C2314yes—
609#376C2314yes—
610#376C2314yes—
611#376C2312yes—
612C2×#95C2314yes—
613C43C2312yes—
614C22×Q8C2414yes—
615C22×Q8C2412yes—
616C22×Q8C2412yes—
617C23×C4C2411yescharacteristic
618C23×C4C2412yes—
619C23×C4C2412yes—
620C23×C4C2412yes—
621#126—48no—
622#125—28no—
623#125—28no—
624#125—48no—
625#125—48no—
626C22⋊Q8—44no—
627C22⋊Q8—44no—
628C4×Q8—48no—
629#117—42no—
630#117—42no—
631#117—44no—
632#117—44no—
633#117—42no—
634#117—42no—
635C2×C4⋊C4—42no—
636C2×C4⋊C4—42no—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2411yescharacteristic
711C2×C22⋊C4C2411yescharacteristic
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C42—24no—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2414yes—
739C2×C42C2411yescharacteristic
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2412yes—
745#95C2412yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2412yes—
761#95C2412yes—
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#95C2414yes—
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#95C2412yes—
796#95C2412yes—
797#95C2412yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2412yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826C24C2511yescharacteristic
827C2×Q8—44no—
828C2×Q8—44no—
829C2×Q8—44no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—44no—
833C2×Q8—44no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—41no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—42no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—42no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—42no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—24no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—41no—
944C22⋊C4—41no—
945C42—24no—
946C42—22no—
947C42—24no—
948C42—24no—
949C42—42no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—44no—
954C42—44no—
955C42—44no—
956C42—44no—
957C42—44no—
958C42—44no—
959C42—42no—
960C42—42no—
961C42—44no—
962C42—44no—
963C42—44no—
964C42—44no—
965C42—44no—
966C42—44no—
967C422−1+414yes—
968C23—21no—
969C23—21no—
970C23—22no—
971C23—22no—
972C23#58512yes—
973C23C2611yescharacteristic
974Q8—88no—
975Q8—162no—
976Q8—162no—
977C2×C4—28no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—84no—
1038C2×C4—84no—
1039C2×C4—84no—
1040C2×C4C2×2−1+412yes—
1041C2×C4C2×2−1+414yes—
1042C2×C4#58512yes—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—42no—
1047C22—42no—
1048C22C22×2−1+411yescharacteristic
1049C22C2×#58511yescharacteristic
1050C22C2×#58511yescharacteristic
1051C222−1+612yes—
1052C222−1+612yes—
1053C4—22no—
1054C4—22no—
1055C4—24no—
1056C4—44no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—44no—
1062C4—42no—
1063C4—42no—
1064C4—42no—
1065C4—42no—
1066C4—42no—
1067C4—42no—
1068C4—44no—
1069C4—44no—
1070C4—44no—
1071C4—44no—
1072C4—44no—
1073C4—44no—
1074C4—42no—
1075C2—42no—
1076C2#6282511yescharacteristic
1077C2#6288912yes—
1078C2#6305312yes—
1079C2#6306411yescharacteristic
1080C2#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
1. #58541C2semidirect
2. #58288C2semidirect
4. #54710C2semidirect
5. #54651C2semidirect
13. #47474C2semidirect
14. #47323C2semidirect
15. #46243C2semidirect
16. #46243C2semidirect
18. #46160C2semidirect
19. #46160C2semidirect

Maximal subgroups

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

subgroupindex
#585412
#582882
#557692
#547102
#546512
#542192
#509942
#501842
#501832
#491672
#478212
#477912
#474742
#473232
#462432
#462352
#461602
#461452
#353392
#351422