Finite Group Databasebeta

← #8757202

Subgroups — #8757202

Order 512.

4768 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57998C214yesmaximal, complemented
2#57588C214yesmaximal, complemented
3#57383C214yesmaximal, complemented
4#56471C214yesmaximal, complemented
5#54873C214yesmaximal, complemented
6#53408C214yesmaximal, complemented
7#50744C214yesmaximal, complemented
8#49637C214yesmaximal, complemented
9#48599C214yesmaximal, complemented
10#47204C214yesmaximal, complemented
11#46731C214yesmaximal, complemented
12#46415C214yesmaximal, complemented
13#46224C212yesmaximal, complemented
14#46144C211yesmaximal, characteristic, complemented
15#46133C212yesmaximal, complemented
16#45990C212yesmaximal, complemented
17#45988C212yesmaximal, complemented
18#45988C211yesmaximal, characteristic, complemented
19#45974C212yesmaximal, complemented
20#35328C211yesmaximal, characteristic, complemented
21#35130C212yesmaximal, complemented
22C2×#562C2212yes—
23C2×#540C2214yes—
24C2×#537C2212yes—
25C2×#532C2211yescharacteristic
26C2×#529C2212yes—
27C2×C4×#41C2211yescharacteristic
28#2851C2212yes—
29#2851C2212yes—
30#2850C2212yes—
31#2850C2212yes—
32#2850C2212yes—
33#2850C2212yes—
34#2845C2211yescharacteristic
35#2845C2211yescharacteristic
36#2839C2214yes—
37#2836C2214yes—
38#2827C2214yes—
39#2826C2214yes—
40#2822C2211yescharacteristic
41#2820C2212yes—
42#2819C2212yes—
43#2819C2211yescharacteristic
44#2814C2214yes—
45#2813C2214yes—
46#2813C2214yes—
47#2791C2214yes—
48#2790C2214yes—
49#2783C2214yes—
50#2781C2214yes—
51#2781C2214yes—
52#2781C2214yes—
53#2780C2214yes—
54#2779C2214yes—
55#2772C2214yes—
56#2768C2214yes—
57#2767C2214yes—
58#2767C2214yes—
59#2761C2214yes—
60#2761C2214yes—
61#2755C2214yes—
62#2754C2214yes—
63#2754C2214yes—
64#2754C2214yes—
65#2750C2214yes—
66#2748C2214yes—
67#2748C2214yes—
68#2747C2214yes—
69#2747C2214yes—
70#2744C2214yes—
71#2744C2214yes—
72#2741C2214yes—
73#2741C2214yes—
74#2729C2214yes—
75#2728C2214yes—
76#2720C2214yes—
77#2719C2214yes—
78#2718C2214yes—
79#2714C2214yes—
80#2708C2214yes—
81#2708C2214yes—
82#2706C2214yes—
83#2706C2214yes—
84#2706C2214yes—
85#2706C2214yes—
86#2703C2214yes—
87#2703C2214yes—
88#2702C2214yes—
89#2696C2214yes—
90#2696C2214yes—
91#2695C2214yes—
92#2694C2214yes—
93#2693C2214yes—
94#2693C2214yes—
95#2688C2214yes—
96#2688C2214yes—
97#2688C2214yes—
98#2688C2214yes—
99#2681C2214yes—
100#2681C2214yes—
101#2680C2214yes—
102#2675C2214yes—
103#2675C2214yes—
104#2673C2214yes—
105#2673C2214yes—
106#2673C2214yes—
107#2673C2214yes—
108#2673C2214yes—
109#2671C2214yes—
110#2671C2214yes—
111#2671C2214yes—
112#2671C2214yes—
113#2671C2214yes—
114#2671C2214yes—
115#2652C2214yes—
116#2648C2214yes—
117#2648C2214yes—
118#2646C2214yes—
119#2637C2214yes—
120#2636C2214yes—
121#2630C2214yes—
122#2630C2214yes—
123#2621C2212yes—
124#2619C2212yes—
125#2609C2214yes—
126#2609C2214yes—
127#2581C2212yes—
128#2580C2212yes—
129#2579C2214yes—
130#2569C2214yes—
131#2569C2214yes—
132#2564C2214yes—
133#2543C2214yes—
134#2543C2214yes—
135#2543C2214yes—
136#2543C2214yes—
137#2543C2214yes—
138#2537C2214yes—
139#2536C2214yes—
140#2536C2212yes—
141#2535C2214yes—
142#2535C2212yes—
143#2535C2214yes—
144#2505C2214yes—
145#2498C2214yes—
146#2498C2214yes—
147#2485C2214yes—
148#2477C2214yes—
149#2476C2214yes—
150#2476C2214yes—
151#2473C2214yes—
152#2470C2214yes—
153#2463C2214yes—
154#2460C2214yes—
155#2458C2214yes—
156#2457C2214yes—
157#2457C2214yes—
158#2456C2214yes—
159#2456C2214yes—
160#2456C2214yes—
161#2456C2214yes—
162#2455C2214yes—
163#2450C2214yes—
164#2450C2214yes—
165#2450C2214yes—
166#2450C2214yes—
167#2444C2214yes—
168#2444C2214yes—
169#2443C2214yes—
170#2443C2214yes—
171#2443C2214yes—
172#2438C2214yes—
173#2438C2214yes—
174#2430C2214yes—
175#2430C2214yes—
176#2428C2214yes—
177#2428C2214yes—
178#2425C2214yes—
179#2425C2214yes—
180#2425C2214yes—
181#2425C2214yes—
182#2423C2214yes—
183#2419C2214yes—
184#2419C2214yes—
185#2417C2212yes—
186#2417C2212yes—
187#2416C2212yes—
188#2416C2212yes—
189#2414C2214yes—
190#2413C2214yes—
191#2407C2214yes—
192#2382C2212yes—
193#2379C2212yes—
194#2379C2212yes—
195#2377C2214yes—
196#2364C2214yes—
197#2325C2214yes—
198#2325C2214yes—
199#2325C2214yes—
200#2311C2212yes—
201C2×#382C2211yescharacteristic
202C2×#382C2212yes—
203C22×#41C2311yescharacteristic
204C22×#41C2312yes—
205#562—48no—
206#540—416no—
207#537—48no—
208#532—44no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#127C2314yes—
212#529—48no—
213C2×#126C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#124C2312yes—
217C2×#124C2312yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2312yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259C4×#41—44no—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×#117C2311yescharacteristic
275C2×#117C2312yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2312yes—
281C22×C42C2312yes—
282C22×C42C2311yescharacteristic
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
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#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#395C2314yes—
358#395C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#392C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#392C2314yes—
392#392C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2314yes—
396#392C2314yes—
397#392C2314yes—
398#392C2314yes—
399#392C2314yes—
400#392C2314yes—
401#392C2314yes—
402#392C2314yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2314yes—
408#391C2314yes—
409#390C2312yes—
410#390C2312yes—
411#390C2312yes—
412#390C2312yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#389C2312yes—
418#389C2312yes—
419#389C2314yes—
420#389C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
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#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#384C2314yes—
546#382C2311yescharacteristic
547#382C2312yes—
548#382C2312yes—
549#382C2311yescharacteristic
550#382C2312yes—
551#382C2312yes—
552#382C2314yes—
553#382C2312yes—
554#382C2314yes—
555#382C2314yes—
556#382C2314yes—
557#381C2314yes—
558#381C2314yes—
559#381C2314yes—
560#380C2314yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2312yes—
565#380C2314yes—
566#380C2314yes—
567#380C2314yes—
568#380C2314yes—
569#380C2314yes—
570#380C2314yes—
571#380C2314yes—
572#380C2312yes—
573#380C2312yes—
574#380C2312yes—
575#380C2314yes—
576#380C2314yes—
577#380C2314yes—
578C4×C22⋊C4C2314yes—
579C4×C22⋊C4C2314yes—
580C4×C22⋊C4C2314yes—
581C2×#95C2314yes—
582C2×#95C2314yes—
583C2×#95C2314yes—
584C2×#95C2314yes—
585C2×#95C2314yes—
586C2×#41—24no—
587C2×#41—42no—
588C2×#41—44no—
589C2×#41—42no—
590C2×#41—44no—
591C2×#41—44no—
592C22×Q8C2411yescharacteristic
593C22×Q8C2412yes—
594C22×Q8C2412yes—
595C22×D4C2412yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C22×D4C2412yes—
600C22×D4C2414yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2412yes—
604C22×D4C2414yes—
605C22×D4C2414yes—
606C22×D4C2414yes—
607C22×D4C2414yes—
608C22×D4C2414yes—
609C22×D4C2414yes—
610C22×D4C2411yescharacteristic
611C23×C4C2411yescharacteristic
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2414yes—
615C23×C4C2412yes—
616C23×C4C2414yes—
617C23×C4C2412yes—
618C23×C4C2414yes—
619C23×C4C2414yes—
620C23×C4C2414yes—
621C23×C4C2414yes—
622C23×C4C2414yes—
623C23×C4C2414yes—
624C23×C4C2414yes—
625C4⋊Q8—42no—
626#127—42no—
627#127—48no—
628#126—48no—
629#125—28no—
630#125—48no—
631#124—28no—
632#124—28no—
633#123—48no—
634#123—48no—
635#123—48no—
636#123—48no—
637#123—48no—
638#123—48no—
639#123—48no—
640#123—84no—
641#123—84no—
642#123—84no—
643#123—84no—
644C22⋊Q8—44no—
645C22⋊Q8—44no—
646C22⋊Q8—48no—
647C22⋊Q8—48no—
648C22⋊Q8—44no—
649C22⋊Q8—48no—
650C22⋊Q8—82no—
651C22⋊Q8—82no—
652#121—216no—
653#121—216no—
654#121—48no—
655#121—48no—
656#121—48no—
657#121—48no—
658#121—48no—
659#121—48no—
660#121—48no—
661#121—48no—
662#121—48no—
663#121—48no—
664#121—44no—
665#121—44no—
666#121—44no—
667#121—48no—
668#121—84no—
669#121—84no—
670#121—82no—
671#121—82no—
672#121—84no—
673#121—84no—
674C4×Q8—44no—
675C4×Q8—44no—
676C4×D4—48no—
677C4×D4—44no—
678C4×D4—44no—
679C4×D4—44no—
680C4×D4—44no—
681C4×D4—48no—
682C4×D4—48no—
683C4×D4—48no—
684C4×D4—84no—
685C4×D4—84no—
686C4×D4—84no—
687C4×D4—84no—
688#117—42no—
689#117—44no—
690#117—48no—
691#117—48no—
692C2×C4⋊C4—44no—
693C2×C4⋊C4—82no—
694C2×C4⋊C4—82no—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2411yescharacteristic
749C2×C22⋊C4C2411yescharacteristic
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C42—28no—
787C2×C42—24no—
788C2×C42C2412yes—
789C2×C42C2411yescharacteristic
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798C2×C42C2411yescharacteristic
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#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—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845C24C2514yes—
846C24C2514yes—
847C24C2512yes—
848C24C2511yescharacteristic
849#41—416no—
850#41—816no—
851C2×Q8—22no—
852C2×Q8—24no—
853C2×Q8—24no—
854C2×Q8—41no—
855C2×Q8—41no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—42no—
859C2×Q8—42no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—28no—
863C2×D4—28no—
864C2×D4—28no—
865C2×D4—28no—
866C2×D4—28no—
867C2×D4—28no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—41no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—42no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—42no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—42no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4H(5,𝔽2)14yes—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—24no—
912C22×C4—28no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—28no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—41no—
1025C22⋊C4—42no—
1026C22⋊C4—41no—
1027C22⋊C4—42no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C42—24no—
1059C42—22no—
1060C42—24no—
1061C42—24no—
1062C42—24no—
1063C42—44no—
1064C42—44no—
1065C42—44no—
1066C42—44no—
1067C42—44no—
1068C42H(5,𝔽2)14yes—
1069C23—22no—
1070C23—21no—
1071C23—21no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—24no—
1080C23—24no—
1081C23—24no—
1082C23—24no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23—24no—
1091C23—24no—
1092C23—24no—
1093C23C2×H(5,𝔽2)14yes—
1094C23#58512yes—
1095C23C2611yescharacteristic
1096Q8—44no—
1097Q8—84no—
1098Q8—84no—
1099D4—44no—
1100D4—48no—
1101D4—84no—
1102D4—84no—
1103D4—88no—
1104D4—88no—
1105D4—88no—
1106D4—88no—
1107D4—88no—
1108D4—88no—
1109D4—88no—
1110D4—88no—
1111D4—88no—
1112D4—164no—
1113D4—164no—
1114D4—164no—
1115C2×C4—28no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—48no—
1165C2×C4—48no—
1166C2×C4—84no—
1167C2×C4—84no—
1168C2×C4—88no—
1169C2×C4—88no—
1170C2×C4—88no—
1171C2×C4—164no—
1172C2×C4—164no—
1173C2×C4—164no—
1174C2×C4—164no—
1175C2×C4—164no—
1176C2×C4—164no—
1177C2×C4C2×H(5,𝔽2)14yes—
1178C2×C4C2×H(5,𝔽2)12yes—
1179C2×C4C2×H(5,𝔽2)12yes—
1180C22—24no—
1181C22—24no—
1182C22—22no—
1183C22—22no—
1184C22—22no—
1185C22—24no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—44no—
1193C22—44no—
1194C22—44no—
1195C22—44no—
1196C22—44no—
1197C22—44no—
1198C22—44no—
1199C22—44no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22C22×H(5,𝔽2)11yescharacteristic
1207C22C22×H(5,𝔽2)11yescharacteristic
1208C22C2×#58511yescharacteristic
1209C22H(7,𝔽2)12yes—
1210C222−1+612yes—
1211C4—22no—
1212C4—22no—
1213C4—24no—
1214C4—44no—
1215C4—44no—
1216C4—44no—
1217C4—44no—
1218C4—44no—
1219C4—44no—
1220C4—42no—
1221C4—44no—
1222C4—44no—
1223C4—42no—
1224C4—42no—
1225C4—44no—
1226C4—42no—
1227C4—44no—
1228C2—44no—
1229C2—42no—
1230C2—84no—
1231C2—84no—
1232C2#6281811yescharacteristic
1233C2#6287512yes—
1234C2#6304912yes—
1235C2#6305511yescharacteristic
1236C2#6306811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57998C2semidirect
2. #57588C2semidirect
3. #57383C2semidirect
4. #56471C2semidirect
5. #54873C2semidirect
6. #53408C2semidirect
7. #50744C2semidirect
8. #49637C2semidirect
9. #48599C2semidirect
10. #47204C2semidirect
11. #46731C2semidirect
12. #46415C2semidirect
13. #46224C2semidirect
14. #46144C2semidirect
15. #46133C2semidirect
16. #45990C2semidirect
17. #45988C2semidirect
18. #45988C2semidirect
19. #45974C2semidirect
20. #35328C2semidirect
21. #35130C2semidirect

Maximal subgroups

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

subgroupindex
#579982
#575882
#573832
#564712
#548732
#534082
#507442
#496372
#485992
#472042
#467312
#464152
#462242
#461442
#461332
#459902
#459882
#459742
#353282
#351302