Finite Group Databasebeta

← #8757193

Subgroups — #8757193

Order 512.

4348 conjugacy classes of subgroups.

The subgroup lattice has 1231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58844C214yesmaximal, complemented
2#58638C214yesmaximal, complemented
3#57997C214yesmaximal, complemented
4#57318C214yesmaximal, complemented
5#56172C214yesmaximal, complemented
6#55125C214yesmaximal, complemented
7#50761C214yesmaximal, complemented
8#50182C212yesmaximal, complemented
9#49591C212yesmaximal, complemented
10#48571C214yesmaximal, complemented
11#47665C212yesmaximal, complemented
12#47663C212yesmaximal, complemented
13#47090C214yesmaximal, complemented
14#46443C214yesmaximal, complemented
15#46227C212yesmaximal, complemented
16#46145C211yesmaximal, characteristic, complemented
17#46145C212yesmaximal, complemented
18#46132C212yesmaximal, complemented
19#45991C211yesmaximal, characteristic, complemented
20#45989C212yesmaximal, complemented
21#45975C212yesmaximal, complemented
22#35334C211yesmaximal, characteristic, complemented
23#35130C212yesmaximal, complemented
24C2×#563C2212yes—
25C2×#533C2211yescharacteristic
26C2×#529C2212yes—
27C2×C4×#41C2211yescharacteristic
28#2851C2212yes—
29#2851C2212yes—
30#2851C2212yes—
31#2851C2212yes—
32#2850C2212yes—
33#2850C2212yes—
34#2844C2211yescharacteristic
35#2844C2211yescharacteristic
36#2841C2214yes—
37#2837C2214yes—
38#2833C2212yes—
39#2833C2214yes—
40#2832C2212yes—
41#2831C2214yes—
42#2824C2214yes—
43#2822C2211yescharacteristic
44#2822C2212yes—
45#2821C2214yes—
46#2820C2212yes—
47#2819C2211yescharacteristic
48#2807C2214yes—
49#2806C2214yes—
50#2804C2212yes—
51#2789C2214yes—
52#2789C2212yes—
53#2788C2214yes—
54#2788C2214yes—
55#2785C2212yes—
56#2782C2212yes—
57#2775C2214yes—
58#2774C2214yes—
59#2774C2214yes—
60#2774C2214yes—
61#2773C2214yes—
62#2769C2214yes—
63#2769C2212yes—
64#2768C2214yes—
65#2766C2214yes—
66#2766C2214yes—
67#2766C2214yes—
68#2765C2214yes—
69#2764C2214yes—
70#2763C2214yes—
71#2762C2214yes—
72#2762C2214yes—
73#2760C2214yes—
74#2760C2214yes—
75#2759C2214yes—
76#2759C2214yes—
77#2757C2214yes—
78#2753C2214yes—
79#2746C2214yes—
80#2746C2214yes—
81#2745C2214yes—
82#2743C2214yes—
83#2740C2214yes—
84#2739C2214yes—
85#2738C2214yes—
86#2737C2214yes—
87#2737C2214yes—
88#2732C2214yes—
89#2729C2214yes—
90#2729C2214yes—
91#2723C2214yes—
92#2722C2214yes—
93#2716C2214yes—
94#2716C2214yes—
95#2714C2214yes—
96#2708C2214yes—
97#2705C2214yes—
98#2705C2214yes—
99#2702C2214yes—
100#2699C2212yes—
101#2699C2212yes—
102#2698C2214yes—
103#2696C2214yes—
104#2695C2214yes—
105#2695C2214yes—
106#2692C2214yes—
107#2692C2214yes—
108#2692C2214yes—
109#2692C2214yes—
110#2692C2214yes—
111#2689C2214yes—
112#2688C2214yes—
113#2687C2214yes—
114#2687C2214yes—
115#2683C2212yes—
116#2681C2214yes—
117#2681C2214yes—
118#2677C2214yes—
119#2677C2214yes—
120#2667C2212yes—
121#2666C2214yes—
122#2665C2212yes—
123#2655C2214yes—
124#2643C2214yes—
125#2638C2214yes—
126#2637C2214yes—
127#2636C2214yes—
128#2628C2212yes—
129#2628C2212yes—
130#2624C2212yes—
131#2616C2212yes—
132#2609C2214yes—
133#2609C2214yes—
134#2598C2214yes—
135#2594C2214yes—
136#2591C2212yes—
137#2590C2214yes—
138#2586C2212yes—
139#2583C2212yes—
140#2583C2214yes—
141#2581C2214yes—
142#2581C2212yes—
143#2580C2214yes—
144#2580C2212yes—
145#2572C2214yes—
146#2572C2212yes—
147#2564C2214yes—
148#2564C2214yes—
149#2564C2214yes—
150#2549C2214yes—
151#2549C2214yes—
152#2536C2212yes—
153#2535C2212yes—
154#2516C2214yes—
155#2510C2214yes—
156#2498C2214yes—
157#2493C2214yes—
158#2493C2214yes—
159#2493C2214yes—
160#2492C2214yes—
161#2488C2214yes—
162#2484C2212yes—
163#2484C2214yes—
164#2481C2214yes—
165#2479C2214yes—
166#2479C2214yes—
167#2478C2214yes—
168#2477C2214yes—
169#2476C2214yes—
170#2471C2214yes—
171#2469C2214yes—
172#2469C2214yes—
173#2468C2214yes—
174#2467C2214yes—
175#2466C2214yes—
176#2463C2214yes—
177#2458C2214yes—
178#2456C2214yes—
179#2452C2214yes—
180#2451C2214yes—
181#2450C2214yes—
182#2450C2214yes—
183#2449C2214yes—
184#2446C2214yes—
185#2444C2214yes—
186#2439C2214yes—
187#2438C2214yes—
188#2438C2214yes—
189#2438C2214yes—
190#2438C2214yes—
191#2430C2214yes—
192#2430C2214yes—
193#2429C2214yes—
194#2419C2214yes—
195#2417C2212yes—
196#2417C2212yes—
197#2416C2212yes—
198#2416C2212yes—
199#2415C2214yes—
200#2407C2214yes—
201#2406C2212yes—
202#2382C2212yes—
203#2382C2212yes—
204#2379C2212yes—
205#2378C2212yes—
206#2377C2212yes—
207#2347C2212yes—
208#2339C2212yes—
209#2333C2214yes—
210#2325C2214yes—
211#2325C2214yes—
212#2324C2214yes—
213#2316C2211yescharacteristic
214#2316C2211yescharacteristic
215#2311C2211yescharacteristic
216#2311C2211yescharacteristic
217C2×#382C2211yescharacteristic
218C2×#382C2212yes—
219C22×#41C2311yescharacteristic
220C22×#41C2312yes—
221#563—48no—
222#533—44no—
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2314yes—
226#529—48no—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#125C2312yes—
232C2×#125C2312yes—
233C2×#124C2312yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×#121C2314yes—
250C2×#121C2314yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C4×#41—44no—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2312yes—
270C2×#117C2312yes—
271C2×#117C2314yes—
272C2×#117C2314yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C42C2311yescharacteristic
278C22×C42C2312yes—
279#401C2314yes—
280#401C2314yes—
281#401C2314yes—
282#401C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2312yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2312yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2312yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2312yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2312yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2312yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2312yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2312yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2312yes—
373#395C2312yes—
374#395C2314yes—
375#394C2312yes—
376#394C2312yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2312yes—
383#394C2314yes—
384#394C2314yes—
385#394C2312yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#391C2312yes—
408#391C2312yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#390C2312yes—
423#390C2312yes—
424#390C2314yes—
425#390C2314yes—
426#390C2312yes—
427#390C2312yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
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#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#383C2314yes—
564#383C2314yes—
565#383C2314yes—
566#383C2314yes—
567#382C2311yescharacteristic
568#382C2312yes—
569#382C2312yes—
570#382C2311yescharacteristic
571#382C2314yes—
572#382C2312yes—
573#382C2312yes—
574#382C2314yes—
575#382C2311yescharacteristic
576#382C2311yescharacteristic
577#382C2314yes—
578#382C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2312yes—
585#381C2312yes—
586#381C2314yes—
587#381C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2314yes—
598#380C2314yes—
599#380C2312yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C2×#95C2314yes—
615C2×#95C2314yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C2×#41—24no—
619C2×#41—42no—
620C2×#41—42no—
621C2×#41—44no—
622C2×#41—84no—
623C22×Q8C2411yescharacteristic
624C22×Q8C2412yes—
625C22×Q8C2414yes—
626C22×Q8C2412yes—
627C22×Q8C2414yes—
628C22×Q8C2412yes—
629C22×D4C2412yes—
630C22×D4C2412yes—
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2412yes—
635C22×D4C2412yes—
636C22×D4C2411yescharacteristic
637C23×C4C2411yescharacteristic
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2414yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C4⋊Q8—44no—
650C4⋊Q8—48no—
651C4⋊Q8—84no—
652#126—48no—
653#126—48no—
654#126—48no—
655#126—84no—
656#125—28no—
657#125—28no—
658#124—28no—
659#123—48no—
660#123—48no—
661#123—84no—
662C22⋊Q8—44no—
663C22⋊Q8—48no—
664C22⋊Q8—48no—
665C22⋊Q8—48no—
666C22⋊Q8—44no—
667C22⋊Q8—84no—
668C22⋊Q8—84no—
669C22⋊Q8—84no—
670C22⋊Q8—82no—
671C22⋊Q8—84no—
672C22⋊Q8—84no—
673C22⋊Q8—82no—
674#121—216no—
675#121—48no—
676#121—44no—
677#121—44no—
678#121—82no—
679#121—82no—
680C4×Q8—44no—
681C4×Q8—48no—
682C4×Q8—44no—
683C4×D4—44no—
684C4×D4—44no—
685C4×D4—44no—
686C4×D4—44no—
687C4×D4—48no—
688C4×D4—84no—
689C4×D4—84no—
690#117—42no—
691#117—44no—
692#117—48no—
693#117—44no—
694#117—42no—
695#117—42no—
696#117—84no—
697C2×C4⋊C4—42no—
698C2×C4⋊C4—42no—
699C2×C4⋊C4—82no—
700C2×C4⋊C4—82no—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2411yescharacteristic
760C2×C22⋊C4C2411yescharacteristic
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C42—28no—
794C2×C42—24no—
795C2×C42C2412yes—
796C2×C42C2411yescharacteristic
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2411yescharacteristic
810#95C2412yes—
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#95C2412yes—
827#95C2414yes—
828#95C2414yes—
829#95C2412yes—
830#95C2412yes—
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—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2412yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2412yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872C24C2514yes—
873C24C2512yes—
874C24C2511yescharacteristic
875#41—416no—
876#41—816no—
877C2×Q8—24no—
878C2×Q8—22no—
879C2×Q8—41no—
880C2×Q8—41no—
881C2×Q8—44no—
882C2×Q8—42no—
883C2×Q8—44no—
884C2×Q8—44no—
885C2×Q8—42no—
886C2×Q8—44no—
887C2×Q8—42no—
888C2×Q8—44no—
889C2×Q8—42no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—24no—
899C2×D4—41no—
900C2×D4—42no—
901C2×D4—44no—
902C2×D4—41no—
903C2×D4—42no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—42no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—42no—
911C2×D4—44no—
912C2×D4—42no—
913C2×D4—44no—
914C2×D42−1+414yes—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—42no—
938C22×C4—42no—
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×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2512yes—
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2511yescharacteristic
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—28no—
974C4⋊C4—24no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—42no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—42no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—41no—
1035C22⋊C4—42no—
1036C22⋊C4—41no—
1037C22⋊C4—42no—
1038C22⋊C4—44no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
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—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C42—24no—
1062C42—22no—
1063C42—24no—
1064C42—24no—
1065C42—24no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—42no—
1070C42—42no—
1071C42—44no—
1072C42—44no—
1073C42—44no—
1074C42—44no—
1075C42H(5,𝔽2)14yes—
1076C23—21no—
1077C23—22no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23—24no—
1091C23—24no—
1092C23—24no—
1093C23C2×2−1+414yes—
1094C23#58512yes—
1095C23C2611yescharacteristic
1096Q8—44no—
1097Q8—84no—
1098Q8—88no—
1099Q8—84no—
1100Q8—162no—
1101Q8—164no—
1102D4—44no—
1103D4—48no—
1104D4—48no—
1105D4—84no—
1106D4—88no—
1107D4—88no—
1108D4—88no—
1109D4—162no—
1110C2×C4—28no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—48no—
1165C2×C4—48no—
1166C2×C4—84no—
1167C2×C4—84no—
1168C2×C4—88no—
1169C2×C4—84no—
1170C2×C4—84no—
1171C2×C4—88no—
1172C2×C4—88no—
1173C2×C4—164no—
1174C2×C4—164no—
1175C2×C4C2×H(5,𝔽2)12yes—
1176C2×C4C2×H(5,𝔽2)14yes—
1177C2×C4C2×2−1+412yes—
1178C22—22no—
1179C22—24no—
1180C22—24no—
1181C22—22no—
1182C22—22no—
1183C22—24no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—44no—
1191C22—44no—
1192C22—44no—
1193C22—44no—
1194C22—44no—
1195C22—44no—
1196C22—44no—
1197C22C22×H(5,𝔽2)11yescharacteristic
1198C22C22×2−1+411yescharacteristic
1199C22C2×#58511yescharacteristic
1200C22H(7,𝔽2)12yes—
1201C222−1+612yes—
1202C4—22no—
1203C4—22no—
1204C4—24no—
1205C4—42no—
1206C4—44no—
1207C4—42no—
1208C4—44no—
1209C4—44no—
1210C4—44no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—44no—
1215C4—42no—
1216C4—42no—
1217C4—44no—
1218C4—42no—
1219C4—44no—
1220C4—44no—
1221C4—44no—
1222C2—42no—
1223C2—44no—
1224C2—84no—
1225C2#6281911yescharacteristic
1226C2#6287512yes—
1227C2#6304611yescharacteristic
1228C2#6305812yes—
1229C2#6306411yescharacteristic
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. #58844C2semidirect
2. #58638C2semidirect
3. #57997C2semidirect
4. #57318C2semidirect
5. #56172C2semidirect
6. #55125C2semidirect
7. #50761C2semidirect
8. #50182C2semidirect
9. #49591C2semidirect
10. #48571C2semidirect
11. #47665C2semidirect
12. #47663C2semidirect
13. #47090C2semidirect
14. #46443C2semidirect
15. #46227C2semidirect
16. #46145C2semidirect
17. #46145C2semidirect
18. #46132C2semidirect
19. #45991C2semidirect
20. #45989C2semidirect
21. #45975C2semidirect
22. #35334C2semidirect
23. #35130C2semidirect

Maximal subgroups

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

subgroupindex
#588442
#586382
#579972
#573182
#561722
#551252
#507612
#501822
#495912
#485712
#476652
#476632
#470902
#464432
#462272
#461452
#461322
#459912
#459892
#459752
#353342
#351302