Finite Group Databasebeta

← #9912958

Subgroups — #9912958

Order 512.

4349 conjugacy classes of subgroups.

The subgroup lattice has 1247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58418C214yesmaximal, complemented
2#58195C214yesmaximal, complemented
3#58131C214yesmaximal, complemented
4#58021C214yesmaximal, complemented
5#56554C214yesmaximal, complemented
6#56388C214yesmaximal, complemented
7#56371C214yesmaximal, complemented
8#53748C212yesmaximal, complemented
9#53376C212yesmaximal, complemented
10#53218C214yesmaximal, complemented
11#52082C212yesmaximal, complemented
12#51988C212yesmaximal, complemented
13#51923C212yesmaximal, complemented
14#51533C214yesmaximal, complemented
15#49548C212yesmaximal, complemented
16#46275C212yesmaximal, complemented
17#46240C211yesmaximal, characteristic, complemented
18#46166C214yesmaximal, complemented
19#45963C212yesmaximal, complemented
20#38956C211yesmaximal, characteristic
21#38093C212yesmaximal, complemented
22#37306C212yesmaximal, complemented
23#37208C211yesmaximal, characteristic, complemented
24C2×#552C2212yes—
25C2×#550C2211yescharacteristic
26C2×#547C2211yescharacteristic
27C2×#544C2212yes—
28#2864C2212yes—
29#2863C2212yes—
30#2858C2211yescharacteristic
31#2857C2214yes—
32#2853C2214yes—
33#2850C2212yes—
34#2845C2212yes—
35#2838C2214yes—
36#2837C2214yes—
37#2830C2214yes—
38#2829C2214yes—
39#2829C2214yes—
40#2827C2214yes—
41#2826C2214yes—
42#2824C2212yes—
43#2824C2214yes—
44#2811C2211yescharacteristic
45#2811C2212yes—
46#2809C2212yes—
47#2809C2212yes—
48#2808C2212yes—
49#2808C2212yes—
50#2808C2212yes—
51#2804C2214yes—
52#2800C2214yes—
53#2799C2214yes—
54#2797C2214yes—
55#2793C2214yes—
56#2790C2214yes—
57#2789C2212yes—
58#2787C2214yes—
59#2786C2214yes—
60#2781C2214yes—
61#2777C2214yes—
62#2775C2214yes—
63#2775C2214yes—
64#2774C2214yes—
65#2772C2214yes—
66#2768C2214yes—
67#2761C2214yes—
68#2759C2214yes—
69#2757C2214yes—
70#2757C2214yes—
71#2755C2214yes—
72#2749C2214yes—
73#2748C2212yes—
74#2746C2214yes—
75#2737C2214yes—
76#2734C2211yescharacteristic
77#2734C2212yes—
78#2734C2214yes—
79#2732C2214yes—
80#2732C2212yes—
81#2731C2214yes—
82#2731C2212yes—
83#2730C2214yes—
84#2730C2214yes—
85#2728C2214yes—
86#2727C2212yes—
87#2727C2212yes—
88#2726C2212yes—
89#2723C2214yes—
90#2721C2214yes—
91#2720C2214yes—
92#2716C2214yes—
93#2716C2214yes—
94#2715C2214yes—
95#2715C2214yes—
96#2713C2214yes—
97#2712C2214yes—
98#2712C2214yes—
99#2712C2212yes—
100#2710C2214yes—
101#2710C2214yes—
102#2709C2214yes—
103#2709C2214yes—
104#2709C2214yes—
105#2707C2214yes—
106#2705C2214yes—
107#2704C2214yes—
108#2703C2214yes—
109#2703C2214yes—
110#2702C2214yes—
111#2700C2214yes—
112#2698C2214yes—
113#2696C2214yes—
114#2693C2212yes—
115#2692C2214yes—
116#2692C2214yes—
117#2692C2214yes—
118#2692C2214yes—
119#2692C2214yes—
120#2692C2214yes—
121#2691C2214yes—
122#2691C2214yes—
123#2690C2214yes—
124#2686C2214yes—
125#2683C2212yes—
126#2683C2214yes—
127#2681C2214yes—
128#2680C2214yes—
129#2674C2214yes—
130#2674C2214yes—
131#2674C2214yes—
132#2674C2214yes—
133#2672C2214yes—
134#2672C2214yes—
135#2666C2214yes—
136#2662C2214yes—
137#2662C2214yes—
138#2653C2214yes—
139#2651C2214yes—
140#2641C2212yes—
141#2638C2212yes—
142#2630C2214yes—
143#2628C2214yes—
144#2621C2214yes—
145#2620C2212yes—
146#2619C2212yes—
147#2616C2212yes—
148#2609C2214yes—
149#2609C2214yes—
150#2605C2214yes—
151#2597C2214yes—
152#2588C2214yes—
153#2586C2214yes—
154#2579C2212yes—
155#2577C2214yes—
156#2574C2214yes—
157#2568C2211yescharacteristic
158#2565C2212yes—
159#2560C2214yes—
160#2548C2212yes—
161#2544C2214yes—
162#2541C2211yescharacteristic
163#2527C2214yes—
164#2522C2214yes—
165#2522C2214yes—
166#2521C2214yes—
167#2521C2214yes—
168#2520C2214yes—
169#2518C2214yes—
170#2517C2214yes—
171#2511C2214yes—
172#2504C2212yes—
173#2504C2212yes—
174#2500C2212yes—
175#2479C2214yes—
176#2478C2214yes—
177#2477C2214yes—
178#2476C2214yes—
179#2476C2214yes—
180#2476C2214yes—
181#2475C2214yes—
182#2474C2214yes—
183#2473C2214yes—
184#2473C2214yes—
185#2470C2214yes—
186#2465C2214yes—
187#2463C2212yes—
188#2461C2214yes—
189#2460C2214yes—
190#2460C2214yes—
191#2451C2214yes—
192#2449C2214yes—
193#2443C2214yes—
194#2440C2214yes—
195#2440C2214yes—
196#2439C2214yes—
197#2439C2214yes—
198#2432C2212yes—
199#2432C2212yes—
200#2432C2214yes—
201#2431C2214yes—
202#2431C2212yes—
203#2427C2214yes—
204#2415C2214yes—
205#2406C2212yes—
206#2382C2214yes—
207#2381C2212yes—
208#2379C2211yescharacteristic
209#2379C2211yescharacteristic
210#2378C2212yes—
211#2369C2212yes—
212#2327C2212yes—
213#2311C2212yes—
214#2311C2212yes—
215C4×#124C2211yescharacteristic
216#2297C2212yes—
217#2293C2211yescharacteristic
218#2290C2212yes—
219C22×#41C2312yes—
220C22×#41C2312yes—
221#552—48no—
222#550—44no—
223#547—44no—
224#544—48no—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2314yes—
230C2×#127C2311yescharacteristic
231C2×#127C2312yes—
232C2×#127C2312yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#125C2314yes—
237C2×#125C2312yes—
238C2×#125C2314yes—
239C2×#124C2311yescharacteristic
240C2×#124C2312yes—
241C2×#124C2314yes—
242C2×#124C2312yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266C2×#121C2314yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2314yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2312yes—
281C22×C42C2312yes—
282#401C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#399C2314yes—
294#399C2314yes—
295#399C2314yes—
296#399C2314yes—
297#399C2314yes—
298#399C2314yes—
299#399C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
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#398C2312yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2312yes—
337#397C2314yes—
338#397C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
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#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2312yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
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#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#393C2314yes—
395#393C2312yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#392C2314yes—
406#392C2312yes—
407#392C2312yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2311yescharacteristic
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#390C2314yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2311yescharacteristic
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
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#387C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2312yes—
548#386C2312yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#385C2312yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2312yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#384C2312yes—
581#384C2314yes—
582#383C2314yes—
583#383C2314yes—
584#382C2312yes—
585#382C2312yes—
586#382C2312yes—
587#382C2312yes—
588#382C2311yescharacteristic
589#382C2312yes—
590#382C2314yes—
591#382C2314yes—
592#381C2314yes—
593#381C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2311yescharacteristic
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616#376C2312yes—
617C43C2311yescharacteristic
618C2×#41—28no—
619C2×#41—44no—
620C2×#41—44no—
621C2×#41—82no—
622C2×#41—84no—
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C22×Q8C2412yes—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×Q8C2414yes—
629C22×Q8C2411yescharacteristic
630C22×D4C2412yes—
631C22×D4C2411yescharacteristic
632C22×D4C2411yescharacteristic
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2411yescharacteristic
638C22×D4C2412yes—
639C22×D4C2412yes—
640C22×D4C2411yescharacteristic
641C22×D4C2414yes—
642C22×D4C2414yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2414yes—
649C23×C4C2412yes—
650C23×C4C2414yes—
651C23×C4C2414yes—
652C4⋊Q8—28no—
653C4⋊Q8—48no—
654C4⋊Q8—42no—
655C4⋊Q8—48no—
656C4⋊Q8—84no—
657#127—42no—
658#127—44no—
659#127—82no—
660#126—48no—
661#126—84no—
662#126—84no—
663#125—216no—
664#125—44no—
665#125—48no—
666#124—24no—
667#124—82no—
668#124—82no—
669#124—84no—
670#124—84no—
671#124—84no—
672#124—84no—
673#123—48no—
674#123—48no—
675#123—84no—
676#123—84no—
677C22⋊Q8—28no—
678C22⋊Q8—48no—
679C22⋊Q8—44no—
680C22⋊Q8—44no—
681C22⋊Q8—44no—
682C22⋊Q8—84no—
683C22⋊Q8—84no—
684C22⋊Q8—84no—
685C22⋊Q8—84no—
686C22⋊Q8—84no—
687C22⋊Q8—84no—
688C22⋊Q8—84no—
689#121—44no—
690#121—44no—
691#121—44no—
692#121—44no—
693#121—84no—
694C4×Q8—42no—
695C4×Q8—44no—
696C4×D4—24no—
697C4×D4—28no—
698C4×D4—42no—
699C4×D4—84no—
700#117—44no—
701#117—48no—
702#117—48no—
703#117—82no—
704#117—82no—
705C2×C4⋊C4—44no—
706C2×C4⋊C4—44no—
707C2×C4⋊C4—44no—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C42—82no—
805C2×C42C2414yes—
806C2×C42C2411yescharacteristic
807C2×C42C2412yes—
808C2×C42C2411yescharacteristic
809C2×C42C2412yes—
810C2×C42C2411yescharacteristic
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2414yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
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—
845#95C2412yes—
846#95C2412yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875C24C2512yes—
876C24C2512yes—
877C24C2512yes—
878C24C2512yes—
879#41—816no—
880#41—816no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—41no—
884C2×Q8—41no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×Q8—42no—
889C2×Q8—44no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—44no—
899C2×Q82−1+414yes—
900C2×D4—22no—
901C2×D4—24no—
902C2×D4—22no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—42no—
907C2×D4—41no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—44no—
919C2×D4—41no—
920C2×D4—42no—
921C2×D4—44no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—41no—
925C2×D4—41no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—42no—
956C22×C4—44no—
957C22×C4C2512yes—
958C22×C4C2514yes—
959C22×C4C2512yes—
960C22×C4C2511yescharacteristic
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2514yes—
966C22×C4C2512yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2511yescharacteristic
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2511yescharacteristic
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—44no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—42no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—41no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—44no—
1007C4⋊C4—42no—
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—42no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4H(5,𝔽2)14yes—
1027C22⋊C4—24no—
1028C22⋊C4—28no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—28no—
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—42no—
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—42no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—42no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C42—28no—
1073C42—22no—
1074C42—24no—
1075C42—22no—
1076C42—24no—
1077C42—42no—
1078C42—42no—
1079C42—44no—
1080C42—42no—
1081C42—44no—
1082C42—44no—
1083C42—41no—
1084C42—42no—
1085C42—42no—
1086C42—44no—
1087C42—42no—
1088C42—44no—
1089C42—44no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—24no—
1099C23—22no—
1100C23—24no—
1101C23—24no—
1102C23—22no—
1103C23—22no—
1104C23—24no—
1105C23—22no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—24no—
1110C23C2611yescharacteristic
1111Q8—44no—
1112Q8—84no—
1113Q8—84no—
1114Q8—162no—
1115Q8—164no—
1116Q8—162no—
1117Q8—164no—
1118D4—44no—
1119D4—84no—
1120D4—82no—
1121D4—84no—
1122D4—84no—
1123D4—84no—
1124D4—88no—
1125D4—88no—
1126D4—162no—
1127D4—162no—
1128D4—161no—
1129D4—161no—
1130D4—164no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—21no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—48no—
1181C2×C4—48no—
1182C2×C4—48no—
1183C2×C4—48no—
1184C2×C4—84no—
1185C2×C4—88no—
1186C2×C4—88no—
1187C2×C4—88no—
1188C2×C4—162no—
1189C2×C4C2×H(5,𝔽2)12yes—
1190C2×C4C2×H(5,𝔽2)14yes—
1191C2×C4C2×2−1+414yes—
1192C2×C4C2×2−1+412yes—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—44no—
1198C22—44no—
1199C22—44no—
1200C22—44no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22C22×H(5,𝔽2)11yescharacteristic
1214C22C22×2−1+411yescharacteristic
1215C22H(7,𝔽2)12yes—
1216C22H(7,𝔽2)11yescharacteristic
1217C222−1+612yes—
1218C4—22no—
1219C4—24no—
1220C4—22no—
1221C4—24no—
1222C4—44no—
1223C4—42no—
1224C4—41no—
1225C4—42no—
1226C4—44no—
1227C4—42no—
1228C4—44no—
1229C4—44no—
1230C4—44no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—44no—
1235C4—44no—
1236C4—42no—
1237C2—82no—
1238C2—82no—
1239C2—82no—
1240C2—82no—
1241C2#6287411yescharacteristic
1242C2#6289411yescharacteristic
1243C2#6297512yes—
1244C2#6304811yescharacteristic
1245C2#6306112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#38956C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58418C2semidirect
2. #58195C2semidirect
3. #58131C2semidirect
4. #58021C2semidirect
5. #56554C2semidirect
6. #56388C2semidirect
7. #56371C2semidirect
8. #53748C2semidirect
9. #53376C2semidirect
10. #53218C2semidirect
11. #52082C2semidirect
12. #51988C2semidirect
13. #51923C2semidirect
14. #51533C2semidirect
15. #49548C2semidirect
16. #46275C2semidirect
17. #46240C2semidirect
18. #46166C2semidirect
19. #45963C2semidirect
21. #38093C2semidirect
22. #37306C2semidirect
23. #37208C2semidirect

Maximal subgroups

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

subgroupindex
#584182
#581952
#581312
#580212
#565542
#563882
#563712
#537482
#533762
#532182
#520822
#519882
#519232
#515332
#495482
#462752
#462402
#461662
#459632
#389562
#380932
#373062
#372082