Finite Group Databasebeta

← #8057950

Subgroups — #8057950

Order 512.

4461 conjugacy classes of subgroups.

The subgroup lattice has 1223 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52072C212yesmaximal, complemented
2#51988C212yesmaximal, complemented
3#51820C214yesmaximal, complemented
4#51726C212yesmaximal, complemented
5#50624C214yesmaximal, complemented
6#50098C214yesmaximal, complemented
7#47548C214yesmaximal, complemented
8#47546C212yesmaximal, complemented
9#46316C212yesmaximal, complemented
10#46313C211yesmaximal, characteristic, complemented
11#45336C212yesmaximal, complemented
12#44665C214yesmaximal, complemented
13#42106C214yesmaximal, complemented
14#41654C214yesmaximal, complemented
15#41498C214yesmaximal, complemented
16#39363C211yesmaximal, characteristic
17#38527C214yesmaximal, complemented
18#38473C212yesmaximal, complemented
19#38093C212yesmaximal
20#37145C212yesmaximal, complemented
21#36928C214yesmaximal, complemented
22#34491C211yesmaximal, characteristic, complemented
23#34413C212yesmaximal, complemented
24C2×Q82C2211yescharacteristic
25C2×#557C2212yes—
26C2×#552C2212yes—
27C2×#550C2211yescharacteristic
28C2×D4×Q8C2211yescharacteristic
29C2×#536C2212yes—
30#2863C2212yes—
31#2858C2211yescharacteristic
32#2855C2214yes—
33#2850C2212yes—
34#2843C2212yes—
35#2832C2214yes—
36#2832C2212yes—
37#2830C2214yes—
38#2811C2211yescharacteristic
39#2809C2211yescharacteristic
40#2808C2212yes—
41#2808C2212yes—
42#2808C2212yes—
43#2808C2214yes—
44#2806C2212yes—
45#2806C2212yes—
46#2804C2212yes—
47#2800C2214yes—
48#2792C2214yes—
49#2786C2214yes—
50#2785C2214yes—
51#2785C2212yes—
52#2784C2214yes—
53#2783C2214yes—
54#2782C2212yes—
55#2781C2214yes—
56#2779C2214yes—
57#2777C2214yes—
58#2775C2214yes—
59#2767C2214yes—
60#2766C2214yes—
61#2765C2214yes—
62#2764C2214yes—
63#2762C2214yes—
64#2761C2214yes—
65#2759C2214yes—
66#2757C2214yes—
67#2755C2214yes—
68#2751C2214yes—
69#2737C2214yes—
70#2737C2214yes—
71#2734C2212yes—
72#2734C2212yes—
73#2732C2212yes—
74#2731C2214yes—
75#2727C2212yes—
76#2726C2212yes—
77#2719C2214yes—
78#2716C2214yes—
79#2715C2214yes—
80#2713C2214yes—
81#2713C2214yes—
82#2709C2214yes—
83#2709C2214yes—
84#2704C2214yes—
85#2700C2214yes—
86#2700C2214yes—
87#2694C2214yes—
88#2692C2214yes—
89#2691C2214yes—
90#2691C2214yes—
91#2690C2214yes—
92#2690C2214yes—
93#2681C2214yes—
94#2681C2214yes—
95#2677C2214yes—
96#2677C2214yes—
97#2674C2214yes—
98#2674C2214yes—
99#2666C2214yes—
100#2653C2214yes—
101#2651C2214yes—
102#2651C2214yes—
103#2651C2214yes—
104#2650C2214yes—
105#2649C2214yes—
106#2641C2212yes—
107#2637C2214yes—
108#2632C2214yes—
109#2620C2212yes—
110#2620C2212yes—
111#2599C2214yes—
112#2599C2214yes—
113#2599C2214yes—
114#2597C2214yes—
115#2595C2214yes—
116#2593C2214yes—
117#2585C2214yes—
118#2581C2212yes—
119#2578C2214yes—
120#2577C2214yes—
121#2576C2214yes—
122#2574C2214yes—
123#2572C2212yes—
124#2570C2214yes—
125#2565C2212yes—
126#2560C2214yes—
127#2560C2214yes—
128#2558C2214yes—
129#2548C2211yescharacteristic
130#2548C2212yes—
131#2546C2211yescharacteristic
132#2536C2212yes—
133#2532C2214yes—
134#2531C2214yes—
135#2531C2214yes—
136#2529C2214yes—
137#2528C2214yes—
138#2526C2214yes—
139#2524C2214yes—
140#2523C2214yes—
141#2523C2214yes—
142#2522C2214yes—
143#2521C2214yes—
144#2520C2214yes—
145#2520C2214yes—
146#2519C2214yes—
147#2518C2214yes—
148#2518C2214yes—
149#2516C2214yes—
150#2504C2212yes—
151#2500C2212yes—
152#2478C2214yes—
153#2476C2214yes—
154#2476C2214yes—
155#2475C2214yes—
156#2473C2214yes—
157#2469C2214yes—
158#2469C2214yes—
159#2465C2214yes—
160#2465C2214yes—
161#2465C2214yes—
162#2465C2214yes—
163#2465C2214yes—
164#2465C2214yes—
165#2462C2214yes—
166#2462C2214yes—
167#2460C2214yes—
168#2460C2214yes—
169#2460C2214yes—
170#2458C2214yes—
171#2458C2214yes—
172#2458C2214yes—
173#2458C2214yes—
174#2452C2214yes—
175#2445C2214yes—
176#2439C2214yes—
177#2436C2212yes—
178#2434C2214yes—
179#2432C2212yes—
180#2432C2212yes—
181#2432C2212yes—
182#2429C2214yes—
183#2421C2214yes—
184#2398C2212yes—
185#2396C2214yes—
186#2381C2212yes—
187#2381C2212yes—
188#2381C2212yes—
189#2381C2212yes—
190#2376C2214yes—
191#2374C2214yes—
192#2369C2212yes—
193#2369C2211yescharacteristic
194#2365C2214yes—
195#2362C2214yes—
196#2360C2214yes—
197#2356C2214yes—
198#2355C2212yes—
199#2347C2214yes—
200Q8×C22⋊C4C2214yes—
201#2337C2214yes—
202#2337C2214yes—
203#2336C2214yes—
204#2335C2214yes—
205#2335C2214yes—
206#2331C2214yes—
207#2327C2212yes—
208#2327C2212yes—
209#2327C2212yes—
210#2323C2214yes—
211#2320C2214yes—
212#2311C2212yes—
213C4×C4⋊Q8C2211yescharacteristic
214C4×C22⋊Q8C2214yes—
215#2297C2212yes—
216#2295C2212yes—
217#2293C2211yescharacteristic
218#2290C2212yes—
219C22×#41C2312yes—
220C23×Q8C2312yes—
221Q82—28no—
222#557—48no—
223#552—48no—
224#550—44no—
225D4×Q8—44no—
226#536—216no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×#127C2311yescharacteristic
236C2×#127C2312yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#125C2314yes—
240C2×#125C2312yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×#121C2312yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2314yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×#117C2312yes—
276C2×#117C2312yes—
277C2×#117C2314yes—
278C2×#117C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C42C2312yes—
281#401C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2312yes—
285#400C2314yes—
286#400C2314yes—
287#400C2312yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#399C2314yes—
295#399C2314yes—
296#399C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
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#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
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#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2312yes—
345#395C2314yes—
346#395C2312yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2312yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2312yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#391C2312yes—
387#391C2314yes—
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2314yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2312yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#390C2314yes—
412#390C2314yes—
413#390C2312yes—
414#390C2312yes—
415#390C2312yes—
416#390C2314yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2312yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
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#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
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#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
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#385C2314yes—
564#385C2314yes—
565#384C2311yescharacteristic
566#384C2312yes—
567#383C2314yes—
568#383C2314yes—
569#383C2314yes—
570#383C2314yes—
571#383C2314yes—
572#383C2314yes—
573#382C2312yes—
574#382C2314yes—
575#382C2314yes—
576#382C2312yes—
577#382C2312yes—
578#382C2314yes—
579#382C2312yes—
580#382C2314yes—
581#381C2314yes—
582#381C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2311yescharacteristic
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2312yes—
616#376C2314yes—
617#376C2312yes—
618#376C2312yes—
619C43C2311yescharacteristic
620C2×#41—28no—
621C2×#41—44no—
622C2×#41—82no—
623C22×Q8—28no—
624C22×Q8—44no—
625C22×Q8—82no—
626C22×Q8C2414yes—
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2411yescharacteristic
634C22×Q8C2411yescharacteristic
635C22×D4C2411yescharacteristic
636C22×D4C2412yes—
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2412yes—
640C22×D4C2411yescharacteristic
641C22×D4C2412yes—
642C22×D4C2411yescharacteristic
643C22×D4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2414yes—
650C4⋊Q8—28no—
651C4⋊Q8—28no—
652C4⋊Q8—28no—
653C4⋊Q8—216no—
654C4⋊Q8—28no—
655C4⋊Q8—42no—
656C4⋊Q8—48no—
657C4⋊Q8#4118yes—
658#127—44no—
659#127—42no—
660#126—48no—
661#126—84no—
662#125—216no—
663#125—44no—
664#125—48no—
665#125—48no—
666#124—28no—
667#124—28no—
668#124—82no—
669#124—82no—
670#124—82no—
671#123—216no—
672#123—216no—
673#123—48no—
674C22⋊Q8—216no—
675C22⋊Q8—216no—
676C22⋊Q8—48no—
677C22⋊Q8—44no—
678C22⋊Q8—44no—
679C22⋊Q8—44no—
680C22⋊Q8—84no—
681C22⋊Q8—84no—
682#121—44no—
683#121—44no—
684#121—44no—
685C4×Q8—216no—
686C4×Q8—28no—
687C4×Q8—42no—
688C4×Q8—42no—
689C4×Q8—44no—
690C4×Q8—48no—
691C4×Q8—44no—
692C4×Q8—44no—
693C4×Q8—48no—
694C4×Q8—84no—
695C4×D4—24no—
696C4×D4—28no—
697C4×D4—44no—
698#117—28no—
699#117—44no—
700#117—48no—
701#117—82no—
702C2×C4⋊C4—44no—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C42—82no—
792C2×C42C2414yes—
793C2×C42C2412yes—
794C2×C42C2412yes—
795C2×C42C2412yes—
796C2×C42C2411yescharacteristic
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2412yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2411yescharacteristic
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2411yescharacteristic
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—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2412yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875C24C2512yes—
876C24C2512yes—
877C24C2512yes—
878#41—816no—
879C2×Q8—24no—
880C2×Q8—28no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—28no—
885C2×Q8—42no—
886C2×Q8—41no—
887C2×Q8—41no—
888C2×Q8—44no—
889C2×Q8—41no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—44no—
893C2×Q8—41no—
894C2×Q8—42no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—816no—
904C2×Q8C2×#4114yes—
905C2×Q8C2×#4114yes—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—22no—
910C2×D4—24no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—41no—
922C2×D4—41no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—44no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—28no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
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×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2514yes—
948C22×C4C2514yes—
949C22×C4C2512yes—
950C22×C4C2512yes—
951C22×C4C2511yescharacteristic
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2512yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2511yescharacteristic
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2511yescharacteristic
964C22×C4C2512yes—
965C4⋊C4—28no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—24no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—44no—
984C4⋊C4—42no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—42no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—41no—
1002C4⋊C4—42no—
1003C4⋊C4—41no—
1004C4⋊C4—44no—
1005C4⋊C4—42no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—42no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—42no—
1015C4⋊C4C2×#41116yes—
1016C4⋊C4H(5,𝔽2)14yes—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
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—
1053C42—24no—
1054C42—24no—
1055C42—24no—
1056C42—28no—
1057C42—28no—
1058C42—24no—
1059C42—22no—
1060C42—24no—
1061C42—42no—
1062C42—44no—
1063C42—42no—
1064C42—42no—
1065C42—44no—
1066C42—42no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C42—42no—
1071C42—44no—
1072C42—44no—
1073C42—44no—
1074C42—42no—
1075C42—44no—
1076C42—41no—
1077C42C2×#4114yes—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23—24no—
1091C23—24no—
1092C23—24no—
1093C23C2611yescharacteristic
1094Q8—44no—
1095Q8—44no—
1096Q8—416no—
1097Q8—48no—
1098Q8—48no—
1099Q8—84no—
1100Q8—84no—
1101Q8—84no—
1102Q8—162no—
1103D4—44no—
1104D4—84no—
1105D4—84no—
1106D4—84no—
1107D4—84no—
1108D4—162no—
1109D4—162no—
1110D4—161no—
1111D4—161no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—48no—
1163C2×C4—48no—
1164C2×C4—48no—
1165C2×C4—88no—
1166C2×C4—88no—
1167C2×C4—88no—
1168C2×C4C22×#4114yes—
1169C2×C4C22×#4112yes—
1170C2×C4C22×#4114yes—
1171C2×C4C22×#4114yes—
1172C2×C4C2×H(5,𝔽2)12yes—
1173C2×C4C2×H(5,𝔽2)14yes—
1174C22—44no—
1175C22—44no—
1176C22—44no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—44no—
1184C22—44no—
1185C22—44no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22C23×#4111yescharacteristic
1190C22C22×H(5,𝔽2)11yescharacteristic
1191C22H(7,𝔽2)11yescharacteristic
1192C222−1+612yes—
1193C222−1+612yes—
1194C4—24no—
1195C4—22no—
1196C4—24no—
1197C4—24no—
1198C4—24no—
1199C4—22no—
1200C4—44no—
1201C4—44no—
1202C4—44no—
1203C4—42no—
1204C4—44no—
1205C4—44no—
1206C4—42no—
1207C4—41no—
1208C4—44no—
1209C4—42no—
1210C4—44no—
1211C4—44no—
1212C4—44no—
1213C4—44no—
1214C2—82no—
1215C2—82no—
1216C2—82no—
1217C2#6285012yes—
1218C2#6288611yescharacteristic
1219C2#6297712yes—
1220C2#6298311yescharacteristic
1221C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52072C2semidirect
2. #51988C2semidirect
3. #51820C2semidirect
4. #51726C2semidirect
5. #50624C2semidirect
6. #50098C2semidirect
7. #47548C2semidirect
8. #47546C2semidirect
9. #46316C2semidirect
10. #46313C2semidirect
11. #45336C2semidirect
12. #44665C2semidirect
13. #42106C2semidirect
14. #41654C2semidirect
15. #41498C2semidirect
17. #38527C2semidirect
18. #38473C2semidirect
20. #37145C2semidirect
21. #36928C2semidirect
22. #34491C2semidirect
23. #34413C2semidirect

Maximal subgroups

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

subgroupindex
#520722
#519882
#518202
#517262
#506242
#500982
#475482
#475462
#463162
#463132
#453362
#446652
#421062
#416542
#414982
#393632
#385272
#384732
#380932
#371452
#369282
#344912
#344132