Finite Group Databasebeta

← #9040126

Subgroups — #9040126

Order 512.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57990C214yesmaximal, complemented
2#56040C214yesmaximal, complemented
3#55164C214yesmaximal, complemented
4#55112C214yesmaximal, complemented
5#55049C214yesmaximal, complemented
6#54998C214yesmaximal, complemented
7#52083C211yesmaximal, characteristic
8#51681C212yesmaximal, complemented
9#51542C211yesmaximal, characteristic, complemented
10#51317C212yesmaximal, complemented
11#51089C212yesmaximal, complemented
12#51071C212yesmaximal, complemented
13#48110C214yesmaximal, complemented
14#47907C214yesmaximal, complemented
15#42681C212yesmaximal, complemented
16#42163C212yesmaximal, complemented
17#41248C214yesmaximal, complemented
18#40530C214yesmaximal, complemented
19#37233C212yesmaximal, complemented
20#36836C212yesmaximal, complemented
21#36821C212yesmaximal, complemented
22#35738C212yesmaximal, complemented
23#35667C211yesmaximal, characteristic, complemented
24C2×#563C2211yescharacteristic
25C2×#559C2212yes—
26C2×#555C2211yescharacteristic
27C2×#554C2212yes—
28C2×#539C2212yes—
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C2×#519C2211yescharacteristic
33#2853C2214yes—
34#2838C2214yes—
35#2838C2214yes—
36#2836C2214yes—
37#2832C2214yes—
38#2826C2214yes—
39#2820C2214yes—
40#2816C2214yes—
41#2814C2214yes—
42#2811C2212yes—
43#2806C2214yes—
44#2805C2214yes—
45#2801C2214yes—
46#2800C2214yes—
47#2798C2214yes—
48#2798C2214yes—
49#2796C2214yes—
50#2791C2214yes—
51#2789C2214yes—
52#2789C2214yes—
53#2788C2214yes—
54#2788C2214yes—
55#2784C2214yes—
56#2776C2214yes—
57#2776C2214yes—
58#2775C2214yes—
59#2774C2214yes—
60#2771C2214yes—
61#2766C2214yes—
62#2762C2214yes—
63#2760C2214yes—
64#2759C2214yes—
65#2759C2214yes—
66#2756C2214yes—
67#2752C2214yes—
68#2751C2214yes—
69#2743C2214yes—
70#2743C2214yes—
71#2742C2214yes—
72#2739C2214yes—
73#2739C2214yes—
74#2738C2214yes—
75#2734C2212yes—
76#2733C2212yes—
77#2731C2212yes—
78#2731C2212yes—
79#2724C2212yes—
80#2717C2212yes—
81#2717C2214yes—
82#2716C2214yes—
83#2716C2214yes—
84#2716C2214yes—
85#2713C2214yes—
86#2713C2214yes—
87#2712C2214yes—
88#2710C2214yes—
89#2710C2214yes—
90#2709C2214yes—
91#2709C2212yes—
92#2706C2214yes—
93#2702C2214yes—
94#2700C2214yes—
95#2700C2214yes—
96#2700C2214yes—
97#2700C2214yes—
98#2698C2214yes—
99#2696C2214yes—
100#2692C2214yes—
101#2690C2214yes—
102#2686C2214yes—
103#2681C2214yes—
104#2680C2214yes—
105#2677C2214yes—
106#2677C2214yes—
107#2676C2214yes—
108#2674C2214yes—
109#2674C2214yes—
110#2674C2214yes—
111#2673C2214yes—
112#2665C2214yes—
113#2662C2214yes—
114#2660C2212yes—
115#2653C2214yes—
116#2653C2214yes—
117#2650C2214yes—
118#2648C2214yes—
119#2644C2214yes—
120#2637C2214yes—
121#2634C2212yes—
122#2634C2212yes—
123#2631C2212yes—
124#2630C2214yes—
125#2630C2214yes—
126#2628C2212yes—
127#2625C2214yes—
128#2623C2214yes—
129#2618C2214yes—
130#2612C2214yes—
131#2611C2212yes—
132#2611C2212yes—
133#2608C2214yes—
134#2607C2212yes—
135#2605C2214yes—
136#2605C2212yes—
137#2598C2212yes—
138#2598C2212yes—
139#2596C2214yes—
140#2591C2212yes—
141#2591C2212yes—
142#2583C2212yes—
143#2579C2214yes—
144#2576C2214yes—
145#2576C2214yes—
146#2573C2214yes—
147#2572C2214yes—
148#2572C2214yes—
149#2568C2212yes—
150#2565C2214yes—
151#2562C2212yes—
152#2557C2214yes—
153#2553C2214yes—
154#2553C2214yes—
155#2546C2212yes—
156#2546C2212yes—
157#2545C2212yes—
158#2545C2212yes—
159#2536C2212yes—
160#2531C2214yes—
161#2528C2214yes—
162#2527C2214yes—
163#2526C2214yes—
164#2521C2214yes—
165#2492C2214yes—
166#2484C2214yes—
167#2481C2214yes—
168#2477C2214yes—
169#2477C2214yes—
170#2477C2214yes—
171#2474C2214yes—
172#2471C2214yes—
173#2467C2214yes—
174#2465C2214yes—
175#2465C2214yes—
176#2465C2214yes—
177#2465C2214yes—
178#2463C2214yes—
179#2462C2214yes—
180#2461C2214yes—
181#2460C2214yes—
182#2451C2214yes—
183#2449C2214yes—
184#2441C2214yes—
185#2440C2214yes—
186#2439C2214yes—
187#2436C2212yes—
188#2434C2212yes—
189#2431C2212yes—
190#2429C2214yes—
191#2429C2214yes—
192#2422C2214yes—
193#2421C2214yes—
194#2420C2214yes—
195#2417C2214yes—
196#2413C2214yes—
197#2413C2214yes—
198#2409C2214yes—
199#2406C2212yes—
200#2398C2212yes—
201#2398C2212yes—
202#2392C2212yes—
203#2381C2211yescharacteristic
204#2381C2212yes—
205#2376C2212yes—
206#2372C2212yes—
207#2372C2211yescharacteristic
208#2360C2214yes—
209#2356C2212yes—
210#2352C2214yes—
211#2336C2212yes—
212#2333C2212yes—
213#2319C2212yes—
214#2313C2212yes—
215#2313C2212yes—
216#2310C2211yescharacteristic
217#2297C2211yescharacteristic
218#2296C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222#563—44no—
223#559—48no—
224#555—44no—
225#554—48no—
226#539—48no—
227#536—44no—
228#536—44no—
229C2×C4⋊Q8—44no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2311yescharacteristic
239C2×#127C2312yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2312yes—
243C2×#125C2314yes—
244C2×#125C2312yes—
245C2×#124C2311yescharacteristic
246C2×#124C2314yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2311yescharacteristic
252C2×#124C2314yes—
253C2×#123C2312yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2312yes—
258C2×#123C2312yes—
259C2×#123C2314yes—
260C2×#123C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×#121C2314yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273#519—44no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2314yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2314yes—
294C22×C42C2311yescharacteristic
295#401C2314yes—
296#401C2314yes—
297#401C2314yes—
298#400C2314yes—
299#400C2312yes—
300#400C2312yes—
301#400C2312yes—
302#400C2312yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2312yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2312yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2312yes—
325#399C2312yes—
326#398C2314yes—
327#398C2314yes—
328#398C2312yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2312yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2312yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#394C2312yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2312yes—
405#394C2312yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#392C2314yes—
423#392C2312yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2312yes—
450#390C2314yes—
451#390C2314yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
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#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
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#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2312yes—
562#386C2314yes—
563#386C2312yes—
564#386C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#384C2314yes—
580#383C2314yes—
581#383C2312yes—
582#383C2314yes—
583#383C2312yes—
584#382C2314yes—
585#382C2314yes—
586#382C2312yes—
587#382C2314yes—
588#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#381C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620#376C2312yes—
621#376C2314yes—
622#376C2312yes—
623C2×#41—42no—
624C2×#41—42no—
625C2×#41—42no—
626C22×Q8—24no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8—42no—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2411yescharacteristic
636C22×Q8C2411yescharacteristic
637C22×Q8C2411yescharacteristic
638C22×Q8C2414yes—
639C22×Q8C2412yes—
640C22×Q8C2414yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2411yescharacteristic
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2412yes—
648C22×D4C2414yes—
649C23×C4C2411yescharacteristic
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2414yes—
658C23×C4C2412yes—
659C23×C4C2411yescharacteristic
660C4⋊Q8—24no—
661C4⋊Q8—44no—
662C4⋊Q8—42no—
663C4⋊Q8—44no—
664C4⋊Q8—48no—
665C4⋊Q8—44no—
666C4⋊Q8—44no—
667C4⋊Q8—44no—
668C4⋊Q8—44no—
669#127—44no—
670#126—48no—
671#126—48no—
672#125—28no—
673#125—48no—
674#125—44no—
675#124—24no—
676#124—48no—
677#124—42no—
678#124—48no—
679#124—44no—
680#124—44no—
681#124—44no—
682#124—44no—
683#123—28no—
684#123—48no—
685#123—44no—
686#123—48no—
687#123—48no—
688#123—44no—
689#123—48no—
690#123—44no—
691C22⋊Q8—44no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700#121—44no—
701#121—48no—
702#121—44no—
703C4×Q8—28no—
704C4×Q8—44no—
705C4×Q8—44no—
706C4×Q8—48no—
707C4×Q8—44no—
708C4×D4—216no—
709C4×D4—28no—
710C4×D4—44no—
711C4×D4—44no—
712C4×D4—48no—
713#117—24no—
714#117—44no—
715#117—44no—
716#117—42no—
717#117—42no—
718#117—48no—
719C2×C4⋊C4—28no—
720C2×C4⋊C4—44no—
721C2×C4⋊C4—48no—
722C2×C4⋊C4—44no—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C42—42no—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2411yescharacteristic
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2411yescharacteristic
818C2×C42C2412yes—
819C2×C42C2411yescharacteristic
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2411yescharacteristic
833#95C2412yes—
834#95C2412yes—
835#95C2414yes—
836#95C2414yes—
837#95C2412yes—
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#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
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—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891C24C2512yes—
892C24C2514yes—
893C24C2511yescharacteristic
894#41—88no—
895C2×Q8—24no—
896C2×Q8—24no—
897C2×Q8—24no—
898C2×Q8—22no—
899C2×Q8—22no—
900C2×Q8—22no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—42no—
904C2×Q8—42no—
905C2×Q8—44no—
906C2×Q8—42no—
907C2×Q8—41no—
908C2×Q8—41no—
909C2×Q8—42no—
910C2×Q8—41no—
911C2×Q8—41no—
912C2×Q8—41no—
913C2×Q8—44no—
914C2×Q8—44no—
915C2×Q8—41no—
916C2×Q8—42no—
917C2×Q8—44no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—44no—
921C2×Q8—44no—
922C2×Q8—416no—
923C2×Q8—88no—
924C2×D4—28no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—22no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—42no—
931C2×D4—41no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—41no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—44no—
946C2×D4—44no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—24no—
951C22×C4—22no—
952C22×C4—24no—
953C22×C4—28no—
954C22×C4—28no—
955C22×C4—24no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—44no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—44no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4—42no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—42no—
971C22×C4—44no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4H(5,𝔽2)14yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2514yes—
994C22×C4C2511yescharacteristic
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—24no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
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—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C22⋊C4—24no—
1046C22⋊C4—28no—
1047C22⋊C4—24no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—42no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—42no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
1084C22⋊C4—44no—
1085C42—22no—
1086C42—24no—
1087C42—24no—
1088C42—28no—
1089C42—42no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—42no—
1095C42—42no—
1096C42—42no—
1097C42—41no—
1098C42—41no—
1099C42—42no—
1100C42—42no—
1101C42—44no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42H(5,𝔽2)14yes—
1107C23—21no—
1108C23—21no—
1109C23—24no—
1110C23—22no—
1111C23—22no—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—22no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23—24no—
1122C23C2×H(5,𝔽2)12yes—
1123C23C2611yescharacteristic
1124Q8—48no—
1125Q8—48no—
1126Q8—84no—
1127Q8—82no—
1128Q8—82no—
1129Q8—82no—
1130Q8—88no—
1131Q8—162no—
1132Q8—164no—
1133D4—48no—
1134D4—82no—
1135D4—88no—
1136D4—84no—
1137D4—88no—
1138D4—162no—
1139D4—162no—
1140D4—164no—
1141C2×C4—28no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—44no—
1195C2×C4—48no—
1196C2×C4—44no—
1197C2×C4—88no—
1198C2×C4—88no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—162no—
1203C2×C4—164no—
1204C2×C4C2×H(5,𝔽2)14yes—
1205C2×C4C2×H(5,𝔽2)14yes—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4#58512yes—
1208C22—22no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—42no—
1222C22—44no—
1223C22—44no—
1224C22C22×H(5,𝔽2)11yescharacteristic
1225C22C22×H(5,𝔽2)11yescharacteristic
1226C22C2×#58511yescharacteristic
1227C222−1+614yes—
1228C4—22no—
1229C4—22no—
1230C4—24no—
1231C4—24no—
1232C4—42no—
1233C4—44no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—44no—
1238C4—44no—
1239C4—44no—
1240C4—44no—
1241C4—42no—
1242C4—44no—
1243C4—42no—
1244C4—44no—
1245C4—42no—
1246C4—44no—
1247C4—44no—
1248C2—42no—
1249C2—82no—
1250C2—84no—
1251C2#6281811yescharacteristic
1252C2#6288612yes—
1253C2#6288712yes—
1254C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52083C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57990C2semidirect
2. #56040C2semidirect
3. #55164C2semidirect
4. #55112C2semidirect
5. #55049C2semidirect
6. #54998C2semidirect
8. #51681C2semidirect
9. #51542C2semidirect
10. #51317C2semidirect
11. #51089C2semidirect
12. #51071C2semidirect
13. #48110C2semidirect
14. #47907C2semidirect
15. #42681C2semidirect
16. #42163C2semidirect
17. #41248C2semidirect
18. #40530C2semidirect
19. #37233C2semidirect
20. #36836C2semidirect
21. #36821C2semidirect
22. #35738C2semidirect
23. #35667C2semidirect

Maximal subgroups

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

subgroupindex
#579902
#560402
#551642
#551122
#550492
#549982
#520832
#516812
#515422
#513172
#510892
#510712
#481102
#479072
#426812
#421632
#412482
#405302
#372332
#368362
#368212
#357382
#356672