Finite Group Databasebeta

← #7644057

Subgroups — #7644057

Order 512.

4072 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42398C212yesmaximal, complemented
2#42396C212yesmaximal, complemented
3#42332C212yesmaximal, complemented
4#42330C212yesmaximal, complemented
5#42323C214yesmaximal, complemented
6#42320C214yesmaximal, complemented
7#42319C214yesmaximal, complemented
8#42159C214yesmaximal, complemented
9#41395C212yesmaximal
10#41394C212yesmaximal, complemented
11#41393C212yesmaximal, complemented
12#41392C212yesmaximal
13#37596C214yesmaximal, complemented
14#37585C214yesmaximal, complemented
15#37147C214yesmaximal, complemented
16#37146C214yesmaximal, complemented
17#35461C214yesmaximal, complemented
18#35458C214yesmaximal, complemented
19#35146C211yesmaximal, characteristic, complemented
20#35139C211yesmaximal, characteristic
21#34602C211yesmaximal, characteristic
22C2×#2634C211yesmaximal, characteristic, complemented
23#34239C211yesmaximal, characteristic, complemented
24#34234C211yesmaximal, characteristic
25#34059C211yesmaximal, characteristic, complemented
26C2×#529C2211yescharacteristic
27C22×#125C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29#2863C2214yes—
30#2861C2212yes—
31#2859C2212yes—
32#2839C2214yes—
33#2839C2214yes—
34#2839C2214yes—
35#2838C2214yes—
36#2838C2214yes—
37#2836C2214yes—
38#2833C2214yes—
39#2831C2214yes—
40#2810C2214yes—
41#2807C2214yes—
42#2806C2214yes—
43#2805C2214yes—
44#2805C2214yes—
45#2799C2214yes—
46#2798C2214yes—
47#2796C2214yes—
48#2794C2214yes—
49#2794C2214yes—
50#2791C2214yes—
51#2791C2214yes—
52#2789C2214yes—
53#2788C2214yes—
54#2786C2214yes—
55#2776C2214yes—
56#2776C2214yes—
57#2775C2214yes—
58#2774C2214yes—
59#2774C2214yes—
60#2773C2214yes—
61#2771C2214yes—
62#2767C2214yes—
63#2767C2214yes—
64#2762C2214yes—
65#2762C2214yes—
66#2759C2214yes—
67#2758C2214yes—
68#2755C2214yes—
69#2751C2214yes—
70#2745C2214yes—
71#2740C2214yes—
72#2667C2214yes—
73#2666C2214yes—
74#2666C2214yes—
75#2666C2214yes—
76#2666C2214yes—
77#2666C2214yes—
78#2665C2214yes—
79#2664C2214yes—
80#2655C2214yes—
81#2655C2214yes—
82#2655C2214yes—
83#2655C2214yes—
84#2654C2214yes—
85#2654C2214yes—
86#2652C2214yes—
87#2652C2214yes—
88#2650C2214yes—
89#2650C2214yes—
90#2637C2212yes—
91#2637C2212yes—
92#2634C2212yes—
93#2634C2214yes—
94#2634C2212yes—
95#2634C2212yes—
96#2634C2212yes—
97#2634C2212yes—
98#2634C2212yes—
99#2634C2212yes—
100#2632C2212yes—
101#2627C2212yes—
102#2623C2212yes—
103#2618C2212yes—
104#2614C2212yes—
105#2611C2214yes—
106#2606C2212yes—
107#2606C2212yes—
108#2605C2212yes—
109#2605C2212yes—
110#2596C2214yes—
111#2594C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2586C2214yes—
117#2585C2214yes—
118#2577C2214yes—
119#2577C2214yes—
120#2575C2214yes—
121#2575C2214yes—
122#2574C2214yes—
123#2574C2214yes—
124#2573C2214yes—
125#2573C2214yes—
126#2569C2212yes—
127#2569C2214yes—
128#2566C2212yes—
129#2565C2212yes—
130#2564C2214yes—
131#2549C2212yes—
132#2533C2214yes—
133#2533C2214yes—
134#2533C2214yes—
135#2532C2214yes—
136#2530C2214yes—
137#2529C2214yes—
138#2528C2214yes—
139#2528C2214yes—
140#2528C2214yes—
141#2527C2214yes—
142#2524C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2524C2214yes—
146#2523C2214yes—
147#2522C2214yes—
148#2520C2214yes—
149#2520C2214yes—
150#2517C2214yes—
151#2515C2214yes—
152#2514C2214yes—
153#2510C2214yes—
154#2508C2214yes—
155#2505C2214yes—
156#2505C2214yes—
157#2504C2211yescharacteristic
158#2503C2211yescharacteristic
159#2503C2214yes—
160#2502C2211yescharacteristic
161#2501C2211yescharacteristic
162#2498C2214yes—
163#2493C2214yes—
164#2493C2214yes—
165#2493C2214yes—
166#2493C2214yes—
167#2488C2214yes—
168#2486C2214yes—
169#2484C2214yes—
170#2438C2214yes—
171#2438C2214yes—
172#2419C2214yes—
173#2419C2214yes—
174#2413C2214yes—
175#2413C2214yes—
176#2399C2211yescharacteristic
177#2399C2211yescharacteristic
178#2398C2211yescharacteristic
179#2398C2211yescharacteristic
180#2396C2214yes—
181C2×#400C2212yes—
182C2×#400C2212yes—
183C2×#398C2212yes—
184C2×#395C2212yes—
185#2371C2212yes—
186#2371C2212yes—
187#2370C2214yes—
188#2368C2212yes—
189#2364C2212yes—
190#2359C2214yes—
191#2356C2212yes—
192#2353C2212yes—
193#2347C2212yes—
194#2345C2212yes—
195#2344C2214yes—
196#2344C2212yes—
197#2343C2212yes—
198#2337C2212yes—
199#2336C2212yes—
200#2336C2214yes—
201#2329C2214yes—
202#2322C2214yes—
203#2320C2214yes—
204#2320C2212yes—
205#2320C2212yes—
206#2318C2212yes—
207#2316C2212yes—
208#2313C2212yes—
209#2313C2212yes—
210#2313C2212yes—
211#2310C2212yes—
212C4×#125C2214yes—
213C4×#126C2214yes—
214C4×#123C2214yes—
215#2295C2214yes—
216#2295C2212yes—
217#2295C2212yes—
218C2×#387C2214yes—
219#2283C2212yes—
220#2283C2212yes—
221#2283C2211yescharacteristic
222C2×#383C2211yescharacteristic
223#2275C2212yes—
224#2274C2212yes—
225C4×#117C2211yescharacteristic
226C4×#117C2211yescharacteristic
227C23×Q8C2311yescharacteristic
228#529—28no—
229C2×#126C2312yes—
230C2×#125—28no—
231C2×#125C2312yes—
232C2×#125C2312yes—
233C2×#125C2311yescharacteristic
234C2×#125C2312yes—
235C2×#125C2312yes—
236C2×#124C2311yescharacteristic
237C2×#123C2312yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2314yes—
242C2×#121C2311yescharacteristic
243C2×C4×Q8—28no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2314yes—
265C22×C42C2312yes—
266C22×C42C2311yescharacteristic
267#401C2314yes—
268#401C2314yes—
269#401C2314yes—
270#401C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2312yes—
293#400C2314yes—
294#400C2312yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2312yes—
307#400C2312yes—
308#400C2312yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2312yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2314yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2312yes—
345#398C2312yes—
346#398C2312yes—
347#398C2314yes—
348#398C2312yes—
349#398C2312yes—
350#398C2314yes—
351#398C2314yes—
352#397C2312yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2312yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2312yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2312yes—
379#395C2312yes—
380#395C2312yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#394C2312yes—
385#394C2312yes—
386#393C2314yes—
387#393C2312yes—
388#393C2314yes—
389#393C2314yes—
390#393C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#390C2312yes—
407#390C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#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#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#384C2312yes—
542#384C2312yes—
543#383C2312yes—
544#383C2314yes—
545#383C2314yes—
546#383C2312yes—
547#383C2314yes—
548#383C2314yes—
549#383C2312yes—
550#383C2312yes—
551#383C2311yescharacteristic
552#383C2311yescharacteristic
553#383C2312yes—
554#383C2314yes—
555#383C2314yes—
556#382C2312yes—
557#382C2312yes—
558#382C2312yes—
559#382C2312yes—
560#382C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#381C2312yes—
567#381C2312yes—
568#381C2312yes—
569#381C2312yes—
570#381C2314yes—
571#381C2312yes—
572#381C2314yes—
573#381C2314yes—
574#381C2314yes—
575#381C2312yes—
576#381C2314yes—
577#380C2312yes—
578#380C2314yes—
579#380C2312yes—
580#380C2312yes—
581#380C2312yes—
582#380C2314yes—
583#380C2312yes—
584#380C2312yes—
585#380C2314yes—
586#380C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2311yescharacteristic
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2311yescharacteristic
614C4×C22⋊C4C2311yescharacteristic
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2311yescharacteristic
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2312yes—
623#376C2312yes—
624#376C2312yes—
625#376C2312yes—
626#376C2311yescharacteristic
627#376C2311yescharacteristic
628#376C2314yes—
629#376C2314yes—
630C2×#95C2314yes—
631C2×#95C2312yes—
632C2×#95C2312yes—
633C2×#95C2312yes—
634C2×#95C2312yes—
635C2×#95C2314yes—
636C2×#95C2314yes—
637C43C2312yes—
638C43C2312yes—
639C22×Q8—24no—
640C22×Q8—44no—
641C22×Q8C2412yes—
642C22×Q8C2411yescharacteristic
643C22×Q8C2411yescharacteristic
644C22×Q8C2411yescharacteristic
645C22×Q8C2414yes—
646C22×D4C2412yes—
647C22×D4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2414yes—
654C23×C4C2412yes—
655C23×C4C2414yes—
656C23×C4C2411yescharacteristic
657C23×C4C2411yescharacteristic
658#126—28no—
659#125—28no—
660#125—28no—
661#125—28no—
662#125—28no—
663#125—24no—
664#124—24no—
665#123—28no—
666#123—48no—
667#123—48no—
668C22⋊Q8—24no—
669C22⋊Q8—48no—
670#121—24no—
671C4×Q8—28no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—28no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×D4—28no—
679C4×D4—24no—
680C4×D4—48no—
681#117—28no—
682#117—44no—
683#117—48no—
684#117—44no—
685C2×C4⋊C4—28no—
686C2×C4⋊C4—24no—
687C2×C4⋊C4—24no—
688C2×C4⋊C4—28no—
689C2×C4⋊C4—28no—
690C2×C4⋊C4—24no—
691C2×C4⋊C4—48no—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×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×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C42—28no—
770C2×C42#4118yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797#95C2412yes—
798#95C2412yes—
799#95C2412yes—
800#95C2412yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2412yes—
809#95C2414yes—
810#95C2414yes—
811#95C2412yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2412yes—
822#95C2414yes—
823#95C2414yes—
824#95C2412yes—
825#95C2412yes—
826#95C2412yes—
827#95C2412yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2412yes—
834#95C2412yes—
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#95C2414yes—
856#95C2414yes—
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—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878C24C2512yes—
879C24C2511yescharacteristic
880C2×Q8—24no—
881C2×Q8—22no—
882C2×Q8—22no—
883C2×Q8—22no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—416no—
893C2×D4—24no—
894C2×D4—28no—
895C2×D4—22no—
896C2×D4—42no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—28no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—28no—
906C22×C4—24no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—44no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4C2×#4114yes—
919C22×C4C2×#4114yes—
920C22×C4C2×#4114yes—
921C22×C4C2514yes—
922C22×C4C2514yes—
923C22×C4C2514yes—
924C22×C4C2512yes—
925C22×C4C2514yes—
926C22×C4C2514yes—
927C22×C4C2512yes—
928C22×C4C2512yes—
929C22×C4C2512yes—
930C22×C4C2514yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2514yes—
935C22×C4C2514yes—
936C22×C4C2512yes—
937C22×C4C2514yes—
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—22no—
962C4⋊C4—24no—
963C4⋊C4—22no—
964C4⋊C4—24no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C22⋊C4—24no—
1001C22⋊C4—24no—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—28no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—24no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C42—24no—
1022C42—24no—
1023C42—24no—
1024C42—24no—
1025C42—24no—
1026C42—42no—
1027C42—42no—
1028C42—44no—
1029C42—44no—
1030C42—42no—
1031C42—42no—
1032C42—42no—
1033C42—42no—
1034C42—44no—
1035C42—44no—
1036C42—44no—
1037C42—44no—
1038C42—44no—
1039C42—44no—
1040C42—44no—
1041C42—44no—
1042C42—44no—
1043C42C2×#4114yes—
1044C42C2×#4114yes—
1045C42C2×#4114yes—
1046C42C2×#4114yes—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—24no—
1051C23—22no—
1052C23—24no—
1053C23—22no—
1054C23C22×#4112yes—
1055C23#58514yes—
1056C23C2611yescharacteristic
1057Q8—48no—
1058Q8—44no—
1059Q8—44no—
1060Q8—82no—
1061Q8—164no—
1062D4—48no—
1063D4—82no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—28no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—48no—
1121C2×C4—48no—
1122C2×C4—84no—
1123C2×C4—84no—
1124C2×C4—84no—
1125C2×C4—88no—
1126C2×C4—164no—
1127C2×C4C22×#4112yes—
1128C2×C4C22×#4112yes—
1129C2×C4C22×#4112yes—
1130C2×C4C22×#4112yes—
1131C2×C4C22×#4112yes—
1132C2×C4C22×#4112yes—
1133C22—22no—
1134C22—22no—
1135C22—28no—
1136C22—42no—
1137C22—42no—
1138C22—44no—
1139C22—44no—
1140C22—42no—
1141C22#345514yes—
1142C22C23×#4111yescharacteristic
1143C22C2×#58512yes—
1144C222−1+612yes—
1145C222−1+612yes—
1146C4—22no—
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—22no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—44no—
1156C4—42no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—44no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C2—24no—
1170C2—82no—
1171C2C2×#345511yescharacteristic
1172C2#6286011yescharacteristic
1173C2#6286011yescharacteristic
1174C2#6287314yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42398C2semidirect
2. #42396C2semidirect
3. #42332C2semidirect
4. #42330C2semidirect
5. #42323C2semidirect
6. #42320C2semidirect
7. #42319C2semidirect
8. #42159C2semidirect
10. #41394C2semidirect
11. #41393C2semidirect
13. #37596C2semidirect
14. #37585C2semidirect
15. #37147C2semidirect
16. #37146C2semidirect
17. #35461C2semidirect
18. #35458C2semidirect
19. #35146C2semidirect
22. C2×#2634C2semidirect
23. #34239C2semidirect
25. #34059C2semidirect

Maximal subgroups

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

subgroupindex
#423982
#423962
#423322
#423302
#423232
#423202
#423192
#421592
#413952
#413942
#413932
#413922
#375962
#375852
#371472
#371462
#354612
#354582
#351462
#351392
#346022
C2×#26342
#342392
#342342
#340592