Finite Group Databasebeta

← #7657153

Subgroups — #7657153

Order 512.

4222 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42354C214yesmaximal, complemented
2#42330C212yesmaximal, complemented
3#42241C214yesmaximal, complemented
4#42215C214yesmaximal, complemented
5#42211C214yesmaximal, complemented
6#42199C214yesmaximal, complemented
7#42162C212yesmaximal, complemented
8#39559C214yesmaximal, complemented
9#39473C212yesmaximal, complemented
10#39151C212yesmaximal, complemented
11#38259C214yesmaximal, complemented
12#37562C211yesmaximal, characteristic, complemented
13#37557C211yesmaximal, characteristic
14#37466C212yesmaximal, complemented
15#37463C212yesmaximal
16#36569C212yesmaximal, complemented
17#36358C212yesmaximal, complemented
18#36008C212yesmaximal, complemented
19#35835C214yesmaximal, complemented
20#35760C212yesmaximal, complemented
21#35179C211yesmaximal, characteristic, complemented
22#35013C212yesmaximal, complemented
23#34602C211yesmaximal, characteristic
24#34584C212yesmaximal
25#34221C211yesmaximal, characteristic, complemented
26#34220C211yesmaximal, characteristic
27C2×#2356C211yesmaximal, characteristic, complemented
28C2×#533C2211yescharacteristic
29C2×#529C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31#2855C2212yes—
32#2855C2212yes—
33#2855C2214yes—
34#2851C2214yes—
35#2843C2214yes—
36#2839C2214yes—
37#2838C2214yes—
38#2833C2214yes—
39#2831C2214yes—
40#2821C2212yes—
41#2821C2212yes—
42#2799C2214yes—
43#2798C2214yes—
44#2798C2214yes—
45#2793C2214yes—
46#2791C2214yes—
47#2789C2214yes—
48#2777C2214yes—
49#2777C2214yes—
50#2774C2214yes—
51#2773C2214yes—
52#2773C2214yes—
53#2773C2214yes—
54#2767C2214yes—
55#2766C2214yes—
56#2762C2214yes—
57#2762C2214yes—
58#2762C2214yes—
59#2759C2214yes—
60#2759C2214yes—
61#2758C2214yes—
62#2758C2214yes—
63#2755C2214yes—
64#2754C2214yes—
65#2754C2214yes—
66#2666C2214yes—
67#2666C2214yes—
68#2666C2214yes—
69#2666C2214yes—
70#2659C2212yes—
71#2659C2212yes—
72#2655C2214yes—
73#2655C2214yes—
74#2655C2214yes—
75#2655C2214yes—
76#2654C2214yes—
77#2651C2214yes—
78#2651C2214yes—
79#2650C2214yes—
80#2646C2212yes—
81#2643C2214yes—
82#2639C2212yes—
83#2638C2214yes—
84#2637C2214yes—
85#2634C2212yes—
86#2634C2214yes—
87#2634C2212yes—
88#2634C2212yes—
89#2633C2212yes—
90#2632C2212yes—
91#2632C2212yes—
92#2627C2212yes—
93#2627C2211yescharacteristic
94#2627C2211yescharacteristic
95#2627C2212yes—
96#2623C2214yes—
97#2623C2212yes—
98#2618C2211yescharacteristic
99#2618C2211yescharacteristic
100#2614C2212yes—
101#2612C2214yes—
102#2611C2214yes—
103#2611C2214yes—
104#2607C2214yes—
105#2606C2212yes—
106#2605C2212yes—
107#2605C2214yes—
108#2599C2214yes—
109#2590C2214yes—
110#2589C2214yes—
111#2589C2214yes—
112#2588C2214yes—
113#2588C2214yes—
114#2586C2214yes—
115#2586C2214yes—
116#2586C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2582C2214yes—
120#2581C2214yes—
121#2575C2214yes—
122#2573C2214yes—
123#2569C2212yes—
124#2568C2212yes—
125#2567C2212yes—
126#2565C2212yes—
127#2565C2212yes—
128#2564C2212yes—
129#2564C2212yes—
130#2556C2214yes—
131#2556C2214yes—
132#2549C2212yes—
133#2533C2214yes—
134#2533C2214yes—
135#2533C2214yes—
136#2530C2214yes—
137#2528C2214yes—
138#2528C2214yes—
139#2528C2214yes—
140#2528C2214yes—
141#2527C2214yes—
142#2527C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2523C2214yes—
146#2523C2214yes—
147#2522C2214yes—
148#2520C2214yes—
149#2520C2214yes—
150#2520C2214yes—
151#2520C2214yes—
152#2517C2214yes—
153#2517C2214yes—
154#2515C2214yes—
155#2514C2214yes—
156#2510C2214yes—
157#2506C2214yes—
158#2505C2214yes—
159#2499C2214yes—
160#2498C2214yes—
161#2493C2214yes—
162#2493C2214yes—
163#2488C2214yes—
164#2473C2214yes—
165#2465C2214yes—
166#2462C2214yes—
167#2462C2214yes—
168#2462C2214yes—
169#2449C2214yes—
170#2438C2214yes—
171#2419C2214yes—
172#2402C2214yes—
173#2401C2214yes—
174#2399C2212yes—
175#2398C2212yes—
176#2396C2214yes—
177#2396C2214yes—
178#2395C2214yes—
179#2373C2214yes—
180#2371C2214yes—
181#2371C2212yes—
182#2371C2212yes—
183#2370C2214yes—
184#2368C2212yes—
185#2368C2212yes—
186#2368C2214yes—
187#2359C2214yes—
188#2356C2214yes—
189#2356C2212yes—
190#2356C2212yes—
191#2356C2212yes—
192#2356C2214yes—
193#2356C2212yes—
194#2356C2214yes—
195#2353C2212yes—
196#2349C2212yes—
197#2346C2212yes—
198#2343C2214yes—
199#2343C2214yes—
200#2343C2212yes—
201#2331C2212yes—
202#2330C2212yes—
203#2329C2214yes—
204#2327C2212yes—
205#2326C2212yes—
206#2320C2211yescharacteristic
207#2320C2212yes—
208#2319C2211yescharacteristic
209#2317C2212yes—
210#2313C2214yes—
211#2310C2212yes—
212C4×C22⋊Q8C2212yes—
213C4×C22⋊Q8C2212yes—
214C4×C22⋊Q8C2212yes—
215C4×#123C2212yes—
216C4×#123C2214yes—
217C4×#123C2212yes—
218C4×#121C2212yes—
219C2×#391C2212yes—
220#2290C2214yes—
221C2×#387C2212yes—
222C2×#387C2212yes—
223#2285C2211yescharacteristic
224#2283C2211yescharacteristic
225C2×#383C2211yescharacteristic
226C2×#383C2211yescharacteristic
227C2×#382C2211yescharacteristic
228#2276C2211yescharacteristic
229#2276C2212yes—
230#2275C2211yescharacteristic
231C2×C4×C4⋊C4C2212yes—
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×#376C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236#533—28no—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239#529—28no—
240C2×#126C2312yes—
241C2×#125C2312yes—
242C2×#125C2311yescharacteristic
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#124C2311yescharacteristic
246C2×#123C2312yes—
247C2×#123C2312yes—
248C2×#123C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2311yescharacteristic
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×#121C2311yescharacteristic
255C2×C4×Q8—28no—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2312yes—
273C2×#117C2314yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2312yes—
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284C22×C42C2311yescharacteristic
285#401C2314yes—
286#401C2314yes—
287#401C2314yes—
288#401C2314yes—
289#400C2312yes—
290#400C2312yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#399C2312yes—
322#399C2312yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#395C2312yes—
374#395C2312yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2312yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2312yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#394C2312yes—
389#394C2312yes—
390#394C2314yes—
391#393C2312yes—
392#393C2312yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#390C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#388C2314yes—
444#388C2314yes—
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#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#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2312yes—
537#386C2312yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2312yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2312yes—
552#385C2314yes—
553#384C2312yes—
554#384C2312yes—
555#384C2312yes—
556#383C2312yes—
557#383C2312yes—
558#383C2312yes—
559#383C2314yes—
560#383C2312yes—
561#383C2312yes—
562#383C2314yes—
563#383C2312yes—
564#383C2312yes—
565#383C2314yes—
566#383C2312yes—
567#383C2314yes—
568#383C2314yes—
569#382C2312yes—
570#382C2312yes—
571#382C2312yes—
572#382C2314yes—
573#382C2312yes—
574#382C2312yes—
575#382C2312yes—
576#382C2314yes—
577#382C2314yes—
578#382C2312yes—
579#382C2314yes—
580#382C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2312yes—
584#381C2312yes—
585#381C2312yes—
586#381C2314yes—
587#381C2312yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2312yes—
592#380C2312yes—
593#380C2311yescharacteristic
594#380C2311yescharacteristic
595#380C2312yes—
596C4×C4⋊C4C2311yescharacteristic
597C4×C4⋊C4C2311yescharacteristic
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2312yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2312yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636#376C2311yescharacteristic
637#376C2311yescharacteristic
638#376C2312yes—
639#376C2312yes—
640#376C2312yes—
641#376C2311yescharacteristic
642#376C2314yes—
643#376C2312yes—
644#376C2312yes—
645#376C2314yes—
646#376C2311yescharacteristic
647#376C2312yes—
648#376C2314yes—
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2312yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C2×#95C2312yes—
661C22×Q8—24no—
662C22×Q8—24no—
663C22×Q8—42no—
664C22×Q8C2412yes—
665C22×Q8C2412yes—
666C22×Q8C2411yescharacteristic
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2414yes—
670C22×D4C2412yes—
671C22×D4C2411yescharacteristic
672C23×C4C2411yescharacteristic
673C23×C4C2412yes—
674C23×C4C2411yescharacteristic
675C23×C4C2411yescharacteristic
676C23×C4C2411yescharacteristic
677C23×C4C2411yescharacteristic
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2414yes—
682C23×C4C2412yes—
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C4⋊Q8—24no—
686C4⋊Q8—24no—
687#126—28no—
688#125—24no—
689#125—28no—
690#125—48no—
691#125—48no—
692#124—24no—
693#123—28no—
694#123—28no—
695#123—44no—
696C22⋊Q8—24no—
697C22⋊Q8—28no—
698C22⋊Q8—28no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701#121—24no—
702C4×Q8—28no—
703C4×Q8—28no—
704C4×Q8—28no—
705C4×Q8—28no—
706C4×Q8—24no—
707C4×Q8—28no—
708C4×Q8—28no—
709C4×Q8—44no—
710C4×Q8—44no—
711C4×Q8—44no—
712C4×D4—28no—
713C4×D4—24no—
714C4×D4—44no—
715C4×D4—48no—
716#117—28no—
717#117—28no—
718#117—48no—
719#117—44no—
720C2×C4⋊C4—24no—
721C2×C4⋊C4—24no—
722C2×C4⋊C4—24no—
723C2×C4⋊C4—28no—
724C2×C4⋊C4—44no—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
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×C42—24no—
802C2×C42—24no—
803C2×C42—44no—
804C2×C42—44no—
805C2×C42—44no—
806C2×C42#4118yes—
807C2×C42C2412yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2412yes—
839#95C2412yes—
840#95C2412yes—
841#95C2411yescharacteristic
842#95C2414yes—
843#95C2412yes—
844#95C2412yes—
845#95C2412yes—
846#95C2412yes—
847#95C2412yes—
848#95C2414yes—
849#95C2412yes—
850#95C2414yes—
851#95C2412yes—
852#95C2412yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
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—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917C24C2512yes—
918C24C2511yescharacteristic
919C2×Q8—24no—
920C2×Q8—24no—
921C2×Q8—22no—
922C2×Q8—24no—
923C2×Q8—24no—
924C2×Q8—24no—
925C2×Q8—24no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—416no—
936C2×D4—24no—
937C2×D4—24no—
938C2×D4—24no—
939C2×D4—22no—
940C2×D4—42no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—24no—
950C22×C4—22no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4C2×#4114yes—
972C22×C4C2×#4114yes—
973C22×C4C2×#4114yes—
974C22×C42−1+414yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—22no—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—24no—
1061C22⋊C4—24no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—28no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C42—24no—
1077C42—24no—
1078C42—24no—
1079C42—24no—
1080C42—24no—
1081C42—28no—
1082C42—28no—
1083C42—24no—
1084C42—24no—
1085C42—28no—
1086C42—42no—
1087C42—42no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—42no—
1096C42—42no—
1097C42—44no—
1098C42—44no—
1099C42—44no—
1100C42C2×#4114yes—
1101C42C2×#4114yes—
1102C42C2×#4114yes—
1103C42C2×#4114yes—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—24no—
1109C23—22no—
1110C23—24no—
1111C23C22×#4112yes—
1112C23C2×2−1+412yes—
1113C23#58512yes—
1114C23C2611yescharacteristic
1115Q8—48no—
1116Q8—48no—
1117Q8—44no—
1118Q8—48no—
1119Q8—84no—
1120Q8—164no—
1121D4—44no—
1122D4—48no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—28no—
1136C2×C4—28no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
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—22no—
1184C2×C4—44no—
1185C2×C4—44no—
1186C2×C4—48no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—44no—
1190C2×C4—84no—
1191C2×C4—88no—
1192C2×C4—84no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4C22×#4112yes—
1196C2×C4C22×#4112yes—
1197C2×C4C22×#4112yes—
1198C2×C4C22×#4112yes—
1199C2×C4C22×#4112yes—
1200C2×C4C22×#4112yes—
1201C2×C4C2×2−1+414yes—
1202C2×C4#58514yes—
1203C22—22no—
1204C22—24no—
1205C22—24no—
1206C22—22no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—44no—
1211C22—42no—
1212C22#349514yes—
1213C22C23×#4111yescharacteristic
1214C22C22×2−1+411yescharacteristic
1215C22C2×#58511yescharacteristic
1216C22C2×#58512yes—
1217C222−1+612yes—
1218C4—22no—
1219C4—22no—
1220C4—24no—
1221C4—22no—
1222C4—22no—
1223C4—24no—
1224C4—22no—
1225C4—22no—
1226C4—42no—
1227C4—42no—
1228C4—42no—
1229C4—44no—
1230C4—44no—
1231C4—42no—
1232C4—44no—
1233C4—44no—
1234C4—44no—
1235C4—44no—
1236C4—42no—
1237C4—42no—
1238C4—44no—
1239C4—42no—
1240C4—42no—
1241C4—42no—
1242C4—44no—
1243C2—24no—
1244C2—82no—
1245C2#6268611yescharacteristic
1246C2C2×#349511yescharacteristic
1247C2#6286011yescharacteristic
1248C2#6290912yes—
1249C2#6293212yes—
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. #42354C2semidirect
2. #42330C2semidirect
3. #42241C2semidirect
4. #42215C2semidirect
5. #42211C2semidirect
6. #42199C2semidirect
7. #42162C2semidirect
8. #39559C2semidirect
9. #39473C2semidirect
10. #39151C2semidirect
11. #38259C2semidirect
12. #37562C2semidirect
14. #37466C2semidirect
16. #36569C2semidirect
17. #36358C2semidirect
18. #36008C2semidirect
19. #35835C2semidirect
20. #35760C2semidirect
21. #35179C2semidirect
22. #35013C2semidirect
25. #34221C2semidirect
27. C2×#2356C2semidirect

Maximal subgroups

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

subgroupindex
#423542
#423302
#422412
#422152
#422112
#421992
#421622
#395592
#394732
#391512
#382592
#375622
#375572
#374662
#374632
#365692
#363582
#360082
#358352
#357602
#351792
#350132
#346022
#345842
#342212
#342202
C2×#23562