Finite Group Databasebeta

← #7713236

Subgroups — #7713236

Order 512.

4486 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48851C214yesmaximal, complemented
2#48850C214yesmaximal, complemented
3#47976C214yesmaximal, complemented
4#47975C214yesmaximal, complemented
5#47022C214yesmaximal, complemented
6#46846C214yesmaximal, complemented
7#46444C214yesmaximal, complemented
8#46437C214yesmaximal, complemented
9#39752C212yesmaximal, complemented
10#39624C212yesmaximal, complemented
11#39492C212yesmaximal
12#39364C212yesmaximal
13#37877C212yesmaximal, complemented
14#37876C212yesmaximal
15#37689C212yesmaximal, complemented
16#37688C212yesmaximal
17#37478C212yesmaximal
18#36752C212yesmaximal, complemented
19#36751C212yesmaximal, complemented
20#35173C211yesmaximal, characteristic, complemented
21#35167C211yesmaximal, characteristic, complemented
22#35033C211yesmaximal, characteristic
23#35015C211yesmaximal, characteristic, complemented
24#35015C211yesmaximal, characteristic, complemented
25#35002C211yesmaximal, characteristic
26#34380C212yesmaximal
27C2×#2332C211yesmaximal, characteristic
28C2×#544C2212yes—
29C2×#543C2212yes—
30C2×#533C2212yes—
31C22×C22⋊Q8C2211yescharacteristic
32#2857C2212yes—
33#2857C2212yes—
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2212yes—
38#2857C2211yescharacteristic
39#2855C2212yes—
40#2855C2212yes—
41#2851C2212yes—
42#2841C2214yes—
43#2841C2214yes—
44#2811C2214yescomplemented
45#2809C2214yescomplemented
46#2807C2214yes—
47#2806C2214yescomplemented
48#2806C2214yescomplemented
49#2806C2214yescomplemented
50#2806C2214yescomplemented
51#2806C2214yescomplemented
52#2805C2214yescomplemented
53#2802C2214yescomplemented
54#2802C2214yescomplemented
55#2799C2214yescomplemented
56#2799C2214yescomplemented
57#2792C2214yescomplemented
58#2792C2214yescomplemented
59#2792C2214yescomplemented
60#2791C2214yescomplemented
61#2791C2214yescomplemented
62#2791C2214yescomplemented
63#2790C2214yes—
64#2790C2214yes—
65#2788C2214yes—
66#2774C2214yescomplemented
67#2774C2214yescomplemented
68#2774C2214yescomplemented
69#2768C2214yes—
70#2763C2214yes—
71#2755C2214yescomplemented
72#2755C2214yescomplemented
73#2755C2214yescomplemented
74#2734C2214yescomplemented
75#2734C2214yescomplemented
76#2729C2214yes—
77#2729C2214yes—
78#2729C2214yes—
79#2726C2214yescomplemented
80#2726C2214yescomplemented
81#2720C2214yes—
82#2720C2214yes—
83#2720C2214yes—
84#2713C2214yescomplemented
85#2713C2214yescomplemented
86#2713C2214yescomplemented
87#2713C2214yescomplemented
88#2704C2214yes—
89#2704C2214yes—
90#2677C2214yes—
91#2677C2214yes—
92#2667C2214yes—
93#2665C2214yes—
94#2659C2212yes—
95#2659C2212yes—
96#2659C2212yes—
97#2659C2212yes—
98#2659C2212yes—
99#2659C2212yes—
100#2646C2212yes—
101#2646C2212yes—
102#2627C2212yes—
103#2627C2212yes—
104#2627C2214yes—
105#2627C2214yes—
106#2626C2212yes—
107#2626C2212yes—
108#2608C2214yes—
109#2607C2214yes—
110#2590C2214yescomplemented
111#2590C2214yescomplemented
112#2590C2214yescomplemented
113#2589C2214yes—
114#2589C2214yes—
115#2588C2214yescomplemented
116#2588C2214yescomplemented
117#2588C2214yescomplemented
118#2587C2214yes—
119#2587C2214yes—
120#2586C2214yescomplemented
121#2585C2214yescomplemented
122#2584C2214yescomplemented
123#2584C2214yescomplemented
124#2582C2214yescomplemented
125#2581C2214yescomplemented
126#2574C2214yes—
127#2569C2214yes—
128#2569C2214yes—
129#2567C2212yescomplemented
130#2567C2212yescomplemented
131#2567C2214yescomplemented
132#2565C2214yescomplemented
133#2556C2214yes—
134#2556C2214yes—
135#2556C2214yes—
136#2552C2212yescomplemented
137#2552C2212yescomplemented
138#2551C2212yescomplemented
139#2551C2212yescomplemented
140#2550C2214yescomplemented
141#2550C2214yescomplemented
142#2549C2214yes—
143#2549C2214yes—
144#2549C2214yes—
145#2549C2214yes—
146#2546C2212yescomplemented
147#2546C2212yescomplemented
148#2522C2214yes—
149#2511C2212yescomplemented
150#2511C2212yescomplemented
151#2507C2212yescomplemented
152#2507C2212yescomplemented
153#2492C2214yes—
154#2465C2214yes—
155#2465C2214yes—
156#2465C2214yes—
157#2462C2214yescomplemented
158#2462C2214yescomplemented
159#2453C2214yescomplemented
160#2451C2214yescomplemented
161#2451C2214yescomplemented
162#2451C2214yescomplemented
163#2451C2214yescomplemented
164#2451C2212yescomplemented
165#2451C2212yescomplemented
166#2446C2214yescomplemented
167#2446C2212yescomplemented
168#2446C2212yescomplemented
169#2442C2214yes—
170#2441C2212yes—
171#2441C2212yes—
172#2440C2214yes—
173#2440C2212yes—
174#2440C2212yes—
175#2440C2212yes—
176#2440C2212yes—
177#2439C2212yes—
178#2439C2212yes—
179#2438C2214yes—
180#2438C2214yes—
181#2438C2214yes—
182#2438C2214yes—
183#2438C2214yes—
184#2438C2214yes—
185#2437C2214yes—
186#2437C2214yes—
187#2429C2214yes—
188#2429C2214yes—
189#2423C2214yes—
190#2378C2214yes—
191#2378C2214yes—
192#2360C2214yes—
193#2360C2214yes—
194#2344C2214yes—
195#2342C2214yes—
196#2342C2214yes—
197Q8×C22⋊C4C2214yes—
198#2332C2214yes—
199#2332C2214yes—
200#2332C2214yes—
201#2332C2214yes—
202#2329C2212yes—
203#2329C2212yes—
204#2329C2214yes—
205#2329C2214yes—
206#2329C2212yes—
207#2329C2212yes—
208#2323C2214yes—
209#2323C2214yes—
210#2316C2212yes—
211#2316C2212yes—
212#2316C2212yes—
213#2315C2212yes—
214#2313C2212yes—
215#2313C2212yes—
216C4×C22⋊Q8C2212yes—
217C4×C22⋊Q8C2212yes—
218C2×#391C2211yescharacteristic
219C2×#391C2211yescharacteristic
220C2×#388C2211yescharacteristic
221C2×#388C2211yescharacteristic
222C2×#388C2211yescharacteristic
223C2×#388C2211yescharacteristic
224C2×#387C2211yescharacteristic
225C2×#387C2211yescharacteristic
226C2×#387C2211yescharacteristic
227C2×#387C2211yescharacteristic
228#2285C2212yes—
229#2280C2212yes—
230C2×#381C2211yescharacteristic
231C2×#380C2212yes—
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×C4×C4⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C24×C4C2311yescharacteristic
237#544—48no—
238#543—48no—
239#533—48no—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2314yes—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2312yes—
252C2×#125C2314yes—
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2312yes—
257C2×C22⋊Q8Q8116yescomplemented
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×#117C2314yes—
281C2×#117C2314yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#398C2314yes—
327#398C2314yes—
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#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
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#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2314yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
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#388C2314yes—
506#388C2314yes—
507#388C2314yes—
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#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
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#384C2312yes—
579#384C2311yescharacteristic
580#384C2311yescharacteristic
581#384C2312yes—
582#384C2314yes—
583#384C2311yescharacteristic
584#384C2312yes—
585#384C2311yescharacteristic
586#384C2312yes—
587#384C2312yes—
588#382C2314yes—
589#382C2312yes—
590#382C2314yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#381C2314yes—
595#381C2314yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2312yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611#380C2312yes—
612#380C2312yes—
613#380C2312yes—
614#380C2314yes—
615#380C2312yes—
616#380C2312yes—
617#379C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C2×#95C2311yescharacteristic
648C2×#95C2311yescharacteristic
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2314yes—
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C2×#95C2311yescharacteristic
661C2×#95C2311yescharacteristic
662C25C2411yescharacteristic
663C22×Q8—81no—
664C22×Q8—81no—
665C22×Q8C2×Q818yes—
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2412yes—
670C22×Q8C2414yes—
671C22×Q8C2414yes—
672C22×Q8C2414yes—
673C22×Q8C2414yes—
674C23×C4—81no—
675C23×C4—81no—
676C23×C4C2×Q818yes—
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C23×C4C2411yescharacteristic
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2414yes—
686C23×C4C2414yes—
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2411yescharacteristic
695C4⋊Q8—44no—
696C4⋊Q8—44no—
697C4⋊Q8—48no—
698C4⋊Q8—48no—
699C4⋊Q8—81no—
700C4⋊Q8—82no—
701C4⋊Q8—81no—
702C4⋊Q8—81no—
703C4⋊Q8—81no—
704C4⋊Q8—82no—
705C4⋊Q8—82no—
706C4⋊Q8—84no—
707#125—48no—
708#125—48no—
709#125—48no—
710#125—82no—
711#125—84no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—48no—
721C22⋊Q8—48no—
722C22⋊Q8—48no—
723C22⋊Q8—84no—
724C22⋊Q8—84no—
725C22⋊Q8C2×Q8132yes—
726C22⋊Q8C2×Q8132yes—
727C4×Q8—48no—
728C4×Q8—44no—
729C4×Q8—44no—
730C4×Q8—82no—
731C4×Q8—82no—
732C4×Q8—84no—
733C4×Q8—84no—
734#117—48no—
735#117—48no—
736#117—82no—
737#117—82no—
738C2×C4⋊C4—24no—
739C2×C4⋊C4—24no—
740C2×C4⋊C4—82no—
741C2×C4⋊C4—82no—
742C2×C4⋊C4—81no—
743C2×C4⋊C4—81no—
744C2×C4⋊C4C2×Q818yes—
745C2×C4⋊C4C2×Q818yes—
746C2×C4⋊C4C2×Q818yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C22⋊C4—24no—
820C2×C22⋊C4—24no—
821C2×C22⋊C4—48no—
822C2×C22⋊C4—81no—
823C2×C22⋊C4—81no—
824C2×C22⋊C4C2×Q818yes—
825C2×C22⋊C4C2×Q818yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C42—24no—
845C2×C42—24no—
846C2×C42—81no—
847C2×C42—81no—
848C2×C42—81no—
849C2×C42—81no—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
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—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940C24—22no—
941C24—22no—
942C24—41no—
943C24—41no—
944C24—41no—
945C24—41no—
946C24C22×Q814yes—
947C24C2512yes—
948C24C2511yescharacteristic
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—44no—
954C2×Q8—44no—
955C2×Q8—44no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—44no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—44no—
972C2×Q8—88no—
973C2×Q8C22×Q8116yes—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—41no—
988C22×C4—41no—
989C22×C4—41no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—41no—
993C22×C4—41no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—88no—
1019C22×C4C22×Q814yes—
1020C22×C4C22×Q814yes—
1021C22×C4C22×Q814yes—
1022C22×C4C22×Q814yes—
1023C22×C4C22×Q814yes—
1024C22×C4C22×Q814yes—
1025C22×C4C22×Q818yes—
1026C22×C4C22×Q818yes—
1027C22×C4H(5,𝔽2)14yes—
1028C22×C42−1+414yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4C22×Q8116yes—
1122C4⋊C4C22×Q818yes—
1123C4⋊C4C22×Q818yes—
1124C4⋊C4C22×Q818yes—
1125C4⋊C4C22×Q818yes—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—24no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4C22×Q8116yes—
1143C22⋊C4C22×Q8116yes—
1144C42—24no—
1145C42—24no—
1146C42—24no—
1147C42—24no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—41no—
1152C42—42no—
1153C42—41no—
1154C42—41no—
1155C42—41no—
1156C42—42no—
1157C42—42no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—28no—
1179C23—44no—
1180C23—44no—
1181C23—82no—
1182C23—82no—
1183C23—82no—
1184C23—82no—
1185C23C23×Q814yes—
1186C23C23×Q812yes—
1187C23C2×H(5,𝔽2)12yes—
1188C23C2×2−1+412yes—
1189C23C2611yescharacteristic
1190Q8—416no—
1191Q8—84no—
1192Q8—84no—
1193Q8—84no—
1194Q8—84no—
1195Q8—88no—
1196Q8—164no—
1197Q8—164no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—28no—
1221C2×C4—28no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—44no—
1265C2×C4—48no—
1266C2×C4—48no—
1267C2×C4—44no—
1268C2×C4—44no—
1269C2×C4—44no—
1270C2×C4—44no—
1271C2×C4—44no—
1272C2×C4—82no—
1273C2×C4—82no—
1274C2×C4—82no—
1275C2×C4—82no—
1276C2×C4—82no—
1277C2×C4—82no—
1278C2×C4—164no—
1279C2×C4—164no—
1280C2×C4C23×Q814yes—
1281C2×C4C23×Q814yes—
1282C2×C4C23×Q814yes—
1283C2×C4C23×Q814yes—
1284C2×C4C23×Q812yes—
1285C2×C4C23×Q812yes—
1286C2×C4C23×Q814yes—
1287C2×C4C2×H(5,𝔽2)12yes—
1288C2×C4C2×H(5,𝔽2)12yes—
1289C2×C4C2×2−1+412yes—
1290C2×C4C2×2−1+412yes—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—88no—
1305C22#350314yes—
1306C22C24×Q811yescharacteristic
1307C22C22×H(5,𝔽2)11yescharacteristic
1308C22C22×2−1+411yescharacteristic
1309C22H(7,𝔽2)11yescharacteristic
1310C22H(7,𝔽2)11yescharacteristic
1311C222−1+611yescharacteristic
1312C222−1+611yescharacteristic
1313C4—24no—
1314C4—24no—
1315C4—22no—
1316C4—22no—
1317C4—24no—
1318C4—24no—
1319C4—24no—
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—42no—
1325C4—44no—
1326C4—42no—
1327C4—44no—
1328C4—44no—
1329C4—44no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—42no—
1337C4—42no—
1338C2—24no—
1339C2—44no—
1340C2C2×#350311yescharacteristic
1341C2#6284311yescharacteristic
1342C2#6284911yescharacteristic
1343C2#6286511yescharacteristic
1344C2#6286611yescharacteristic
1345C2#6287811yescharacteristic
1346C2#6287911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48851C2semidirect
2. #48850C2semidirect
3. #47976C2semidirect
4. #47975C2semidirect
5. #47022C2semidirect
6. #46846C2semidirect
7. #46444C2semidirect
8. #46437C2semidirect
9. #39752C2semidirect
10. #39624C2semidirect
13. #37877C2semidirect
15. #37689C2semidirect
18. #36752C2semidirect
19. #36751C2semidirect
20. #35173C2semidirect
21. #35167C2semidirect
23. #35015C2semidirect
24. #35015C2semidirect
44. #2811C22semidirect
45. #2809C22semidirect
47. #2806C22semidirect
48. #2806C22semidirect
49. #2806C22semidirect
50. #2806C22semidirect
51. #2806C22semidirect
52. #2805C22semidirect
53. #2802C22semidirect
54. #2802C22semidirect
55. #2799C22semidirect
56. #2799C22semidirect
57. #2792C22semidirect
58. #2792C22semidirect
59. #2792C22semidirect
60. #2791C22semidirect
61. #2791C22semidirect
62. #2791C22semidirect
66. #2774C22semidirect
67. #2774C22semidirect
68. #2774C22semidirect
71. #2755C22semidirect
72. #2755C22semidirect
73. #2755C22semidirect
74. #2734C22semidirect
75. #2734C22semidirect
79. #2726C22semidirect
80. #2726C22semidirect
84. #2713C22semidirect
85. #2713C22semidirect
86. #2713C22semidirect
87. #2713C22semidirect
110. #2590C22semidirect
111. #2590C22semidirect
112. #2590C22semidirect
115. #2588C22semidirect
116. #2588C22semidirect
117. #2588C22semidirect
120. #2586C22semidirect
121. #2585C22semidirect
122. #2584C22semidirect
123. #2584C22semidirect
124. #2582C22semidirect
125. #2581C22semidirect
129. #2567C22semidirect
130. #2567C22semidirect
131. #2567C22semidirect
132. #2565C22semidirect
136. #2552C22semidirect
137. #2552C22semidirect
138. #2551C22semidirect
139. #2551C22semidirect
140. #2550C22semidirect
141. #2550C22semidirect
146. #2546C22semidirect
147. #2546C22semidirect
149. #2511C22semidirect
150. #2511C22semidirect
151. #2507C22semidirect
152. #2507C22semidirect
157. #2462C22semidirect
158. #2462C22semidirect
159. #2453C22semidirect
160. #2451C22semidirect
161. #2451C22semidirect
162. #2451C22semidirect
163. #2451C22semidirect
164. #2451C22semidirect
165. #2451C22semidirect
166. #2446C22semidirect
167. #2446C22semidirect
168. #2446C22semidirect
257. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#488512
#488502
#479762
#479752
#470222
#468462
#464442
#464372
#397522
#396242
#394922
#393642
#378772
#378762
#376892
#376882
#374782
#367522
#367512
#351732
#351672
#350332
#350152
#350022
#343802
C2×#23322