Finite Group Databasebeta

← #7646731

Subgroups — #7646731

Order 512.

4582 conjugacy classes of subgroups.

The subgroup lattice has 1221 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40629C214yesmaximal, complemented
2#40628C214yesmaximal, complemented
3#40625C214yesmaximal, complemented
4#40624C214yesmaximal, complemented
5#38103C214yesmaximal, complemented
6#38103C214yesmaximal, complemented
7#37877C214yesmaximal, complemented
8#37689C214yesmaximal, complemented
9#37478C212yesmaximal
10#37478C212yesmaximal
11#37135C214yesmaximal, complemented
12#36752C212yesmaximal, complemented
13#36751C212yesmaximal, complemented
14#35403C214yesmaximal, complemented
15#35253C212yesmaximal
16#35065C212yesmaximal
17#35065C212yesmaximal
18#35015C212yesmaximal, complemented
19#35013C212yesmaximal, complemented
20#34739C212yesmaximal
21#34178C211yesmaximal, characteristic
22C2×#2344C211yesmaximal, characteristic
23C2×#2313C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#533C2212yes—
26C22×#117C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29#2857C2212yes—
30#2857C2212yes—
31#2855C2214yes—
32#2855C2214yes—
33#2855C2214yes—
34#2855C2214yes—
35#2851C2212yes—
36#2851C2212yes—
37#2841C2214yes—
38#2841C2214yes—
39#2841C2214yes—
40#2841C2214yes—
41#2806C2214yescomplemented
42#2806C2214yescomplemented
43#2805C2214yescomplemented
44#2805C2214yescomplemented
45#2802C2214yescomplemented
46#2802C2214yescomplemented
47#2802C2214yescomplemented
48#2802C2214yescomplemented
49#2792C2214yescomplemented
50#2792C2214yescomplemented
51#2792C2214yescomplemented
52#2792C2214yescomplemented
53#2791C2214yescomplemented
54#2791C2214yescomplemented
55#2791C2214yescomplemented
56#2791C2214yescomplemented
57#2774C2214yescomplemented
58#2774C2214yescomplemented
59#2774C2214yescomplemented
60#2774C2214yescomplemented
61#2755C2214yescomplemented
62#2755C2214yescomplemented
63#2755C2214yescomplemented
64#2755C2214yescomplemented
65#2734C2214yescomplemented
66#2734C2214yescomplemented
67#2726C2214yescomplemented
68#2726C2214yescomplemented
69#2713C2214yescomplemented
70#2713C2214yescomplemented
71#2713C2214yescomplemented
72#2713C2214yescomplemented
73#2667C2212yes—
74#2667C2214yes—
75#2667C2212yes—
76#2667C2214yes—
77#2667C2214yes—
78#2665C2214yes—
79#2665C2212yes—
80#2665C2212yes—
81#2665C2214yes—
82#2665C2214yes—
83#2659C2214yes—
84#2659C2212yes—
85#2659C2212yes—
86#2646C2212yes—
87#2646C2212yes—
88#2646C2214yes—
89#2629C2212yes—
90#2629C2212yes—
91#2628C2212yes—
92#2628C2212yes—
93#2627C2214yes—
94#2627C2214yes—
95#2627C2214yes—
96#2627C2214yes—
97#2608C2212yes—
98#2608C2214yes—
99#2608C2212yes—
100#2607C2212yes—
101#2607C2214yes—
102#2607C2212yes—
103#2590C2214yescomplemented
104#2590C2214yescomplemented
105#2590C2214yescomplemented
106#2590C2214yescomplemented
107#2588C2214yescomplemented
108#2588C2214yescomplemented
109#2588C2214yescomplemented
110#2588C2214yescomplemented
111#2586C2214yescomplemented
112#2586C2214yescomplemented
113#2586C2214yescomplemented
114#2586C2214yescomplemented
115#2585C2214yescomplemented
116#2585C2214yescomplemented
117#2585C2214yescomplemented
118#2585C2214yescomplemented
119#2569C2214yes—
120#2569C2214yes—
121#2569C2214yes—
122#2569C2212yes—
123#2569C2212yes—
124#2549C2214yes—
125#2549C2214yes—
126#2549C2212yes—
127#2549C2214yes—
128#2549C2212yes—
129#2520C2214yescomplemented
130#2520C2214yescomplemented
131#2520C2214yescomplemented
132#2520C2214yescomplemented
133#2511C2214yescomplemented
134#2511C2214yescomplemented
135#2507C2214yescomplemented
136#2507C2214yescomplemented
137#2462C2214yescomplemented
138#2462C2214yescomplemented
139#2462C2214yescomplemented
140#2462C2214yescomplemented
141#2451C2214yescomplemented
142#2451C2214yescomplemented
143#2446C2214yescomplemented
144#2446C2214yescomplemented
145#2442C2214yes—
146#2442C2214yes—
147#2441C2214yes—
148#2441C2214yes—
149#2440C2214yes—
150#2440C2214yes—
151#2439C2214yes—
152#2439C2214yes—
153#2438C2214yes—
154#2438C2214yes—
155#2438C2214yes—
156#2438C2214yes—
157#2438C2214yes—
158#2438C2214yes—
159#2438C2214yes—
160#2438C2214yes—
161#2438C2214yes—
162#2438C2214yes—
163#2438C2214yes—
164#2438C2214yes—
165#2437C2214yes—
166#2437C2214yes—
167#2437C2214yes—
168#2437C2214yes—
169#2396C2214yes—
170#2396C2214yes—
171#2345C2214yes—
172#2345C2214yes—
173#2344C2214yes—
174#2344C2214yes—
175#2344C2214yes—
176#2344C2214yes—
177#2344C2214yes—
178#2344C2214yes—
179#2329C2214yes—
180#2329C2214yes—
181#2329C2214yes—
182#2329C2214yes—
183#2317C2212yes—
184#2317C2212yes—
185#2316C2212yes—
186#2316C2212yes—
187#2313C2212yes—
188#2313C2212yes—
189#2313C2212yes—
190#2313C2211yescharacteristic
191#2313C2211yescharacteristic
192#2313C2211yescharacteristic
193#2313C2211yescharacteristic
194#2313C2214yes—
195#2313C2214yes—
196#2313C2212yes—
197C4×C22⋊Q8C2214yes—
198C4×C22⋊Q8C2214yes—
199#2296C2212yes—
200#2296C2212yes—
201C2×#389C2212yes—
202C2×#387C2212yes—
203C2×#387C2212yes—
204C2×#387C2214yes—
205C2×#387C2214yes—
206#2285C2212yes—
207#2280C2212yes—
208#2280C2212yes—
209#2280C2212yes—
210C2×#381C2211yescharacteristic
211C2×#381C2211yescharacteristic
212C2×#381C2212yes—
213C2×#380C2211yescharacteristic
214C2×#380C2212yes—
215#2274C2212yes—
216C2×C4×C4⋊C4C2212yes—
217C2×C4×C22⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2212yes—
219C24×C4C2311yescharacteristic
220C24×C4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222#544—48no—
223#533—48no—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2314yes—
227C2×C4⋊Q8C2314yes—
228C2×#125C2312yes—
229C2×#125C2312yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×#117—44no—
243C2×#117—44no—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2314yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2314yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C22×C4⋊C4Q8116yescomplemented
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2314yes—
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2314yes—
272C22×C22⋊C4C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2312yes—
276C22×C42C2312yes—
277C22×C42C2312yes—
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#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
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#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#393C2314yes—
371#393C2314yes—
372#393C2314yes—
373#393C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#389C2312yes—
395#389C2314yes—
396#389C2312yes—
397#389C2312yes—
398#389C2314yes—
399#389C2312yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2312yes—
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#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
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#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#384C2312yes—
527#384C2312yes—
528#384C2314yes—
529#384C2314yes—
530#382C2312yes—
531#382C2312yes—
532#382C2314yes—
533#382C2314yes—
534#381C2314yes—
535#381C2314yes—
536#381C2312yes—
537#381C2312yes—
538#381C2312yes—
539#381C2312yes—
540#381C2312yes—
541#381C2312yes—
542#381C2314yes—
543#381C2314yes—
544#381C2314yes—
545#381C2312yes—
546#381C2312yes—
547#381C2314yes—
548#381C2314yes—
549#380C2314yes—
550#380C2314yes—
551#380C2312yes—
552#380C2312yes—
553#380C2312yes—
554#380C2312yes—
555#380C2314yes—
556#380C2312yes—
557#380C2312yes—
558#380C2314yes—
559#380C2314yes—
560#380C2314yes—
561#380C2314yes—
562#380C2314yes—
563#380C2312yes—
564#380C2314yes—
565#380C2312yes—
566#380C2314yes—
567#380C2314yes—
568#380C2312yes—
569#380C2312yes—
570#380C2312yes—
571#380C2312yes—
572#380C2314yes—
573#380C2314yes—
574#380C2314yes—
575#379C2314yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2312yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2312yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C2×#95C2312yes—
609C2×#95C2312yes—
610C2×#95C2312yes—
611C2×#95C2312yes—
612C2×#95C2312yes—
613C2×#95C2314yes—
614C2×#95C2312yes—
615C2×#95C2314yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2314yes—
619C25C2411yescharacteristic
620C22×Q8C2414yes—
621C22×Q8C2414yes—
622C22×Q8C2414yes—
623C22×Q8C2414yes—
624C23×C4—42no—
625C23×C4—42no—
626C23×C4—44no—
627C23×C4—42no—
628C23×C4—42no—
629C23×C4C2×Q818yes—
630C23×C4C2×Q818yes—
631C23×C4C2×Q818yes—
632C23×C4C2412yes—
633C23×C4C2412yes—
634C23×C4C2411yescharacteristic
635C23×C4C2411yescharacteristic
636C23×C4C2412yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2414yes—
640C23×C4C2414yes—
641C23×C4C2412yes—
642C23×C4C2411yescharacteristic
643C23×C4C2411yescharacteristic
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2412yes—
650C4⋊Q8—44no—
651C4⋊Q8—44no—
652C4⋊Q8—48no—
653C4⋊Q8—48no—
654#125—44no—
655#125—44no—
656#125—48no—
657#125—48no—
658C22⋊Q8—216no—
659C22⋊Q8—48no—
660C22⋊Q8—48no—
661C22⋊Q8—48no—
662C22⋊Q8—48no—
663C22⋊Q8—48no—
664C22⋊Q8—48no—
665C22⋊Q8—48no—
666C4×Q8—48no—
667C4×Q8—48no—
668#117—28no—
669#117—28no—
670#117—48no—
671#117—44no—
672#117—44no—
673#117—44no—
674#117—44no—
675#117—44no—
676#117—44no—
677#117—48no—
678#117—44no—
679#117—44no—
680C2×C4⋊C4—44no—
681C2×C4⋊C4—44no—
682C2×C4⋊C4—44no—
683C2×C4⋊C4—44no—
684C2×C4⋊C4—44no—
685C2×C4⋊C4C2×Q8132yes—
686C2×C4⋊C4C2×Q818yes—
687C2×C4⋊C4C2×Q818yes—
688C2×C4⋊C4C2×Q818yes—
689C2×C4⋊C4C2×Q818yes—
690C2×C4⋊C4C2×Q8132yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C22⋊C4—24no—
754C2×C22⋊C4—48no—
755C2×C22⋊C4—42no—
756C2×C22⋊C4—42no—
757C2×C22⋊C4—42no—
758C2×C22⋊C4C2411yescharacteristic
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2411yescharacteristic
778C2×C42—44no—
779C2×C42—44no—
780C2×C42—44no—
781C2×C42—44no—
782C2×C42—44no—
783C2×C42C2414yes—
784C2×C42C2412yes—
785C2×C42C2412yes—
786C2×C42C2414yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2412yes—
791C2×C42C2414yes—
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2412yes—
822#95C2412yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2412yes—
833#95C2412yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2412yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
845#95C2412yes—
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—
873C24—22no—
874C24—24no—
875C24—22no—
876C24—42no—
877C24C22×Q814yes—
878C24C2511yescharacteristic
879C24C2511yescharacteristic
880C24C2511yescharacteristic
881C2×Q8—28no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—44no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—44no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—28no—
901C22×C4—28no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—416no—
913C22×C4—416no—
914C22×C4—416no—
915C22×C4—41no—
916C22×C4—42no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—42no—
922C22×C4—41no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—44no—
927C22×C4—42no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—44no—
934C22×C4C22×Q814yes—
935C22×C4C22×Q814yes—
936C22×C4C22×Q818yes—
937C22×C4C22×Q818yes—
938C22×C4C22×Q818yes—
939C22×C4C22×Q818yes—
940C22×C4C22×Q818yes—
941C22×C4C22×Q814yes—
942C22×C4C22×Q814yes—
943C22×C4C22×Q814yes—
944C22×C4C22×Q814yes—
945C22×C4C22×Q818yes—
946C22×C4C2514yes—
947C22×C4C2514yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2514yes—
956C22×C4C2512yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C4⋊C4—24no—
967C4⋊C4—28no—
968C4⋊C4—24no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—44no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
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—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—44no—
1002C4⋊C4—42no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
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⋊C4C22×Q8116yes—
1025C4⋊C4C22×Q8116yes—
1026C4⋊C4C22×Q8116yes—
1027C4⋊C4C22×Q8116yes—
1028C22⋊C4—22no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—24no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—24no—
1039C22⋊C4—44no—
1040C22⋊C4—42no—
1041C22⋊C4—44no—
1042C22⋊C4—41no—
1043C22⋊C4—42no—
1044C22⋊C4—41no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4H(5,𝔽2)14yes—
1048C42—28no—
1049C42—24no—
1050C42—24no—
1051C42—44no—
1052C42—44no—
1053C42—42no—
1054C42—44no—
1055C42—42no—
1056C42—44no—
1057C42—42no—
1058C42—42no—
1059C42—44no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—44no—
1065C42—44no—
1066C42—44no—
1067C42—42no—
1068C42—42no—
1069C42—44no—
1070C23—21no—
1071C23—21no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—21no—
1076C23—22no—
1077C23—21no—
1078C23—22no—
1079C23—28no—
1080C23—28no—
1081C23—44no—
1082C23—48no—
1083C23—48no—
1084C23C23×Q812yes—
1085C23C23×Q812yes—
1086C23C23×Q812yes—
1087C23C2×H(5,𝔽2)12yes—
1088C23#58514yes—
1089C23#58512yes—
1090C23C2611yescharacteristic
1091Q8—88no—
1092Q8—88no—
1093Q8—164no—
1094Q8—164no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—28no—
1108C2×C4—28no—
1109C2×C4—216no—
1110C2×C4—216no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—44no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—48no—
1155C2×C4—48no—
1156C2×C4—48no—
1157C2×C4—48no—
1158C2×C4—48no—
1159C2×C4—84no—
1160C2×C4—84no—
1161C2×C4—88no—
1162C2×C4—88no—
1163C2×C4—84no—
1164C2×C4C23×Q814yes—
1165C2×C4C23×Q814yes—
1166C2×C4C23×Q814yes—
1167C2×C4C23×Q814yes—
1168C2×C4C23×Q814yes—
1169C2×C4C23×Q814yes—
1170C2×C4C2×H(5,𝔽2)14yes—
1171C22—22no—
1172C22—22no—
1173C22—22no—
1174C22—24no—
1175C22—24no—
1176C22—24no—
1177C22—24no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—22no—
1182C22—416no—
1183C22—42no—
1184C22—42no—
1185C22#345814yes—
1186C22#350114yes—
1187C22C24×Q811yescharacteristic
1188C22C22×H(5,𝔽2)11yescharacteristic
1189C22C2×#58511yescharacteristic
1190C22C2×#58512yes—
1191C222−1+612yes—
1192C4—24no—
1193C4—24no—
1194C4—24no—
1195C4—24no—
1196C4—24no—
1197C4—24no—
1198C4—24no—
1199C4—42no—
1200C4—42no—
1201C4—44no—
1202C4—44no—
1203C4—44no—
1204C4—42no—
1205C4—44no—
1206C4—44no—
1207C4—44no—
1208C4—44no—
1209C4—44no—
1210C4—44no—
1211C4—44no—
1212C2—24no—
1213C2—24no—
1214C2—42no—
1215C2C2×#345811yescharacteristic
1216C2C2×#350111yescharacteristic
1217C2#6284911yescharacteristic
1218C2#6289812yes—
1219C2#6290912yes—
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. #40629C2semidirect
2. #40628C2semidirect
3. #40625C2semidirect
4. #40624C2semidirect
5. #38103C2semidirect
6. #38103C2semidirect
7. #37877C2semidirect
8. #37689C2semidirect
11. #37135C2semidirect
12. #36752C2semidirect
13. #36751C2semidirect
14. #35403C2semidirect
18. #35015C2semidirect
19. #35013C2semidirect
41. #2806C22semidirect
42. #2806C22semidirect
43. #2805C22semidirect
44. #2805C22semidirect
45. #2802C22semidirect
46. #2802C22semidirect
47. #2802C22semidirect
48. #2802C22semidirect
49. #2792C22semidirect
50. #2792C22semidirect
51. #2792C22semidirect
52. #2792C22semidirect
53. #2791C22semidirect
54. #2791C22semidirect
55. #2791C22semidirect
56. #2791C22semidirect
57. #2774C22semidirect
58. #2774C22semidirect
59. #2774C22semidirect
60. #2774C22semidirect
61. #2755C22semidirect
62. #2755C22semidirect
63. #2755C22semidirect
64. #2755C22semidirect
65. #2734C22semidirect
66. #2734C22semidirect
67. #2726C22semidirect
68. #2726C22semidirect
69. #2713C22semidirect
70. #2713C22semidirect
71. #2713C22semidirect
72. #2713C22semidirect
103. #2590C22semidirect
104. #2590C22semidirect
105. #2590C22semidirect
106. #2590C22semidirect
107. #2588C22semidirect
108. #2588C22semidirect
109. #2588C22semidirect
110. #2588C22semidirect
111. #2586C22semidirect
112. #2586C22semidirect
113. #2586C22semidirect
114. #2586C22semidirect
115. #2585C22semidirect
116. #2585C22semidirect
117. #2585C22semidirect
118. #2585C22semidirect
129. #2520C22semidirect
130. #2520C22semidirect
131. #2520C22semidirect
132. #2520C22semidirect
133. #2511C22semidirect
134. #2511C22semidirect
135. #2507C22semidirect
136. #2507C22semidirect
137. #2462C22semidirect
138. #2462C22semidirect
139. #2462C22semidirect
140. #2462C22semidirect
141. #2451C22semidirect
142. #2451C22semidirect
143. #2446C22semidirect
144. #2446C22semidirect
256. C22×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#406292
#406282
#406252
#406242
#381032
#378772
#376892
#374782
#371352
#367522
#367512
#354032
#352532
#350652
#350152
#350132
#347392
#341782
C2×#23442
C2×#23132