Finite Group Databasebeta

← #8093842

Subgroups — #8093842

Order 512.

5180 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52800C214yesmaximal, complemented
2#52585C214yesmaximal, complemented
3#52451C214yesmaximal, complemented
4#52427C214yesmaximal, complemented
5#52341C214yesmaximal, complemented
6#52311C214yesmaximal, complemented
7#46032C214yesmaximal, complemented
8#46032C214yesmaximal, complemented
9#45726C214yesmaximal, complemented
10#45581C214yesmaximal, complemented
11#45548C214yesmaximal, complemented
12#45475C214yesmaximal, complemented
13#35360C212yesmaximal, complemented
14#35359C212yesmaximal, complemented
15#35358C212yesmaximal, complemented
16#35000C212yesmaximal, complemented
17#34993C211yesmaximal, characteristic, complemented
18#34993C211yesmaximal, characteristic, complemented
19#34985C212yesmaximal, complemented
20C2×#2569C211yesmaximal, characteristic, complemented
21C2×#2444C212yesmaximal, complemented
22C2×#543C2211yescharacteristic
23C2×#543C2211yescharacteristic
24C2×#534C2211yescharacteristic
25C2×#534C2212yes—
26C2×#534C2211yescharacteristic
27C22×#121C2212yes—
28C2×#518C2212yes—
29C22×C4×D4C2212yes—
30#2855C2214yescomplemented
31#2854C2214yes—
32#2850C2214yescomplemented
33#2850C2214yescomplemented
34#2848C2214yescomplemented
35#2847C2214yes—
36#2841C2214yescomplemented
37#2839C2214yescomplemented
38#2837C2214yescomplemented
39#2836C2214yescomplemented
40#2836C2214yescomplemented
41#2832C2214yescomplemented
42#2831C2214yescomplemented
43#2831C2214yescomplemented
44#2831C2214yescomplemented
45#2830C2214yescomplemented
46#2829C2214yescomplemented
47#2829C2214yescomplemented
48#2829C2214yescomplemented
49#2827C2214yescomplemented
50#2827C2214yescomplemented
51#2826C2214yescomplemented
52#2824C2214yescomplemented
53#2816C2214yescomplemented
54#2814C2214yescomplemented
55#2813C2214yescomplemented
56#2802C2214yescomplemented
57#2800C2214yescomplemented
58#2800C2214yescomplemented
59#2798C2214yescomplemented
60#2788C2214yescomplemented
61#2786C2214yescomplemented
62#2783C2214yescomplemented
63#2783C2214yescomplemented
64#2779C2214yescomplemented
65#2761C2214yescomplemented
66#2761C2214yescomplemented
67#2755C2214yescomplemented
68#2755C2214yescomplemented
69#2751C2214yescomplemented
70#2750C2214yescomplemented
71#2750C2214yescomplemented
72#2747C2214yescomplemented
73#2744C2214yescomplemented
74#2744C2214yescomplemented
75#2743C2214yescomplemented
76#2741C2214yescomplemented
77#2741C2214yescomplemented
78#2740C2214yescomplemented
79#2740C2214yescomplemented
80#2739C2214yescomplemented
81#2730C2214yescomplemented
82#2730C2214yescomplemented
83#2708C2214yescomplemented
84#2701C2214yescomplemented
85#2700C2214yescomplemented
86#2700C2214yescomplemented
87#2696C2214yescomplemented
88#2692C2214yescomplemented
89#2687C2214yescomplemented
90#2686C2214yescomplemented
91#2686C2214yescomplemented
92#2681C2214yescomplemented
93#2676C2214yescomplemented
94#2676C2214yescomplemented
95#2671C2214yescomplemented
96#2639C2214yescomplemented
97#2639C2214yescomplemented
98#2627C2214yescomplemented
99#2626C2214yescomplemented
100#2618C2214yes—
101#2617C2214yes—
102#2569C2214yescomplemented
103#2569C2214yescomplemented
104#2569C2214yescomplemented
105#2569C2214yescomplemented
106#2564C2214yescomplemented
107#2564C2214yescomplemented
108#2543C2214yescomplemented
109#2543C2214yescomplemented
110#2543C2214yescomplemented
111#2543C2214yescomplemented
112#2534C2214yescomplemented
113#2534C2214yescomplemented
114#2498C2214yescomplemented
115#2498C2214yescomplemented
116#2488C2214yescomplemented
117#2488C2214yescomplemented
118#2488C2214yescomplemented
119#2488C2214yescomplemented
120#2486C2214yescomplemented
121#2472C2214yescomplemented
122#2472C2214yescomplemented
123#2472C2214yescomplemented
124#2472C2214yescomplemented
125#2450C2214yescomplemented
126#2450C2214yescomplemented
127#2450C2214yescomplemented
128#2450C2214yescomplemented
129#2450C2214yescomplemented
130#2450C2214yescomplemented
131#2449C2214yescomplemented
132#2449C2214yescomplemented
133#2449C2214yescomplemented
134#2449C2214yescomplemented
135#2449C2214yescomplemented
136#2449C2214yescomplemented
137#2444C2214yes—
138#2444C2214yes—
139#2444C2214yes—
140#2444C2214yes—
141#2444C2214yescomplemented
142#2444C2214yescomplemented
143#2444C2214yescomplemented
144#2444C2214yescomplemented
145#2444C2214yescomplemented
146#2444C2214yescomplemented
147#2443C2214yescomplemented
148#2443C2214yescomplemented
149#2438C2214yescomplemented
150#2438C2214yescomplemented
151#2437C2214yescomplemented
152#2437C2214yescomplemented
153#2425C2214yes—
154#2425C2214yes—
155#2424C2214yes—
156#2424C2214yes—
157#2419C2214yescomplemented
158#2419C2214yescomplemented
159#2418C2214yescomplemented
160#2418C2214yescomplemented
161#2417C2214yescomplemented
162#2417C2214yescomplemented
163#2416C2214yescomplemented
164#2416C2214yescomplemented
165#2416C2214yescomplemented
166#2416C2214yescomplemented
167#2413C2214yescomplemented
168#2412C2214yescomplemented
169#2412C2214yescomplemented
170#2412C2214yescomplemented
171#2411C2214yescomplemented
172#2410C2214yescomplemented
173#2408C2214yescomplemented
174C2×#400C2212yescomplemented
175C2×#400C2212yescomplemented
176C2×#398C2212yescomplemented
177C2×#397C2212yescomplemented
178C2×#397C2212yescomplemented
179C2×#394C2212yescomplemented
180#2378C2214yescomplemented
181#2378C2214yescomplemented
182#2377C2214yescomplemented
183#2377C2214yescomplemented
184#2315C2212yes—
185#2308C2212yes—
186#2308C2212yes—
187#2308C2212yes—
188C2×#388C2212yescomplemented
189C2×#387C2212yescomplemented
190C2×#387C2212yescomplemented
191C2×#387C2212yescomplemented
192C2×#386C2212yes—
193C2×#386C2212yes—
194C2×#386C2212yes—
195C2×#386C2212yescomplemented
196C2×#385C2212yes—
197C2×#385C2212yes—
198C2×#381C2212yescomplemented
199C2×#380C2212yes—
200C2×#380C2211yescharacteristic
201C2×C4×C22⋊C4C2211yescharacteristic
202C22×#95C2211yescharacteristic
203C23×D4C2312yes—
204C23×D4C2312yes—
205C23×D4C2312yes—
206C24×C4C2312yes—
207C24×C4C2311yescharacteristic
208C24×C4C2312yes—
209#543—44no—
210#543—44no—
211#534—48no—
212#534—44no—
213#534—44no—
214C2×#124C2314yes—
215C2×#124C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×#121—48no—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#120C2314yes—
246C2×#120C2314yes—
247C2×#120C2314yes—
248C2×#120C2314yes—
249#518—48no—
250C2×C4×D4—48no—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×#117C2314yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2314yes—
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C42C2312yes—
285C22×C42C2312yes—
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#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#399C2314yes—
305#399C2314yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
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#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#390C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
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#388C2314yes—
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#386C2314yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
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#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#382C2314yes—
535#382C2314yes—
536#381C2314yes—
537#381C2314yes—
538#381C2314yes—
539#381C2314yes—
540#381C2314yes—
541#381C2314yes—
542#381C2314yes—
543#381C2314yes—
544#381C2314yes—
545#380C2314yes—
546#380C2314yes—
547#380C2314yes—
548#380C2314yes—
549#380C2314yes—
550#380C2314yes—
551#380C2314yes—
552#380C2314yes—
553#380C2314yes—
554#380C2314yes—
555#380C2314yes—
556#380C2314yes—
557#380C2314yes—
558#380C2314yes—
559#380C2314yes—
560#380C2314yes—
561#379C2314yes—
562#379C2314yes—
563#379C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C2×#95C2312yes—
567C2×#95C2312yes—
568C2×#95C2312yes—
569C2×#95C2312yes—
570C2×#95C2312yes—
571C2×#95C2312yes—
572C2×#95C2312yes—
573C2×#95C2312yes—
574C2×#95C2312yes—
575C2×#95C2312yes—
576C2×#95C2311yescharacteristic
577C2×#95C2312yes—
578C2×#95C2311yescharacteristic
579C2×#95C2312yes—
580C2×#95C2312yes—
581C2×#95C2312yes—
582C2×#95C2312yes—
583C2×#95C2312yes—
584C2×#95C2312yes—
585C2×#95C2312yes—
586C2×#95C2311yescharacteristic
587C2×#95C2311yescharacteristic
588C25C2412yes—
589C25C2412yes—
590C25C2411yescharacteristic
591C22×Q8C2414yes—
592C22×Q8C2414yes—
593C22×D4—28no—
594C22×D4—28no—
595C22×D4—28no—
596C22×D4—28no—
597C22×D4—28no—
598C22×D4—28no—
599C22×D4—44no—
600C22×D4—44no—
601C22×D4—82no—
602C22×D4C2414yes—
603C22×D4C2414yes—
604C22×D4C2414yes—
605C22×D4C2414yes—
606C22×D4C2414yes—
607C22×D4C2414yes—
608C22×D4C2414yes—
609C22×D4C2414yes—
610C22×D4C2414yes—
611C22×D4C2414yes—
612C23×C4—28no—
613C23×C4—24no—
614C23×C4—44no—
615C23×C4—44no—
616C23×C4—44no—
617C23×C4—82no—
618C23×C4—82no—
619C23×C4—82no—
620C23×C4C2412yes—
621C23×C4C2412yes—
622C23×C4C2412yes—
623C23×C4C2412yes—
624C23×C4C2412yes—
625C23×C4C2412yes—
626C23×C4C2412yes—
627C23×C4C2412yes—
628C23×C4C2412yes—
629C23×C4C2412yes—
630C23×C4C2412yes—
631C23×C4C2412yes—
632C23×C4C2412yes—
633C23×C4C2412yes—
634C23×C4C2412yes—
635C23×C4C2412yes—
636C23×C4C2412yes—
637C23×C4C2411yescharacteristic
638C23×C4C2412yes—
639C23×C4C2414yes—
640C23×C4C2411yescharacteristic
641C23×C4C2414yes—
642C23×C4C2414yes—
643C23×C4C2414yes—
644#124—84no—
645#124—84no—
646#123—48no—
647#123—48no—
648#123—48no—
649#123—48no—
650#123—84no—
651#123—84no—
652C22⋊Q8—48no—
653C22⋊Q8—48no—
654C22⋊Q8—48no—
655C22⋊Q8—48no—
656C22⋊Q8—48no—
657C22⋊Q8—48no—
658C22⋊Q8—48no—
659C22⋊Q8—48no—
660C22⋊Q8—84no—
661C22⋊Q8—84no—
662#121—48no—
663#121—48no—
664#121—48no—
665#121—48no—
666#121—48no—
667#121—48no—
668#121—48no—
669#121—48no—
670#121—48no—
671#121—48no—
672#121—84no—
673#121—84no—
674#120—48no—
675#120—48no—
676#120—48no—
677#120—48no—
678C4×D4—48no—
679C4×D4—48no—
680C4×D4—48no—
681C4×D4—48no—
682C4×D4—48no—
683C4×D4—48no—
684C4×D4—48no—
685C4×D4—48no—
686#117—48no—
687C2×C4⋊C4—44no—
688C2×C4⋊C4—44no—
689C2×C4⋊C4—44no—
690C2×C4⋊C4—44no—
691C2×C4⋊C4—44no—
692C2×C4⋊C4—82no—
693C2×C4⋊C4—82no—
694C2×C4⋊C4—82no—
695C2×C4⋊C4—82no—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
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×C22⋊C4—28no—
731C2×C22⋊C4—28no—
732C2×C22⋊C4—28no—
733C2×C22⋊C4—24no—
734C2×C22⋊C4—24no—
735C2×C22⋊C4—44no—
736C2×C22⋊C4—48no—
737C2×C22⋊C4—44no—
738C2×C22⋊C4—44no—
739C2×C22⋊C4—44no—
740C2×C22⋊C4—82no—
741C2×C22⋊C4—82no—
742C2×C22⋊C4—82no—
743C2×C22⋊C4—82no—
744C2×C22⋊C4—82no—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C42—44no—
794C2×C42—82no—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798C2×C42C2414yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801#95C2411yescharacteristic
802#95C2412yes—
803#95C2412yes—
804#95C2412yes—
805#95C2411yescharacteristic
806#95C2412yes—
807#95C2412yes—
808#95C2412yes—
809#95C2411yescharacteristic
810#95C2411yescharacteristic
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
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—
855C24—24no—
856C24—24no—
857C24—24no—
858C24—24no—
859C24—24no—
860C24—24no—
861C24—42no—
862C24—42no—
863C24—42no—
864C24—42no—
865C24—42no—
866C24—42no—
867C24—42no—
868C24—42no—
869C24—42no—
870C24—42no—
871C24H(5,𝔽2)14yes—
872C24H(5,𝔽2)14yes—
873C242−1+414yes—
874C24C2514yes—
875C24C2514yes—
876C24C2512yes—
877C24C2511yescharacteristic
878C2×Q8—44no—
879C2×Q8—44no—
880C2×Q8—44no—
881C2×Q8—44no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—432no—
915C2×D4—432no—
916C2×D4—816no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—28no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
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—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—816no—
988C22×C4—88no—
989C22×C4—816no—
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2512yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
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⋊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—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—24no—
1102C23—24no—
1103C23—24no—
1104C23—24no—
1105C23—24no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—24no—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—48no—
1116C23—44no—
1117C23—48no—
1118C23—44no—
1119C23—48no—
1120C23—48no—
1121C23—48no—
1122C23—48no—
1123C23—84no—
1124C23—84no—
1125C23—84no—
1126C23—84no—
1127C23—84no—
1128C23—84no—
1129C23—84no—
1130C23—84no—
1131C23—84no—
1132C23—84no—
1133C23#562116yes—
1134C23C2×H(5,𝔽2)14yes—
1135C23C2×H(5,𝔽2)14yes—
1136C23C2×H(5,𝔽2)12yes—
1137C23C2×H(5,𝔽2)12yes—
1138C23C2×2−1+414yes—
1139C23C2×2−1+412yes—
1140C23C2611yescharacteristic
1141Q8—164no—
1142Q8—164no—
1143D4—416no—
1144D4—416no—
1145D4—416no—
1146D4—416no—
1147D4—88no—
1148D4—88no—
1149D4—164no—
1150D4—164no—
1151D4—164no—
1152D4—164no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—48no—
1202C2×C4—48no—
1203C2×C4—48no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—48no—
1207C2×C4—48no—
1208C2×C4—88no—
1209C2×C4—84no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—84no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—84no—
1217C2×C4—84no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4—88no—
1223C2×C4—164no—
1224C2×C4—164no—
1225C2×C4#58514yes—
1226C22—24no—
1227C22—22no—
1228C22—22no—
1229C22—24no—
1230C22—24no—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—416no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—816no—
1252C22—168no—
1253C22C2×#56218yes—
1254C22C2×#56214yes—
1255C22C22×H(5,𝔽2)11yescharacteristic
1256C22C22×H(5,𝔽2)11yescharacteristic
1257C22C22×2−1+411yescharacteristic
1258C22C2×#58512yes—
1259C22H(7,𝔽2)12yes—
1260C4—24no—
1261C4—42no—
1262C4—41no—
1263C4—41no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—44no—
1268C4—44no—
1269C4—44no—
1270C4—44no—
1271C4—44no—
1272C4—44no—
1273C4—44no—
1274C4—44no—
1275C4—44no—
1276C4—44no—
1277C2—28no—
1278C2—24no—
1279C2—84no—
1280C2—84no—
1281C2C22×#56211yescharacteristic
1282C2#6282311yescharacteristic
1283C2#6286411yescharacteristic
1284C2#6290012yes—
1285C2#6290512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52800C2semidirect
2. #52585C2semidirect
3. #52451C2semidirect
4. #52427C2semidirect
5. #52341C2semidirect
6. #52311C2semidirect
7. #46032C2semidirect
8. #46032C2semidirect
9. #45726C2semidirect
10. #45581C2semidirect
11. #45548C2semidirect
12. #45475C2semidirect
13. #35360C2semidirect
14. #35359C2semidirect
15. #35358C2semidirect
16. #35000C2semidirect
17. #34993C2semidirect
18. #34993C2semidirect
19. #34985C2semidirect
20. C2×#2569C2semidirect
21. C2×#2444C2semidirect
30. #2855C22semidirect
32. #2850C22semidirect
33. #2850C22semidirect
34. #2848C22semidirect
36. #2841C22semidirect
37. #2839C22semidirect
38. #2837C22semidirect
39. #2836C22semidirect
40. #2836C22semidirect
41. #2832C22semidirect
42. #2831C22semidirect
43. #2831C22semidirect
44. #2831C22semidirect
45. #2830C22semidirect
46. #2829C22semidirect
47. #2829C22semidirect
48. #2829C22semidirect
49. #2827C22semidirect
50. #2827C22semidirect
51. #2826C22semidirect
52. #2824C22semidirect
53. #2816C22semidirect
54. #2814C22semidirect
55. #2813C22semidirect
56. #2802C22semidirect
57. #2800C22semidirect
58. #2800C22semidirect
59. #2798C22semidirect
60. #2788C22semidirect
61. #2786C22semidirect
62. #2783C22semidirect
63. #2783C22semidirect
64. #2779C22semidirect
65. #2761C22semidirect
66. #2761C22semidirect
67. #2755C22semidirect
68. #2755C22semidirect
69. #2751C22semidirect
70. #2750C22semidirect
71. #2750C22semidirect
72. #2747C22semidirect
73. #2744C22semidirect
74. #2744C22semidirect
75. #2743C22semidirect
76. #2741C22semidirect
77. #2741C22semidirect
78. #2740C22semidirect
79. #2740C22semidirect
80. #2739C22semidirect
81. #2730C22semidirect
82. #2730C22semidirect
83. #2708C22semidirect
84. #2701C22semidirect
85. #2700C22semidirect
86. #2700C22semidirect
87. #2696C22semidirect
88. #2692C22semidirect
89. #2687C22semidirect
90. #2686C22semidirect
91. #2686C22semidirect
92. #2681C22semidirect
93. #2676C22semidirect
94. #2676C22semidirect
95. #2671C22semidirect
96. #2639C22semidirect
97. #2639C22semidirect
98. #2627C22semidirect
99. #2626C22semidirect
102. #2569C22semidirect
103. #2569C22semidirect
104. #2569C22semidirect
105. #2569C22semidirect
106. #2564C22semidirect
107. #2564C22semidirect
108. #2543C22semidirect
109. #2543C22semidirect
110. #2543C22semidirect
111. #2543C22semidirect
112. #2534C22semidirect
113. #2534C22semidirect
114. #2498C22semidirect
115. #2498C22semidirect
116. #2488C22semidirect
117. #2488C22semidirect
118. #2488C22semidirect
119. #2488C22semidirect
120. #2486C22semidirect
121. #2472C22semidirect
122. #2472C22semidirect
123. #2472C22semidirect
124. #2472C22semidirect
125. #2450C22semidirect
126. #2450C22semidirect
127. #2450C22semidirect
128. #2450C22semidirect
129. #2450C22semidirect
130. #2450C22semidirect
131. #2449C22semidirect
132. #2449C22semidirect
133. #2449C22semidirect
134. #2449C22semidirect
135. #2449C22semidirect
136. #2449C22semidirect
141. #2444C22semidirect
142. #2444C22semidirect
143. #2444C22semidirect
144. #2444C22semidirect
145. #2444C22semidirect
146. #2444C22semidirect
147. #2443C22semidirect
148. #2443C22semidirect
149. #2438C22semidirect
150. #2438C22semidirect
151. #2437C22semidirect
152. #2437C22semidirect
157. #2419C22semidirect
158. #2419C22semidirect
159. #2418C22semidirect
160. #2418C22semidirect
161. #2417C22semidirect
162. #2417C22semidirect
163. #2416C22semidirect
164. #2416C22semidirect
165. #2416C22semidirect
166. #2416C22semidirect
167. #2413C22semidirect
168. #2412C22semidirect
169. #2412C22semidirect
170. #2412C22semidirect
171. #2411C22semidirect
172. #2410C22semidirect
173. #2408C22semidirect
174. C2×#400C22semidirect
175. C2×#400C22semidirect
176. C2×#398C22semidirect
177. C2×#397C22semidirect
178. C2×#397C22semidirect
179. C2×#394C22semidirect
180. #2378C22semidirect
181. #2378C22semidirect
182. #2377C22semidirect
183. #2377C22semidirect
188. C2×#388C22semidirect
189. C2×#387C22semidirect
190. C2×#387C22semidirect
191. C2×#387C22semidirect
195. C2×#386C22semidirect
198. C2×#381C22semidirect

Maximal subgroups

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

subgroupindex
#528002
#525852
#524512
#524272
#523412
#523112
#460322
#457262
#455812
#455482
#454752
#353602
#353592
#353582
#350002
#349932
#349852
C2×#25692
C2×#24442