Finite Group Databasebeta

← #8901524

Subgroups — #8901524

Order 512.

5242 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58950C214yesmaximal, complemented
2#58436C214yesmaximal, complemented
3#58017C214yesmaximal, complemented
4#52076C212yesmaximal, complemented
5#51531C212yesmaximal, complemented
6#51202C214yesmaximal, complemented
7#51104C214yesmaximal, complemented
8#47624C214yesmaximal, complemented
9#47224C212yesmaximal, complemented
10#46507C212yesmaximal, complemented
11#46507C212yesmaximal, complemented
12#46436C214yesmaximal, complemented
13#46423C212yesmaximal, complemented
14#46356C212yesmaximal, complemented
15#39958C214yesmaximal, complemented
16#39690C214yesmaximal, complemented
17#38357C214yesmaximal, complemented
18#37296C212yesmaximal, complemented
19#36707C211yesmaximal, characteristic, complemented
20#35634C211yesmaximal, characteristic, complemented
21#35440C212yesmaximal, complemented
22#35422C212yesmaximal, complemented
23#35391C211yesmaximal, characteristic, complemented
24C2×#563C2212yescomplemented
25C2×#555C2212yescomplemented
26C2×#553C2214yes—
27C2×#543C2211yescharacteristic
28C2×#537C2212yes—
29C2×#537C2211yescharacteristic
30C2×#537C2211yescharacteristic
31C2×#536C2212yes—
32C2×#525C2212yes—
33C22×C22⋊Q8C2211yescharacteristic
34#2857C2212yescomplemented
35#2856C2212yescomplemented
36#2847C2212yes—
37#2841C2214yescomplemented
38#2837C2214yescomplemented
39#2829C2214yescomplemented
40#2826C2212yes—
41#2826C2212yes—
42#2816C2212yes—
43#2807C2212yes—
44#2807C2212yes—
45#2807C2214yescomplemented
46#2798C2214yescomplemented
47#2791C2214yescomplemented
48#2786C2214yescomplemented
49#2780C2214yes—
50#2780C2214yes—
51#2780C2214yescomplemented
52#2734C2212yescomplemented
53#2733C2212yescomplemented
54#2732C2214yes—
55#2732C2214yescomplemented
56#2732C2214yescomplemented
57#2731C2212yescomplemented
58#2731C2212yescomplemented
59#2729C2214yescomplemented
60#2727C2214yescomplemented
61#2721C2214yescomplemented
62#2720C2214yescomplemented
63#2718C2214yescomplemented
64#2711C2214yes—
65#2711C2214yes—
66#2707C2214yes—
67#2707C2214yescomplemented
68#2704C2214yes—
69#2704C2214yescomplemented
70#2703C2214yes—
71#2703C2214yes—
72#2702C2214yescomplemented
73#2701C2214yescomplemented
74#2695C2214yes—
75#2692C2214yes—
76#2692C2214yes—
77#2692C2214yes—
78#2692C2214yescomplemented
79#2691C2214yes—
80#2686C2214yescomplemented
81#2682C2214yes—
82#2682C2214yes—
83#2682C2214yes—
84#2681C2214yes—
85#2681C2214yes—
86#2681C2214yescomplemented
87#2676C2214yes—
88#2676C2214yes—
89#2676C2214yes—
90#2676C2214yes—
91#2675C2212yes—
92#2675C2214yes—
93#2675C2212yes—
94#2674C2214yescomplemented
95#2672C2214yes—
96#2672C2214yescomplemented
97#2672C2214yescomplemented
98#2672C2214yescomplemented
99#2671C2214yes—
100#2671C2214yes—
101#2671C2214yes—
102#2671C2214yescomplemented
103#2671C2214yescomplemented
104#2671C2214yescomplemented
105#2662C2214yescomplemented
106#2662C2214yescomplemented
107#2636C2214yes—
108#2630C2214yes—
109#2629C2214yescomplemented
110#2628C2214yescomplemented
111#2620C2212yescomplemented
112#2620C2212yescomplemented
113#2618C2212yes—
114#2609C2214yes—
115#2608C2212yes—
116#2601C2214yes—
117#2601C2214yescomplemented
118#2601C2214yescomplemented
119#2589C2214yes—
120#2589C2214yescomplemented
121#2588C2214yescomplemented
122#2587C2214yescomplemented
123#2583C2212yes—
124#2583C2212yes—
125#2579C2214yes—
126#2559C2214yes—
127#2558C2214yes—
128#2558C2214yes—
129#2554C2214yes—
130#2550C2214yescomplemented
131#2549C2214yes—
132#2549C2214yes—
133#2549C2214yescomplemented
134#2543C2214yes—
135#2543C2214yes—
136#2542C2214yes—
137#2542C2214yes—
138#2540C2214yes—
139#2540C2214yes—
140#2540C2214yes—
141#2539C2212yes—
142#2539C2212yes—
143#2539C2211yescharacteristic
144#2539C2211yescharacteristic
145#2507C2214yescomplemented
146#2506C2214yescomplemented
147#2502C2212yes—
148#2502C2212yescomplemented
149#2501C2212yes—
150#2501C2212yes—
151#2501C2212yescomplemented
152#2476C2214yes—
153#2475C2214yescomplemented
154#2474C2214yescomplemented
155#2470C2214yes—
156#2470C2214yes—
157#2467C2214yes—
158#2461C2214yescomplemented
159#2459C2214yes—
160#2457C2214yes—
161#2455C2212yes—
162#2455C2212yes—
163#2454C2214yes—
164#2454C2214yes—
165#2454C2214yescomplemented
166#2452C2214yes—
167#2452C2214yescomplemented
168#2450C2214yes—
169#2450C2214yescomplemented
170#2449C2214yes—
171#2449C2214yes—
172#2449C2214yescomplemented
173#2441C2214yescomplemented
174#2440C2214yes—
175#2440C2214yes—
176#2438C2214yescomplemented
177#2436C2211yescharacteristic
178#2436C2211yescharacteristic
179#2434C2212yes—
180#2432C2212yes—
181#2432C2212yescomplemented
182#2431C2212yes—
183#2431C2212yescomplemented
184#2430C2214yes—
185#2430C2214yescomplemented
186#2428C2214yes—
187#2428C2214yescomplemented
188#2424C2214yes—
189#2424C2214yes—
190#2424C2214yes—
191#2424C2214yes—
192#2416C2214yes—
193#2414C2214yes—
194#2414C2214yes—
195#2414C2214yescomplemented
196#2407C2214yes—
197#2407C2214yes—
198#2406C2212yes—
199#2404C2212yes—
200#2379C2212yescomplemented
201#2369C2212yescomplemented
202#2349C2214yes—
203#2334C2214yescomplemented
204#2333C2214yes—
205#2333C2212yes—
206#2332C2212yes—
207#2325C2214yes—
208#2324C2214yes—
209#2324C2214yes—
210#2324C2214yes—
211#2315C2212yes—
212#2313C2211yescharacteristic
213C4×#121C2214yes—
214#2297C2212yes—
215#2296C2214yescomplemented
216C2×#385C2212yes—
217#2274C2211yescharacteristic
218#2273C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2312yes—
221C22×#41C2312yes—
222C23×Q8C2311yescharacteristic
223C24×C4C2311yescharacteristic
224#563—48no—
225#555—48no—
226#553—416no—
227#543—44no—
228#537—44no—
229#537—44no—
230#537—48no—
231#536—48no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×#127C2312yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#124C2312yes—
245C2×#124C2314yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251#525—48no—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2312yes—
259C2×#123C2312yes—
260C2×#123C2314yes—
261C2×C22⋊Q8—44no—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2311yescharacteristic
291C2×#121C2314yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2311yescharacteristic
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#120C2314yes—
303C2×#120C2312yes—
304C2×#120C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×#117C2314yes—
314C2×#117C2312yes—
315C2×#117C2314yes—
316C2×#117C2314yes—
317C2×#117C2312yes—
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2314yes—
321C22×C4⋊C4C2311yescharacteristic
322C22×C4⋊C4C2312yes—
323C22×C22⋊C4C2312yes—
324C22×C22⋊C4C2311yescharacteristic
325C22×C22⋊C4C2311yescharacteristic
326C22×C22⋊C4C2312yes—
327C22×C42C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#399C2314yes—
335#399C2312yes—
336#399C2312yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2312yes—
347#399C2312yes—
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#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#392C2312yes—
427#392C2312yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2312yes—
437#392C2314yes—
438#392C2314yes—
439#392C2312yes—
440#391C2314yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2312yes—
464#390C2312yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#388C2314yes—
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#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
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#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2312yes—
544#386C2312yes—
545#386C2314yes—
546#386C2314yes—
547#386C2312yes—
548#386C2312yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#385C2312yes—
554#385C2312yes—
555#385C2312yes—
556#385C2312yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
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#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#384C2312yes—
586#384C2312yes—
587#384C2312yes—
588#384C2312yes—
589#384C2314yes—
590#382C2314yes—
591#381C2312yes—
592#381C2314yes—
593#380C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C22⋊C4C2311yescharacteristic
612C4×C22⋊C4C2311yescharacteristic
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2312yes—
622C2×#95C2314yes—
623C2×#95C2314yes—
624C25C2411yescharacteristic
625C2×#41—28no—
626C2×#41—44no—
627C2×#41—44no—
628C2×#41—44no—
629C2×#41—44no—
630C2×#41—82no—
631C2×#41—82no—
632C2×#41—82no—
633C2×#41—82no—
634C22×Q8—42no—
635C22×Q8—44no—
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×Q8C2412yes—
641C22×Q8C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2412yes—
651C22×D4C2412yes—
652C22×D4C2412yes—
653C22×D4C2412yes—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2411yescharacteristic
657C22×D4C2412yes—
658C22×D4C2414yes—
659C22×D4C2411yescharacteristic
660C23×C4—44no—
661C23×C4—42no—
662C23×C4C2411yescharacteristic
663C23×C4C2414yes—
664C23×C4C2411yescharacteristic
665C23×C4C2414yes—
666C23×C4C2411yescharacteristic
667C23×C4C2411yescharacteristic
668C23×C4C2411yescharacteristic
669C23×C4C2414yes—
670C23×C4C2412yes—
671C23×C4C2414yes—
672C23×C4C2412yes—
673C23×C4C2414yes—
674C23×C4C2412yes—
675C23×C4C2412yes—
676C23×C4C2414yes—
677C23×C4C2414yes—
678C23×C4C2411yescharacteristic
679C4⋊Q8—28no—
680C4⋊Q8—44no—
681C4⋊Q8—44no—
682C4⋊Q8—44no—
683C4⋊Q8—82no—
684#127—82no—
685#126—216no—
686#126—48no—
687#126—48no—
688#125—48no—
689#125—48no—
690#125—84no—
691#124—28no—
692#124—48no—
693#124—44no—
694#124—44no—
695#124—44no—
696#124—82no—
697#124—82no—
698#123—48no—
699#123—48no—
700#123—48no—
701#123—48no—
702#123—48no—
703#123—48no—
704#123—82no—
705#123—84no—
706#123—82no—
707C22⋊Q8—28no—
708C22⋊Q8—44no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—48no—
715C22⋊Q8—48no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—44no—
721C22⋊Q8—44no—
722C22⋊Q8—44no—
723#121—28no—
724#121—216no—
725#121—216no—
726#121—48no—
727#121—48no—
728#121—48no—
729#121—48no—
730#121—48no—
731#121—48no—
732#121—48no—
733#121—48no—
734#121—48no—
735#121—48no—
736#121—48no—
737#121—44no—
738#121—44no—
739#121—44no—
740#121—44no—
741#121—42no—
742#121—42no—
743#121—44no—
744#121—84no—
745#121—84no—
746#121—84no—
747#120—48no—
748#120—82no—
749#120—82no—
750C4×D4—216no—
751C4×D4—48no—
752C4×D4—48no—
753C4×D4—48no—
754C4×D4—48no—
755C4×D4—48no—
756C4×D4—84no—
757C4×D4—84no—
758#117—28no—
759#117—216no—
760#117—48no—
761#117—84no—
762#117—82no—
763C2×C4⋊C4—24no—
764C2×C4⋊C4—24no—
765C2×C4⋊C4—44no—
766C2×C4⋊C4—48no—
767C2×C4⋊C4—42no—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
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×C22⋊C4—24no—
816C2×C22⋊C4—28no—
817C2×C22⋊C4—44no—
818C2×C22⋊C4—42no—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C42—82no—
873C2×C42C2414yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
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—
926C24—22no—
927C24—24no—
928C24—42no—
929C24—42no—
930C24C2512yes—
931C24C2514yes—
932C24C2512yes—
933C24C2511yescharacteristic
934C24C2512yes—
935#41—816no—
936#41—816no—
937#41—816no—
938C2×Q8—24no—
939C2×Q8—24no—
940C2×Q8—24no—
941C2×Q8—24no—
942C2×Q8—24no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—42no—
947C2×Q8—42no—
948C2×Q8—42no—
949C2×Q8—42no—
950C2×Q8—42no—
951C2×Q8—42no—
952C2×Q8—42no—
953C2×Q8—42no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—88no—
957C2×D4—28no—
958C2×D4—28no—
959C2×D4—24no—
960C2×D4—24no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—24no—
966C2×D4—24no—
967C2×D4—24no—
968C2×D4—28no—
969C2×D4—28no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—42no—
980C2×D4—42no—
981C2×D4—42no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—42no—
992C2×D4—42no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—44no—
997C2×D4—42no—
998C2×D4—41no—
999C2×D4—41no—
1000C2×D4—42no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—42no—
1007C22×C4—22no—
1008C22×C4—24no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—24no—
1014C22×C4—28no—
1015C22×C4—24no—
1016C22×C4—28no—
1017C22×C4—28no—
1018C22×C4—28no—
1019C22×C4—28no—
1020C22×C4—28no—
1021C22×C4—44no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—88no—
1050C22×C4H(5,𝔽2)14yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—41no—
1101C4⋊C4—41no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
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—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—44no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—42no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C42−1+418yes—
1169C42—28no—
1170C42—24no—
1171C42—44no—
1172C42—42no—
1173C42—42no—
1174C42—42no—
1175C42—44no—
1176C42—42no—
1177C42—42no—
1178C42—44no—
1179C42—44no—
1180C42—42no—
1181C42—42no—
1182C42—42no—
1183C42H(5,𝔽2)18yes—
1184C23—28no—
1185C23—22no—
1186C23—22no—
1187C23—24no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—24no—
1192C23—24no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—24no—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—22no—
1204C23—24no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—24no—
1209C23—82no—
1210C23—82no—
1211C23—88no—
1212C23C2×H(5,𝔽2)12yes—
1213C23C2×2−1+414yes—
1214C23C2611yescharacteristic
1215Q8—84no—
1216Q8—84no—
1217Q8—84no—
1218Q8—84no—
1219Q8—84no—
1220Q8—162no—
1221D4—416no—
1222D4—88no—
1223D4—88no—
1224D4—84no—
1225D4—84no—
1226D4—84no—
1227D4—88no—
1228D4—88no—
1229D4—88no—
1230D4—88no—
1231D4—84no—
1232D4—84no—
1233D4—88no—
1234D4—162no—
1235D4—161no—
1236D4—161no—
1237D4—164no—
1238D4—162no—
1239C2×C4—28no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—44no—
1287C2×C4—416no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—88no—
1291C2×C4—88no—
1292C2×C4—88no—
1293C2×C4—88no—
1294C2×C4—82no—
1295C2×C4—82no—
1296C2×C4—82no—
1297C2×C4—82no—
1298C2×C4—88no—
1299C2×C4—164no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4C2×H(5,𝔽2)18yes—
1303C2×C4C2×H(5,𝔽2)14yes—
1304C2×C4C2×H(5,𝔽2)14yes—
1305C2×C4C2×2−1+418yes—
1306C22—22no—
1307C22—22no—
1308C22—24no—
1309C22—22no—
1310C22—28no—
1311C22—42no—
1312C22—42no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—42no—
1317C22—42no—
1318C22—44no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—88no—
1333C22C22×H(5,𝔽2)11yescharacteristic
1334C22C22×H(5,𝔽2)12yes—
1335C22C22×2−1+412yes—
1336C22H(7,𝔽2)12yes—
1337C4—24no—
1338C4—24no—
1339C4—28no—
1340C4—28no—
1341C4—42no—
1342C4—44no—
1343C4—41no—
1344C4—41no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—44no—
1352C4—44no—
1353C4—44no—
1354C4—44no—
1355C2—42no—
1356C2—44no—
1357C2—84no—
1358C2—82no—
1359C2—82no—
1360C2#6283211yescharacteristic
1361C2#6283311yescharacteristic
1362C2#6286211yescharacteristic
1363C2#6294414yes—
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. #58950C2semidirect
2. #58436C2semidirect
3. #58017C2semidirect
4. #52076C2semidirect
5. #51531C2semidirect
6. #51202C2semidirect
7. #51104C2semidirect
8. #47624C2semidirect
9. #47224C2semidirect
10. #46507C2semidirect
11. #46507C2semidirect
12. #46436C2semidirect
13. #46423C2semidirect
14. #46356C2semidirect
15. #39958C2semidirect
16. #39690C2semidirect
17. #38357C2semidirect
18. #37296C2semidirect
19. #36707C2semidirect
20. #35634C2semidirect
21. #35440C2semidirect
22. #35422C2semidirect
23. #35391C2semidirect
24. C2×#563C22semidirect
25. C2×#555C22semidirect
34. #2857C22semidirect
35. #2856C22semidirect
37. #2841C22semidirect
38. #2837C22semidirect
39. #2829C22semidirect
45. #2807C22semidirect
46. #2798C22semidirect
47. #2791C22semidirect
48. #2786C22semidirect
51. #2780C22semidirect
52. #2734C22semidirect
53. #2733C22semidirect
55. #2732C22semidirect
56. #2732C22semidirect
57. #2731C22semidirect
58. #2731C22semidirect
59. #2729C22semidirect
60. #2727C22semidirect
61. #2721C22semidirect
62. #2720C22semidirect
63. #2718C22semidirect
67. #2707C22semidirect
69. #2704C22semidirect
72. #2702C22semidirect
73. #2701C22semidirect
78. #2692C22semidirect
80. #2686C22semidirect
86. #2681C22semidirect
94. #2674C22semidirect
96. #2672C22semidirect
97. #2672C22semidirect
98. #2672C22semidirect
102. #2671C22semidirect
103. #2671C22semidirect
104. #2671C22semidirect
105. #2662C22semidirect
106. #2662C22semidirect
109. #2629C22semidirect
110. #2628C22semidirect
111. #2620C22semidirect
112. #2620C22semidirect
117. #2601C22semidirect
118. #2601C22semidirect
120. #2589C22semidirect
121. #2588C22semidirect
122. #2587C22semidirect
130. #2550C22semidirect
133. #2549C22semidirect
145. #2507C22semidirect
146. #2506C22semidirect
148. #2502C22semidirect
151. #2501C22semidirect
153. #2475C22semidirect
154. #2474C22semidirect
158. #2461C22semidirect
165. #2454C22semidirect
167. #2452C22semidirect
169. #2450C22semidirect
172. #2449C22semidirect
173. #2441C22semidirect
176. #2438C22semidirect
181. #2432C22semidirect
183. #2431C22semidirect
185. #2430C22semidirect
187. #2428C22semidirect
195. #2414C22semidirect
200. #2379C22semidirect
201. #2369C22semidirect
203. #2334C22semidirect
215. #2296C22semidirect

Maximal subgroups

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

subgroupindex
#589502
#584362
#580172
#520762
#515312
#512022
#511042
#476242
#472242
#465072
#464362
#464232
#463562
#399582
#396902
#383572
#372962
#367072
#356342
#354402
#354222
#353912