Finite Group Databasebeta

← #7714781

Subgroups — #7714781

Order 512.

5242 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51840C212yesmaximal, complemented
2#51831C212yesmaximal, complemented
3#51681C212yesmaximal, complemented
4#51680C214yesmaximal, complemented
5#51668C212yesmaximal, complemented
6#51667C214yesmaximal, complemented
7#46625C214yesmaximal, complemented
8#46621C214yesmaximal, complemented
9#46611C214yesmaximal, complemented
10#46607C214yesmaximal, complemented
11#39559C214yesmaximal, complemented
12#39431C214yesmaximal, complemented
13#37855C214yesmaximal, complemented
14#37667C214yesmaximal, complemented
15#37518C212yesmaximal, complemented
16#37194C211yesmaximal, characteristic, complemented
17#37190C211yesmaximal, characteristic, complemented
18#37140C212yesmaximal, complemented
19#35242C212yesmaximal, complemented
20#35094C212yesmaximal, complemented
21#35093C212yesmaximal, complemented
22#34409C212yesmaximal, complemented
23C2×#2310C211yesmaximal, characteristic, complemented
24C24×Q8C2211yescharacteristic
25C2×#539C2212yes—
26C2×#538C2212yes—
27C2×#536C2212yes—
28C2×#536C2212yes—
29C2×#525C2212yes—
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32#2855C2212yes—
33#2855C2212yes—
34#2854C2212yes—
35#2854C2212yes—
36#2849C2214yes—
37#2849C2214yes—
38#2833C2212yescomplemented
39#2832C2212yescomplemented
40#2831C2214yescomplemented
41#2811C2211yescharacteristic, complemented
42#2809C2212yescomplemented
43#2809C2211yescharacteristic, complemented
44#2808C2212yescomplemented
45#2806C2214yescomplemented
46#2806C2212yescomplemented
47#2806C2212yescomplemented
48#2805C2212yescomplemented
49#2804C2212yescomplemented
50#2799C2214yescomplemented
51#2799C2214yescomplemented
52#2799C2212yescomplemented
53#2798C2214yescomplemented
54#2798C2214yescomplemented
55#2789C2214yescomplemented
56#2788C2214yescomplemented
57#2775C2214yescomplemented
58#2774C2214yescomplemented
59#2759C2214yescomplemented
60#2759C2214yescomplemented
61#2758C2214yescomplemented
62#2755C2214yescomplemented
63#2754C2214yescomplemented
64#2751C2214yescomplemented
65#2746C2214yes—
66#2745C2214yes—
67#2745C2214yescomplemented
68#2744C2214yes—
69#2743C2214yes—
70#2740C2214yes—
71#2739C2214yes—
72#2738C2214yes—
73#2737C2214yes—
74#2734C2211yescharacteristic, complemented
75#2733C2211yescharacteristic, complemented
76#2732C2212yescomplemented
77#2731C2212yescomplemented
78#2730C2214yescomplemented
79#2729C2214yescomplemented
80#2728C2212yescomplemented
81#2716C2214yescomplemented
82#2713C2214yescomplemented
83#2710C2214yescomplemented
84#2701C2214yes—
85#2700C2214yes—
86#2700C2214yescomplemented
87#2699C2214yes—
88#2698C2214yes—
89#2692C2214yescomplemented
90#2690C2214yescomplemented
91#2689C2214yes—
92#2689C2214yescomplemented
93#2688C2214yes—
94#2687C2214yes—
95#2687C2214yescomplemented
96#2686C2214yes—
97#2666C2214yescomplemented
98#2665C2214yescomplemented
99#2653C2214yescomplemented
100#2650C2214yescomplemented
101#2627C2212yes—
102#2626C2212yes—
103#2623C2214yes—
104#2622C2214yes—
105#2618C2212yes—
106#2617C2212yes—
107#2614C2214yes—
108#2614C2214yes—
109#2607C2214yescomplemented
110#2605C2214yescomplemented
111#2589C2214yescomplemented
112#2588C2214yescomplemented
113#2588C2214yescomplemented
114#2586C2212yescomplemented
115#2576C2214yes—
116#2575C2214yes—
117#2574C2214yescomplemented
118#2573C2214yes—
119#2572C2214yes—
120#2572C2212yescomplemented
121#2560C2214yescomplemented
122#2557C2214yescomplemented
123#2556C2214yescomplemented
124#2550C2214yescomplemented
125#2549C2214yescomplemented
126#2527C2214yes—
127#2527C2214yescomplemented
128#2526C2214yes—
129#2523C2214yescomplemented
130#2521C2214yescomplemented
131#2520C2214yescomplemented
132#2516C2214yes—
133#2515C2214yes—
134#2498C2214yes—
135#2493C2214yes—
136#2493C2214yes—
137#2492C2214yescomplemented
138#2488C2214yes—
139#2488C2214yes—
140#2488C2214yescomplemented
141#2479C2214yes—
142#2479C2214yes—
143#2478C2214yes—
144#2478C2214yes—
145#2477C2214yes—
146#2477C2214yes—
147#2476C2214yes—
148#2476C2214yes—
149#2475C2214yes—
150#2475C2214yes—
151#2474C2214yes—
152#2474C2214yes—
153#2471C2214yes—
154#2471C2214yes—
155#2470C2214yes—
156#2470C2214yes—
157#2468C2214yes—
158#2466C2214yes—
159#2459C2214yes—
160#2457C2214yes—
161#2447C2214yes—
162#2444C2214yes—
163#2438C2214yes—
164#2438C2214yes—
165#2436C2212yes—
166#2436C2212yes—
167#2436C2212yes—
168#2436C2212yes—
169#2434C2212yes—
170#2434C2212yes—
171#2434C2212yes—
172#2434C2212yes—
173#2430C2214yes—
174#2425C2214yes—
175#2425C2214yes—
176#2420C2214yes—
177#2419C2214yes—
178#2419C2214yes—
179#2419C2214yes—
180#2409C2214yes—
181#2409C2214yes—
182#2409C2214yes—
183#2409C2214yes—
184#2381C2212yescomplemented
185#2379C2212yescomplemented
186#2378C2214yescomplemented
187#2372C2212yescomplemented
188#2369C2212yescomplemented
189#2368C2214yescomplemented
190#2359C2214yes—
191#2359C2214yes—
192#2343C2214yes—
193#2339C2214yes—
194#2337C2214yescomplemented
195#2332C2214yescomplemented
196#2331C2214yescomplemented
197#2329C2214yescomplemented
198#2322C2214yes—
199#2321C2214yes—
200#2313C2212yes—
201#2312C2212yes—
202#2310C2214yes—
203#2310C2214yes—
204#2310C2212yes—
205#2310C2212yes—
206#2310C2212yes—
207#2310C2212yes—
208#2310C2212yes—
209#2310C2212yes—
210C4×#123C2214yes—
211C4×#123C2214yes—
212C2×#391C2214yes—
213C2×#391C2211yescharacteristic
214C2×#391C2211yescharacteristic
215C2×#391C2211yescharacteristic
216C2×#391C2211yescharacteristic
217#2280C2212yes—
218C2×#381C2214yes—
219C22×#41C2312yes—
220C23×Q8—28no—
221C23×Q8—44no—
222C23×Q8—44no—
223C23×Q8C2312yes—
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226C23×Q8C2312yes—
227C23×Q8C2312yes—
228C23×Q8C2311yescharacteristic
229C23×Q8C2311yescharacteristic
230C24×C4C2311yescharacteristic
231C24×C4C2312yes—
232#539—48no—
233#538—48no—
234#536—216no—
235#536—48no—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2314yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2314yes—
248#525—48no—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×#121C2312yes—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×#120C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×#117—44no—
276C2×#117—44no—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2314yes—
281C2×#117C2312yes—
282C2×#117C2314yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C42C2311yescharacteristic
292C22×C42C2312yes—
293C22×C42C2311yescharacteristic
294#401C2314yes—
295#401C2314yes—
296#400C2314yes—
297#400C2312yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
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#395C2314yes—
357#395C2314yes—
358#395C2312yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2312yes—
367#395C2314yes—
368#395C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2312yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2312yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#392C2314yes—
393#392C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2314yes—
406#391C2311yescharacteristic
407#391C2314yes—
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2314yes—
412#391C2312yes—
413#391C2314yes—
414#391C2312yes—
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2314yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2312yes—
443#390C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#386C2314yes—
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#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#383C2314yes—
567#383C2314yes—
568#383C2314yes—
569#382C2314yes—
570#382C2314yes—
571#382C2314yes—
572#381C2314yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#379C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618#376C2314yes—
619C2×#95C2314yes—
620C2×#95C2314yes—
621C2×#95C2314yes—
622C2×#95C2314yes—
623C2×#95C2314yes—
624C25C2411yescharacteristic
625C2×#41—28no—
626C2×#41—44no—
627C2×#41—44no—
628C22×Q8—28no—
629C22×Q8—28no—
630C22×Q8—28no—
631C22×Q8—28no—
632C22×Q8—28no—
633C22×Q8—24no—
634C22×Q8—28no—
635C22×Q8—44no—
636C22×Q8—42no—
637C22×Q8—42no—
638C22×Q8—42no—
639C22×Q8—42no—
640C22×Q8—44no—
641C22×Q8—44no—
642C22×Q8—44no—
643C22×Q8—44no—
644C22×Q8—44no—
645C22×Q8—44no—
646C22×Q8—44no—
647C22×Q8—44no—
648C22×Q8—464no—
649C22×Q8#4118yes—
650C22×Q8C2412yes—
651C22×Q8C2412yes—
652C22×Q8C2412yes—
653C22×Q8C2412yes—
654C22×Q8C2412yes—
655C22×Q8C2412yes—
656C22×Q8C2411yescharacteristic
657C22×Q8C2411yescharacteristic
658C22×Q8C2412yes—
659C22×Q8C2412yes—
660C22×Q8C2411yescharacteristic
661C22×Q8C2412yes—
662C22×Q8C2411yescharacteristic
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2414yes—
666C22×D4C2412yes—
667C22×D4C2412yes—
668C22×D4C2412yes—
669C23×C4—24no—
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—28no—
673C23×C4—28no—
674C23×C4—44no—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2412yes—
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2412yes—
689C23×C4C2414yes—
690C23×C4C2414yes—
691C23×C4C2414yes—
692C4⋊Q8—28no—
693C4⋊Q8—28no—
694C4⋊Q8—44no—
695C4⋊Q8—44no—
696#126—48no—
697#126—48no—
698#125—48no—
699#124—28no—
700#124—28no—
701#124—48no—
702#124—44no—
703#124—44no—
704#123—216no—
705#123—216no—
706#123—216no—
707#123—48no—
708#123—48no—
709#123—48no—
710#123—48no—
711C22⋊Q8—216no—
712C22⋊Q8—216no—
713C22⋊Q8—44no—
714C22⋊Q8—44no—
715C22⋊Q8—44no—
716C22⋊Q8—44no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720#121—48no—
721#121—44no—
722#121—44no—
723#121—44no—
724#121—44no—
725#120—216no—
726C4×D4—48no—
727C4×D4—48no—
728C4×D4—48no—
729C4×D4—48no—
730#117—28no—
731#117—44no—
732#117—48no—
733#117—44no—
734#117—44no—
735#117—44no—
736#117—44no—
737#117—48no—
738#117—44no—
739C2×C4⋊C4—28no—
740C2×C4⋊C4—42no—
741C2×C4⋊C4—42no—
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⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C22⋊C4—28no—
786C2×C22⋊C4—44no—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C42—44no—
823C2×C42—42no—
824C2×C42—42no—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2411yescharacteristic
832C2×C42C2412yes—
833C2×C42C2411yescharacteristic
834C2×C42C2414yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
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—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2412yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905C24—22no—
906C24—22no—
907C24—42no—
908C24—42no—
909C24H(5,𝔽2)14yes—
910C24C2514yes—
911C24C2512yes—
912C24C2511yescharacteristic
913#41—816no—
914C2×Q8—24no—
915C2×Q8—24no—
916C2×Q8—24no—
917C2×Q8—24no—
918C2×Q8—24no—
919C2×Q8—22no—
920C2×Q8—22no—
921C2×Q8—24no—
922C2×Q8—24no—
923C2×Q8—24no—
924C2×Q8—24no—
925C2×Q8—24no—
926C2×Q8—416no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—41no—
930C2×Q8—42no—
931C2×Q8—42no—
932C2×Q8—42no—
933C2×Q8—41no—
934C2×Q8—42no—
935C2×Q8—41no—
936C2×Q8—41no—
937C2×Q8—41no—
938C2×Q8—42no—
939C2×Q8—41no—
940C2×Q8—42no—
941C2×Q8—41no—
942C2×Q8—41no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—42no—
946C2×Q8—42no—
947C2×Q8—42no—
948C2×Q8—44no—
949C2×Q8—42no—
950C2×Q8—432no—
951C2×Q8—432no—
952C2×Q8—432no—
953C2×Q8—432no—
954C2×Q8—432no—
955C2×Q8—416no—
956C2×Q8C2×#4114yes—
957C2×Q8C2×#4118yes—
958C2×Q8C2×#4114yes—
959C2×D4—28no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—28no—
964C2×D4—24no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—42no—
972C2×D4—42no—
973C2×D4—42no—
974C2×D4—44no—
975C2×D4—42no—
976C22×C4—232no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—28no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—432no—
1024C22×C4C2×#4118yes—
1025C22×C4C2×#4114yes—
1026C22×C4H(5,𝔽2)14yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—41no—
1059C4⋊C4—42no—
1060C4⋊C4—41no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C42—24no—
1126C42—24no—
1127C42—44no—
1128C42—44no—
1129C42—42no—
1130C42—42no—
1131C42—41no—
1132C42—42no—
1133C42—41no—
1134C42—44no—
1135C42—44no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—42no—
1140C42—42no—
1141C42—44no—
1142C42—44no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—24no—
1148C23—24no—
1149C23—28no—
1150C23—24no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—44no—
1158C23—44no—
1159C23—48no—
1160C23—48no—
1161C23C22×#4112yes—
1162C23C2×H(5,𝔽2)14yes—
1163C23C2×H(5,𝔽2)12yes—
1164C23C2×H(5,𝔽2)12yes—
1165C23C2611yescharacteristic
1166Q8—44no—
1167Q8—48no—
1168Q8—44no—
1169Q8—48no—
1170Q8—48no—
1171Q8—48no—
1172Q8—48no—
1173Q8—48no—
1174Q8—44no—
1175Q8—44no—
1176Q8—84no—
1177Q8—162no—
1178Q8—162no—
1179D4—416no—
1180D4—84no—
1181D4—88no—
1182D4—88no—
1183D4—162no—
1184D4—162no—
1185C2×C4—216no—
1186C2×C4—216no—
1187C2×C4—22no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—28no—
1198C2×C4—28no—
1199C2×C4—216no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—48no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—48no—
1247C2×C4—48no—
1248C2×C4—88no—
1249C2×C4—84no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—164no—
1254C2×C4—164no—
1255C2×C4C22×#4114yes—
1256C2×C4C22×#4112yes—
1257C2×C4C22×#4112yes—
1258C2×C4C22×#4114yes—
1259C2×C4C2×H(5,𝔽2)14yes—
1260C22—24no—
1261C22—22no—
1262C22—22no—
1263C22—24no—
1264C22—24no—
1265C22—24no—
1266C22—24no—
1267C22—416no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22#349014yes—
1278C22C23×#4111yescharacteristic
1279C22C22×H(5,𝔽2)11yescharacteristic
1280C22C22×H(5,𝔽2)11yescharacteristic
1281C222−1+612yes—
1282C222−1+612yes—
1283C4—22no—
1284C4—22no—
1285C4—24no—
1286C4—24no—
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—44no—
1291C4—44no—
1292C4—44no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C4—44no—
1300C4—42no—
1301C4—42no—
1302C4—44no—
1303C2—24no—
1304C2—44no—
1305C2—84no—
1306C2C2×#349011yescharacteristic
1307C2#6285012yes—
1308C2#6287111yescharacteristic
1309C2#6287111yescharacteristic
1310C2#6288712yes—
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. #51840C2semidirect
2. #51831C2semidirect
3. #51681C2semidirect
4. #51680C2semidirect
5. #51668C2semidirect
6. #51667C2semidirect
7. #46625C2semidirect
8. #46621C2semidirect
9. #46611C2semidirect
10. #46607C2semidirect
11. #39559C2semidirect
12. #39431C2semidirect
13. #37855C2semidirect
14. #37667C2semidirect
15. #37518C2semidirect
16. #37194C2semidirect
17. #37190C2semidirect
18. #37140C2semidirect
19. #35242C2semidirect
20. #35094C2semidirect
21. #35093C2semidirect
22. #34409C2semidirect
23. C2×#2310C2semidirect
38. #2833C22semidirect
39. #2832C22semidirect
40. #2831C22semidirect
41. #2811C22semidirect
42. #2809C22semidirect
43. #2809C22semidirect
44. #2808C22semidirect
45. #2806C22semidirect
46. #2806C22semidirect
47. #2806C22semidirect
48. #2805C22semidirect
49. #2804C22semidirect
50. #2799C22semidirect
51. #2799C22semidirect
52. #2799C22semidirect
53. #2798C22semidirect
54. #2798C22semidirect
55. #2789C22semidirect
56. #2788C22semidirect
57. #2775C22semidirect
58. #2774C22semidirect
59. #2759C22semidirect
60. #2759C22semidirect
61. #2758C22semidirect
62. #2755C22semidirect
63. #2754C22semidirect
64. #2751C22semidirect
67. #2745C22semidirect
74. #2734C22semidirect
75. #2733C22semidirect
76. #2732C22semidirect
77. #2731C22semidirect
78. #2730C22semidirect
79. #2729C22semidirect
80. #2728C22semidirect
81. #2716C22semidirect
82. #2713C22semidirect
83. #2710C22semidirect
86. #2700C22semidirect
89. #2692C22semidirect
90. #2690C22semidirect
92. #2689C22semidirect
95. #2687C22semidirect
97. #2666C22semidirect
98. #2665C22semidirect
99. #2653C22semidirect
100. #2650C22semidirect
109. #2607C22semidirect
110. #2605C22semidirect
111. #2589C22semidirect
112. #2588C22semidirect
113. #2588C22semidirect
114. #2586C22semidirect
117. #2574C22semidirect
120. #2572C22semidirect
121. #2560C22semidirect
122. #2557C22semidirect
123. #2556C22semidirect
124. #2550C22semidirect
125. #2549C22semidirect
127. #2527C22semidirect
129. #2523C22semidirect
130. #2521C22semidirect
131. #2520C22semidirect
137. #2492C22semidirect
140. #2488C22semidirect
184. #2381C22semidirect
185. #2379C22semidirect
186. #2378C22semidirect
187. #2372C22semidirect
188. #2369C22semidirect
189. #2368C22semidirect
194. #2337C22semidirect
195. #2332C22semidirect
196. #2331C22semidirect
197. #2329C22semidirect

Maximal subgroups

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

subgroupindex
#518402
#518312
#516812
#516802
#516682
#516672
#466252
#466212
#466112
#466072
#395592
#394312
#378552
#376672
#375182
#371942
#371902
#371402
#352422
#350942
#350932
#344092
C2×#23102