Finite Group Databasebeta

← #7714755

Subgroups — #7714755

Order 512.

5250 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51828C214yesmaximal, complemented
2#51676C214yesmaximal, complemented
3#51663C214yesmaximal, complemented
4#51662C214yesmaximal, complemented
5#47664C212yesmaximal, complemented
6#47660C212yesmaximal, complemented
7#47656C214yesmaximal, complemented
8#47175C214yesmaximal, complemented
9#47174C212yesmaximal, complemented
10#47171C212yesmaximal, complemented
11#37967C214yesmaximal, complemented
12#37855C214yesmaximal, complemented
13#37779C214yesmaximal, complemented
14#37667C214yesmaximal, complemented
15#37518C212yesmaximal, complemented
16#37194C211yesmaximal, characteristic, complemented
17#37190C211yesmaximal, characteristic, complemented
18#37140C212yesmaximal, complemented
19#35242C212yesmaximal, complemented
20#35118C212yesmaximal, complemented
21#35093C212yesmaximal, complemented
22#34409C212yesmaximal, complemented
23C2×#2310C211yesmaximal, characteristic, complemented
24C24×Q8C2211yescharacteristic
25C2×#538C2212yes—
26C2×#536C2212yes—
27C2×#536C2212yes—
28C2×#529C2212yes—
29C2×#525C2212yes—
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32#2855C2212yes—
33#2854C2212yes—
34#2853C2214yes—
35#2849C2214yes—
36#2849C2214yes—
37#2833C2212yescomplemented
38#2832C2212yescomplemented
39#2831C2214yescomplemented
40#2811C2211yescharacteristic, complemented
41#2809C2211yescharacteristic, complemented
42#2809C2212yescomplemented
43#2808C2212yescomplemented
44#2806C2212yescomplemented
45#2806C2212yescomplemented
46#2806C2214yescomplemented
47#2805C2212yescomplemented
48#2804C2212yescomplemented
49#2799C2212yescomplemented
50#2799C2214yescomplemented
51#2788C2214yescomplemented
52#2775C2214yescomplemented
53#2774C2214yescomplemented
54#2764C2214yescomplemented
55#2763C2214yescomplemented
56#2762C2214yescomplemented
57#2762C2214yescomplemented
58#2759C2214yescomplemented
59#2759C2214yescomplemented
60#2758C2214yescomplemented
61#2755C2214yescomplemented
62#2754C2214yescomplemented
63#2751C2214yescomplemented
64#2746C2214yes—
65#2745C2214yes—
66#2745C2214yescomplemented
67#2744C2214yes—
68#2743C2214yes—
69#2740C2214yes—
70#2739C2214yes—
71#2738C2214yes—
72#2737C2214yes—
73#2734C2211yescharacteristic, complemented
74#2733C2211yescharacteristic, complemented
75#2732C2212yescomplemented
76#2731C2212yescomplemented
77#2730C2214yescomplemented
78#2729C2214yescomplemented
79#2728C2212yescomplemented
80#2716C2214yescomplemented
81#2715C2214yescomplemented
82#2713C2214yescomplemented
83#2712C2214yescomplemented
84#2704C2214yescomplemented
85#2702C2214yescomplemented
86#2701C2214yes—
87#2700C2214yes—
88#2700C2214yescomplemented
89#2699C2214yes—
90#2698C2214yes—
91#2698C2214yescomplemented
92#2689C2214yes—
93#2688C2214yes—
94#2687C2214yes—
95#2686C2214yes—
96#2666C2214yescomplemented
97#2665C2214yescomplemented
98#2653C2214yescomplemented
99#2650C2214yescomplemented
100#2627C2212yes—
101#2627C2212yes—
102#2626C2212yes—
103#2622C2214yes—
104#2618C2212yes—
105#2618C2212yes—
106#2617C2212yes—
107#2614C2214yes—
108#2614C2214yes—
109#2612C2214yescomplemented
110#2611C2212yes—
111#2611C2212yes—
112#2610C2212yes—
113#2610C2212yes—
114#2609C2214yes—
115#2609C2214yes—
116#2605C2214yescomplemented
117#2601C2214yes—
118#2601C2214yes—
119#2599C2212yes—
120#2599C2212yes—
121#2598C2212yes—
122#2598C2212yes—
123#2589C2214yescomplemented
124#2586C2214yescomplemented
125#2586C2212yescomplemented
126#2576C2214yes—
127#2575C2214yes—
128#2574C2214yescomplemented
129#2573C2214yes—
130#2572C2214yes—
131#2572C2212yescomplemented
132#2532C2214yescomplemented
133#2532C2214yescomplemented
134#2527C2214yes—
135#2527C2214yescomplemented
136#2526C2214yes—
137#2520C2214yescomplemented
138#2516C2214yes—
139#2515C2214yes—
140#2498C2214yes—
141#2493C2214yes—
142#2493C2214yes—
143#2488C2214yes—
144#2488C2214yes—
145#2478C2214yes—
146#2478C2214yes—
147#2477C2214yescomplemented
148#2476C2214yes—
149#2476C2214yes—
150#2474C2214yes—
151#2474C2214yes—
152#2474C2214yescomplemented
153#2470C2214yes—
154#2470C2214yes—
155#2468C2214yes—
156#2466C2214yes—
157#2465C2214yescomplemented
158#2459C2214yes—
159#2459C2214yescomplemented
160#2457C2214yes—
161#2451C2214yescomplemented
162#2450C2214yescomplemented
163#2447C2214yes—
164#2444C2214yes—
165#2439C2214yescomplemented
166#2438C2214yes—
167#2438C2214yes—
168#2438C2214yescomplemented
169#2436C2214yes—
170#2436C2214yes—
171#2434C2214yes—
172#2434C2214yes—
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#2322C2214yes—
200#2321C2214yes—
201#2312C2212yes—
202#2310C2212yes—
203#2310C2212yes—
204#2310C2212yes—
205#2310C2212yes—
206#2310C2212yes—
207#2310C2212yes—
208#2310C2214yes—
209#2310C2214yes—
210C4×#123C2214yes—
211C2×#391C2211yescharacteristic
212C2×#391C2211yescharacteristic
213C2×#391C2214yes—
214C2×#391C2211yescharacteristic
215C2×#391C2211yescharacteristic
216#2283C2212yes—
217#2280C2212yes—
218C2×#381C2214yes—
219C22×#41C2312yes—
220C23×Q8—28no—
221C23×Q8—44no—
222C23×Q8—44no—
223C23×Q8C2312yes—
224C23×Q8C2312yes—
225C23×Q8C2314yes—
226C23×Q8C2312yes—
227C23×Q8C2311yescharacteristic
228C23×Q8C2311yescharacteristic
229C24×C4C2311yescharacteristic
230C24×C4C2312yes—
231#538—48no—
232#536—216no—
233#536—48no—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237#529—48no—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#125C2312yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246#525—48no—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×#121C2312yes—
261C2×#121C2312yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#120C2314yes—
265C2×C4×Q8C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×#117—44no—
272C2×#117—44no—
273C2×#117C2312yes—
274C2×#117C2312yes—
275C2×#117C2312yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2314yes—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2314yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2311yescharacteristic
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2312yes—
289C22×C42C2312yes—
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292#401C2314yes—
293#401C2314yes—
294#400C2314yes—
295#400C2312yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#399C2312yes—
313#399C2314yes—
314#399C2312yes—
315#398C2314yes—
316#398C2314yes—
317#398C2312yes—
318#398C2314yes—
319#398C2314yes—
320#398C2312yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2312yes—
338#397C2312yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2312yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2312yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#394C2314yes—
369#394C2312yes—
370#394C2314yes—
371#394C2314yes—
372#394C2312yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#393C2312yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2312yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#392C2312yes—
394#392C2312yes—
395#392C2314yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2314yes—
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2311yescharacteristic
412#391C2314yes—
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#388C2314yes—
457#388C2314yes—
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#386C2314yes—
525#386C2314yes—
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#385C2314yes—
545#385C2314yes—
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#383C2312yes—
569#383C2312yes—
570#383C2314yes—
571#382C2314yes—
572#382C2314yes—
573#382C2314yes—
574#382C2314yes—
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#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#380C2312yes—
592#380C2312yes—
593#380C2314yes—
594#380C2314yes—
595#380C2312yes—
596#380C2312yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#379C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616#376C2314yes—
617#376C2312yes—
618#376C2312yes—
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—216no—
630C22×Q8—28no—
631C22×Q8—28no—
632C22×Q8—24no—
633C22×Q8—28no—
634C22×Q8—42no—
635C22×Q8—42no—
636C22×Q8—44no—
637C22×Q8—42no—
638C22×Q8—42no—
639C22×Q8—44no—
640C22×Q8—48no—
641C22×Q8—44no—
642C22×Q8—44no—
643C22×Q8—48no—
644C22×Q8—44no—
645C22×Q8—464no—
646C22×Q8#4118yes—
647C22×Q8C2414yes—
648C22×Q8C2414yes—
649C22×Q8C2412yes—
650C22×Q8C2412yes—
651C22×Q8C2412yes—
652C22×Q8C2412yes—
653C22×Q8C2412yes—
654C22×Q8C2411yescharacteristic
655C22×Q8C2412yes—
656C22×Q8C2411yescharacteristic
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2412yes—
661C22×D4C2412yes—
662C22×D4C2412yes—
663C23×C4—24no—
664C23×C4—24no—
665C23×C4—24no—
666C23×C4—28no—
667C23×C4—28no—
668C23×C4—44no—
669C23×C4C2412yes—
670C23×C4C2412yes—
671C23×C4C2412yes—
672C23×C4C2414yes—
673C23×C4C2414yes—
674C23×C4C2411yescharacteristic
675C23×C4C2412yes—
676C23×C4C2411yescharacteristic
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2414yes—
684C4⋊Q8—28no—
685C4⋊Q8—28no—
686C4⋊Q8—48no—
687#126—48no—
688#126—48no—
689#125—44no—
690#124—28no—
691#124—28no—
692#124—44no—
693#124—48no—
694#124—48no—
695#123—216no—
696#123—216no—
697#123—216no—
698#123—48no—
699#123—48no—
700#123—48no—
701C22⋊Q8—216no—
702C22⋊Q8—216no—
703C22⋊Q8—48no—
704C22⋊Q8—44no—
705C22⋊Q8—44no—
706C22⋊Q8—48no—
707C22⋊Q8—48no—
708#121—48no—
709#121—48no—
710#121—44no—
711#121—44no—
712#120—216no—
713C4×Q8—44no—
714C4×D4—44no—
715C4×D4—48no—
716C4×D4—48no—
717C4×D4—48no—
718C4×D4—48no—
719#117—28no—
720#117—44no—
721#117—44no—
722#117—44no—
723#117—44no—
724#117—48no—
725#117—44no—
726#117—48no—
727#117—44no—
728#117—44no—
729#117—44no—
730C2×C4⋊C4—42no—
731C2×C4⋊C4—42no—
732C2×C4⋊C4—44no—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C22⋊C4—28no—
778C2×C22⋊C4—44no—
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⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
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×C42—28no—
817C2×C42—42no—
818C2×C42—42no—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
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—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2412yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
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#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901C24—22no—
902C24—22no—
903C24—42no—
904C24—42no—
905C24H(5,𝔽2)14yes—
906C24C2514yes—
907C24C2512yes—
908C24C2511yescharacteristic
909#41—816no—
910C2×Q8—28no—
911C2×Q8—28no—
912C2×Q8—24no—
913C2×Q8—24no—
914C2×Q8—24no—
915C2×Q8—28no—
916C2×Q8—28no—
917C2×Q8—416no—
918C2×Q8—41no—
919C2×Q8—42no—
920C2×Q8—41no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—44no—
924C2×Q8—41no—
925C2×Q8—42no—
926C2×Q8—44no—
927C2×Q8—41no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—42no—
932C2×Q8—42no—
933C2×Q8—44no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×Q8—42no—
937C2×Q8—432no—
938C2×Q8—432no—
939C2×Q8—464no—
940C2×Q8—432no—
941C2×Q8—416no—
942C2×Q8C2×#4114yes—
943C2×Q8C2×#4118yes—
944C2×Q8C2×#4114yes—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—28no—
949C2×D4—28no—
950C2×D4—24no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C22×C4—232no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—28no—
977C22×C4—28no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—28no—
985C22×C4—28no—
986C22×C4—28no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—44no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—432no—
1004C22×C4C2×#4118yes—
1005C22×C4C2×#4114yes—
1006C22×C4H(5,𝔽2)14yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2514yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2514yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2512yes—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—42no—
1039C4⋊C4—41no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C42—24no—
1109C42—24no—
1110C42—24no—
1111C42—24no—
1112C42—24no—
1113C42—24no—
1114C42—42no—
1115C42—42no—
1116C42—41no—
1117C42—42no—
1118C42—41no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C42—44no—
1123C42—42no—
1124C42—42no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—24no—
1133C23—24no—
1134C23—28no—
1135C23—24no—
1136C23—24no—
1137C23—24no—
1138C23—24no—
1139C23—24no—
1140C23—24no—
1141C23—24no—
1142C23—48no—
1143C23—48no—
1144C23—44no—
1145C23—44no—
1146C23C22×#4112yes—
1147C23C2×H(5,𝔽2)14yes—
1148C23C2×H(5,𝔽2)12yes—
1149C23C2×H(5,𝔽2)12yes—
1150C23C2611yescharacteristic
1151Q8—44no—
1152Q8—48no—
1153Q8—44no—
1154Q8—416no—
1155Q8—416no—
1156Q8—48no—
1157Q8—48no—
1158Q8—84no—
1159Q8—84no—
1160Q8—162no—
1161D4—416no—
1162D4—84no—
1163D4—88no—
1164D4—88no—
1165D4—84no—
1166D4—162no—
1167C2×C4—216no—
1168C2×C4—216no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—28no—
1180C2×C4—28no—
1181C2×C4—216no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—416no—
1224C2×C4—416no—
1225C2×C4—48no—
1226C2×C4—88no—
1227C2×C4—84no—
1228C2×C4—84no—
1229C2×C4—84no—
1230C2×C4—84no—
1231C2×C4—88no—
1232C2×C4—164no—
1233C2×C4C22×#4114yes—
1234C2×C4C22×#4112yes—
1235C2×C4C22×#4112yes—
1236C2×C4C22×#4114yes—
1237C2×C4C2×H(5,𝔽2)14yes—
1238C22—24no—
1239C22—24no—
1240C22—22no—
1241C22—22no—
1242C22—24no—
1243C22—28no—
1244C22—416no—
1245C22—44no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22#349014yes—
1256C22C23×#4111yescharacteristic
1257C22C22×H(5,𝔽2)11yescharacteristic
1258C22C22×H(5,𝔽2)11yescharacteristic
1259C222−1+612yes—
1260C222−1+612yes—
1261C4—22no—
1262C4—22no—
1263C4—24no—
1264C4—24no—
1265C4—24no—
1266C4—44no—
1267C4—44no—
1268C4—44no—
1269C4—44no—
1270C4—44no—
1271C4—42no—
1272C4—42no—
1273C4—44no—
1274C4—44no—
1275C4—42no—
1276C4—42no—
1277C4—44no—
1278C4—42no—
1279C4—42no—
1280C4—44no—
1281C2—24no—
1282C2—44no—
1283C2—84no—
1284C2C2×#349011yescharacteristic
1285C2#6285012yes—
1286C2#6287112yes—
1287C2#6288611yescharacteristic
1288C2#6288611yescharacteristic
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. #51828C2semidirect
2. #51676C2semidirect
3. #51663C2semidirect
4. #51662C2semidirect
5. #47664C2semidirect
6. #47660C2semidirect
7. #47656C2semidirect
8. #47175C2semidirect
9. #47174C2semidirect
10. #47171C2semidirect
11. #37967C2semidirect
12. #37855C2semidirect
13. #37779C2semidirect
14. #37667C2semidirect
15. #37518C2semidirect
16. #37194C2semidirect
17. #37190C2semidirect
18. #37140C2semidirect
19. #35242C2semidirect
20. #35118C2semidirect
21. #35093C2semidirect
22. #34409C2semidirect
23. C2×#2310C2semidirect
37. #2833C22semidirect
38. #2832C22semidirect
39. #2831C22semidirect
40. #2811C22semidirect
41. #2809C22semidirect
42. #2809C22semidirect
43. #2808C22semidirect
44. #2806C22semidirect
45. #2806C22semidirect
46. #2806C22semidirect
47. #2805C22semidirect
48. #2804C22semidirect
49. #2799C22semidirect
50. #2799C22semidirect
51. #2788C22semidirect
52. #2775C22semidirect
53. #2774C22semidirect
54. #2764C22semidirect
55. #2763C22semidirect
56. #2762C22semidirect
57. #2762C22semidirect
58. #2759C22semidirect
59. #2759C22semidirect
60. #2758C22semidirect
61. #2755C22semidirect
62. #2754C22semidirect
63. #2751C22semidirect
66. #2745C22semidirect
73. #2734C22semidirect
74. #2733C22semidirect
75. #2732C22semidirect
76. #2731C22semidirect
77. #2730C22semidirect
78. #2729C22semidirect
79. #2728C22semidirect
80. #2716C22semidirect
81. #2715C22semidirect
82. #2713C22semidirect
83. #2712C22semidirect
84. #2704C22semidirect
85. #2702C22semidirect
88. #2700C22semidirect
91. #2698C22semidirect
96. #2666C22semidirect
97. #2665C22semidirect
98. #2653C22semidirect
99. #2650C22semidirect
109. #2612C22semidirect
116. #2605C22semidirect
123. #2589C22semidirect
124. #2586C22semidirect
125. #2586C22semidirect
128. #2574C22semidirect
131. #2572C22semidirect
132. #2532C22semidirect
133. #2532C22semidirect
135. #2527C22semidirect
137. #2520C22semidirect
147. #2477C22semidirect
152. #2474C22semidirect
157. #2465C22semidirect
159. #2459C22semidirect
161. #2451C22semidirect
162. #2450C22semidirect
165. #2439C22semidirect
168. #2438C22semidirect
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
#518282
#516762
#516632
#516622
#476642
#476602
#476562
#471752
#471742
#471712
#379672
#378552
#377792
#376672
#375182
#371942
#371902
#371402
#352422
#351182
#350932
#344092
C2×#23102