Finite Group Databasebeta

← #7732443

Subgroups — #7732443

Order 512.

4424 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51229C212yesmaximal, complemented
2#51091C212yesmaximal, complemented
3#50919C212yesmaximal, complemented
4#50718C212yesmaximal, complemented
5#47764C214yesmaximal, complemented
6#47740C214yesmaximal, complemented
7#44024C214yesmaximal, complemented
8#44000C214yesmaximal, complemented
9#40322C214yesmaximal, complemented
10#39798C212yesmaximal, complemented
11#39797C212yesmaximal, complemented
12#39767C212yesmaximal, complemented
13#39764C212yesmaximal, complemented
14#38722C214yesmaximal, complemented
15#38481C214yesmaximal, complemented
16#37557C211yesmaximal, characteristic, complemented
17#37026C212yesmaximal, complemented
18#36837C212yesmaximal, complemented
19#36249C214yesmaximal, complemented
20#35500C212yesmaximal, complemented
21#35445C212yesmaximal, complemented
22#35303C211yesmaximal, characteristic
23#35180C211yesmaximal, characteristic, complemented
24C2×#2606C211yesmaximal, characteristic, complemented
25#34388C211yesmaximal, characteristic, complemented
26#34221C211yesmaximal, characteristic, complemented
27#34083C211yesmaximal, characteristic, complemented
28C2×#533C2211yescharacteristic
29C2×#532C2211yescharacteristic
30C2×#529C2211yescharacteristic
31#2865C2214yes—
32#2856C2212yes—
33#2853C2214yes—
34#2850C2212yes—
35#2850C2212yes—
36#2850C2212yes—
37#2821C2212yes—
38#2821C2212yes—
39#2808C2214yes—
40#2798C2214yes—
41#2796C2214yes—
42#2796C2214yes—
43#2796C2214yes—
44#2796C2214yes—
45#2794C2214yes—
46#2788C2214yes—
47#2783C2214yes—
48#2777C2214yes—
49#2773C2214yes—
50#2767C2214yes—
51#2767C2214yes—
52#2764C2214yes—
53#2762C2214yes—
54#2761C2214yes—
55#2758C2214yes—
56#2757C2214yes—
57#2756C2214yes—
58#2755C2214yes—
59#2755C2214yes—
60#2754C2214yes—
61#2751C2214yes—
62#2748C2214yes—
63#2747C2214yes—
64#2746C2214yes—
65#2745C2214yes—
66#2744C2214yes—
67#2741C2214yes—
68#2740C2214yes—
69#2740C2214yes—
70#2738C2214yes—
71#2724C2214yes—
72#2722C2214yes—
73#2715C2214yes—
74#2715C2214yes—
75#2710C2214yes—
76#2709C2214yes—
77#2706C2214yes—
78#2705C2214yes—
79#2660C2211yescharacteristic
80#2659C2211yescharacteristic
81#2659C2211yescharacteristic
82#2657C2211yescharacteristic
83#2654C2214yes—
84#2649C2214yes—
85#2641C2211yescharacteristic
86#2640C2211yescharacteristic
87#2639C2211yescharacteristic
88#2639C2212yes—
89#2639C2211yescharacteristic
90#2639C2212yes—
91#2634C2212yes—
92#2634C2212yes—
93#2633C2212yes—
94#2632C2212yes—
95#2612C2214yes—
96#2610C2212yes—
97#2610C2212yes—
98#2606C2212yes—
99#2606C2214yes—
100#2606C2212yes—
101#2606C2214yes—
102#2606C2212yes—
103#2606C2212yes—
104#2604C2214yes—
105#2603C2214yes—
106#2603C2214yes—
107#2601C2214yes—
108#2599C2212yes—
109#2599C2212yes—
110#2597C2214yes—
111#2596C2214yes—
112#2595C2214yes—
113#2595C2214yes—
114#2592C2212yes—
115#2592C2212yes—
116#2591C2214yes—
117#2589C2214yes—
118#2588C2214yes—
119#2580C2214yes—
120#2579C2214yes—
121#2577C2214yes—
122#2577C2214yes—
123#2577C2214yes—
124#2576C2214yes—
125#2575C2214yes—
126#2570C2214yes—
127#2569C2214yes—
128#2568C2212yes—
129#2564C2214yes—
130#2563C2212yes—
131#2562C2214yes—
132#2557C2214yes—
133#2554C2214yes—
134#2553C2214yes—
135#2548C2212yes—
136#2547C2212yes—
137#2543C2214yes—
138#2532C2214yes—
139#2531C2214yes—
140#2531C2214yes—
141#2530C2214yes—
142#2529C2214yes—
143#2528C2214yes—
144#2528C2214yes—
145#2523C2214yes—
146#2522C2214yes—
147#2521C2214yes—
148#2520C2214yes—
149#2520C2214yes—
150#2516C2214yes—
151#2516C2214yes—
152#2513C2214yes—
153#2510C2214yes—
154#2505C2214yes—
155#2504C2214yes—
156#2498C2214yes—
157#2498C2214yes—
158#2487C2214yes—
159#2481C2214yes—
160#2481C2214yes—
161#2481C2214yes—
162#2479C2214yes—
163#2479C2214yes—
164#2478C2214yes—
165#2474C2214yes—
166#2470C2214yes—
167#2469C2214yes—
168#2467C2214yes—
169#2458C2214yes—
170#2445C2214yes—
171#2444C2214yes—
172#2443C2214yes—
173#2443C2214yes—
174#2443C2214yes—
175#2430C2212yes—
176#2430C2212yes—
177#2419C2214yes—
178C2×#398C2212yes—
179C2×#398C2212yes—
180#2381C2212yes—
181#2380C2212yes—
182#2371C2214yes—
183#2368C2214yes—
184#2364C2214yes—
185#2364C2214yes—
186#2361C2214yes—
187#2356C2212yes—
188#2356C2212yes—
189#2353C2214yes—
190#2353C2214yes—
191#2352C2214yes—
192#2343C2212yes—
193#2343C2212yes—
194#2339C2214yes—
195#2337C2212yes—
196#2337C2212yes—
197#2337C2212yes—
198#2336C2212yes—
199#2335C2214yes—
200#2334C2214yes—
201#2334C2214yes—
202#2331C2212yes—
203#2329C2212yes—
204#2328C2212yes—
205#2327C2212yes—
206#2326C2212yes—
207#2325C2212yes—
208#2325C2212yes—
209#2325C2212yes—
210#2322C2214yes—
211#2320C2211yescharacteristic
212#2320C2211yescharacteristic
213#2318C2214yes—
214#2311C2214yes—
215C4×#126C2214yes—
216C4×C22⋊Q8C2212yes—
217C4×C22⋊Q8C2212yes—
218#2298C2212yes—
219#2296C2212yes—
220#2295C2212yes—
221C2×#389C2212yes—
222C2×#389C2212yes—
223#2290C2212yes—
224#2290C2212yes—
225#2290C2214yes—
226C2×#387C2212yes—
227C2×#387C2212yes—
228#2283C2211yescharacteristic
229C2×#383C2211yescharacteristic
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232C42×D4C2212yes—
233C2×C4×C4⋊C4C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C22×#41C2312yes—
236#533—28no—
237#532—28no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2312yes—
243#529—28no—
244C2×#126C2312yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125C2312yes—
249C2×#125C2311yescharacteristic
250C2×#124C2312yes—
251C2×#124C2311yescharacteristic
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#123C2312yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×#121C2312yes—
264C2×#121C2311yescharacteristic
265C2×#121C2312yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2314yes—
285C2×#117C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C42C2312yes—
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2312yes—
297C22×C42C2311yescharacteristic
298#401C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#398C2314yes—
325#398C2312yes—
326#398C2312yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2312yes—
342#398C2314yes—
343#397C2312yes—
344#397C2312yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#395C2314yes—
369#395C2312yes—
370#395C2312yes—
371#395C2312yes—
372#395C2312yes—
373#395C2312yes—
374#395C2312yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2312yes—
384#394C2312yes—
385#394C2312yes—
386#394C2312yes—
387#394C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2312yes—
392#393C2312yes—
393#393C2312yes—
394#393C2312yes—
395#392C2312yes—
396#392C2314yes—
397#392C2312yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#390C2312yes—
411#390C2312yes—
412#390C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
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#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#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#387C2314yes—
527#387C2314yes—
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#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
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#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#384C2312yes—
573#383C2314yes—
574#383C2312yes—
575#383C2312yes—
576#383C2312yes—
577#383C2314yes—
578#383C2312yes—
579#383C2312yes—
580#383C2312yes—
581#383C2312yes—
582#382C2312yes—
583#382C2312yes—
584#382C2314yes—
585#382C2314yes—
586#382C2312yes—
587#382C2312yes—
588#382C2312yes—
589#382C2314yes—
590#382C2312yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#381C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2311yescharacteristic
614C4×C4⋊C4C2311yescharacteristic
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2312yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638#376C2311yescharacteristic
639#376C2312yes—
640#376C2312yes—
641#376C2312yes—
642#376C2312yes—
643#376C2314yes—
644#376C2311yescharacteristic
645#376C2311yescharacteristic
646#376C2311yescharacteristic
647#376C2312yes—
648#376C2312yes—
649C2×#95C2312yes—
650C2×#95C2314yes—
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2312yes—
660C43C2312yes—
661C2×#41—28no—
662C2×#41—48no—
663C22×Q8C2411yescharacteristic
664C22×Q8C2411yescharacteristic
665C22×Q8C2411yescharacteristic
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×D4C2412yes—
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2412yes—
672C22×D4C2411yescharacteristic
673C22×D4C2412yes—
674C22×D4C2412yes—
675C22×D4C2414yes—
676C23×C4C2412yes—
677C23×C4C2411yescharacteristic
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2412yes—
682C23×C4C2412yes—
683C23×C4C2412yes—
684C23×C4C2414yes—
685C23×C4C2414yes—
686C23×C4C2414yes—
687C23×C4C2414yes—
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C4⋊Q8—24no—
691C4⋊Q8—24no—
692C4⋊Q8—24no—
693#127—24no—
694#127—44no—
695#126—28no—
696#126—48no—
697#126—48no—
698#126—84no—
699#125—24no—
700#125—28no—
701#124—24no—
702#124—28no—
703#124—44no—
704#124—82no—
705#124—82no—
706#123—28no—
707#123—48no—
708#123—84no—
709#123—84no—
710C22⋊Q8—24no—
711C22⋊Q8—28no—
712C22⋊Q8—24no—
713C22⋊Q8—24no—
714#121—24no—
715#121—28no—
716#121—28no—
717#121—48no—
718#121—48no—
719C4×Q8—24no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—28no—
723C4×Q8—44no—
724C4×Q8—44no—
725C4×D4—28no—
726C4×D4—24no—
727C4×D4—28no—
728C4×D4—28no—
729C4×D4—48no—
730C4×D4—48no—
731C4×D4—48no—
732C4×D4—48no—
733#117—28no—
734#117—28no—
735#117—82no—
736#117—84no—
737C2×C4⋊C4—44no—
738C2×C4⋊C4—44no—
739C2×C4⋊C4—44no—
740C2×C4⋊C4—44no—
741C2×C4⋊C4—44no—
742C2×C4⋊C4—82no—
743C2×C4⋊C4—82no—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
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×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
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×C42—44no—
832C2×C42—81no—
833C2×C42—82no—
834C2×C42—81no—
835C2×C42#4118yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2414yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2414yes—
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862#95C2414yes—
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2412yes—
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
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—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929C24C2512yes—
930C24C2514yes—
931C24C2511yescharacteristic
932#41—816no—
933C2×Q8—22no—
934C2×Q8—22no—
935C2×Q8—22no—
936C2×Q8—24no—
937C2×Q8—24no—
938C2×Q8—42no—
939C2×Q8—42no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—42no—
943C2×Q8—44no—
944C2×D4—24no—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—28no—
949C2×D4—22no—
950C2×D4—24no—
951C2×D4—24no—
952C2×D4—24no—
953C2×D4—28no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—44no—
960C2×D4—42no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—28no—
975C22×C4—42no—
976C22×C4—41no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—41no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4C2×#4114yes—
1003C22×C4C2×#4114yes—
1004C22×C4C2×#4114yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2514yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2514yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2511yescharacteristic
1028C22×C4C2512yes—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—22no—
1036C4⋊C4—24no—
1037C4⋊C4—22no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C22⋊C4—24no—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—28no—
1081C22⋊C4—24no—
1082C22⋊C4—24no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
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—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C42—24no—
1117C42—24no—
1118C42—24no—
1119C42—24no—
1120C42—24no—
1121C42—28no—
1122C42—42no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—44no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—44no—
1132C42—44no—
1133C42—44no—
1134C42—44no—
1135C42—44no—
1136C42—44no—
1137C42—44no—
1138C42C2×#4114yes—
1139C42C2×#4114yes—
1140C42C2×#4114yes—
1141C42C2×#4114yes—
1142C23—22no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—24no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—22no—
1155C23—22no—
1156C23—24no—
1157C23C22×#4112yes—
1158C23#58514yes—
1159C23C2611yescharacteristic
1160Q8—44no—
1161Q8—44no—
1162Q8—82no—
1163Q8—84no—
1164Q8—84no—
1165D4—48no—
1166D4—416no—
1167D4—82no—
1168D4—84no—
1169D4—84no—
1170D4—88no—
1171D4—84no—
1172D4—164no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—28no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
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—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—48no—
1234C2×C4—48no—
1235C2×C4—48no—
1236C2×C4—88no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—84no—
1241C2×C4—88no—
1242C2×C4—88no—
1243C2×C4—164no—
1244C2×C4C22×#4112yes—
1245C2×C4C22×#4112yes—
1246C2×C4C22×#4112yes—
1247C2×C4C22×#4112yes—
1248C2×C4C22×#4112yes—
1249C2×C4C22×#4112yes—
1250C2×C4#58514yes—
1251C22—22no—
1252C22—22no—
1253C22—24no—
1254C22—24no—
1255C22—44no—
1256C22—42no—
1257C22—42no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22#351014yes—
1268C22C23×#4111yescharacteristic
1269C22C2×#58512yes—
1270C22C2×#58512yes—
1271C22H(7,𝔽2)11yescharacteristic
1272C222−1+611yescharacteristic
1273C4—22no—
1274C4—22no—
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—24no—
1280C4—44no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—44no—
1290C4—44no—
1291C4—44no—
1292C4—42no—
1293C4—44no—
1294C4—44no—
1295C4—44no—
1296C4—42no—
1297C2—24no—
1298C2—84no—
1299C2—82no—
1300C2C2×#351011yescharacteristic
1301C2#6281511yescharacteristic
1302C2#6285611yescharacteristic
1303C2#6290912yes—
1304C2#6293512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35303C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51229C2semidirect
2. #51091C2semidirect
3. #50919C2semidirect
4. #50718C2semidirect
5. #47764C2semidirect
6. #47740C2semidirect
7. #44024C2semidirect
8. #44000C2semidirect
9. #40322C2semidirect
10. #39798C2semidirect
11. #39797C2semidirect
12. #39767C2semidirect
13. #39764C2semidirect
14. #38722C2semidirect
15. #38481C2semidirect
16. #37557C2semidirect
17. #37026C2semidirect
18. #36837C2semidirect
19. #36249C2semidirect
20. #35500C2semidirect
21. #35445C2semidirect
23. #35180C2semidirect
24. C2×#2606C2semidirect
25. #34388C2semidirect
26. #34221C2semidirect
27. #34083C2semidirect

Maximal subgroups

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

subgroupindex
#512292
#510912
#509192
#507182
#477642
#477402
#440242
#440002
#403222
#397982
#397972
#397672
#397642
#387222
#384812
#375572
#370262
#368372
#362492
#355002
#354452
#353032
#351802
C2×#26062
#343882
#342212
#340832