Finite Group Databasebeta

← #7711629

Subgroups — #7711629

Order 512.

4726 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60043C212yesmaximal, complemented
2#60042C212yesmaximal, complemented
3#59923C211yesmaximal, characteristic, complemented
4#59886C212yesmaximal, complemented
5#59885C211yesmaximal, characteristic
6#46326C212yesmaximal, complemented
7#46325C212yesmaximal, complemented
8#46313C211yesmaximal, characteristic, complemented
9#46312C211yesmaximal, characteristic, complemented
10#46285C212yesmaximal, complemented
11#40470C214yesmaximal, complemented
12#40468C214yesmaximal, complemented
13#38855C214yesmaximal, complemented
14#38854C214yesmaximal, complemented
15#38481C214yesmaximal, complemented
16#38441C214yesmaximal, complemented
17#37602C212yesmaximal, complemented
18#37267C211yesmaximal, characteristic, complemented
19#37266C211yesmaximal, characteristic, complemented
20#37265C212yesmaximal, complemented
21#36638C212yesmaximal, complemented
22#36205C214yesmaximal, complemented
23#36145C214yesmaximal, complemented
24#35246C212yesmaximal, complemented
25#35245C212yesmaximal, complemented
26#34521C212yesmaximal, complemented
27C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
28C2×#563C2212yes—
29C22×C4⋊Q8C2211yescharacteristic
30C2×#529C2212yes—
31C2×#529C2212yes—
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34#2866C2214yes—
35#2865C2214yes—
36#2864C2212yes—
37#2863C2212yes—
38#2861C2212yes—
39#2860C2212yes—
40#2855C2212yes—
41#2854C2212yes—
42#2853C2214yes—
43#2853C2214yes—
44#2853C2214yes—
45#2852C2214yes—
46#2851C2212yes—
47#2850C2212yes—
48#2843C2212yes—
49#2823C2212yes—
50#2821C2214yes—
51#2811C2211yescharacteristic
52#2809C2211yescharacteristic
53#2808C2212yes—
54#2807C2214yes—
55#2806C2212yes—
56#2806C2212yes—
57#2805C2212yes—
58#2804C2212yes—
59#2802C2214yes—
60#2798C2214yes—
61#2796C2214yes—
62#2794C2212yes—
63#2793C2214yes—
64#2792C2214yes—
65#2791C2214yes—
66#2774C2214yes—
67#2773C2214yes—
68#2768C2214yes—
69#2767C2214yes—
70#2755C2214yes—
71#2734C2211yescharacteristic
72#2734C2212yes—
73#2733C2211yescharacteristic
74#2732C2212yes—
75#2731C2212yes—
76#2729C2214yes—
77#2726C2214yes—
78#2721C2214yes—
79#2720C2214yes—
80#2720C2214yes—
81#2718C2214yes—
82#2716C2214yes—
83#2715C2214yes—
84#2713C2214yes—
85#2710C2214yes—
86#2705C2214yes—
87#2704C2214yes—
88#2680C2212yes—
89#2677C2214yes—
90#2674C2214yes—
91#2667C2214yes—
92#2666C2214yes—
93#2654C2214yes—
94#2649C2214yes—
95#2637C2214yes—
96#2637C2214yes—
97#2634C2212yes—
98#2634C2212yes—
99#2632C2212yes—
100#2632C2212yes—
101#2612C2214yes—
102#2606C2214yes—
103#2604C2214yes—
104#2604C2214yes—
105#2599C2214yes—
106#2599C2214yes—
107#2591C2212yes—
108#2591C2212yes—
109#2589C2214yes—
110#2586C2214yes—
111#2586C2212yes—
112#2583C2212yes—
113#2583C2212yes—
114#2581C2212yes—
115#2581C2212yes—
116#2579C2214yes—
117#2579C2214yes—
118#2574C2214yes—
119#2572C2212yes—
120#2569C2214yes—
121#2565C2212yes—
122#2565C2212yes—
123#2564C2214yes—
124#2549C2214yes—
125#2545C2212yes—
126#2545C2212yes—
127#2543C2214yes—
128#2536C2212yes—
129#2536C2212yes—
130#2533C2214yes—
131#2533C2214yes—
132#2532C2214yes—
133#2532C2214yes—
134#2532C2214yes—
135#2530C2214yes—
136#2529C2214yes—
137#2524C2214yes—
138#2524C2214yes—
139#2521C2214yes—
140#2521C2214yes—
141#2520C2214yes—
142#2520C2214yes—
143#2520C2214yes—
144#2519C2214yes—
145#2519C2214yes—
146#2519C2214yes—
147#2519C2214yes—
148#2515C2214yes—
149#2515C2214yes—
150#2504C2212yes—
151#2502C2212yes—
152#2487C2214yes—
153#2481C2214yes—
154#2481C2214yes—
155#2479C2214yes—
156#2479C2214yes—
157#2479C2214yes—
158#2478C2214yes—
159#2478C2214yes—
160#2473C2214yes—
161#2473C2214yes—
162#2470C2214yes—
163#2465C2214yes—
164#2462C2214yes—
165#2462C2214yes—
166#2461C2214yes—
167#2461C2214yes—
168#2459C2214yes—
169#2451C2214yes—
170#2450C2214yes—
171#2449C2214yes—
172#2449C2214yes—
173#2443C2214yes—
174#2443C2214yes—
175#2441C2214yes—
176#2438C2214yes—
177#2436C2212yes—
178#2434C2212yes—
179#2409C2214yes—
180#2383C2214yes—
181#2381C2212yes—
182#2373C2214yes—
183#2373C2214yes—
184#2372C2212yes—
185#2371C2214yes—
186#2371C2214yes—
187#2369C2212yes—
188#2368C2214yes—
189#2368C2214yes—
190#2364C2214yes—
191#2362C2214yes—
192#2362C2214yes—
193#2359C2214yes—
194#2359C2214yes—
195#2353C2214yes—
196#2349C2214yes—
197#2335C2214yes—
198#2334C2214yes—
199#2330C2214yes—
200#2329C2214yes—
201#2327C2212yes—
202#2327C2212yes—
203#2326C2212yes—
204#2326C2212yes—
205#2323C2214yes—
206#2323C2214yes—
207C4×C4⋊Q8C2214yes—
208C4×C4⋊Q8C2211yescharacteristic
209C4×C4⋊Q8C2211yescharacteristic
210C4×C4⋊Q8C2211yescharacteristic
211C4×C4⋊Q8C2211yescharacteristic
212C4×C4⋊Q8C2214yes—
213C4×C4⋊Q8C2211yescharacteristic
214C4×C4⋊Q8C2211yescharacteristic
215C4×C4⋊Q8C2211yescharacteristic
216C4×C4⋊Q8C2211yescharacteristic
217C4×#125C2212yes—
218C4×#126C2214yes—
219C4×#124C2212yes—
220C4×C22⋊Q8C2212yes—
221C4×#123C2214yes—
222C4×#121C2212yes—
223#2298C2214yes—
224#2295C2212yes—
225C2×#391C2211yescharacteristic
226C2×#391C2211yescharacteristic
227#2293C2212yes—
228C2×#389C2214yes—
229#2290C2214yes—
230C2×#384C2211yescharacteristic
231#2283C2212yes—
232#2283C2212yes—
233C2×C4×C4⋊C4C2214yes—
234C2×C43C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237#563—216no—
238C2×C4⋊Q8—28no—
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2311yescharacteristic
246#529—48no—
247#529—48no—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2314yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×C4×Q8—44no—
277C2×C4×Q8—44no—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×#117C2314yes—
300C2×#117C2314yes—
301C2×#117C2314yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2314yes—
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2312yes—
311C22×C42C2312yes—
312C22×C42C2312yes—
313C22×C42C2312yes—
314C22×C42C2311yescharacteristic
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2312yes—
348#398C2312yes—
349#398C2312yes—
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#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2312yes—
381#395C2312yes—
382#395C2312yes—
383#395C2312yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#394C2312yes—
391#394C2314yes—
392#394C2312yes—
393#394C2312yes—
394#394C2312yes—
395#394C2314yes—
396#394C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#392C2314yes—
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2314yes—
406#391C2314yes—
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
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#388C2314yes—
489#388C2314yes—
490#388C2314yes—
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#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#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
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#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#384C2311yescharacteristic
590#384C2311yescharacteristic
591#384C2311yescharacteristic
592#384C2314yes—
593#384C2311yescharacteristic
594#384C2312yes—
595#384C2312yes—
596#383C2314yes—
597#383C2314yes—
598#383C2314yes—
599#383C2312yes—
600#383C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2312yes—
604#382C2314yes—
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2314yes—
609#381C2314yes—
610#381C2314yes—
611#380C2314yes—
612#380C2314yes—
613#380C2312yes—
614#380C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2312yes—
650#376C2312yes—
651#376C2312yes—
652#376C2314yes—
653#376C2314yes—
654#376C2314yes—
655C2×#95C2314yes—
656C2×#95C2314yes—
657C2×#95C2314yes—
658C43C2311yescharacteristic
659C43C2312yes—
660C43C2311yescharacteristic
661C43C2311yescharacteristic
662C43C2312yes—
663C43C2311yescharacteristic
664C22×Q8—24no—
665C22×Q8—24no—
666C22×Q8—42no—
667C22×Q8—42no—
668C22×Q8—42no—
669C22×Q8—42no—
670C22×Q8C2412yes—
671C22×Q8C2412yes—
672C22×Q8C2411yescharacteristic
673C22×Q8C2411yescharacteristic
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2411yescharacteristic
678C22×Q8C2411yescharacteristic
679C22×D4C2414yes—
680C22×D4C2412yes—
681C22×D4C2412yes—
682C22×D4C2412yes—
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2414yes—
692C23×C4C2414yes—
693C23×C4C2414yes—
694C23×C4C2412yes—
695C4⋊Q8—24no—
696C4⋊Q8—24no—
697C4⋊Q8—28no—
698C4⋊Q8—216no—
699C4⋊Q8—24no—
700C4⋊Q8—44no—
701C4⋊Q8#4118yes—
702#126—216no—
703#126—216no—
704#126—48no—
705#126—48no—
706#126—48no—
707#125—216no—
708#125—44no—
709#125—44no—
710#125—44no—
711#125—48no—
712#124—28no—
713#124—44no—
714#124—44no—
715#124—44no—
716#124—44no—
717#123—216no—
718#123—216no—
719#123—48no—
720C22⋊Q8—216no—
721C22⋊Q8—28no—
722C22⋊Q8—216no—
723C22⋊Q8—44no—
724C22⋊Q8—44no—
725C22⋊Q8—48no—
726C22⋊Q8—48no—
727#121—28no—
728#121—44no—
729#121—44no—
730C4×Q8—42no—
731C4×Q8—42no—
732C4×Q8—44no—
733C4×Q8—44no—
734C4×Q8—42no—
735C4×Q8—42no—
736C4×Q8—44no—
737C4×Q8—44no—
738C4×Q8—42no—
739C4×Q8—42no—
740C4×Q8—42no—
741C4×Q8—42no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×Q8—44no—
745C4×D4—216no—
746C4×D4—44no—
747C4×D4—44no—
748C4×D4—44no—
749C4×D4—48no—
750C4×D4—48no—
751#117—48no—
752#117—48no—
753#117—48no—
754C2×C4⋊C4—216no—
755C2×C4⋊C4—48no—
756C2×C4⋊C4—42no—
757C2×C4⋊C4—42no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4C2414yes—
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⋊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⋊C4C2412yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊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×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
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×C42—24no—
848C2×C42—28no—
849C2×C42—28no—
850C2×C42—28no—
851C2×C42—24no—
852C2×C42—44no—
853C2×C42—42no—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2411yescharacteristic
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891#95C2414yes—
892#95C2414yes—
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#95C2412yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949C24C2514yes—
950C24C2511yescharacteristic
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—22no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—41no—
960C2×Q8—42no—
961C2×Q8—41no—
962C2×Q8—42no—
963C2×Q8—41no—
964C2×Q8—41no—
965C2×Q8—41no—
966C2×Q8—41no—
967C2×Q8—41no—
968C2×Q8—41no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—416no—
976C2×Q8—416no—
977C2×Q8C2×#4114yes—
978C2×Q8C2×#4114yes—
979C2×D4—28no—
980C2×D4—28no—
981C2×D4—28no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—42no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—42no—
989C2×D4—42no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—22no—
995C22×C4—24no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—28no—
1005C22×C4—28no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4H(5,𝔽2)14yes—
1021C22×C42−1+418yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2511yescharacteristic
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—28no—
1057C4⋊C4—28no—
1058C4⋊C4—28no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—41no—
1074C4⋊C4—42no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—42no—
1078C4⋊C4—41no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4C2×#41116yes—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C42—22no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—22no—
1143C42—22no—
1144C42—22no—
1145C42—22no—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—24no—
1151C42—24no—
1152C42—24no—
1153C42—24no—
1154C42—28no—
1155C42—24no—
1156C42—24no—
1157C42—24no—
1158C42—41no—
1159C42—42no—
1160C42—41no—
1161C42—42no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—42no—
1167C42—44no—
1168C42—44no—
1169C42—42no—
1170C42C2×#4114yes—
1171C23—21no—
1172C23—22no—
1173C23—21no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—24no—
1179C23—24no—
1180C23—24no—
1181C23C2×H(5,𝔽2)12yes—
1182C23C2×2−1+414yes—
1183C23C2611yescharacteristic
1184Q8—44no—
1185Q8—44no—
1186Q8—48no—
1187Q8—48no—
1188Q8—44no—
1189Q8—44no—
1190Q8—84no—
1191Q8—84no—
1192Q8—84no—
1193D4—416no—
1194D4—84no—
1195D4—84no—
1196D4—84no—
1197C2×C4—216no—
1198C2×C4—28no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—28no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—48no—
1258C2×C4—48no—
1259C2×C4—48no—
1260C2×C4—44no—
1261C2×C4—88no—
1262C2×C4—88no—
1263C2×C4—84no—
1264C2×C4—84no—
1265C2×C4—88no—
1266C2×C4C22×#4114yes—
1267C2×C4C22×#4114yes—
1268C2×C4C22×#4112yes—
1269C2×C4C22×#4114yes—
1270C2×C4C2×H(5,𝔽2)12yes—
1271C2×C4C2×H(5,𝔽2)12yes—
1272C2×C4C2×2−1+414yes—
1273C2×C4C2×2−1+414yes—
1274C2×C4#58514yes—
1275C2×C4#58512yes—
1276C22—22no—
1277C22—22no—
1278C22—24no—
1279C22—24no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22#354414yes—
1288C22C23×#4111yescharacteristic
1289C22C22×H(5,𝔽2)11yescharacteristic
1290C22C22×2−1+412yes—
1291C22C2×#58512yes—
1292C22C2×#58511yescharacteristic
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—24no—
1298C4—24no—
1299C4—24no—
1300C4—24no—
1301C4—24no—
1302C4—24no—
1303C4—44no—
1304C4—41no—
1305C4—41no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—44no—
1318C2—24no—
1319C2—84no—
1320C2C2×#354411yescharacteristic
1321C2#6275911yescharacteristic
1322C2#6277311yescharacteristic
1323C2#6278812yes—
1324C2#6282312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59885C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60043C2semidirect
2. #60042C2semidirect
3. #59923C2semidirect
4. #59886C2semidirect
6. #46326C2semidirect
7. #46325C2semidirect
8. #46313C2semidirect
9. #46312C2semidirect
10. #46285C2semidirect
11. #40470C2semidirect
12. #40468C2semidirect
13. #38855C2semidirect
14. #38854C2semidirect
15. #38481C2semidirect
16. #38441C2semidirect
17. #37602C2semidirect
18. #37267C2semidirect
19. #37266C2semidirect
20. #37265C2semidirect
21. #36638C2semidirect
22. #36205C2semidirect
23. #36145C2semidirect
24. #35246C2semidirect
25. #35245C2semidirect
26. #34521C2semidirect
27. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#600432
#600422
#599232
#598862
#598852
#463262
#463252
#463132
#463122
#462852
#404702
#404682
#388552
#388542
#384812
#384412
#376022
#372672
#372662
#372652
#366382
#362052
#361452
#352462
#352452
#345212
C2×C4×C4⋊Q82