Finite Group Databasebeta

← #7722342

Subgroups — #7722342

Order 512.

5336 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51472C212yesmaximal, complemented
2#51348C212yesmaximal, complemented
3#51339C212yesmaximal, complemented
4#51336C212yesmaximal, complemented
5#47034C212yesmaximal, complemented
6#47032C212yesmaximal, complemented
7#46455C212yesmaximal, complemented
8#46453C212yesmaximal, complemented
9#44795C214yesmaximal, complemented
10#44761C214yesmaximal, complemented
11#39676C214yesmaximal, complemented
12#39559C214yesmaximal, complemented
13#39465C214yesmaximal, complemented
14#38233C214yesmaximal, complemented
15#38065C214yesmaximal, complemented
16#37447C211yesmaximal, characteristic
17#36810C214yesmaximal, complemented
18#36223C214yesmaximal, complemented
19#35398C214yesmaximal, complemented
20#35242C211yesmaximal, characteristic
21#35065C211yesmaximal, characteristic, complemented
22C2×#2434C211yesmaximal, characteristic, complemented
23#34359C211yesmaximal, characteristic, complemented
24#34228C211yesmaximal, characteristic
25C2×#2310C211yesmaximal, characteristic, complemented
26C24×Q8C2211yescharacteristic
27C2×#552C2214yes—
28C2×#536C2212yes—
29C22×C4⋊Q8C2212yes—
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×#117C2212yes—
33#2855C2214yes—
34#2852C2214yes—
35#2851C2214yes—
36#2849C2212yes—
37#2849C2212yes—
38#2817C2212yes—
39#2816C2212yes—
40#2799C2214yescomplemented
41#2799C2214yescomplemented
42#2798C2214yescomplemented
43#2798C2214yescomplemented
44#2789C2214yescomplemented
45#2789C2214yescomplemented
46#2771C2214yes—
47#2765C2214yes—
48#2765C2214yes—
49#2764C2214yes—
50#2762C2214yescomplemented
51#2762C2214yescomplemented
52#2761C2214yes—
53#2759C2214yescomplemented
54#2758C2214yescomplemented
55#2758C2214yescomplemented
56#2758C2214yescomplemented
57#2755C2214yescomplemented
58#2755C2214yescomplemented
59#2755C2214yescomplemented
60#2754C2214yescomplemented
61#2751C2214yes—
62#2750C2214yes—
63#2743C2214yes—
64#2716C2214yescomplemented
65#2716C2214yescomplemented
66#2716C2214yescomplemented
67#2716C2214yescomplemented
68#2715C2214yescomplemented
69#2713C2214yescomplemented
70#2713C2214yescomplemented
71#2713C2214yescomplemented
72#2713C2214yescomplemented
73#2713C2214yescomplemented
74#2713C2214yescomplemented
75#2704C2214yescomplemented
76#2700C2214yescomplemented
77#2698C2214yescomplemented
78#2690C2214yescomplemented
79#2689C2214yescomplemented
80#2667C2212yes—
81#2665C2212yes—
82#2659C2212yes—
83#2646C2214yes—
84#2643C2214yes—
85#2639C2212yes—
86#2638C2212yes—
87#2638C2212yes—
88#2623C2212yes—
89#2614C2212yes—
90#2614C2214yes—
91#2612C2214yescomplemented
92#2611C2214yes—
93#2609C2214yes—
94#2608C2212yes—
95#2607C2212yes—
96#2607C2214yescomplemented
97#2605C2214yescomplemented
98#2605C2214yescomplemented
99#2605C2214yescomplemented
100#2601C2214yes—
101#2599C2214yes—
102#2589C2214yescomplemented
103#2588C2214yescomplemented
104#2588C2214yescomplemented
105#2588C2214yescomplemented
106#2588C2214yescomplemented
107#2586C2214yescomplemented
108#2569C2212yes—
109#2564C2214yes—
110#2556C2214yescomplemented
111#2550C2214yescomplemented
112#2550C2214yescomplemented
113#2550C2214yescomplemented
114#2549C2212yes—
115#2549C2214yescomplemented
116#2527C2214yescomplemented
117#2523C2214yescomplemented
118#2521C2214yescomplemented
119#2520C2214yescomplemented
120#2520C2214yescomplemented
121#2520C2214yescomplemented
122#2510C2214yes—
123#2505C2214yes—
124#2505C2214yes—
125#2503C2214yes—
126#2498C2214yes—
127#2493C2214yes—
128#2493C2214yes—
129#2492C2214yescomplemented
130#2492C2214yescomplemented
131#2488C2214yes—
132#2486C2214yes—
133#2484C2214yes—
134#2484C2214yes—
135#2484C2212yes—
136#2481C2214yes—
137#2479C2214yes—
138#2477C2214yes—
139#2475C2214yes—
140#2475C2214yes—
141#2474C2214yescomplemented
142#2473C2214yes—
143#2473C2214yes—
144#2465C2214yescomplemented
145#2451C2214yescomplemented
146#2451C2214yescomplemented
147#2451C2214yescomplemented
148#2450C2214yes—
149#2449C2214yes—
150#2439C2214yescomplemented
151#2439C2214yescomplemented
152#2438C2214yes—
153#2438C2214yes—
154#2438C2214yescomplemented
155#2437C2214yes—
156#2436C2212yes—
157#2436C2211yescharacteristic
158#2436C2211yescharacteristic
159#2434C2212yes—
160#2434C2212yes—
161#2434C2214yes—
162#2434C2211yescharacteristic
163#2434C2212yes—
164#2434C2212yes—
165#2434C2212yes—
166#2434C2212yes—
167#2434C2211yescharacteristic
168#2434C2212yes—
169#2419C2214yes—
170#2413C2214yes—
171#2413C2214yes—
172#2412C2214yes—
173#2409C2212yes—
174#2409C2214yes—
175#2409C2212yes—
176#2406C2212yes—
177C2×#395C2214yes—
178#2378C2212yes—
179#2378C2212yes—
180#2368C2214yes—
181#2368C2212yes—
182#2364C2212yes—
183#2359C2214yes—
184#2358C2214yes—
185#2357C2212yes—
186#2353C2212yes—
187#2344C2214yes—
188#2344C2214yes—
189#2343C2214yes—
190#2343C2212yes—
191#2342C2214yes—
192#2339C2212yes—
193#2333C2212yes—
194#2332C2212yes—
195#2332C2212yes—
196#2332C2212yes—
197#2329C2214yes—
198#2329C2214yes—
199#2329C2214yes—
200#2318C2214yes—
201#2318C2212yes—
202#2313C2212yes—
203#2310C2211yescharacteristic
204#2310C2212yes—
205#2310C2214yes—
206#2310C2212yes—
207#2310C2211yescharacteristic
208#2310C2211yescharacteristic
209#2310C2211yescharacteristic
210#2310C2212yes—
211#2310C2212yes—
212#2310C2214yes—
213C4×C22⋊Q8C2214yes—
214C4×#123C2214yes—
215C2×#391C2214yes—
216C2×#391C2214yes—
217C2×#391C2212yes—
218#2290C2214yes—
219C2×#385C2212yes—
220C2×#385C2212yes—
221#2280C2211yescharacteristic
222C2×#381C2211yescharacteristic
223C2×#381C2211yescharacteristic
224C2×#381C2212yes—
225#2275C2212yes—
226C2×C4×C22⋊C4C2211yescharacteristic
227C22×#41C2311yescharacteristic
228C23×Q8—28no—
229C23×Q8—48no—
230C23×Q8C2312yes—
231C23×Q8C2312yes—
232C23×Q8C2311yescharacteristic
233C23×Q8C2311yescharacteristic
234C23×Q8C2311yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×Q8C2312yes—
237C23×Q8C2312yes—
238C23×Q8C2311yescharacteristic
239C24×C4C2311yescharacteristic
240C24×C4C2311yescharacteristic
241C24×C4C2311yescharacteristic
242#552—416no—
243#536—48no—
244C2×C4⋊Q8—48no—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2314yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2312yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260#525—28no—
261C2×#123C2314yes—
262C2×#123C2312yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8—28no—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2311yescharacteristic
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2311yescharacteristic
278C2×#121C2311yescharacteristic
279C2×#120C2312yes—
280C2×C4×Q8C2314yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2314yes—
285C2×#117—48no—
286C2×#117C2311yescharacteristic
287C2×#117C2314yes—
288C2×#117C2312yes—
289C2×#117C2314yes—
290C2×#117C2312yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2314yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2314yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2312yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2312yes—
305C22×C42C2314yes—
306C22×C42C2312yes—
307#401C2314yes—
308#401C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2312yes—
356#397C2312yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2312yes—
381#395C2312yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2312yes—
396#393C2312yes—
397#393C2314yes—
398#393C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2312yes—
439#390C2314yes—
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#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#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
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#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2312yes—
531#386C2312yes—
532#386C2312yes—
533#386C2312yes—
534#386C2314yes—
535#386C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2312yes—
549#385C2312yes—
550#385C2312yes—
551#385C2312yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#383C2312yes—
564#383C2314yes—
565#383C2314yes—
566#383C2314yes—
567#382C2312yes—
568#382C2314yes—
569#382C2314yes—
570#382C2314yes—
571#382C2314yes—
572#381C2312yes—
573#381C2312yes—
574#381C2312yes—
575#381C2312yes—
576#381C2312yes—
577#381C2311yescharacteristic
578#381C2311yescharacteristic
579#381C2311yescharacteristic
580#381C2311yescharacteristic
581#381C2312yes—
582#381C2314yes—
583#381C2314yes—
584#381C2312yes—
585#381C2312yes—
586#381C2312yes—
587#381C2312yes—
588#381C2312yes—
589#381C2314yes—
590#381C2314yes—
591#381C2314yes—
592#381C2312yes—
593#381C2314yes—
594#381C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2312yes—
599#380C2314yes—
600#380C2312yes—
601#380C2314yes—
602#380C2314yes—
603#380C2312yes—
604#380C2314yes—
605#379C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2311yescharacteristic
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2311yescharacteristic
623C4×C22⋊C4C2311yescharacteristic
624C4×C22⋊C4C2312yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2312yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2312yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2311yescharacteristic
632#376C2312yes—
633#376C2314yes—
634C2×#95C2312yes—
635C2×#95C2312yes—
636C2×#95C2314yes—
637C2×#95C2312yes—
638C2×#95C2312yes—
639C2×#95C2312yes—
640C2×#95C2314yes—
641C2×#95C2312yes—
642C2×#95C2314yes—
643C2×#95C2314yes—
644C25C2411yescharacteristic
645C2×#41—24no—
646C2×#41—44no—
647C22×Q8—28no—
648C22×Q8—28no—
649C22×Q8—24no—
650C22×Q8—24no—
651C22×Q8—28no—
652C22×Q8—24no—
653C22×Q8—24no—
654C22×Q8—28no—
655C22×Q8—24no—
656C22×Q8—28no—
657C22×Q8—28no—
658C22×Q8—44no—
659C22×Q8—44no—
660C22×Q8—44no—
661C22×Q8—44no—
662C22×Q8—44no—
663C22×Q8—44no—
664C22×Q8—44no—
665C22×Q8—44no—
666C22×Q8—44no—
667C22×Q8—44no—
668C22×Q8—44no—
669C22×Q8—464no—
670C22×Q8C2412yes—
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C22×Q8C2412yes—
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2412yes—
678C22×Q8C2414yes—
679C22×Q8C2412yes—
680C22×Q8C2412yes—
681C22×Q8C2411yescharacteristic
682C22×D4C2412yes—
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2411yescharacteristic
686C23×C4—24no—
687C23×C4—28no—
688C23×C4—24no—
689C23×C4—44no—
690C23×C4—44no—
691C23×C4#4118yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2414yes—
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2412yes—
701C23×C4C2412yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2414yes—
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C23×C4C2411yescharacteristic
709C23×C4C2411yescharacteristic
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C23×C4C2411yescharacteristic
713C4⋊Q8—44no—
714C4⋊Q8—48no—
715C4⋊Q8—44no—
716C4⋊Q8—48no—
717C4⋊Q8—44no—
718C4⋊Q8—44no—
719C4⋊Q8—44no—
720C4⋊Q8—44no—
721#126—48no—
722#126—48no—
723#125—48no—
724#125—48no—
725#125—48no—
726#124—44no—
727#124—44no—
728#123—28no—
729#123—216no—
730#123—48no—
731#123—48no—
732C22⋊Q8—28no—
733C22⋊Q8—28no—
734C22⋊Q8—28no—
735C22⋊Q8—28no—
736C22⋊Q8—24no—
737C22⋊Q8—24no—
738C22⋊Q8—216no—
739C22⋊Q8—48no—
740C22⋊Q8—48no—
741C22⋊Q8—48no—
742C22⋊Q8—48no—
743#121—24no—
744#121—24no—
745#120—28no—
746C4×Q8—48no—
747C4×D4—28no—
748C4×D4—28no—
749C4×D4—216no—
750C4×D4—48no—
751#117—24no—
752#117—216no—
753#117—44no—
754#117—44no—
755#117—48no—
756#117—48no—
757#117—44no—
758#117—48no—
759#117—44no—
760#117—44no—
761C2×C4⋊C4—28no—
762C2×C4⋊C4—24no—
763C2×C4⋊C4—216no—
764C2×C4⋊C4—48no—
765C2×C4⋊C4—48no—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C22⋊C4—28no—
812C2×C22⋊C4—28no—
813C2×C22⋊C4—44no—
814C2×C22⋊C4—44no—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C42—48no—
847C2×C42—44no—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865#95C2412yes—
866#95C2412yes—
867#95C2414yes—
868#95C2412yes—
869#95C2412yes—
870#95C2414yes—
871#95C2412yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
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#95C2412yes—
904#95C2414yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935C24—24no—
936C24—24no—
937C24—42no—
938C24C2×#4114yes—
939C24C2512yes—
940C24C2511yescharacteristic
941C24C2511yescharacteristic
942C24C2511yescharacteristic
943#41—88no—
944C2×Q8—24no—
945C2×Q8—24no—
946C2×Q8—24no—
947C2×Q8—24no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—24no—
963C2×Q8—28no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—42no—
974C2×Q8—44no—
975C2×Q8—42no—
976C2×Q8—42no—
977C2×Q8—44no—
978C2×Q8—432no—
979C2×Q8—432no—
980C2×Q8—432no—
981C2×Q8—432no—
982C2×Q8—416no—
983C2×Q8—416no—
984C2×Q8—416no—
985C2×Q8—416no—
986C2×Q8—88no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—28no—
990C2×D4—28no—
991C2×D4—24no—
992C2×D4—22no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—42no—
996C22×C4—232no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—28no—
1014C22×C4—28no—
1015C22×C4—24no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—28no—
1019C22×C4—28no—
1020C22×C4—28no—
1021C22×C4—24no—
1022C22×C4—28no—
1023C22×C4—416no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—416no—
1042C22×C4C2×#4114yes—
1043C22×C4C2×#4114yes—
1044C22×C4C2×#4114yes—
1045C22×C4C2×#4114yes—
1046C22×C4C2×#4114yes—
1047C22×C4C2×#4114yes—
1048C22×C4H(5,𝔽2)18yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—24no—
1124C22⋊C4—28no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C42−1+418yes—
1146C42—24no—
1147C42—28no—
1148C42—28no—
1149C42—28no—
1150C42—44no—
1151C42—44no—
1152C42—42no—
1153C42—44no—
1154C42—42no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—42no—
1161C42—42no—
1162C42—44no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—28no—
1171C23—28no—
1172C23—22no—
1173C23—24no—
1174C23—24no—
1175C23—22no—
1176C23—22no—
1177C23—44no—
1178C23—416no—
1179C23C22×#4112yes—
1180C23C22×#4112yes—
1181C23C22×#4112yes—
1182C23C2×H(5,𝔽2)14yes—
1183C23C2×2−1+414yes—
1184C23C2611yescharacteristic
1185Q8—48no—
1186Q8—48no—
1187Q8—48no—
1188Q8—48no—
1189Q8—48no—
1190Q8—48no—
1191Q8—48no—
1192Q8—48no—
1193Q8—88no—
1194Q8—84no—
1195Q8—84no—
1196Q8—82no—
1197D4—48no—
1198D4—48no—
1199D4—82no—
1200D4—84no—
1201C2×C4—216no—
1202C2×C4—28no—
1203C2×C4—28no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—216no—
1215C2×C4—28no—
1216C2×C4—28no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—22no—
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—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—44no—
1258C2×C4—44no—
1259C2×C4—44no—
1260C2×C4—44no—
1261C2×C4—416no—
1262C2×C4—48no—
1263C2×C4—44no—
1264C2×C4—44no—
1265C2×C4—48no—
1266C2×C4—48no—
1267C2×C4—88no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—88no—
1271C2×C4—88no—
1272C2×C4C22×#4112yes—
1273C2×C4C22×#4112yes—
1274C2×C4C22×#4112yes—
1275C2×C4C22×#4112yes—
1276C2×C4C2×H(5,𝔽2)14yes—
1277C2×C4C2×H(5,𝔽2)14yes—
1278C2×C4C2×2−1+418yes—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—28no—
1284C22—28no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—416no—
1289C22—44no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—44no—
1294C22—44no—
1295C22#349014yes—
1296C22#350914yes—
1297C22C23×#4111yescharacteristic
1298C22C22×H(5,𝔽2)12yes—
1299C22C22×2−1+412yes—
1300C222−1+612yes—
1301C4—24no—
1302C4—24no—
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—22no—
1307C4—28no—
1308C4—42no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—44no—
1316C4—44no—
1317C4—44no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—44no—
1322C2—24no—
1323C2—24no—
1324C2—42no—
1325C2—82no—
1326C2C2×#349011yescharacteristic
1327C2C2×#350911yescharacteristic
1328C2#6286011yescharacteristic
1329C2#6294214yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51472C2semidirect
2. #51348C2semidirect
3. #51339C2semidirect
4. #51336C2semidirect
5. #47034C2semidirect
6. #47032C2semidirect
7. #46455C2semidirect
8. #46453C2semidirect
9. #44795C2semidirect
10. #44761C2semidirect
11. #39676C2semidirect
12. #39559C2semidirect
13. #39465C2semidirect
14. #38233C2semidirect
15. #38065C2semidirect
17. #36810C2semidirect
18. #36223C2semidirect
19. #35398C2semidirect
21. #35065C2semidirect
22. C2×#2434C2semidirect
23. #34359C2semidirect
25. C2×#2310C2semidirect
40. #2799C22semidirect
41. #2799C22semidirect
42. #2798C22semidirect
43. #2798C22semidirect
44. #2789C22semidirect
45. #2789C22semidirect
50. #2762C22semidirect
51. #2762C22semidirect
53. #2759C22semidirect
54. #2758C22semidirect
55. #2758C22semidirect
56. #2758C22semidirect
57. #2755C22semidirect
58. #2755C22semidirect
59. #2755C22semidirect
60. #2754C22semidirect
64. #2716C22semidirect
65. #2716C22semidirect
66. #2716C22semidirect
67. #2716C22semidirect
68. #2715C22semidirect
69. #2713C22semidirect
70. #2713C22semidirect
71. #2713C22semidirect
72. #2713C22semidirect
73. #2713C22semidirect
74. #2713C22semidirect
75. #2704C22semidirect
76. #2700C22semidirect
77. #2698C22semidirect
78. #2690C22semidirect
79. #2689C22semidirect
91. #2612C22semidirect
96. #2607C22semidirect
97. #2605C22semidirect
98. #2605C22semidirect
99. #2605C22semidirect
102. #2589C22semidirect
103. #2588C22semidirect
104. #2588C22semidirect
105. #2588C22semidirect
106. #2588C22semidirect
107. #2586C22semidirect
110. #2556C22semidirect
111. #2550C22semidirect
112. #2550C22semidirect
113. #2550C22semidirect
115. #2549C22semidirect
116. #2527C22semidirect
117. #2523C22semidirect
118. #2521C22semidirect
119. #2520C22semidirect
120. #2520C22semidirect
121. #2520C22semidirect
129. #2492C22semidirect
130. #2492C22semidirect
141. #2474C22semidirect
144. #2465C22semidirect
145. #2451C22semidirect
146. #2451C22semidirect
147. #2451C22semidirect
150. #2439C22semidirect
151. #2439C22semidirect
154. #2438C22semidirect

Maximal subgroups

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

subgroupindex
#514722
#513482
#513392
#513362
#470342
#470322
#464552
#464532
#447952
#447612
#396762
#395592
#394652
#382332
#380652
#374472
#368102
#362232
#353982
#352422
#350652
C2×#24342
#343592
#342282
C2×#23102