Finite Group Databasebeta

← #7683754

Subgroups — #7683754

Order 512.

4624 conjugacy classes of subgroups.

The subgroup lattice has 1293 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59571C214yesmaximal, complemented
2#59495C214yesmaximal, complemented
3#59448C212yesmaximal, complemented
4#59437C212yesmaximal, complemented
5#59336C214yesmaximal, complemented
6#59333C212yesmaximal, complemented
7#59255C214yesmaximal, complemented
8#59064C212yesmaximal
9#45436C211yesmaximal, characteristic, complemented
10#45366C212yesmaximal, complemented
11#45362C211yesmaximal, characteristic, complemented
12#45152C211yesmaximal, characteristic, complemented
13#45150C212yesmaximal, complemented
14#45137C211yesmaximal, characteristic, complemented
15#43703C214yesmaximal, complemented
16#43700C214yesmaximal, complemented
17#43641C214yesmaximal, complemented
18#43627C214yesmaximal, complemented
19#35656C212yesmaximal, complemented
20#35632C212yesmaximal, complemented
21#35622C212yesmaximal, complemented
22#34945C212yesmaximal, complemented
23#34882C211yesmaximal, characteristic, complemented
24#34329C212yesmaximal, complemented
25#34281C211yesmaximal, characteristic, complemented
26#34260C212yesmaximal, complemented
27#34208C211yesmaximal, characteristic
28C2×#559C2212yes—
29C2×#541C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×#520C2212yes—
32#2789C2214yes—
33#2787C2214yes—
34#2787C2214yes—
35#2784C2214yes—
36#2780C2214yes—
37#2769C2214yes—
38#2769C2214yes—
39#2767C2214yes—
40#2767C2214yes—
41#2765C2214yes—
42#2762C2214yes—
43#2750C2214yes—
44#2746C2214yes—
45#2745C2214yes—
46#2744C2214yes—
47#2743C2214yes—
48#2743C2214yes—
49#2739C2214yes—
50#2739C2214yes—
51#2738C2214yes—
52#2717C2214yes—
53#2717C2214yes—
54#2708C2214yes—
55#2708C2214yes—
56#2612C2214yes—
57#2612C2214yes—
58#2609C2214yes—
59#2590C2214yes—
60#2588C2214yes—
61#2588C2214yes—
62#2586C2212yes—
63#2585C2212yes—
64#2581C2212yes—
65#2580C2212yes—
66#2579C2214yes—
67#2577C2214yes—
68#2577C2214yes—
69#2577C2214yes—
70#2577C2214yes—
71#2576C2214yes—
72#2575C2214yes—
73#2574C2212yes—
74#2573C2214yes—
75#2573C2214yes—
76#2572C2214yes—
77#2571C2212yes—
78#2570C2212yes—
79#2570C2212yes—
80#2569C2214yes—
81#2568C2212yes—
82#2568C2212yes—
83#2568C2212yes—
84#2566C2212yes—
85#2565C2212yes—
86#2556C2212yes—
87#2547C2212yes—
88#2547C2212yes—
89#2547C2212yes—
90#2546C2212yes—
91#2546C2212yes—
92#2538C2212yes—
93#2533C2214yes—
94#2533C2214yes—
95#2530C2214yes—
96#2530C2214yes—
97#2528C2214yes—
98#2528C2214yes—
99#2528C2214yes—
100#2527C2214yes—
101#2524C2214yes—
102#2524C2214yes—
103#2524C2214yes—
104#2523C2214yes—
105#2522C2212yes—
106#2520C2212yes—
107#2520C2214yes—
108#2517C2214yes—
109#2515C2214yes—
110#2514C2212yes—
111#2514C2212yes—
112#2514C2212yes—
113#2514C2212yes—
114#2511C2212yes—
115#2511C2212yes—
116#2505C2214yes—
117#2505C2214yes—
118#2503C2212yes—
119#2502C2212yes—
120#2495C2214yes—
121#2494C2214yes—
122#2494C2214yes—
123#2493C2214yes—
124#2493C2214yes—
125#2493C2214yes—
126#2493C2214yes—
127#2493C2214yes—
128#2477C2214yes—
129#2475C2214yes—
130#2475C2214yes—
131#2475C2214yes—
132#2473C2214yes—
133#2473C2214yes—
134#2468C2214yes—
135#2468C2214yes—
136#2466C2214yes—
137#2466C2214yes—
138#2465C2212yes—
139#2462C2212yes—
140#2449C2214yes—
141#2447C2212yes—
142#2447C2212yes—
143#2447C2212yes—
144#2447C2212yes—
145#2447C2214yes—
146#2446C2212yes—
147#2446C2212yes—
148#2442C2214yes—
149#2438C2214yes—
150#2438C2214yes—
151#2432C2212yes—
152#2432C2212yes—
153#2427C2214yes—
154#2421C2214yes—
155#2420C2214yes—
156#2419C2214yes—
157#2419C2214yes—
158#2419C2214yes—
159#2419C2214yes—
160#2401C2214yes—
161#2401C2214yes—
162#2399C2211yescharacteristic
163#2399C2211yescharacteristic
164#2396C2211yescharacteristic
165#2396C2211yescharacteristic
166#2374C2214yes—
167#2373C2214yes—
168#2373C2214yes—
169#2372C2214yes—
170#2371C2214yes—
171#2370C2214yes—
172#2367C2212yes—
173#2367C2212yes—
174#2366C2212yes—
175#2364C2214yes—
176#2364C2214yes—
177#2359C2214yes—
178#2357C2212yes—
179#2356C2212yes—
180#2356C2212yes—
181#2355C2212yes—
182#2355C2212yes—
183#2354C2212yes—
184#2353C2214yes—
185#2353C2214yes—
186#2352C2214yes—
187#2352C2214yes—
188#2352C2214yes—
189#2349C2212yes—
190#2349C2214yes—
191D4×C4⋊C4C2212yes—
192#2345C2214yes—
193#2345C2212yes—
194#2344C2212yes—
195#2343C2214yes—
196#2343C2214yes—
197#2343C2214yes—
198#2343C2214yes—
199#2339C2212yes—
200#2339C2212yes—
201#2337C2214yes—
202#2335C2214yes—
203#2330C2211yescharacteristic
204#2328C2211yescharacteristic
205#2328C2211yescharacteristic
206#2327C2212yes—
207#2327C2211yescharacteristic
208#2327C2211yescharacteristic
209#2327C2211yescharacteristic
210#2326C2212yes—
211#2323C2212yes—
212#2320C2212yes—
213#2318C2214yes—
214#2314C2211yescharacteristic
215#2313C2214yes—
216#2311C2212yes—
217C4×C4⋊Q8C2212yes—
218C4×C4⋊Q8C2211yescharacteristic
219C4×#125C2212yes—
220C4×#125C2211yescharacteristic
221C4×#124C2212yes—
222C4×#124C2212yes—
223C4×#124C2212yes—
224C4×C22⋊Q8C2212yes—
225C4×C22⋊Q8C2214yes—
226C4×C22⋊Q8C2212yes—
227C4×#123C2214yes—
228#2298C2212yes—
229#2295C2212yes—
230#2295C2211yescharacteristic
231#2295C2212yes—
232#2295C2212yes—
233#2290C2214yes—
234#2290C2214yes—
235C2×#387C2214yes—
236#2283C2214yes—
237C2×#382C2211yescharacteristic
238#2276C2212yes—
239#2275C2212yes—
240C42×Q8C2211yescharacteristic
241C42×D4C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244#559—216no—
245#541—28no—
246#532—28no—
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×#127C2311yescharacteristic
252C2×#126C2314yes—
253C2×#125C2311yescharacteristic
254C2×#125C2314yes—
255C2×#125C2312yes—
256C2×#124C2312yes—
257C2×#124C2314yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×#121C2314yes—
266#520—216no—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×#117C2314yes—
288C2×#117C2311yescharacteristic
289C2×#117C2314yes—
290C2×#117C2314yes—
291C2×#117C2311yescharacteristic
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2314yes—
294C22×C4⋊C4C2314yes—
295C22×C42C2311yescharacteristic
296C22×C42C2314yes—
297#401C2314yes—
298#401C2314yes—
299#401C2314yes—
300#401C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2311yescharacteristic
318#400C2314yes—
319#400C2314yes—
320#400C2311yescharacteristic
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#399C2314yes—
327#399C2311yescharacteristic
328#399C2311yescharacteristic
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2312yes—
344#398C2312yes—
345#398C2314yes—
346#398C2314yes—
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#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2312yes—
366#396C2312yes—
367#395C2312yes—
368#395C2314yes—
369#395C2311yescharacteristic
370#395C2312yes—
371#395C2312yes—
372#395C2312yes—
373#395C2311yescharacteristic
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#393C2311yescharacteristic
379#393C2314yes—
380#393C2311yescharacteristic
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#391C2314yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2314yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2314yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2312yes—
403#390C2312yes—
404#390C2312yes—
405#390C2312yes—
406#390C2312yes—
407#390C2314yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2314yes—
419#389C2312yes—
420#389C2314yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2312yes—
438#388C2312yes—
439#388C2312yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2312yes—
451#388C2314yes—
452#388C2314yes—
453#387C2312yes—
454#387C2312yes—
455#387C2312yes—
456#387C2312yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2312yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2312yes—
482#387C2312yes—
483#387C2312yes—
484#387C2314yes—
485#387C2314yes—
486#387C2312yes—
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#387C2312yes—
506#387C2312yes—
507#387C2312yes—
508#387C2312yes—
509#387C2312yes—
510#387C2312yes—
511#387C2312yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2312yes—
543#385C2314yes—
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#385C2312yes—
559#384C2312yes—
560#384C2311yescharacteristic
561#384C2312yes—
562#383C2314yes—
563#383C2314yes—
564#383C2314yes—
565#383C2314yes—
566#383C2314yes—
567#383C2314yes—
568#383C2314yes—
569#382C2311yescharacteristic
570#382C2312yes—
571#382C2312yes—
572#382C2312yes—
573#382C2314yes—
574#382C2314yes—
575#382C2314yes—
576#382C2311yescharacteristic
577#382C2312yes—
578#382C2314yes—
579#382C2314yes—
580#382C2314yes—
581#382C2311yescharacteristic
582#382C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2314yes—
592#381C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2312yes—
600#380C2314yes—
601#380C2312yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2311yescharacteristic
640C4×C4⋊C4C2311yescharacteristic
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662#376C2312yes—
663#376C2311yescharacteristic
664#376C2311yescharacteristic
665#376C2314yes—
666#376C2314yes—
667#376C2314yes—
668#376C2314yes—
669#376C2314yes—
670C2×#95C2314yes—
671C2×#95C2314yes—
672C2×#95C2314yes—
673C2×#95C2314yes—
674C2×#95C2314yes—
675C43C2311yescharacteristic
676C43C2312yes—
677C43C2311yescharacteristic
678C2×#41—28no—
679C2×#41—28no—
680C2×#41—44no—
681C22×Q8C2412yes—
682C22×Q8C2412yes—
683C22×Q8C2411yescharacteristic
684C22×Q8C2412yes—
685C22×Q8C2411yescharacteristic
686C22×D4C2414yes—
687C22×D4C2412yes—
688C22×D4C2414yes—
689C23×C4C2414yes—
690C23×C4C2411yescharacteristic
691C23×C4C2414yes—
692C23×C4C2414yes—
693C23×C4C2414yes—
694C23×C4C2414yes—
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2412yes—
698C23×C4C2414yes—
699C4⋊Q8—24no—
700C4⋊Q8—24no—
701C4⋊Q8—44no—
702C4⋊Q8—44no—
703#127#4118yes—
704#126—216no—
705#125—216no—
706#125—24no—
707#125—44no—
708#124—28no—
709#124—28no—
710#124—28no—
711#124—216no—
712#123—216no—
713#123—216no—
714C22⋊Q8—28no—
715C22⋊Q8—44no—
716C22⋊Q8—48no—
717#121—216no—
718C4×Q8—28no—
719C4×Q8—28no—
720C4×Q8—28no—
721C4×Q8—28no—
722C4×Q8—28no—
723C4×Q8—42no—
724C4×Q8—42no—
725C4×Q8—44no—
726C4×Q8—44no—
727C4×D4—216no—
728C4×D4—28no—
729C4×D4—28no—
730C4×D4—216no—
731C4×D4—216no—
732C4×D4—216no—
733C4×D4—28no—
734C4×D4—28no—
735C4×D4—44no—
736C4×D4—44no—
737C4×D4—48no—
738#117—216no—
739#117—42no—
740#117—48no—
741#117—48no—
742#117#4118yes—
743C2×C4⋊C4—28no—
744C2×C4⋊C4—216no—
745C2×C4⋊C4—48no—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
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⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C42—24no—
832C2×C42—48no—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2411yescharacteristic
837C2×C42C2411yescharacteristic
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2411yescharacteristic
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2411yescharacteristic
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864#95C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2414yes—
868#95C2412yes—
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#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2412yes—
893#95C2412yes—
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#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2411yescharacteristic
922#95C2412yes—
923#95C2411yescharacteristic
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2411yescharacteristic
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2411yescharacteristic
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945C24C2514yes—
946C24C2511yescharacteristic
947#41—432no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—41no—
957C2×Q8—41no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4C2×#4118yes—
969C2×D4C2×#41116yes—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—28no—
973C22×C4—28no—
974C22×C4—28no—
975C22×C4—28no—
976C22×C4—28no—
977C22×C4—24no—
978C22×C4—28no—
979C22×C4—28no—
980C22×C4—28no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—42no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4C2×#4114yes—
1000C22×C4C2514yes—
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2514yes—
1008C22×C4C2511yescharacteristic
1009C22×C4C2512yes—
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2512yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2511yescharacteristic
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—28no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—41no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—41no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4C2×#4118yes—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—24no—
1093C22⋊C4—28no—
1094C22⋊C4—44no—
1095C22⋊C4—42no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—42no—
1099C22⋊C4—44no—
1100C22⋊C4—41no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—41no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—42no—
1109C22⋊C4C2×#4118yes—
1110C42—24no—
1111C42—22no—
1112C42—28no—
1113C42—28no—
1114C42—28no—
1115C42—24no—
1116C42—24no—
1117C42—28no—
1118C42—24no—
1119C42—28no—
1120C42—22no—
1121C42—22no—
1122C42—24no—
1123C42—24no—
1124C42—44no—
1125C42—44no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C42—44no—
1134C42—42no—
1135C42—42no—
1136C42—44no—
1137C42—42no—
1138C42C2×#4114yes—
1139C42C2×#4114yes—
1140C42C2×#4114yes—
1141C23—24no—
1142C23—21no—
1143C23—22no—
1144C23—24no—
1145C23—21no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—22no—
1150C23—24no—
1151C23C22×#4118yes—
1152C23C22×#4112yes—
1153C23C2611yescharacteristic
1154Q8—44no—
1155Q8—48no—
1156Q8—48no—
1157Q8—84no—
1158Q8—82no—
1159D4—216no—
1160D4—416no—
1161D4—416no—
1162C2×C4—21no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—28no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—21no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—416no—
1227C2×C4—84no—
1228C2×C4—88no—
1229C2×C4—88no—
1230C2×C4—88no—
1231C2×C4—88no—
1232C2×C4—88no—
1233C2×C4—88no—
1234C2×C4—164no—
1235C2×C4C22×#4114yes—
1236C2×C4C22×#4114yes—
1237C2×C4C22×#4114yes—
1238C2×C4C22×#4112yes—
1239C2×C4C22×#4112yes—
1240C2×C4C22×#4112yes—
1241C2×C4#58514yes—
1242C2×C4#58512yes—
1243C22—28no—
1244C22—28no—
1245C22—24no—
1246C22—22no—
1247C22—28no—
1248C22—42no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—41no—
1253C22—41no—
1254C22—44no—
1255C22C23×#4111yescharacteristic
1256C22C23×#4111yescharacteristic
1257C22C2×#58512yes—
1258C22C2×#58511yescharacteristic
1259C222−1+612yes—
1260C4—24no—
1261C4—24no—
1262C4—24no—
1263C4—24no—
1264C4—22no—
1265C4—42no—
1266C4—44no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—42no—
1271C4—44no—
1272C4—44no—
1273C4—44no—
1274C4—41no—
1275C4—44no—
1276C4—42no—
1277C4—41no—
1278C4—41no—
1279C4—42no—
1280C4—42no—
1281C4—41no—
1282C4—44no—
1283C4—44no—
1284C4#347514yes—
1285C2—48no—
1286C2—42no—
1287C2C2×#347511yescharacteristic
1288C2#6282911yescharacteristic
1289C2#6289011yescharacteristic
1290C2#6299112yes—
1291C2#6299512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59571C2semidirect
2. #59495C2semidirect
3. #59448C2semidirect
4. #59437C2semidirect
5. #59336C2semidirect
6. #59333C2semidirect
7. #59255C2semidirect
9. #45436C2semidirect
10. #45366C2semidirect
11. #45362C2semidirect
12. #45152C2semidirect
13. #45150C2semidirect
14. #45137C2semidirect
15. #43703C2semidirect
16. #43700C2semidirect
17. #43641C2semidirect
18. #43627C2semidirect
19. #35656C2semidirect
20. #35632C2semidirect
21. #35622C2semidirect
22. #34945C2semidirect
23. #34882C2semidirect
24. #34329C2semidirect
25. #34281C2semidirect
26. #34260C2semidirect

Maximal subgroups

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

subgroupindex
#595712
#594952
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