Finite Group Databasebeta

← #7683546

Subgroups — #7683546

Order 512.

4860 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59964C214yesmaximal, complemented
2#59747C214yesmaximal, complemented
3#59729C214yesmaximal, complemented
4#59646C212yesmaximal, complemented
5#59602C214yesmaximal, complemented
6#59449C212yesmaximal, complemented
7#59332C212yesmaximal, complemented
8#59049C212yesmaximal, complemented
9#45437C211yesmaximal, characteristic, complemented
10#45395C211yesmaximal, characteristic, complemented
11#45393C212yesmaximal, complemented
12#45266C211yesmaximal, characteristic, complemented
13#44965C211yesmaximal, characteristic, complemented
14#44960C212yesmaximal, complemented
15#44036C214yesmaximal, complemented
16#44032C214yesmaximal, complemented
17#44018C214yesmaximal, complemented
18#44005C214yesmaximal, complemented
19#35605C212yesmaximal, complemented
20#35562C212yesmaximal, complemented
21#35534C212yesmaximal, complemented
22#34954C212yesmaximal, complemented
23#34882C211yesmaximal, characteristic, complemented
24#34326C212yesmaximal, complemented
25#34280C211yesmaximal, characteristic, complemented
26#34263C212yesmaximal, complemented
27#34208C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#540C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×#520C2212yes—
32#2803C2214yes—
33#2803C2214yes—
34#2792C2214yes—
35#2791C2214yes—
36#2786C2214yes—
37#2777C2214yes—
38#2773C2214yes—
39#2772C2214yes—
40#2754C2214yes—
41#2752C2214yes—
42#2749C2214yes—
43#2748C2214yes—
44#2741C2214yes—
45#2741C2214yes—
46#2723C2214yes—
47#2723C2214yes—
48#2717C2214yes—
49#2715C2214yes—
50#2714C2214yes—
51#2714C2214yes—
52#2706C2214yes—
53#2705C2214yes—
54#2699C2214yes—
55#2699C2214yes—
56#2610C2214yes—
57#2602C2214yes—
58#2602C2214yes—
59#2601C2214yes—
60#2597C2214yes—
61#2595C2214yes—
62#2593C2214yes—
63#2593C2214yes—
64#2588C2214yes—
65#2586C2212yes—
66#2585C2214yes—
67#2585C2212yes—
68#2582C2212yes—
69#2581C2212yes—
70#2580C2212yes—
71#2578C2214yes—
72#2575C2214yes—
73#2575C2214yes—
74#2574C2212yes—
75#2571C2212yes—
76#2570C2212yes—
77#2570C2212yes—
78#2566C2212yes—
79#2565C2212yes—
80#2559C2214yes—
81#2557C2214yes—
82#2557C2214yes—
83#2556C2212yes—
84#2555C2214yes—
85#2555C2214yes—
86#2554C2214yes—
87#2553C2214yes—
88#2548C2212yes—
89#2548C2212yes—
90#2548C2212yes—
91#2548C2212yes—
92#2548C2212yes—
93#2548C2212yes—
94#2541C2212yes—
95#2541C2212yes—
96#2540C2214yes—
97#2531C2214yes—
98#2531C2214yes—
99#2529C2214yes—
100#2526C2214yes—
101#2522C2212yes—
102#2521C2214yes—
103#2521C2214yes—
104#2520C2212yes—
105#2519C2214yes—
106#2517C2214yes—
107#2517C2214yes—
108#2516C2214yes—
109#2515C2214yes—
110#2513C2214yes—
111#2513C2212yes—
112#2513C2212yes—
113#2513C2212yes—
114#2513C2212yes—
115#2512C2212yes—
116#2512C2212yes—
117#2504C2212yes—
118#2501C2212yes—
119#2500C2214yes—
120#2498C2214yes—
121#2490C2214yes—
122#2488C2214yes—
123#2479C2214yes—
124#2479C2214yes—
125#2479C2214yes—
126#2476C2214yes—
127#2474C2214yes—
128#2474C2214yes—
129#2471C2214yes—
130#2471C2214yes—
131#2471C2214yes—
132#2471C2214yes—
133#2467C2214yes—
134#2467C2214yes—
135#2467C2214yes—
136#2465C2212yes—
137#2464C2214yes—
138#2464C2214yes—
139#2462C2212yes—
140#2459C2214yes—
141#2456C2214yes—
142#2456C2214yes—
143#2448C2212yes—
144#2448C2212yes—
145#2448C2212yes—
146#2448C2214yes—
147#2448C2212yes—
148#2445C2212yes—
149#2445C2212yes—
150#2444C2214yes—
151#2443C2214yes—
152#2443C2214yes—
153#2431C2212yes—
154#2431C2212yes—
155#2427C2214yes—
156#2425C2214yes—
157#2422C2214yes—
158#2419C2214yes—
159#2414C2214yes—
160#2399C2211yescharacteristic
161#2399C2211yescharacteristic
162#2396C2211yescharacteristic
163#2396C2211yescharacteristic
164#2395C2214yes—
165#2395C2214yes—
166#2374C2214yes—
167#2373C2214yes—
168#2373C2214yes—
169#2373C2214yes—
170#2368C2214yes—
171#2367C2212yes—
172#2367C2212yes—
173#2365C2212yes—
174#2364C2214yes—
175#2364C2214yes—
176#2364C2214yes—
177#2363C2214yes—
178#2363C2214yes—
179#2363C2214yes—
180#2359C2214yes—
181#2359C2214yes—
182#2357C2214yes—
183#2357C2212yes—
184#2357C2212yes—
185#2356C2212yes—
186#2355C2212yes—
187#2355C2212yes—
188#2354C2214yes—
189#2354C2212yes—
190#2352C2214yes—
191#2352C2214yes—
192#2351C2212yes—
193Q8×C4⋊C4C2212yes—
194#2345C2214yes—
195#2345C2212yes—
196#2344C2212yes—
197#2344C2214yes—
198#2343C2214yes—
199#2341C2212yes—
200#2341C2212yes—
201#2334C2214yes—
202#2332C2214yes—
203#2330C2211yescharacteristic
204#2328C2212yes—
205#2328C2211yescharacteristic
206#2328C2211yescharacteristic
207#2328C2211yescharacteristic
208#2327C2211yescharacteristic
209#2327C2211yescharacteristic
210#2326C2212yes—
211#2324C2212yes—
212#2319C2214yes—
213#2319C2212yes—
214#2314C2214yes—
215#2314C2211yescharacteristic
216#2311C2212yes—
217C4×#127C2212yes—
218C4×#127C2211yescharacteristic
219C4×#125C2211yescharacteristic
220C4×#125C2212yes—
221C4×#126C2214yes—
222C4×#124C2212yes—
223C4×#124C2212yes—
224C4×#124C2212yes—
225C4×#124C2214yes—
226C4×C22⋊Q8C2212yes—
227C4×#121C2212yes—
228#2298C2214yes—
229#2298C2212yes—
230#2298C2214yes—
231#2295C2211yescharacteristic
232#2295C2212yes—
233#2293C2212yes—
234#2293C2214yes—
235#2293C2214yes—
236#2293C2212yes—
237C2×#382C2211yescharacteristic
238#2276C2212yes—
239#2275C2212yes—
240C42×Q8C2212yes—
241C42×Q8C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244#556—216no—
245#540—28no—
246#532—28no—
247C2×C4⋊Q8C2311yescharacteristic
248C2×#127C2311yescharacteristic
249C2×#127C2311yescharacteristic
250C2×#127C2312yes—
251C2×#127C2312yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2311yescharacteristic
257C2×#125C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278#520—216no—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×#117C2314yes—
302C2×#117C2314yes—
303C2×#117C2311yescharacteristic
304C2×#117C2314yes—
305C2×#117C2314yes—
306C2×#117C2314yes—
307C2×#117C2314yes—
308C2×#117C2311yescharacteristic
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2314yes—
311C22×C42C2311yescharacteristic
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2311yescharacteristic
317#400C2314yes—
318#400C2311yescharacteristic
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2311yescharacteristic
325#399C2311yescharacteristic
326#399C2314yes—
327#399C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2312yes—
333#398C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2312yes—
337#398C2312yes—
338#398C2312yes—
339#398C2312yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2312yes—
359#396C2314yes—
360#396C2312yes—
361#396C2314yes—
362#395C2312yes—
363#395C2314yes—
364#395C2311yescharacteristic
365#395C2312yes—
366#395C2312yes—
367#395C2311yescharacteristic
368#395C2312yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#393C2311yescharacteristic
386#393C2314yes—
387#393C2311yescharacteristic
388#392C2314yes—
389#392C2314yes—
390#392C2314yes—
391#392C2314yes—
392#392C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2314yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2314yes—
406#390C2312yes—
407#390C2312yes—
408#390C2314yes—
409#390C2314yes—
410#390C2314yes—
411#390C2312yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#390C2314yes—
416#390C2312yes—
417#390C2312yes—
418#390C2314yes—
419#390C2312yes—
420#390C2314yes—
421#390C2312yes—
422#390C2312yes—
423#390C2314yes—
424#390C2314yes—
425#390C2312yes—
426#390C2312yes—
427#390C2314yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2312yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2312yes—
466#388C2312yes—
467#388C2314yes—
468#388C2312yes—
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#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#387C2312yes—
507#387C2314yes—
508#387C2314yes—
509#387C2312yes—
510#387C2312yes—
511#387C2312yes—
512#387C2312yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2312yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2312yes—
537#387C2312yes—
538#387C2312yes—
539#387C2314yes—
540#387C2312yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
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#386C2314yes—
570#386C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2312yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2312yes—
582#384C2312yes—
583#384C2311yescharacteristic
584#384C2312yes—
585#384C2314yes—
586#383C2314yes—
587#382C2311yescharacteristic
588#382C2312yes—
589#382C2312yes—
590#382C2312yes—
591#382C2314yes—
592#382C2311yescharacteristic
593#382C2312yes—
594#382C2314yes—
595#382C2314yes—
596#382C2311yescharacteristic
597#382C2314yes—
598#381C2314yes—
599#381C2314yes—
600#381C2314yes—
601#381C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2312yes—
605#380C2314yes—
606#380C2314yes—
607#380C2312yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2311yescharacteristic
643C4×C4⋊C4C2311yescharacteristic
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⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667#376C2312yes—
668#376C2314yes—
669#376C2311yescharacteristic
670#376C2311yescharacteristic
671#376C2314yes—
672C2×#95C2314yes—
673C2×#95C2314yes—
674C43C2314yes—
675C43C2311yescharacteristic
676C43C2312yes—
677C43C2311yescharacteristic
678C2×#41—28no—
679C2×#41—28no—
680C2×#41—44no—
681C22×Q8C2411yescharacteristic
682C22×Q8C2412yes—
683C22×Q8C2412yes—
684C22×Q8C2411yescharacteristic
685C22×D4C2412yes—
686C22×D4C2412yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C23×C4C2414yes—
696C23×C4C2411yescharacteristic
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2414yes—
704C4⋊Q8#4118yes—
705#127—24no—
706#127—24no—
707#127—44no—
708#127—44no—
709#126—216no—
710#126—216no—
711#126—48no—
712#126—84no—
713#125—24no—
714#125—44no—
715#124—28no—
716#124—28no—
717#124—28no—
718#124—48no—
719#124—84no—
720#124—84no—
721#123—216no—
722#123—48no—
723#123—84no—
724#123—84no—
725#123—84no—
726C22⋊Q8—216no—
727C22⋊Q8—44no—
728#121—28no—
729#121—216no—
730#121—216no—
731#121—48no—
732#121—48no—
733#121—84no—
734#121—84no—
735C4×Q8—28no—
736C4×Q8—28no—
737C4×Q8—28no—
738C4×Q8—28no—
739C4×Q8—28no—
740C4×Q8—42no—
741C4×Q8—42no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×Q8—44no—
745C4×D4—216no—
746C4×D4—216no—
747C4×D4—216no—
748C4×D4—28no—
749C4×D4—28no—
750C4×D4—28no—
751C4×D4—28no—
752C4×D4—44no—
753C4×D4—48no—
754C4×D4—84no—
755C4×D4—84no—
756C4×D4—84no—
757#117—216no—
758#117—216no—
759#117—42no—
760#117—84no—
761#117—84no—
762#117—84no—
763#117—84no—
764#117#4118yes—
765C2×C4⋊C4—28no—
766C2×C4⋊C4—216no—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊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⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2411yescharacteristic
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C42—24no—
867C2×C42C2411yescharacteristic
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2411yescharacteristic
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2411yescharacteristic
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2412yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2411yescharacteristic
957#95C2411yescharacteristic
958#95C2414yes—
959#95C2414yes—
960C24C2514yes—
961C24C2514yes—
962C24C2511yescharacteristic
963#41—432no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—41no—
969C2×Q8—41no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×Q8C2×#4118yes—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—28no—
980C2×D4—24no—
981C2×D4—28no—
982C2×D4—28no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—28no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—28no—
1007C22×C4—28no—
1008C22×C4—28no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—28no—
1013C22×C4—28no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4C2×#4114yes—
1031C22×C4C2512yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2514yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2514yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2512yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—41no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—41no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4C2×#4118yes—
1105C4⋊C4C2×#41116yes—
1106C22⋊C4—28no—
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—24no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—44no—
1123C22⋊C4—42no—
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—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—44no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4C2×#4118yes—
1154C42—24no—
1155C42—22no—
1156C42—28no—
1157C42—28no—
1158C42—28no—
1159C42—28no—
1160C42—24no—
1161C42—24no—
1162C42—22no—
1163C42—22no—
1164C42—24no—
1165C42—24no—
1166C42—24no—
1167C42—42no—
1168C42—44no—
1169C42—42no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—42no—
1174C42—42no—
1175C42—44no—
1176C42—44no—
1177C42—42no—
1178C42—42no—
1179C42—44no—
1180C42—44no—
1181C42—42no—
1182C42—44no—
1183C42C2×#4114yes—
1184C42C2×#4114yes—
1185C42C2×#4114yes—
1186C23—21no—
1187C23—22no—
1188C23—21no—
1189C23—22no—
1190C23—24no—
1191C23—24no—
1192C23—24no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23C22×#4112yes—
1205C23C2611yescharacteristic
1206Q8—216no—
1207Q8—44no—
1208Q8—84no—
1209Q8—82no—
1210D4—416no—
1211D4—48no—
1212D4—48no—
1213D4—88no—
1214D4—88no—
1215D4—88no—
1216D4—88no—
1217D4—88no—
1218D4—164no—
1219D4—164no—
1220C2×C4—24no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—28no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—416no—
1281C2×C4—84no—
1282C2×C4—88no—
1283C2×C4—88no—
1284C2×C4—88no—
1285C2×C4—88no—
1286C2×C4—88no—
1287C2×C4—164no—
1288C2×C4C22×#4114yes—
1289C2×C4C22×#4114yes—
1290C2×C4C22×#4118yes—
1291C2×C4C22×#4114yes—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4112yes—
1294C2×C4C22×#4112yes—
1295C2×C4#58514yes—
1296C2×C4#58512yes—
1297C22—24no—
1298C22—22no—
1299C22—42no—
1300C22—41no—
1301C22—41no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22C23×#4111yescharacteristic
1317C22C23×#4111yescharacteristic
1318C22C2×#58512yes—
1319C22C2×#58511yescharacteristic
1320C22H(7,𝔽2)12yes—
1321C4—24no—
1322C4—24no—
1323C4—24no—
1324C4—24no—
1325C4—22no—
1326C4—28no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—41no—
1337C4—42no—
1338C4—41no—
1339C4—44no—
1340C4—41no—
1341C4—42no—
1342C4—42no—
1343C4—41no—
1344C4#347514yes—
1345C2—42no—
1346C2—84no—
1347C2—84no—
1348C2C2×#347511yescharacteristic
1349C2#6282911yescharacteristic
1350C2#6288311yescharacteristic
1351C2#6300612yes—
1352C2#6301012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59964C2semidirect
2. #59747C2semidirect
3. #59729C2semidirect
4. #59646C2semidirect
5. #59602C2semidirect
6. #59449C2semidirect
7. #59332C2semidirect
8. #59049C2semidirect
9. #45437C2semidirect
10. #45395C2semidirect
11. #45393C2semidirect
12. #45266C2semidirect
13. #44965C2semidirect
14. #44960C2semidirect
15. #44036C2semidirect
16. #44032C2semidirect
17. #44018C2semidirect
18. #44005C2semidirect
19. #35605C2semidirect
20. #35562C2semidirect
21. #35534C2semidirect
22. #34954C2semidirect
23. #34882C2semidirect
24. #34326C2semidirect
25. #34280C2semidirect
26. #34263C2semidirect
27. #34208C2semidirect

Maximal subgroups

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

subgroupindex
#599642
#597472
#597292
#596462
#596022
#594492
#593322
#590492
#454372
#453952
#453932
#452662
#449652
#449602
#440362
#440322
#440182
#440052
#356052
#355622
#355342
#349542
#348822
#343262
#342802
#342632
#342082