Finite Group Databasebeta

← #8175751

Subgroups — #8175751

Order 512.

4530 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59315C212yesmaximal, complemented
2#59212C212yesmaximal, complemented
3#56438C214yesmaximal, complemented
4#56437C214yesmaximal, complemented
5#54275C214yesmaximal, complemented
6#53702C214yesmaximal, complemented
7#53075C211yesmaximal, characteristic, complemented
8#52987C211yesmaximal, characteristic, complemented
9#52985C211yesmaximal, characteristic, complemented
10#52985C211yesmaximal, characteristic, complemented
11#52809C214yesmaximal, complemented
12#44600C214yesmaximal, complemented
13#42508C212yesmaximal, complemented
14#42493C212yesmaximal, complemented
15#42261C214yesmaximal, complemented
16#41825C214yesmaximal, complemented
17#40010C212yesmaximal, complemented
18#39958C212yesmaximal, complemented
19#39262C212yesmaximal, complemented
20#38101C212yesmaximal, complemented
21#38050C212yesmaximal, complemented
22#37505C212yesmaximal, complemented
23#37370C212yesmaximal, complemented
24#36361C212yesmaximal, complemented
25#35271C211yesmaximal, characteristic, complemented
26#34876C211yesmaximal, characteristic, complemented
27#34638C211yesmaximal, characteristic, complemented
28C2×#555C2212yes—
29C2×#553C2212yes—
30C2×#529C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2856C2211yescharacteristic
33#2854C2212yes—
34#2854C2212yes—
35#2851C2212yes—
36#2851C2211yescharacteristic
37#2841C2214yes—
38#2838C2214yes—
39#2838C2214yes—
40#2837C2214yes—
41#2837C2214yes—
42#2837C2214yes—
43#2834C2214yes—
44#2833C2214yes—
45#2827C2214yes—
46#2827C2214yes—
47#2824C2214yes—
48#2824C2214yes—
49#2807C2214yes—
50#2805C2214yes—
51#2802C2214yes—
52#2796C2214yes—
53#2787C2214yes—
54#2783C2214yes—
55#2782C2214yes—
56#2778C2214yes—
57#2778C2214yes—
58#2778C2214yes—
59#2777C2214yes—
60#2776C2214yes—
61#2770C2214yes—
62#2768C2214yes—
63#2768C2214yes—
64#2763C2214yes—
65#2748C2214yes—
66#2746C2214yes—
67#2746C2214yes—
68#2743C2214yes—
69#2742C2214yes—
70#2741C2214yes—
71#2740C2214yes—
72#2729C2214yes—
73#2728C2214yes—
74#2724C2214yes—
75#2717C2214yes—
76#2710C2214yes—
77#2708C2214yes—
78#2708C2214yes—
79#2708C2214yes—
80#2708C2214yes—
81#2708C2214yes—
82#2706C2214yes—
83#2703C2214yes—
84#2693C2214yes—
85#2688C2214yes—
86#2677C2214yes—
87#2676C2214yes—
88#2675C2214yes—
89#2674C2214yes—
90#2672C2214yes—
91#2671C2214yes—
92#2671C2214yes—
93#2671C2214yes—
94#2671C2214yes—
95#2671C2214yes—
96#2671C2214yes—
97#2663C2214yes—
98#2662C2214yes—
99#2655C2214yes—
100#2652C2214yes—
101#2649C2214yes—
102#2647C2212yes—
103#2647C2211yescharacteristic
104#2647C2212yes—
105#2647C2211yescharacteristic
106#2647C2211yescharacteristic
107#2647C2211yescharacteristic
108#2647C2211yescharacteristic
109#2646C2214yes—
110#2646C2214yes—
111#2646C2214yes—
112#2644C2212yes—
113#2643C2214yes—
114#2641C2211yescharacteristic
115#2639C2214yes—
116#2635C2214yes—
117#2628C2214yes—
118#2628C2212yes—
119#2624C2212yes—
120#2611C2212yes—
121#2610C2212yes—
122#2604C2212yes—
123#2603C2212yes—
124#2601C2214yes—
125#2598C2214yes—
126#2595C2214yes—
127#2595C2214yes—
128#2584C2212yes—
129#2583C2214yes—
130#2580C2212yes—
131#2580C2212yes—
132#2577C2214yes—
133#2575C2214yes—
134#2571C2212yes—
135#2564C2212yes—
136#2550C2212yes—
137#2546C2212yes—
138#2543C2214yes—
139#2543C2212yes—
140#2540C2214yes—
141#2537C2212yes—
142#2535C2212yes—
143#2535C2214yes—
144#2531C2214yes—
145#2526C2214yes—
146#2521C2214yes—
147#2521C2214yes—
148#2510C2214yes—
149#2509C2212yes—
150#2508C2212yes—
151#2505C2214yes—
152#2504C2212yes—
153#2504C2212yes—
154#2498C2212yes—
155#2495C2212yes—
156#2494C2214yes—
157#2494C2212yes—
158#2494C2212yes—
159#2494C2212yes—
160#2491C2214yes—
161#2487C2212yes—
162#2487C2212yes—
163#2487C2214yes—
164#2486C2212yes—
165#2485C2214yes—
166#2485C2212yes—
167#2485C2212yes—
168#2485C2212yes—
169#2479C2214yes—
170#2479C2214yes—
171#2478C2214yes—
172#2476C2214yes—
173#2475C2214yes—
174#2470C2214yes—
175#2469C2214yes—
176#2464C2214yes—
177#2461C2214yes—
178#2455C2214yes—
179#2454C2212yes—
180#2452C2212yes—
181#2450C2214yes—
182#2449C2214yes—
183#2444C2214yes—
184#2443C2214yes—
185#2443C2214yes—
186#2442C2212yes—
187#2442C2212yes—
188#2441C2212yes—
189#2441C2212yes—
190#2440C2212yes—
191#2440C2212yes—
192#2438C2214yes—
193#2430C2214yes—
194#2430C2212yes—
195#2428C2212yes—
196#2428C2212yes—
197#2427C2214yes—
198#2425C2214yes—
199#2425C2214yes—
200#2422C2212yes—
201#2422C2212yes—
202#2416C2212yes—
203#2416C2212yes—
204#2416C2212yes—
205#2414C2212yes—
206#2414C2212yes—
207#2414C2212yes—
208#2402C2214yes—
209#2402C2214yes—
210#2399C2211yescharacteristic
211#2398C2211yescharacteristic
212#2398C2211yescharacteristic
213#2397C2211yescharacteristic
214#2363C2214yes—
215#2361C2214yes—
216#2359C2214yes—
217#2359C2214yes—
218#2354C2212yes—
219#2352C2212yes—
220#2352C2212yes—
221#2352C2212yes—
222#2349C2212yes—
223D4×C4⋊C4C2212yes—
224#2335C2214yes—
225#2330C2211yescharacteristic
226#2328C2211yescharacteristic
227#2324C2214yes—
228#2324C2212yes—
229#2319C2212yes—
230#2316C2212yes—
231C4×#121C2212yes—
232C4×#121C2212yes—
233C4×#121C2212yes—
234C4×#121C2212yes—
235#2296C2212yes—
236#2296C2212yes—
237C2×#389C2212yes—
238#2290C2212yes—
239#2290C2212yes—
240#2285C2211yescharacteristic
241#2285C2211yescharacteristic
242C2×#376C2211yescharacteristic
243C22×#41C2311yescharacteristic
244#555—48no—
245#553—48no—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2314yes—
248C2×#127C2311yescharacteristic
249#529—44no—
250C2×#126C2314yes—
251C2×#126C2312yes—
252C2×#125C2312yes—
253C2×#125C2311yescharacteristic
254C2×#125C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2314yes—
257C2×#124C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2312yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2311yescharacteristic
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#121C2312yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2311yescharacteristic
278C2×#121C2314yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C4×#41—44no—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2314yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2311yescharacteristic
312C2×#117C2314yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2314yes—
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#399C2312yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2312yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#395C2312yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2312yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2312yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#393C2312yes—
436#393C2314yes—
437#393C2314yes—
438#393C2312yes—
439#393C2314yes—
440#393C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2312yes—
444#392C2312yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#391C2314yes—
450#391C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2314yes—
462#390C2312yes—
463#390C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2312yes—
500#388C2314yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2312yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2312yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#387C2312yes—
530#387C2312yes—
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#387C2312yes—
547#387C2312yes—
548#387C2314yes—
549#387C2314yes—
550#386C2312yes—
551#386C2312yes—
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#386C2312yes—
568#386C2312yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2312yes—
573#386C2312yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2312yes—
578#386C2314yes—
579#386C2314yes—
580#386C2312yes—
581#385C2312yes—
582#385C2312yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#384C2312yes—
612#384C2311yescharacteristic
613#384C2311yescharacteristic
614#384C2311yescharacteristic
615#383C2314yes—
616#382C2312yes—
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#382C2311yescharacteristic
621#382C2312yes—
622#382C2311yescharacteristic
623#382C2311yescharacteristic
624#381C2314yes—
625#381C2314yes—
626#380C2312yes—
627#380C2312yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668#376C2311yescharacteristic
669#376C2311yescharacteristic
670#376C2312yes—
671#376C2312yes—
672#376C2311yescharacteristic
673#376C2311yescharacteristic
674C2×#95C2312yes—
675C2×#95C2314yes—
676C2×#95C2314yes—
677C2×#95C2312yes—
678C2×#41—42no—
679C2×#41—44no—
680C22×Q8C2411yescharacteristic
681C22×Q8C2411yescharacteristic
682C22×Q8C2414yes—
683C22×D4C2412yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2411yescharacteristic
687C22×D4C2414yes—
688C22×D4C2412yes—
689C22×D4C2414yes—
690C22×D4C2414yes—
691C22×D4C2412yes—
692C22×D4C2411yescharacteristic
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2411yescharacteristic
699C23×C4C2414yes—
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2414yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2412yes—
711C4⋊Q8—44no—
712C4⋊Q8—84no—
713#127—42no—
714#126—44no—
715#126—48no—
716#125—42no—
717#125—42no—
718#125—44no—
719#124—42no—
720#124—48no—
721#124—48no—
722#123—48no—
723#123—48no—
724#123—48no—
725#123—48no—
726#123—44no—
727#123—84no—
728#123—84no—
729C22⋊Q8—42no—
730C22⋊Q8—84no—
731C22⋊Q8—84no—
732C22⋊Q8—84no—
733#121—28no—
734#121—44no—
735#121—48no—
736#121—44no—
737#121—48no—
738#121—48no—
739#121—48no—
740#121—48no—
741#121—44no—
742#121—44no—
743#121—44no—
744#121—44no—
745#121—42no—
746#121—84no—
747#121—84no—
748#121—84no—
749#121—84no—
750C4×Q8—42no—
751C4×Q8—42no—
752C4×Q8—42no—
753C4×D4—28no—
754C4×D4—28no—
755C4×D4—28no—
756C4×D4—28no—
757C4×D4—42no—
758C4×D4—48no—
759C4×D4—44no—
760C4×D4—44no—
761C4×D4—44no—
762C4×D4—42no—
763C4×D4—42no—
764C4×D4—44no—
765C4×D4—84no—
766C4×D4—84no—
767C4×D4—84no—
768#117—28no—
769#117—44no—
770#117—44no—
771#117—48no—
772#117—42no—
773#117—44no—
774#117—44no—
775#117—84no—
776C2×C4⋊C4—44no—
777C2×C4⋊C4—44no—
778C2×C4⋊C4—44no—
779C2×C4⋊C4—84no—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C42—24no—
886C2×C42—24no—
887C2×C42—44no—
888C2×C42—42no—
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892C2×C42C2412yes—
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968C24C2512yes—
969C24C2514yes—
970C24C2511yescharacteristic
971C24C2512yes—
972#41—416no—
973C2×Q8—41no—
974C2×Q8—42no—
975C2×Q8—41no—
976C2×Q8—42no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—44no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—28no—
986C2×D4—28no—
987C2×D4—28no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—41no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—44no—
997C2×D4—41no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—24no—
1021C22×C4—22no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—28no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—44no—
1049C22×C4—42no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4H(5,𝔽2)14yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2514yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—41no—
1101C4⋊C4—42no—
1102C4⋊C4—41no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—41no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—41no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C22⋊C4—28no—
1137C22⋊C4—24no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—28no—
1141C22⋊C4—24no—
1142C22⋊C4—28no—
1143C22⋊C4—24no—
1144C22⋊C4—28no—
1145C22⋊C4—24no—
1146C22⋊C4—24no—
1147C22⋊C4—28no—
1148C22⋊C4—24no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—44no—
1160C22⋊C4—42no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C42—22no—
1189C42—22no—
1190C42—22no—
1191C42—22no—
1192C42—24no—
1193C42—28no—
1194C42—24no—
1195C42—24no—
1196C42—22no—
1197C42—22no—
1198C42—22no—
1199C42—42no—
1200C42—42no—
1201C42—42no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C422−1+414yes—
1208C23—22no—
1209C23—22no—
1210C23—21no—
1211C23—21no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—24no—
1220C23—22no—
1221C23—24no—
1222C23—24no—
1223C23—22no—
1224C23—22no—
1225C23—24no—
1226C23—22no—
1227C23—24no—
1228C23—24no—
1229C23—22no—
1230C23—24no—
1231C23—22no—
1232C23C2×H(5,𝔽2)12yes—
1233C23#58514yes—
1234C23C2611yescharacteristic
1235Q8—44no—
1236Q8—82no—
1237Q8—164no—
1238D4—48no—
1239D4—48no—
1240D4—44no—
1241D4—48no—
1242D4—84no—
1243D4—88no—
1244D4—88no—
1245D4—84no—
1246D4—88no—
1247D4—82no—
1248D4—164no—
1249D4—164no—
1250D4—164no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—28no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—44no—
1313C2×C4—48no—
1314C2×C4—48no—
1315C2×C4—48no—
1316C2×C4—84no—
1317C2×C4—88no—
1318C2×C4—82no—
1319C2×C4—88no—
1320C2×C4—84no—
1321C2×C4—88no—
1322C2×C4—84no—
1323C2×C4—164no—
1324C2×C4—164no—
1325C2×C4—164no—
1326C2×C4C2×H(5,𝔽2)12yes—
1327C2×C4C2×H(5,𝔽2)12yes—
1328C2×C4C2×2−1+414yes—
1329C2×C4C2×2−1+412yes—
1330C2×C4#58512yes—
1331C22—22no—
1332C22—24no—
1333C22—22no—
1334C22—22no—
1335C22—24no—
1336C22—24no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—44no—
1344C22—42no—
1345C22—42no—
1346C22—44no—
1347C22—44no—
1348C22—42no—
1349C22—44no—
1350C22—42no—
1351C22—44no—
1352C22—42no—
1353C22—42no—
1354C22—44no—
1355C22—42no—
1356C22—44no—
1357C22C22×H(5,𝔽2)11yescharacteristic
1358C22C22×2−1+411yescharacteristic
1359C22C2×#58512yes—
1360C22C2×#58511yescharacteristic
1361C22H(7,𝔽2)12yes—
1362C4—22no—
1363C4—24no—
1364C4—41no—
1365C4—41no—
1366C4—42no—
1367C4—42no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4—41no—
1372C4—42no—
1373C4—41no—
1374C4—44no—
1375C4—44no—
1376C4—42no—
1377C4—42no—
1378C4—44no—
1379C4—44no—
1380C4—42no—
1381C4—44no—
1382C4—42no—
1383C4—44no—
1384C4#355914yes—
1385C2—42no—
1386C2—44no—
1387C2—84no—
1388C2—82no—
1389C2#6272911yescharacteristic
1390C2C2×#355911yescharacteristic
1391C2#6288011yescharacteristic
1392C2#6295812yes—
1393C2#6297012yes—
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. #59315C2semidirect
2. #59212C2semidirect
3. #56438C2semidirect
4. #56437C2semidirect
5. #54275C2semidirect
6. #53702C2semidirect
7. #53075C2semidirect
8. #52987C2semidirect
9. #52985C2semidirect
10. #52985C2semidirect
11. #52809C2semidirect
12. #44600C2semidirect
13. #42508C2semidirect
14. #42493C2semidirect
15. #42261C2semidirect
16. #41825C2semidirect
17. #40010C2semidirect
18. #39958C2semidirect
19. #39262C2semidirect
20. #38101C2semidirect
21. #38050C2semidirect
22. #37505C2semidirect
23. #37370C2semidirect
24. #36361C2semidirect
25. #35271C2semidirect
26. #34876C2semidirect
27. #34638C2semidirect

Maximal subgroups

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

subgroupindex
#593152
#592122
#564382
#564372
#542752
#537022
#530752
#529872
#529852
#528092
#446002
#425082
#424932
#422612
#418252
#400102
#399582
#392622
#381012
#380502
#375052
#373702
#363612
#352712
#348762
#346382