Finite Group Databasebeta

← #7650921

Subgroups — #7650921

Order 512.

4284 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42958C211yesmaximal, characteristic, complemented
2#42958C211yesmaximal, characteristic, complemented
3#42689C212yesmaximal, complemented
4#42684C211yesmaximal, characteristic, complemented
5#42510C212yesmaximal, complemented
6#42506C211yesmaximal, characteristic, complemented
7#41603C214yesmaximal, complemented
8#41591C214yesmaximal, complemented
9#41544C214yesmaximal, complemented
10#41542C214yesmaximal, complemented
11#40085C214yesmaximal, complemented
12#40010C212yesmaximal, complemented
13#40001C212yesmaximal, complemented
14#38988C214yesmaximal, complemented
15#38977C212yesmaximal, complemented
16#38974C212yesmaximal, complemented
17#37930C214yesmaximal, complemented
18#37920C214yesmaximal, complemented
19#35663C212yesmaximal, complemented
20#35652C212yesmaximal, complemented
21#35648C212yesmaximal, complemented
22#35337C211yesmaximal, characteristic, complemented
23#35228C212yesmaximal, complemented
24#34880C211yesmaximal, characteristic
25#34780C212yesmaximal, complemented
26#34254C211yesmaximal, characteristic, complemented
27#34241C212yesmaximal, complemented
28C2×#529C2212yes—
29C2×#519C2211yescharacteristic
30#2862C2211yescharacteristic
31#2859C2211yescharacteristic
32#2855C2214yes—
33#2853C2214yes—
34#2851C2212yes—
35#2836C2214yes—
36#2834C2212yes—
37#2833C2212yes—
38#2833C2212yes—
39#2833C2214yes—
40#2826C2212yes—
41#2799C2214yes—
42#2793C2214yes—
43#2792C2212yes—
44#2789C2212yes—
45#2785C2212yes—
46#2782C2214yes—
47#2775C2214yes—
48#2774C2214yes—
49#2770C2214yes—
50#2769C2214yes—
51#2768C2214yes—
52#2766C2214yes—
53#2765C2214yes—
54#2765C2214yes—
55#2765C2214yes—
56#2764C2212yes—
57#2764C2212yes—
58#2762C2214yes—
59#2762C2214yes—
60#2762C2214yes—
61#2760C2212yes—
62#2760C2212yes—
63#2751C2214yes—
64#2751C2214yes—
65#2749C2214yes—
66#2746C2214yes—
67#2745C2214yes—
68#2743C2214yes—
69#2743C2214yes—
70#2739C2214yes—
71#2739C2214yes—
72#2738C2214yes—
73#2708C2214yes—
74#2706C2214yes—
75#2700C2214yes—
76#2680C2212yes—
77#2667C2214yes—
78#2666C2214yes—
79#2665C2214yes—
80#2665C2214yes—
81#2655C2214yes—
82#2655C2214yes—
83#2655C2214yes—
84#2653C2214yes—
85#2650C2214yes—
86#2650C2214yes—
87#2647C2212yes—
88#2645C2214yes—
89#2643C2214yes—
90#2638C2214yes—
91#2630C2214yes—
92#2628C2211yescharacteristic
93#2628C2211yescharacteristic
94#2595C2214yes—
95#2594C2214yes—
96#2589C2214yes—
97#2589C2214yes—
98#2589C2214yes—
99#2588C2214yes—
100#2588C2214yes—
101#2585C2214yes—
102#2582C2212yes—
103#2581C2212yes—
104#2577C2214yes—
105#2577C2214yes—
106#2576C2214yes—
107#2575C2214yes—
108#2575C2214yes—
109#2572C2212yes—
110#2572C2214yes—
111#2572C2212yes—
112#2556C2212yes—
113#2555C2212yes—
114#2554C2212yes—
115#2553C2212yes—
116#2538C2212yes—
117#2536C2212yes—
118#2533C2214yes—
119#2532C2214yes—
120#2531C2214yes—
121#2528C2214yes—
122#2527C2214yes—
123#2527C2214yes—
124#2525C2214yes—
125#2525C2214yes—
126#2524C2214yes—
127#2524C2214yes—
128#2521C2212yes—
129#2520C2214yes—
130#2519C2212yes—
131#2517C2212yes—
132#2515C2214yes—
133#2515C2214yes—
134#2514C2212yes—
135#2514C2214yes—
136#2514C2212yes—
137#2514C2212yes—
138#2511C2212yes—
139#2509C2212yes—
140#2508C2214yes—
141#2508C2212yes—
142#2508C2212yes—
143#2507C2212yes—
144#2505C2214yes—
145#2503C2212yes—
146#2503C2212yes—
147#2503C2212yes—
148#2499C2212yes—
149#2495C2212yes—
150#2494C2212yes—
151#2494C2212yes—
152#2494C2212yes—
153#2494C2214yes—
154#2493C2214yes—
155#2493C2214yes—
156#2492C2212yes—
157#2492C2212yes—
158#2489C2212yes—
159#2489C2212yes—
160#2488C2214yes—
161#2487C2212yes—
162#2486C2212yes—
163#2486C2212yes—
164#2485C2212yes—
165#2485C2212yes—
166#2485C2212yes—
167#2478C2214yes—
168#2476C2214yes—
169#2474C2214yes—
170#2470C2214yes—
171#2469C2214yes—
172#2465C2214yes—
173#2464C2212yes—
174#2462C2214yes—
175#2461C2212yes—
176#2458C2214yes—
177#2457C2214yes—
178#2455C2212yes—
179#2447C2214yes—
180#2444C2214yes—
181#2442C2212yes—
182#2442C2212yes—
183#2440C2212yes—
184#2439C2212yes—
185#2419C2214yes—
186#2417C2212yes—
187#2417C2212yes—
188#2417C2212yes—
189#2415C2212yes—
190#2409C2212yes—
191#2409C2212yes—
192#2402C2214yes—
193#2401C2214yes—
194#2399C2211yescharacteristic
195#2397C2211yescharacteristic
196#2392C2211yescharacteristic
197#2392C2211yescharacteristic
198#2373C2214yes—
199#2373C2214yes—
200#2368C2214yes—
201#2364C2214yes—
202#2356C2214yes—
203#2355C2212yes—
204#2355C2212yes—
205#2355C2214yes—
206#2352C2212yes—
207#2352C2212yes—
208#2352C2212yes—
209#2352C2212yes—
210D4×C4⋊C4C2212yes—
211D4×C4⋊C4C2212yes—
212#2343C2214yes—
213#2343C2214yes—
214#2337C2214yes—
215#2336C2214yes—
216#2335C2214yes—
217#2332C2214yes—
218#2331C2211yescharacteristic
219#2331C2211yescharacteristic
220#2323C2212yes—
221#2323C2212yes—
222#2320C2212yes—
223#2320C2212yes—
224#2319C2214yes—
225#2318C2214yes—
226#2317C2211yescharacteristic
227#2314C2212yes—
228#2314C2212yes—
229#2310C2211yescharacteristic
230C4×#125C2212yes—
231C4×#124C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×#123C2214yes—
235C4×#123C2214yes—
236C4×#123C2214yes—
237C4×#121C2212yes—
238#2296C2211yescharacteristic
239#2295C2212yes—
240#2295C2212yes—
241C2×#391C2211yescharacteristic
242#2293C2211yescharacteristic
243#2290C2212yes—
244#2283C2214yes—
245#2283C2212yes—
246#2274C2212yes—
247#2274C2211yescharacteristic
248C42×D4C2211yescharacteristic
249C4×#117C2211yescharacteristic
250C2×C4×C4⋊C4C2212yes—
251C23×Q8C2311yescharacteristic
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2311yescharacteristic
254#529—216no—
255C2×#126C2312yes—
256C2×#126C2312yes—
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#123C2312yes—
262C2×#123C2312yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273#519—28no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×#117C2312yes—
288C2×#117C2311yescharacteristic
289C2×#117C2314yes—
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2312yes—
293C2×#117C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C42C2312yes—
299C22×C42C2311yescharacteristic
300C22×C42C2314yes—
301#401C2314yes—
302#401C2314yes—
303#401C2314yes—
304#401C2314yes—
305#401C2314yes—
306#401C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2312yes—
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#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#399C2312yes—
336#399C2314yes—
337#399C2312yes—
338#399C2312yes—
339#399C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2311yescharacteristic
343#398C2311yescharacteristic
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2312yes—
360#398C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2311yescharacteristic
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2311yescharacteristic
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2312yes—
382#396C2312yes—
383#396C2314yes—
384#396C2314yes—
385#395C2312yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2312yes—
390#395C2312yes—
391#395C2314yes—
392#395C2312yes—
393#394C2314yes—
394#394C2314yes—
395#394C2311yescharacteristic
396#394C2311yescharacteristic
397#394C2314yes—
398#394C2314yes—
399#394C2312yes—
400#394C2314yes—
401#394C2312yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2312yes—
407#393C2312yes—
408#393C2314yes—
409#392C2311yescharacteristic
410#392C2312yes—
411#392C2311yescharacteristic
412#392C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2312yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2312yes—
438#390C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2312yes—
477#388C2314yes—
478#388C2314yes—
479#388C2312yes—
480#388C2312yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2312yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2312yes—
495#388C2312yes—
496#388C2314yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
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#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#386C2314yes—
553#386C2312yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2312yes—
558#386C2314yes—
559#386C2312yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2312yes—
565#386C2314yes—
566#385C2312yes—
567#385C2312yes—
568#385C2314yes—
569#385C2314yes—
570#385C2312yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2312yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#384C2312yes—
586#384C2312yes—
587#384C2312yes—
588#383C2314yes—
589#383C2314yes—
590#383C2314yes—
591#383C2314yes—
592#383C2314yes—
593#383C2314yes—
594#383C2314yes—
595#382C2312yes—
596#382C2312yes—
597#382C2312yes—
598#382C2312yes—
599#382C2314yes—
600#382C2314yes—
601#382C2314yes—
602#382C2314yes—
603#382C2311yescharacteristic
604#382C2311yescharacteristic
605#382C2312yes—
606#382C2312yes—
607#382C2314yes—
608#382C2312yes—
609#382C2314yes—
610#381C2312yes—
611#381C2312yes—
612#381C2314yes—
613#381C2314yes—
614#381C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#381C2314yes—
620#381C2314yes—
621#380C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2314yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683#376C2314yes—
684#376C2311yescharacteristic
685#376C2311yescharacteristic
686#376C2314yes—
687#376C2314yes—
688C2×#95C2314yes—
689C2×#95C2314yes—
690C43C2311yescharacteristic
691C43C2311yescharacteristic
692C22×Q8—24no—
693C22×Q8—42no—
694C22×Q8—42no—
695C22×Q8C2412yes—
696C22×Q8C2412yes—
697C22×Q8C2412yes—
698C22×Q8C2412yes—
699C22×Q8C2412yes—
700C22×D4C2412yes—
701C22×D4C2412yes—
702C22×D4C2411yescharacteristic
703C22×D4C2412yes—
704C22×D4C2412yes—
705C22×D4C2411yescharacteristic
706C23×C4C2412yes—
707C23×C4C2412yes—
708C23×C4C2412yes—
709C23×C4C2411yescharacteristic
710C23×C4C2414yes—
711C23×C4C2414yes—
712C23×C4C2412yes—
713C23×C4C2412yes—
714C23×C4C2412yes—
715C23×C4C2414yes—
716C23×C4C2412yes—
717C4⋊Q8—42no—
718C4⋊Q8—42no—
719#126—28no—
720#126—28no—
721#125—28no—
722#125—44no—
723#124—28no—
724#124—44no—
725#123—28no—
726#123—28no—
727#123—48no—
728#123—48no—
729C22⋊Q8—28no—
730C22⋊Q8—48no—
731C22⋊Q8—44no—
732C22⋊Q8—44no—
733C22⋊Q8—44no—
734C22⋊Q8—44no—
735#121—28no—
736#121—44no—
737C4×Q8—216no—
738C4×Q8—28no—
739C4×Q8—28no—
740C4×Q8—28no—
741C4×D4—28no—
742C4×D4—28no—
743C4×D4—28no—
744C4×D4—44no—
745C4×D4—42no—
746C4×D4—42no—
747C4×D4—48no—
748C4×D4—48no—
749C4×D4—44no—
750#117—24no—
751#117—216no—
752#117—28no—
753#117—42no—
754#117—42no—
755#117—44no—
756#117#4118yes—
757C2×C4⋊C4—42no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4—44no—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C42—28no—
857C2×C42—42no—
858C2×C42—48no—
859C2×C42C2411yescharacteristic
860C2×C42C2412yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2411yescharacteristic
910#95C2412yes—
911#95C2411yescharacteristic
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
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#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2411yescharacteristic
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965C24C2512yes—
966C24C2511yescharacteristic
967C24C2512yes—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×Q8—42no—
976C2×Q8—42no—
977C2×Q8—44no—
978C2×Q8—42no—
979C2×Q8—42no—
980C2×Q8—44no—
981C2×Q8—416no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—41no—
990C2×D4—42no—
991C2×D4—42no—
992C2×D4—42no—
993C2×D4—41no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—42no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—28no—
1003C22×C4—28no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—44no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4C2×#4114yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2512yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
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—42no—
1107C4⋊C4—42no—
1108C4⋊C4C2×#4118yes—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—28no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—28no—
1116C22⋊C4—24no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—44no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4C2×#4118yes—
1149C42—24no—
1150C42—24no—
1151C42—24no—
1152C42—24no—
1153C42—24no—
1154C42—28no—
1155C42—28no—
1156C42—22no—
1157C42—22no—
1158C42—22no—
1159C42—22no—
1160C42—44no—
1161C42—44no—
1162C42—42no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—42no—
1167C42—42no—
1168C42—44no—
1169C42—42no—
1170C42—44no—
1171C42—42no—
1172C42—44no—
1173C42—44no—
1174C42—42no—
1175C42C2×#4114yes—
1176C42C2×#4114yes—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—21no—
1182C23—21no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23C22×#4112yes—
1195C23#58514yes—
1196C23C2611yescharacteristic
1197Q8—48no—
1198Q8—48no—
1199Q8—84no—
1200Q8—162no—
1201Q8—162no—
1202D4—48no—
1203D4—48no—
1204D4—44no—
1205D4—84no—
1206D4—84no—
1207D4—82no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—28no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—48no—
1272C2×C4—48no—
1273C2×C4—48no—
1274C2×C4—48no—
1275C2×C4—84no—
1276C2×C4—88no—
1277C2×C4—88no—
1278C2×C4—84no—
1279C2×C4—162no—
1280C2×C4—164no—
1281C2×C4C22×#4114yes—
1282C2×C4C22×#4114yes—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4112yes—
1285C2×C4#58512yes—
1286C2×C4#58512yes—
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—22no—
1292C22—42no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22C23×#4111yescharacteristic
1307C22C2×#58512yes—
1308C22C2×#58511yescharacteristic
1309C22C2×#58511yescharacteristic
1310C222−1+612yes—
1311C4—24no—
1312C4—24no—
1313C4—22no—
1314C4—44no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—44no—
1320C4—44no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—44no—
1325C4—41no—
1326C4—42no—
1327C4—44no—
1328C4—44no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4#345514yes—
1335C2—44no—
1336C2—42no—
1337C2—82no—
1338C2C2×#345511yescharacteristic
1339C2#6282911yescharacteristic
1340C2#6289111yescharacteristic
1341C2#6294012yes—
1342C2#6299312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34880C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42958C2semidirect
2. #42958C2semidirect
3. #42689C2semidirect
4. #42684C2semidirect
5. #42510C2semidirect
6. #42506C2semidirect
7. #41603C2semidirect
8. #41591C2semidirect
9. #41544C2semidirect
10. #41542C2semidirect
11. #40085C2semidirect
12. #40010C2semidirect
13. #40001C2semidirect
14. #38988C2semidirect
15. #38977C2semidirect
16. #38974C2semidirect
17. #37930C2semidirect
18. #37920C2semidirect
19. #35663C2semidirect
20. #35652C2semidirect
21. #35648C2semidirect
22. #35337C2semidirect
23. #35228C2semidirect
25. #34780C2semidirect
26. #34254C2semidirect
27. #34241C2semidirect

Maximal subgroups

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

subgroupindex
#429582
#426892
#426842
#425102
#425062
#416032
#415912
#415442
#415422
#400852
#400102
#400012
#389882
#389772
#389742
#379302
#379202
#356632
#356522
#356482
#353372
#352282
#348802
#347802
#342542
#342412