Finite Group Databasebeta

← #7652253

Subgroups — #7652253

Order 512.

4420 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42958C211yesmaximal, characteristic, complemented
2#42937C211yesmaximal, characteristic, complemented
3#42511C212yesmaximal, complemented
4#42510C212yesmaximal, complemented
5#42506C211yesmaximal, characteristic, complemented
6#42502C211yesmaximal, characteristic, complemented
7#41583C214yesmaximal, complemented
8#41578C214yesmaximal, complemented
9#40860C214yesmaximal, complemented
10#40851C214yesmaximal, complemented
11#40133C214yesmaximal, complemented
12#40005C212yesmaximal, complemented
13#40001C212yesmaximal, complemented
14#39649C214yesmaximal, complemented
15#39633C212yesmaximal, complemented
16#39632C212yesmaximal, complemented
17#38524C214yesmaximal, complemented
18#38518C214yesmaximal, complemented
19#35663C212yesmaximal, complemented
20#35608C212yesmaximal, complemented
21#35599C212yesmaximal, complemented
22#35283C211yesmaximal, characteristic, complemented
23#35228C212yesmaximal, complemented
24#34880C211yesmaximal, characteristic
25#34772C212yesmaximal, complemented
26#34254C211yesmaximal, characteristic, complemented
27#34243C212yesmaximal, complemented
28C2×#529C2212yes—
29C2×#519C2211yescharacteristic
30#2868C2211yescharacteristic
31#2862C2211yescharacteristic
32#2857C2212yes—
33#2855C2214yes—
34#2853C2214yes—
35#2839C2214yes—
36#2836C2214yes—
37#2835C2212yes—
38#2834C2212yes—
39#2833C2212yes—
40#2832C2212yes—
41#2806C2214yes—
42#2804C2214yes—
43#2799C2214yes—
44#2792C2212yes—
45#2790C2214yes—
46#2790C2214yes—
47#2788C2214yes—
48#2788C2214yes—
49#2786C2214yes—
50#2782C2212yes—
51#2776C2214yes—
52#2771C2212yes—
53#2769C2212yes—
54#2768C2214yes—
55#2765C2214yes—
56#2764C2212yes—
57#2762C2214yes—
58#2760C2212yes—
59#2758C2214yes—
60#2755C2214yes—
61#2752C2212yes—
62#2751C2214yes—
63#2751C2214yes—
64#2750C2214yes—
65#2749C2214yes—
66#2743C2214yes—
67#2738C2214yes—
68#2729C2214yes—
69#2729C2214yes—
70#2720C2214yes—
71#2719C2214yes—
72#2706C2214yes—
73#2700C2214yes—
74#2690C2214yes—
75#2681C2214yes—
76#2680C2212yes—
77#2667C2214yes—
78#2665C2214yes—
79#2655C2214yes—
80#2655C2214yes—
81#2650C2214yes—
82#2650C2214yes—
83#2650C2214yes—
84#2650C2214yes—
85#2647C2212yes—
86#2647C2214yes—
87#2646C2214yes—
88#2638C2214yes—
89#2634C2214yes—
90#2633C2214yes—
91#2630C2214yes—
92#2628C2211yescharacteristic
93#2628C2211yescharacteristic
94#2594C2214yes—
95#2590C2214yes—
96#2590C2214yes—
97#2588C2214yes—
98#2586C2212yes—
99#2582C2212yes—
100#2581C2212yes—
101#2578C2214yes—
102#2577C2214yes—
103#2574C2214yes—
104#2573C2214yes—
105#2572C2212yes—
106#2558C2214yes—
107#2558C2214yes—
108#2556C2212yes—
109#2555C2212yes—
110#2554C2212yes—
111#2553C2212yes—
112#2538C2212yes—
113#2536C2212yes—
114#2532C2214yes—
115#2532C2214yes—
116#2527C2214yes—
117#2527C2214yes—
118#2525C2214yes—
119#2524C2214yes—
120#2522C2214yes—
121#2521C2212yes—
122#2520C2214yes—
123#2520C2214yes—
124#2519C2212yes—
125#2514C2212yes—
126#2511C2212yes—
127#2511C2212yes—
128#2511C2212yes—
129#2511C2214yes—
130#2509C2212yes—
131#2507C2212yes—
132#2506C2212yes—
133#2506C2212yes—
134#2505C2214yes—
135#2503C2212yes—
136#2502C2212yes—
137#2502C2212yes—
138#2499C2212yes—
139#2497C2212yes—
140#2497C2212yes—
141#2495C2212yes—
142#2494C2212yes—
143#2493C2214yes—
144#2492C2212yes—
145#2492C2212yes—
146#2492C2212yes—
147#2492C2214yes—
148#2492C2212yes—
149#2489C2214yes—
150#2488C2214yes—
151#2487C2212yes—
152#2486C2212yes—
153#2486C2212yes—
154#2485C2212yes—
155#2485C2212yes—
156#2485C2212yes—
157#2478C2214yes—
158#2477C2214yes—
159#2476C2214yes—
160#2475C2214yes—
161#2474C2214yes—
162#2470C2214yes—
163#2469C2214yes—
164#2465C2214yes—
165#2464C2212yes—
166#2463C2212yes—
167#2462C2214yes—
168#2462C2214yes—
169#2461C2212yes—
170#2458C2214yes—
171#2458C2214yes—
172#2457C2214yes—
173#2455C2212yes—
174#2453C2214yes—
175#2452C2214yes—
176#2451C2214yes—
177#2451C2214yes—
178#2450C2214yes—
179#2450C2214yes—
180#2450C2214yes—
181#2440C2212yes—
182#2440C2212yes—
183#2440C2212yes—
184#2439C2212yes—
185#2423C2214yes—
186#2417C2212yes—
187#2417C2212yes—
188#2417C2212yes—
189#2415C2212yes—
190#2409C2212yes—
191#2409C2212yes—
192#2402C2214yes—
193#2399C2211yescharacteristic
194#2397C2211yescharacteristic
195#2396C2214yes—
196#2392C2211yescharacteristic
197#2392C2211yescharacteristic
198#2370C2214yes—
199#2367C2214yes—
200#2359C2214yes—
201#2359C2214yes—
202#2356C2214yes—
203#2355C2212yes—
204#2355C2214yes—
205#2354C2212yes—
206#2352C2212yes—
207#2352C2212yes—
208Q8×C4⋊C4C2212yes—
209D4×C4⋊C4C2212yes—
210D4×C4⋊C4C2212yes—
211D4×C4⋊C4C2212yes—
212#2343C2214yes—
213#2343C2214yes—
214#2334C2214yes—
215#2334C2214yes—
216#2332C2214yes—
217#2332C2214yes—
218#2331C2211yescharacteristic
219#2331C2211yescharacteristic
220#2326C2214yes—
221#2325C2214yes—
222#2323C2212yes—
223#2323C2212yes—
224#2320C2212yes—
225#2320C2212yes—
226#2317C2211yescharacteristic
227#2314C2212yes—
228#2314C2212yes—
229#2310C2211yescharacteristic
230C4×C4⋊Q8C2212yes—
231C4×#124C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2214yes—
235C4×C22⋊Q8C2214yes—
236C4×#121C2212yes—
237C4×#121C2214yes—
238#2296C2211yescharacteristic
239#2295C2212yes—
240#2295C2212yes—
241C2×#391C2211yescharacteristic
242#2293C2211yescharacteristic
243#2290C2212yes—
244#2290C2214yes—
245#2285C2212yes—
246#2274C2212yes—
247#2274C2211yescharacteristic
248C42×D4C2211yescharacteristic
249C4×#117C2211yescharacteristic
250C2×C4×C4⋊C4C2212yes—
251C23×Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2314yes—
256#529—216no—
257C2×#126C2312yes—
258C2×#126C2312yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#123C2312yes—
265C2×#123C2312yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279#519—28no—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2314yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×#117C2312yes—
297C2×#117C2311yescharacteristic
298C2×#117C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2311yescharacteristic
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C42C2312yes—
309C22×C42C2311yescharacteristic
310C22×C42C2314yes—
311#401C2314yes—
312#401C2314yes—
313#400C2312yes—
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#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#399C2312yes—
340#399C2312yes—
341#399C2312yes—
342#399C2314yes—
343#399C2312yes—
344#398C2314yes—
345#398C2311yescharacteristic
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2311yescharacteristic
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2311yescharacteristic
375#397C2314yes—
376#397C2311yescharacteristic
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2312yes—
388#396C2312yes—
389#396C2314yes—
390#396C2314yes—
391#395C2314yes—
392#395C2312yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2312yes—
398#395C2312yes—
399#395C2314yes—
400#395C2312yes—
401#394C2311yescharacteristic
402#394C2311yescharacteristic
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2312yes—
407#394C2314yes—
408#394C2312yes—
409#394C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2312yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#392C2312yes—
420#392C2311yescharacteristic
421#392C2311yescharacteristic
422#392C2312yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#390C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2312yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2312yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2312yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2312yes—
517#388C2312yes—
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#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2314yes—
564#386C2314yes—
565#386C2312yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2312yes—
573#386C2312yes—
574#386C2314yes—
575#386C2312yes—
576#385C2312yes—
577#385C2312yes—
578#385C2314yes—
579#385C2312yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
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#385C2312yes—
599#384C2312yes—
600#384C2312yes—
601#384C2312yes—
602#384C2312yes—
603#384C2314yes—
604#384C2312yes—
605#384C2312yes—
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#382C2312yes—
611#382C2312yes—
612#382C2312yes—
613#382C2314yes—
614#382C2314yes—
615#382C2311yescharacteristic
616#382C2311yescharacteristic
617#382C2314yes—
618#382C2312yes—
619#381C2312yes—
620#381C2312yes—
621#381C2314yes—
622#381C2314yes—
623#381C2314yes—
624#381C2314yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2314yes—
634#380C2314yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2314yes—
639#380C2312yes—
640#380C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
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×Q8C2414yes—
699C22×Q8C2412yes—
700C22×Q8C2412yes—
701C22×D4C2412yes—
702C22×D4C2412yes—
703C22×D4C2412yes—
704C22×D4C2411yescharacteristic
705C22×D4C2412yes—
706C22×D4C2411yescharacteristic
707C23×C4C2412yes—
708C23×C4C2412yes—
709C23×C4C2412yes—
710C23×C4C2412yes—
711C23×C4C2411yescharacteristic
712C23×C4C2414yes—
713C23×C4C2412yes—
714C23×C4C2412yes—
715C23×C4C2412yes—
716C23×C4C2414yes—
717C23×C4C2414yes—
718C4⋊Q8—44no—
719C4⋊Q8—42no—
720C4⋊Q8—42no—
721C4⋊Q8—84no—
722#126—28no—
723#126—28no—
724#125—28no—
725#125—84no—
726#125—84no—
727#124—28no—
728#124—28no—
729#123—28no—
730#123—28no—
731#123—84no—
732#123—84no—
733C22⋊Q8—28no—
734C22⋊Q8—216no—
735C22⋊Q8—44no—
736C22⋊Q8—44no—
737C22⋊Q8—44no—
738C22⋊Q8—44no—
739C22⋊Q8—84no—
740C22⋊Q8—84no—
741C22⋊Q8—84no—
742#121—28no—
743#121—28no—
744C4×Q8—216no—
745C4×Q8—28no—
746C4×Q8—28no—
747C4×Q8—28no—
748C4×Q8—84no—
749C4×Q8—84no—
750C4×D4—28no—
751C4×D4—28no—
752C4×D4—28no—
753C4×D4—28no—
754C4×D4—44no—
755C4×D4—42no—
756C4×D4—42no—
757C4×D4—84no—
758C4×D4—84no—
759C4×D4—84no—
760#117—24no—
761#117—216no—
762#117—28no—
763#117—42no—
764#117—42no—
765#117—44no—
766#117—84no—
767#117#4118yes—
768C2×C4⋊C4—42no—
769C2×C4⋊C4—44no—
770C2×C4⋊C4—44no—
771C2×C4⋊C4—44no—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2411yescharacteristic
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C42—28no—
873C2×C42—42no—
874C2×C42—84no—
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2411yescharacteristic
923#95C2411yescharacteristic
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2411yescharacteristic
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2411yescharacteristic
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975C24C2512yes—
976C24C2511yescharacteristic
977C24C2512yes—
978C2×Q8—24no—
979C2×Q8—24no—
980C2×Q8—24no—
981C2×Q8—24no—
982C2×Q8—28no—
983C2×Q8—24no—
984C2×Q8—24no—
985C2×Q8—42no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—44no—
989C2×Q8—44no—
990C2×Q8—44no—
991C2×Q8—44no—
992C2×Q8—42no—
993C2×Q8—42no—
994C2×Q8—416no—
995C2×D4—24no—
996C2×D4—24no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—41no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—41no—
1009C2×D4—42no—
1010C2×D4—42no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—28no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4C2×#4114yes—
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—41no—
1094C4⋊C4—41no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4C2×#4118yes—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—24no—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—41no—
1143C22⋊C4—41no—
1144C22⋊C4—42no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—42no—
1161C22⋊C4—42no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4C2×#4118yes—
1166C22⋊C42−1+418yes—
1167C42—24no—
1168C42—24no—
1169C42—24no—
1170C42—24no—
1171C42—24no—
1172C42—28no—
1173C42—28no—
1174C42—24no—
1175C42—24no—
1176C42—22no—
1177C42—22no—
1178C42—22no—
1179C42—22no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—42no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—42no—
1191C42—44no—
1192C42—42no—
1193C42C2×#4114yes—
1194C42C2×#4114yes—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—21no—
1201C23—21no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23C22×#4112yes—
1213C23C2×2−1+414yes—
1214C23C2611yescharacteristic
1215Q8—48no—
1216Q8—48no—
1217Q8—48no—
1218Q8—88no—
1219Q8—162no—
1220Q8—162no—
1221D4—48no—
1222D4—48no—
1223D4—48no—
1224D4—44no—
1225D4—84no—
1226D4—82no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—28no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—48no—
1292C2×C4—48no—
1293C2×C4—84no—
1294C2×C4—88no—
1295C2×C4—88no—
1296C2×C4—162no—
1297C2×C4—164no—
1298C2×C4C22×#4114yes—
1299C2×C4C22×#4114yes—
1300C2×C4C22×#4112yes—
1301C2×C4C22×#4112yes—
1302C2×C4C2×2−1+414yes—
1303C2×C4C2×2−1+414yes—
1304C2×C4#58512yes—
1305C2×C4#58512yes—
1306C22—24no—
1307C22—24no—
1308C22—24no—
1309C22—22no—
1310C22—24no—
1311C22—42no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22C23×#4111yescharacteristic
1326C22C22×2−1+412yes—
1327C22C2×#58511yescharacteristic
1328C22C2×#58511yescharacteristic
1329C22H(7,𝔽2)12yes—
1330C4—24no—
1331C4—24no—
1332C4—24no—
1333C4—22no—
1334C4—24no—
1335C4—44no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—41no—
1340C4—41no—
1341C4—44no—
1342C4—44no—
1343C4—44no—
1344C4—41no—
1345C4—41no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—44no—
1350C4—42no—
1351C4—44no—
1352C4—44no—
1353C4#345514yes—
1354C2—44no—
1355C2—42no—
1356C2—82no—
1357C2C2×#345511yescharacteristic
1358C2#6283711yescharacteristic
1359C2#6288511yescharacteristic
1360C2#6295112yes—
1361C2#6300012yes—
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. #42937C2semidirect
3. #42511C2semidirect
4. #42510C2semidirect
5. #42506C2semidirect
6. #42502C2semidirect
7. #41583C2semidirect
8. #41578C2semidirect
9. #40860C2semidirect
10. #40851C2semidirect
11. #40133C2semidirect
12. #40005C2semidirect
13. #40001C2semidirect
14. #39649C2semidirect
15. #39633C2semidirect
16. #39632C2semidirect
17. #38524C2semidirect
18. #38518C2semidirect
19. #35663C2semidirect
20. #35608C2semidirect
21. #35599C2semidirect
22. #35283C2semidirect
23. #35228C2semidirect
25. #34772C2semidirect
26. #34254C2semidirect
27. #34243C2semidirect

Maximal subgroups

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

subgroupindex
#429582
#429372
#425112
#425102
#425062
#425022
#415832
#415782
#408602
#408512
#401332
#400052
#400012
#396492
#396332
#396322
#385242
#385182
#356632
#356082
#355992
#352832
#352282
#348802
#347722
#342542
#342432