Finite Group Databasebeta

← #8508898

Subgroups — #8508898

Order 512.

4573 conjugacy classes of subgroups.

The subgroup lattice has 1468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59827C211yesmaximal, characteristic, complemented
2#58561C214yesmaximal, complemented
3#57549C214yesmaximal, complemented
4#57371C214yesmaximal, complemented
5#57328C214yesmaximal, complemented
6#55329C214yesmaximal, complemented
7#53377C212yesmaximal, complemented
8#53348C212yesmaximal, complemented
9#53016C212yesmaximal, complemented
10#52152C211yesmaximal, characteristic, complemented
11#48472C214yesmaximal, complemented
12#46014C212yesmaximal, complemented
13#45711C212yesmaximal, complemented
14#45275C212yesmaximal, complemented
15#45196C212yesmaximal, complemented
16#42877C212yesmaximal, complemented
17#42769C212yesmaximal, complemented
18#42440C212yesmaximal, complemented
19#40103C212yesmaximal, complemented
20#39692C212yesmaximal, complemented
21#39483C211yesmaximal, characteristic, complemented
22#39373C211yesmaximal, characteristic, complemented
23#39130C212yesmaximal, complemented
24#37389C212yesmaximal, complemented
25#37378C212yesmaximal, complemented
26#37152C212yesmaximal, complemented
27#36535C211yesmaximal, characteristic, complemented
28#35209C211yesmaximal, characteristic, complemented
29#35198C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×#553C2212yes—
32C2×#542C2212yes—
33C2×#541C2212yes—
34C2×#541C2212yes—
35C2×#529C2212yes—
36#2864C2212yes—
37#2860C2212yes—
38#2860C2212yes—
39#2859C2211yescharacteristic
40#2859C2212yes—
41#2858C2212yes—
42#2857C2212yes—
43#2851C2212yes—
44#2850C2212yes—
45#2841C2214yes—
46#2837C2214yes—
47#2829C2214yes—
48#2826C2214yes—
49#2820C2214yes—
50#2820C2214yes—
51#2814C2214yes—
52#2814C2214yes—
53#2802C2214yes—
54#2798C2214yes—
55#2790C2214yes—
56#2781C2214yes—
57#2780C2214yes—
58#2780C2214yes—
59#2774C2214yes—
60#2773C2214yes—
61#2772C2214yes—
62#2768C2214yes—
63#2768C2214yes—
64#2768C2214yes—
65#2763C2214yes—
66#2761C2214yes—
67#2753C2214yes—
68#2751C2214yes—
69#2743C2214yes—
70#2740C2214yes—
71#2740C2214yes—
72#2733C2214yes—
73#2730C2214yes—
74#2729C2214yes—
75#2727C2212yes—
76#2727C2211yescharacteristic
77#2727C2212yes—
78#2727C2212yes—
79#2727C2212yes—
80#2726C2214yes—
81#2726C2212yes—
82#2726C2211yescharacteristic
83#2726C2212yes—
84#2725C2214yes—
85#2725C2214yes—
86#2725C2214yes—
87#2725C2212yes—
88#2724C2212yes—
89#2724C2212yes—
90#2724C2211yescharacteristic
91#2722C2214yes—
92#2722C2214yes—
93#2721C2214yes—
94#2718C2212yes—
95#2715C2214yes—
96#2715C2214yes—
97#2715C2214yes—
98#2715C2214yes—
99#2714C2214yes—
100#2710C2214yes—
101#2710C2212yes—
102#2707C2214yes—
103#2707C2214yes—
104#2707C2214yes—
105#2707C2214yes—
106#2706C2214yes—
107#2705C2214yes—
108#2705C2214yes—
109#2705C2214yes—
110#2704C2214yes—
111#2704C2214yes—
112#2704C2214yes—
113#2701C2214yes—
114#2701C2212yes—
115#2695C2214yes—
116#2695C2214yes—
117#2695C2214yes—
118#2694C2214yes—
119#2694C2214yes—
120#2694C2214yes—
121#2691C2214yes—
122#2691C2214yes—
123#2689C2212yes—
124#2682C2212yes—
125#2682C2212yes—
126#2682C2211yescharacteristic
127#2676C2214yes—
128#2674C2212yes—
129#2673C2214yes—
130#2672C2214yes—
131#2667C2214yes—
132#2664C2214yes—
133#2662C2214yes—
134#2662C2214yes—
135#2654C2214yes—
136#2651C2214yes—
137#2636C2214yes—
138#2630C2214yes—
139#2629C2212yes—
140#2629C2212yes—
141#2621C2212yes—
142#2620C2212yes—
143#2619C2212yes—
144#2618C2214yes—
145#2590C2214yes—
146#2588C2214yes—
147#2587C2214yes—
148#2586C2214yes—
149#2582C2212yes—
150#2581C2212yes—
151#2579C2214yes—
152#2571C2211yescharacteristic
153#2570C2212yes—
154#2568C2212yes—
155#2567C2212yes—
156#2566C2212yes—
157#2566C2214yes—
158#2565C2212yes—
159#2562C2214yes—
160#2556C2214yes—
161#2554C2214yes—
162#2552C2211yescharacteristic
163#2552C2211yescharacteristic
164#2551C2211yescharacteristic
165#2550C2212yes—
166#2550C2214yes—
167#2548C2211yescharacteristic
168#2547C2212yes—
169#2547C2212yes—
170#2546C2211yescharacteristic
171#2545C2212yes—
172#2545C2212yes—
173#2542C2211yescharacteristic
174#2541C2211yescharacteristic
175#2540C2212yes—
176#2540C2212yes—
177#2538C2211yescharacteristic
178#2538C2211yescharacteristic
179#2537C2212yes—
180#2536C2212yes—
181#2535C2212yes—
182#2522C2214yes—
183#2519C2214yes—
184#2519C2214yes—
185#2519C2214yes—
186#2513C2214yes—
187#2512C2214yes—
188#2512C2212yes—
189#2508C2212yes—
190#2506C2212yes—
191#2506C2212yes—
192#2501C2212yes—
193#2500C2212yes—
194#2491C2212yes—
195#2490C2214yes—
196#2489C2212yes—
197#2486C2214yes—
198#2473C2214yes—
199#2467C2214yes—
200#2467C2214yes—
201#2461C2214yes—
202#2457C2214yes—
203#2456C2214yes—
204#2455C2214yes—
205#2455C2214yes—
206#2454C2212yes—
207#2454C2212yes—
208#2454C2214yes—
209#2454C2214yes—
210#2452C2212yes—
211#2447C2212yes—
212#2447C2214yes—
213#2447C2212yes—
214#2445C2212yes—
215#2445C2214yes—
216#2440C2212yes—
217#2439C2212yes—
218#2429C2212yes—
219#2427C2212yes—
220#2427C2212yes—
221#2426C2212yes—
222#2426C2212yes—
223#2426C2212yes—
224#2423C2212yes—
225#2423C2212yes—
226#2417C2212yes—
227#2417C2212yes—
228#2417C2214yes—
229#2415C2212yes—
230#2415C2212yes—
231#2396C2212yes—
232#2395C2212yes—
233#2392C2212yes—
234#2379C2214yes—
235#2370C2212yes—
236#2362C2212yes—
237#2360C2212yes—
238#2355C2211yescharacteristic
239#2355C2211yescharacteristic
240#2355C2212yes—
241#2351C2212yes—
242D4×C4⋊C4C2212yes—
243D4×C4⋊C4C2212yes—
244#2335C2214yes—
245#2324C2212yes—
246#2324C2212yes—
247#2323C2212yes—
248#2317C2212yes—
249C4×C4⋊Q8C2211yescharacteristic
250C4×C4⋊Q8C2211yescharacteristic
251C4×#127C2211yescharacteristic
252C4×#125C2212yes—
253C4×#123C2212yes—
254C4×#121C2212yes—
255#2296C2212yes—
256#2293C2211yescharacteristic
257#2293C2211yescharacteristic
258C42×Q8C2211yescharacteristic
259#559—48no—
260#553—48no—
261#542—48no—
262#541—48no—
263#541—48no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×#127C2311yescharacteristic
270C2×#127C2312yes—
271#529—48no—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2312yes—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#124C2314yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2312yes—
300C2×#123C2312yes—
301C2×#123C2314yes—
302C2×#123C2312yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2314yes—
346C22×C42C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2312yes—
363#399C2312yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2314yes—
403#397C2312yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2312yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2312yes—
434#396C2312yes—
435#396C2312yes—
436#396C2314yes—
437#396C2314yes—
438#395C2312yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2312yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2312yes—
458#394C2314yes—
459#394C2312yes—
460#394C2314yes—
461#394C2312yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#393C2314yes—
468#393C2312yes—
469#393C2314yes—
470#392C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#392C2312yes—
475#392C2314yes—
476#392C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2314yes—
495#390C2312yes—
496#390C2312yes—
497#390C2314yes—
498#390C2311yescharacteristic
499#390C2314yes—
500#390C2312yes—
501#390C2312yes—
502#390C2311yescharacteristic
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2312yes—
507#390C2314yes—
508#390C2314yes—
509#390C2314yes—
510#390C2311yescharacteristic
511#390C2311yescharacteristic
512#390C2314yes—
513#390C2314yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2311yescharacteristic
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2311yescharacteristic
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2312yes—
557#389C2311yescharacteristic
558#389C2312yes—
559#389C2312yes—
560#389C2311yescharacteristic
561#389C2312yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2312yes—
586#388C2314yes—
587#388C2314yes—
588#388C2312yes—
589#388C2312yes—
590#388C2312yes—
591#388C2314yes—
592#388C2314yes—
593#388C2312yes—
594#388C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2312yes—
617#386C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2312yes—
648#385C2312yes—
649#385C2312yes—
650#384C2311yescharacteristic
651#384C2311yescharacteristic
652#384C2311yescharacteristic
653#384C2312yes—
654#384C2312yes—
655#384C2312yes—
656#384C2311yescharacteristic
657#384C2311yescharacteristic
658#384C2312yes—
659#382C2312yes—
660#382C2314yes—
661#382C2314yes—
662#382C2312yes—
663#382C2312yes—
664#382C2314yes—
665#382C2312yes—
666#382C2312yes—
667#382C2312yes—
668#381C2314yes—
669#381C2314yes—
670#381C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2314yes—
686#380C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2311yescharacteristic
709C4×C4⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C43C2312yes—
717C43C2311yescharacteristic
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C22×D4C2411yescharacteristic
725C22×D4C2411yescharacteristic
726C22×D4C2414yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2412yes—
731C22×D4C2414yes—
732C22×D4C2414yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C4⋊Q8—24no—
742C4⋊Q8—42no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—82no—
746#127—24no—
747#127—82no—
748#126—48no—
749#126—48no—
750#126—48no—
751#126—44no—
752#126—44no—
753#126—48no—
754#126—48no—
755#126—48no—
756#125—28no—
757#125—44no—
758#125—44no—
759#125—48no—
760#125—48no—
761#125—44no—
762#125—48no—
763#125—48no—
764#125—84no—
765#124—48no—
766#124—48no—
767#124—44no—
768#124—44no—
769#124—44no—
770#124—48no—
771#124—44no—
772#123—48no—
773#123—44no—
774#123—44no—
775#123—48no—
776#123—48no—
777#123—44no—
778#123—48no—
779#123—48no—
780#123—84no—
781C22⋊Q8—28no—
782C22⋊Q8—44no—
783C22⋊Q8—48no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8—84no—
790#121—28no—
791#121—44no—
792#121—48no—
793#121—44no—
794#121—44no—
795#121—44no—
796#121—84no—
797C4×Q8—24no—
798C4×Q8—28no—
799C4×Q8—24no—
800C4×Q8—28no—
801C4×Q8—24no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×D4—24no—
805C4×D4—28no—
806C4×D4—24no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—48no—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4—48no—
814C4×D4—82no—
815C4×D4—84no—
816#117—28no—
817#117—28no—
818#117—44no—
819#117—44no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4—84no—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C42—44no—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2411yescharacteristic
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973C2×C42C2414yes—
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029C24C2512yes—
1030C24C2512yes—
1031C24C2514yes—
1032C2×Q8—22no—
1033C2×Q8—22no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—44no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—22no—
1048C2×D4—22no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—28no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—44no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4—44no—
1064C2×D4—41no—
1065C2×D4—41no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2512yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—22no—
1135C4⋊C4—22no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—22no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—22no—
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—41no—
1162C4⋊C4—41no—
1163C4⋊C4—41no—
1164C4⋊C4—42no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—41no—
1202C4⋊C42−1+414yes—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—28no—
1209C22⋊C4—24no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—24no—
1259C42—28no—
1260C42—24no—
1261C42—24no—
1262C42—22no—
1263C42—24no—
1264C42—22no—
1265C42—24no—
1266C42—42no—
1267C42—42no—
1268C42—42no—
1269C42—41no—
1270C42—44no—
1271C42—41no—
1272C42—44no—
1273C42—41no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42—42no—
1278C42H(5,𝔽2)14yes—
1279C42H(5,𝔽2)14yes—
1280C23—22no—
1281C23—22no—
1282C23—24no—
1283C23—22no—
1284C23—22no—
1285C23—24no—
1286C23—22no—
1287C23—24no—
1288C23—22no—
1289C23—22no—
1290C23—24no—
1291C23—22no—
1292C23—22no—
1293C23—24no—
1294C23—22no—
1295C23—22no—
1296C23—24no—
1297C23—24no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23C2611yescharacteristic
1302Q8—44no—
1303Q8—48no—
1304Q8—84no—
1305Q8—164no—
1306D4—48no—
1307D4—48no—
1308D4—88no—
1309D4—82no—
1310D4—84no—
1311D4—82no—
1312D4—84no—
1313D4—88no—
1314D4—84no—
1315D4—164no—
1316D4—164no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—21no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—21no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—48no—
1387C2×C4—48no—
1388C2×C4—88no—
1389C2×C4—84no—
1390C2×C4—84no—
1391C2×C4—164no—
1392C2×C4—164no—
1393C2×C4—164no—
1394C2×C4C2×H(5,𝔽2)12yes—
1395C2×C4C2×H(5,𝔽2)12yes—
1396C2×C4C2×H(5,𝔽2)12yes—
1397C2×C4C2×H(5,𝔽2)12yes—
1398C2×C4C2×H(5,𝔽2)12yes—
1399C2×C4C2×H(5,𝔽2)12yes—
1400C2×C4C2×2−1+414yes—
1401C2×C4C2×2−1+412yes—
1402C2×C4#58512yes—
1403C22—42no—
1404C22—42no—
1405C22—44no—
1406C22—42no—
1407C22—44no—
1408C22—42no—
1409C22—42no—
1410C22—44no—
1411C22—42no—
1412C22—42no—
1413C22—44no—
1414C22—42no—
1415C22—42no—
1416C22—44no—
1417C22—42no—
1418C22—42no—
1419C22—44no—
1420C22—42no—
1421C22—44no—
1422C22—42no—
1423C22—42no—
1424C22C22×H(5,𝔽2)11yescharacteristic
1425C22C22×H(5,𝔽2)11yescharacteristic
1426C22C22×2−1+411yescharacteristic
1427C22C2×#58511yescharacteristic
1428C22H(7,𝔽2)11yescharacteristic
1429C222−1+611yescharacteristic
1430C222−1+611yescharacteristic
1431C4—24no—
1432C4—22no—
1433C4—22no—
1434C4—22no—
1435C4—22no—
1436C4—22no—
1437C4—42no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—41no—
1442C4—42no—
1443C4—42no—
1444C4—44no—
1445C4—42no—
1446C4—42no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—42no—
1452C4—44no—
1453C4—44no—
1454C4—42no—
1455C4—42no—
1456C4#354814yes—
1457C2—82no—
1458C2—82no—
1459C2—84no—
1460C2C2×#354811yescharacteristic
1461C2#6287811yescharacteristic
1462C2#6288811yescharacteristic
1463C2#6292511yescharacteristic
1464C2#6294911yescharacteristic
1465C2#6296111yescharacteristic
1466C2#6305811yescharacteristic
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. #59827C2semidirect
2. #58561C2semidirect
3. #57549C2semidirect
4. #57371C2semidirect
5. #57328C2semidirect
6. #55329C2semidirect
7. #53377C2semidirect
8. #53348C2semidirect
9. #53016C2semidirect
10. #52152C2semidirect
11. #48472C2semidirect
12. #46014C2semidirect
13. #45711C2semidirect
14. #45275C2semidirect
15. #45196C2semidirect
16. #42877C2semidirect
17. #42769C2semidirect
18. #42440C2semidirect
19. #40103C2semidirect
20. #39692C2semidirect
21. #39483C2semidirect
22. #39373C2semidirect
23. #39130C2semidirect
24. #37389C2semidirect
25. #37378C2semidirect
26. #37152C2semidirect
27. #36535C2semidirect
28. #35209C2semidirect
29. #35198C2semidirect

Maximal subgroups

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

subgroupindex
#598272
#585612
#575492
#573712
#573282
#553292
#533772
#533482
#530162
#521522
#484722
#460142
#457112
#452752
#451962
#428772
#427692
#424402
#401032
#396922
#394832
#393732
#391302
#373892
#373782
#371522
#365352
#352092
#351982