Finite Group Databasebeta

← #8107439

Subgroups — #8107439

Order 512.

4614 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53153C212yesmaximal, complemented
2#53098C212yesmaximal, complemented
3#52460C214yesmaximal, complemented
4#52404C214yesmaximal, complemented
5#45136C212yesmaximal, complemented
6#45024C212yesmaximal, complemented
7#43259C214yesmaximal, complemented
8#43210C214yesmaximal, complemented
9#42958C211yesmaximal, characteristic, complemented
10#42952C211yesmaximal, characteristic, complemented
11#42883C211yesmaximal, characteristic, complemented
12#42743C212yesmaximal, complemented
13#42684C211yesmaximal, characteristic, complemented
14#42598C212yesmaximal, complemented
15#41142C214yesmaximal, complemented
16#41116C214yesmaximal, complemented
17#40853C214yesmaximal, complemented
18#40828C214yesmaximal, complemented
19#36392C212yesmaximal, complemented
20#36374C212yesmaximal, complemented
21#36361C212yesmaximal, complemented
22#36292C212yesmaximal, complemented
23#35313C211yesmaximal, characteristic, complemented
24#35296C211yesmaximal, characteristic, complemented
25#35044C212yesmaximal, complemented
26#35026C212yesmaximal, complemented
27#34547C211yesmaximal, characteristic, complemented
28C2×#553C2212yes—
29C2×#548C2212yes—
30C2×C4×#41C2212yes—
31#2864C2211yescharacteristic
32#2863C2212yes—
33#2863C2212yes—
34#2858C2211yescharacteristic
35#2855C2212yes—
36#2854C2212yes—
37#2854C2212yes—
38#2851C2212yes—
39#2850C2212yes—
40#2838C2214yes—
41#2838C2214yes—
42#2838C2214yes—
43#2838C2214yes—
44#2837C2214yes—
45#2835C2214yes—
46#2833C2212yes—
47#2827C2214yes—
48#2826C2212yes—
49#2825C2214yes—
50#2824C2214yes—
51#2823C2212yes—
52#2815C2212yes—
53#2813C2214yes—
54#2800C2214yes—
55#2798C2214yes—
56#2793C2214yes—
57#2789C2212yes—
58#2785C2212yes—
59#2780C2214yes—
60#2779C2214yes—
61#2778C2214yes—
62#2778C2214yes—
63#2773C2214yes—
64#2770C2214yes—
65#2767C2214yes—
66#2765C2214yes—
67#2765C2214yes—
68#2764C2212yes—
69#2763C2214yes—
70#2760C2214yes—
71#2760C2212yes—
72#2746C2214yes—
73#2743C2214yes—
74#2743C2214yes—
75#2738C2214yes—
76#2733C2212yes—
77#2730C2214yes—
78#2728C2212yes—
79#2715C2214yes—
80#2703C2214yes—
81#2703C2214yes—
82#2701C2214yes—
83#2698C2214yes—
84#2693C2212yes—
85#2688C2214yes—
86#2688C2214yes—
87#2688C2214yes—
88#2675C2212yes—
89#2671C2214yes—
90#2665C2214yes—
91#2655C2214yes—
92#2653C2214yes—
93#2653C2214yes—
94#2652C2214yes—
95#2648C2214yes—
96#2645C2212yes—
97#2645C2212yes—
98#2645C2214yes—
99#2644C2212yes—
100#2643C2214yes—
101#2636C2214yes—
102#2635C2214yes—
103#2635C2214yes—
104#2631C2214yes—
105#2628C2211yescharacteristic
106#2619C2211yescharacteristic
107#2602C2214yes—
108#2600C2214yes—
109#2600C2212yes—
110#2598C2214yes—
111#2597C2214yes—
112#2595C2214yes—
113#2594C2214yes—
114#2592C2212yes—
115#2585C2214yes—
116#2584C2212yes—
117#2581C2212yes—
118#2580C2212yes—
119#2578C2214yes—
120#2576C2214yes—
121#2576C2214yes—
122#2575C2214yes—
123#2573C2214yes—
124#2572C2212yes—
125#2557C2214yes—
126#2557C2214yes—
127#2537C2212yes—
128#2531C2214yes—
129#2530C2214yes—
130#2526C2214yes—
131#2522C2214yes—
132#2518C2214yes—
133#2517C2212yes—
134#2514C2212yes—
135#2514C2214yes—
136#2513C2212yes—
137#2511C2214yes—
138#2510C2214yes—
139#2509C2212yes—
140#2508C2212yes—
141#2503C2212yes—
142#2494C2212yes—
143#2494C2212yes—
144#2493C2214yes—
145#2493C2214yes—
146#2493C2214yes—
147#2492C2212yes—
148#2489C2212yes—
149#2487C2212yes—
150#2486C2212yes—
151#2485C2212yes—
152#2485C2212yes—
153#2479C2214yes—
154#2477C2214yes—
155#2474C2214yes—
156#2474C2214yes—
157#2471C2214yes—
158#2470C2214yes—
159#2470C2214yes—
160#2469C2214yes—
161#2465C2214yes—
162#2459C2214yes—
163#2459C2214yes—
164#2459C2214yes—
165#2456C2214yes—
166#2455C2214yes—
167#2454C2212yes—
168#2453C2212yes—
169#2450C2214yes—
170#2448C2212yes—
171#2447C2212yes—
172#2444C2214yes—
173#2444C2214yes—
174#2443C2214yes—
175#2443C2214yes—
176#2442C2212yes—
177#2439C2212yes—
178#2431C2212yes—
179#2430C2214yes—
180#2430C2214yes—
181#2428C2212yes—
182#2427C2212yes—
183#2421C2212yes—
184#2420C2212yes—
185#2420C2214yes—
186#2420C2214yes—
187#2419C2214yes—
188#2419C2214yes—
189#2417C2212yes—
190#2417C2212yes—
191#2416C2212yes—
192#2416C2212yes—
193#2416C2212yes—
194#2415C2212yes—
195#2414C2212yes—
196#2414C2212yes—
197#2409C2212yes—
198#2407C2212yes—
199#2407C2212yes—
200#2407C2212yes—
201#2399C2211yescharacteristic
202#2398C2212yes—
203#2397C2211yescharacteristic
204#2396C2212yes—
205#2396C2212yes—
206#2395C2212yes—
207#2395C2212yes—
208#2392C2212yes—
209#2392C2211yescharacteristic
210#2392C2212yes—
211#2392C2211yescharacteristic
212#2392C2212yes—
213#2388C2212yes—
214#2388C2212yes—
215#2364C2214yes—
216#2364C2214yes—
217#2361C2214yes—
218#2361C2212yes—
219#2360C2212yes—
220#2359C2214yes—
221#2359C2214yes—
222#2353C2214yes—
223#2352C2212yes—
224#2352C2212yes—
225#2352C2214yes—
226#2346C2212yes—
227#2343C2214yes—
228#2339C2212yes—
229#2337C2214yes—
230#2333C2214yes—
231#2331C2211yescharacteristic
232#2328C2211yescharacteristic
233#2324C2212yes—
234#2322C2214yes—
235#2317C2211yescharacteristic
236#2316C2211yescharacteristic
237#2313C2214yes—
238#2310C2211yescharacteristic
239#2310C2211yescharacteristic
240C4×C22⋊Q8C2212yes—
241C4×#121C2212yes—
242#2297C2212yes—
243#2296C2211yescharacteristic
244C2×#391C2211yescharacteristic
245#2293C2212yes—
246C2×#389C2212yes—
247C42×D4C2211yescharacteristic
248C42×D4C2211yescharacteristic
249C42×D4C2212yes—
250C4×#117C2211yescharacteristic
251C22×#41C2312yes—
252C22×#41C2312yes—
253C23×Q8C2311yescharacteristic
254#553—48no—
255#548—48no—
256C2×C4⋊Q8C2311yescharacteristic
257C2×#127C2311yescharacteristic
258C2×#126C2314yes—
259C2×#125C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C4×#41—48no—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2312yes—
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2314yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C42C2311yescharacteristic
318C22×C42C2312yes—
319C22×C42C2312yes—
320#401C2314yes—
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#401C2314yes—
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#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#399C2312yes—
348#399C2312yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2312yes—
354#398C2311yescharacteristic
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2311yescharacteristic
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2311yescharacteristic
384#397C2314yes—
385#397C2312yes—
386#397C2311yescharacteristic
387#397C2312yes—
388#397C2312yes—
389#397C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2312yes—
399#396C2312yes—
400#396C2312yes—
401#396C2312yes—
402#395C2314yes—
403#395C2312yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2312yes—
408#394C2314yes—
409#394C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2311yescharacteristic
418#394C2314yes—
419#394C2314yes—
420#394C2312yes—
421#394C2314yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2312yes—
428#394C2312yes—
429#394C2312yes—
430#394C2312yes—
431#394C2311yescharacteristic
432#394C2314yes—
433#393C2312yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2312yes—
438#393C2314yes—
439#393C2314yes—
440#393C2312yes—
441#392C2314yes—
442#392C2312yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2311yescharacteristic
447#392C2312yes—
448#392C2312yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#392C2311yescharacteristic
454#392C2312yes—
455#392C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2314yes—
471#390C2312yes—
472#390C2314yes—
473#390C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2314yes—
477#390C2312yes—
478#390C2312yes—
479#390C2314yes—
480#390C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
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#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#387C2314yes—
563#387C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#385C2314yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#384C2312yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#382C2312yes—
619#382C2314yes—
620#382C2314yes—
621#382C2312yes—
622#382C2312yes—
623#382C2311yescharacteristic
624#382C2311yescharacteristic
625#382C2314yes—
626#381C2312yes—
627#381C2312yes—
628#381C2314yes—
629#381C2314yes—
630#381C2314yes—
631#381C2314yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2311yescharacteristic
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685#376C2311yescharacteristic
686#376C2314yes—
687#376C2311yescharacteristic
688C2×#95C2314yes—
689C2×#95C2314yes—
690C2×#95C2314yes—
691C43C2311yescharacteristic
692C43C2311yescharacteristic
693C2×#41—44no—
694C2×#41—44no—
695C2×#41—44no—
696C2×#41—44no—
697C2×#41—44no—
698C2×#41—44no—
699C22×Q8—24no—
700C22×Q8—42no—
701C22×Q8—42no—
702C22×Q8C2412yes—
703C22×Q8C2412yes—
704C22×Q8C2412yes—
705C22×Q8C2412yes—
706C22×D4C2412yes—
707C22×D4C2411yescharacteristic
708C22×D4C2412yes—
709C22×D4C2412yes—
710C22×D4C2412yes—
711C22×D4C2412yes—
712C22×D4C2414yes—
713C22×D4C2414yes—
714C22×D4C2414yes—
715C22×D4C2411yescharacteristic
716C22×D4C2414yes—
717C22×D4C2412yes—
718C22×D4C2414yes—
719C22×D4C2412yes—
720C23×C4C2412yes—
721C23×C4C2412yes—
722C23×C4C2412yes—
723C23×C4C2412yes—
724C23×C4C2411yescharacteristic
725C23×C4C2412yes—
726C23×C4C2414yes—
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2414yes—
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2414yes—
735C4⋊Q8—42no—
736#127—42no—
737#126—48no—
738#125—44no—
739#124—48no—
740#124—44no—
741#124—48no—
742#123—48no—
743#123—48no—
744#123—48no—
745#123—48no—
746C22⋊Q8—48no—
747C22⋊Q8—44no—
748C22⋊Q8—44no—
749C22⋊Q8—44no—
750#121—28no—
751#121—48no—
752#121—48no—
753#121—48no—
754#121—48no—
755#121—44no—
756#121—44no—
757#121—44no—
758#121—48no—
759#121—48no—
760C4×Q8—44no—
761C4×Q8—44no—
762C4×Q8—44no—
763C4×D4—28no—
764C4×D4—28no—
765C4×D4—44no—
766C4×D4—48no—
767C4×D4—44no—
768C4×D4—44no—
769C4×D4—44no—
770C4×D4—44no—
771C4×D4—42no—
772C4×D4—42no—
773C4×D4—44no—
774C4×D4—44no—
775C4×D4—48no—
776C4×D4—44no—
777C4×D4—48no—
778C4×D4—44no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4—48no—
782#117—24no—
783#117—42no—
784#117—42no—
785#117—48no—
786#117—44no—
787#117—44no—
788#117—44no—
789#117—42no—
790#117—44no—
791C2×C4⋊C4—42no—
792C2×C4⋊C4—44no—
793C2×C4⋊C4—48no—
794C2×C4⋊C4—44no—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C42—24no—
896C2×C42—44no—
897C2×C42—44no—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2411yescharacteristic
953#95C2412yes—
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—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988C24C2514yes—
989C24C2512yes—
990C24C2511yescharacteristic
991C24C2512yes—
992#41—432no—
993#41—816no—
994C2×Q8—24no—
995C2×Q8—24no—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—42no—
999C2×Q8—42no—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—42no—
1003C2×Q8—44no—
1004C2×Q8—42no—
1005C2×Q8—88no—
1006C2×D4—24no—
1007C2×D4—24no—
1008C2×D4—24no—
1009C2×D4—24no—
1010C2×D4—24no—
1011C2×D4—24no—
1012C2×D4—28no—
1013C2×D4—28no—
1014C2×D4—28no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C2×D4—41no—
1021C2×D4—42no—
1022C2×D4—41no—
1023C2×D4—42no—
1024C2×D4—42no—
1025C2×D4—42no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—42no—
1043C2×D4—42no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4H(5,𝔽2)14yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—41no—
1136C4⋊C4—41no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—28no—
1168C22⋊C4—42no—
1169C22⋊C4—41no—
1170C22⋊C4—41no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C42—22no—
1212C42—24no—
1213C42—22no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—22no—
1219C42—22no—
1220C42—22no—
1221C42—22no—
1222C42—24no—
1223C42—42no—
1224C42—42no—
1225C42—42no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—42no—
1231C42—42no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C23—22no—
1236C23—21no—
1237C23—22no—
1238C23—22no—
1239C23—21no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—24no—
1246C23—22no—
1247C23—24no—
1248C23—24no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—24no—
1253C23—22no—
1254C23—24no—
1255C23—24no—
1256C23—22no—
1257C23—22no—
1258C23—24no—
1259C23C2×H(5,𝔽2)12yes—
1260C23#58514yes—
1261C23C2611yescharacteristic
1262Q8—48no—
1263Q8—48no—
1264Q8—84no—
1265Q8—162no—
1266D4—44no—
1267D4—48no—
1268D4—48no—
1269D4—48no—
1270D4—48no—
1271D4—44no—
1272D4—48no—
1273D4—88no—
1274D4—88no—
1275D4—88no—
1276D4—88no—
1277D4—88no—
1278D4—162no—
1279D4—162no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—28no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—48no—
1342C2×C4—48no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—48no—
1346C2×C4—84no—
1347C2×C4—84no—
1348C2×C4—88no—
1349C2×C4—84no—
1350C2×C4—88no—
1351C2×C4—88no—
1352C2×C4—164no—
1353C2×C4—164no—
1354C2×C4—162no—
1355C2×C4C2×H(5,𝔽2)12yes—
1356C2×C4C2×H(5,𝔽2)12yes—
1357C2×C4#58514yes—
1358C2×C4#58512yes—
1359C2×C4#58512yes—
1360C22—22no—
1361C22—24no—
1362C22—24no—
1363C22—24no—
1364C22—24no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—41no—
1370C22—42no—
1371C22—41no—
1372C22—42no—
1373C22—44no—
1374C22—44no—
1375C22—42no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—42no—
1380C22—44no—
1381C22—44no—
1382C22—44no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22C22×H(5,𝔽2)11yescharacteristic
1387C22C2×#58511yescharacteristic
1388C22C2×#58511yescharacteristic
1389C22C2×#58512yes—
1390C22C2×#58512yes—
1391C4—22no—
1392C4—24no—
1393C4—42no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—44no—
1398C4—44no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—44no—
1406C4—44no—
1407C4—44no—
1408C4—41no—
1409C4—41no—
1410C4—41no—
1411C4—41no—
1412C4—44no—
1413C4#356014yes—
1414C2—42no—
1415C2—44no—
1416C2—82no—
1417C2—84no—
1418C2C2×#356011yescharacteristic
1419C2#6274312yes—
1420C2#6282112yes—
1421C2#6282911yescharacteristic
1422C2#6283911yescharacteristic
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. #53153C2semidirect
2. #53098C2semidirect
3. #52460C2semidirect
4. #52404C2semidirect
5. #45136C2semidirect
6. #45024C2semidirect
7. #43259C2semidirect
8. #43210C2semidirect
9. #42958C2semidirect
10. #42952C2semidirect
11. #42883C2semidirect
12. #42743C2semidirect
13. #42684C2semidirect
14. #42598C2semidirect
15. #41142C2semidirect
16. #41116C2semidirect
17. #40853C2semidirect
18. #40828C2semidirect
19. #36392C2semidirect
20. #36374C2semidirect
21. #36361C2semidirect
22. #36292C2semidirect
23. #35313C2semidirect
24. #35296C2semidirect
25. #35044C2semidirect
26. #35026C2semidirect
27. #34547C2semidirect

Maximal subgroups

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

subgroupindex
#531532
#530982
#524602
#524042
#451362
#450242
#432592
#432102
#429582
#429522
#428832
#427432
#426842
#425982
#411422
#411162
#408532
#408282
#363922
#363742
#363612
#362922
#353132
#352962
#350442
#350262
#345472