Finite Group Databasebeta

← #7715098

Subgroups — #7715098

Order 512.

4758 conjugacy classes of subgroups.

The subgroup lattice has 1431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51972C214yesmaximal, complemented
2#51950C214yesmaximal, complemented
3#51738C214yesmaximal, complemented
4#51692C214yesmaximal, complemented
5#46962C214yesmaximal, complemented
6#46930C214yesmaximal, complemented
7#46731C214yesmaximal, complemented
8#46571C214yesmaximal, complemented
9#39059C212yesmaximal, complemented
10#39058C212yesmaximal, complemented
11#39041C212yesmaximal, complemented
12#39040C212yesmaximal, complemented
13#37892C212yesmaximal, complemented
14#37884C212yesmaximal, complemented
15#37711C212yesmaximal, complemented
16#37699C212yesmaximal, complemented
17#37519C211yesmaximal, characteristic, complemented
18#37515C211yesmaximal, characteristic, complemented
19#37382C211yesmaximal, characteristic, complemented
20#37286C211yesmaximal, characteristic, complemented
21#37272C212yesmaximal, complemented
22#35328C211yesmaximal, characteristic, complemented
23#35280C211yesmaximal, characteristic, complemented
24#35270C212yesmaximal, complemented
25#35258C212yesmaximal, complemented
26#34414C212yesmaximal, complemented
27#34070C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×#537C2212yes—
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2857C2212yes—
36#2857C2212yes—
37#2855C2212yes—
38#2855C2212yes—
39#2854C2212yes—
40#2854C2212yes—
41#2850C2212yes—
42#2850C2212yes—
43#2827C2214yes—
44#2825C2214yes—
45#2795C2214yes—
46#2793C2214yes—
47#2791C2214yes—
48#2790C2214yes—
49#2781C2214yes—
50#2779C2214yes—
51#2776C2214yes—
52#2773C2214yes—
53#2767C2214yes—
54#2767C2214yes—
55#2765C2214yes—
56#2762C2214yes—
57#2761C2214yes—
58#2756C2214yes—
59#2754C2214yes—
60#2750C2214yes—
61#2749C2214yes—
62#2748C2214yes—
63#2747C2214yes—
64#2747C2214yes—
65#2746C2214yes—
66#2744C2214yes—
67#2744C2214yes—
68#2743C2214yes—
69#2739C2214yes—
70#2730C2214yes—
71#2730C2214yes—
72#2729C2214yes—
73#2728C2214yes—
74#2723C2214yes—
75#2718C2214yes—
76#2718C2214yes—
77#2705C2214yes—
78#2703C2214yes—
79#2703C2214yes—
80#2701C2214yes—
81#2699C2214yes—
82#2696C2214yes—
83#2693C2214yes—
84#2693C2214yes—
85#2691C2214yes—
86#2688C2214yes—
87#2686C2214yes—
88#2682C2214yes—
89#2681C2214yes—
90#2676C2214yes—
91#2673C2214yes—
92#2671C2214yes—
93#2666C2214yes—
94#2661C2214yes—
95#2653C2214yes—
96#2651C2214yes—
97#2647C2212yes—
98#2645C2212yes—
99#2644C2212yes—
100#2640C2212yes—
101#2629C2211yescharacteristic
102#2629C2211yescharacteristic
103#2629C2211yescharacteristic
104#2629C2211yescharacteristic
105#2628C2212yes—
106#2621C2211yescharacteristic
107#2621C2211yescharacteristic
108#2620C2212yes—
109#2619C2211yescharacteristic
110#2619C2211yescharacteristic
111#2616C2212yes—
112#2615C2212yes—
113#2602C2214yes—
114#2601C2214yes—
115#2591C2214yes—
116#2590C2214yes—
117#2587C2214yes—
118#2582C2214yes—
119#2579C2214yes—
120#2578C2214yes—
121#2577C2214yes—
122#2576C2214yes—
123#2569C2214yes—
124#2553C2214yes—
125#2543C2214yes—
126#2543C2214yes—
127#2538C2214yes—
128#2536C2214yes—
129#2535C2214yes—
130#2535C2214yes—
131#2532C2214yes—
132#2530C2214yes—
133#2529C2214yes—
134#2527C2214yes—
135#2518C2214yes—
136#2518C2214yes—
137#2512C2212yes—
138#2511C2212yes—
139#2510C2214yes—
140#2509C2212yes—
141#2508C2212yes—
142#2498C2214yes—
143#2495C2212yes—
144#2494C2214yes—
145#2494C2212yes—
146#2493C2214yes—
147#2490C2212yes—
148#2489C2212yes—
149#2488C2214yes—
150#2488C2214yes—
151#2487C2212yes—
152#2486C2212yes—
153#2481C2214yes—
154#2471C2214yes—
155#2469C2214yes—
156#2469C2214yes—
157#2467C2214yes—
158#2466C2214yes—
159#2465C2214yes—
160#2463C2214yes—
161#2461C2214yes—
162#2459C2214yes—
163#2459C2214yes—
164#2458C2214yes—
165#2457C2214yes—
166#2457C2214yes—
167#2457C2214yes—
168#2456C2214yes—
169#2455C2214yes—
170#2454C2212yes—
171#2453C2212yes—
172#2450C2214yes—
173#2450C2214yes—
174#2448C2214yes—
175#2446C2212yes—
176#2445C2212yes—
177#2443C2214yes—
178#2438C2214yes—
179#2429C2212yes—
180#2428C2212yes—
181#2425C2214yes—
182#2423C2212yes—
183#2422C2212yes—
184#2421C2214yes—
185#2419C2214yes—
186#2419C2214yes—
187#2417C2212yes—
188#2417C2214yes—
189#2417C2214yes—
190#2416C2212yes—
191#2415C2212yes—
192#2414C2212yes—
193#2407C2212yes—
194#2407C2212yes—
195#2378C2214yes—
196#2377C2214yes—
197#2368C2214yes—
198#2363C2214yes—
199#2363C2212yes—
200#2362C2212yes—
201#2361C2212yes—
202#2360C2212yes—
203#2345C2212yes—
204#2344C2212yes—
205#2341C2212yes—
206#2339C2212yes—
207#2333C2214yes—
208#2333C2214yes—
209#2331C2212yes—
210#2328C2212yes—
211#2327C2212yes—
212#2326C2212yes—
213#2326C2212yes—
214#2326C2212yes—
215#2325C2212yes—
216#2325C2212yes—
217#2325C2212yes—
218#2325C2212yes—
219#2325C2214yes—
220#2324C2212yes—
221#2324C2214yes—
222#2323C2212yes—
223#2320C2212yes—
224#2319C2212yes—
225#2316C2212yes—
226#2314C2212yes—
227#2311C2212yes—
228#2311C2212yes—
229C4×C22⋊Q8C2212yes—
230C4×C22⋊Q8C2212yes—
231C4×#121C2212yes—
232C4×#121C2212yes—
233#2297C2211yescharacteristic
234#2297C2211yescharacteristic
235#2290C2212yes—
236#2290C2212yes—
237#2290C2212yes—
238#2290C2212yes—
239#2285C2211yescharacteristic
240C2×#384C2211yescharacteristic
241C2×#382C2211yescharacteristic
242C2×#376C2211yescharacteristic
243C22×#41C2312yes—
244C22×#41C2311yescharacteristic
245C22×#41C2311yescharacteristic
246#542—48no—
247#537—216no—
248#533—44no—
249#532—28no—
250#532—44no—
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×#127C2311yescharacteristic
255C2×#127C2311yescharacteristic
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#125C2311yescharacteristic
259C2×#125C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2314yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C4×#41—44no—
292C4×#41—44no—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×#117C2312yes—
313C2×#117C2311yescharacteristic
314C2×#117C2312yes—
315C2×#117C2311yescharacteristic
316C2×#117C2311yescharacteristic
317C2×#117C2311yescharacteristic
318C2×#117C2314yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2312yes—
327C22×C42C2311yescharacteristic
328#401C2314yes—
329#401C2314yes—
330#400C2314yes—
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#400C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#397C2314yes—
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#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#395C2314yes—
393#395C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#390C2312yes—
438#390C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2314yes—
442#390C2312yes—
443#390C2314yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2312yes—
450#390C2314yes—
451#390C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2312yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
488#388C2312yes—
489#388C2312yes—
490#388C2312yes—
491#388C2312yes—
492#388C2312yes—
493#388C2312yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#387C2312yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
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#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2312yes—
555#386C2314yes—
556#386C2312yes—
557#386C2314yes—
558#386C2312yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2311yescharacteristic
563#386C2314yes—
564#386C2314yes—
565#386C2311yescharacteristic
566#386C2311yescharacteristic
567#386C2311yescharacteristic
568#386C2312yes—
569#386C2312yes—
570#386C2312yes—
571#386C2312yes—
572#386C2312yes—
573#386C2312yes—
574#386C2312yes—
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#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2312yes—
600#385C2312yes—
601#385C2312yes—
602#385C2312yes—
603#385C2312yes—
604#385C2312yes—
605#385C2312yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#384C2312yes—
611#384C2312yes—
612#384C2314yes—
613#384C2311yescharacteristic
614#384C2311yescharacteristic
615#383C2314yes—
616#383C2314yes—
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#382C2312yes—
621#382C2311yescharacteristic
622#382C2311yescharacteristic
623#382C2314yes—
624#382C2314yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#381C2314yes—
629#381C2314yes—
630#381C2314yes—
631#380C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2312yes—
646#380C2312yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673#376C2312yes—
674#376C2312yes—
675#376C2312yes—
676#376C2312yes—
677C2×#95C2314yes—
678C2×#95C2312yes—
679C2×#95C2312yes—
680C2×#95C2314yes—
681C2×#41—24no—
682C2×#41—28no—
683C2×#41—42no—
684C2×#41—42no—
685C2×#41—42no—
686C2×#41—42no—
687C2×#41—44no—
688C2×#41—44no—
689C2×#41#4118yes—
690C22×Q8C2412yes—
691C22×Q8C2411yescharacteristic
692C22×Q8C2414yes—
693C22×Q8C2411yescharacteristic
694C22×D4C2412yes—
695C22×D4C2412yes—
696C22×D4C2411yescharacteristic
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2412yes—
700C22×D4C2412yes—
701C22×D4C2414yes—
702C22×D4C2414yes—
703C22×D4C2414yes—
704C22×D4C2414yes—
705C22×D4C2411yescharacteristic
706C22×D4C2411yescharacteristic
707C22×D4C2411yescharacteristic
708C23×C4C2412yes—
709C23×C4C2411yescharacteristic
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C23×C4C2412yes—
713C23×C4C2414yes—
714C23×C4C2412yes—
715C23×C4C2412yes—
716C23×C4C2414yes—
717C23×C4C2412yes—
718C23×C4C2414yes—
719C23×C4C2411yescharacteristic
720C23×C4C2412yes—
721C23×C4C2414yes—
722C23×C4C2414yes—
723C23×C4C2412yes—
724C23×C4C2411yescharacteristic
725C4⋊Q8—24no—
726C4⋊Q8—28no—
727C4⋊Q8—42no—
728#127—24no—
729#127—42no—
730#126—48no—
731#126—84no—
732#125—42no—
733#125—42no—
734#124—24no—
735#124—24no—
736#124—28no—
737#124—48no—
738#123—48no—
739#123—84no—
740#123—84no—
741#123—84no—
742#123—84no—
743#123—84no—
744C22⋊Q8—216no—
745C22⋊Q8—28no—
746C22⋊Q8—28no—
747C22⋊Q8—48no—
748C22⋊Q8—44no—
749C22⋊Q8—48no—
750C22⋊Q8—44no—
751C22⋊Q8—84no—
752C22⋊Q8—84no—
753#121—28no—
754#121—28no—
755#121—216no—
756#121—216no—
757#121—216no—
758#121—28no—
759#121—28no—
760#121—48no—
761#121—44no—
762#121—44no—
763#121—84no—
764#121—84no—
765C4×Q8—44no—
766C4×Q8—44no—
767C4×Q8—44no—
768C4×Q8—48no—
769C4×Q8—44no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—44no—
773C4×D4—48no—
774C4×D4—44no—
775C4×D4—44no—
776C4×D4—44no—
777C4×D4—44no—
778C4×D4—44no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4—84no—
782C4×D4—84no—
783C4×D4—84no—
784#117—28no—
785#117—42no—
786#117—42no—
787#117—42no—
788#117—42no—
789#117—44no—
790#117—84no—
791C2×C4⋊C4—28no—
792C2×C4⋊C4—44no—
793C2×C4⋊C4—84no—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C42—24no—
893C2×C42—24no—
894C2×C42—24no—
895C2×C42—24no—
896C2×C42—44no—
897C2×C42—42no—
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2411yescharacteristic
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980C24C2512yes—
981C24C2514yes—
982C24C2511yescharacteristic
983C24C2511yescharacteristic
984C24C2511yescharacteristic
985#41—416no—
986#41—416no—
987#41—816no—
988C2×Q8—24no—
989C2×Q8—22no—
990C2×Q8—24no—
991C2×Q8—28no—
992C2×Q8—24no—
993C2×Q8—41no—
994C2×Q8—41no—
995C2×Q8—41no—
996C2×Q8—41no—
997C2×Q8—44no—
998C2×Q8—44no—
999C2×Q8C2×#4114yes—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—28no—
1004C2×D4—28no—
1005C2×D4—28no—
1006C2×D4—24no—
1007C2×D4—22no—
1008C2×D4—24no—
1009C2×D4—24no—
1010C2×D4—41no—
1011C2×D4—41no—
1012C2×D4—41no—
1013C2×D4—41no—
1014C2×D4—42no—
1015C2×D4—41no—
1016C2×D4—41no—
1017C2×D4—41no—
1018C2×D4—41no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—42no—
1028C2×D4—44no—
1029C2×D4—42no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—42no—
1033C2×D4—42no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4C2×#4114yes—
1040C2×D4C2×#4114yes—
1041C2×D4C2×#4114yes—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—28no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—41no—
1062C22×C4—41no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4C2×#4114yes—
1089C22×C4C2×#4114yes—
1090C22×C4C2×#4114yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2514yes—
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
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—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—42no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C22⋊C4—41no—
1184C22⋊C4—41no—
1185C22⋊C4—44no—
1186C22⋊C4—42no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
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—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C42—24no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—22no—
1216C42—22no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—42no—
1223C42—42no—
1224C42—42no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42H(5,𝔽2)14yes—
1233C23—21no—
1234C23—21no—
1235C23—21no—
1236C23—21no—
1237C23—21no—
1238C23—21no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—24no—
1247C23—22no—
1248C23—24no—
1249C23—22no—
1250C23—24no—
1251C23—22no—
1252C23—24no—
1253C23—24no—
1254C23—22no—
1255C23—24no—
1256C23—22no—
1257C23—22no—
1258C23—24no—
1259C23C22×#4112yes—
1260C23C22×#4112yes—
1261C23C22×#4112yes—
1262C23C2611yescharacteristic
1263Q8—44no—
1264Q8—44no—
1265Q8—48no—
1266Q8—88no—
1267D4—44no—
1268D4—44no—
1269D4—44no—
1270D4—44no—
1271D4—48no—
1272D4—48no—
1273D4—88no—
1274D4—88no—
1275D4—84no—
1276D4—84no—
1277D4—88no—
1278D4—88no—
1279D4—88no—
1280D4—164no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—28no—
1290C2×C4—28no—
1291C2×C4—28no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—84no—
1346C2×C4—84no—
1347C2×C4—88no—
1348C2×C4—84no—
1349C2×C4—88no—
1350C2×C4—84no—
1351C2×C4—84no—
1352C2×C4—82no—
1353C2×C4—82no—
1354C2×C4—164no—
1355C2×C4—164no—
1356C2×C4—164no—
1357C2×C4C22×#4112yes—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C2×H(5,𝔽2)14yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4#58512yes—
1364C22—22no—
1365C22—22no—
1366C22—22no—
1367C22—24no—
1368C22—24no—
1369C22—24no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—41no—
1377C22—41no—
1378C22—41no—
1379C22—42no—
1380C22—44no—
1381C22—44no—
1382C22—42no—
1383C22—42no—
1384C22—44no—
1385C22—42no—
1386C22—42no—
1387C22—44no—
1388C22—44no—
1389C22—44no—
1390C22—42no—
1391C22—42no—
1392C22—44no—
1393C22C23×#4111yescharacteristic
1394C22C22×H(5,𝔽2)11yescharacteristic
1395C22C2×#58511yescharacteristic
1396C22H(7,𝔽2)12yes—
1397C222−1+612yes—
1398C4—22no—
1399C4—22no—
1400C4—22no—
1401C4—24no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—44no—
1406C4—44no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—44no—
1415C4—42no—
1416C4—44no—
1417C4—44no—
1418C4—42no—
1419C4#350514yes—
1420C2—42no—
1421C2—42no—
1422C2—42no—
1423C2—82no—
1424C2—84no—
1425C2C2×#350511yescharacteristic
1426C2#6285712yes—
1427C2#6287512yes—
1428C2#6288311yescharacteristic
1429C2#6289011yescharacteristic
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. #51972C2semidirect
2. #51950C2semidirect
3. #51738C2semidirect
4. #51692C2semidirect
5. #46962C2semidirect
6. #46930C2semidirect
7. #46731C2semidirect
8. #46571C2semidirect
9. #39059C2semidirect
10. #39058C2semidirect
11. #39041C2semidirect
12. #39040C2semidirect
13. #37892C2semidirect
14. #37884C2semidirect
15. #37711C2semidirect
16. #37699C2semidirect
17. #37519C2semidirect
18. #37515C2semidirect
19. #37382C2semidirect
20. #37286C2semidirect
21. #37272C2semidirect
22. #35328C2semidirect
23. #35280C2semidirect
24. #35270C2semidirect
25. #35258C2semidirect
26. #34414C2semidirect
27. #34070C2semidirect

Maximal subgroups

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

subgroupindex
#519722
#519502
#517382
#516922
#469622
#469302
#467312
#465712
#390592
#390582
#390412
#390402
#378922
#378842
#377112
#376992
#375192
#375152
#373822
#372862
#372722
#353282
#352802
#352702
#352582
#344142
#340702