Finite Group Databasebeta

← #7642082

Subgroups — #7642082

Order 512.

4454 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37019C212yesmaximal, complemented
2#37017C212yesmaximal, complemented
3#37013C212yesmaximal, complemented
4#37011C212yesmaximal, complemented
5#36994C214yesmaximal, complemented
6#36989C214yesmaximal, complemented
7#36974C214yesmaximal, complemented
8#36821C212yesmaximal, complemented
9#36819C212yesmaximal, complemented
10#36815C212yesmaximal, complemented
11#36813C212yesmaximal, complemented
12#36788C214yesmaximal, complemented
13#36783C214yesmaximal, complemented
14#36764C212yesmaximal, complemented
15#36763C212yesmaximal, complemented
16#36762C212yesmaximal, complemented
17#36761C212yesmaximal, complemented
18#36726C214yesmaximal, complemented
19#35069C214yesmaximal, complemented
20#35067C214yesmaximal, complemented
21#35057C211yesmaximal, characteristic, complemented
22#35057C211yesmaximal, characteristic, complemented
23#35033C211yesmaximal, characteristic, complemented
24#35032C211yesmaximal, characteristic
25#34082C211yesmaximal, characteristic, complemented
26#34082C211yesmaximal, characteristic, complemented
27C2×#2313C211yesmaximal, characteristic, complemented
28C2×#525C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31#2866C2214yescomplemented
32#2865C2214yescomplemented
33#2864C2214yescomplemented
34#2863C2214yescomplemented
35#2857C2211yescharacteristic
36#2857C2212yes—
37#2856C2211yescharacteristic
38#2855C2214yescomplemented
39#2853C2214yescomplemented
40#2852C2214yescomplemented
41#2851C2212yes—
42#2851C2214yescomplemented
43#2850C2211yescharacteristic
44#2850C2211yescharacteristic
45#2849C2212yes—
46#2849C2212yes—
47#2849C2212yes—
48#2849C2212yes—
49#2802C2214yescomplemented
50#2800C2214yescomplemented
51#2799C2214yescomplemented
52#2796C2214yescomplemented
53#2794C2214yescomplemented
54#2793C2214yescomplemented
55#2791C2214yescomplemented
56#2790C2214yescomplemented
57#2789C2214yescomplemented
58#2786C2214yescomplemented
59#2780C2214yescomplemented
60#2777C2214yescomplemented
61#2776C2214yescomplemented
62#2772C2214yescomplemented
63#2771C2214yes—
64#2767C2214yescomplemented
65#2766C2214yescomplemented
66#2765C2214yes—
67#2765C2214yes—
68#2765C2214yescomplemented
69#2764C2214yes—
70#2762C2214yescomplemented
71#2761C2214yes—
72#2761C2214yes—
73#2761C2214yescomplemented
74#2760C2214yes—
75#2758C2214yescomplemented
76#2755C2214yescomplemented
77#2752C2214yes—
78#2751C2214yes—
79#2751C2214yes—
80#2751C2214yescomplemented
81#2750C2214yes—
82#2750C2214yes—
83#2749C2214yes—
84#2749C2214yes—
85#2746C2214yes—
86#2745C2214yes—
87#2744C2214yes—
88#2743C2214yes—
89#2743C2214yes—
90#2743C2214yes—
91#2740C2214yes—
92#2740C2214yescomplemented
93#2739C2214yes—
94#2739C2214yescomplemented
95#2738C2214yes—
96#2737C2214yes—
97#2729C2214yescomplemented
98#2719C2214yescomplemented
99#2716C2214yescomplemented
100#2715C2214yescomplemented
101#2713C2214yescomplemented
102#2709C2214yescomplemented
103#2707C2214yes—
104#2707C2214yescomplemented
105#2706C2214yes—
106#2705C2214yes—
107#2700C2214yescomplemented
108#2696C2214yes—
109#2695C2214yes—
110#2694C2214yes—
111#2693C2214yes—
112#2687C2214yes—
113#2655C2214yescomplemented
114#2655C2214yescomplemented
115#2654C2214yescomplemented
116#2653C2214yescomplemented
117#2652C2214yescomplemented
118#2652C2214yescomplemented
119#2650C2214yescomplemented
120#2649C2214yescomplemented
121#2627C2212yes—
122#2627C2212yes—
123#2626C2214yes—
124#2618C2212yes—
125#2618C2212yes—
126#2617C2214yes—
127#2608C2212yes—
128#2608C2212yes—
129#2607C2212yes—
130#2607C2212yes—
131#2602C2214yes—
132#2602C2214yes—
133#2591C2212yes—
134#2591C2212yes—
135#2590C2214yescomplemented
136#2589C2214yescomplemented
137#2588C2214yescomplemented
138#2587C2214yescomplemented
139#2583C2212yes—
140#2583C2212yes—
141#2579C2214yes—
142#2579C2214yes—
143#2578C2214yescomplemented
144#2577C2214yescomplemented
145#2576C2214yescomplemented
146#2575C2214yescomplemented
147#2533C2214yescomplemented
148#2530C2214yescomplemented
149#2528C2214yescomplemented
150#2527C2214yescomplemented
151#2510C2214yes—
152#2505C2214yes—
153#2500C2211yescharacteristic
154#2500C2211yescharacteristic
155#2499C2211yescharacteristic
156#2499C2211yescharacteristic
157#2493C2214yes—
158#2493C2214yes—
159#2488C2214yes—
160#2488C2214yes—
161#2484C2212yes—
162#2484C2212yes—
163#2481C2214yes—
164#2478C2214yescomplemented
165#2477C2214yescomplemented
166#2475C2214yescomplemented
167#2473C2214yes—
168#2470C2214yescomplemented
169#2450C2214yes—
170#2449C2214yes—
171#2444C2214yes—
172#2443C2214yes—
173#2441C2212yes—
174#2441C2212yes—
175#2439C2212yes—
176#2439C2212yes—
177#2432C2211yescharacteristic
178#2432C2211yescharacteristic
179#2431C2211yescharacteristic
180#2431C2211yescharacteristic
181#2425C2214yes—
182#2425C2214yes—
183#2419C2214yes—
184#2419C2214yes—
185#2413C2212yes—
186#2413C2212yes—
187#2413C2212yes—
188#2413C2212yes—
189#2406C2212yes—
190#2406C2212yes—
191#2335C2214yes—
192#2335C2214yes—
193#2333C2212yes—
194#2333C2212yes—
195#2332C2212yes—
196#2332C2212yes—
197#2329C2212yes—
198#2329C2212yes—
199#2329C2214yes—
200#2325C2212yes—
201#2325C2212yes—
202#2325C2214yes—
203#2322C2214yes—
204#2322C2214yes—
205#2321C2214yes—
206#2321C2214yes—
207#2313C2214yes—
208#2313C2214yes—
209#2313C2212yes—
210#2313C2212yes—
211#2313C2212yes—
212#2313C2212yes—
213#2298C2212yes—
214#2298C2212yes—
215#2297C2212yes—
216#2297C2212yes—
217#2293C2212yes—
218#2293C2212yes—
219#2290C2212yes—
220#2290C2212yes—
221#2290C2212yes—
222#2290C2212yes—
223C2×#387C2212yes—
224C2×#387C2212yes—
225C2×#387C2212yes—
226C2×#387C2212yes—
227#2280C2211yescharacteristic
228#2280C2211yescharacteristic
229C2×#381C2212yes—
230C2×#380C2212yes—
231C42×D4C2212yes—
232C42×D4C2212yes—
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2311yescharacteristic
237C24×C4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2312yes—
242C2×#127C2311yescharacteristic
243C2×#126C2314yes—
244C2×#125C2312yes—
245C2×#125C2314yes—
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248#525—28no—
249#525—28no—
250C2×#123C2312yes—
251C2×#123C2312yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2312yes—
255C2×#123C2312yes—
256C2×#123C2312yes—
257C2×#123C2312yes—
258C2×#123C2314yes—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#121C2311yescharacteristic
269C2×#121C2314yes—
270C2×#120C2312yes—
271C2×#120C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2312yes—
285C2×#117C2312yes—
286C22×C4⋊C4—28no—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2312yes—
300C22×C42C2312yes—
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303#401C2314yes—
304#401C2314yes—
305#401C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#392C2314yes—
398#392C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2314yes—
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2314yes—
411#390C2314yes—
412#390C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2314yes—
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2312yes—
431#389C2312yes—
432#389C2314yes—
433#389C2314yes—
434#389C2312yes—
435#389C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2312yes—
548#386C2312yes—
549#386C2312yes—
550#386C2312yes—
551#386C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2312yes—
573#385C2312yes—
574#385C2312yes—
575#385C2312yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#384C2311yescharacteristic
580#384C2312yes—
581#384C2311yescharacteristic
582#383C2314yes—
583#383C2314yes—
584#383C2314yes—
585#382C2314yes—
586#382C2314yes—
587#382C2311yescharacteristic
588#382C2311yescharacteristic
589#382C2312yes—
590#382C2314yes—
591#381C2314yes—
592#381C2314yes—
593#381C2314yes—
594#381C2314yes—
595#381C2314yes—
596#381C2314yes—
597#381C2314yes—
598#381C2314yes—
599#381C2312yes—
600#381C2312yes—
601#381C2312yes—
602#381C2312yes—
603#381C2312yes—
604#381C2312yes—
605#381C2314yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611#380C2314yes—
612#380C2312yes—
613#380C2312yes—
614#380C2312yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619#379C2312yes—
620#379C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C22⋊C4C2312yes—
628C4×C22⋊C4C2312yes—
629C4×C22⋊C4C2312yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2311yescharacteristic
634C4×C22⋊C4C2311yescharacteristic
635C4×C22⋊C4C2311yescharacteristic
636C4×C22⋊C4C2311yescharacteristic
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2312yes—
649#376C2312yes—
650#376C2312yes—
651C2×#95C2312yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C43C2312yes—
660C43C2312yes—
661C25C2411yescharacteristic
662C2×#41—24no—
663C2×#41—24no—
664C2×#41—81no—
665C2×#41—81no—
666C2×#41—81no—
667C2×#41—81no—
668C22×Q8C2411yescharacteristic
669C22×Q8C2411yescharacteristic
670C22×Q8C2414yes—
671C22×D4C2412yes—
672C22×D4C2412yes—
673C22×D4C2412yes—
674C22×D4C2412yes—
675C22×D4C2412yes—
676C22×D4C2412yes—
677C22×D4C2411yescharacteristic
678C22×D4C2411yescharacteristic
679C22×D4C2414yes—
680C23×C4—24no—
681C23×C4—24no—
682C23×C4—44no—
683C23×C4—81no—
684C23×C4—81no—
685C23×C4—81no—
686C23×C4—81no—
687C23×C4#4118yes—
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2411yescharacteristic
708C4⋊Q8—82no—
709C4⋊Q8—81no—
710#127—81no—
711#126—84no—
712#125—84no—
713#125—82no—
714#124—81no—
715#124—81no—
716#123—28no—
717#123—28no—
718#123—48no—
719#123—48no—
720#123—82no—
721#123—84no—
722#123—82no—
723#123—82no—
724#123—82no—
725C22⋊Q8—24no—
726C22⋊Q8—24no—
727C22⋊Q8—24no—
728C22⋊Q8—24no—
729C22⋊Q8—48no—
730C22⋊Q8—84no—
731#121—24no—
732#121—24no—
733#121—24no—
734#121—24no—
735#121—48no—
736#120—28no—
737#120—28no—
738C4×D4—28no—
739C4×D4—28no—
740C4×D4—28no—
741C4×D4—28no—
742C4×D4—48no—
743C4×D4—48no—
744#117—24no—
745#117—24no—
746#117—81no—
747#117—81no—
748#117—82no—
749#117—82no—
750#117—81no—
751#117—81no—
752C2×C4⋊C4—28no—
753C2×C4⋊C4—28no—
754C2×C4⋊C4—28no—
755C2×C4⋊C4—28no—
756C2×C4⋊C4—28no—
757C2×C4⋊C4—28no—
758C2×C4⋊C4—82no—
759C2×C4⋊C4—82no—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C22⋊C4—44no—
807C2×C22⋊C4—44no—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C42—81no—
853C2×C42—81no—
854C2×C42—82no—
855C2×C42—82no—
856C2×C42—81no—
857C2×C42—81no—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942C24—24no—
943C24—41no—
944C24—41no—
945C24—42no—
946C24C2×#4114yes—
947C24C2512yes—
948C24C2512yes—
949C24C2511yescharacteristic
950C24C2511yescharacteristic
951C24C2511yescharacteristic
952#41—88no—
953#41—88no—
954C2×Q8—22no—
955C2×Q8—22no—
956C2×Q8—41no—
957C2×Q8—41no—
958C2×Q8—41no—
959C2×Q8—41no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—24no—
971C2×D4—22no—
972C2×D4—22no—
973C2×D4—42no—
974C2×D4—42no—
975C2×D4—42no—
976C2×D4—42no—
977C2×D4—41no—
978C2×D4—41no—
979C2×D4—41no—
980C2×D4—41no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—416no—
1039C22×C4—88no—
1040C22×C4—88no—
1041C22×C4C2×#4114yes—
1042C22×C4C2×#4114yes—
1043C22×C4C2×#4114yes—
1044C22×C4C2×#4114yes—
1045C22×C4C2×#4114yes—
1046C22×C4C2×#4114yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—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—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—42no—
1143C22⋊C4—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C42—24no—
1160C42—24no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—41no—
1168C42—41no—
1169C42—42no—
1170C42—44no—
1171C42—44no—
1172C42—41no—
1173C42—42no—
1174C42—41no—
1175C42—44no—
1176C42—44no—
1177C42—42no—
1178C42—42no—
1179C42—44no—
1180C42—44no—
1181C23—21no—
1182C23—21no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—22no—
1191C23—22no—
1192C23—28no—
1193C23—22no—
1194C23—22no—
1195C23—24no—
1196C23—24no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—24no—
1202C23—24no—
1203C23—44no—
1204C23—44no—
1205C23—48no—
1206C23—48no—
1207C23C22×#4112yes—
1208C23C22×#4112yes—
1209C23C22×#4112yes—
1210C23#58514yes—
1211C23C2611yescharacteristic
1212Q8—82no—
1213Q8—82no—
1214Q8—164no—
1215D4—48no—
1216D4—48no—
1217D4—82no—
1218D4—82no—
1219D4—84no—
1220D4—84no—
1221D4—84no—
1222D4—84no—
1223D4—164no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—44no—
1283C2×C4—44no—
1284C2×C4—44no—
1285C2×C4—44no—
1286C2×C4—44no—
1287C2×C4—44no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—48no—
1292C2×C4—48no—
1293C2×C4—48no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—88no—
1301C2×C4—88no—
1302C2×C4C22×#4112yes—
1303C2×C4C22×#4112yes—
1304C2×C4C22×#4112yes—
1305C2×C4C22×#4112yes—
1306C22—22no—
1307C22—22no—
1308C22—24no—
1309C22—24no—
1310C22—22no—
1311C22—22no—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—416no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—42no—
1330C22—42no—
1331C22#345514yes—
1332C22C23×#4111yescharacteristic
1333C22C2×#58512yes—
1334C22H(7,𝔽2)11yescharacteristic
1335C22H(7,𝔽2)11yescharacteristic
1336C222−1+612yes—
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—22no—
1341C4—44no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—44no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—44no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4—44no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C2—24no—
1360C2—42no—
1361C2—42no—
1362C2—82no—
1363C2—82no—
1364C2C2×#345511yescharacteristic
1365C2#6284411yescharacteristic
1366C2#6286011yescharacteristic
1367C2#6286812yes—
1368C2#6286812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35032C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37019C2semidirect
2. #37017C2semidirect
3. #37013C2semidirect
4. #37011C2semidirect
5. #36994C2semidirect
6. #36989C2semidirect
7. #36974C2semidirect
8. #36821C2semidirect
9. #36819C2semidirect
10. #36815C2semidirect
11. #36813C2semidirect
12. #36788C2semidirect
13. #36783C2semidirect
14. #36764C2semidirect
15. #36763C2semidirect
16. #36762C2semidirect
17. #36761C2semidirect
18. #36726C2semidirect
19. #35069C2semidirect
20. #35067C2semidirect
21. #35057C2semidirect
22. #35057C2semidirect
23. #35033C2semidirect
25. #34082C2semidirect
26. #34082C2semidirect
27. C2×#2313C2semidirect
31. #2866C22semidirect
32. #2865C22semidirect
33. #2864C22semidirect
34. #2863C22semidirect
38. #2855C22semidirect
39. #2853C22semidirect
40. #2852C22semidirect
42. #2851C22semidirect
49. #2802C22semidirect
50. #2800C22semidirect
51. #2799C22semidirect
52. #2796C22semidirect
53. #2794C22semidirect
54. #2793C22semidirect
55. #2791C22semidirect
56. #2790C22semidirect
57. #2789C22semidirect
58. #2786C22semidirect
59. #2780C22semidirect
60. #2777C22semidirect
61. #2776C22semidirect
62. #2772C22semidirect
64. #2767C22semidirect
65. #2766C22semidirect
68. #2765C22semidirect
70. #2762C22semidirect
73. #2761C22semidirect
75. #2758C22semidirect
76. #2755C22semidirect
80. #2751C22semidirect
92. #2740C22semidirect
94. #2739C22semidirect
97. #2729C22semidirect
98. #2719C22semidirect
99. #2716C22semidirect
100. #2715C22semidirect
101. #2713C22semidirect
102. #2709C22semidirect
104. #2707C22semidirect
107. #2700C22semidirect
113. #2655C22semidirect
114. #2655C22semidirect
115. #2654C22semidirect
116. #2653C22semidirect
117. #2652C22semidirect
118. #2652C22semidirect
119. #2650C22semidirect
120. #2649C22semidirect
135. #2590C22semidirect
136. #2589C22semidirect
137. #2588C22semidirect
138. #2587C22semidirect
143. #2578C22semidirect
144. #2577C22semidirect
145. #2576C22semidirect
146. #2575C22semidirect
147. #2533C22semidirect
148. #2530C22semidirect
149. #2528C22semidirect
150. #2527C22semidirect
164. #2478C22semidirect
165. #2477C22semidirect
166. #2475C22semidirect
168. #2470C22semidirect

Maximal subgroups

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

subgroupindex
#370192
#370172
#370132
#370112
#369942
#369892
#369742
#368212
#368192
#368152
#368132
#367882
#367832
#367642
#367632
#367622
#367612
#367262
#350692
#350672
#350572
#350332
#350322
#340822
C2×#23132