Finite Group Databasebeta

← #7699047

Subgroups — #7699047

Order 512.

5329 conjugacy classes of subgroups.

The subgroup lattice has 1453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59946C211yesmaximal, characteristic, complemented
2#59891C214yesmaximal, complemented
3#59425C212yesmaximal, complemented
4#59340C212yesmaximal, complemented
5#52257C211yesmaximal, characteristic, complemented
6C2×#2789C212yesmaximal, complemented
7#45340C212yesmaximal, complemented
8#45308C211yesmaximal, characteristic, complemented
9#45251C211yesmaximal, characteristic, complemented
10#45117C212yesmaximal, complemented
11#44795C212yesmaximal, complemented
12#44474C214yesmaximal, complemented
13#43623C214yesmaximal, complemented
14#43342C212yesmaximal, complemented
15#39566C212yesmaximal, complemented
16#39559C214yesmaximal, complemented
17#38251C212yesmaximal, complemented
18#38245C214yesmaximal, complemented
19#38115C214yesmaximal, complemented
20#38113C212yesmaximal, complemented
21#36219C212yesmaximal, complemented
22#36164C211yesmaximal, characteristic, complemented
23#36085C211yesmaximal, characteristic
24#36067C212yesmaximal, complemented
25#36053C212yesmaximal, complemented
26#35998C211yesmaximal, characteristic, complemented
27#34289C212yesmaximal, complemented
28#34260C212yesmaximal, complemented
29#34259C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×#547C2212yes—
33C2×#547C2211yescharacteristic
34C2×#520C2212yes—
35C2×#520C2211yescharacteristic
36C2×C4×#41C2212yes—
37#2862C2211yescharacteristic
38#2855C2214yes—
39#2851C2212yes—
40#2850C2212yes—
41#2799C2211yescharacteristic
42#2799C2214yes—
43#2798C2212yes—
44#2798C2214yes—
45#2797C2212yes—
46#2796C2212yes—
47#2796C2214yes—
48#2789C2211yescharacteristic
49#2789C2214yes—
50#2789C2214yes—
51#2789C2212yes—
52#2789C2214yes—
53#2789C2212yes—
54#2789C2214yes—
55#2789C2214yes—
56#2789C2212yes—
57#2789C2214yes—
58#2786C2212yes—
59#2782C2211yescharacteristic
60#2778C2212yes—
61#2762C2214yes—
62#2760C2212yes—
63#2759C2214yes—
64#2758C2214yes—
65#2758C2214yes—
66#2755C2214yes—
67#2755C2214yes—
68#2754C2214yes—
69#2751C2214yes—
70#2747C2214yes—
71#2746C2214yes—
72#2746C2214yes—
73#2745C2214yes—
74#2744C2214yes—
75#2742C2212yes—
76#2740C2214yes—
77#2738C2214yes—
78#2730C2212yes—
79#2728C2211yescharacteristic
80#2717C2212yes—
81#2645C2212yes—
82#2643C2214yes—
83#2625C2212yes—
84#2625C2211yescharacteristic
85#2623C2214yes—
86#2623C2212yes—
87#2616C2211yescharacteristic
88#2614C2212yes—
89#2612C2212yes—
90#2609C2212yes—
91#2607C2212yes—
92#2605C2214yes—
93#2605C2214yes—
94#2595C2214yes—
95#2589C2214yes—
96#2588C2214yes—
97#2588C2214yes—
98#2586C2212yes—
99#2581C2212yes—
100#2579C2214yes—
101#2577C2214yes—
102#2576C2214yes—
103#2576C2214yes—
104#2568C2211yescharacteristic
105#2565C2212yes—
106#2564C2214yes—
107#2563C2211yescharacteristic
108#2531C2214yes—
109#2530C2214yes—
110#2527C2214yes—
111#2527C2214yes—
112#2523C2214yes—
113#2523C2212yes—
114#2522C2214yes—
115#2520C2214yes—
116#2520C2214yes—
117#2517C2214yes—
118#2516C2214yes—
119#2515C2214yes—
120#2515C2214yes—
121#2514C2212yes—
122#2514C2212yes—
123#2514C2212yes—
124#2510C2214yes—
125#2510C2214yes—
126#2510C2214yes—
127#2510C2214yes—
128#2510C2214yes—
129#2505C2214yes—
130#2505C2214yes—
131#2504C2212yes—
132#2503C2212yes—
133#2503C2212yes—
134#2502C2211yescharacteristic
135#2498C2214yes—
136#2498C2212yes—
137#2494C2212yes—
138#2494C2212yes—
139#2494C2212yes—
140#2493C2214yes—
141#2493C2214yes—
142#2493C2214yes—
143#2493C2214yes—
144#2493C2214yes—
145#2489C2212yes—
146#2489C2212yes—
147#2488C2214yes—
148#2488C2214yes—
149#2487C2212yes—
150#2486C2211yescharacteristic
151#2484C2212yes—
152#2484C2214yes—
153#2471C2214yes—
154#2453C2212yes—
155#2451C2212yes—
156#2450C2214yes—
157#2449C2214yes—
158#2446C2212yes—
159#2446C2212yes—
160#2446C2212yes—
161#2444C2214yes—
162#2444C2214yes—
163#2443C2214yes—
164#2441C2212yes—
165#2439C2212yes—
166#2438C2214yes—
167#2438C2214yes—
168#2438C2214yes—
169#2434C2211yescharacteristic
170#2434C2212yes—
171#2430C2214yes—
172#2430C2212yes—
173#2423C2212yes—
174#2421C2212yes—
175#2421C2212yes—
176#2419C2214yes—
177#2419C2214yes—
178#2419C2214yes—
179#2409C2211yescharacteristic
180#2409C2212yes—
181#2406C2212yes—
182#2406C2214yes—
183#2401C2212yes—
184C2×#401C2214yes—
185#2395C2212yes—
186#2395C2211yescharacteristic
187C2×#400C2214yes—
188C2×#398C2212yes—
189#2388C2211yescharacteristic
190C2×#395C2212yes—
191#2374C2212yes—
192#2365C2212yes—
193#2364C2214yes—
194#2362C2212yes—
195#2360C2212yes—
196#2359C2214yes—
197#2359C2214yes—
198#2356C2212yes—
199#2355C2212yes—
200#2353C2214yes—
201#2352C2212yes—
202#2352C2214yes—
203#2349C2212yes—
204#2349C2212yes—
205#2349C2212yes—
206D4×C4⋊C4C2212yes—
207#2345C2212yes—
208#2344C2212yes—
209#2344C2214yes—
210#2343C2214yes—
211#2343C2214yes—
212#2343C2214yes—
213Q8×C22⋊C4C2212yes—
214Q8×C22⋊C4C2212yes—
215Q8×C22⋊C4C2212yes—
216Q8×C22⋊C4C2212yes—
217#2339C2212yes—
218#2339C2212yes—
219#2339C2214yes—
220#2339C2214yes—
221#2339C2214yes—
222#2339C2212yes—
223#2339C2212yes—
224#2339C2212yes—
225#2339C2211yescharacteristic
226#2339C2214yes—
227#2339C2212yes—
228#2339C2211yescharacteristic
229#2327C2212yes—
230#2325C2214yes—
231#2323C2212yes—
232#2322C2214yes—
233#2320C2212yes—
234#2318C2214yes—
235#2314C2212yes—
236#2313C2214yes—
237#2311C2214yes—
238#2311C2212yes—
239#2310C2212yes—
240#2310C2214yes—
241C4×#124C2211yescharacteristic
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×#123C2214yes—
245#2298C2212yes—
246#2297C2212yes—
247#2297C2214yes—
248#2295C2212yes—
249C2×#391C2214yes—
250C2×#391C2212yes—
251#2290C2212yes—
252#2290C2214yes—
253C2×#387C2214yes—
254C2×#387C2214yes—
255C2×#387C2214yes—
256C2×#382C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C2×2−1+4—216no—
260C2×2−1+4—44no—
261C22×#41C2311yescharacteristic
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2314yes—
265C22×#41C2312yes—
266C22×#41C2312yes—
267C23×Q8C2312yes—
268C23×Q8C2312yes—
269C23×Q8C2311yescharacteristic
270#554—44no—
271#547—216no—
272#547—44no—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×#125C2312yes—
277C2×#124C2311yescharacteristic
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2312yes—
290C2×#121C2314yes—
291C2×#121C2312yes—
292#520—216no—
293#520—44no—
294C4×#41—48no—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×#117C2312yes—
315C2×#117C2314yes—
316C2×#117C2314yes—
317C2×#117C2312yes—
318C2×#117C2311yescharacteristic
319C2×#117C2314yes—
320C2×#117C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2314yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2312yes—
329C22×C42C2312yes—
330C22×C42C2312yes—
331C22×C42C2314yes—
332#401C2314yes—
333#401C2314yes—
334#401C2314yes—
335#401C2312yes—
336#401C2314yes—
337#401C2314yes—
338#401C2314yes—
339#401C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2311yescharacteristic
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2312yes—
363#400C2312yes—
364#400C2312yes—
365#400C2314yes—
366#399C2314yes—
367#399C2312yes—
368#399C2314yes—
369#399C2314yes—
370#399C2311yescharacteristic
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2312yes—
381#398C2311yescharacteristic
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2311yescharacteristic
392#397C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2312yes—
403#397C2312yes—
404#397C2312yes—
405#396C2314yes—
406#396C2314yes—
407#396C2312yes—
408#395C2314yes—
409#395C2314yes—
410#395C2312yes—
411#395C2312yes—
412#395C2314yes—
413#395C2314yes—
414#395C2312yes—
415#395C2311yescharacteristic
416#395C2314yes—
417#395C2312yes—
418#394C2312yes—
419#394C2312yes—
420#394C2314yes—
421#394C2311yescharacteristic
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#393C2312yes—
426#393C2312yes—
427#393C2314yes—
428#393C2314yes—
429#393C2311yescharacteristic
430#393C2312yes—
431#392C2312yes—
432#392C2311yescharacteristic
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2311yescharacteristic
455#391C2314yes—
456#391C2312yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#391C2312yes—
468#390C2312yes—
469#390C2314yes—
470#390C2312yes—
471#390C2311yescharacteristic
472#390C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#388C2314yes—
488#388C2314yes—
489#388C2312yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2314yes—
506#388C2312yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2312yes—
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#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2312yes—
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#387C2312yes—
565#387C2314yes—
566#387C2312yes—
567#387C2312yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2312yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2312yes—
582#386C2314yes—
583#386C2312yes—
584#386C2314yes—
585#386C2312yes—
586#386C2312yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2312yes—
592#386C2312yes—
593#386C2314yes—
594#385C2312yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2312yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#384C2312yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#383C2314yes—
622#383C2314yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2314yes—
634#382C2311yescharacteristic
635#381C2314yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2312yes—
646#381C2312yes—
647#381C2312yes—
648#381C2314yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2314yes—
655#380C2312yes—
656#380C2312yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2311yescharacteristic
665#380C2311yescharacteristic
666#380C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702#376C2312yes—
703#376C2314yes—
704#376C2314yes—
705C2×#95C2314yes—
706C2×#95C2314yes—
707C2×#95C2314yes—
708C2×#95C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
7202−1+4—464no—
721C2×#41—28no—
722C2×#41—28no—
723C2×#41—216no—
724C2×#41—216no—
725C2×#41—28no—
726C2×#41—28no—
727C2×#41—24no—
728C2×#41—24no—
729C2×#41—28no—
730C2×#41—216no—
731C2×#41—42no—
732C2×#41—48no—
733C2×#41—44no—
734C2×#41#41116yes—
735C22×Q8—28no—
736C22×Q8—28no—
737C22×Q8—216no—
738C22×Q8—28no—
739C22×Q8—44no—
740C22×Q8—44no—
741C22×Q8—42no—
742C22×Q8C2411yescharacteristic
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2414yes—
746C22×Q8C2412yes—
747C22×Q8C2412yes—
748C22×Q8C2411yescharacteristic
749C22×Q8C2412yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2411yescharacteristic
753C22×D4C2412yes—
754C22×D4C2414yes—
755C22×D4C2411yescharacteristic
756C22×D4C2412yes—
757C22×D4C2411yescharacteristic
758C23×C4C2412yes—
759C23×C4C2411yescharacteristic
760C23×C4C2412yes—
761C23×C4C2411yescharacteristic
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2412yes—
765C23×C4C2414yes—
766C23×C4C2412yes—
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2414yes—
771C23×C4C2414yes—
772C23×C4C2414yes—
773C23×C4C2412yes—
774C23×C4C2412yes—
775C23×C4C2412yes—
776C4⋊Q8—28no—
777C4⋊Q8—42no—
778C4⋊Q8—42no—
779#125—44no—
780#124—42no—
781#123—216no—
782#123—216no—
783#123—44no—
784#123—44no—
785#123—44no—
786C22⋊Q8—28no—
787C22⋊Q8—28no—
788C22⋊Q8—44no—
789C22⋊Q8—48no—
790C22⋊Q8—44no—
791C22⋊Q8—42no—
792C22⋊Q8—42no—
793#121—216no—
794#121—44no—
795C4×Q8—28no—
796C4×Q8—28no—
797C4×Q8—42no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×D4—216no—
802C4×D4—216no—
803C4×D4—28no—
804C4×D4—28no—
805C4×D4—28no—
806C4×D4—28no—
807C4×D4—28no—
808C4×D4—24no—
809C4×D4—28no—
810C4×D4—42no—
811C4×D4—48no—
812C4×D4—48no—
813C4×D4—48no—
814#117—216no—
815#117—28no—
816#117—42no—
817#117—48no—
818#117—48no—
819#117—44no—
820#117—44no—
821C2×C4⋊C4—216no—
822C2×C4⋊C4—28no—
823C2×C4⋊C4—216no—
824C2×C4⋊C4—48no—
825C2×C4⋊C4—42no—
826C2×C4⋊C4—44no—
827C2×C4⋊C4—44no—
828C2×C4⋊C4—44no—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2411yescharacteristic
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C42—44no—
920C2×C42—44no—
921C2×C42—48no—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2411yescharacteristic
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2412yes—
955#95C2411yescharacteristic
956#95C2411yescharacteristic
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#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2411yescharacteristic
1015#95C2411yescharacteristic
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027C24C2511yescharacteristic
1028C24C2511yescharacteristic
1029C24C2512yes—
1030C24C2512yes—
1031#41—264no—
1032#41—416no—
1033#41—464no—
1034#41—432no—
1035#41—416no—
1036#41—416no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—28no—
1040C2×Q8—28no—
1041C2×Q8—24no—
1042C2×Q8—28no—
1043C2×Q8—24no—
1044C2×Q8—24no—
1045C2×Q8—22no—
1046C2×Q8—22no—
1047C2×Q8—22no—
1048C2×Q8—41no—
1049C2×Q8—44no—
1050C2×Q8—42no—
1051C2×Q8—41no—
1052C2×Q8—41no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—432no—
1056C2×Q8—432no—
1057C2×Q8—416no—
1058C2×Q8C2×#4118yes—
1059C2×D4—28no—
1060C2×D4—28no—
1061C2×D4—28no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—28no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—22no—
1070C2×D4—42no—
1071C2×D4—41no—
1072C2×D4—41no—
1073C2×D4—41no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4C2×#41116yes—
1077C2×D4C2×#4118yes—
1078C2×D4H(5,𝔽2)14yes—
1079C22×C4—28no—
1080C22×C4—28no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—28no—
1085C22×C4—28no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—28no—
1090C22×C4—28no—
1091C22×C4—28no—
1092C22×C4—28no—
1093C22×C4—28no—
1094C22×C4—28no—
1095C22×C4—24no—
1096C22×C4—28no—
1097C22×C4—28no—
1098C22×C4—24no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—24no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—42no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—42no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4C2×#41116yes—
1127C22×C4C2×#4118yes—
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2514yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2514yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2512yes—
1147C22×C4C2511yescharacteristic
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C4⋊C4—24no—
1154C4⋊C4—28no—
1155C4⋊C4—24no—
1156C4⋊C4—28no—
1157C4⋊C4—28no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—28no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—28no—
1171C4⋊C4—41no—
1172C4⋊C4—42no—
1173C4⋊C4—41no—
1174C4⋊C4—41no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—41no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—28no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—28no—
1215C22⋊C4—24no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—41no—
1235C22⋊C4—41no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C42—28no—
1244C42—28no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—24no—
1250C42—22no—
1251C42—22no—
1252C42—24no—
1253C42—42no—
1254C42—44no—
1255C42—42no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—41no—
1260C42—44no—
1261C42—44no—
1262C42—42no—
1263C42—44no—
1264C42—44no—
1265C23—22no—
1266C23—24no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—21no—
1277C23—21no—
1278C23—21no—
1279C23—21no—
1280C23—22no—
1281C23—22no—
1282C23—21no—
1283C23—21no—
1284C23C22×#4114yes—
1285C23C22×#4118yes—
1286C23C2×H(5,𝔽2)14yes—
1287C23C2611yescharacteristic
1288Q8—216no—
1289Q8—44no—
1290Q8—416no—
1291Q8—48no—
1292Q8—44no—
1293Q8—44no—
1294Q8—82no—
1295Q8—162no—
1296D4—232no—
1297D4—48no—
1298D4—44no—
1299D4—48no—
1300D4—48no—
1301D4—82no—
1302D4—84no—
1303D4#551116yes—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—21no—
1310C2×C4—232no—
1311C2×C4—216no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—48no—
1371C2×C4—48no—
1372C2×C4—416no—
1373C2×C4—48no—
1374C2×C4—48no—
1375C2×C4—44no—
1376C2×C4—44no—
1377C2×C4—88no—
1378C2×C4—88no—
1379C2×C4—88no—
1380C2×C4—88no—
1381C2×C4—88no—
1382C2×C4—88no—
1383C2×C4—84no—
1384C2×C4—84no—
1385C2×C4—162no—
1386C2×C4C22×#4118yes—
1387C2×C4C22×#4114yes—
1388C2×C4C22×#4114yes—
1389C2×C4C2×H(5,𝔽2)12yes—
1390C2×C4#58512yes—
1391C22—28no—
1392C22—24no—
1393C22—28no—
1394C22—24no—
1395C22—24no—
1396C22—24no—
1397C22—24no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—41no—
1405C22—41no—
1406C22—42no—
1407C22—42no—
1408C22—41no—
1409C22—41no—
1410C22—41no—
1411C22—41no—
1412C22C2×#55118yes—
1413C22C23×#4112yes—
1414C22C22×H(5,𝔽2)11yescharacteristic
1415C22C2×#58511yescharacteristic
1416C222−1+612yes—
1417C222−1+611yescharacteristic
1418C4—22no—
1419C4—24no—
1420C4—28no—
1421C4—42no—
1422C4—42no—
1423C4—44no—
1424C4—44no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—44no—
1429C4—41no—
1430C4—42no—
1431C4—42no—
1432C4—44no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—44no—
1437C4—42no—
1438C4—41no—
1439C4—41no—
1440C4—42no—
1441C4—42no—
1442C4C2×#55114yes—
1443C2—28no—
1444C2—44no—
1445C2—81no—
1446C2—81no—
1447C2C22×#55111yescharacteristic
1448C2#6286112yes—
1449C2#6289811yescharacteristic
1450C2#6299512yes—
1451C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36085C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59946C2semidirect
2. #59891C2semidirect
3. #59425C2semidirect
4. #59340C2semidirect
5. #52257C2semidirect
6. C2×#2789C2semidirect
7. #45340C2semidirect
8. #45308C2semidirect
9. #45251C2semidirect
10. #45117C2semidirect
11. #44795C2semidirect
12. #44474C2semidirect
13. #43623C2semidirect
14. #43342C2semidirect
15. #39566C2semidirect
16. #39559C2semidirect
17. #38251C2semidirect
18. #38245C2semidirect
19. #38115C2semidirect
20. #38113C2semidirect
21. #36219C2semidirect
22. #36164C2semidirect
24. #36067C2semidirect
25. #36053C2semidirect
26. #35998C2semidirect
27. #34289C2semidirect
28. #34260C2semidirect
29. #34259C2semidirect

Maximal subgroups

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

subgroupindex
#599462
#598912
#594252
#593402
#522572
C2×#27892
#453402
#453082
#452512
#451172
#447952
#444742
#436232
#433422
#395662
#395592
#382512
#382452
#381152
#381132
#362192
#361642
#360852
#360672
#360532
#359982
#342892
#342602
#342592