Finite Group Databasebeta

← #8701679

Subgroups — #8701679

Order 512.

4213 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59927C212yesmaximal, complemented
2#59922C212yesmaximal, complemented
3#59292C212yesmaximal, complemented
4#59218C212yesmaximal, complemented
5#54908C214yesmaximal, complemented
6#54742C214yesmaximal, complemented
7#54261C214yesmaximal, complemented
8#52303C211yesmaximal, characteristic
9#52077C214yesmaximal, complemented
10#50983C214yesmaximal, complemented
11#50338C214yesmaximal, complemented
12#46158C211yesmaximal, characteristic, complemented
13#46153C211yesmaximal, characteristic, complemented
14#46147C211yesmaximal, characteristic, complemented
15#45310C212yesmaximal, complemented
16#45025C212yesmaximal, complemented
17#45017C212yesmaximal, complemented
18#42935C212yesmaximal, complemented
19#42849C212yesmaximal, complemented
20#42455C212yesmaximal, complemented
21#40004C212yesmaximal, complemented
22#39658C212yesmaximal, complemented
23#39353C212yesmaximal, complemented
24#37191C212yesmaximal, complemented
25#37152C212yesmaximal
26#37143C212yesmaximal, complemented
27#36447C211yesmaximal, characteristic, complemented
28#36312C211yesmaximal, characteristic, complemented
29#36312C211yesmaximal, characteristic, complemented
30C2×#563C2212yes—
31C2×#541C2214yes—
32#2860C2212yes—
33#2860C2212yes—
34#2859C2212yes—
35#2859C2211yescharacteristic
36#2859C2211yescharacteristic
37#2859C2211yescharacteristic
38#2857C2212yes—
39#2845C2212yes—
40#2839C2214yes—
41#2837C2214yes—
42#2836C2214yes—
43#2822C2212yes—
44#2820C2212yes—
45#2808C2211yescharacteristic
46#2806C2211yescharacteristic
47#2805C2212yes—
48#2802C2214yes—
49#2802C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2800C2214yes—
53#2793C2214yes—
54#2791C2214yes—
55#2790C2214yes—
56#2788C2214yes—
57#2783C2214yes—
58#2783C2212yes—
59#2783C2214yes—
60#2781C2214yes—
61#2781C2212yes—
62#2773C2214yes—
63#2772C2214yes—
64#2772C2214yes—
65#2768C2214yes—
66#2767C2214yes—
67#2761C2214yes—
68#2747C2214yes—
69#2744C2212yes—
70#2744C2214yes—
71#2740C2214yes—
72#2739C2214yes—
73#2734C2212yes—
74#2732C2211yescharacteristic
75#2732C2214yes—
76#2730C2212yes—
77#2729C2214yes—
78#2728C2214yes—
79#2727C2212yes—
80#2727C2214yes—
81#2726C2212yes—
82#2726C2212yes—
83#2726C2214yes—
84#2726C2214yes—
85#2725C2214yes—
86#2725C2214yes—
87#2725C2214yes—
88#2725C2214yes—
89#2724C2212yes—
90#2723C2214yes—
91#2722C2214yes—
92#2722C2214yes—
93#2721C2214yes—
94#2720C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2707C2214yes—
99#2705C2214yes—
100#2704C2214yes—
101#2702C2214yes—
102#2698C2214yes—
103#2698C2214yes—
104#2694C2214yes—
105#2694C2212yes—
106#2691C2214yes—
107#2686C2212yes—
108#2682C2211yescharacteristic
109#2667C2214yes—
110#2664C2214yes—
111#2664C2214yes—
112#2664C2214yes—
113#2654C2214yes—
114#2654C2214yes—
115#2651C2214yes—
116#2637C2214yes—
117#2629C2212yes—
118#2625C2214yes—
119#2612C2214yes—
120#2611C2214yes—
121#2608C2214yes—
122#2604C2214yes—
123#2601C2214yes—
124#2601C2214yes—
125#2601C2214yes—
126#2590C2214yes—
127#2590C2214yes—
128#2589C2214yes—
129#2588C2214yes—
130#2588C2214yes—
131#2587C2214yes—
132#2586C2214yes—
133#2585C2214yes—
134#2585C2214yes—
135#2585C2214yes—
136#2584C2214yes—
137#2584C2212yes—
138#2582C2211yescharacteristic
139#2582C2211yescharacteristic
140#2571C2211yescharacteristic
141#2571C2212yes—
142#2560C2214yes—
143#2558C2214yes—
144#2556C2214yes—
145#2554C2214yes—
146#2552C2212yes—
147#2552C2212yes—
148#2552C2211yescharacteristic
149#2552C2212yes—
150#2552C2212yes—
151#2552C2212yes—
152#2546C2212yes—
153#2538C2211yescharacteristic
154#2538C2212yes—
155#2538C2212yes—
156#2538C2211yescharacteristic
157#2530C2214yes—
158#2529C2214yes—
159#2529C2214yes—
160#2529C2214yes—
161#2522C2214yes—
162#2520C2214yes—
163#2519C2214yes—
164#2519C2214yes—
165#2519C2214yes—
166#2512C2214yes—
167#2509C2212yes—
168#2508C2212yes—
169#2508C2214yes—
170#2508C2214yes—
171#2508C2212yes—
172#2508C2212yes—
173#2507C2212yes—
174#2507C2212yes—
175#2507C2212yes—
176#2507C2212yes—
177#2506C2214yes—
178#2506C2212yes—
179#2506C2212yes—
180#2497C2212yes—
181#2497C2214yes—
182#2497C2212yes—
183#2497C2212yes—
184#2496C2212yes—
185#2496C2212yes—
186#2496C2212yes—
187#2496C2212yes—
188#2496C2212yes—
189#2496C2212yes—
190#2496C2212yes—
191#2490C2214yes—
192#2487C2212yes—
193#2486C2212yes—
194#2485C2212yes—
195#2485C2212yes—
196#2485C2212yes—
197#2485C2212yes—
198#2462C2214yes—
199#2453C2212yes—
200#2453C2214yes—
201#2451C2212yes—
202#2448C2212yes—
203#2448C2212yes—
204#2446C2214yes—
205#2441C2212yes—
206#2441C2212yes—
207#2441C2212yes—
208#2440C2212yes—
209#2440C2212yes—
210#2439C2212yes—
211#2423C2212yes—
212#2423C2212yes—
213#2423C2214yes—
214#2421C2214yes—
215#2396C2212yes—
216#2395C2212yes—
217#2392C2212yes—
218#2382C2212yes—
219#2382C2212yes—
220#2371C2214yes—
221#2370C2212yes—
222#2370C2214yes—
223#2369C2214yes—
224#2365C2212yes—
225#2362C2212yes—
226#2362C2212yes—
227#2362C2212yes—
228#2360C2212yes—
229#2354C2211yescharacteristic
230#2354C2212yes—
231#2354C2211yescharacteristic
232#2352C2212yes—
233#2351C2212yes—
234Q8×C4⋊C4C2212yes—
235Q8×C4⋊C4C2211yescharacteristic
236Q8×C4⋊C4C2211yescharacteristic
237Q8×C4⋊C4C2211yescharacteristic
238Q8×C4⋊C4C2211yescharacteristic
239#2346C2212yes—
240#2346C2212yes—
241#2335C2214yes—
242#2334C2214yes—
243#2323C2212yes—
244#2316C2212yes—
245#2314C2212yes—
246C4×#125C2212yes—
247C4×#125C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×#123C2212yes—
253C4×#121C2212yes—
254#2296C2212yes—
255#2295C2212yes—
256#2295C2212yes—
257#2285C2212yes—
258C42×Q8C2211yescharacteristic
259#563—48no—
260#541—416no—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2312yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#125C2312yes—
271C2×#125C2311yescharacteristic
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#124C2311yescharacteristic
283C2×#124C2311yescharacteristic
284C2×#123C2312yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2314yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C42C2312yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2312yes—
338#399C2314yes—
339#399C2312yes—
340#399C2314yes—
341#399C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2312yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2312yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2312yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2312yes—
414#396C2312yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2312yes—
419#395C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#394C2312yes—
429#393C2314yes—
430#393C2312yes—
431#392C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2311yescharacteristic
443#391C2311yescharacteristic
444#390C2312yes—
445#390C2314yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2311yescharacteristic
450#390C2311yescharacteristic
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#389C2311yescharacteristic
455#389C2312yes—
456#389C2311yescharacteristic
457#389C2312yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
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#388C2314yes—
536#388C2312yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2312yes—
607#387C2312yes—
608#386C2314yes—
609#386C2312yes—
610#386C2312yes—
611#386C2312yes—
612#386C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2312yes—
622#385C2314yes—
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2312yes—
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2312yes—
634#384C2312yes—
635#384C2314yes—
636#384C2312yes—
637#382C2311yescharacteristic
638#382C2312yes—
639#382C2312yes—
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2314yes—
643#382C2312yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2314yes—
648#382C2311yescharacteristic
649#382C2314yes—
650#381C2314yes—
651#381C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2314yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2314yes—
711#376C2314yes—
712C43C2311yescharacteristic
713C43C2312yes—
714C22×Q8C2411yescharacteristic
715C22×Q8C2411yescharacteristic
716C22×Q8C2414yes—
717C22×Q8C2411yescharacteristic
718C22×D4C2411yescharacteristic
719C22×D4C2412yes—
720C22×D4C2411yescharacteristic
721C22×D4C2412yes—
722C23×C4C2412yes—
723C23×C4C2412yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2414yes—
727C4⋊Q8—216no—
728C4⋊Q8—44no—
729#126—48no—
730#126—48no—
731#126—48no—
732#126—48no—
733#126—48no—
734#126—48no—
735#126—48no—
736#125—28no—
737#125—24no—
738#125—44no—
739#125—44no—
740#125—48no—
741#125—48no—
742#125—48no—
743#125—44no—
744#125—44no—
745#125—48no—
746#125—48no—
747#125—48no—
748#124—24no—
749#124—42no—
750#123—28no—
751#123—48no—
752C22⋊Q8—28no—
753C22⋊Q8—28no—
754C22⋊Q8—28no—
755C22⋊Q8—48no—
756C22⋊Q8—48no—
757C22⋊Q8—48no—
758#121—44no—
759C4×Q8—28no—
760C4×Q8—24no—
761C4×Q8—42no—
762C4×Q8—42no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×Q8—42no—
766C4×Q8—42no—
767C4×Q8—44no—
768C4×Q8—48no—
769C4×D4—44no—
770C4×D4—44no—
771C4×D4—42no—
772C4×D4—42no—
773#117—44no—
774#117—48no—
775#117—44no—
776#117—44no—
777#117—44no—
778C2×C4⋊C4—44no—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
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×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C42—44no—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996C24C2512yes—
997C24C2512yes—
998C2×Q8—28no—
999C2×Q8—22no—
1000C2×Q8—22no—
1001C2×Q8—22no—
1002C2×Q8—41no—
1003C2×Q8—41no—
1004C2×Q8—41no—
1005C2×Q8—41no—
1006C2×Q8—44no—
1007C2×Q8—44no—
1008C2×Q8H(5,𝔽2)14yes—
1009C2×Q82−1+414yes—
1010C2×D4—22no—
1011C2×D4—24no—
1012C2×D4—22no—
1013C2×D4—42no—
1014C2×D4—41no—
1015C2×D4—41no—
1016C2×D4—42no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—41no—
1020C2×D4—41no—
1021C2×D4—42no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C4⋊C4—28no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—22no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—44no—
1096C4⋊C4—41no—
1097C4⋊C4—42no—
1098C4⋊C4—41no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—42no—
1113C4⋊C4—41no—
1114C4⋊C4—41no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C42−1+414yes—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—42no—
1161C22⋊C4—42no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—42no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C42—28no—
1184C42—28no—
1185C42—24no—
1186C42—22no—
1187C42—24no—
1188C42—22no—
1189C42—24no—
1190C42—22no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—22no—
1196C42—22no—
1197C42—24no—
1198C42—22no—
1199C42—42no—
1200C42—42no—
1201C42—41no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—42no—
1207C42—42no—
1208C42—44no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23C2611yescharacteristic
1228Q8—28no—
1229Q8—44no—
1230Q8—44no—
1231Q8—88no—
1232D4—84no—
1233D4—82no—
1234D4—82no—
1235D4—84no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—48no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—84no—
1312C2×C4—164no—
1313C2×C4C2×H(5,𝔽2)14yes—
1314C2×C4C2×H(5,𝔽2)12yes—
1315C2×C4C2×2−1+412yes—
1316C2×C4C2×2−1+414yes—
1317C2×C4C2×2−1+414yes—
1318C2×C4C2×2−1+412yes—
1319C2×C4#58512yes—
1320C2×C4#58512yes—
1321C2×C4#58512yes—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22C22×H(5,𝔽2)11yescharacteristic
1337C22C22×2−1+411yescharacteristic
1338C22C22×2−1+411yescharacteristic
1339C22C2×#58511yescharacteristic
1340C22C2×#58511yescharacteristic
1341C22C2×#58511yescharacteristic
1342C222−1+611yescharacteristic
1343C4—24no—
1344C4—24no—
1345C4—24no—
1346C4—22no—
1347C4—22no—
1348C4—22no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—41no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4—41no—
1357C4—41no—
1358C4—44no—
1359C4—44no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—44no—
1366C4—44no—
1367C4—42no—
1368C4—42no—
1369C4#355314yes—
1370C2—82no—
1371C2—82no—
1372C2C2×#355311yescharacteristic
1373C2#6290111yescharacteristic
1374C2#6290711yescharacteristic
1375C2#6294711yescharacteristic
1376C2#6302511yescharacteristic
1377C2#6303911yescharacteristic
1378C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2682C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59927C2semidirect
2. #59922C2semidirect
3. #59292C2semidirect
4. #59218C2semidirect
5. #54908C2semidirect
6. #54742C2semidirect
7. #54261C2semidirect
9. #52077C2semidirect
10. #50983C2semidirect
11. #50338C2semidirect
12. #46158C2semidirect
13. #46153C2semidirect
14. #46147C2semidirect
15. #45310C2semidirect
16. #45025C2semidirect
17. #45017C2semidirect
18. #42935C2semidirect
19. #42849C2semidirect
20. #42455C2semidirect
21. #40004C2semidirect
22. #39658C2semidirect
23. #39353C2semidirect
24. #37191C2semidirect
26. #37143C2semidirect
27. #36447C2semidirect
28. #36312C2semidirect
29. #36312C2semidirect

Maximal subgroups

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

subgroupindex
#599272
#599222
#592922
#592182
#549082
#547422
#542612
#523032
#520772
#509832
#503382
#461582
#461532
#461472
#453102
#450252
#450172
#429352
#428492
#424552
#400042
#396582
#393532
#371912
#371522
#371432
#364472
#363122