Finite Group Databasebeta

← #7898471

Subgroups — #7898471

Order 512.

4425 conjugacy classes of subgroups.

The subgroup lattice has 1387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59827C211yesmaximal, characteristic
2#59290C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic
4#52060C214yesmaximal, complemented
5#51741C214yesmaximal, complemented
6#50620C214yesmaximal, complemented
7#47335C214yesmaximal, complemented
8#46284C212yesmaximal, complemented
9#45165C212yesmaximal, complemented
10#45058C212yesmaximal, complemented
11#44990C212yesmaximal, complemented
12#43540C214yesmaximal
13#42865C212yesmaximal, complemented
14#42813C212yesmaximal, complemented
15#41765C214yesmaximal, complemented
16#40219C212yesmaximal, complemented
17#39749C211yesmaximal, characteristic, complemented
18#39637C211yesmaximal, characteristic, complemented
19#39484C212yesmaximal, complemented
20#38472C212yesmaximal, complemented
21#38100C212yesmaximal, complemented
22#37960C212yesmaximal, complemented
23#37143C212yesmaximal, complemented
24#36270C211yesmaximal, characteristic
25#35911C212yesmaximal, complemented
26#35604C212yesmaximal, complemented
27#35208C211yesmaximal, characteristic, complemented
28#34465C212yesmaximal, complemented
29#34335C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×Q82C2211yescharacteristic
32C2×#552C2212yes—
33C2×#552C2214yes—
34#2863C2212yes—
35#2860C2212yes—
36#2859C2212yes—
37#2859C2211yescharacteristic
38#2851C2212yes—
39#2836C2214yes—
40#2821C2214yes—
41#2810C2214yes—
42#2809C2212yes—
43#2809C2212yes—
44#2808C2211yescharacteristic
45#2808C2211yescharacteristic
46#2806C2212yes—
47#2806C2212yes—
48#2805C2212yes—
49#2805C2212yes—
50#2804C2211yescharacteristic
51#2796C2212yes—
52#2796C2212yes—
53#2794C2212yes—
54#2793C2214yes—
55#2793C2214yes—
56#2791C2214yes—
57#2790C2214yes—
58#2789C2214yes—
59#2789C2214yes—
60#2788C2214yes—
61#2788C2214yes—
62#2787C2214yes—
63#2783C2214yes—
64#2783C2214yes—
65#2776C2214yes—
66#2776C2214yes—
67#2765C2214yes—
68#2765C2214yes—
69#2759C2214yes—
70#2755C2214yes—
71#2754C2214yes—
72#2751C2212yes—
73#2751C2212yes—
74#2745C2214yes—
75#2744C2214yes—
76#2744C2214yes—
77#2726C2212yes—
78#2726C2214yes—
79#2726C2212yes—
80#2724C2214yes—
81#2724C2212yes—
82#2724C2211yescharacteristic
83#2724C2212yes—
84#2719C2214yes—
85#2715C2214yes—
86#2713C2214yes—
87#2713C2214yes—
88#2709C2212yes—
89#2707C2214yes—
90#2700C2214yes—
91#2698C2214yes—
92#2694C2214yes—
93#2674C2214yes—
94#2674C2214yes—
95#2667C2214yes—
96#2666C2214yes—
97#2660C2212yes—
98#2655C2214yes—
99#2655C2214yes—
100#2652C2214yes—
101#2647C2212yes—
102#2637C2214yes—
103#2629C2212yes—
104#2621C2214yes—
105#2605C2214yes—
106#2601C2214yes—
107#2599C2214yes—
108#2596C2214yes—
109#2594C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2589C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2585C2214yes—
116#2585C2214yes—
117#2584C2212yes—
118#2582C2211yescharacteristic
119#2582C2212yes—
120#2579C2214yes—
121#2577C2214yes—
122#2573C2214yes—
123#2570C2212yes—
124#2570C2212yes—
125#2567C2211yescharacteristic
126#2567C2211yescharacteristic
127#2565C2214yes—
128#2562C2212yes—
129#2558C2214yes—
130#2558C2214yes—
131#2552C2212yes—
132#2552C2211yescharacteristic
133#2547C2212yes—
134#2547C2212yes—
135#2538C2211yescharacteristic
136#2538C2211yescharacteristic
137#2536C2212yes—
138#2530C2214yes—
139#2530C2214yes—
140#2529C2214yes—
141#2528C2214yes—
142#2527C2214yes—
143#2527C2214yes—
144#2527C2214yes—
145#2521C2214yes—
146#2520C2214yes—
147#2511C2212yes—
148#2507C2212yes—
149#2507C2212yes—
150#2506C2212yes—
151#2506C2212yes—
152#2506C2212yes—
153#2505C2214yes—
154#2502C2214yes—
155#2499C2214yes—
156#2497C2212yes—
157#2497C2212yes—
158#2496C2212yes—
159#2496C2212yes—
160#2495C2212yes—
161#2494C2212yes—
162#2494C2212yes—
163#2494C2212yes—
164#2486C2212yes—
165#2486C2212yes—
166#2485C2214yes—
167#2484C2214yes—
168#2478C2214yes—
169#2478C2214yes—
170#2478C2214yes—
171#2478C2214yes—
172#2478C2214yes—
173#2474C2214yes—
174#2474C2214yes—
175#2474C2214yes—
176#2468C2214yes—
177#2466C2214yes—
178#2462C2214yes—
179#2462C2214yes—
180#2462C2214yes—
181#2458C2214yes—
182#2453C2214yes—
183#2453C2212yes—
184#2450C2214yes—
185#2447C2214yes—
186#2447C2214yes—
187#2445C2212yes—
188#2442C2212yes—
189#2442C2212yes—
190#2440C2212yes—
191#2440C2212yes—
192#2439C2212yes—
193#2439C2212yes—
194#2438C2214yes—
195#2423C2212yes—
196#2423C2212yes—
197#2421C2212yes—
198#2421C2212yes—
199#2419C2214yes—
200#2398C2212yes—
201#2398C2212yes—
202#2395C2214yes—
203#2395C2212yes—
204#2383C2214yes—
205#2382C2214yes—
206#2370C2212yes—
207#2369C2212yes—
208#2369C2211yescharacteristic
209#2365C2214yes—
210#2365C2212yes—
211#2360C2212yes—
212#2360C2212yes—
213#2359C2214yes—
214#2355C2212yes—
215#2355C2212yes—
216#2355C2211yescharacteristic
217#2354C2211yescharacteristic
218#2352C2212yes—
219#2351C2212yes—
220Q8×C4⋊C4C2211yescharacteristic
221D4×C4⋊C4C2212yes—
222D4×C4⋊C4C2212yes—
223D4×C4⋊C4C2211yescharacteristic
224#2346C2212yes—
225#2345C2212yes—
226#2344C2212yes—
227#2344C2212yes—
228#2343C2214yes—
229#2335C2214yes—
230#2334C2214yes—
231#2331C2212yes—
232#2331C2212yes—
233#2331C2214yes—
234#2330C2212yes—
235#2330C2212yes—
236#2330C2214yes—
237#2323C2212yes—
238#2322C2214yes—
239#2320C2212yes—
240#2317C2214yes—
241#2317C2212yes—
242#2314C2212yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×#123C2212yes—
249#2295C2212yes—
250#2295C2211yescharacteristic
251#2295C2211yescharacteristic
252#2293C2212yes—
253C2×#389C2212yes—
254#2290C2212yes—
255#2290C2212yes—
256#2285C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259#559—48no—
260Q82—28no—
261#552—216no—
262#552—416no—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×#127C2311yescharacteristic
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#124C2314yes—
279C2×#124C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×#117C2314yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2314yes—
310C2×#117C2314yes—
311C2×#117C2314yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C42C2312yes—
317#401C2314yes—
318#401C2314yes—
319#401C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2312yes—
345#398C2312yes—
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#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#397C2312yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2312yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2312yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2312yes—
412#394C2312yes—
413#394C2312yes—
414#394C2312yes—
415#394C2312yes—
416#394C2312yes—
417#393C2314yes—
418#393C2314yes—
419#393C2312yes—
420#393C2312yes—
421#393C2312yes—
422#393C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2311yescharacteristic
441#391C2312yes—
442#391C2311yescharacteristic
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#390C2312yes—
446#390C2311yescharacteristic
447#390C2312yes—
448#390C2311yescharacteristic
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#389C2312yes—
453#389C2311yescharacteristic
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2311yescharacteristic
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2311yescharacteristic
503#389C2314yes—
504#389C2312yes—
505#389C2311yescharacteristic
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2312yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2312yes—
524#388C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2312yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#386C2312yes—
598#386C2312yes—
599#386C2314yes—
600#386C2312yes—
601#386C2312yes—
602#386C2312yes—
603#385C2312yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2312yes—
622#385C2312yes—
623#385C2312yes—
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2314yes—
629#384C2312yes—
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2312yes—
633#384C2311yescharacteristic
634#384C2312yes—
635#384C2312yes—
636#383C2314yes—
637#383C2314yes—
638#382C2314yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#381C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2314yes—
651#381C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2314yes—
658#380C2312yes—
659#380C2314yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665#380C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2312yes—
710#376C2314yes—
711#376C2312yes—
712#376C2314yes—
713C2×#95C2314yes—
714C43C2311yescharacteristic
715C43C2312yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2411yescharacteristic
718C22×Q8C2414yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×D4C2412yes—
723C22×D4C2412yes—
724C22×D4C2411yescharacteristic
725C22×D4C2411yescharacteristic
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2414yes—
729C23×C4C2412yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C23×C4C2412yes—
733C4⋊Q8—28no—
734C4⋊Q8—216no—
735C4⋊Q8—28no—
736C4⋊Q8—24no—
737C4⋊Q8—24no—
738#127—24no—
739#126—216no—
740#126—48no—
741#126—48no—
742#125—216no—
743#125—28no—
744#125—44no—
745#125—48no—
746#125—48no—
747#125—48no—
748#124—48no—
749#124—48no—
750#123—28no—
751#123—216no—
752#123—216no—
753#123—48no—
754C22⋊Q8—28no—
755C22⋊Q8—28no—
756C22⋊Q8—48no—
757C22⋊Q8—48no—
758C4×Q8—28no—
759C4×Q8—28no—
760C4×Q8—24no—
761C4×Q8—24no—
762C4×Q8—24no—
763C4×Q8—48no—
764C4×Q8—44no—
765C4×Q8—44no—
766C4×Q8—44no—
767C4×Q8—42no—
768C4×Q8#4118yes—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—42no—
773C4×D4—42no—
774C4×D4—48no—
775C4×D4—48no—
776#117—28no—
777#117—216no—
778#117—44no—
779#117—48no—
780#117—48no—
781#117—48no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—44no—
784C2×C4⋊C4—44no—
785C2×C4⋊C4—48no—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C42—44no—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999C24C2512yes—
1000C24C2512yes—
1001C2×Q8—22no—
1002C2×Q8—28no—
1003C2×Q8—24no—
1004C2×Q8—22no—
1005C2×Q8—22no—
1006C2×Q8—24no—
1007C2×Q8—22no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—44no—
1011C2×Q8—42no—
1012C2×Q8—42no—
1013C2×Q8—41no—
1014C2×Q8—41no—
1015C2×Q8—44no—
1016C2×Q8—42no—
1017C2×Q8—42no—
1018C2×Q8C2×#4114yes—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—24no—
1022C2×D4—22no—
1023C2×D4—24no—
1024C2×D4—41no—
1025C2×D4—41no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—41no—
1029C2×D4—41no—
1030C2×D4H(5,𝔽2)14yes—
1031C22×C4—24no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—42no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—22no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—22no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—22no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—41no—
1115C4⋊C4—41no—
1116C4⋊C4—42no—
1117C4⋊C4—41no—
1118C4⋊C4—41no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4C2×#4114yes—
1152C4⋊C4C2×#4118yes—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—42no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C42—28no—
1187C42—28no—
1188C42—24no—
1189C42—24no—
1190C42—22no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—22no—
1196C42—42no—
1197C42—42no—
1198C42—42no—
1199C42—41no—
1200C42—41no—
1201C42—42no—
1202C42—41no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—44no—
1209C42—44no—
1210C42—44no—
1211C42—42no—
1212C42—44no—
1213C42C2×#4118yes—
1214C42C2×#4114yes—
1215C422−1+414yes—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23C2×H(5,𝔽2)14yes—
1230C23C2611yescharacteristic
1231Q8—28no—
1232Q8—44no—
1233Q8—88no—
1234Q8—84no—
1235Q8—82no—
1236Q8—84no—
1237D4—44no—
1238D4—48no—
1239D4—48no—
1240D4—82no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—416no—
1313C2×C4—48no—
1314C2×C4—48no—
1315C2×C4—48no—
1316C2×C4—88no—
1317C2×C4—84no—
1318C2×C4—164no—
1319C2×C4C22×#4114yes—
1320C2×C4C22×#4114yes—
1321C2×C4C22×#4112yes—
1322C2×C4C22×#4112yes—
1323C2×C4C22×#4112yes—
1324C2×C4C2×H(5,𝔽2)12yes—
1325C2×C4C2×2−1+412yes—
1326C2×C4C2×2−1+412yes—
1327C2×C4C2×2−1+412yes—
1328C2×C4#58512yes—
1329C22—24no—
1330C22—24no—
1331C22—24no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22C23×#4111yescharacteristic
1344C22C22×H(5,𝔽2)11yescharacteristic
1345C22C22×2−1+411yescharacteristic
1346C22C2×#58511yescharacteristic
1347C222−1+611yescharacteristic
1348C222−1+611yescharacteristic
1349C222−1+611yescharacteristic
1350C4—24no—
1351C4—22no—
1352C4—24no—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—44no—
1358C4—44no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—41no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—44no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—44no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—44no—
1376C4#350714yes—
1377C2—44no—
1378C2—82no—
1379C2C2×#350711yescharacteristic
1380C2#6285011yescharacteristic
1381C2#6288911yescharacteristic
1382C2#6290111yescharacteristic
1383C2#6291511yescharacteristic
1384C2#6298511yescharacteristic
1385C2#6305311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59290C2semidirect
4. #52060C2semidirect
5. #51741C2semidirect
6. #50620C2semidirect
7. #47335C2semidirect
8. #46284C2semidirect
9. #45165C2semidirect
10. #45058C2semidirect
11. #44990C2semidirect
13. #42865C2semidirect
14. #42813C2semidirect
15. #41765C2semidirect
16. #40219C2semidirect
17. #39749C2semidirect
18. #39637C2semidirect
19. #39484C2semidirect
20. #38472C2semidirect
21. #38100C2semidirect
22. #37960C2semidirect
23. #37143C2semidirect
25. #35911C2semidirect
26. #35604C2semidirect
27. #35208C2semidirect
28. #34465C2semidirect
29. #34335C2semidirect

Maximal subgroups

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

subgroupindex
#598272
#592902
#522732
#520602
#517412
#506202
#473352
#462842
#451652
#450582
#449902
#435402
#428652
#428132
#417652
#402192
#397492
#396372
#394842
#384722
#381002
#379602
#371432
#362702
#359112
#356042
#352082
#344652
#343352