Finite Group Databasebeta

← #7895512

Subgroups — #7895512

Order 512.

4139 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59960C212yesmaximal
2#59875C211yesmaximal, characteristic, complemented
3#52274C211yesmaximal, characteristic, complemented
4#51147C214yesmaximal, complemented
5#48799C214yesmaximal, complemented
6#48226C214yesmaximal, complemented
7#46937C214yesmaximal, complemented
8#45809C212yesmaximal, complemented
9#45363C212yesmaximal, complemented
10#45231C212yesmaximal
11#45008C212yesmaximal
12#43484C214yesmaximal, complemented
13#42676C212yesmaximal
14#42600C212yesmaximal, complemented
15#42353C214yesmaximal, complemented
16#39757C211yesmaximal, characteristic, complemented
17#39637C211yesmaximal, characteristic, complemented
18#39512C212yesmaximal, complemented
19#39241C212yesmaximal, complemented
20#38465C212yesmaximal, complemented
21#38239C212yesmaximal, complemented
22#38224C212yesmaximal
23#37323C212yesmaximal, complemented
24#36261C211yesmaximal, characteristic
25#35867C212yesmaximal, complemented
26#35643C212yesmaximal, complemented
27#35177C211yesmaximal, characteristic
28#34489C212yesmaximal
29#34324C211yesmaximal, characteristic
30C2×#556C2211yescharacteristic
31C2×#554C2212yes—
32#2863C2212yes—
33#2859C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2855C2212yes—
37#2833C2214yes—
38#2817C2214yes—
39#2810C2212yes—
40#2810C2212yes—
41#2810C2212yes—
42#2810C2212yes—
43#2809C2211yescharacteristic
44#2809C2214yes—
45#2809C2212yes—
46#2806C2211yescharacteristic
47#2806C2214yes—
48#2806C2212yes—
49#2805C2211yescharacteristic
50#2805C2212yes—
51#2805C2212yes—
52#2805C2212yes—
53#2805C2214yes—
54#2802C2212yes—
55#2802C2214yes—
56#2799C2212yes—
57#2794C2214yes—
58#2791C2212yes—
59#2789C2214yes—
60#2776C2214yes—
61#2776C2214yes—
62#2776C2214yes—
63#2774C2212yes—
64#2774C2214yes—
65#2766C2214yes—
66#2766C2214yes—
67#2765C2214yes—
68#2765C2214yes—
69#2765C2214yes—
70#2764C2214yes—
71#2764C2214yes—
72#2764C2214yes—
73#2762C2214yes—
74#2762C2214yes—
75#2762C2214yes—
76#2755C2212yes—
77#2747C2214yes—
78#2747C2214yes—
79#2747C2214yes—
80#2745C2214yes—
81#2744C2214yes—
82#2726C2211yescharacteristic
83#2726C2212yes—
84#2713C2212yes—
85#2713C2214yes—
86#2698C2214yes—
87#2698C2214yes—
88#2690C2214yes—
89#2690C2214yes—
90#2690C2214yes—
91#2689C2214yes—
92#2689C2214yes—
93#2666C2214yes—
94#2665C2214yes—
95#2655C2214yes—
96#2655C2214yes—
97#2647C2212yes—
98#2645C2212yes—
99#2642C2212yes—
100#2634C2214yes—
101#2627C2214yes—
102#2625C2214yes—
103#2612C2214yes—
104#2612C2214yes—
105#2605C2214yes—
106#2605C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2599C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2588C2214yes—
113#2588C2214yes—
114#2586C2214yes—
115#2585C2214yes—
116#2584C2212yes—
117#2584C2212yes—
118#2583C2214yes—
119#2581C2214yes—
120#2581C2212yes—
121#2577C2214yes—
122#2573C2214yes—
123#2573C2214yes—
124#2570C2212yes—
125#2570C2212yes—
126#2570C2214yes—
127#2568C2212yes—
128#2568C2212yes—
129#2568C2212yes—
130#2567C2211yescharacteristic
131#2563C2211yescharacteristic
132#2552C2211yescharacteristic
133#2551C2211yescharacteristic
134#2551C2211yescharacteristic
135#2550C2212yes—
136#2549C2214yes—
137#2538C2211yescharacteristic
138#2533C2214yes—
139#2533C2214yes—
140#2533C2214yes—
141#2530C2214yes—
142#2527C2214yes—
143#2527C2214yes—
144#2527C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2520C2214yes—
148#2515C2214yes—
149#2514C2212yes—
150#2514C2212yes—
151#2514C2214yes—
152#2514C2214yes—
153#2514C2212yes—
154#2514C2212yes—
155#2514C2214yes—
156#2511C2212yes—
157#2511C2214yes—
158#2511C2212yes—
159#2509C2212yes—
160#2509C2212yes—
161#2508C2212yes—
162#2507C2212yes—
163#2507C2212yes—
164#2506C2212yes—
165#2506C2214yes—
166#2506C2212yes—
167#2503C2214yes—
168#2497C2212yes—
169#2493C2214yes—
170#2493C2214yes—
171#2493C2214yes—
172#2492C2212yes—
173#2484C2214yes—
174#2484C2214yes—
175#2475C2214yes—
176#2473C2214yes—
177#2465C2214yes—
178#2462C2214yes—
179#2453C2212yes—
180#2453C2214yes—
181#2453C2212yes—
182#2453C2214yes—
183#2452C2212yes—
184#2451C2212yes—
185#2451C2212yes—
186#2451C2214yes—
187#2451C2212yes—
188#2451C2212yes—
189#2447C2212yes—
190#2447C2212yes—
191#2447C2212yes—
192#2447C2212yes—
193#2446C2214yes—
194#2446C2214yes—
195#2440C2212yes—
196#2440C2212yes—
197#2438C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2399C2214yes—
201#2399C2212yes—
202#2378C2214yes—
203#2378C2214yes—
204#2373C2214yes—
205#2370C2212yes—
206#2370C2212yes—
207#2369C2212yes—
208#2367C2212yes—
209#2365C2211yescharacteristic
210#2365C2212yes—
211#2365C2212yes—
212#2362C2212yes—
213#2362C2214yes—
214#2360C2214yes—
215#2357C2212yes—
216#2357C2212yes—
217#2356C2212yes—
218#2355C2212yes—
219#2355C2212yes—
220#2355C2212yes—
221#2355C2212yes—
222#2354C2211yescharacteristic
223Q8×C4⋊C4C2211yescharacteristic
224#2349C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2211yescharacteristic
227#2346C2212yes—
228#2344C2214yes—
229#2336C2214yes—
230#2334C2214yes—
231#2332C2214yes—
232#2332C2214yes—
233#2331C2212yes—
234#2331C2212yes—
235#2331C2212yes—
236#2330C2212yes—
237#2326C2212yes—
238#2323C2214yes—
239#2320C2212yes—
240#2319C2212yes—
241#2319C2212yes—
242#2313C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×C22⋊Q8C2212yes—
249#2296C2212yes—
250#2295C2211yescharacteristic
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2212yes—
255#2293C2212yes—
256C2×#389C2212yes—
257#2276C2212yes—
258C42×D4C2211yescharacteristic
259#556—28no—
260#554—216no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×#126C2314yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#124C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2311yescharacteristic
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2314yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C42C2312yes—
303#401C2314yes—
304#401C2314yes—
305#401C2314yes—
306#401C2314yes—
307#401C2314yes—
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#400C2312yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#396C2314yes—
391#396C2314yes—
392#395C2312yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2312yes—
405#395C2312yes—
406#395C2314yes—
407#393C2314yes—
408#393C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2312yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2311yescharacteristic
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#391C2311yescharacteristic
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2311yescharacteristic
460#389C2312yes—
461#389C2311yescharacteristic
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2311yescharacteristic
496#389C2312yes—
497#389C2314yes—
498#389C2311yescharacteristic
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2311yescharacteristic
510#389C2311yescharacteristic
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#387C2314yes—
527#387C2312yes—
528#387C2312yes—
529#387C2314yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
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#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
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#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2314yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2312yes—
602#387C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#384C2311yescharacteristic
616#384C2311yescharacteristic
617#384C2311yescharacteristic
618#384C2312yes—
619#384C2312yes—
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#383C2314yes—
624#383C2314yes—
625#383C2314yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2314yes—
635#382C2314yes—
636#382C2314yes—
637#382C2314yes—
638#382C2312yes—
639#382C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2314yes—
709#376C2314yes—
710#376C2314yes—
711C2×#95C2314yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C22×Q8C2412yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2414yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×D4C2411yescharacteristic
722C23×C4C2412yes—
723C23×C4C2414yes—
724C23×C4C2414yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C4⋊Q8—28no—
728C4⋊Q8—28no—
729C4⋊Q8—24no—
730C4⋊Q8—24no—
731C4⋊Q8—42no—
732C4⋊Q8—82no—
733C4⋊Q8—82no—
734#126—216no—
735#125—28no—
736#125—28no—
737#125—48no—
738#125—44no—
739#125—84no—
740#124—28no—
741C22⋊Q8—216no—
742C22⋊Q8—28no—
743C22⋊Q8—216no—
744C22⋊Q8—216no—
745C22⋊Q8—48no—
746C22⋊Q8—82no—
747C4×Q8—28no—
748C4×Q8—28no—
749C4×Q8—28no—
750C4×Q8—24no—
751C4×Q8—28no—
752C4×Q8—24no—
753C4×Q8—44no—
754C4×Q8—82no—
755C4×Q8—84no—
756C4×Q8—84no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—24no—
760C4×D4—24no—
761C4×D4#4118yes—
762#117—28no—
763#117—84no—
764#117—82no—
765C2×C4⋊C4—216no—
766C2×C4⋊C4—44no—
767C2×C4⋊C4—82no—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C42—82no—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2411yescharacteristic
866C2×C42C2412yes—
867C2×C42C2411yescharacteristic
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2411yescharacteristic
889C2×C42C2411yescharacteristic
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985C24C2512yes—
986C2×Q8—22no—
987C2×Q8—24no—
988C2×Q8—24no—
989C2×Q8—28no—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—22no—
993C2×Q8—28no—
994C2×Q8—24no—
995C2×Q8—41no—
996C2×Q8—41no—
997C2×Q8—42no—
998C2×Q8—44no—
999C2×Q8—44no—
1000C2×Q8—44no—
1001C2×Q8—41no—
1002C2×Q8—42no—
1003C2×Q8—42no—
1004C2×Q8—42no—
1005C2×Q8—41no—
1006C2×Q8—44no—
1007C2×D4—22no—
1008C2×D4—22no—
1009C2×D4C2×#4114yes—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4C2×#4118yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2512yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2512yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C4⋊C4—24no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—22no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—22no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—44no—
1085C4⋊C4—41no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—41no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
1131C4⋊C4C2×#4114yes—
1132C4⋊C42−1+414yes—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—24no—
1138C22⋊C4—24no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4C2×#4118yes—
1146C42—28no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—22no—
1151C42—24no—
1152C42—28no—
1153C42—28no—
1154C42—24no—
1155C42—24no—
1156C42—22no—
1157C42—41no—
1158C42—42no—
1159C42—42no—
1160C42—42no—
1161C42—41no—
1162C42—41no—
1163C42—44no—
1164C42—42no—
1165C42—44no—
1166C42—42no—
1167C42—42no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—42no—
1176C42C2×#4114yes—
1177C422−1+414yes—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23C22×#4114yes—
1185C23C2611yescharacteristic
1186Q8—44no—
1187Q8—48no—
1188Q8—84no—
1189Q8—88no—
1190Q8—82no—
1191Q8—84no—
1192Q8—88no—
1193D4—28no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—48no—
1269C2×C4—48no—
1270C2×C4—84no—
1271C2×C4—88no—
1272C2×C4—88no—
1273C2×C4C22×#4114yes—
1274C2×C4C22×#4112yes—
1275C2×C4C22×#4112yes—
1276C2×C4C22×#4112yes—
1277C2×C4C2×2−1+412yes—
1278C2×C4C2×2−1+414yes—
1279C2×C4C2×2−1+412yes—
1280C2×C4C2×2−1+412yes—
1281C2×C4C2×2−1+412yes—
1282C2×C4#58512yes—
1283C22—24no—
1284C22—24no—
1285C22—24no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22C23×#4111yescharacteristic
1291C22C22×2−1+411yescharacteristic
1292C22C22×2−1+411yescharacteristic
1293C22C2×#58511yescharacteristic
1294C22H(7,𝔽2)11yescharacteristic
1295C222−1+611yescharacteristic
1296C222−1+611yescharacteristic
1297C4—22no—
1298C4—22no—
1299C4—24no—
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—24no—
1304C4—42no—
1305C4—44no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—41no—
1310C4—42no—
1311C4—44no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—44no—
1321C4—42no—
1322C4—44no—
1323C4—42no—
1324C4#350914yes—
1325C2—44no—
1326C2C2×#350911yescharacteristic
1327C2#6284711yescharacteristic
1328C2#6287911yescharacteristic
1329C2#6293211yescharacteristic
1330C2#6294811yescharacteristic
1331C2#6300911yescharacteristic
1332C2#6305711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59875C2semidirect
3. #52274C2semidirect
4. #51147C2semidirect
5. #48799C2semidirect
6. #48226C2semidirect
7. #46937C2semidirect
8. #45809C2semidirect
9. #45363C2semidirect
12. #43484C2semidirect
14. #42600C2semidirect
15. #42353C2semidirect
16. #39757C2semidirect
17. #39637C2semidirect
18. #39512C2semidirect
19. #39241C2semidirect
20. #38465C2semidirect
21. #38239C2semidirect
23. #37323C2semidirect
25. #35867C2semidirect
26. #35643C2semidirect

Maximal subgroups

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

subgroupindex
#599602
#598752
#522742
#511472
#487992
#482262
#469372
#458092
#453632
#452312
#450082
#434842
#426762
#426002
#423532
#397572
#396372
#395122
#392412
#384652
#382392
#382242
#373232
#362612
#358672
#356432
#351772
#344892
#343242