Finite Group Databasebeta

← #8115415

Subgroups — #8115415

Order 512.

3676 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57817C214yesmaximal, complemented
2#57808C214yesmaximal
3#56975C214yesmaximal
4#56938C214yesmaximal, complemented
5#56010C214yesmaximal, complemented
6#55769C214yesmaximal
7#54457C214yesmaximal
8#54387C214yesmaximal, complemented
9#53143C212yesmaximal, complemented
10#53143C212yesmaximal, complemented
11#45405C212yesmaximal
12#45390C212yesmaximal
13#42981C211yesmaximal, characteristic
14#42941C211yesmaximal, characteristic
15#42850C212yesmaximal, complemented
16#42818C211yesmaximal, characteristic
17#42744C212yesmaximal, complemented
18#42697C211yesmaximal, characteristic
19#38243C212yesmaximal, complemented
20#38227C212yesmaximal, complemented
21#38072C212yesmaximal
22#38057C212yesmaximal
23#37413C212yesmaximal, complemented
24#37401C212yesmaximal, complemented
25#35324C211yesmaximal, characteristic
26#35313C211yesmaximal, characteristic
27#34644C211yesmaximal, characteristic
28#2864C2211yescharacteristic
29#2863C2212yes—
30#2863C2212yes—
31#2862C2211yescharacteristic
32#2855C2212yes—
33#2844C2212yes—
34#2841C2212yes—
35#2839C2214yes—
36#2839C2214yes—
37#2839C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2835C2212yes—
42#2833C2214yes—
43#2833C2212yes—
44#2833C2214yes—
45#2833C2214yes—
46#2833C2214yes—
47#2810C2214yes—
48#2810C2214yes—
49#2809C2212yes—
50#2807C2212yes—
51#2806C2214yes—
52#2805C2214yes—
53#2805C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2802C2214yes—
57#2799C2214yes—
58#2799C2212yes—
59#2794C2214yes—
60#2794C2214yes—
61#2794C2212yes—
62#2792C2214yes—
63#2792C2212yes—
64#2791C2214yes—
65#2791C2214yes—
66#2789C2214yes—
67#2788C2214yes—
68#2776C2214yes—
69#2776C2214yes—
70#2776C2214yes—
71#2776C2214yes—
72#2776C2214yes—
73#2776C2214yes—
74#2774C2214yes—
75#2774C2214yes—
76#2774C2214yes—
77#2771C2214yes—
78#2771C2212yes—
79#2769C2214yes—
80#2768C2214yes—
81#2767C2214yes—
82#2767C2214yes—
83#2767C2214yes—
84#2767C2214yes—
85#2766C2214yes—
86#2766C2214yes—
87#2766C2214yes—
88#2766C2214yes—
89#2766C2214yes—
90#2766C2214yes—
91#2766C2214yes—
92#2765C2214yes—
93#2765C2214yes—
94#2764C2212yes—
95#2762C2214yes—
96#2762C2214yes—
97#2762C2214yes—
98#2762C2214yes—
99#2762C2214yes—
100#2762C2214yes—
101#2758C2214yes—
102#2758C2214yes—
103#2758C2214yes—
104#2758C2214yes—
105#2758C2214yes—
106#2755C2214yes—
107#2755C2214yes—
108#2755C2214yes—
109#2744C2214yes—
110#2742C2214yes—
111#2742C2212yes—
112#2739C2214yes—
113#2738C2214yes—
114#2738C2214yes—
115#2667C2214yes—
116#2667C2212yes—
117#2667C2212yes—
118#2666C2212yes—
119#2666C2212yes—
120#2666C2212yes—
121#2666C2212yes—
122#2666C2214yes—
123#2666C2214yes—
124#2665C2212yes—
125#2665C2212yes—
126#2655C2214yes—
127#2655C2214yes—
128#2652C2214yes—
129#2647C2212yes—
130#2647C2214yes—
131#2645C2212yes—
132#2645C2212yes—
133#2645C2212yes—
134#2645C2214yes—
135#2645C2212yes—
136#2645C2212yes—
137#2642C2212yes—
138#2628C2211yescharacteristic
139#2621C2211yescharacteristic
140#2612C2214yes—
141#2612C2214yes—
142#2612C2212yes—
143#2607C2212yes—
144#2605C2214yes—
145#2590C2214yes—
146#2590C2214yes—
147#2588C2214yes—
148#2588C2214yes—
149#2586C2212yes—
150#2584C2212yes—
151#2584C2212yes—
152#2582C2212yes—
153#2582C2212yes—
154#2581C2212yes—
155#2581C2212yes—
156#2575C2214yes—
157#2573C2214yes—
158#2571C2212yes—
159#2569C2214yes—
160#2568C2212yes—
161#2568C2212yes—
162#2565C2212yes—
163#2550C2212yes—
164#2546C2212yes—
165#2533C2214yes—
166#2533C2214yes—
167#2533C2214yes—
168#2533C2214yes—
169#2528C2214yes—
170#2528C2214yes—
171#2528C2214yes—
172#2528C2214yes—
173#2527C2214yes—
174#2527C2214yes—
175#2524C2214yes—
176#2524C2214yes—
177#2522C2214yes—
178#2517C2212yes—
179#2514C2212yes—
180#2514C2212yes—
181#2514C2214yes—
182#2514C2212yes—
183#2511C2212yes—
184#2511C2212yes—
185#2511C2212yes—
186#2511C2214yes—
187#2509C2212yes—
188#2509C2212yes—
189#2509C2214yes—
190#2509C2214yes—
191#2509C2212yes—
192#2508C2212yes—
193#2508C2214yes—
194#2507C2212yes—
195#2507C2212yes—
196#2505C2214yes—
197#2499C2212yes—
198#2497C2214yes—
199#2493C2214yes—
200#2493C2214yes—
201#2493C2214yes—
202#2493C2214yes—
203#2453C2212yes—
204#2453C2212yes—
205#2453C2212yes—
206#2453C2212yes—
207#2453C2212yes—
208#2451C2212yes—
209#2446C2212yes—
210#2446C2212yes—
211#2446C2212yes—
212#2446C2212yes—
213#2446C2212yes—
214#2446C2212yes—
215#2442C2212yes—
216#2441C2212yes—
217#2434C2212yes—
218#2402C2212yes—
219#2399C2211yescharacteristic
220#2399C2211yescharacteristic
221#2396C2211yescharacteristic
222#2396C2212yes—
223#2396C2211yescharacteristic
224#2370C2212yes—
225#2365C2212yes—
226#2362C2212yes—
227#2360C2212yes—
228#2356C2212yes—
229Q8×C4⋊C4C2212yes—
230#2346C2212yes—
231Q8×C22⋊C4C2212yes—
232#2331C2211yescharacteristic
233#2330C2212yes—
234#2327C2212yes—
235#2327C2211yescharacteristic
236#2323C2212yes—
237#2320C2212yes—
238#2320C2212yes—
239#2317C2211yescharacteristic
240#2316C2211yescharacteristic
241#2310C2211yescharacteristic
242#2310C2211yescharacteristic
243#2296C2211yescharacteristic
244#2295C2212yes—
245#2295C2211yescharacteristic
246#2295C2212yes—
247#2295C2211yescharacteristic
248C2×#391C2211yescharacteristic
249#2283C2212yes—
250C4×#117C2211yescharacteristic
251C23×Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2311yescharacteristic
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C42C2311yescharacteristic
273#401C2314yes—
274#401C2314yes—
275#401C2314yes—
276#401C2314yes—
277#401C2314yes—
278#401C2314yes—
279#401C2314yes—
280#401C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2311yescharacteristic
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2311yescharacteristic
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#399C2312yes—
347#399C2311yescharacteristic
348#399C2314yes—
349#399C2312yes—
350#399C2311yescharacteristic
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#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#397C2314yes—
397#397C2312yes—
398#397C2312yes—
399#397C2314yes—
400#396C2312yes—
401#396C2314yes—
402#396C2312yes—
403#396C2312yes—
404#396C2312yes—
405#395C2312yes—
406#395C2312yes—
407#395C2312yes—
408#395C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2311yescharacteristic
416#395C2314yes—
417#395C2312yes—
418#395C2314yes—
419#395C2312yes—
420#395C2311yescharacteristic
421#393C2311yescharacteristic
422#393C2312yes—
423#393C2311yescharacteristic
424#393C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2314yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
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#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#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
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#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#384C2312yes—
612#384C2312yes—
613#384C2312yes—
614#384C2314yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#383C2314yes—
620#383C2314yes—
621#383C2312yes—
622#383C2312yes—
623#383C2314yes—
624#383C2314yes—
625#382C2311yescharacteristic
626#382C2314yes—
627#382C2314yes—
628#382C2311yescharacteristic
629#382C2312yes—
630#382C2314yes—
631#382C2312yes—
632#382C2314yes—
633#382C2314yes—
634#382C2314yes—
635#382C2312yes—
636#382C2314yes—
637#382C2314yes—
638#382C2312yes—
639#382C2312yes—
640#381C2314yes—
641#381C2312yes—
642#381C2312yes—
643#381C2314yes—
644#381C2312yes—
645#381C2312yes—
646#380C2312yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680#376C2312yes—
681#376C2312yes—
682#376C2311yescharacteristic
683#376C2314yes—
684#376C2314yes—
685#376C2314yes—
686#376C2311yescharacteristic
687C2×#95C2314yes—
688C43C2311yescharacteristic
689C43C2311yescharacteristic
690C22×Q8—24no—
691C22×Q8—42no—
692C22×Q8—42no—
693C22×Q8C2412yes—
694C22×Q8C2412yes—
695C22×Q8C2412yes—
696C22×Q8C2411yescharacteristic
697C22×Q8C2412yes—
698C22×Q8C2411yescharacteristic
699C22×Q8C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C4⋊Q8—42no—
705C4⋊Q8—42no—
706C4⋊Q8—44no—
707C4⋊Q8—44no—
708#125—44no—
709#125—44no—
710C22⋊Q8—28no—
711C4×Q8—42no—
712C4×Q8—44no—
713C4×Q8—42no—
714C4×Q8—44no—
715C4×Q8—44no—
716C4×Q8—44no—
717C4×Q8—44no—
718C4×Q8—44no—
719#117—24no—
720#117—42no—
721#117—42no—
722#117—42no—
723C2×C4⋊C4—42no—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C42—24no—
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2411yescharacteristic
818C2×C42C2411yescharacteristic
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2412yes—
840#95C2412yes—
841#95C2412yes—
842#95C2412yes—
843#95C2412yes—
844#95C2412yes—
845#95C2412yes—
846#95C2414yes—
847#95C2412yes—
848#95C2412yes—
849#95C2412yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2412yes—
874#95C2414yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2414yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2412yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937C24C2511yescharacteristic
938C2×Q8—24no—
939C2×Q8—24no—
940C2×Q8—24no—
941C2×Q8—24no—
942C2×Q8—24no—
943C2×Q8—24no—
944C2×Q8—24no—
945C2×Q8—41no—
946C2×Q8—42no—
947C2×Q8—41no—
948C2×Q8—42no—
949C2×Q8—42no—
950C2×Q8—42no—
951C2×Q8—42no—
952C2×Q8—42no—
953C2×Q8—42no—
954C2×Q8—42no—
955C2×Q8—44no—
956C2×Q8—88no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—44no—
967C22×C42−1+414yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2514yes—
973C22×C4C2511yescharacteristic
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2511yescharacteristic
978C22×C4C2512yes—
979C22×C4C2511yescharacteristic
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2511yescharacteristic
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2514yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—44no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—42no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—44no—
1044C4⋊C4—41no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—41no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C22⋊C4—24no—
1067C22⋊C4—28no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—44no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—42no—
1077C42—24no—
1078C42—22no—
1079C42—22no—
1080C42—24no—
1081C42—22no—
1082C42—22no—
1083C42—22no—
1084C42—22no—
1085C42—24no—
1086C42—24no—
1087C42—24no—
1088C42—24no—
1089C42—44no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—42no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—44no—
1100C42—44no—
1101C42—44no—
1102C42—44no—
1103C42—44no—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—22no—
1108C23C2×2−1+412yes—
1109C23C2611yescharacteristic
1110Q8—48no—
1111Q8—48no—
1112Q8—84no—
1113Q8—84no—
1114Q8—82no—
1115Q8—82no—
1116Q8—162no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—28no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—84no—
1189C2×C4—84no—
1190C2×C4—162no—
1191C2×C4C2×2−1+412yes—
1192C2×C4C2×2−1+412yes—
1193C2×C4#58512yes—
1194C2×C4#58512yes—
1195C22—22no—
1196C22—24no—
1197C22—42no—
1198C22—41no—
1199C22—41no—
1200C22C22×2−1+411yescharacteristic
1201C22C2×#58511yescharacteristic
1202C22C2×#58511yescharacteristic
1203C222−1+612yes—
1204C222−1+612yes—
1205C4—22no—
1206C4—44no—
1207C4—44no—
1208C4—44no—
1209C4—44no—
1210C4—42no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—42no—
1215C4—44no—
1216C4—44no—
1217C4—42no—
1218C4—42no—
1219C4—42no—
1220C4—42no—
1221C4—41no—
1222C4—42no—
1223C4—44no—
1224C4—42no—
1225C4—41no—
1226C4—41no—
1227C4—42no—
1228C4—44no—
1229C4—41no—
1230C4#356414yes—
1231C2—42no—
1232C2C2×#356411yescharacteristic
1233C2#6288912yes—
1234C2#6289012yes—
1235C2#6289111yescharacteristic
1236C2#6289111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57817C2semidirect
4. #56938C2semidirect
5. #56010C2semidirect
8. #54387C2semidirect
9. #53143C2semidirect
10. #53143C2semidirect
15. #42850C2semidirect
17. #42744C2semidirect
19. #38243C2semidirect
20. #38227C2semidirect
23. #37413C2semidirect
24. #37401C2semidirect

Maximal subgroups

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

subgroupindex
#578172
#578082
#569752
#569382
#560102
#557692
#544572
#543872
#531432
#454052
#453902
#429812
#429412
#428502
#428182
#427442
#426972
#382432
#382272
#380722
#380572
#374132
#374012
#353242
#353132
#346442