Finite Group Databasebeta

← #7715258

Subgroups — #7715258

Order 512.

4048 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52041C214yesmaximal, complemented
2#52037C214yesmaximal, complemented
3#51606C214yesmaximal, complemented
4#51603C214yesmaximal, complemented
5#47022C214yesmaximal
6#46845C214yesmaximal
7#46446C214yesmaximal
8#46437C214yesmaximal
9#39754C212yesmaximal, complemented
10#39753C212yesmaximal, complemented
11#39622C212yesmaximal, complemented
12#39621C212yesmaximal, complemented
13#39182C212yesmaximal, complemented
14#39180C212yesmaximal, complemented
15#39177C212yesmaximal, complemented
16#39176C212yesmaximal, complemented
17#37624C212yesmaximal
18#37428C211yesmaximal, characteristic
19#37311C212yesmaximal
20#37309C211yesmaximal, characteristic
21#35337C211yesmaximal, characteristic
22#35304C212yesmaximal
23#35284C211yesmaximal, characteristic
24#35282C212yesmaximal
25#34375C211yesmaximal, characteristic
26#34374C211yesmaximal, characteristic
27#34074C211yesmaximal, characteristic
28C2×#533C2211yescharacteristic
29#2868C2211yescharacteristic
30#2864C2212yes—
31#2862C2211yescharacteristic
32#2859C2211yescharacteristic
33#2859C2212yes—
34#2859C2211yescharacteristic
35#2857C2212yes—
36#2857C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2841C2214yes—
40#2841C2214yes—
41#2811C2214yes—
42#2809C2214yes—
43#2807C2214yes—
44#2806C2214yes—
45#2806C2214yes—
46#2806C2214yes—
47#2806C2214yes—
48#2806C2214yes—
49#2806C2214yes—
50#2805C2214yes—
51#2805C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2799C2214yes—
57#2799C2214yes—
58#2792C2214yes—
59#2792C2214yes—
60#2792C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2788C2214yes—
65#2774C2214yes—
66#2774C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2768C2214yes—
71#2763C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2755C2214yes—
75#2755C2214yes—
76#2755C2214yes—
77#2734C2214yes—
78#2729C2214yes—
79#2726C2214yes—
80#2726C2214yes—
81#2726C2214yes—
82#2720C2214yes—
83#2713C2214yes—
84#2713C2214yes—
85#2713C2214yes—
86#2713C2214yes—
87#2704C2214yes—
88#2704C2214yes—
89#2666C2214yes—
90#2666C2214yes—
91#2660C2212yes—
92#2660C2212yes—
93#2660C2214yes—
94#2660C2212yes—
95#2660C2212yes—
96#2647C2211yescharacteristic
97#2647C2212yes—
98#2647C2211yescharacteristic
99#2647C2211yescharacteristic
100#2647C2212yes—
101#2647C2211yescharacteristic
102#2647C2214yes—
103#2629C2212yes—
104#2629C2212yes—
105#2628C2212yes—
106#2628C2212yes—
107#2612C2214yes—
108#2612C2214yes—
109#2606C2214yes—
110#2605C2214yes—
111#2590C2214yes—
112#2589C2214yes—
113#2589C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2588C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2586C2214yes—
121#2586C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2585C2214yes—
125#2584C2214yes—
126#2584C2214yes—
127#2582C2214yes—
128#2581C2214yes—
129#2574C2214yes—
130#2571C2212yes—
131#2571C2212yes—
132#2571C2212yes—
133#2571C2212yes—
134#2570C2212yes—
135#2570C2212yes—
136#2570C2212yes—
137#2570C2212yes—
138#2569C2214yes—
139#2568C2214yes—
140#2565C2214yes—
141#2556C2214yes—
142#2552C2212yes—
143#2552C2212yes—
144#2552C2212yes—
145#2552C2212yes—
146#2552C2212yes—
147#2552C2212yes—
148#2551C2212yes—
149#2551C2212yes—
150#2550C2212yes—
151#2550C2212yes—
152#2550C2212yes—
153#2550C2212yes—
154#2550C2212yes—
155#2550C2212yes—
156#2550C2214yes—
157#2550C2212yes—
158#2550C2212yes—
159#2550C2214yes—
160#2549C2214yes—
161#2522C2214yes—
162#2520C2214yes—
163#2520C2214yes—
164#2511C2214yes—
165#2508C2214yes—
166#2508C2214yes—
167#2507C2214yes—
168#2507C2214yes—
169#2507C2214yes—
170#2506C2214yes—
171#2506C2214yes—
172#2497C2214yes—
173#2465C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2453C2214yes—
177#2453C2214yes—
178#2453C2214yes—
179#2451C2214yes—
180#2451C2214yes—
181#2451C2214yes—
182#2446C2214yes—
183#2446C2214yes—
184#2441C2214yes—
185#2439C2214yes—
186#2438C2214yes—
187#2438C2214yes—
188#2429C2214yes—
189#2382C2214yes—
190#2381C2214yes—
191#2371C2214yes—
192#2365C2214yes—
193#2355C2212yes—
194#2355C2212yes—
195#2355C2212yes—
196#2355C2212yes—
197#2355C2212yes—
198#2355C2212yes—
199Q8×C4⋊C4C2212yes—
200Q8×C4⋊C4C2212yes—
201#2332C2214yes—
202#2332C2214yes—
203#2331C2212yes—
204#2331C2212yes—
205#2331C2212yes—
206#2331C2212yes—
207#2331C2212yes—
208#2331C2212yes—
209#2330C2212yes—
210#2330C2212yes—
211#2330C2212yes—
212#2330C2212yes—
213#2330C2212yes—
214#2330C2212yes—
215#2329C2212yes—
216#2329C2212yes—
217#2329C2212yes—
218#2329C2212yes—
219#2323C2214yes—
220#2323C2214yes—
221#2314C2211yescharacteristic
222#2314C2211yescharacteristic
223#2314C2211yescharacteristic
224#2314C2212yes—
225#2314C2211yescharacteristic
226#2314C2212yes—
227C4×C4⋊Q8C2212yes—
228C4×C4⋊Q8C2212yes—
229C4×#125C2212yes—
230C4×#125C2212yes—
231#2296C2211yescharacteristic
232#2296C2211yescharacteristic
233#2295C2212yes—
234#2295C2212yes—
235#2295C2212yes—
236#2295C2212yes—
237#2285C2211yescharacteristic
238#2285C2212yes—
239#2283C2212yes—
240C4×#117C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×#376C2211yescharacteristic
243#533Q8116yescomplemented
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2314yes—
251C2×C4⋊Q8C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×#117C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2314yes—
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#399C2314yes—
303#399C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#393C2314yes—
375#393C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2312yes—
379#391C2314yes—
380#391C2312yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2312yes—
389#391C2314yes—
390#391C2312yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2314yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
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#385C2314yes—
565#385C2314yes—
566#385C2312yes—
567#385C2312yes—
568#385C2312yes—
569#385C2312yes—
570#385C2314yes—
571#385C2314yes—
572#384C2312yes—
573#384C2312yes—
574#384C2314yes—
575#384C2311yescharacteristic
576#384C2311yescharacteristic
577#384C2312yes—
578#384C2311yescharacteristic
579#384C2312yes—
580#384C2311yescharacteristic
581#384C2312yes—
582#384C2312yes—
583#384C2312yes—
584#384C2314yes—
585#384C2312yes—
586#384C2312yes—
587#384C2314yes—
588#383C2314yes—
589#382C2312yes—
590#382C2312yes—
591#382C2314yes—
592#382C2314yes—
593#382C2314yes—
594#382C2312yes—
595#382C2311yescharacteristic
596#382C2311yescharacteristic
597#382C2311yescharacteristic
598#382C2311yescharacteristic
599#382C2312yes—
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2314yes—
604#382C2314yes—
605#382C2312yes—
606#382C2312yes—
607#382C2314yes—
608#381C2314yes—
609#380C2314yes—
610#380C2314yes—
611#380C2314yes—
612#380C2312yes—
613#380C2312yes—
614#380C2312yes—
615#380C2312yes—
616#380C2312yes—
617#380C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2311yescharacteristic
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2311yescharacteristic
658C4×C22⋊C4C2311yescharacteristic
659C4×C22⋊C4C2311yescharacteristic
660#376C2311yescharacteristic
661#376C2311yescharacteristic
662#376C2311yescharacteristic
663#376C2312yes—
664#376C2312yes—
665#376C2312yes—
666#376C2311yescharacteristic
667#376C2311yescharacteristic
668#376C2311yescharacteristic
669#376C2314yes—
670C2×#95C2312yes—
671C2×#95C2312yes—
672C43C2311yescharacteristic
673C43C2312yes—
674C43C2311yescharacteristic
675C22×Q8C2414yes—
676C22×Q8C2414yes—
677C22×Q8C2414yes—
678C22×Q8C2414yes—
679C22×Q8C2412yes—
680C22×Q8C2412yes—
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2412yes—
685C23×C4C2412yes—
686C4⋊Q8—28no—
687C4⋊Q8—44no—
688C4⋊Q8—44no—
689C4⋊Q8—44no—
690C4⋊Q8—84no—
691C4⋊Q8—84no—
692C4⋊Q8—84no—
693C4⋊Q8C2×Q8116yes—
694#125—28no—
695#125—44no—
696#125—44no—
697#125—44no—
698#125—84no—
699#125—84no—
700#125—84no—
701#125—84no—
702#125—84no—
703#125C2×Q8116yes—
704C22⋊Q8—84no—
705C22⋊Q8—84no—
706C22⋊Q8C2×Q8116yes—
707C22⋊Q8C2×Q8116yes—
708C4×Q8—84no—
709C4×Q8—84no—
710C4×Q8—84no—
711C4×Q8—84no—
712C4×Q8C2×Q8116yes—
713C4×Q8C2×Q8116yes—
714#117—42no—
715#117—42no—
716#117—84no—
717#117C2×Q818yes—
718#117C2×Q818yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2411yescharacteristic
807C2×C42—24no—
808C2×C42—42no—
809C2×C42C2×Q818yes—
810C2×C42C2411yescharacteristic
811C2×C42C2412yes—
812C2×C42C2411yescharacteristic
813C2×C42C2412yes—
814C2×C42C2411yescharacteristic
815C2×C42C2411yescharacteristic
816C2×C42C2411yescharacteristic
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2411yescharacteristic
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846#95C2412yes—
847#95C2412yes—
848#95C2412yes—
849#95C2412yes—
850#95C2412yes—
851#95C2412yes—
852#95C2412yes—
853#95C2412yes—
854#95C2412yes—
855#95C2412yes—
856#95C2412yes—
857#95C2412yes—
858#95C2412yes—
859#95C2412yes—
860#95C2412yes—
861#95C2412yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2414yes—
873#95C2412yes—
874#95C2414yes—
875#95C2412yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
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#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926C24C2511yescharacteristic
927C2×Q8—28no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—42no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—44no—
936C2×Q8—44no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×Q8—44no—
940C2×Q8—44no—
941C2×Q8—44no—
942C2×Q8—44no—
943C2×Q8C22×Q818yes—
944C2×Q8C22×Q818yes—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4C22×Q814yes—
957C22×C4C22×Q818yes—
958C22×C4C2511yescharacteristic
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2511yescharacteristic
966C22×C4C2514yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2514yes—
970C22×C4C2512yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2511yescharacteristic
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2511yescharacteristic
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—44no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—44no—
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—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4C22×Q818yes—
1055C4⋊C4C22×Q818yes—
1056C4⋊C4C22×Q818yes—
1057C4⋊C4C22×Q818yes—
1058C4⋊C4C22×Q818yes—
1059C4⋊C4C22×Q818yes—
1060C4⋊C4C22×Q818yes—
1061C4⋊C4C22×Q818yes—
1062C22⋊C4—44no—
1063C22⋊C4—41no—
1064C22⋊C4—42no—
1065C22⋊C4—41no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4C22×Q814yes—
1070C22⋊C4C22×Q818yes—
1071C22⋊C4C22×Q814yes—
1072C42—22no—
1073C42—22no—
1074C42—22no—
1075C42—24no—
1076C42—22no—
1077C42—24no—
1078C42—22no—
1079C42—41no—
1080C42—41no—
1081C42—42no—
1082C42—44no—
1083C42—42no—
1084C42—44no—
1085C42—42no—
1086C42—44no—
1087C42—42no—
1088C42—44no—
1089C42—44no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—42no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—42no—
1099C42—44no—
1100C42—42no—
1101C42C22×Q818yes—
1102C42C22×Q814yes—
1103C42C22×Q814yes—
1104C42C22×Q814yes—
1105C42C22×Q818yes—
1106C42C22×Q814yes—
1107C422−1+414yes—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23C23×Q812yes—
1113C23C2611yescharacteristic
1114Q8—48no—
1115Q8—48no—
1116Q8—88no—
1117Q8—88no—
1118Q8—164no—
1119Q8—164no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—28no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—48no—
1184C2×C4—82no—
1185C2×C4—82no—
1186C2×C4—84no—
1187C2×C4C23×Q812yes—
1188C2×C4C23×Q814yes—
1189C2×C4C23×Q814yes—
1190C2×C4C23×Q814yes—
1191C2×C4C23×Q814yes—
1192C2×C4C23×Q814yes—
1193C2×C4C23×Q814yes—
1194C2×C4C23×Q812yes—
1195C2×C4C2×2−1+412yes—
1196C2×C4C2×2−1+412yes—
1197C2×C4C2×2−1+412yes—
1198C2×C4#58512yes—
1199C22—22no—
1200C22—24no—
1201C22—41no—
1202C22—42no—
1203C22—41no—
1204C22C24×Q811yescharacteristic
1205C22C22×2−1+411yescharacteristic
1206C22C2×#58511yescharacteristic
1207C22H(7,𝔽2)12yes—
1208C222−1+612yes—
1209C4—22no—
1210C4—24no—
1211C4—24no—
1212C4—24no—
1213C4—24no—
1214C4—24no—
1215C4—24no—
1216C4—22no—
1217C4—22no—
1218C4—44no—
1219C4—41no—
1220C4—44no—
1221C4—44no—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—44no—
1227C4—42no—
1228C4—44no—
1229C4—44no—
1230C4—42no—
1231C4—44no—
1232C4—44no—
1233C4—41no—
1234C4#350214yes—
1235C2—42no—
1236C2C2×#350211yescharacteristic
1237C2#6285412yes—
1238C2#6288111yescharacteristic
1239C2#6288212yes—
1240C2#6288911yescharacteristic
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. #52041C2semidirect
2. #52037C2semidirect
3. #51606C2semidirect
4. #51603C2semidirect
9. #39754C2semidirect
10. #39753C2semidirect
11. #39622C2semidirect
12. #39621C2semidirect
13. #39182C2semidirect
14. #39180C2semidirect
15. #39177C2semidirect
16. #39176C2semidirect
243. #533Q8semidirect

Maximal subgroups

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

subgroupindex
#520412
#520372
#516062
#516032
#470222
#468452
#464462
#464372
#397542
#397532
#396222
#396212
#391822
#391802
#391772
#391762
#376242
#374282
#373112
#373092
#353372
#353042
#352842
#352822
#343752
#343742
#340742