Finite Group Databasebeta

← #7683913

Subgroups — #7683913

Order 512.

4444 conjugacy classes of subgroups.

The subgroup lattice has 1247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59997C214yesmaximal, complemented
2#59985C214yesmaximal
3#59930C214yesmaximal, complemented
4#59681C212yesmaximal, complemented
5#59519C214yesmaximal
6#59447C212yesmaximal, complemented
7#59330C212yesmaximal
8#59144C212yesmaximal
9#45436C211yesmaximal, characteristic, complemented
10#45395C211yesmaximal, characteristic, complemented
11#45390C212yesmaximal
12#45334C211yesmaximal, characteristic, complemented
13#45152C211yesmaximal, characteristic, complemented
14#45149C212yesmaximal
15#44528C214yesmaximal, complemented
16#44516C214yesmaximal
17#44507C214yesmaximal, complemented
18#44500C214yesmaximal
19#35670C212yesmaximal
20#35656C212yesmaximal, complemented
21#35656C212yesmaximal, complemented
22#34951C212yesmaximal, complemented
23#34882C211yesmaximal, characteristic
24#34328C212yesmaximal, complemented
25#34281C211yesmaximal, characteristic
26#34262C212yesmaximal
27#34209C211yesmaximal, characteristic
28C2×#557C2212yes—
29C2×#541C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#519C2212yes—
32#2802C2214yes—
33#2802C2214yes—
34#2792C2214yes—
35#2791C2214yes—
36#2789C2214yes—
37#2769C2214yes—
38#2769C2214yes—
39#2767C2214yes—
40#2766C2214yes—
41#2762C2214yes—
42#2762C2214yes—
43#2758C2214yes—
44#2755C2214yes—
45#2747C2214yes—
46#2745C2214yes—
47#2744C2214yes—
48#2739C2214yes—
49#2738C2214yes—
50#2719C2214yes—
51#2719C2214yes—
52#2719C2214yes—
53#2713C2214yes—
54#2713C2214yes—
55#2690C2214yes—
56#2612C2214yes—
57#2612C2214yes—
58#2612C2214yes—
59#2606C2214yes—
60#2605C2214yes—
61#2590C2214yes—
62#2590C2214yes—
63#2590C2214yes—
64#2590C2214yes—
65#2590C2214yes—
66#2588C2214yes—
67#2588C2214yes—
68#2588C2214yes—
69#2588C2214yes—
70#2586C2212yes—
71#2586C2214yes—
72#2585C2214yes—
73#2585C2212yes—
74#2585C2214yes—
75#2585C2214yes—
76#2582C2212yes—
77#2581C2212yes—
78#2581C2212yes—
79#2577C2214yes—
80#2575C2214yes—
81#2574C2212yes—
82#2573C2214yes—
83#2570C2214yes—
84#2570C2212yes—
85#2570C2212yes—
86#2568C2212yes—
87#2568C2212yes—
88#2568C2212yes—
89#2565C2212yes—
90#2565C2212yes—
91#2556C2212yes—
92#2552C2212yes—
93#2550C2214yes—
94#2546C2212yes—
95#2546C2212yes—
96#2546C2212yes—
97#2546C2212yes—
98#2546C2212yes—
99#2533C2214yes—
100#2533C2214yes—
101#2533C2214yes—
102#2533C2214yes—
103#2533C2214yes—
104#2530C2214yes—
105#2528C2214yes—
106#2528C2214yes—
107#2528C2214yes—
108#2528C2214yes—
109#2528C2214yes—
110#2527C2214yes—
111#2524C2214yes—
112#2524C2214yes—
113#2524C2214yes—
114#2524C2214yes—
115#2524C2214yes—
116#2524C2214yes—
117#2522C2212yes—
118#2520C2214yes—
119#2520C2214yes—
120#2520C2214yes—
121#2520C2212yes—
122#2520C2214yes—
123#2515C2214yes—
124#2514C2212yes—
125#2514C2212yes—
126#2511C2212yes—
127#2511C2212yes—
128#2511C2212yes—
129#2511C2212yes—
130#2509C2214yes—
131#2509C2214yes—
132#2507C2214yes—
133#2499C2212yes—
134#2499C2212yes—
135#2478C2214yes—
136#2478C2214yes—
137#2478C2214yes—
138#2478C2214yes—
139#2473C2214yes—
140#2473C2214yes—
141#2465C2212yes—
142#2462C2214yes—
143#2462C2214yes—
144#2462C2214yes—
145#2462C2214yes—
146#2462C2212yes—
147#2462C2214yes—
148#2462C2214yes—
149#2453C2214yes—
150#2451C2214yes—
151#2446C2212yes—
152#2446C2212yes—
153#2446C2212yes—
154#2446C2212yes—
155#2446C2212yes—
156#2446C2212yes—
157#2442C2214yes—
158#2434C2212yes—
159#2434C2212yes—
160#2402C2214yes—
161#2402C2214yes—
162#2399C2211yescharacteristic
163#2399C2211yescharacteristic
164#2396C2211yescharacteristic
165#2396C2211yescharacteristic
166#2373C2214yes—
167#2373C2214yes—
168#2371C2214yes—
169#2371C2214yes—
170#2371C2214yes—
171#2371C2214yes—
172#2371C2214yes—
173#2370C2214yes—
174#2370C2214yes—
175#2370C2214yes—
176#2365C2212yes—
177#2365C2212yes—
178#2365C2212yes—
179#2365C2214yes—
180#2365C2214yes—
181#2360C2214yes—
182#2356C2212yes—
183#2356C2212yes—
184#2356C2214yes—
185#2356C2212yes—
186#2356C2214yes—
187#2355C2212yes—
188#2355C2212yes—
189#2355C2214yes—
190#2355C2212yes—
191#2351C2212yes—
192Q8×C4⋊C4C2212yes—
193#2347C2212yes—
194#2347C2214yes—
195#2346C2212yes—
196#2346C2214yes—
197#2344C2214yes—
198#2344C2214yes—
199Q8×C22⋊C4C2212yes—
200Q8×C22⋊C4C2212yes—
201#2336C2214yes—
202#2336C2214yes—
203#2330C2211yescharacteristic
204#2327C2211yescharacteristic
205#2327C2211yescharacteristic
206#2327C2211yescharacteristic
207#2327C2212yes—
208#2327C2212yes—
209#2327C2211yescharacteristic
210#2327C2211yescharacteristic
211#2323C2212yes—
212#2320C2212yes—
213#2320C2214yes—
214#2314C2214yes—
215#2314C2211yescharacteristic
216#2310C2212yes—
217C4×C4⋊Q8C2212yes—
218C4×C4⋊Q8C2211yescharacteristic
219C4×C4⋊Q8C2212yes—
220C4×C4⋊Q8C2212yes—
221C4×C4⋊Q8C2212yes—
222C4×#125C2214yes—
223C4×#125C2214yes—
224C4×#125C2212yes—
225C4×#125C2211yescharacteristic
226C4×C22⋊Q8C2212yes—
227C4×C22⋊Q8C2212yes—
228#2298C2212yes—
229#2298C2214yes—
230#2295C2214yes—
231#2295C2212yes—
232#2295C2214yes—
233#2295C2211yescharacteristic
234#2295C2212yes—
235#2295C2212yes—
236#2295C2214yes—
237#2285C2211yescharacteristic
238#2276C2212yes—
239#2276C2212yes—
240C42×Q8C2212yes—
241C42×Q8C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C23×Q8C2312yes—
244#557—216no—
245#541—28no—
246C2×C4⋊Q8—28no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2314yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2311yescharacteristic
256C2×#126C2314yes—
257C2×#125C2311yescharacteristic
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266#519—216no—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×#117C2312yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C22×C4⋊C4C2314yes—
291C22×C42C2311yescharacteristic
292#401C2314yes—
293#401C2314yes—
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#400C2311yescharacteristic
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2311yescharacteristic
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#399C2311yescharacteristic
323#399C2311yescharacteristic
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2312yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2312yes—
354#398C2312yes—
355#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2312yes—
361#396C2312yes—
362#395C2312yes—
363#395C2314yes—
364#395C2314yes—
365#395C2311yescharacteristic
366#395C2312yes—
367#395C2314yes—
368#395C2312yes—
369#395C2311yescharacteristic
370#395C2314yes—
371#395C2312yes—
372#395C2314yes—
373#395C2314yes—
374#393C2311yescharacteristic
375#393C2311yescharacteristic
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#391C2312yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2314yes—
388#391C2314yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2314yes—
408#391C2314yes—
409#389C2312yes—
410#389C2314yes—
411#389C2312yes—
412#389C2314yes—
413#389C2312yes—
414#389C2312yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2312yes—
432#389C2314yes—
433#389C2312yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#388C2312yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2312yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2312yes—
461#388C2312yes—
462#387C2312yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2312yes—
470#387C2312yes—
471#387C2312yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2312yes—
495#387C2312yes—
496#387C2314yes—
497#387C2314yes—
498#387C2312yes—
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#387C2312yes—
522#387C2314yes—
523#387C2312yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2312yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2312yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2312yes—
536#387C2312yes—
537#387C2314yes—
538#387C2312yes—
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#387C2312yes—
562#387C2312yes—
563#385C2314yes—
564#385C2312yes—
565#385C2314yes—
566#385C2312yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#384C2312yes—
571#384C2312yes—
572#384C2312yes—
573#384C2311yescharacteristic
574#384C2314yes—
575#383C2314yes—
576#383C2314yes—
577#383C2314yes—
578#383C2314yes—
579#383C2314yes—
580#383C2314yes—
581#383C2314yes—
582#382C2314yes—
583#382C2311yescharacteristic
584#382C2312yes—
585#382C2314yes—
586#382C2312yes—
587#382C2312yes—
588#382C2314yes—
589#382C2314yes—
590#382C2314yes—
591#382C2311yescharacteristic
592#382C2314yes—
593#382C2314yes—
594#382C2314yes—
595#382C2311yescharacteristic
596#381C2314yes—
597#381C2314yes—
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#380C2312yes—
602#380C2314yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2311yescharacteristic
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663#376C2312yes—
664#376C2314yes—
665#376C2311yescharacteristic
666#376C2311yescharacteristic
667#376C2314yes—
668#376C2314yes—
669#376C2314yes—
670#376C2314yes—
671#376C2314yes—
672#376C2314yes—
673#376C2314yes—
674C43C2311yescharacteristic
675C43C2314yes—
676C43C2311yescharacteristic
677C43C2312yes—
678C22×Q8—28no—
679C22×Q8—28no—
680C22×Q8—44no—
681C22×Q8C2412yes—
682C22×Q8C2412yes—
683C22×Q8C2412yes—
684C22×Q8C2411yescharacteristic
685C22×Q8C2414yes—
686C22×Q8C2412yes—
687C22×Q8C2411yescharacteristic
688C23×C4C2414yes—
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C4⋊Q8—28no—
692C4⋊Q8—28no—
693C4⋊Q8—28no—
694C4⋊Q8—216no—
695C4⋊Q8—24no—
696C4⋊Q8—24no—
697C4⋊Q8—44no—
698C4⋊Q8—44no—
699C4⋊Q8#4118yes—
700#126—216no—
701#125—216no—
702#125—216no—
703#125—216no—
704#125—216no—
705#125—28no—
706#125—216no—
707#125—24no—
708C22⋊Q8—28no—
709C22⋊Q8—28no—
710C4×Q8—28no—
711C4×Q8—28no—
712C4×Q8—216no—
713C4×Q8—216no—
714C4×Q8—216no—
715C4×Q8—28no—
716C4×Q8—28no—
717C4×Q8—28no—
718C4×Q8—28no—
719C4×Q8—28no—
720C4×Q8—28no—
721C4×Q8—28no—
722C4×Q8—28no—
723C4×Q8—42no—
724C4×Q8—42no—
725C4×Q8—44no—
726C4×Q8—44no—
727C4×Q8—44no—
728#117—28no—
729#117—216no—
730#117—216no—
731#117—42no—
732#117#4118yes—
733C2×C4⋊C4—216no—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C42—24no—
815C2×C42C2414yes—
816C2×C42C2411yescharacteristic
817C2×C42C2411yescharacteristic
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2414yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2412yes—
835C2×C42C2411yescharacteristic
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853#95C2412yes—
854#95C2412yes—
855#95C2412yes—
856#95C2414yes—
857#95C2414yes—
858#95C2412yes—
859#95C2412yes—
860#95C2412yes—
861#95C2414yes—
862#95C2412yes—
863#95C2412yes—
864#95C2412yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2412yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2414yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2411yescharacteristic
901#95C2412yes—
902#95C2411yescharacteristic
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2411yescharacteristic
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2411yescharacteristic
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940C24C2511yescharacteristic
941C2×Q8—24no—
942C2×Q8—24no—
943C2×Q8—28no—
944C2×Q8—24no—
945C2×Q8—24no—
946C2×Q8—24no—
947C2×Q8—28no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—41no—
955C2×Q8—44no—
956C2×Q8—42no—
957C2×Q8—41no—
958C2×Q8—42no—
959C2×Q8—432no—
960C2×Q8C2×#4118yes—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—28no—
964C22×C4—24no—
965C22×C4—28no—
966C22×C4—24no—
967C22×C4—42no—
968C22×C4—44no—
969C22×C4C2×#4114yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2511yescharacteristic
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2511yescharacteristic
984C22×C4C2514yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2511yescharacteristic
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2511yescharacteristic
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—24no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—42no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—41no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—41no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4C2×#41116yes—
1064C4⋊C4C2×#4118yes—
1065C4⋊C42−1+418yes—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—44no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4C2×#4118yes—
1076C42—22no—
1077C42—24no—
1078C42—28no—
1079C42—28no—
1080C42—28no—
1081C42—28no—
1082C42—28no—
1083C42—28no—
1084C42—28no—
1085C42—28no—
1086C42—24no—
1087C42—24no—
1088C42—28no—
1089C42—24no—
1090C42—24no—
1091C42—24no—
1092C42—24no—
1093C42—28no—
1094C42—22no—
1095C42—22no—
1096C42—24no—
1097C42—24no—
1098C42—42no—
1099C42—42no—
1100C42—44no—
1101C42—42no—
1102C42—44no—
1103C42—42no—
1104C42—44no—
1105C42—44no—
1106C42—44no—
1107C42—44no—
1108C42—44no—
1109C42—44no—
1110C42—44no—
1111C42C2×#4114yes—
1112C42C2×#4114yes—
1113C42C2×#4114yes—
1114C23—21no—
1115C23—22no—
1116C23—21no—
1117C23—22no—
1118C23C22×#4112yes—
1119C23C2611yescharacteristic
1120Q8—216no—
1121Q8—48no—
1122Q8—44no—
1123Q8—416no—
1124Q8—48no—
1125Q8—48no—
1126Q8—82no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—28no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—48no—
1192C2×C4—416no—
1193C2×C4C22×#4114yes—
1194C2×C4C22×#4114yes—
1195C2×C4C22×#4112yes—
1196C2×C4C22×#4114yes—
1197C2×C4C22×#4118yes—
1198C2×C4C22×#4112yes—
1199C2×C4C22×#4112yes—
1200C2×C4C2×2−1+414yes—
1201C2×C4C2×2−1+414yes—
1202C2×C4C2×2−1+414yes—
1203C2×C4#58512yes—
1204C22—24no—
1205C22—22no—
1206C22—42no—
1207C22—41no—
1208C22—41no—
1209C22C23×#4111yescharacteristic
1210C22C23×#4111yescharacteristic
1211C22C22×2−1+412yes—
1212C22C2×#58511yescharacteristic
1213C222−1+612yes—
1214C4—24no—
1215C4—24no—
1216C4—24no—
1217C4—24no—
1218C4—24no—
1219C4—24no—
1220C4—22no—
1221C4—28no—
1222C4—44no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—44no—
1227C4—44no—
1228C4—44no—
1229C4—41no—
1230C4—42no—
1231C4—41no—
1232C4—41no—
1233C4—42no—
1234C4—44no—
1235C4—41no—
1236C4—42no—
1237C4—44no—
1238C4—44no—
1239C4#347514yes—
1240C2—42no—
1241C2C2×#347511yescharacteristic
1242C2#6283711yescharacteristic
1243C2#6289011yescharacteristic
1244C2#6299812yes—
1245C2#6300112yes—
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. #59997C2semidirect
3. #59930C2semidirect
4. #59681C2semidirect
6. #59447C2semidirect
9. #45436C2semidirect
10. #45395C2semidirect
12. #45334C2semidirect
13. #45152C2semidirect
15. #44528C2semidirect
17. #44507C2semidirect
20. #35656C2semidirect
21. #35656C2semidirect
22. #34951C2semidirect
24. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#599972
#599852
#599302
#596812
#595192
#594472
#593302
#591442
#454362
#453952
#453902
#453342
#451522
#451492
#445282
#445162
#445072
#445002
#356702
#356562
#349512
#348822
#343282
#342812
#342622
#342092