Finite Group Databasebeta

← #7658073

Subgroups — #7658073

Order 512.

4161 conjugacy classes of subgroups.

The subgroup lattice has 1265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41790C214yesmaximal
2#41786C214yesmaximal, complemented
3#41779C214yesmaximal, complemented
4#41770C214yesmaximal, complemented
5#41599C214yesmaximal, complemented
6#41577C214yesmaximal, complemented
7#39553C212yesmaximal, complemented
8#39546C212yesmaximal, complemented
9#39494C211yesmaximal, characteristic, complemented
10#39484C211yesmaximal, characteristic, complemented
11#38915C212yesmaximal
12#38267C212yesmaximal, complemented
13#38261C212yesmaximal, complemented
14#37580C212yesmaximal, complemented
15#37510C212yesmaximal, complemented
16#37504C212yesmaximal, complemented
17#36574C211yesmaximal, characteristic, complemented
18#36567C211yesmaximal, characteristic, complemented
19#36384C212yesmaximal, complemented
20#35975C214yesmaximal, complemented
21#35902C214yesmaximal, complemented
22#35336C211yesmaximal, characteristic, complemented
23#35265C212yesmaximal, complemented
24#34629C211yesmaximal, characteristic, complemented
25#34629C212yesmaximal, complemented
26#34314C212yesmaximal, complemented
27#34151C211yesmaximal, characteristic
28C2×#552C2212yes—
29C2×#529C2211yescharacteristic
30#2864C2212yes—
31#2864C2212yes—
32#2859C2211yescharacteristic
33#2859C2211yescharacteristic
34#2859C2212yes—
35#2859C2212yes—
36#2851C2212yes—
37#2839C2214yes—
38#2839C2214yes—
39#2836C2214yes—
40#2834C2214yes—
41#2833C2214yes—
42#2827C2214yes—
43#2802C2214yes—
44#2802C2214yes—
45#2796C2214yes—
46#2791C2214yes—
47#2787C2214yes—
48#2780C2214yes—
49#2777C2214yes—
50#2777C2214yes—
51#2776C2214yes—
52#2771C2214yes—
53#2770C2214yes—
54#2767C2214yes—
55#2766C2214yes—
56#2766C2214yes—
57#2765C2214yes—
58#2765C2214yes—
59#2761C2214yes—
60#2747C2214yes—
61#2726C2214yes—
62#2724C2214yes—
63#2720C2214yes—
64#2719C2214yes—
65#2717C2214yes—
66#2708C2214yes—
67#2666C2214yes—
68#2664C2214yes—
69#2655C2214yes—
70#2655C2214yes—
71#2655C2214yes—
72#2655C2214yes—
73#2655C2214yes—
74#2655C2214yes—
75#2655C2214yes—
76#2655C2214yes—
77#2654C2214yes—
78#2652C2214yes—
79#2652C2214yes—
80#2652C2214yes—
81#2652C2214yes—
82#2649C2214yes—
83#2647C2212yes—
84#2647C2211yescharacteristic
85#2647C2212yes—
86#2647C2212yes—
87#2646C2214yes—
88#2645C2212yes—
89#2645C2212yes—
90#2645C2212yes—
91#2643C2214yes—
92#2642C2211yescharacteristic
93#2629C2211yescharacteristic
94#2629C2211yescharacteristic
95#2629C2212yes—
96#2629C2211yescharacteristic
97#2625C2212yes—
98#2625C2212yes—
99#2625C2212yes—
100#2621C2212yes—
101#2621C2211yescharacteristic
102#2611C2214yes—
103#2611C2214yes—
104#2601C2214yes—
105#2597C2214yes—
106#2594C2214yes—
107#2594C2214yes—
108#2590C2214yes—
109#2590C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2587C2214yes—
115#2587C2214yes—
116#2587C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2585C2214yes—
120#2584C2212yes—
121#2584C2214yes—
122#2581C2212yes—
123#2577C2214yes—
124#2570C2212yes—
125#2565C2212yes—
126#2553C2214yes—
127#2533C2214yes—
128#2533C2214yes—
129#2530C2214yes—
130#2528C2214yes—
131#2528C2214yes—
132#2528C2214yes—
133#2528C2214yes—
134#2522C2214yes—
135#2519C2214yes—
136#2517C2214yes—
137#2514C2212yes—
138#2511C2212yes—
139#2509C2214yes—
140#2509C2214yes—
141#2508C2214yes—
142#2508C2214yes—
143#2508C2212yes—
144#2507C2214yes—
145#2507C2212yes—
146#2507C2212yes—
147#2506C2214yes—
148#2506C2214yes—
149#2506C2212yes—
150#2505C2214yes—
151#2505C2214yes—
152#2502C2212yes—
153#2499C2212yes—
154#2496C2214yes—
155#2496C2212yes—
156#2494C2212yes—
157#2494C2214yes—
158#2487C2212yes—
159#2485C2212yes—
160#2481C2214yes—
161#2478C2214yes—
162#2478C2214yes—
163#2478C2214yes—
164#2478C2214yes—
165#2475C2214yes—
166#2475C2214yes—
167#2473C2214yes—
168#2473C2214yes—
169#2473C2214yes—
170#2470C2214yes—
171#2462C2214yes—
172#2453C2212yes—
173#2453C2212yes—
174#2442C2212yes—
175#2441C2212yes—
176#2423C2212yes—
177#2421C2212yes—
178#2417C2212yes—
179#2415C2212yes—
180#2402C2214yes—
181#2402C2214yes—
182#2402C2214yes—
183#2401C2214yes—
184#2401C2214yes—
185#2401C2214yes—
186#2374C2212yes—
187#2374C2212yes—
188#2373C2214yes—
189#2373C2214yes—
190#2373C2212yes—
191#2373C2212yes—
192#2371C2214yes—
193#2370C2212yes—
194#2370C2214yes—
195#2370C2212yes—
196#2370C2214yes—
197#2370C2214yes—
198#2367C2212yes—
199#2363C2212yes—
200#2362C2212yes—
201#2362C2212yes—
202#2360C2212yes—
203#2359C2214yes—
204#2352C2212yes—
205#2351C2212yes—
206#2347C2212yes—
207#2344C2212yes—
208#2343C2214yes—
209#2336C2214yes—
210#2334C2214yes—
211#2330C2211yescharacteristic
212#2330C2211yescharacteristic
213#2322C2214yes—
214#2317C2212yes—
215#2317C2212yes—
216#2317C2212yes—
217#2316C2212yes—
218#2314C2212yes—
219C4×C4⋊Q8C2211yescharacteristic
220C4×C4⋊Q8C2212yes—
221C4×#125C2212yes—
222C4×#125C2211yescharacteristic
223C4×#125C2212yes—
224C4×C22⋊Q8C2212yes—
225C4×C22⋊Q8C2212yes—
226C4×C22⋊Q8C2212yes—
227#2298C2212yes—
228#2296C2212yes—
229#2295C2212yes—
230#2295C2212yes—
231#2295C2212yes—
232#2295C2211yescharacteristic
233#2293C2211yescharacteristic
234#2293C2212yes—
235C2×#389C2212yes—
236#2290C2212yes—
237#2274C2214yes—
238C42×Q8C2211yescharacteristic
239C42×D4C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C4×#117C2212yes—
243#552—216no—
244C2×C4⋊Q8C2311yescharacteristic
245#529—28no—
246C2×#126C2314yes—
247C2×#126C2312yes—
248C2×#126C2314yes—
249C2×#125C2311yescharacteristic
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#125C2311yescharacteristic
253C2×#125C2314yes—
254C2×#125C2311yescharacteristic
255C2×#125C2311yescharacteristic
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#124C2311yescharacteristic
259C2×#123C2314yes—
260C2×#123C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×#121C2311yescharacteristic
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C2×#117C2312yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C2×#117C2314yes—
279C2×#117C2312yes—
280C2×#117C2314yes—
281C2×#117C2312yes—
282C2×#117C2311yescharacteristic
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2314yes—
286C22×C42C2311yescharacteristic
287C22×C42C2312yes—
288#401C2314yes—
289#401C2314yes—
290#401C2314yes—
291#401C2314yes—
292#401C2314yes—
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#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#400C2314yes—
326#400C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
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#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#395C2314yes—
389#395C2314yes—
390#394C2314yes—
391#394C2314yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#390C2312yes—
402#390C2312yes—
403#390C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2314yes—
418#389C2312yes—
419#389C2314yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
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#389C2314yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2312yes—
464#388C2314yes—
465#388C2314yes—
466#388C2312yes—
467#388C2312yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2312yes—
473#388C2312yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2312yes—
483#388C2312yes—
484#388C2312yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
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#387C2312yes—
505#387C2314yes—
506#387C2312yes—
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#387C2312yes—
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#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#386C2312yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2312yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2312yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2312yes—
574#385C2314yes—
575#385C2314yes—
576#384C2312yes—
577#384C2311yescharacteristic
578#384C2312yes—
579#384C2312yes—
580#384C2314yes—
581#384C2311yescharacteristic
582#384C2311yescharacteristic
583#383C2314yes—
584#383C2314yes—
585#382C2312yes—
586#382C2312yes—
587#382C2311yescharacteristic
588#382C2312yes—
589#382C2312yes—
590#382C2314yes—
591#382C2314yes—
592#382C2314yes—
593#382C2314yes—
594#382C2314yes—
595#381C2314yes—
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2312yes—
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2311yescharacteristic
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2311yescharacteristic
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2311yescharacteristic
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2311yescharacteristic
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663#376C2311yescharacteristic
664#376C2314yes—
665#376C2314yes—
666#376C2314yes—
667#376C2311yescharacteristic
668#376C2311yescharacteristic
669#376C2311yescharacteristic
670#376C2312yes—
671C2×#95C2314yes—
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C43C2312yes—
675C43C2312yes—
676C22×Q8C2412yes—
677C22×Q8C2411yescharacteristic
678C22×D4C2412yes—
679C22×D4C2411yescharacteristic
680C23×C4C2411yescharacteristic
681C23×C4C2412yes—
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2414yes—
687C23×C4C2412yes—
688C4⋊Q8—24no—
689#126—28no—
690#126—216no—
691#126—48no—
692#125—24no—
693#125—216no—
694#125—28no—
695#125—24no—
696#125—42no—
697#125—48no—
698#125—42no—
699#125—48no—
700#125—48no—
701#124—24no—
702#123—216no—
703#123—28no—
704C22⋊Q8—28no—
705C22⋊Q8—28no—
706C22⋊Q8—24no—
707C22⋊Q8—44no—
708#121—24no—
709C4×Q8—24no—
710C4×Q8—28no—
711C4×Q8—44no—
712C4×Q8—44no—
713C4×Q8—44no—
714C4×D4—28no—
715C4×D4—44no—
716C4×D4#4118yes—
717#117—28no—
718#117—28no—
719#117—216no—
720#117—28no—
721#117—24no—
722#117—42no—
723#117—44no—
724#117—48no—
725#117—44no—
726C2×C4⋊C4—28no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4—48no—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C42—24no—
821C2×C42—44no—
822C2×C42C2414yes—
823C2×C42C2411yescharacteristic
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2411yescharacteristic
828C2×C42C2414yes—
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
866#95C2414yes—
867#95C2412yes—
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2412yes—
875#95C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2412yes—
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—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934C24C2511yescharacteristic
935C24C2512yes—
936C2×Q8—24no—
937C2×Q8—22no—
938C2×Q8—24no—
939C2×Q8—24no—
940C2×Q8—42no—
941C2×D4—24no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4C2×#4114yes—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—24no—
955C22×C4—44no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4C2×#4118yes—
968C22×C4C2512yes—
969C22×C4C2511yescharacteristic
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2511yescharacteristic
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2511yescharacteristic
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2511yescharacteristic
988C22×C4C2512yes—
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2511yescharacteristic
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—22no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
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—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4C2×#4114yes—
1059C22⋊C4—24no—
1060C22⋊C4—28no—
1061C22⋊C4—24no—
1062C22⋊C4—28no—
1063C22⋊C4—24no—
1064C22⋊C4—28no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—44no—
1077C22⋊C4—42no—
1078C22⋊C4—44no—
1079C22⋊C4—42no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4C2×#4118yes—
1084C42—22no—
1085C42—22no—
1086C42—22no—
1087C42—28no—
1088C42—24no—
1089C42—28no—
1090C42—22no—
1091C42—24no—
1092C42—22no—
1093C42—24no—
1094C42—24no—
1095C42—22no—
1096C42—28no—
1097C42—24no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—44no—
1104C42—44no—
1105C42—42no—
1106C42—42no—
1107C42—44no—
1108C42—42no—
1109C42—44no—
1110C42—44no—
1111C42—42no—
1112C42—42no—
1113C42—44no—
1114C42—44no—
1115C42—42no—
1116C42—42no—
1117C42C2×#4114yes—
1118C422−1+414yes—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—21no—
1126C23—21no—
1127C23—22no—
1128C23—21no—
1129C23—22no—
1130C23C22×#4114yes—
1131C23C2611yescharacteristic
1132Q8—44no—
1133Q8—48no—
1134D4—44no—
1135D4—84no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—216no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—21no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—44no—
1201C2×C4—416no—
1202C2×C4—44no—
1203C2×C4—82no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—164no—
1207C2×C4C22×#4112yes—
1208C2×C4C22×#4114yes—
1209C2×C4C22×#4112yes—
1210C2×C4C22×#4112yes—
1211C2×C4C2×2−1+414yes—
1212C2×C4C2×2−1+412yes—
1213C2×C4#58514yes—
1214C2×C4#58512yes—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—42no—
1226C22—42no—
1227C22C23×#4111yescharacteristic
1228C22C22×2−1+411yescharacteristic
1229C22C2×#58511yescharacteristic
1230C22C2×#58512yes—
1231C222−1+612yes—
1232C4—24no—
1233C4—22no—
1234C4—22no—
1235C4—24no—
1236C4—24no—
1237C4—41no—
1238C4—44no—
1239C4—44no—
1240C4—41no—
1241C4—42no—
1242C4—41no—
1243C4—44no—
1244C4—44no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—42no—
1249C4—44no—
1250C4—42no—
1251C4—44no—
1252C4—42no—
1253C4—42no—
1254C4—44no—
1255C4—44no—
1256C4#351514yes—
1257C2—44no—
1258C2—81no—
1259C2#6268611yescharacteristic
1260C2C2×#351511yescharacteristic
1261C2#6286111yescharacteristic
1262C2#6295612yes—
1263C2#6297112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #41786C2semidirect
3. #41779C2semidirect
4. #41770C2semidirect
5. #41599C2semidirect
6. #41577C2semidirect
7. #39553C2semidirect
8. #39546C2semidirect
9. #39494C2semidirect
10. #39484C2semidirect
12. #38267C2semidirect
13. #38261C2semidirect
14. #37580C2semidirect
15. #37510C2semidirect
16. #37504C2semidirect
17. #36574C2semidirect
18. #36567C2semidirect
19. #36384C2semidirect
20. #35975C2semidirect
21. #35902C2semidirect
22. #35336C2semidirect
23. #35265C2semidirect
24. #34629C2semidirect
25. #34629C2semidirect
26. #34314C2semidirect

Maximal subgroups

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

subgroupindex
#417902
#417862
#417792
#417702
#415992
#415772
#395532
#395462
#394942
#394842
#389152
#382672
#382612
#375802
#375102
#375042
#365742
#365672
#363842
#359752
#359022
#353362
#352652
#346292
#343142
#341512