Finite Group Databasebeta

← #7716072

Subgroups — #7716072

Order 512.

4116 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50502C214yesmaximal, complemented
2#50361C214yesmaximal, complemented
3#49344C214yesmaximal, complemented
4#49155C214yesmaximal, complemented
5#44863C214yesmaximal, complemented
6#44854C214yesmaximal, complemented
7#44712C214yesmaximal, complemented
8#44507C214yesmaximal, complemented
9#39679C212yesmaximal
10#39636C212yesmaximal
11#37959C212yesmaximal
12#37935C212yesmaximal
13#37935C212yesmaximal
14#37886C212yesmaximal
15#36959C212yesmaximal
16#36762C212yesmaximal
17#36199C212yesmaximal
18#36177C212yesmaximal
19#35315C212yesmaximal
20#35167C211yesmaximal, characteristic
21#35120C211yesmaximal, characteristic
22#35120C211yesmaximal, characteristic
23#35013C211yesmaximal, characteristic
24#35013C211yesmaximal, characteristic
25#34595C211yesmaximal, characteristic
26#34432C212yesmaximal
27C2×#2371C211yesmaximal, characteristic
28C2×#544C2212yes—
29C22×#125C2211yescharacteristic
30#2857C2212yes—
31#2857C2212yes—
32#2855C2212yes—
33#2855C2212yes—
34#2855C2212yes—
35#2855C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2851C2212yes—
39#2851C2212yes—
40#2809C2214yes—
41#2805C2214yes—
42#2802C2214yes—
43#2802C2214yes—
44#2799C2214yes—
45#2794C2214yes—
46#2794C2214yes—
47#2791C2214yes—
48#2791C2214yes—
49#2789C2214yes—
50#2789C2214yes—
51#2776C2214yes—
52#2774C2214yes—
53#2769C2214yes—
54#2769C2214yes—
55#2767C2214yes—
56#2767C2214yes—
57#2767C2214yes—
58#2767C2214yes—
59#2766C2214yes—
60#2766C2214yes—
61#2766C2214yes—
62#2762C2214yes—
63#2762C2214yes—
64#2758C2214yes—
65#2758C2214yes—
66#2758C2214yes—
67#2758C2214yes—
68#2755C2214yes—
69#2719C2214yes—
70#2719C2214yes—
71#2719C2214yes—
72#2719C2214yes—
73#2719C2214yes—
74#2713C2214yes—
75#2713C2214yes—
76#2713C2214yes—
77#2713C2214yes—
78#2713C2214yes—
79#2713C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2659C2211yescharacteristic
83#2659C2211yescharacteristic
84#2659C2211yescharacteristic
85#2659C2211yescharacteristic
86#2659C2212yes—
87#2647C2212yes—
88#2646C2212yes—
89#2646C2212yes—
90#2646C2212yes—
91#2645C2212yes—
92#2645C2212yes—
93#2642C2212yes—
94#2627C2212yes—
95#2627C2212yes—
96#2627C2212yes—
97#2627C2212yes—
98#2612C2214yes—
99#2612C2214yes—
100#2612C2214yes—
101#2612C2214yes—
102#2612C2214yes—
103#2612C2214yes—
104#2606C2214yes—
105#2606C2214yes—
106#2605C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2590C2214yes—
110#2588C2214yes—
111#2586C2214yes—
112#2586C2214yes—
113#2585C2214yes—
114#2585C2214yes—
115#2585C2214yes—
116#2585C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2583C2214yes—
120#2581C2214yes—
121#2571C2212yes—
122#2570C2212yes—
123#2568C2212yes—
124#2565C2212yes—
125#2552C2214yes—
126#2551C2214yes—
127#2550C2214yes—
128#2550C2214yes—
129#2533C2214yes—
130#2533C2214yes—
131#2533C2214yes—
132#2533C2214yes—
133#2533C2214yes—
134#2533C2214yes—
135#2533C2214yes—
136#2528C2214yes—
137#2528C2214yes—
138#2528C2214yes—
139#2528C2214yes—
140#2528C2214yes—
141#2528C2214yes—
142#2528C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2524C2214yes—
146#2524C2214yes—
147#2520C2214yes—
148#2520C2214yes—
149#2520C2214yes—
150#2514C2212yes—
151#2514C2214yes—
152#2514C2212yes—
153#2514C2212yes—
154#2511C2212yes—
155#2509C2212yes—
156#2509C2212yes—
157#2509C2214yes—
158#2508C2214yes—
159#2508C2212yes—
160#2506C2212yes—
161#2505C2214yes—
162#2505C2214yes—
163#2505C2214yes—
164#2503C2214yes—
165#2493C2214yes—
166#2493C2214yes—
167#2493C2214yes—
168#2493C2214yes—
169#2484C2214yes—
170#2484C2214yes—
171#2473C2214yes—
172#2462C2214yes—
173#2462C2214yes—
174#2462C2214yes—
175#2453C2214yes—
176#2402C2214yes—
177#2399C2214yes—
178#2382C2214yes—
179#2381C2214yes—
180#2371C2214yes—
181#2371C2214yes—
182#2371C2214yes—
183#2371C2214yes—
184#2371C2214yes—
185#2371C2214yes—
186#2370C2212yes—
187#2368C2214yes—
188#2365C2212yes—
189#2365C2214yes—
190#2360C2214yes—
191#2356C2212yes—
192#2356C2214yes—
193#2355C2212yes—
194#2343C2214yes—
195#2343C2214yes—
196#2336C2214yes—
197#2336C2214yes—
198#2331C2214yes—
199#2330C2212yes—
200#2329C2212yes—
201#2329C2212yes—
202#2329C2212yes—
203#2329C2212yes—
204#2329C2212yes—
205#2329C2212yes—
206#2327C2214yes—
207#2327C2212yes—
208#2320C2212yes—
209#2320C2212yes—
210#2316C2212yes—
211#2313C2212yes—
212#2313C2212yes—
213C4×C22⋊Q8C2212yes—
214C4×C22⋊Q8C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C2×#387C2211yescharacteristic
218C2×#387C2211yescharacteristic
219C2×#387C2211yescharacteristic
220C2×#387C2211yescharacteristic
221C2×#387C2211yescharacteristic
222C2×#387C2211yescharacteristic
223C2×#387C2211yescharacteristic
224C2×#387C2211yescharacteristic
225#2285C2212yes—
226#2283C2212yes—
227#2283C2212yes—
228#2283C2212yes—
229C2×C4×C4⋊C4C2211yescharacteristic
230C2×C4×C4⋊C4C2211yescharacteristic
231C2×C4×C4⋊C4C2211yescharacteristic
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×#376C2211yescharacteristic
234C2×#376C2211yescharacteristic
235#544—216no—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×#125—28no—
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#125C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278#401C2314yes—
279#401C2314yes—
280#401C2314yes—
281#401C2314yes—
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#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#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#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
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#391C2312yes—
367#391C2312yes—
368#391C2312yes—
369#391C2314yes—
370#391C2314yes—
371#391C2312yes—
372#391C2312yes—
373#391C2312yes—
374#391C2312yes—
375#391C2312yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2312yes—
381#391C2312yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#391C2312yes—
389#391C2314yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#389C2312yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2314yes—
426#389C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2314yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2312yes—
439#389C2314yes—
440#389C2314yes—
441#389C2312yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
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#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#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#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#384C2312yes—
551#384C2312yes—
552#384C2312yes—
553#384C2312yes—
554#383C2314yes—
555#383C2314yes—
556#383C2314yes—
557#383C2314yes—
558#383C2314yes—
559#383C2314yes—
560#383C2314yes—
561#383C2314yes—
562#383C2314yes—
563#382C2312yes—
564#382C2312yes—
565#382C2312yes—
566#382C2312yes—
567#382C2312yes—
568#382C2314yes—
569#382C2312yes—
570#382C2312yes—
571#382C2314yes—
572#382C2314yes—
573#382C2312yes—
574#382C2314yes—
575#382C2314yes—
576#382C2314yes—
577#382C2314yes—
578#382C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2314yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633#376C2312yes—
634#376C2312yes—
635#376C2314yes—
636#376C2314yes—
637#376C2314yes—
638#376C2314yes—
639#376C2314yes—
640#376C2314yes—
641#376C2314yes—
642#376C2312yes—
643#376C2312yes—
644C2×#95C2311yescharacteristic
645C2×#95C2311yescharacteristic
646C2×#95C2311yescharacteristic
647C2×#95C2311yescharacteristic
648C2×#95C2311yescharacteristic
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2311yescharacteristic
654C2×#95C2311yescharacteristic
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C22×Q8C2412yes—
661C22×Q8C2412yes—
662C22×Q8C2414yes—
663C22×Q8C2412yes—
664C22×Q8C2412yes—
665C23×C4C2411yescharacteristic
666C23×C4C2411yescharacteristic
667C23×C4C2411yescharacteristic
668C23×C4C2411yescharacteristic
669C23×C4C2411yescharacteristic
670C23×C4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C23×C4C2411yescharacteristic
673C23×C4C2411yescharacteristic
674C23×C4C2411yescharacteristic
675C23×C4C2411yescharacteristic
676C23×C4C2411yescharacteristic
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C4⋊Q8—216no—
681C4⋊Q8—216no—
682C4⋊Q8—44no—
683C4⋊Q8—44no—
684#125—216no—
685#125—216no—
686#125—216no—
687#125—216no—
688#125—44no—
689#125—44no—
690#125—48no—
691C22⋊Q8—28no—
692C22⋊Q8—28no—
693C22⋊Q8—216no—
694C22⋊Q8—28no—
695C22⋊Q8—28no—
696C4×Q8—44no—
697C4×Q8—44no—
698C4×Q8—44no—
699C4×Q8—44no—
700C4×Q8—48no—
701#117—216no—
702C2×C4⋊C4—24no—
703C2×C4⋊C4—24no—
704C2×C4⋊C4—24no—
705C2×C4⋊C4—24no—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—24no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—42no—
710C2×C4⋊C4—42no—
711C2×C4⋊C4#4118yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
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×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C42—24no—
784C2×C42—24no—
785C2×C42—24no—
786C2×C42—24no—
787C2×C42—24no—
788C2×C42—42no—
789C2×C42—42no—
790C2×C42—42no—
791C2×C42—42no—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2412yes—
796C2×C42C2412yes—
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2412yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2412yes—
806C2×C42C2412yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2412yes—
825#95C2414yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2412yes—
829#95C2412yes—
830#95C2412yes—
831#95C2414yes—
832#95C2412yes—
833#95C2412yes—
834#95C2414yes—
835#95C2414yes—
836#95C2412yes—
837#95C2414yes—
838#95C2412yes—
839#95C2412yes—
840#95C2414yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
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#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908C24C2511yescharacteristic
909C2×Q8—24no—
910C2×Q8—24no—
911C2×Q8—28no—
912C2×Q8—24no—
913C2×Q8—24no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—42no—
918C2×Q8—44no—
919C2×Q8—44no—
920C2×Q8—42no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—42no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4C2×#4114yes—
965C22×C4C2×#4114yes—
966C22×C4C2×#4114yes—
967C22×C42−1+414yes—
968C22×C42−1+414yes—
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2512yes—
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2512yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
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—28no—
1021C4⋊C4—28no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4C2×#41116yes—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C42—24no—
1067C42—24no—
1068C42—28no—
1069C42—28no—
1070C42—24no—
1071C42—24no—
1072C42—24no—
1073C42—24no—
1074C42—24no—
1075C42—24no—
1076C42—24no—
1077C42—24no—
1078C42—24no—
1079C42—24no—
1080C42—24no—
1081C42—24no—
1082C42—28no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23C22×#4112yes—
1101C23C2×2−1+412yes—
1102C23C2×2−1+412yes—
1103C23C2611yescharacteristic
1104Q8—88no—
1105Q8—84no—
1106Q8—84no—
1107Q8—84no—
1108Q8—84no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—28no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—24no—
1181C2×C4—44no—
1182C2×C4—44no—
1183C2×C4—44no—
1184C2×C4—44no—
1185C2×C4—44no—
1186C2×C4—44no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—44no—
1190C2×C4—44no—
1191C2×C4—82no—
1192C2×C4—82no—
1193C2×C4—82no—
1194C2×C4—82no—
1195C2×C4C22×#4114yes—
1196C2×C4C22×#4114yes—
1197C2×C4C22×#4114yes—
1198C2×C4C2×2−1+414yes—
1199C2×C4C2×2−1+414yes—
1200C2×C4#58512yes—
1201C2×C4#58512yes—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22#350914yes—
1209C22C23×#4111yescharacteristic
1210C22C22×2−1+411yescharacteristic
1211C22C22×2−1+411yescharacteristic
1212C22C2×#58511yescharacteristic
1213C22C2×#58511yescharacteristic
1214C222−1+611yescharacteristic
1215C222−1+611yescharacteristic
1216C4—24no—
1217C4—24no—
1218C4—24no—
1219C4—24no—
1220C4—24no—
1221C4—22no—
1222C4—22no—
1223C4—42no—
1224C4—44no—
1225C4—44no—
1226C4—41no—
1227C4—41no—
1228C4—42no—
1229C4—44no—
1230C4—44no—
1231C4—42no—
1232C4—42no—
1233C4—42no—
1234C4—44no—
1235C4—44no—
1236C4—44no—
1237C4—44no—
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—42no—
1242C2—24no—
1243C2#6278111yescharacteristic
1244C2C2×#350911yescharacteristic
1245C2#6285011yescharacteristic
1246C2#6290411yescharacteristic
1247C2#6290411yescharacteristic
1248C2#6292811yescharacteristic
1249C2#6292811yescharacteristic
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. #50502C2semidirect
2. #50361C2semidirect
3. #49344C2semidirect
4. #49155C2semidirect
5. #44863C2semidirect
6. #44854C2semidirect
7. #44712C2semidirect
8. #44507C2semidirect

Maximal subgroups

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

subgroupindex
#505022
#503612
#493442
#491552
#448632
#448542
#447122
#445072
#396792
#396362
#379592
#379352
#378862
#369592
#367622
#361992
#361772
#353152
#351672
#351202
#350132
#345952
#344322
C2×#23712