Finite Group Databasebeta

← #7710150

Subgroups — #7710150

Order 512.

4632 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59348C214yesmaximal, complemented
2#59347C214yesmaximal, complemented
3#45983C214yesmaximal, complemented
4#45983C214yesmaximal, complemented
5#39151C212yesmaximal, complemented
6#38925C212yesmaximal, complemented
7#38071C214yesmaximal, complemented
8#37915C214yesmaximal, complemented
9#37914C214yesmaximal, complemented
10#37914C214yesmaximal, complemented
11#37913C214yesmaximal, complemented
12#37562C211yesmaximal, characteristic, complemented
13#37557C211yesmaximal, characteristic, complemented
14#36980C212yesmaximal, complemented
15#36979C212yesmaximal, complemented
16#36625C211yesmaximal, characteristic, complemented
17#36621C211yesmaximal, characteristic
18#36572C212yesmaximal, complemented
19#36206C212yesmaximal, complemented
20#36206C214yesmaximal, complemented
21#35052C212yesmaximal, complemented
22#34997C212yesmaximal
23#34401C211yesmaximal, characteristic, complemented
24#34389C211yesmaximal, characteristic, complemented
25C22×#383C211yesmaximal, characteristic, complemented
26C2×#533C2211yescharacteristic
27C2×#529C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2857C2212yes—
30#2857C2212yes—
31#2855C2211yescharacteristic
32#2855C2212yes—
33#2855C2212yes—
34#2854C2211yescharacteristic
35#2853C2212yes—
36#2852C2214yes—
37#2851C2212yes—
38#2851C2214yes—
39#2850C2212yes—
40#2849C2212yes—
41#2849C2214yes—
42#2848C2211yescharacteristic
43#2848C2212yes—
44#2848C2212yes—
45#2848C2214yes—
46#2847C2211yescharacteristic
47#2843C2214yescomplemented
48#2821C2212yescomplemented
49#2821C2212yescomplemented
50#2777C2214yescomplemented
51#2777C2214yescomplemented
52#2776C2214yescomplemented
53#2776C2214yescomplemented
54#2776C2214yescomplemented
55#2775C2214yescomplemented
56#2775C2214yescomplemented
57#2770C2214yescomplemented
58#2770C2214yescomplemented
59#2769C2214yescomplemented
60#2769C2214yescomplemented
61#2769C2214yescomplemented
62#2766C2214yescomplemented
63#2766C2214yescomplemented
64#2766C2214yescomplemented
65#2764C2214yescomplemented
66#2764C2214yescomplemented
67#2762C2214yescomplemented
68#2762C2214yescomplemented
69#2762C2214yescomplemented
70#2759C2214yescomplemented
71#2759C2214yescomplemented
72#2758C2214yescomplemented
73#2758C2214yescomplemented
74#2758C2214yescomplemented
75#2758C2214yescomplemented
76#2758C2214yescomplemented
77#2758C2214yescomplemented
78#2757C2214yescomplemented
79#2738C2214yescomplemented
80#2738C2214yescomplemented
81#2737C2214yescomplemented
82#2666C2214yescomplemented
83#2666C2214yescomplemented
84#2659C2212yes—
85#2659C2212yes—
86#2646C2214yes—
87#2646C2212yes—
88#2643C2214yes—
89#2639C2212yes—
90#2634C2212yescomplemented
91#2634C2212yescomplemented
92#2633C2212yescomplemented
93#2632C2212yescomplemented
94#2606C2212yescomplemented
95#2605C2212yescomplemented
96#2599C2214yescomplemented
97#2577C2214yescomplemented
98#2573C2214yescomplemented
99#2569C2212yes—
100#2569C2214yes—
101#2569C2214yes—
102#2569C2214yes—
103#2564C2212yes—
104#2564C2214yes—
105#2564C2214yes—
106#2564C2212yes—
107#2549C2214yes—
108#2549C2214yes—
109#2549C2214yes—
110#2549C2212yes—
111#2533C2214yescomplemented
112#2533C2214yescomplemented
113#2532C2214yescomplemented
114#2525C2214yescomplemented
115#2524C2214yescomplemented
116#2524C2214yescomplemented
117#2524C2214yescomplemented
118#2524C2214yescomplemented
119#2523C2214yescomplemented
120#2515C2214yescomplemented
121#2514C2214yescomplemented
122#2514C2214yescomplemented
123#2510C2214yes—
124#2510C2214yes—
125#2510C2214yes—
126#2510C2214yes—
127#2505C2214yes—
128#2505C2214yes—
129#2505C2214yes—
130#2505C2214yes—
131#2505C2214yes—
132#2505C2214yes—
133#2505C2214yes—
134#2498C2214yes—
135#2498C2214yes—
136#2498C2214yes—
137#2495C2214yescomplemented
138#2493C2214yes—
139#2493C2214yes—
140#2493C2214yes—
141#2493C2214yes—
142#2493C2214yes—
143#2493C2214yes—
144#2493C2214yes—
145#2493C2214yescomplemented
146#2488C2214yes—
147#2488C2214yes—
148#2488C2214yes—
149#2488C2214yes—
150#2450C2214yes—
151#2450C2214yes—
152#2450C2214yes—
153#2450C2214yes—
154#2444C2214yes—
155#2438C2214yes—
156#2438C2214yes—
157#2438C2214yes—
158#2438C2214yes—
159#2438C2214yes—
160#2438C2214yes—
161#2438C2214yes—
162#2425C2214yes—
163#2419C2214yes—
164#2419C2214yes—
165#2419C2214yes—
166#2419C2214yes—
167#2383C2214yescomplemented
168#2381C2212yescomplemented
169#2381C2212yescomplemented
170#2368C2212yes—
171#2368C2214yes—
172#2368C2214yes—
173#2368C2212yes—
174#2359C2214yes—
175#2359C2214yes—
176#2359C2214yes—
177#2356C2214yescomplemented
178#2353C2214yes—
179#2353C2212yes—
180#2349C2212yes—
181#2349C2214yes—
182#2347C2212yescomplemented
183#2343C2214yes—
184#2343C2214yes—
185#2343C2214yes—
186#2343C2212yescomplemented
187#2337C2212yescomplemented
188#2336C2214yescomplemented
189#2336C2212yescomplemented
190#2329C2212yes—
191#2329C2212yes—
192#2329C2212yes—
193#2329C2214yes—
194#2325C2212yes—
195#2320C2212yescomplemented
196#2320C2214yescomplemented
197#2318C2214yes—
198#2318C2212yescomplemented
199C4×C22⋊Q8C2212yes—
200C4×C22⋊Q8C2214yes—
201C4×C22⋊Q8C2212yes—
202C4×C22⋊Q8C2212yes—
203C4×#123C2212yes—
204C4×#121C2212yes—
205C4×#120C2212yes—
206C4×#120C2214yes—
207#2296C2212yes—
208#2290C2214yes—
209#2285C2211yescharacteristic
210#2283C2211yescharacteristic
211C2×#383C2211yescharacteristic
212C2×#383C2214yes—
213C2×#383C2214yes—
214C2×#383C2211yescharacteristic
215C2×#383C2212yes—
216C2×#383C2214yes—
217C2×#383C2211yescharacteristic
218C2×#383C2212yes—
219C2×#383C2214yes—
220C2×#383C2211yescharacteristic
221#2280C2212yes—
222#2280C2214yes—
223C22×#95C2212yes—
224C22×#95C2211yescharacteristic
225C22×#95C2212yes—
226C22×#95C2211yescharacteristic
227C24×C4C2311yescharacteristic
228C24×C4C2311yescharacteristic
229C24×C4C2311yescharacteristic
230C24×C4C2312yes—
231C24×C4C2312yes—
232#533—28no—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235#529—28no—
236C2×#126C2312yes—
237C2×#125C2312yes—
238C2×#125C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#123C2312yes—
241C2×#123C2312yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2312yes—
254C2×#121C2311yescharacteristic
255C2×#121C2312yes—
256C2×#120C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2312yes—
271C22×C42—28no—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2312yes—
279C22×C42C2311yescharacteristic
280#401C2314yes—
281#401C2314yes—
282#401C2314yes—
283#401C2314yes—
284#400C2312yes—
285#400C2312yes—
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#399C2312yes—
317#399C2312yes—
318#399C2314yes—
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#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#396C2314yes—
349#396C2314yes—
350#395C2312yes—
351#395C2312yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#394C2314yes—
359#393C2312yes—
360#393C2312yes—
361#393C2314yes—
362#393C2314yes—
363#393C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2312yes—
372#391C2312yes—
373#391C2314yes—
374#391C2312yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#390C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
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#386C2314yes—
469#386C2314yes—
470#386C2314yes—
471#386C2314yes—
472#386C2314yes—
473#386C2314yes—
474#386C2312yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2312yes—
481#386C2314yes—
482#385C2314yes—
483#385C2314yes—
484#385C2314yes—
485#385C2314yes—
486#385C2314yes—
487#385C2314yes—
488#385C2314yes—
489#385C2314yes—
490#385C2314yes—
491#385C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2312yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2312yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#384C2312yes—
515#383C2312yes—
516#383C2314yes—
517#383C2314yes—
518#383C2312yes—
519#383C2312yes—
520#383C2314yes—
521#383C2312yes—
522#383C2314yes—
523#383C2312yes—
524#383C2314yes—
525#383C2314yes—
526#383C2312yes—
527#383C2312yes—
528#383C2314yes—
529#383C2312yes—
530#383C2312yes—
531#383C2312yes—
532#383C2314yes—
533#383C2314yes—
534#383C2314yes—
535#383C2314yes—
536#383C2314yes—
537#383C2314yes—
538#383C2314yes—
539#383C2314yes—
540#383C2314yes—
541#383C2314yes—
542#382C2314yes—
543#382C2312yes—
544#382C2312yes—
545#382C2314yes—
546#382C2312yes—
547#382C2314yes—
548#382C2314yes—
549#382C2314yes—
550#381C2312yes—
551#381C2314yes—
552#381C2312yes—
553#381C2314yes—
554#381C2314yes—
555#381C2312yes—
556#381C2314yes—
557#381C2314yes—
558#381C2314yes—
559#381C2314yes—
560#380C2314yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2312yes—
567#380C2312yes—
568#380C2314yes—
569#380C2312yes—
570#380C2314yes—
571#380C2314yes—
572#380C2314yes—
573#380C2314yes—
574#380C2312yes—
575#380C2312yes—
576#380C2311yescharacteristic
577#380C2311yescharacteristic
578#380C2312yes—
579#380C2312yes—
580#380C2314yes—
581#379C2312yes—
582#379C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2311yescharacteristic
591C4×C4⋊C4C2311yescharacteristic
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609#376C2312yes—
610#376C2314yes—
611#376C2312yes—
612C2×#95C2311yescharacteristic
613C2×#95C2311yescharacteristic
614C2×#95C2314yes—
615C2×#95C2314yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C2×#95C2312yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C2×#95C2314yes—
624C2×#95C2314yes—
625C2×#95C2311yescharacteristic
626C2×#95C2314yes—
627C2×#95C2311yescharacteristic
628C2×#95C2314yes—
629C2×#95C2312yes—
630C2×#95C2312yes—
631C2×#95C2314yes—
632C2×#95C2314yes—
633C2×#95C2314yes—
634C2×#95C2312yes—
635C2×#95C2314yes—
636C2×#95C2312yes—
637C2×#95C2312yes—
638C2×#95C2312yes—
639C25C2411yescharacteristic
640C22×Q8C2411yescharacteristic
641C22×Q8C2412yes—
642C22×Q8C2412yes—
643C22×Q8C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2411yescharacteristic
647C23×C4—24no—
648C23×C4—28no—
649C23×C4—24no—
650C23×C4—24no—
651C23×C4—24no—
652C23×C4—42no—
653C23×C4—44no—
654C23×C4—44no—
655C23×C4—44no—
656C23×C4—44no—
657C23×C4—44no—
658C23×C4—44no—
659C23×C4—44no—
660C23×C4C2414yes—
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2411yescharacteristic
669C23×C4C2412yes—
670C23×C4C2412yes—
671C23×C4C2414yes—
672C23×C4C2414yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2414yes—
676C23×C4C2412yes—
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2414yes—
680C23×C4C2411yescharacteristic
681C23×C4C2411yescharacteristic
682C4⋊Q8—24no—
683C4⋊Q8—24no—
684#126—28no—
685#125—24no—
686#125—28no—
687#124—24no—
688#123—28no—
689#123—48no—
690#123—48no—
691#123—44no—
692C22⋊Q8—24no—
693C22⋊Q8—28no—
694C22⋊Q8—28no—
695C22⋊Q8—44no—
696C22⋊Q8—48no—
697C22⋊Q8—48no—
698C22⋊Q8—44no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—44no—
702#121—24no—
703#121—44no—
704#120—28no—
705C4×Q8—24no—
706C4×Q8—28no—
707C4×Q8—28no—
708C4×D4—28no—
709C4×D4—24no—
710C4×D4—48no—
711C4×D4—48no—
712C4×D4—48no—
713C4×D4—48no—
714#117—28no—
715#117—28no—
716#117—44no—
717#117—48no—
718#117—48no—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
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×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C42—24no—
791C2×C42—24no—
792C2×C42—24no—
793C2×C42—28no—
794C2×C42—28no—
795C2×C42—28no—
796C2×C42—28no—
797C2×C42#4118yes—
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2412yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2411yescharacteristic
817C2×C42C2411yescharacteristic
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820#95C2412yes—
821#95C2412yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2412yes—
844#95C2414yes—
845#95C2412yes—
846#95C2414yes—
847#95C2414yes—
848#95C2412yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2412yes—
853#95C2412yes—
854#95C2414yes—
855#95C2414yes—
856#95C2412yes—
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—
898C24—22no—
899C24—24no—
900C24—24no—
901C24—22no—
902C242−1+414yes—
903C24C2512yes—
904C24C2511yescharacteristic
905C24C2512yes—
906C2×Q8—22no—
907C2×Q8—24no—
908C2×Q8—24no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—44no—
912C2×Q8—42no—
913C2×Q8—44no—
914C2×Q8—44no—
915C2×Q8—44no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—28no—
919C2×D4—24no—
920C2×D4—28no—
921C2×D4—28no—
922C2×D4—22no—
923C2×D4—42no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—22no—
932C22×C4—28no—
933C22×C4—28no—
934C22×C4—28no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—28no—
943C22×C4—24no—
944C22×C4—28no—
945C22×C4—28no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—416no—
983C22×C4—416no—
984C22×C4—416no—
985C22×C4—816no—
986C22×C4—816no—
987C22×C4C2×#4114yes—
988C22×C4C2×#4114yes—
989C22×C4C2×#4114yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2514yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2512yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2512yes—
1005C22×C4C2514yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2511yescharacteristic
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—22no—
1017C4⋊C4—24no—
1018C4⋊C4—22no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
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—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
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—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C22⋊C4—28no—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—24no—
1068C22⋊C4—28no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C42—24no—
1084C42—24no—
1085C42—24no—
1086C42—24no—
1087C42—24no—
1088C42—24no—
1089C42—24no—
1090C42—28no—
1091C42—42no—
1092C42—42no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42—44no—
1100C42—44no—
1101C42C2×#4114yes—
1102C42C2×#4114yes—
1103C42C2×#4114yes—
1104C42C2×#4114yes—
1105C23—28no—
1106C23—28no—
1107C23—216no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—28no—
1115C23—216no—
1116C23—22no—
1117C23—22no—
1118C23—24no—
1119C23—22no—
1120C23—24no—
1121C23C22×#4112yes—
1122C23C2×2−1+412yes—
1123C23C2×2−1+414yes—
1124C23#58512yes—
1125C23#58514yes—
1126C23#58514yes—
1127C23C2611yescharacteristic
1128Q8—82no—
1129Q8—84no—
1130Q8—84no—
1131Q8—164no—
1132D4—48no—
1133D4—416no—
1134D4—82no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—28no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
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—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—44no—
1191C2×C4—44no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—48no—
1196C2×C4—48no—
1197C2×C4—48no—
1198C2×C4—44no—
1199C2×C4—44no—
1200C2×C4—44no—
1201C2×C4—416no—
1202C2×C4—84no—
1203C2×C4—84no—
1204C2×C4—88no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—88no—
1208C2×C4—88no—
1209C2×C4—84no—
1210C2×C4—164no—
1211C2×C4C22×#4112yes—
1212C2×C4C22×#4112yes—
1213C2×C4C22×#4112yes—
1214C2×C4C22×#4112yes—
1215C2×C4C22×#4112yes—
1216C2×C4C22×#4112yes—
1217C22—232no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—22no—
1222C22—22no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—44no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—44no—
1233C22#349514yes—
1234C22#356418yes—
1235C22C23×#4111yescharacteristic
1236C22C22×2−1+411yescharacteristic
1237C22C2×#58512yes—
1238C22C2×#58512yes—
1239C22C2×#58511yescharacteristic
1240C4—22no—
1241C4—22no—
1242C4—22no—
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—42no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—42no—
1254C4—42no—
1255C4—44no—
1256C4—44no—
1257C4—44no—
1258C4—44no—
1259C4—44no—
1260C4—44no—
1261C4—44no—
1262C2—24no—
1263C2—28no—
1264C2—82no—
1265C2C2×#356412yes—
1266C2C2×#349511yescharacteristic
1267C2#6281411yescharacteristic
1268C2#6281411yescharacteristic
1269C2#6282612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2847C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59348C2semidirect
2. #59347C2semidirect
3. #45983C2semidirect
4. #45983C2semidirect
5. #39151C2semidirect
6. #38925C2semidirect
7. #38071C2semidirect
8. #37915C2semidirect
9. #37914C2semidirect
10. #37914C2semidirect
11. #37913C2semidirect
12. #37562C2semidirect
13. #37557C2semidirect
14. #36980C2semidirect
15. #36979C2semidirect
16. #36625C2semidirect
18. #36572C2semidirect
19. #36206C2semidirect
20. #36206C2semidirect
21. #35052C2semidirect
23. #34401C2semidirect
24. #34389C2semidirect
25. C22×#383C2semidirect
47. #2843C22semidirect
48. #2821C22semidirect
49. #2821C22semidirect
50. #2777C22semidirect
51. #2777C22semidirect
52. #2776C22semidirect
53. #2776C22semidirect
54. #2776C22semidirect
55. #2775C22semidirect
56. #2775C22semidirect
57. #2770C22semidirect
58. #2770C22semidirect
59. #2769C22semidirect
60. #2769C22semidirect
61. #2769C22semidirect
62. #2766C22semidirect
63. #2766C22semidirect
64. #2766C22semidirect
65. #2764C22semidirect
66. #2764C22semidirect
67. #2762C22semidirect
68. #2762C22semidirect
69. #2762C22semidirect
70. #2759C22semidirect
71. #2759C22semidirect
72. #2758C22semidirect
73. #2758C22semidirect
74. #2758C22semidirect
75. #2758C22semidirect
76. #2758C22semidirect
77. #2758C22semidirect
78. #2757C22semidirect
79. #2738C22semidirect
80. #2738C22semidirect
81. #2737C22semidirect
82. #2666C22semidirect
83. #2666C22semidirect
90. #2634C22semidirect
91. #2634C22semidirect
92. #2633C22semidirect
93. #2632C22semidirect
94. #2606C22semidirect
95. #2605C22semidirect
96. #2599C22semidirect
97. #2577C22semidirect
98. #2573C22semidirect
111. #2533C22semidirect
112. #2533C22semidirect
113. #2532C22semidirect
114. #2525C22semidirect
115. #2524C22semidirect
116. #2524C22semidirect
117. #2524C22semidirect
118. #2524C22semidirect
119. #2523C22semidirect
120. #2515C22semidirect
121. #2514C22semidirect
122. #2514C22semidirect
137. #2495C22semidirect
145. #2493C22semidirect
167. #2383C22semidirect
168. #2381C22semidirect
169. #2381C22semidirect
177. #2356C22semidirect
182. #2347C22semidirect
186. #2343C22semidirect
187. #2337C22semidirect
188. #2336C22semidirect
189. #2336C22semidirect
195. #2320C22semidirect
196. #2320C22semidirect
198. #2318C22semidirect

Maximal subgroups

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

subgroupindex
#593482
#593472
#459832
#391512
#389252
#380712
#379152
#379142
#379132
#375622
#375572
#369802
#369792
#366252
#366212
#365722
#362062
#350522
#349972
#344012
#343892
C22×#3832