Finite Group Databasebeta

← #8901554

Subgroups — #8901554

Order 512.

4906 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58952C214yesmaximal, complemented
2#54345C214yesmaximal, complemented
3#54292C214yesmaximal, complemented
4#52072C212yesmaximal, complemented
5#51542C212yesmaximal, complemented
6#50914C214yesmaximal, complemented
7#50894C214yesmaximal, complemented
8#47214C212yesmaximal, complemented
9#46858C212yesmaximal, complemented
10#46854C212yesmaximal, complemented
11#46847C214yesmaximal, complemented
12#46816C212yesmaximal, complemented
13#46724C214yesmaximal, complemented
14#46475C212yesmaximal, complemented
15#40302C214yesmaximal, complemented
16#39617C214yesmaximal, complemented
17#38359C214yesmaximal, complemented
18#37303C212yesmaximal, complemented
19#36708C211yesmaximal, characteristic, complemented
20#35634C211yesmaximal, characteristic
21#35507C212yesmaximal, complemented
22#35474C212yesmaximal, complemented
23#35391C211yesmaximal, characteristic, complemented
24C2×#563C2212yescomplemented
25C2×Q82C2212yescomplemented
26C2×#554C2214yes—
27C2×#544C2211yescharacteristic
28C2×#543C2211yescharacteristic
29C2×#542C2212yes—
30C2×#537C2211yescharacteristic
31C2×#536C2212yes—
32C2×#525C2212yes—
33C22×C22⋊Q8C2211yescharacteristic
34#2868C2212yescomplemented
35#2861C2212yescomplemented
36#2848C2212yes—
37#2841C2214yescomplemented
38#2838C2214yescomplemented
39#2838C2214yescomplemented
40#2834C2212yes—
41#2824C2212yes—
42#2816C2212yes—
43#2807C2214yescomplemented
44#2791C2214yescomplemented
45#2791C2214yescomplemented
46#2791C2214yescomplemented
47#2786C2214yes—
48#2786C2214yes—
49#2778C2214yes—
50#2754C2214yescomplemented
51#2754C2214yescomplemented
52#2742C2214yes—
53#2742C2212yes—
54#2740C2214yescomplemented
55#2734C2212yescomplemented
56#2734C2214yescomplemented
57#2734C2212yescomplemented
58#2731C2212yescomplemented
59#2731C2212yescomplemented
60#2730C2214yes—
61#2723C2214yes—
62#2723C2214yes—
63#2723C2214yescomplemented
64#2721C2214yescomplemented
65#2721C2214yescomplemented
66#2721C2214yescomplemented
67#2721C2214yescomplemented
68#2717C2214yescomplemented
69#2712C2212yes—
70#2701C2214yes—
71#2698C2214yescomplemented
72#2698C2214yescomplemented
73#2698C2214yescomplemented
74#2694C2214yes—
75#2693C2212yes—
76#2692C2214yes—
77#2692C2214yes—
78#2692C2214yescomplemented
79#2690C2214yes—
80#2690C2214yes—
81#2690C2214yes—
82#2687C2214yes—
83#2686C2214yes—
84#2686C2214yescomplemented
85#2681C2214yes—
86#2681C2214yescomplemented
87#2680C2214yes—
88#2680C2214yes—
89#2680C2214yes—
90#2677C2212yes—
91#2677C2214yes—
92#2677C2214yes—
93#2677C2214yes—
94#2677C2214yes—
95#2677C2214yescomplemented
96#2677C2214yescomplemented
97#2677C2214yescomplemented
98#2677C2214yescomplemented
99#2677C2214yescomplemented
100#2677C2214yescomplemented
101#2674C2214yes—
102#2674C2214yes—
103#2674C2214yes—
104#2672C2214yes—
105#2660C2212yescomplemented
106#2660C2214yescomplemented
107#2660C2214yescomplemented
108#2651C2214yescomplemented
109#2640C2212yescomplemented
110#2638C2214yes—
111#2633C2214yes—
112#2632C2214yescomplemented
113#2627C2212yes—
114#2611C2214yes—
115#2607C2212yes—
116#2607C2214yescomplemented
117#2605C2214yescomplemented
118#2599C2214yes—
119#2588C2214yescomplemented
120#2588C2214yescomplemented
121#2583C2212yes—
122#2583C2212yes—
123#2579C2214yes—
124#2575C2214yes—
125#2567C2214yescomplemented
126#2567C2212yescomplemented
127#2566C2212yescomplemented
128#2565C2214yescomplemented
129#2565C2214yescomplemented
130#2565C2212yescomplemented
131#2564C2214yes—
132#2563C2214yes—
133#2561C2211yescharacteristic
134#2561C2211yescharacteristic
135#2560C2214yes—
136#2560C2214yes—
137#2560C2214yescomplemented
138#2559C2214yescomplemented
139#2557C2214yes—
140#2553C2214yes—
141#2553C2214yes—
142#2549C2214yes—
143#2549C2214yes—
144#2549C2214yes—
145#2542C2214yes—
146#2542C2214yes—
147#2542C2214yes—
148#2542C2212yescomplemented
149#2540C2214yes—
150#2540C2214yes—
151#2539C2212yes—
152#2539C2212yes—
153#2531C2214yes—
154#2531C2214yes—
155#2528C2214yescomplemented
156#2528C2214yescomplemented
157#2527C2214yes—
158#2526C2214yescomplemented
159#2517C2212yes—
160#2517C2214yes—
161#2502C2212yes—
162#2501C2212yes—
163#2501C2212yes—
164#2500C2212yes—
165#2499C2212yes—
166#2484C2212yes—
167#2482C2212yes—
168#2472C2214yes—
169#2472C2214yes—
170#2467C2214yes—
171#2467C2214yes—
172#2465C2214yescomplemented
173#2465C2214yescomplemented
174#2465C2214yescomplemented
175#2463C2214yes—
176#2463C2212yes—
177#2458C2214yes—
178#2458C2214yes—
179#2444C2214yes—
180#2443C2214yes—
181#2443C2214yescomplemented
182#2440C2214yes—
183#2440C2214yes—
184#2440C2214yes—
185#2440C2214yescomplemented
186#2440C2214yescomplemented
187#2440C2214yescomplemented
188#2434C2212yes—
189#2434C2211yescharacteristic
190#2434C2211yescharacteristic
191#2432C2214yes—
192#2423C2214yes—
193#2423C2214yes—
194#2423C2214yes—
195#2423C2214yescomplemented
196#2423C2214yescomplemented
197#2418C2214yes—
198#2418C2214yes—
199#2406C2214yes—
200#2381C2212yescomplemented
201#2372C2212yescomplemented
202#2353C2214yes—
203#2336C2214yescomplemented
204#2335C2214yes—
205#2335C2214yes—
206#2333C2212yes—
207#2332C2212yes—
208#2326C2214yes—
209#2326C2214yes—
210#2322C2214yes—
211#2315C2212yes—
212#2313C2211yescharacteristic
213C4×#124C2214yes—
214#2298C2212yes—
215#2295C2214yescomplemented
216C2×#385C2212yes—
217#2274C2211yescharacteristic
218#2273C2211yescharacteristic
219C22×#41C2312yes—
220C23×Q8C2311yescharacteristic
221C24×C4C2311yescharacteristic
222#563—48no—
223Q82—48no—
224#554—416no—
225#544—44no—
226#543—44no—
227#542—48no—
228#537—44no—
229#536—48no—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125C2314yes—
247C2×#125C2312yes—
248C2×#125C2314yes—
249C2×#125C2312yes—
250C2×#124C2314yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#124C2314yes—
254C2×#124C2312yes—
255#525—48no—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×C22⋊Q8—44no—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2311yescharacteristic
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×#121C2312yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2312yes—
289C2×#120C2314yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2314yes—
293C2×C4×Q8C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×#117C2312yes—
300C2×#117C2312yes—
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2314yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2311yescharacteristic
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2312yes—
310#401C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2312yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2312yes—
331#399C2314yes—
332#399C2314yes—
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#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2312yes—
361#397C2312yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2312yes—
412#393C2312yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#392C2312yes—
420#392C2312yes—
421#392C2314yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#390C2314yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2312yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2312yes—
447#390C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2312yes—
546#385C2314yes—
547#385C2312yes—
548#385C2312yes—
549#385C2312yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2312yes—
562#385C2312yes—
563#385C2312yes—
564#385C2312yes—
565#385C2314yes—
566#385C2314yes—
567#384C2312yes—
568#384C2312yes—
569#384C2312yes—
570#384C2312yes—
571#384C2314yes—
572#384C2312yes—
573#384C2314yes—
574#384C2314yes—
575#384C2314yes—
576#384C2312yes—
577#383C2314yes—
578#382C2314yes—
579#382C2314yes—
580#382C2312yes—
581#382C2312yes—
582#382C2314yes—
583#381C2312yes—
584#381C2312yes—
585#381C2312yes—
586#381C2314yes—
587#381C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2312yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#379C2312yes—
598#379C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2311yescharacteristic
609C4×C22⋊C4C2311yescharacteristic
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619#376C2314yes—
620#376C2314yes—
621#376C2312yes—
622C2×#95C2314yes—
623C43C2312yes—
624C25C2411yescharacteristic
625C2×#41—44no—
626C2×#41—44no—
627C2×#41—44no—
628C22×Q8—42no—
629C22×Q8—44no—
630C22×Q8C2414yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2411yescharacteristic
638C22×Q8C2414yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C23×C4—44no—
647C23×C4—42no—
648C23×C4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2414yes—
651C23×C4C2411yescharacteristic
652C23×C4C2411yescharacteristic
653C23×C4C2411yescharacteristic
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2414yes—
660C23×C4C2411yescharacteristic
661C4⋊Q8—28no—
662C4⋊Q8—44no—
663C4⋊Q8—44no—
664C4⋊Q8—44no—
665C4⋊Q8—48no—
666C4⋊Q8—48no—
667C4⋊Q8—48no—
668C4⋊Q8—44no—
669C4⋊Q8—44no—
670C4⋊Q8—48no—
671C4⋊Q8—44no—
672C4⋊Q8—44no—
673C4⋊Q8—44no—
674#126—48no—
675#126—48no—
676#126—48no—
677#125—216no—
678#125—44no—
679#125—44no—
680#125—48no—
681#124—216no—
682#124—28no—
683#124—44no—
684#124—44no—
685#124—48no—
686#123—216no—
687#123—48no—
688#123—48no—
689#123—48no—
690#123—48no—
691#123—48no—
692C22⋊Q8—28no—
693C22⋊Q8—44no—
694C22⋊Q8—42no—
695C22⋊Q8—44no—
696C22⋊Q8—42no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—48no—
702C22⋊Q8—48no—
703C22⋊Q8—48no—
704C22⋊Q8—48no—
705C22⋊Q8—48no—
706C22⋊Q8—48no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714#121—28no—
715#121—48no—
716#121—48no—
717#121—44no—
718#120—48no—
719C4×Q8—216no—
720C4×Q8—44no—
721C4×Q8—48no—
722C4×Q8—48no—
723C4×D4—216no—
724C4×D4—44no—
725C4×D4—48no—
726C4×D4—48no—
727C4×D4—48no—
728#117—28no—
729#117—28no—
730C2×C4⋊C4—24no—
731C2×C4⋊C4—24no—
732C2×C4⋊C4—48no—
733C2×C4⋊C4—48no—
734C2×C4⋊C4—42no—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C22⋊C4—24no—
791C2×C22⋊C4—28no—
792C2×C22⋊C4—44no—
793C2×C22⋊C4—42no—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2412yes—
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#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2412yes—
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—
904C24—22no—
905C24—24no—
906C24—42no—
907C24—42no—
908C24C2514yes—
909C24C2511yescharacteristic
910C24C2512yes—
911#41—816no—
912C2×Q8—28no—
913C2×Q8—24no—
914C2×Q8—24no—
915C2×Q8—24no—
916C2×Q8—24no—
917C2×Q8—28no—
918C2×Q8—44no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—42no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—44no—
929C2×Q8—44no—
930C2×Q8—42no—
931C2×Q8—42no—
932C2×Q8—44no—
933C2×Q8—41no—
934C2×Q8—42no—
935C2×Q8—41no—
936C2×Q8—42no—
937C2×Q8—44no—
938C2×Q8—42no—
939C2×Q8—88no—
940C2×D4—28no—
941C2×D4—28no—
942C2×D4—28no—
943C2×D4—28no—
944C2×D4—24no—
945C2×D4—24no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—44no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—44no—
957C22×C4—22no—
958C22×C4—24no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—28no—
964C22×C4—28no—
965C22×C4—28no—
966C22×C4—28no—
967C22×C4—42no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—88no—
988C22×C4H(5,𝔽2)14yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C22×C4C2512yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2514yes—
1004C22×C4C2512yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—24no—
1017C4⋊C4—24no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—24no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
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—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—41no—
1055C4⋊C4—42no—
1056C4⋊C4—41no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C22⋊C4—28no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—44no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—42no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C42−1+418yes—
1105C42—24no—
1106C42—24no—
1107C42—24no—
1108C42—28no—
1109C42—28no—
1110C42—28no—
1111C42—42no—
1112C42—44no—
1113C42—44no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42—44no—
1119C42—42no—
1120C42—44no—
1121C42—42no—
1122C42—42no—
1123C42H(5,𝔽2)18yes—
1124C23—28no—
1125C23—22no—
1126C23—22no—
1127C23—24no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—24no—
1132C23—24no—
1133C23—24no—
1134C23—24no—
1135C23—24no—
1136C23—24no—
1137C23—24no—
1138C23—24no—
1139C23—82no—
1140C23—82no—
1141C23—88no—
1142C23C2×H(5,𝔽2)12yes—
1143C23C2×2−1+414yes—
1144C23C2611yescharacteristic
1145Q8—416no—
1146Q8—84no—
1147Q8—84no—
1148Q8—84no—
1149Q8—84no—
1150Q8—162no—
1151Q8—164no—
1152Q8—162no—
1153Q8—161no—
1154Q8—161no—
1155D4—416no—
1156D4—84no—
1157D4—84no—
1158D4—88no—
1159D4—88no—
1160D4—162no—
1161C2×C4—28no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—44no—
1211C2×C4—88no—
1212C2×C4—88no—
1213C2×C4—88no—
1214C2×C4—88no—
1215C2×C4—82no—
1216C2×C4—82no—
1217C2×C4—82no—
1218C2×C4—82no—
1219C2×C4—162no—
1220C2×C4—164no—
1221C2×C4—162no—
1222C2×C4C2×H(5,𝔽2)18yes—
1223C2×C4C2×H(5,𝔽2)14yes—
1224C2×C4C2×H(5,𝔽2)14yes—
1225C2×C4C2×2−1+418yes—
1226C22—22no—
1227C22—22no—
1228C22—24no—
1229C22—22no—
1230C22—28no—
1231C22—42no—
1232C22—42no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—88no—
1243C22C22×H(5,𝔽2)11yescharacteristic
1244C22C22×H(5,𝔽2)12yes—
1245C22C22×2−1+412yes—
1246C222−1+612yes—
1247C4—24no—
1248C4—24no—
1249C4—28no—
1250C4—28no—
1251C4—42no—
1252C4—44no—
1253C4—41no—
1254C4—42no—
1255C4—41no—
1256C4—42no—
1257C4—44no—
1258C4—42no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—44no—
1265C4—44no—
1266C4—44no—
1267C2—42no—
1268C2—44no—
1269C2—84no—
1270C2#6283211yescharacteristic
1271C2#6283311yescharacteristic
1272C2#6287111yescharacteristic
1273C2#6294214yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35634C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58952C2semidirect
2. #54345C2semidirect
3. #54292C2semidirect
4. #52072C2semidirect
5. #51542C2semidirect
6. #50914C2semidirect
7. #50894C2semidirect
8. #47214C2semidirect
9. #46858C2semidirect
10. #46854C2semidirect
11. #46847C2semidirect
12. #46816C2semidirect
13. #46724C2semidirect
14. #46475C2semidirect
15. #40302C2semidirect
16. #39617C2semidirect
17. #38359C2semidirect
18. #37303C2semidirect
19. #36708C2semidirect
21. #35507C2semidirect
22. #35474C2semidirect
23. #35391C2semidirect
24. C2×#563C22semidirect
25. C2×Q82C22semidirect
34. #2868C22semidirect
35. #2861C22semidirect
37. #2841C22semidirect
38. #2838C22semidirect
39. #2838C22semidirect
43. #2807C22semidirect
44. #2791C22semidirect
45. #2791C22semidirect
46. #2791C22semidirect
50. #2754C22semidirect
51. #2754C22semidirect
54. #2740C22semidirect
55. #2734C22semidirect
56. #2734C22semidirect
57. #2734C22semidirect
58. #2731C22semidirect
59. #2731C22semidirect
63. #2723C22semidirect
64. #2721C22semidirect
65. #2721C22semidirect
66. #2721C22semidirect
67. #2721C22semidirect
68. #2717C22semidirect
71. #2698C22semidirect
72. #2698C22semidirect
73. #2698C22semidirect
78. #2692C22semidirect
84. #2686C22semidirect
86. #2681C22semidirect
95. #2677C22semidirect
96. #2677C22semidirect
97. #2677C22semidirect
98. #2677C22semidirect
99. #2677C22semidirect
100. #2677C22semidirect
105. #2660C22semidirect
106. #2660C22semidirect
107. #2660C22semidirect
108. #2651C22semidirect
109. #2640C22semidirect
112. #2632C22semidirect
116. #2607C22semidirect
117. #2605C22semidirect
119. #2588C22semidirect
120. #2588C22semidirect
125. #2567C22semidirect
126. #2567C22semidirect
127. #2566C22semidirect
128. #2565C22semidirect
129. #2565C22semidirect
130. #2565C22semidirect
137. #2560C22semidirect
138. #2559C22semidirect
148. #2542C22semidirect
155. #2528C22semidirect
156. #2528C22semidirect
158. #2526C22semidirect
172. #2465C22semidirect
173. #2465C22semidirect
174. #2465C22semidirect
181. #2443C22semidirect
185. #2440C22semidirect
186. #2440C22semidirect
187. #2440C22semidirect
195. #2423C22semidirect
196. #2423C22semidirect
200. #2381C22semidirect
201. #2372C22semidirect
203. #2336C22semidirect
215. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#589522
#543452
#542922
#520722
#515422
#509142
#508942
#472142
#468582
#468542
#468472
#468162
#467242
#464752
#403022
#396172
#383592
#373032
#367082
#356342
#355072
#354742
#353912