Finite Group Databasebeta

← #8935533

Subgroups — #8935533

Order 512.

5712 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58600C214yesmaximal, complemented
2#58010C214yesmaximal, complemented
3#56669C214yesmaximal, complemented
4#51926C214yesmaximal, complemented
5#51337C212yesmaximal, complemented
6#50642C214yesmaximal, complemented
7#49547C212yesmaximal, complemented
8#48558C214yesmaximal, complemented
9#47884C212yesmaximal, complemented
10#47063C212yesmaximal, complemented
11#47031C212yesmaximal, complemented
12#43144C214yesmaximal, complemented
13#43015C214yesmaximal, complemented
14#41172C214yesmaximal, complemented
15#40951C214yesmaximal, complemented
16#40655C212yesmaximal, complemented
17#37769C212yesmaximal, complemented
18#37768C212yesmaximal, complemented
19#36707C211yesmaximal, characteristic, complemented
20#35757C212yesmaximal, complemented
21#35741C212yesmaximal, complemented
22#35659C211yesmaximal, characteristic, complemented
23#35349C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic, complemented
25C2×#550C2212yes—
26C2×#548C2214yescomplemented
27C2×#539C2212yescomplemented
28C2×#538C2212yes—
29C2×#537C2211yescharacteristic, complemented
30C2×#525C2212yes—
31C22×C22⋊Q8C2211yescharacteristic
32C2×#518C2211yescharacteristic
33#2847C2212yes—
34#2829C2214yescomplemented
35#2829C2214yescomplemented
36#2828C2214yescomplemented
37#2824C2212yescomplemented
38#2815C2212yes—
39#2813C2214yescomplemented
40#2806C2214yescomplemented
41#2798C2214yescomplemented
42#2797C2214yescomplemented
43#2784C2214yes—
44#2780C2214yescomplemented
45#2763C2212yescomplemented
46#2761C2214yescomplemented
47#2755C2214yescomplemented
48#2754C2214yescomplemented
49#2752C2214yes—
50#2752C2214yes—
51#2750C2214yescomplemented
52#2748C2214yes—
53#2748C2214yescomplemented
54#2732C2214yes—
55#2730C2214yes—
56#2730C2214yescomplemented
57#2717C2214yescomplemented
58#2715C2214yescomplemented
59#2714C2214yes—
60#2714C2214yes—
61#2711C2214yescomplemented
62#2710C2214yescomplemented
63#2708C2214yescomplemented
64#2706C2214yescomplemented
65#2705C2214yes—
66#2705C2214yescomplemented
67#2705C2214yescomplemented
68#2703C2214yes—
69#2695C2214yescomplemented
70#2694C2214yescomplemented
71#2692C2214yes—
72#2692C2214yescomplemented
73#2691C2214yescomplemented
74#2687C2214yescomplemented
75#2682C2214yescomplemented
76#2682C2214yescomplemented
77#2682C2214yescomplemented
78#2676C2214yes—
79#2676C2214yescomplemented
80#2676C2214yescomplemented
81#2675C2214yescomplemented
82#2675C2212yescomplemented
83#2673C2214yes—
84#2673C2214yes—
85#2673C2214yes—
86#2673C2214yes—
87#2673C2214yescomplemented
88#2672C2214yescomplemented
89#2672C2214yescomplemented
90#2671C2214yescomplemented
91#2671C2214yescomplemented
92#2671C2214yescomplemented
93#2670C2212yes—
94#2670C2212yes—
95#2668C2214yes—
96#2667C2212yescomplemented
97#2662C2214yescomplemented
98#2661C2214yescomplemented
99#2656C2212yes—
100#2656C2212yescomplemented
101#2651C2214yescomplemented
102#2649C2214yescomplemented
103#2637C2214yescomplemented
104#2636C2214yescomplemented
105#2635C2212yes—
106#2635C2212yes—
107#2619C2212yes—
108#2618C2212yescomplemented
109#2618C2212yescomplemented
110#2617C2212yes—
111#2615C2212yescomplemented
112#2615C2214yescomplemented
113#2607C2212yes—
114#2602C2214yescomplemented
115#2589C2214yescomplemented
116#2588C2214yescomplemented
117#2587C2214yescomplemented
118#2580C2214yes—
119#2580C2212yes—
120#2579C2212yes—
121#2579C2212yes—
122#2574C2214yescomplemented
123#2560C2214yescomplemented
124#2557C2214yes—
125#2557C2214yes—
126#2556C2214yescomplemented
127#2553C2214yescomplemented
128#2553C2214yescomplemented
129#2541C2212yes—
130#2539C2212yes—
131#2539C2214yes—
132#2539C2212yes—
133#2535C2214yes—
134#2522C2214yescomplemented
135#2521C2214yescomplemented
136#2517C2214yescomplemented
137#2487C2212yes—
138#2479C2214yescomplemented
139#2471C2214yes—
140#2467C2214yes—
141#2467C2214yescomplemented
142#2466C2214yescomplemented
143#2465C2214yescomplemented
144#2464C2214yes—
145#2464C2214yes—
146#2464C2214yes—
147#2464C2214yescomplemented
148#2463C2212yescomplemented
149#2462C2214yescomplemented
150#2460C2214yescomplemented
151#2458C2214yescomplemented
152#2456C2214yes—
153#2454C2214yes—
154#2450C2214yes—
155#2450C2214yes—
156#2450C2214yescomplemented
157#2449C2214yes—
158#2445C2214yes—
159#2438C2214yes—
160#2437C2214yes—
161#2436C2212yescomplemented
162#2436C2214yescomplemented
163#2433C2214yes—
164#2431C2214yes—
165#2431C2214yes—
166#2431C2214yes—
167#2431C2214yescomplemented
168#2430C2214yescomplemented
169#2430C2214yescomplemented
170#2428C2214yes—
171#2425C2214yescomplemented
172#2425C2214yescomplemented
173#2424C2214yes—
174#2424C2214yes—
175#2424C2214yes—
176#2424C2214yes—
177#2409C2212yes—
178#2409C2214yes—
179#2409C2214yescomplemented
180#2409C2214yescomplemented
181#2407C2214yes—
182#2407C2214yescomplemented
183#2407C2214yescomplemented
184#2407C2214yescomplemented
185#2407C2214yescomplemented
186#2406C2212yescomplemented
187#2406C2212yescomplemented
188#2406C2212yescomplemented
189#2404C2212yes—
190#2404C2212yes—
191#2404C2212yes—
192#2404C2212yes—
193#2396C2212yes—
194#2388C2212yes—
195#2388C2212yes—
196#2388C2214yescomplemented
197#2379C2214yescomplemented
198#2377C2212yescomplemented
199#2368C2214yescomplemented
200#2366C2214yes—
201#2364C2214yes—
202#2363C2214yes—
203#2361C2214yescomplemented
204#2357C2212yes—
205#2341C2212yescomplemented
206Q8×C22⋊C4C2214yescomplemented
207#2333C2214yes—
208#2329C2212yes—
209#2329C2212yescomplemented
210#2325C2214yescomplemented
211#2315C2211yescharacteristic
212#2315C2211yescharacteristic
213#2313C2211yescharacteristic, complemented
214#2311C2212yescomplemented
215#2310C2211yescharacteristic, complemented
216#2308C2211yescharacteristic
217C2×#386C2211yescharacteristic
218C2×#385C2211yescharacteristic
219C2×2−1+4—48no—
220C2×2−1+4—44no—
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2314yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2312yes—
227C23×Q8C2311yescharacteristic
228C23×Q8C2314yes—
229C23×D4C2311yescharacteristic
230C24×C4C2311yescharacteristic
231#550—48no—
232#548—416no—
233#539—48no—
234#538—48no—
235#537—44no—
236C2×#127C2312yes—
237C2×#127C2314yes—
238C2×#127C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2314yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247#525—48no—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×C22⋊Q8—44no—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×#121C2314yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#120C2314yes—
289C2×#120C2314yes—
290C2×#120C2314yes—
291C2×#120C2314yes—
292#518—44no—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2314yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×#117C2312yes—
308C2×#117C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C22⋊C4C2311yescharacteristic
314C22×C22⋊C4C2311yescharacteristic
315C22×C22⋊C4C2311yescharacteristic
316C22×C22⋊C4C2311yescharacteristic
317C22×C22⋊C4C2311yescharacteristic
318C22×C22⋊C4C2312yes—
319C22×C22⋊C4C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2312yes—
329#399C2312yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2312yes—
334#399C2314yes—
335#399C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2312yes—
373#395C2314yes—
374#395C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2312yes—
393#394C2312yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2312yes—
405#393C2312yes—
406#393C2314yes—
407#393C2312yes—
408#393C2312yes—
409#393C2312yes—
410#393C2312yes—
411#393C2314yes—
412#393C2314yes—
413#393C2312yes—
414#392C2312yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2312yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2312yes—
427#392C2312yes—
428#392C2314yes—
429#392C2312yes—
430#392C2312yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2312yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2312yes—
439#392C2312yes—
440#392C2312yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
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#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
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#386C2314yes—
520#386C2312yes—
521#386C2312yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2312yes—
527#386C2312yes—
528#386C2314yes—
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#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#385C2312yes—
557#385C2312yes—
558#385C2314yes—
559#385C2312yes—
560#385C2314yes—
561#385C2312yes—
562#385C2314yes—
563#385C2314yes—
564#385C2312yes—
565#385C2314yes—
566#385C2312yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#382C2314yes—
584#382C2312yes—
585#382C2314yes—
586#381C2312yes—
587#381C2312yes—
588#381C2312yes—
589#381C2312yes—
590#381C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2312yes—
594#380C2312yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2312yes—
599#380C2312yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#379C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2312yes—
610C4×C22⋊C4C2312yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C2×#95C2314yes—
622C2×#95C2312yes—
623C2×#95C2312yes—
624C25C2411yescharacteristic
625C25C2411yescharacteristic
6262−1+4—464no—
627C2×#41—28no—
628C2×#41—28no—
629C2×#41—44no—
630C2×#41—48no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41—44no—
634C2×#41—48no—
635C2×#41—48no—
636C2×#41—48no—
637C2×#41—48no—
638C2×#41—48no—
639C2×#41—44no—
640C2×#41—84no—
641C22×Q8—216no—
642C22×Q8—24no—
643C22×Q8—44no—
644C22×Q8—48no—
645C22×Q8—48no—
646C22×Q8C2412yes—
647C22×Q8C2414yes—
648C22×Q8C2412yes—
649C22×Q8C2412yes—
650C22×Q8C2412yes—
651C22×D4—24no—
652C22×D4—42no—
653C22×D4—42no—
654C22×D4C2412yes—
655C22×D4C2412yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C22×D4C2414yes—
663C22×D4C2414yes—
664C22×D4C2412yes—
665C22×D4C2412yes—
666C22×D4C2412yes—
667C22×D4C2414yes—
668C22×D4C2414yes—
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2414yes—
672C22×D4C2412yes—
673C22×D4C2414yes—
674C22×D4C2412yes—
675C22×D4C2412yes—
676C23×C4—44no—
677C23×C4—42no—
678C23×C4C2411yescharacteristic
679C23×C4C2414yes—
680C23×C4C2414yes—
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2411yescharacteristic
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2414yes—
690C23×C4C2414yes—
691C23×C4C2412yes—
692C23×C4C2411yescharacteristic
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699#127—44no—
700#127—48no—
701#127—48no—
702#126—48no—
703#126—48no—
704#126—84no—
705#125—48no—
706#124—216no—
707#124—48no—
708#124—48no—
709#124—84no—
710#123—48no—
711#123—48no—
712#123—48no—
713#123—48no—
714#123—84no—
715#123—84no—
716#123—84no—
717#123—84no—
718#123—84no—
719C22⋊Q8—28no—
720C22⋊Q8—28no—
721C22⋊Q8—216no—
722C22⋊Q8—48no—
723C22⋊Q8—48no—
724C22⋊Q8—48no—
725C22⋊Q8—48no—
726C22⋊Q8—48no—
727#121—28no—
728#121—216no—
729#121—44no—
730#121—44no—
731#121—48no—
732#121—48no—
733#121—48no—
734#121—48no—
735#121—48no—
736#121—48no—
737#121—48no—
738#121—44no—
739#121—44no—
740#121—48no—
741#121—44no—
742#121—48no—
743#121—44no—
744#121—84no—
745#121—84no—
746#121—84no—
747#121—84no—
748#121—84no—
749#120—48no—
750#120—48no—
751#120—84no—
752#120—84no—
753C4×Q8—48no—
754C4×Q8—44no—
755C4×D4—28no—
756C4×D4—44no—
757C4×D4—48no—
758C4×D4—48no—
759C4×D4—44no—
760C4×D4—48no—
761C4×D4—48no—
762C4×D4—48no—
763C4×D4—48no—
764C4×D4—48no—
765C4×D4—48no—
766C4×D4—44no—
767#117—44no—
768#117—44no—
769C2×C4⋊C4—24no—
770C2×C4⋊C4—44no—
771C2×C4⋊C4—42no—
772C2×C4⋊C4—42no—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C22⋊C4—24no—
809C2×C22⋊C4—44no—
810C2×C22⋊C4—44no—
811C2×C22⋊C4—42no—
812C2×C22⋊C4—42no—
813C2×C22⋊C4—42no—
814C2×C22⋊C4—42no—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925C24—22no—
926C24—22no—
927C24—22no—
928C24—22no—
929C24—41no—
930C24—41no—
931C24—42no—
932C24—42no—
933C24—42no—
934C24—42no—
935C24C2512yes—
936C24C2514yes—
937C24C2514yes—
938C24C2511yescharacteristic
939C24C2511yescharacteristic
940C24C2511yescharacteristic
941#41—432no—
942#41—432no—
943#41—464no—
944#41—432no—
945#41—816no—
946#41—816no—
947C2×Q8—28no—
948C2×Q8—24no—
949C2×Q8—28no—
950C2×Q8—28no—
951C2×Q8—28no—
952C2×Q8—42no—
953C2×Q8—44no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—42no—
957C2×Q8—44no—
958C2×Q8—416no—
959C2×Q8—464no—
960C2×Q8H(5,𝔽2)18yes—
961C2×D4—24no—
962C2×D4—28no—
963C2×D4—24no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—28no—
968C2×D4—28no—
969C2×D4—28no—
970C2×D4—24no—
971C2×D4—24no—
972C2×D4—28no—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—28no—
977C2×D4—42no—
978C2×D4—42no—
979C2×D4—42no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—42no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—416no—
1024C22×C4—22no—
1025C22×C4—24no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—24no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—28no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—41no—
1041C22×C4—41no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—41no—
1065C22×C4—42no—
1066C22×C4—41no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—88no—
1076C22×C4H(5,𝔽2)14yes—
1077C22×C42−1+414yescomplemented
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C42—24no—
1189C42—28no—
1190C42—42no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C23—28no—
1199C23—21no—
1200C23—21no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—21no—
1205C23—21no—
1206C23—21no—
1207C23—21no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—22no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—22no—
1222C23—24no—
1223C23—24no—
1224C23—22no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—24no—
1230C23—44no—
1231C23—82no—
1232C23—82no—
1233C23—84no—
1234C23—84no—
1235C23—84no—
1236C23—161no—
1237C23—161no—
1238C23—162no—
1239C23C2×H(5,𝔽2)12yes—
1240C23C2×2−1+412yes—
1241C23#58512yes—
1242C23C2611yescharacteristic
1243Q8—216no—
1244Q8—48no—
1245Q8—416no—
1246Q8—48no—
1247Q8—84no—
1248D4—48no—
1249D4—48no—
1250D4—416no—
1251D4—48no—
1252D4—48no—
1253D4—48no—
1254D4—88no—
1255D4—84no—
1256D4—88no—
1257D4—88no—
1258D4—88no—
1259D4—88no—
1260D4—88no—
1261D4—88no—
1262D4—88no—
1263D4—88no—
1264D4—88no—
1265D4—84no—
1266D4—162no—
1267D4—164no—
1268D4—164no—
1269D4—164no—
1270C2×C4—28no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—44no—
1313C2×C4—44no—
1314C2×C4—416no—
1315C2×C4—416no—
1316C2×C4—416no—
1317C2×C4—44no—
1318C2×C4—44no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—88no—
1322C2×C4—84no—
1323C2×C4—82no—
1324C2×C4—84no—
1325C2×C4—82no—
1326C2×C4—88no—
1327C2×C4—161no—
1328C2×C4—162no—
1329C2×C4—161no—
1330C2×C4—162no—
1331C2×C4—164no—
1332C2×C4C2×H(5,𝔽2)18yes—
1333C2×C4C2×H(5,𝔽2)14yes—
1334C2×C4C2×H(5,𝔽2)14yes—
1335C2×C4C2×2−1+414yes—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—24no—
1342C22—24no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—44no—
1352C22—44no—
1353C22—42no—
1354C22—42no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—42no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—44no—
1369C22—44no—
1370C22—88no—
1371C22—164no—
1372C22C22×H(5,𝔽2)11yescharacteristic
1373C22C22×H(5,𝔽2)12yes—
1374C22C22×2−1+411yescharacteristic
1375C22C2×#58511yescharacteristic
1376C22H(7,𝔽2)12yes—
1377C4—24no—
1378C4—28no—
1379C4—24no—
1380C4—24no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—44no—
1389C4—44no—
1390C4—44no—
1391C4—44no—
1392C4—44no—
1393C4—44no—
1394C2—42no—
1395C2—42no—
1396C2—42no—
1397C2—84no—
1398C2—84no—
1399C2—82no—
1400C2#6281711yescharacteristic
1401C2#6281911yescharacteristic
1402C2#6287611yescharacteristic
1403C2#6289912yes—
1404C2#6291712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58600C2semidirect
2. #58010C2semidirect
3. #56669C2semidirect
4. #51926C2semidirect
5. #51337C2semidirect
6. #50642C2semidirect
7. #49547C2semidirect
8. #48558C2semidirect
9. #47884C2semidirect
10. #47063C2semidirect
11. #47031C2semidirect
12. #43144C2semidirect
13. #43015C2semidirect
14. #41172C2semidirect
15. #40951C2semidirect
16. #40655C2semidirect
17. #37769C2semidirect
18. #37768C2semidirect
19. #36707C2semidirect
20. #35757C2semidirect
21. #35741C2semidirect
22. #35659C2semidirect
23. #35349C2semidirect
24. C22×2−1+4C22semidirect
26. C2×#548C22semidirect
27. C2×#539C22semidirect
29. C2×#537C22semidirect
34. #2829C22semidirect
35. #2829C22semidirect
36. #2828C22semidirect
37. #2824C22semidirect
39. #2813C22semidirect
40. #2806C22semidirect
41. #2798C22semidirect
42. #2797C22semidirect
44. #2780C22semidirect
45. #2763C22semidirect
46. #2761C22semidirect
47. #2755C22semidirect
48. #2754C22semidirect
51. #2750C22semidirect
53. #2748C22semidirect
56. #2730C22semidirect
57. #2717C22semidirect
58. #2715C22semidirect
61. #2711C22semidirect
62. #2710C22semidirect
63. #2708C22semidirect
64. #2706C22semidirect
66. #2705C22semidirect
67. #2705C22semidirect
69. #2695C22semidirect
70. #2694C22semidirect
72. #2692C22semidirect
73. #2691C22semidirect
74. #2687C22semidirect
75. #2682C22semidirect
76. #2682C22semidirect
77. #2682C22semidirect
79. #2676C22semidirect
80. #2676C22semidirect
81. #2675C22semidirect
82. #2675C22semidirect
87. #2673C22semidirect
88. #2672C22semidirect
89. #2672C22semidirect
90. #2671C22semidirect
91. #2671C22semidirect
92. #2671C22semidirect
96. #2667C22semidirect
97. #2662C22semidirect
98. #2661C22semidirect
100. #2656C22semidirect
101. #2651C22semidirect
102. #2649C22semidirect
103. #2637C22semidirect
104. #2636C22semidirect
108. #2618C22semidirect
109. #2618C22semidirect
111. #2615C22semidirect
112. #2615C22semidirect
114. #2602C22semidirect
115. #2589C22semidirect
116. #2588C22semidirect
117. #2587C22semidirect
122. #2574C22semidirect
123. #2560C22semidirect
126. #2556C22semidirect
127. #2553C22semidirect
128. #2553C22semidirect
134. #2522C22semidirect
135. #2521C22semidirect
136. #2517C22semidirect
138. #2479C22semidirect
141. #2467C22semidirect
142. #2466C22semidirect
143. #2465C22semidirect
147. #2464C22semidirect
148. #2463C22semidirect
149. #2462C22semidirect
150. #2460C22semidirect
151. #2458C22semidirect
156. #2450C22semidirect
161. #2436C22semidirect
162. #2436C22semidirect
167. #2431C22semidirect
168. #2430C22semidirect
169. #2430C22semidirect
171. #2425C22semidirect
172. #2425C22semidirect
179. #2409C22semidirect
180. #2409C22semidirect
182. #2407C22semidirect
183. #2407C22semidirect
184. #2407C22semidirect
185. #2407C22semidirect
186. #2406C22semidirect
187. #2406C22semidirect
188. #2406C22semidirect
196. #2388C22semidirect
197. #2379C22semidirect
198. #2377C22semidirect
199. #2368C22semidirect
203. #2361C22semidirect
205. #2341C22semidirect
206. Q8×C22⋊C4C22semidirect
209. #2329C22semidirect
210. #2325C22semidirect
213. #2313C22semidirect
214. #2311C22semidirect
215. #2310C22semidirect
1077. C22×C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#586002
#580102
#566692
#519262
#513372
#506422
#495472
#485582
#478842
#470632
#470312
#431442
#430152
#411722
#409512
#406552
#377692
#377682
#367072
#357572
#357412
#356592
#353492