Finite Group Databasebeta

← #8108454

Subgroups — #8108454

Order 512.

4688 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59623C212yesmaximal, complemented
2#59371C212yesmaximal, complemented
3#53245C214yesmaximal, complemented
4#53229C214yesmaximal, complemented
5#45871C214yesmaximal, complemented
6#45869C214yesmaximal, complemented
7#45539C212yesmaximal, complemented
8#45537C212yesmaximal, complemented
9#38326C214yesmaximal, complemented
10#38293C214yesmaximal, complemented
11#38177C214yesmaximal, complemented
12#38144C214yesmaximal, complemented
13#37959C212yesmaximal, complemented
14#37950C212yesmaximal, complemented
15#37754C212yesmaximal, complemented
16#37747C212yesmaximal, complemented
17#36800C214yesmaximal, complemented
18#36786C214yesmaximal, complemented
19#36730C212yesmaximal, complemented
20#36720C211yesmaximal, characteristic, complemented
21#36710C211yesmaximal, characteristic
22#36621C212yesmaximal, complemented
23C2×#2853C211yesmaximal, characteristic, complemented
24C2×#543C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#529C2212yes—
27C22×#123C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2855C2212yes—
30#2854C2212yes—
31#2853C2214yes—
32#2853C2214yes—
33#2853C2214yes—
34#2853C2214yes—
35#2853C2214yes—
36#2852C2214yescomplemented
37#2852C2214yescomplemented
38#2851C2212yescomplemented
39#2851C2212yescomplemented
40#2850C2212yescomplemented
41#2850C2212yescomplemented
42#2849C2214yes—
43#2848C2212yes—
44#2847C2212yes—
45#2835C2212yescomplemented
46#2826C2214yes—
47#2824C2212yescomplemented
48#2804C2212yes—
49#2804C2214yescomplemented
50#2797C2214yes—
51#2795C2214yescomplemented
52#2793C2214yescomplemented
53#2789C2214yescomplemented
54#2785C2214yescomplemented
55#2782C2214yescomplemented
56#2782C2214yescomplemented
57#2781C2214yescomplemented
58#2781C2214yescomplemented
59#2778C2214yes—
60#2778C2214yes—
61#2778C2214yescomplemented
62#2775C2214yescomplemented
63#2767C2214yescomplemented
64#2767C2214yescomplemented
65#2763C2212yescomplemented
66#2763C2214yescomplemented
67#2763C2212yescomplemented
68#2762C2214yescomplemented
69#2762C2214yescomplemented
70#2759C2214yescomplemented
71#2759C2214yescomplemented
72#2758C2214yescomplemented
73#2757C2214yes—
74#2756C2214yescomplemented
75#2754C2214yescomplemented
76#2753C2214yescomplemented
77#2753C2214yescomplemented
78#2751C2214yescomplemented
79#2750C2214yescomplemented
80#2750C2214yescomplemented
81#2748C2212yes—
82#2747C2214yescomplemented
83#2746C2214yescomplemented
84#2746C2214yescomplemented
85#2745C2214yescomplemented
86#2745C2214yescomplemented
87#2741C2214yescomplemented
88#2738C2214yescomplemented
89#2737C2214yescomplemented
90#2730C2214yescomplemented
91#2723C2214yescomplemented
92#2712C2212yescomplemented
93#2709C2214yes—
94#2709C2212yes—
95#2709C2212yes—
96#2702C2214yescomplemented
97#2701C2214yescomplemented
98#2700C2214yescomplemented
99#2696C2214yes—
100#2696C2214yes—
101#2693C2214yes—
102#2693C2212yescomplemented
103#2691C2214yescomplemented
104#2690C2214yescomplemented
105#2690C2214yescomplemented
106#2689C2214yescomplemented
107#2687C2214yes—
108#2687C2214yes—
109#2687C2214yescomplemented
110#2686C2214yescomplemented
111#2686C2214yescomplemented
112#2680C2214yes—
113#2680C2214yes—
114#2673C2214yes—
115#2673C2214yes—
116#2659C2212yes—
117#2655C2214yescomplemented
118#2653C2214yescomplemented
119#2650C2214yescomplemented
120#2648C2214yescomplemented
121#2639C2212yes—
122#2627C2212yes—
123#2617C2212yes—
124#2610C2214yescomplemented
125#2605C2214yescomplemented
126#2600C2214yes—
127#2598C2214yescomplemented
128#2597C2214yes—
129#2597C2214yescomplemented
130#2593C2214yescomplemented
131#2591C2212yes—
132#2589C2214yescomplemented
133#2588C2214yescomplemented
134#2576C2214yescomplemented
135#2574C2214yescomplemented
136#2564C2214yescomplemented
137#2561C2212yes—
138#2557C2214yes—
139#2544C2214yes—
140#2534C2214yes—
141#2529C2214yescomplemented
142#2528C2214yescomplemented
143#2525C2214yescomplemented
144#2524C2214yescomplemented
145#2523C2212yescomplemented
146#2515C2214yescomplemented
147#2511C2214yescomplemented
148#2510C2214yes—
149#2510C2214yescomplemented
150#2503C2214yes—
151#2502C2212yes—
152#2493C2214yes—
153#2493C2214yes—
154#2488C2214yes—
155#2488C2214yes—
156#2483C2212yes—
157#2477C2214yescomplemented
158#2477C2214yescomplemented
159#2476C2214yescomplemented
160#2474C2214yescomplemented
161#2472C2214yes—
162#2472C2214yes—
163#2465C2214yescomplemented
164#2463C2214yescomplemented
165#2463C2212yescomplemented
166#2459C2214yes—
167#2459C2214yescomplemented
168#2450C2214yes—
169#2449C2214yes—
170#2444C2214yes—
171#2444C2214yescomplemented
172#2438C2214yescomplemented
173#2433C2212yes—
174#2425C2214yes—
175#2421C2214yescomplemented
176#2418C2214yes—
177#2415C2214yescomplemented
178#2412C2214yes—
179#2406C2214yes—
180#2405C2212yes—
181#2404C2212yes—
182#2404C2212yes—
183#2380C2212yes—
184#2379C2214yescomplemented
185#2376C2212yes—
186#2374C2212yes—
187#2368C2214yes—
188#2366C2212yes—
189#2359C2214yescomplemented
190#2358C2214yes—
191#2352C2214yes—
192#2339C2214yes—
193#2337C2214yescomplemented
194#2332C2214yescomplemented
195#2329C2212yes—
196#2325C2212yes—
197#2318C2214yescomplemented
198#2314C2214yescomplemented
199#2313C2211yescharacteristic
200#2312C2211yescharacteristic
201C4×C22⋊Q8C2212yescomplemented
202C4×C22⋊Q8C2212yescomplemented
203C4×#123C2214yes—
204C4×#121C2212yescomplemented
205C4×#121C2212yescomplemented
206C4×#120C2214yes—
207#2290C2214yescomplemented
208#2290C2214yescomplemented
209C2×#388C2212yes—
210C2×#388C2212yes—
211C2×#387C2212yes—
212C2×#387C2212yes—
213C2×#386C2211yescharacteristic
214C2×#386C2211yescharacteristic
215C2×#385C2211yescharacteristic
216C2×#385C2211yescharacteristic
217#2283C2212yes—
218C2×#381C2211yescharacteristic
219C22×#41C2312yes—
220C23×D4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224#543—44no—
225#537—44no—
226C2×#127C2312yes—
227C2×#127C2312yes—
228#529—48no—
229C2×#126C2314yes—
230C2×#125C2312yes—
231C2×#124C2314yes—
232C2×#124C2312yes—
233C2×#124C2314yes—
234C2×#123—44no—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2312yes—
241C2×#123C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#120C2314yes—
257C2×#120C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2311yescharacteristic
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2311yescharacteristic
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C42—44no—
280C22×C42C2312yes—
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284C22×C42C2312yes—
285C22×C42C2312yes—
286#401C2314yes—
287#401C2314yes—
288#401C2314yes—
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#399C2314yes—
310#399C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#397C2312yes—
321#397C2312yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#393C2312yes—
370#393C2312yes—
371#393C2314yes—
372#393C2314yes—
373#393C2312yes—
374#393C2314yes—
375#393C2314yes—
376#393C2314yes—
377#393C2312yes—
378#393C2314yes—
379#393C2314yes—
380#392C2312yes—
381#392C2314yes—
382#392C2314yes—
383#392C2314yes—
384#392C2312yes—
385#392C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2314yes—
398#391C2314yes—
399#390C2314yes—
400#390C2312yes—
401#390C2312yes—
402#390C2312yes—
403#390C2314yes—
404#390C2314yes—
405#390C2312yes—
406#389C2314yes—
407#389C2314yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
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#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2312yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2312yes—
518#386C2314yes—
519#386C2312yes—
520#386C2312yes—
521#386C2312yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2312yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2312yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2312yes—
550#385C2312yes—
551#385C2312yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#384C2314yes—
559#383C2314yes—
560#383C2314yes—
561#383C2314yes—
562#383C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#382C2312yes—
568#382C2312yes—
569#382C2314yes—
570#381C2314yes—
571#381C2312yes—
572#381C2314yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2312yes—
582#380C2312yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2314yes—
592#379C2314yes—
593#379C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2312yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611#376C2314yes—
612C2×#95C2314yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C25C2411yescharacteristic
620C25C2411yescharacteristic
621C2×#41—44no—
622C2×#41—48no—
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C22×Q8C2412yes—
626C22×Q8C2414yes—
627C22×D4—42no—
628C22×D4—42no—
629C22×D4—42no—
630C22×D4C2414yes—
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2412yes—
639C22×D4C2412yes—
640C23×C4—24no—
641C23×C4—44no—
642C23×C4—44no—
643C23×C4—42no—
644C23×C4—42no—
645C23×C4—42no—
646C23×C4—42no—
647C23×C4C2411yescharacteristic
648C23×C4C2412yes—
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2411yescharacteristic
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2411yescharacteristic
657C23×C4C2411yescharacteristic
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2411yescharacteristic
665C23×C4C2411yescharacteristic
666C23×C4C2412yes—
667C23×C4C2411yescharacteristic
668C23×C4C2411yescharacteristic
669#127—44no—
670#127—44no—
671#126—48no—
672#125—44no—
673#124—48no—
674#124—44no—
675#124—48no—
676#123—48no—
677#123—44no—
678#123—44no—
679#123—48no—
680#123—48no—
681#123—48no—
682#123—48no—
683C22⋊Q8—28no—
684C22⋊Q8—48no—
685C22⋊Q8—44no—
686C22⋊Q8—44no—
687C22⋊Q8—44no—
688C22⋊Q8—48no—
689C22⋊Q8—48no—
690C22⋊Q8—48no—
691C22⋊Q8—48no—
692#121—28no—
693#121—48no—
694#121—44no—
695#121—44no—
696#121—44no—
697#120—48no—
698#120—48no—
699C4×Q8—44no—
700C4×D4—44no—
701C4×D4—48no—
702C4×D4—48no—
703C4×D4—48no—
704C4×D4—48no—
705C4×D4—48no—
706#117—48no—
707#117—48no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—44no—
710C2×C4⋊C4—44no—
711C2×C4⋊C4—42no—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C22⋊C4—24no—
748C2×C22⋊C4—44no—
749C2×C22⋊C4—42no—
750C2×C22⋊C4—42no—
751C2×C22⋊C4—44no—
752C2×C22⋊C4—44no—
753C2×C22⋊C4—42no—
754C2×C22⋊C4—42no—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C42—28no—
803C2×C42—44no—
804C2×C42—44no—
805C2×C42—44no—
806C2×C42—44no—
807C2×C42—44no—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2412yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2412yes—
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#95C2412yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883C24—22no—
884C24—22no—
885C24—22no—
886C24—24no—
887C24—22no—
888C24—24no—
889C24—42no—
890C24—42no—
891C24—41no—
892C24—41no—
893C24C2512yes—
894C24C2514yes—
895C24C2511yescharacteristic
896C24C2511yescharacteristic
897C24C2511yescharacteristic
898#41—816no—
899C2×Q8—24no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—42no—
903C2×Q8—44no—
904C2×Q8—42no—
905C2×Q8—44no—
906C2×Q8—44no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—44no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—88no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—28no—
958C22×C4—41no—
959C22×C4—42no—
960C22×C4—41no—
961C22×C4—42no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
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—44no—
988C22×C4—41no—
989C22×C4—41no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—416no—
998C22×C4—416no—
999C22×C4—416no—
1000C22×C4H(5,𝔽2)14yes—
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
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—44no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—24no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—42no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—42no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
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—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—42no—
1094C22⋊C4—44no—
1095C22⋊C4—42no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C42—24no—
1102C42—24no—
1103C42—24no—
1104C42—24no—
1105C42—28no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—42no—
1117C42—42no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—28no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—21no—
1128C23—21no—
1129C23—22no—
1130C23—22no—
1131C23—24no—
1132C23—24no—
1133C23—24no—
1134C23—24no—
1135C23—24no—
1136C23—24no—
1137C23—24no—
1138C23—24no—
1139C23—24no—
1140C23—22no—
1141C23—22no—
1142C23—48no—
1143C23—48no—
1144C23—44no—
1145C23—44no—
1146C23—44no—
1147C23—82no—
1148C23—84no—
1149C23—82no—
1150C23—84no—
1151C23C2×H(5,𝔽2)12yes—
1152C23#58512yes—
1153C23#58512yes—
1154C23#58514yes—
1155C23C2611yescharacteristic
1156Q8—84no—
1157Q8—84no—
1158Q8—162no—
1159Q8—164no—
1160D4—416no—
1161D4—84no—
1162D4—88no—
1163D4—88no—
1164D4—84no—
1165D4—84no—
1166D4—88no—
1167D4—84no—
1168D4—162no—
1169D4—164no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—22no—
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—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—48no—
1223C2×C4—48no—
1224C2×C4—48no—
1225C2×C4—48no—
1226C2×C4—44no—
1227C2×C4—44no—
1228C2×C4—48no—
1229C2×C4—44no—
1230C2×C4—44no—
1231C2×C4—48no—
1232C2×C4—44no—
1233C2×C4—88no—
1234C2×C4—84no—
1235C2×C4—82no—
1236C2×C4—84no—
1237C2×C4—82no—
1238C2×C4—88no—
1239C2×C4—88no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4C2×H(5,𝔽2)14yes—
1243C2×C4#58514yes—
1244C22—24no—
1245C22—22no—
1246C22—22no—
1247C22—24no—
1248C22—24no—
1249C22—22no—
1250C22—22no—
1251C22—24no—
1252C22—416no—
1253C22—41no—
1254C22—41no—
1255C22—42no—
1256C22—41no—
1257C22—41no—
1258C22—42no—
1259C22—44no—
1260C22—42no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—44no—
1266C22—44no—
1267C22—42no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—164no—
1272C22#354014yes—
1273C22C22×H(5,𝔽2)11yescharacteristic
1274C22C2×#58512yes—
1275C22C2×#58511yescharacteristic
1276C22C2×#58512yes—
1277C22C2×#58511yescharacteristic
1278C4—24no—
1279C4—24no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C4—42no—
1288C4—42no—
1289C4—44no—
1290C4—42no—
1291C4—44no—
1292C4—42no—
1293C4—44no—
1294C4—44no—
1295C4—44no—
1296C2—24no—
1297C2—42no—
1298C2—42no—
1299C2—84no—
1300C2—82no—
1301C2C2×#354011yescharacteristic
1302C2#6275512yes—
1303C2#6282011yescharacteristic
1304C2#6282111yescharacteristic
1305C2#6282812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36710C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59623C2semidirect
2. #59371C2semidirect
3. #53245C2semidirect
4. #53229C2semidirect
5. #45871C2semidirect
6. #45869C2semidirect
7. #45539C2semidirect
8. #45537C2semidirect
9. #38326C2semidirect
10. #38293C2semidirect
11. #38177C2semidirect
12. #38144C2semidirect
13. #37959C2semidirect
14. #37950C2semidirect
15. #37754C2semidirect
16. #37747C2semidirect
17. #36800C2semidirect
18. #36786C2semidirect
19. #36730C2semidirect
20. #36720C2semidirect
22. #36621C2semidirect
23. C2×#2853C2semidirect
36. #2852C22semidirect
37. #2852C22semidirect
38. #2851C22semidirect
39. #2851C22semidirect
40. #2850C22semidirect
41. #2850C22semidirect
45. #2835C22semidirect
47. #2824C22semidirect
49. #2804C22semidirect
51. #2795C22semidirect
52. #2793C22semidirect
53. #2789C22semidirect
54. #2785C22semidirect
55. #2782C22semidirect
56. #2782C22semidirect
57. #2781C22semidirect
58. #2781C22semidirect
61. #2778C22semidirect
62. #2775C22semidirect
63. #2767C22semidirect
64. #2767C22semidirect
65. #2763C22semidirect
66. #2763C22semidirect
67. #2763C22semidirect
68. #2762C22semidirect
69. #2762C22semidirect
70. #2759C22semidirect
71. #2759C22semidirect
72. #2758C22semidirect
74. #2756C22semidirect
75. #2754C22semidirect
76. #2753C22semidirect
77. #2753C22semidirect
78. #2751C22semidirect
79. #2750C22semidirect
80. #2750C22semidirect
82. #2747C22semidirect
83. #2746C22semidirect
84. #2746C22semidirect
85. #2745C22semidirect
86. #2745C22semidirect
87. #2741C22semidirect
88. #2738C22semidirect
89. #2737C22semidirect
90. #2730C22semidirect
91. #2723C22semidirect
92. #2712C22semidirect
96. #2702C22semidirect
97. #2701C22semidirect
98. #2700C22semidirect
102. #2693C22semidirect
103. #2691C22semidirect
104. #2690C22semidirect
105. #2690C22semidirect
106. #2689C22semidirect
109. #2687C22semidirect
110. #2686C22semidirect
111. #2686C22semidirect
117. #2655C22semidirect
118. #2653C22semidirect
119. #2650C22semidirect
120. #2648C22semidirect
124. #2610C22semidirect
125. #2605C22semidirect
127. #2598C22semidirect
129. #2597C22semidirect
130. #2593C22semidirect
132. #2589C22semidirect
133. #2588C22semidirect
134. #2576C22semidirect
135. #2574C22semidirect
136. #2564C22semidirect
141. #2529C22semidirect
142. #2528C22semidirect
143. #2525C22semidirect
144. #2524C22semidirect
145. #2523C22semidirect
146. #2515C22semidirect
147. #2511C22semidirect
149. #2510C22semidirect
157. #2477C22semidirect
158. #2477C22semidirect
159. #2476C22semidirect
160. #2474C22semidirect
163. #2465C22semidirect
164. #2463C22semidirect
165. #2463C22semidirect
167. #2459C22semidirect
171. #2444C22semidirect
172. #2438C22semidirect
175. #2421C22semidirect
177. #2415C22semidirect
184. #2379C22semidirect
189. #2359C22semidirect
193. #2337C22semidirect
194. #2332C22semidirect
197. #2318C22semidirect
198. #2314C22semidirect
201. C4×C22⋊Q8C22semidirect
202. C4×C22⋊Q8C22semidirect
204. C4×#121C22semidirect
205. C4×#121C22semidirect
207. #2290C22semidirect
208. #2290C22semidirect

Maximal subgroups

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

subgroupindex
#596232
#593712
#532452
#532292
#458712
#458692
#455392
#455372
#383262
#382932
#381772
#381442
#379592
#379502
#377542
#377472
#368002
#367862
#367302
#367202
#367102
#366212
C2×#28532