Finite Group Databasebeta

← #8075573

Subgroups — #8075573

Order 512.

5007 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59928C211yesmaximal, characteristic, complemented
2#59877C212yesmaximal, complemented
3#59798C212yesmaximal, complemented
4#59775C214yesmaximal, complemented
5#51978C212yesmaximal, complemented
6#51923C212yesmaximal, complemented
7#51915C214yesmaximal, complemented
8#51873C212yesmaximal, complemented
9#49264C214yesmaximal, complemented
10#48402C214yesmaximal, complemented
11#46686C214yesmaximal, complemented
12#46548C212yesmaximal, complemented
13#44414C214yesmaximal, complemented
14#44238C214yesmaximal, complemented
15#44064C214yesmaximal, complemented
16#43394C214yesmaximal, complemented
17#43005C212yesmaximal, complemented
18#40445C214yesmaximal, complemented
19#39770C212yesmaximal, complemented
20#39361C211yesmaximal, characteristic
21#38093C212yesmaximal, complemented
22#34523C211yesmaximal, characteristic, complemented
23#34415C212yesmaximal, complemented
24C2×#563C2211yescharacteristic
25C2×#552C2212yescomplemented
26C2×#550C2211yescharacteristic
27C2×D42C2211yescharacteristic
28C2×#539C2212yes—
29C2×#535C2212yes—
30#2867C2211yescharacteristic
31#2850C2212yescomplemented
32#2826C2212yescomplemented
33#2811C2211yescharacteristic, complemented
34#2809C2211yescharacteristic, complemented
35#2808C2212yes—
36#2805C2212yescomplemented
37#2803C2214yescomplemented
38#2803C2214yescomplemented
39#2803C2214yescomplemented
40#2800C2214yescomplemented
41#2797C2214yescomplemented
42#2797C2214yescomplemented
43#2795C2214yescomplemented
44#2781C2214yescomplemented
45#2778C2214yescomplemented
46#2761C2214yescomplemented
47#2760C2212yescomplemented
48#2752C2212yescomplemented
49#2752C2214yescomplemented
50#2732C2212yes—
51#2731C2212yescomplemented
52#2731C2212yescomplemented
53#2730C2214yescomplemented
54#2727C2212yes—
55#2727C2214yescomplemented
56#2726C2212yescomplemented
57#2723C2214yescomplemented
58#2712C2214yescomplemented
59#2711C2214yes—
60#2710C2214yescomplemented
61#2709C2214yes—
62#2709C2214yes—
63#2709C2214yes—
64#2709C2214yescomplemented
65#2709C2214yescomplemented
66#2709C2214yescomplemented
67#2707C2214yescomplemented
68#2705C2214yescomplemented
69#2697C2214yescomplemented
70#2692C2214yescomplemented
71#2691C2214yescomplemented
72#2691C2214yescomplemented
73#2685C2214yes—
74#2685C2214yescomplemented
75#2685C2214yescomplemented
76#2685C2214yescomplemented
77#2685C2214yescomplemented
78#2681C2214yescomplemented
79#2681C2214yescomplemented
80#2681C2214yescomplemented
81#2672C2214yes—
82#2669C2214yes—
83#2669C2214yes—
84#2662C2214yescomplemented
85#2653C2214yescomplemented
86#2641C2212yes—
87#2641C2214yescomplemented
88#2620C2212yescomplemented
89#2619C2212yes—
90#2612C2212yescomplemented
91#2611C2214yescomplemented
92#2602C2214yescomplemented
93#2601C2214yescomplemented
94#2601C2214yescomplemented
95#2600C2214yescomplemented
96#2597C2214yescomplemented
97#2596C2214yescomplemented
98#2595C2214yescomplemented
99#2594C2214yescomplemented
100#2594C2214yescomplemented
101#2593C2214yes—
102#2576C2214yescomplemented
103#2574C2214yescomplemented
104#2574C2214yescomplemented
105#2565C2212yescomplemented
106#2564C2212yes—
107#2560C2214yescomplemented
108#2560C2214yescomplemented
109#2559C2214yes—
110#2559C2214yescomplemented
111#2559C2214yescomplemented
112#2559C2214yescomplemented
113#2556C2214yescomplemented
114#2554C2214yescomplemented
115#2554C2214yescomplemented
116#2554C2214yescomplemented
117#2548C2212yes—
118#2548C2211yescharacteristic
119#2548C2212yescomplemented
120#2548C2212yescomplemented
121#2544C2214yescomplemented
122#2544C2214yescomplemented
123#2541C2211yescharacteristic
124#2534C2214yes—
125#2534C2214yescomplemented
126#2531C2214yescomplemented
127#2528C2214yescomplemented
128#2526C2214yescomplemented
129#2526C2214yescomplemented
130#2521C2214yescomplemented
131#2516C2214yescomplemented
132#2504C2212yescomplemented
133#2500C2212yescomplemented
134#2476C2214yescomplemented
135#2476C2214yescomplemented
136#2474C2214yescomplemented
137#2472C2214yes—
138#2472C2214yescomplemented
139#2472C2214yescomplemented
140#2472C2214yescomplemented
141#2472C2214yescomplemented
142#2471C2214yescomplemented
143#2469C2214yescomplemented
144#2467C2214yescomplemented
145#2467C2214yescomplemented
146#2466C2214yescomplemented
147#2463C2212yescomplemented
148#2461C2214yescomplemented
149#2461C2214yescomplemented
150#2461C2214yescomplemented
151#2460C2214yes—
152#2460C2214yescomplemented
153#2459C2214yescomplemented
154#2459C2214yescomplemented
155#2458C2214yescomplemented
156#2449C2214yescomplemented
157#2445C2214yescomplemented
158#2445C2214yescomplemented
159#2445C2214yescomplemented
160#2445C2214yescomplemented
161#2444C2214yescomplemented
162#2443C2214yescomplemented
163#2435C2212yes—
164#2433C2214yes—
165#2433C2212yes—
166#2432C2212yescomplemented
167#2432C2212yescomplemented
168#2431C2212yes—
169#2428C2214yes—
170#2423C2214yescomplemented
171#2418C2214yes—
172#2415C2214yescomplemented
173#2405C2214yes—
174#2405C2214yes—
175#2392C2214yescomplemented
176C2×#394C2212yes—
177#2382C2212yescomplemented
178#2379C2211yescharacteristic
179#2379C2212yescomplemented
180#2375C2214yescomplemented
181#2374C2212yes—
182#2374C2214yescomplemented
183#2373C2214yescomplemented
184#2373C2214yescomplemented
185#2372C2212yes—
186#2372C2212yescomplemented
187#2370C2214yescomplemented
188#2369C2212yescomplemented
189#2368C2214yescomplemented
190#2366C2212yescomplemented
191#2366C2212yescomplemented
192#2364C2212yes—
193#2363C2214yescomplemented
194#2361C2214yescomplemented
195#2360C2214yescomplemented
196#2358C2214yescomplemented
197#2358C2214yescomplemented
198#2346C2214yescomplemented
199D4×C22⋊C4C2214yes—
200#2334C2214yescomplemented
201#2332C2214yescomplemented
202#2328C2214yes—
203#2328C2214yescomplemented
204#2327C2212yescomplemented
205#2324C2214yescomplemented
206#2322C2212yes—
207#2321C2214yescomplemented
208#2321C2214yescomplemented
209#2321C2214yescomplemented
210#2311C2212yescomplemented
211C4×#125C2212yescomplemented
212C4×#124C2211yescharacteristic
213C4×#123C2214yescomplemented
214C4×#121C2214yescomplemented
215#2297C2212yescomplemented
216#2295C2212yescomplemented
217#2293C2211yescharacteristic
218#2290C2212yescomplemented
219C22×#41C2312yes—
220C23×D4C2312yes—
221C23×D4C2312yes—
222#563—28no—
223#552—48no—
224#550—44no—
225D42—44no—
226#539—48no—
227#535—216no—
228C2×C4⋊Q8C2312yes—
229C2×#127C2312yes—
230C2×#127C2312yes—
231C2×#127C2312yes—
232C2×#127C2312yes—
233C2×#127C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#127C2312yes—
236C2×#127C2314yes—
237C2×#127C2312yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#125C2312yes—
244C2×#125C2314yes—
245C2×#125C2312yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249C2×#124C2314yes—
250C2×#124C2314yes—
251C2×#124C2314yes—
252C2×#124C2311yescharacteristic
253C2×#123C2312yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277C2×#120C2314yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2314yes—
297C2×#117C2312yes—
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2314yes—
302C22×C22⋊C4C2314yes—
303C22×C42C2312yes—
304#401C2314yes—
305#400C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#399C2312yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#395C2312yes—
341#395C2314yes—
342#395C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
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#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2312yes—
387#393C2314yes—
388#393C2314yes—
389#392C2312yes—
390#392C2314yes—
391#392C2314yes—
392#392C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2312yes—
396#392C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2314yes—
406#391C2311yescharacteristic
407#390C2314yes—
408#390C2314yes—
409#390C2312yes—
410#390C2312yes—
411#390C2314yes—
412#390C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2312yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2312yes—
425#390C2314yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2314yes—
430#390C2314yes—
431#390C2311yescharacteristic
432#390C2312yes—
433#390C2312yes—
434#390C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
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#388C2314yes—
493#388C2314yes—
494#388C2314yes—
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#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2312yes—
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#385C2314yes—
554#385C2312yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#384C2312yes—
568#382C2312yes—
569#382C2312yes—
570#382C2314yes—
571#382C2312yes—
572#382C2311yescharacteristic
573#381C2314yes—
574#381C2312yes—
575#381C2314yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#379C2314yes—
581#379C2314yes—
582#379C2314yes—
583#379C2314yes—
584#379C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2312yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2311yescharacteristic
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⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2312yes—
615#376C2312yes—
616#376C2314yes—
617#376C2314yes—
618C2×#95C2312yes—
619C43C2311yescharacteristic
620C25C2414yes—
621C2×#41—28no—
622C2×#41—44no—
623C2×#41—82no—
624C22×Q8C2412yes—
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2411yescharacteristic
628C22×D4—28no—
629C22×D4—44no—
630C22×D4—44no—
631C22×D4—82no—
632C22×D4—84no—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2411yescharacteristic
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2412yes—
647C22×D4C2412yes—
648C22×D4C2412yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2411yescharacteristic
652C22×D4C2411yescharacteristic
653C22×D4C2411yescharacteristic
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2414yes—
665C4⋊Q8—28no—
666#127—28no—
667#127—28no—
668#127—44no—
669#127—44no—
670#127—42no—
671#127—42no—
672#127—44no—
673#127—84no—
674#127—82no—
675#126—216no—
676#126—48no—
677#126—48no—
678#126—48no—
679#126—84no—
680#125—216no—
681#125—28no—
682#125—44no—
683#124—28no—
684#124—82no—
685#124—82no—
686#124—84no—
687#124—84no—
688#124—84no—
689#124#4118yes—
690#123—28no—
691#123—48no—
692#123—48no—
693#123—48no—
694#123—48no—
695#123—48no—
696#123—84no—
697C22⋊Q8—216no—
698C22⋊Q8—48no—
699C22⋊Q8—48no—
700C22⋊Q8—44no—
701C22⋊Q8—44no—
702C22⋊Q8—44no—
703C22⋊Q8—84no—
704#121—28no—
705#121—216no—
706#121—216no—
707#121—44no—
708#121—44no—
709#121—44no—
710#121—44no—
711#121—84no—
712#120—216no—
713#120—216no—
714#120—48no—
715#120—48no—
716#120—48no—
717C4×Q8—42no—
718C4×Q8—44no—
719C4×Q8—44no—
720C4×D4—24no—
721C4×D4—28no—
722C4×D4—48no—
723C4×D4—42no—
724C4×D4—84no—
725C4×D4—84no—
726C4×D4—84no—
727C4×D4—84no—
728C4×D4—84no—
729C4×D4—84no—
730C4×D4—84no—
731#117—28no—
732#117—44no—
733#117—48no—
734#117—82no—
735C2×C4⋊C4—44no—
736C2×C4⋊C4—44no—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C22⋊C4—84no—
777C2×C22⋊C4—84no—
778C2×C22⋊C4—84no—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C42—82no—
838C2×C42C2414yes—
839C2×C42C2412yes—
840C2×C42C2411yescharacteristic
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859#95C2412yes—
860#95C2414yes—
861#95C2412yes—
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#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899C24—28no—
900C24—44no—
901C24—44no—
902C24—44no—
903C24—44no—
904C24—44no—
905C24—44no—
906C24C2512yes—
907C24C2514yes—
908C24C2512yes—
909C24C2512yes—
910C24C2512yes—
911#41—816no—
912C2×Q8—24no—
913C2×Q8—24no—
914C2×Q8—41no—
915C2×Q8—41no—
916C2×Q8—42no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—44no—
922C2×Q8C2×#4114yes—
923C2×D4—28no—
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—24no—
927C2×D4—24no—
928C2×D4—28no—
929C2×D4—28no—
930C2×D4—24no—
931C2×D4—24no—
932C2×D4—22no—
933C2×D4—28no—
934C2×D4—24no—
935C2×D4—24no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—41no—
939C2×D4—44no—
940C2×D4—42no—
941C2×D4—41no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—42no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—42no—
971C2×D4—42no—
972C2×D4—41no—
973C2×D4—41no—
974C2×D4—42no—
975C2×D4—42no—
976C2×D4—42no—
977C2×D4—42no—
978C2×D4—816no—
979C2×D4—816no—
980C2×D4C2×#4114yes—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—44no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4C2511yescharacteristic
1013C22×C4C2514yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2512yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2514yes—
1021C22×C4C2514yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—41no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—42no—
1059C4⋊C4—41no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4H(5,𝔽2)14yes—
1069C22⋊C4—28no—
1070C22⋊C4—24no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—24no—
1075C22⋊C4—24no—
1076C22⋊C4—24no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
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—44no—
1094C22⋊C4—42no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—42no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4C2×#41116yes—
1127C42—24no—
1128C42—24no—
1129C42—28no—
1130C42—22no—
1131C42—24no—
1132C42—24no—
1133C42—42no—
1134C42—44no—
1135C42—42no—
1136C42—44no—
1137C42—42no—
1138C42—44no—
1139C42—44no—
1140C42—44no—
1141C42—44no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C42—42no—
1146C42—41no—
1147C42C2×#4114yes—
1148C23—22no—
1149C23—24no—
1150C23—24no—
1151C23—22no—
1152C23—22no—
1153C23—24no—
1154C23—22no—
1155C23—22no—
1156C23—22no—
1157C23—24no—
1158C23—22no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—22no—
1166C23—24no—
1167C23—22no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—22no—
1173C23—24no—
1174C23—88no—
1175C23—88no—
1176C23—88no—
1177C23—88no—
1178C23—88no—
1179C23—164no—
1180C23—164no—
1181C23C22×#4114yes—
1182C23C2611yescharacteristic
1183Q8—44no—
1184Q8—84no—
1185Q8—84no—
1186Q8—162no—
1187D4—44no—
1188D4—416no—
1189D4—44no—
1190D4—88no—
1191D4—88no—
1192D4—88no—
1193D4—88no—
1194D4—84no—
1195D4—84no—
1196D4—84no—
1197D4—84no—
1198D4—84no—
1199D4—84no—
1200D4—88no—
1201D4—88no—
1202D4—88no—
1203D4—162no—
1204D4—162no—
1205D4—161no—
1206D4—161no—
1207D4—162no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—21no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—48no—
1253C2×C4—48no—
1254C2×C4—48no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—88no—
1258C2×C4—88no—
1259C2×C4—164no—
1260C2×C4—164no—
1261C2×C4—162no—
1262C2×C4—164no—
1263C2×C4C22×#4112yes—
1264C2×C4C22×#4114yes—
1265C2×C4C22×#4114yes—
1266C2×C4C2×H(5,𝔽2)12yes—
1267C2×C4C2×H(5,𝔽2)14yes—
1268C2×C4#58514yes—
1269C22—24no—
1270C22—28no—
1271C22—42no—
1272C22—44no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22—44no—
1292C22—42no—
1293C22—44no—
1294C22—42no—
1295C22—42no—
1296C22—1616no—
1297C22C23×#4111yescharacteristic
1298C22C22×H(5,𝔽2)11yescharacteristic
1299C22C2×#58512yes—
1300C22H(7,𝔽2)11yescharacteristic
1301C22H(7,𝔽2)12yes—
1302C4—24no—
1303C4—22no—
1304C4—24no—
1305C4—24no—
1306C4—24no—
1307C4—22no—
1308C4—44no—
1309C4—44no—
1310C4—44no—
1311C4—44no—
1312C4—42no—
1313C4—41no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—44no—
1318C4—44no—
1319C4—42no—
1320C2—44no—
1321C2—82no—
1322C2—82no—
1323C2—84no—
1324C2—82no—
1325C2#6287012yes—
1326C2#6287411yescharacteristic
1327C2#6298311yescharacteristic
1328C2#6301012yes—
1329C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39361C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59928C2semidirect
2. #59877C2semidirect
3. #59798C2semidirect
4. #59775C2semidirect
5. #51978C2semidirect
6. #51923C2semidirect
7. #51915C2semidirect
8. #51873C2semidirect
9. #49264C2semidirect
10. #48402C2semidirect
11. #46686C2semidirect
12. #46548C2semidirect
13. #44414C2semidirect
14. #44238C2semidirect
15. #44064C2semidirect
16. #43394C2semidirect
17. #43005C2semidirect
18. #40445C2semidirect
19. #39770C2semidirect
21. #38093C2semidirect
22. #34523C2semidirect
23. #34415C2semidirect
25. C2×#552C22semidirect
31. #2850C22semidirect
32. #2826C22semidirect
33. #2811C22semidirect
34. #2809C22semidirect
36. #2805C22semidirect
37. #2803C22semidirect
38. #2803C22semidirect
39. #2803C22semidirect
40. #2800C22semidirect
41. #2797C22semidirect
42. #2797C22semidirect
43. #2795C22semidirect
44. #2781C22semidirect
45. #2778C22semidirect
46. #2761C22semidirect
47. #2760C22semidirect
48. #2752C22semidirect
49. #2752C22semidirect
51. #2731C22semidirect
52. #2731C22semidirect
53. #2730C22semidirect
55. #2727C22semidirect
56. #2726C22semidirect
57. #2723C22semidirect
58. #2712C22semidirect
60. #2710C22semidirect
64. #2709C22semidirect
65. #2709C22semidirect
66. #2709C22semidirect
67. #2707C22semidirect
68. #2705C22semidirect
69. #2697C22semidirect
70. #2692C22semidirect
71. #2691C22semidirect
72. #2691C22semidirect
74. #2685C22semidirect
75. #2685C22semidirect
76. #2685C22semidirect
77. #2685C22semidirect
78. #2681C22semidirect
79. #2681C22semidirect
80. #2681C22semidirect
84. #2662C22semidirect
85. #2653C22semidirect
87. #2641C22semidirect
88. #2620C22semidirect
90. #2612C22semidirect
91. #2611C22semidirect
92. #2602C22semidirect
93. #2601C22semidirect
94. #2601C22semidirect
95. #2600C22semidirect
96. #2597C22semidirect
97. #2596C22semidirect
98. #2595C22semidirect
99. #2594C22semidirect
100. #2594C22semidirect
102. #2576C22semidirect
103. #2574C22semidirect
104. #2574C22semidirect
105. #2565C22semidirect
107. #2560C22semidirect
108. #2560C22semidirect
110. #2559C22semidirect
111. #2559C22semidirect
112. #2559C22semidirect
113. #2556C22semidirect
114. #2554C22semidirect
115. #2554C22semidirect
116. #2554C22semidirect
119. #2548C22semidirect
120. #2548C22semidirect
121. #2544C22semidirect
122. #2544C22semidirect
125. #2534C22semidirect
126. #2531C22semidirect
127. #2528C22semidirect
128. #2526C22semidirect
129. #2526C22semidirect
130. #2521C22semidirect
131. #2516C22semidirect
132. #2504C22semidirect
133. #2500C22semidirect
134. #2476C22semidirect
135. #2476C22semidirect
136. #2474C22semidirect
138. #2472C22semidirect
139. #2472C22semidirect
140. #2472C22semidirect
141. #2472C22semidirect
142. #2471C22semidirect
143. #2469C22semidirect
144. #2467C22semidirect
145. #2467C22semidirect
146. #2466C22semidirect
147. #2463C22semidirect
148. #2461C22semidirect
149. #2461C22semidirect
150. #2461C22semidirect
152. #2460C22semidirect
153. #2459C22semidirect
154. #2459C22semidirect
155. #2458C22semidirect
156. #2449C22semidirect
157. #2445C22semidirect
158. #2445C22semidirect
159. #2445C22semidirect
160. #2445C22semidirect
161. #2444C22semidirect
162. #2443C22semidirect
166. #2432C22semidirect
167. #2432C22semidirect
170. #2423C22semidirect
172. #2415C22semidirect
175. #2392C22semidirect
177. #2382C22semidirect
179. #2379C22semidirect
180. #2375C22semidirect
182. #2374C22semidirect
183. #2373C22semidirect
184. #2373C22semidirect
186. #2372C22semidirect
187. #2370C22semidirect
188. #2369C22semidirect
189. #2368C22semidirect
190. #2366C22semidirect
191. #2366C22semidirect
193. #2363C22semidirect
194. #2361C22semidirect
195. #2360C22semidirect
196. #2358C22semidirect
197. #2358C22semidirect
198. #2346C22semidirect
200. #2334C22semidirect
201. #2332C22semidirect
203. #2328C22semidirect
204. #2327C22semidirect
205. #2324C22semidirect
207. #2321C22semidirect
208. #2321C22semidirect
209. #2321C22semidirect
210. #2311C22semidirect
211. C4×#125C22semidirect
213. C4×#123C22semidirect
214. C4×#121C22semidirect
215. #2297C22semidirect
216. #2295C22semidirect
218. #2290C22semidirect

Maximal subgroups

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

subgroupindex
#599282
#598772
#597982
#597752
#519782
#519232
#519152
#518732
#492642
#484022
#466862
#465482
#444142
#442382
#440642
#433942
#430052
#404452
#397702
#393612
#380932
#345232
#344152