Finite Group Databasebeta

← #7658950

Subgroups — #7658950

Order 512.

4770 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42346C214yesmaximal, complemented
2#42058C214yesmaximal, complemented
3#42012C214yesmaximal, complemented
4#41767C214yesmaximal, complemented
5#41753C214yesmaximal, complemented
6#41390C212yesmaximal, complemented
7#41389C212yesmaximal, complemented
8#41135C214yesmaximal, complemented
9#41125C214yesmaximal, complemented
10#40546C212yesmaximal, complemented
11#40545C212yesmaximal, complemented
12#37610C212yesmaximal, complemented
13#37609C211yesmaximal, characteristic, complemented
14#37599C212yesmaximal, complemented
15#37599C212yesmaximal, complemented
16#37539C211yesmaximal, characteristic, complemented
17#37536C211yesmaximal, characteristic
18#36695C212yesmaximal, complemented
19C2×#2820C211yesmaximal, characteristic, complemented
20#36012C212yesmaximal, complemented
21#35837C212yesmaximal, complemented
22#35822C214yesmaximal, complemented
23#35742C212yesmaximal, complemented
24#35732C212yesmaximal, complemented
25#34240C211yesmaximal, characteristic, complemented
26#34239C211yesmaximal, characteristic, complemented
27#34208C211yesmaximal, characteristic, complemented
28C2×#551C2214yes—
29C2×#532C2211yescharacteristic
30C22×#125C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#520C2212yes—
33#2845C2212yescomplemented
34#2844C2212yescomplemented
35#2837C2214yescomplemented
36#2837C2214yescomplemented
37#2831C2214yescomplemented
38#2831C2214yescomplemented
39#2829C2214yes—
40#2829C2214yescomplemented
41#2820C2212yes—
42#2820C2212yes—
43#2820C2214yes—
44#2820C2211yescharacteristic
45#2820C2212yes—
46#2820C2212yes—
47#2820C2211yescharacteristic
48#2820C2211yescharacteristic
49#2820C2211yescharacteristic
50#2820C2212yescomplemented
51#2820C2212yescomplemented
52#2819C2212yes—
53#2819C2212yes—
54#2799C2214yescomplemented
55#2797C2214yescomplemented
56#2793C2214yescomplemented
57#2793C2214yescomplemented
58#2786C2214yes—
59#2786C2214yescomplemented
60#2784C2214yescomplemented
61#2781C2214yescomplemented
62#2780C2214yescomplemented
63#2779C2214yescomplemented
64#2773C2214yescomplemented
65#2755C2214yescomplemented
66#2754C2214yescomplemented
67#2752C2214yescomplemented
68#2750C2214yescomplemented
69#2740C2214yes—
70#2730C2214yescomplemented
71#2715C2214yescomplemented
72#2715C2214yescomplemented
73#2709C2214yes—
74#2709C2214yes—
75#2705C2214yescomplemented
76#2700C2214yescomplemented
77#2695C2214yescomplemented
78#2666C2214yescomplemented
79#2666C2214yescomplemented
80#2665C2214yescomplemented
81#2665C2214yescomplemented
82#2663C2214yescomplemented
83#2663C2214yescomplemented
84#2662C2214yes—
85#2662C2214yescomplemented
86#2660C2212yescomplemented
87#2657C2212yes—
88#2651C2214yescomplemented
89#2651C2214yescomplemented
90#2650C2214yescomplemented
91#2650C2214yescomplemented
92#2649C2214yescomplemented
93#2649C2214yescomplemented
94#2648C2214yes—
95#2648C2214yescomplemented
96#2641C2212yescomplemented
97#2640C2212yes—
98#2637C2214yescomplemented
99#2637C2214yescomplemented
100#2633C2212yescomplemented
101#2633C2212yescomplemented
102#2631C2212yes—
103#2631C2212yes—
104#2630C2214yes—
105#2630C2214yescomplemented
106#2627C2214yes—
107#2618C2212yes—
108#2618C2212yes—
109#2617C2212yes—
110#2617C2212yes—
111#2612C2214yescomplemented
112#2609C2214yescomplemented
113#2602C2214yescomplemented
114#2601C2214yes—
115#2601C2214yescomplemented
116#2588C2214yescomplemented
117#2579C2214yescomplemented
118#2575C2214yescomplemented
119#2574C2214yescomplemented
120#2574C2214yescomplemented
121#2569C2212yes—
122#2569C2212yes—
123#2566C2214yescomplemented
124#2560C2214yes—
125#2557C2214yescomplemented
126#2554C2214yes—
127#2554C2214yescomplemented
128#2553C2214yescomplemented
129#2553C2214yescomplemented
130#2549C2212yes—
131#2549C2212yes—
132#2544C2214yes—
133#2544C2214yes—
134#2534C2214yes—
135#2521C2214yescomplemented
136#2521C2214yescomplemented
137#2521C2214yescomplemented
138#2520C2214yescomplemented
139#2517C2214yescomplemented
140#2516C2214yescomplemented
141#2516C2214yescomplemented
142#2504C2212yes—
143#2501C2212yes—
144#2499C2214yescomplemented
145#2498C2214yes—
146#2496C2214yescomplemented
147#2488C2214yes—
148#2481C2214yes—
149#2481C2214yes—
150#2481C2214yescomplemented
151#2474C2214yescomplemented
152#2474C2214yescomplemented
153#2472C2214yes—
154#2471C2214yescomplemented
155#2470C2214yescomplemented
156#2469C2214yescomplemented
157#2469C2214yescomplemented
158#2467C2214yescomplemented
159#2465C2214yescomplemented
160#2465C2214yescomplemented
161#2461C2214yes—
162#2461C2214yescomplemented
163#2457C2214yes—
164#2457C2214yescomplemented
165#2449C2214yescomplemented
166#2445C2214yes—
167#2436C2212yes—
168#2433C2212yes—
169#2419C2214yes—
170#2418C2214yes—
171#2417C2214yes—
172#2413C2214yescomplemented
173#2412C2214yes—
174#2412C2214yes—
175#2411C2214yes—
176#2406C2214yes—
177#2404C2214yes—
178#2396C2214yescomplemented
179#2396C2214yescomplemented
180#2395C2214yescomplemented
181#2395C2214yescomplemented
182C2×#399C2212yes—
183#2392C2214yes—
184#2392C2214yescomplemented
185C2×#397C2212yes—
186C2×#396C2214yes—
187C2×#395C2212yes—
188C2×#394C2212yes—
189#2372C2214yes—
190#2371C2214yescomplemented
191#2370C2212yescomplemented
192#2370C2212yescomplemented
193#2367C2212yes—
194#2367C2212yes—
195#2364C2212yes—
196#2364C2212yes—
197#2364C2212yes—
198#2364C2212yes—
199#2359C2214yes—
200#2358C2214yes—
201#2352C2214yes—
202#2352C2214yescomplemented
203#2352C2214yescomplemented
204#2345C2211yescharacteristic
205#2345C2211yescharacteristic
206#2344C2212yes—
207#2344C2211yescharacteristic
208#2344C2211yescharacteristic
209#2344C2212yes—
210#2342C2212yes—
211#2342C2212yes—
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214D4×C22⋊C4C2211yescharacteristic
215D4×C22⋊C4C2211yescharacteristic
216#2337C2214yes—
217#2336C2214yescomplemented
218#2328C2212yescomplemented
219#2327C2212yescomplemented
220#2313C2212yes—
221#2312C2212yes—
222#2311C2212yes—
223C4×#125C2212yescomplemented
224C4×#125C2212yescomplemented
225C4×#124C2212yes—
226C4×#124C2212yes—
227C4×#124C2212yescomplemented
228C4×#124C2212yescomplemented
229#2283C2211yescharacteristic
230#2283C2211yescharacteristic
231C2×#382C2211yescharacteristic
232#2274C2212yes—
233#2273C2212yes—
234C4×#117C2211yescharacteristic
235C22×#41C2312yes—
236C23×Q8C2311yescharacteristic
237C23×D4C2311yescharacteristic
238#551—416no—
239#532—28no—
240C2×C4⋊Q8C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#125—28no—
248C2×#125C2311yescharacteristic
249C2×#125C2311yescharacteristic
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#125C2312yes—
254C2×#124—28no—
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#124C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#120C2314yes—
277C2×#120C2314yes—
278#520—48no—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
293C2×#117C2311yescharacteristic
294C2×#117C2312yes—
295C2×#117C2311yescharacteristic
296C2×#117C2312yes—
297C2×#117C2314yes—
298C2×#117C2314yes—
299C2×#117C2314yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2314yes—
306C22×C4⋊C4C2314yes—
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2312yes—
311C22×C22⋊C4C2314yes—
312C22×C22⋊C4C2314yes—
313C22×C42C2311yescharacteristic
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#399C2314yes—
327#399C2312yes—
328#399C2312yes—
329#399C2312yes—
330#399C2312yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#398C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2312yes—
348#398C2312yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#397C2314yes—
353#397C2312yes—
354#397C2314yes—
355#397C2312yes—
356#397C2312yes—
357#397C2312yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2312yes—
366#397C2314yes—
367#397C2312yes—
368#397C2312yes—
369#397C2312yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#395C2312yes—
397#395C2312yes—
398#395C2314yes—
399#395C2312yes—
400#395C2312yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2312yes—
414#394C2314yes—
415#394C2312yes—
416#394C2312yes—
417#394C2312yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2312yes—
429#394C2312yes—
430#394C2312yes—
431#394C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2312yes—
447#392C2312yes—
448#392C2312yes—
449#392C2312yes—
450#391C2314yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
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#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
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#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
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#384C2314yes—
583#383C2312yes—
584#383C2312yes—
585#382C2312yes—
586#382C2312yes—
587#382C2311yescharacteristic
588#382C2311yescharacteristic
589#382C2312yes—
590#382C2312yes—
591#382C2312yes—
592#382C2314yes—
593#382C2314yes—
594#382C2314yes—
595#381C2312yes—
596#381C2312yes—
597#381C2314yes—
598#381C2312yes—
599#381C2312yes—
600#381C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2312yes—
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2311yescharacteristic
608#380C2311yescharacteristic
609#380C2314yes—
610#380C2314yes—
611#380C2314yes—
612#380C2311yescharacteristic
613#380C2311yescharacteristic
614#380C2314yes—
615#380C2314yes—
616#379C2312yes—
617#379C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2311yescharacteristic
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2311yescharacteristic
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2311yescharacteristic
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2311yescharacteristic
650C4×C22⋊C4C2312yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656#376C2312yes—
657#376C2312yes—
658#376C2312yes—
659C2×#95C2312yes—
660C2×#95C2312yes—
661C2×#95C2314yes—
662C43C2312yes—
663C25C2412yes—
664C2×#41—28no—
665C2×#41—44no—
666C2×#41—44no—
667C22×Q8—24no—
668C22×Q8—82no—
669C22×Q8C2411yescharacteristic
670C22×Q8C2411yescharacteristic
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C22×Q8C2414yes—
674C22×D4—24no—
675C22×D4—82no—
676C22×D4C2414yes—
677C22×D4C2411yescharacteristic
678C22×D4C2411yescharacteristic
679C22×D4C2412yes—
680C22×D4C2412yes—
681C22×D4C2412yes—
682C22×D4C2412yes—
683C22×D4C2414yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C22×D4C2414yes—
687C23×C4C2412yes—
688C23×C4C2411yescharacteristic
689C23×C4C2412yes—
690C23×C4C2414yes—
691C23×C4C2412yes—
692C23×C4C2414yes—
693C23×C4C2414yes—
694C23×C4C2414yes—
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C4⋊Q8—24no—
700#127—24no—
701#127—84no—
702#126—48no—
703#126—48no—
704#126—84no—
705#126—84no—
706#125—28no—
707#125—24no—
708#125—24no—
709#125—24no—
710#125—24no—
711#125—28no—
712#124—24no—
713#124—24no—
714#124—28no—
715#124—24no—
716#124—24no—
717#124—28no—
718#124—28no—
719#124—48no—
720#124—84no—
721#124—84no—
722#123—48no—
723#123—48no—
724#123—48no—
725#123—48no—
726#123—84no—
727#123—84no—
728C22⋊Q8—48no—
729C22⋊Q8—48no—
730C22⋊Q8—84no—
731#121—28no—
732#121—28no—
733#120—48no—
734#120—48no—
735C4×Q8—44no—
736C4×Q8—44no—
737C4×Q8—82no—
738C4×Q8—82no—
739C4×D4—216no—
740C4×D4—28no—
741C4×D4—28no—
742C4×D4—44no—
743C4×D4—44no—
744C4×D4—48no—
745C4×D4—48no—
746C4×D4—84no—
747C4×D4—82no—
748C4×D4—82no—
749#117—24no—
750#117—28no—
751#117—48no—
752#117—48no—
753#117—42no—
754#117—44no—
755#117—84no—
756C2×C4⋊C4—24no—
757C2×C4⋊C4—28no—
758C2×C4⋊C4—28no—
759C2×C4⋊C4—24no—
760C2×C4⋊C4—48no—
761C2×C4⋊C4—44no—
762C2×C4⋊C4—84no—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
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×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C22⋊C4—28no—
814C2×C22⋊C4—28no—
815C2×C22⋊C4—28no—
816C2×C22⋊C4—44no—
817C2×C22⋊C4—48no—
818C2×C22⋊C4—84no—
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
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⋊C4C2411yescharacteristic
873C2×C42#4118yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2414yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948C24—24no—
949C24—24no—
950C24—24no—
951C24—44no—
952C24—44no—
953C24C2512yes—
954C24C2512yes—
955C24C2514yes—
956C24C2511yescharacteristic
957#41—432no—
958C2×Q8—22no—
959C2×Q8—22no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—88no—
971C2×D4—28no—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—22no—
975C2×D4—22no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—42no—
981C2×D4—42no—
982C2×D4—42no—
983C2×D4—42no—
984C2×D4—44no—
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—44no—
999C2×D4—88no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—28no—
1009C22×C4—28no—
1010C22×C4—28no—
1011C22×C4—44no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4C2×#4114yes—
1030C22×C4C2×#4114yes—
1031C22×C4C2×#4114yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2512yes—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C22⋊C4—24no—
1106C22⋊C4—22no—
1107C22⋊C4—24no—
1108C22⋊C4—22no—
1109C22⋊C4—24no—
1110C22⋊C4—22no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4H(5,𝔽2)14yes—
1159C42—28no—
1160C42—24no—
1161C42—28no—
1162C42—42no—
1163C42—42no—
1164C42—44no—
1165C42—42no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—42no—
1171C42—42no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42C2×#4114yes—
1176C42C2×#4114yes—
1177C42C2×#4114yes—
1178C42C2×#4114yes—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—24no—
1184C23—22no—
1185C23—24no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—24no—
1190C23—24no—
1191C23—24no—
1192C23—24no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—24no—
1197C23—24no—
1198C23—48no—
1199C23—84no—
1200C23—88no—
1201C23—88no—
1202C23—84no—
1203C23C22×#4112yes—
1204C23C2×H(5,𝔽2)12yes—
1205C23#58512yes—
1206C23C2611yescharacteristic
1207Q8—44no—
1208Q8—44no—
1209Q8—48no—
1210Q8—84no—
1211Q8—164no—
1212D4—44no—
1213D4—44no—
1214D4—48no—
1215D4—416no—
1216D4—84no—
1217D4—84no—
1218D4—84no—
1219D4—88no—
1220D4—88no—
1221D4—164no—
1222D4—164no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—28no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—44no—
1279C2×C4—44no—
1280C2×C4—416no—
1281C2×C4—48no—
1282C2×C4—88no—
1283C2×C4—88no—
1284C2×C4—88no—
1285C2×C4—84no—
1286C2×C4—84no—
1287C2×C4—164no—
1288C2×C4—164no—
1289C2×C4C22×#4112yes—
1290C2×C4C22×#4112yes—
1291C2×C4C22×#4112yes—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4112yes—
1294C2×C4C22×#4112yes—
1295C2×C4C2×H(5,𝔽2)14yes—
1296C22—24no—
1297C22—24no—
1298C22—22no—
1299C22—22no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—42no—
1309C22—42no—
1310C22—44no—
1311C22—44no—
1312C22—42no—
1313C22—42no—
1314C22—44no—
1315C22—42no—
1316C22—42no—
1317C22—168no—
1318C22#346014yes—
1319C22C23×#4111yescharacteristic
1320C22C22×H(5,𝔽2)11yescharacteristic
1321C22C2×#58511yescharacteristic
1322C22H(7,𝔽2)12yes—
1323C222−1+612yes—
1324C4—24no—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C4—42no—
1335C4—44no—
1336C4—42no—
1337C4—44no—
1338C4—42no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C2—24no—
1348C2—84no—
1349C2—82no—
1350C2—82no—
1351C2C2×#346011yescharacteristic
1352C2#6285511yescharacteristic
1353C2#6286011yescharacteristic
1354C2#6304912yes—
1355C2#6305912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37536C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42346C2semidirect
2. #42058C2semidirect
3. #42012C2semidirect
4. #41767C2semidirect
5. #41753C2semidirect
6. #41390C2semidirect
7. #41389C2semidirect
8. #41135C2semidirect
9. #41125C2semidirect
10. #40546C2semidirect
11. #40545C2semidirect
12. #37610C2semidirect
13. #37609C2semidirect
14. #37599C2semidirect
15. #37599C2semidirect
16. #37539C2semidirect
18. #36695C2semidirect
19. C2×#2820C2semidirect
20. #36012C2semidirect
21. #35837C2semidirect
22. #35822C2semidirect
23. #35742C2semidirect
24. #35732C2semidirect
25. #34240C2semidirect
26. #34239C2semidirect
27. #34208C2semidirect
33. #2845C22semidirect
34. #2844C22semidirect
35. #2837C22semidirect
36. #2837C22semidirect
37. #2831C22semidirect
38. #2831C22semidirect
40. #2829C22semidirect
50. #2820C22semidirect
51. #2820C22semidirect
54. #2799C22semidirect
55. #2797C22semidirect
56. #2793C22semidirect
57. #2793C22semidirect
59. #2786C22semidirect
60. #2784C22semidirect
61. #2781C22semidirect
62. #2780C22semidirect
63. #2779C22semidirect
64. #2773C22semidirect
65. #2755C22semidirect
66. #2754C22semidirect
67. #2752C22semidirect
68. #2750C22semidirect
70. #2730C22semidirect
71. #2715C22semidirect
72. #2715C22semidirect
75. #2705C22semidirect
76. #2700C22semidirect
77. #2695C22semidirect
78. #2666C22semidirect
79. #2666C22semidirect
80. #2665C22semidirect
81. #2665C22semidirect
82. #2663C22semidirect
83. #2663C22semidirect
85. #2662C22semidirect
86. #2660C22semidirect
88. #2651C22semidirect
89. #2651C22semidirect
90. #2650C22semidirect
91. #2650C22semidirect
92. #2649C22semidirect
93. #2649C22semidirect
95. #2648C22semidirect
96. #2641C22semidirect
98. #2637C22semidirect
99. #2637C22semidirect
100. #2633C22semidirect
101. #2633C22semidirect
105. #2630C22semidirect
111. #2612C22semidirect
112. #2609C22semidirect
113. #2602C22semidirect
115. #2601C22semidirect
116. #2588C22semidirect
117. #2579C22semidirect
118. #2575C22semidirect
119. #2574C22semidirect
120. #2574C22semidirect
123. #2566C22semidirect
125. #2557C22semidirect
127. #2554C22semidirect
128. #2553C22semidirect
129. #2553C22semidirect
135. #2521C22semidirect
136. #2521C22semidirect
137. #2521C22semidirect
138. #2520C22semidirect
139. #2517C22semidirect
140. #2516C22semidirect
141. #2516C22semidirect
144. #2499C22semidirect
146. #2496C22semidirect
150. #2481C22semidirect
151. #2474C22semidirect
152. #2474C22semidirect
154. #2471C22semidirect
155. #2470C22semidirect
156. #2469C22semidirect
157. #2469C22semidirect
158. #2467C22semidirect
159. #2465C22semidirect
160. #2465C22semidirect
162. #2461C22semidirect
164. #2457C22semidirect
165. #2449C22semidirect
172. #2413C22semidirect
178. #2396C22semidirect
179. #2396C22semidirect
180. #2395C22semidirect
181. #2395C22semidirect
184. #2392C22semidirect
190. #2371C22semidirect
191. #2370C22semidirect
192. #2370C22semidirect
202. #2352C22semidirect
203. #2352C22semidirect
217. #2336C22semidirect
218. #2328C22semidirect
219. #2327C22semidirect
223. C4×#125C22semidirect
224. C4×#125C22semidirect
227. C4×#124C22semidirect
228. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#423462
#420582
#420122
#417672
#417532
#413902
#413892
#411352
#411252
#405462
#405452
#376102
#376092
#375992
#375392
#375362
#366952
C2×#28202
#360122
#358372
#358222
#357422
#357322
#342402
#342392
#342082