Finite Group Databasebeta

← #7656016

Subgroups — #7656016

Order 512.

4592 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41721C214yesmaximal, complemented
2#41615C214yesmaximal, complemented
3#41440C212yesmaximal, complemented
4#41082C214yesmaximal, complemented
5#40942C214yesmaximal, complemented
6#40652C212yesmaximal, complemented
7#40583C214yesmaximal, complemented
8#39601C212yesmaximal, complemented
9#39072C214yesmaximal, complemented
10#38924C212yesmaximal, complemented
11#37966C214yesmaximal, complemented
12#37478C211yesmaximal, characteristic, complemented
13#37461C212yesmaximal, complemented
14#37460C212yesmaximal, complemented
15#37447C211yesmaximal, characteristic, complemented
16#36531C212yesmaximal, complemented
17#36205C212yesmaximal, complemented
18#36052C212yesmaximal, complemented
19#35933C212yesmaximal, complemented
20#35812C214yesmaximal, complemented
21#35021C212yesmaximal, complemented
22#35010C211yesmaximal, characteristic, complemented
23#34595C212yesmaximal, complemented
24#34562C211yesmaximal, characteristic
25#34245C211yesmaximal, characteristic, complemented
26#34233C211yesmaximal, characteristic, complemented
27C2×#2357C211yesmaximal, characteristic, complemented
28C2×#525C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31#2855C2212yes—
32#2853C2214yes—
33#2852C2214yes—
34#2848C2212yes—
35#2841C2214yescomplemented
36#2837C2214yescomplemented
37#2836C2214yescomplemented
38#2832C2214yescomplemented
39#2831C2214yescomplemented
40#2817C2212yescomplemented
41#2816C2212yescomplemented
42#2781C2214yescomplemented
43#2774C2214yescomplemented
44#2770C2214yescomplemented
45#2768C2214yescomplemented
46#2764C2214yescomplemented
47#2763C2214yescomplemented
48#2761C2214yes—
49#2757C2214yes—
50#2756C2214yes—
51#2755C2214yescomplemented
52#2753C2214yes—
53#2749C2214yes—
54#2747C2214yescomplemented
55#2744C2214yescomplemented
56#2743C2214yescomplemented
57#2743C2214yescomplemented
58#2738C2214yescomplemented
59#2737C2214yes—
60#2723C2214yes—
61#2706C2214yes—
62#2702C2214yescomplemented
63#2698C2214yescomplemented
64#2695C2214yescomplemented
65#2687C2214yescomplemented
66#2667C2212yescomplemented
67#2666C2214yescomplemented
68#2666C2214yescomplemented
69#2666C2214yescomplemented
70#2666C2214yescomplemented
71#2665C2212yescomplemented
72#2664C2214yescomplemented
73#2662C2214yescomplemented
74#2659C2212yes—
75#2659C2212yes—
76#2654C2214yescomplemented
77#2654C2214yescomplemented
78#2650C2214yescomplemented
79#2650C2214yescomplemented
80#2646C2214yes—
81#2646C2212yes—
82#2639C2212yes—
83#2638C2212yes—
84#2638C2214yescomplemented
85#2637C2214yescomplemented
86#2635C2212yes—
87#2630C2214yes—
88#2630C2214yescomplemented
89#2627C2211yescharacteristic
90#2627C2214yes—
91#2627C2212yes—
92#2627C2214yescomplemented
93#2626C2211yescharacteristic
94#2626C2212yes—
95#2623C2212yescomplemented
96#2622C2212yes—
97#2618C2211yescharacteristic
98#2617C2211yescharacteristic
99#2614C2212yescomplemented
100#2613C2212yes—
101#2610C2214yes—
102#2603C2214yes—
103#2601C2214yescomplemented
104#2597C2214yes—
105#2593C2214yescomplemented
106#2585C2214yescomplemented
107#2579C2212yes—
108#2579C2212yes—
109#2577C2214yescomplemented
110#2577C2214yescomplemented
111#2575C2214yescomplemented
112#2575C2214yescomplemented
113#2574C2214yescomplemented
114#2574C2214yescomplemented
115#2573C2214yescomplemented
116#2569C2212yes—
117#2564C2212yes—
118#2564C2212yes—
119#2564C2214yes—
120#2562C2214yescomplemented
121#2560C2214yescomplemented
122#2554C2214yes—
123#2549C2212yes—
124#2533C2214yescomplemented
125#2532C2214yescomplemented
126#2531C2214yes—
127#2526C2214yes—
128#2525C2214yescomplemented
129#2524C2214yescomplemented
130#2524C2214yescomplemented
131#2523C2214yescomplemented
132#2521C2214yescomplemented
133#2521C2214yescomplemented
134#2520C2214yescomplemented
135#2520C2214yescomplemented
136#2519C2214yescomplemented
137#2519C2214yescomplemented
138#2515C2214yescomplemented
139#2515C2214yescomplemented
140#2508C2214yescomplemented
141#2505C2214yes—
142#2505C2214yescomplemented
143#2487C2212yes—
144#2484C2212yescomplemented
145#2481C2214yes—
146#2480C2214yes—
147#2480C2214yes—
148#2479C2214yes—
149#2475C2214yescomplemented
150#2473C2214yes—
151#2472C2214yes—
152#2469C2214yescomplemented
153#2469C2214yescomplemented
154#2468C2214yescomplemented
155#2468C2214yescomplemented
156#2468C2214yescomplemented
157#2466C2214yescomplemented
158#2465C2214yescomplemented
159#2461C2214yes—
160#2458C2214yescomplemented
161#2458C2214yescomplemented
162#2450C2214yes—
163#2438C2214yescomplemented
164#2437C2214yes—
165#2421C2214yescomplemented
166#2419C2214yescomplemented
167#2418C2214yes—
168#2417C2214yes—
169#2412C2214yes—
170#2409C2212yes—
171#2406C2212yescomplemented
172#2402C2214yescomplemented
173#2402C2214yescomplemented
174#2399C2214yescomplemented
175#2399C2214yescomplemented
176#2395C2212yes—
177#2392C2214yes—
178#2388C2212yes—
179#2373C2214yescomplemented
180#2373C2214yescomplemented
181#2371C2214yescomplemented
182#2368C2212yes—
183#2368C2212yes—
184#2367C2214yescomplemented
185#2362C2212yescomplemented
186#2362C2212yescomplemented
187#2361C2212yescomplemented
188#2360C2212yescomplemented
189#2358C2214yes—
190#2357C2212yes—
191#2357C2214yes—
192#2357C2212yes—
193#2357C2214yes—
194#2357C2212yes—
195#2357C2212yes—
196#2353C2212yes—
197#2349C2212yes—
198#2347C2211yescharacteristic, complemented
199#2346C2211yescharacteristic, complemented
200#2344C2212yescomplemented
201#2342C2214yes—
202#2341C2211yescharacteristic, complemented
203Q8×C22⋊C4C2212yescomplemented
204#2339C2211yescharacteristic, complemented
205#2335C2214yescomplemented
206#2332C2214yescomplemented
207#2322C2214yes—
208#2318C2214yes—
209#2318C2212yescomplemented
210#2315C2212yes—
211#2313C2212yescomplemented
212#2308C2212yes—
213C4×C22⋊Q8C2212yes—
214C4×C22⋊Q8C2212yes—
215C4×C22⋊Q8C2214yes—
216C4×C22⋊Q8C2212yes—
217C4×#123C2212yes—
218C4×#121C2212yes—
219C4×#120C2212yes—
220C2×#390C2212yes—
221C2×#388C2212yes—
222C2×#388C2212yes—
223#2283C2214yes—
224C2×#382C2211yescharacteristic
225#2280C2211yescharacteristic
226C2×#381C2211yescharacteristic
227C2×#381C2211yescharacteristic
228C2×#380C2211yescharacteristic
229#2275C2212yescomplemented
230#2274C2212yescomplemented
231C2×C4×C4⋊C4C2212yes—
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237C23×D4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#125C2314yes—
245C2×#124C2314yes—
246#525—28no—
247C2×#123C2312yes—
248C2×#123C2312yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×C22⋊Q8—28no—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×#121C2311yescharacteristic
262C2×#121C2311yescharacteristic
263C2×#120C2312yes—
264C2×#120C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×D4—28no—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×#117C2311yescharacteristic
281C2×#117C2314yes—
282C2×#117C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C42C2312yes—
298C22×C42C2311yescharacteristic
299C22×C42C2312yes—
300C22×C42C2312yes—
301#400C2312yes—
302#400C2312yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#399C2312yes—
323#399C2312yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2312yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#395C2312yes—
379#395C2312yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2312yes—
387#395C2314yes—
388#395C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2312yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#393C2312yes—
403#393C2312yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2312yes—
408#393C2314yes—
409#393C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2312yes—
413#391C2314yes—
414#391C2312yes—
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2314yes—
429#389C2312yes—
430#389C2314yes—
431#389C2314yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
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#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#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#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2312yes—
519#386C2312yes—
520#386C2312yes—
521#386C2312yes—
522#386C2314yes—
523#386C2314yes—
524#386C2312yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2312yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2312yes—
538#385C2312yes—
539#385C2312yes—
540#385C2312yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2312yes—
554#385C2312yes—
555#385C2314yes—
556#385C2314yes—
557#383C2314yes—
558#383C2312yes—
559#383C2314yes—
560#383C2314yes—
561#383C2314yes—
562#382C2314yes—
563#382C2312yes—
564#382C2312yes—
565#382C2314yes—
566#382C2314yes—
567#382C2312yes—
568#382C2314yes—
569#382C2314yes—
570#381C2312yes—
571#381C2314yes—
572#381C2314yes—
573#381C2314yes—
574#381C2312yes—
575#381C2312yes—
576#381C2314yes—
577#381C2312yes—
578#381C2312yes—
579#381C2312yes—
580#381C2312yes—
581#381C2312yes—
582#381C2314yes—
583#381C2312yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2312yes—
593#380C2314yes—
594#380C2312yes—
595#380C2314yes—
596#380C2311yescharacteristic
597#380C2311yescharacteristic
598#380C2312yes—
599#380C2312yes—
600#380C2311yescharacteristic
601#380C2311yescharacteristic
602#380C2312yes—
603#379C2314yes—
604#379C2312yes—
605#379C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2311yescharacteristic
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2311yescharacteristic
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2311yescharacteristic
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2311yescharacteristic
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2312yes—
649#376C2312yes—
650#376C2314yes—
651#376C2314yes—
652C2×#95C2311yescharacteristic
653C2×#95C2312yes—
654C2×#95C2311yescharacteristic
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2312yes—
660C2×#95C2312yes—
661C25C2411yescharacteristic
662C25C2411yescharacteristic
663C2×#41—24no—
664C2×#41—82no—
665C22×Q8—24no—
666C22×Q8—82no—
667C22×Q8C2412yes—
668C22×Q8C2411yescharacteristic
669C22×Q8C2412yes—
670C22×Q8C2414yes—
671C22×D4—24no—
672C22×D4—24no—
673C22×D4—42no—
674C22×D4C2412yes—
675C22×D4C2412yes—
676C22×D4C2412yes—
677C22×D4C2412yes—
678C22×D4C2411yescharacteristic
679C22×D4C2412yes—
680C22×D4C2414yes—
681C23×C4—24no—
682C23×C4—82no—
683C23×C4—82no—
684C23×C4#4118yes—
685C23×C4C2412yes—
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705#126—48no—
706#126—48no—
707#126—84no—
708#126—84no—
709#125—48no—
710#124—48no—
711#123—28no—
712#123—28no—
713#123—84no—
714#123—84no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—28no—
719C22⋊Q8—24no—
720C22⋊Q8—24no—
721C22⋊Q8—48no—
722C22⋊Q8—84no—
723C22⋊Q8—84no—
724#121—24no—
725#121—24no—
726#120—28no—
727#120—44no—
728C4×Q8—82no—
729C4×Q8—82no—
730C4×Q8—84no—
731C4×Q8—82no—
732C4×D4—28no—
733C4×D4—28no—
734C4×D4—28no—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—28no—
738C4×D4—48no—
739C4×D4—48no—
740C4×D4—82no—
741C4×D4—84no—
742#117—24no—
743#117—48no—
744#117—82no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—24no—
747C2×C4⋊C4—28no—
748C2×C4⋊C4—44no—
749C2×C4⋊C4—44no—
750C2×C4⋊C4—82no—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C22⋊C4—24no—
798C2×C22⋊C4—28no—
799C2×C22⋊C4—24no—
800C2×C22⋊C4—44no—
801C2×C22⋊C4—44no—
802C2×C22⋊C4—44no—
803C2×C22⋊C4—82no—
804C2×C22⋊C4—82no—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
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×C42—24no—
851C2×C42—28no—
852C2×C42—82no—
853C2×C42—82no—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873#95C2411yescharacteristic
874#95C2412yes—
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2412yes—
878#95C2411yescharacteristic
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2412yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
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—
937C24—22no—
938C24—22no—
939C24—22no—
940C24—22no—
941C24—22no—
942C24—42no—
943C24—42no—
944C24—42no—
945C24—42no—
946C24C2×#4114yes—
947C24C2512yes—
948C24C2512yes—
949C24C2511yescharacteristic
950C24C2511yescharacteristic
951C24C2511yescharacteristic
952#41—88no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—42no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—88no—
964C2×D4—24no—
965C2×D4—24no—
966C2×D4—24no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—24no—
971C2×D4—22no—
972C2×D4—24no—
973C2×D4—24no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—42no—
977C2×D4—42no—
978C2×D4—416no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—24no—
987C22×C4—22no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—44no—
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—88no—
1024C22×C4—88no—
1025C22×C4C2×#4114yes—
1026C22×C4C2×#4114yes—
1027C22×C4C2×#4114yes—
1028C22×C4C2×#4114yes—
1029C22×C4C2×#4114yes—
1030C22×C4C2×#4114yes—
1031C22×C42−1+414yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2514yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—24no—
1108C22⋊C4—28no—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—24no—
1114C22⋊C4—28no—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
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—
1145C42—24no—
1146C42—24no—
1147C42—24no—
1148C42—28no—
1149C42—28no—
1150C42—28no—
1151C42—28no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—44no—
1156C42—42no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C23—22no—
1165C23—22no—
1166C23—21no—
1167C23—21no—
1168C23—22no—
1169C23—22no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—22no—
1174C23—28no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—22no—
1182C23—22no—
1183C23—24no—
1184C23—24no—
1185C23—44no—
1186C23—44no—
1187C23—44no—
1188C23—44no—
1189C23—44no—
1190C23—84no—
1191C23—84no—
1192C23—84no—
1193C23—84no—
1194C23C22×#4112yes—
1195C23C22×#4112yes—
1196C23C22×#4112yes—
1197C23C2×2−1+412yes—
1198C23#58512yes—
1199C23C2611yescharacteristic
1200Q8—48no—
1201Q8—44no—
1202Q8—84no—
1203Q8—88no—
1204D4—48no—
1205D4—48no—
1206D4—44no—
1207D4—48no—
1208D4—48no—
1209D4—84no—
1210D4—88no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—28no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—44no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—44no—
1268C2×C4—44no—
1269C2×C4—44no—
1270C2×C4—48no—
1271C2×C4—44no—
1272C2×C4—48no—
1273C2×C4—44no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—164no—
1282C2×C4—164no—
1283C2×C4C22×#4112yes—
1284C2×C4C22×#4112yes—
1285C2×C4C22×#4112yes—
1286C2×C4C22×#4112yes—
1287C2×C4C2×2−1+414yes—
1288C2×C4#58514yes—
1289C22—22no—
1290C22—22no—
1291C22—24no—
1292C22—24no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—88no—
1314C22—88no—
1315C22#349514yes—
1316C22C23×#4111yescharacteristic
1317C22C22×2−1+411yescharacteristic
1318C22C2×#58511yescharacteristic
1319C22C2×#58512yes—
1320C22H(7,𝔽2)12yes—
1321C4—24no—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—22no—
1326C4—24no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—44no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—44no—
1341C4—44no—
1342C4—44no—
1343C2—24no—
1344C2—42no—
1345C2—42no—
1346C2—82no—
1347C2—82no—
1348C2#6268611yescharacteristic
1349C2C2×#349511yescharacteristic
1350C2#6284411yescharacteristic
1351C2#6295812yes—
1352C2#6296512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34562C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41721C2semidirect
2. #41615C2semidirect
3. #41440C2semidirect
4. #41082C2semidirect
5. #40942C2semidirect
6. #40652C2semidirect
7. #40583C2semidirect
8. #39601C2semidirect
9. #39072C2semidirect
10. #38924C2semidirect
11. #37966C2semidirect
12. #37478C2semidirect
13. #37461C2semidirect
14. #37460C2semidirect
15. #37447C2semidirect
16. #36531C2semidirect
17. #36205C2semidirect
18. #36052C2semidirect
19. #35933C2semidirect
20. #35812C2semidirect
21. #35021C2semidirect
22. #35010C2semidirect
23. #34595C2semidirect
25. #34245C2semidirect
26. #34233C2semidirect
27. C2×#2357C2semidirect
35. #2841C22semidirect
36. #2837C22semidirect
37. #2836C22semidirect
38. #2832C22semidirect
39. #2831C22semidirect
40. #2817C22semidirect
41. #2816C22semidirect
42. #2781C22semidirect
43. #2774C22semidirect
44. #2770C22semidirect
45. #2768C22semidirect
46. #2764C22semidirect
47. #2763C22semidirect
51. #2755C22semidirect
54. #2747C22semidirect
55. #2744C22semidirect
56. #2743C22semidirect
57. #2743C22semidirect
58. #2738C22semidirect
62. #2702C22semidirect
63. #2698C22semidirect
64. #2695C22semidirect
65. #2687C22semidirect
66. #2667C22semidirect
67. #2666C22semidirect
68. #2666C22semidirect
69. #2666C22semidirect
70. #2666C22semidirect
71. #2665C22semidirect
72. #2664C22semidirect
73. #2662C22semidirect
76. #2654C22semidirect
77. #2654C22semidirect
78. #2650C22semidirect
79. #2650C22semidirect
84. #2638C22semidirect
85. #2637C22semidirect
88. #2630C22semidirect
92. #2627C22semidirect
95. #2623C22semidirect
99. #2614C22semidirect
103. #2601C22semidirect
105. #2593C22semidirect
106. #2585C22semidirect
109. #2577C22semidirect
110. #2577C22semidirect
111. #2575C22semidirect
112. #2575C22semidirect
113. #2574C22semidirect
114. #2574C22semidirect
115. #2573C22semidirect
120. #2562C22semidirect
121. #2560C22semidirect
124. #2533C22semidirect
125. #2532C22semidirect
128. #2525C22semidirect
129. #2524C22semidirect
130. #2524C22semidirect
131. #2523C22semidirect
132. #2521C22semidirect
133. #2521C22semidirect
134. #2520C22semidirect
135. #2520C22semidirect
136. #2519C22semidirect
137. #2519C22semidirect
138. #2515C22semidirect
139. #2515C22semidirect
140. #2508C22semidirect
142. #2505C22semidirect
144. #2484C22semidirect
149. #2475C22semidirect
152. #2469C22semidirect
153. #2469C22semidirect
154. #2468C22semidirect
155. #2468C22semidirect
156. #2468C22semidirect
157. #2466C22semidirect
158. #2465C22semidirect
160. #2458C22semidirect
161. #2458C22semidirect
163. #2438C22semidirect
165. #2421C22semidirect
166. #2419C22semidirect
171. #2406C22semidirect
172. #2402C22semidirect
173. #2402C22semidirect
174. #2399C22semidirect
175. #2399C22semidirect
179. #2373C22semidirect
180. #2373C22semidirect
181. #2371C22semidirect
184. #2367C22semidirect
185. #2362C22semidirect
186. #2362C22semidirect
187. #2361C22semidirect
188. #2360C22semidirect
198. #2347C22semidirect
199. #2346C22semidirect
200. #2344C22semidirect
202. #2341C22semidirect
203. Q8×C22⋊C4C22semidirect
204. #2339C22semidirect
205. #2335C22semidirect
206. #2332C22semidirect
209. #2318C22semidirect
211. #2313C22semidirect
229. #2275C22semidirect
230. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#417212
#416152
#414402
#410822
#409422
#406522
#405832
#396012
#390722
#389242
#379662
#374782
#374612
#374602
#374472
#365312
#362052
#360522
#359332
#358122
#350212
#350102
#345952
#345622
#342452
#342332
C2×#23572