Finite Group Databasebeta

← #9040729

Subgroups — #9040729

Order 512.

4575 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52074C211yesmaximal, characteristic, complemented
2#51754C211yesmaximal, characteristic, complemented
3#51295C214yesmaximal, complemented
4#51213C212yesmaximal, complemented
5#51133C214yesmaximal, complemented
6#51092C212yesmaximal, complemented
7#50475C214yesmaximal, complemented
8#50065C214yesmaximal, complemented
9#50020C214yesmaximal, complemented
10#49250C214yesmaximal, complemented
11#49144C214yesmaximal, complemented
12#48674C214yesmaximal, complemented
13#48658C214yesmaximal, complemented
14#36081C212yesmaximal, complemented
15#35948C212yesmaximal, complemented
16#35942C214yesmaximal, complemented
17#35707C214yesmaximal, complemented
18#35703C212yesmaximal, complemented
19#35624C211yesmaximal, characteristic, complemented
20#35500C212yesmaximal, complemented
21#35480C214yesmaximal, complemented
22C2×#562C2211yescharacteristic, complemented
23C2×Q82C2211yescharacteristic, complemented
24C2×#548C2212yes—
25C2×#541C2211yescharacteristic
26C2×#518C2211yescharacteristic
27#2808C2214yes—
28#2799C2214yescomplemented
29#2798C2214yescomplemented
30#2798C2214yescomplemented
31#2781C2214yescomplemented
32#2781C2214yescomplemented
33#2779C2214yes—
34#2762C2214yescomplemented
35#2756C2214yes—
36#2754C2214yescomplemented
37#2754C2214yescomplemented
38#2753C2214yescomplemented
39#2752C2214yescomplemented
40#2751C2214yes—
41#2751C2214yescomplemented
42#2746C2214yescomplemented
43#2741C2214yes—
44#2741C2214yescomplemented
45#2737C2214yescomplemented
46#2736C2214yes—
47#2732C2214yescomplemented
48#2729C2214yes—
49#2728C2214yescomplemented
50#2716C2214yes—
51#2714C2214yes—
52#2713C2214yescomplemented
53#2710C2214yes—
54#2710C2214yescomplemented
55#2706C2214yes—
56#2703C2214yes—
57#2700C2214yescomplemented
58#2698C2214yescomplemented
59#2696C2214yes—
60#2690C2214yescomplemented
61#2688C2214yescomplemented
62#2686C2214yes—
63#2686C2214yes—
64#2685C2214yes—
65#2680C2214yescomplemented
66#2678C2214yes—
67#2676C2214yescomplemented
68#2670C2214yes—
69#2661C2214yes—
70#2653C2214yes—
71#2650C2214yes—
72#2648C2214yes—
73#2646C2214yescomplemented
74#2640C2212yescomplemented
75#2640C2214yescomplemented
76#2638C2212yes—
77#2637C2214yescomplemented
78#2634C2212yescomplemented
79#2631C2212yes—
80#2630C2214yescomplemented
81#2617C2212yes—
82#2610C2212yes—
83#2606C2212yescomplemented
84#2602C2214yescomplemented
85#2601C2214yes—
86#2599C2212yes—
87#2597C2214yescomplemented
88#2595C2214yes—
89#2593C2214yescomplemented
90#2592C2212yescomplemented
91#2592C2214yescomplemented
92#2589C2214yescomplemented
93#2577C2214yescomplemented
94#2574C2214yescomplemented
95#2572C2214yescomplemented
96#2572C2214yescomplemented
97#2570C2214yescomplemented
98#2569C2214yescomplemented
99#2566C2212yes—
100#2561C2212yes—
101#2560C2214yes—
102#2560C2214yescomplemented
103#2559C2214yescomplemented
104#2554C2214yes—
105#2554C2214yescomplemented
106#2547C2212yes—
107#2547C2214yescomplemented
108#2543C2212yes—
109#2534C2214yes—
110#2532C2214yes—
111#2532C2214yes—
112#2532C2214yescomplemented
113#2531C2214yescomplemented
114#2531C2214yescomplemented
115#2530C2214yescomplemented
116#2529C2214yescomplemented
117#2527C2214yescomplemented
118#2527C2214yescomplemented
119#2525C2214yescomplemented
120#2524C2214yescomplemented
121#2522C2214yescomplemented
122#2520C2214yescomplemented
123#2516C2214yes—
124#2515C2214yescomplemented
125#2515C2214yescomplemented
126#2513C2214yes—
127#2510C2214yescomplemented
128#2499C2212yes—
129#2493C2214yescomplemented
130#2492C2214yescomplemented
131#2492C2214yescomplemented
132#2492C2214yescomplemented
133#2491C2214yes—
134#2491C2214yes—
135#2491C2214yescomplemented
136#2490C2214yescomplemented
137#2488C2214yes—
138#2488C2214yescomplemented
139#2480C2214yes—
140#2480C2214yes—
141#2477C2214yes—
142#2477C2214yescomplemented
143#2472C2214yes—
144#2469C2214yes—
145#2469C2214yescomplemented
146#2468C2214yescomplemented
147#2467C2214yes—
148#2467C2214yescomplemented
149#2464C2214yes—
150#2463C2214yes—
151#2462C2214yescomplemented
152#2460C2214yes—
153#2460C2214yes—
154#2459C2214yes—
155#2459C2214yes—
156#2459C2214yescomplemented
157#2458C2214yes—
158#2458C2214yescomplemented
159#2456C2214yescomplemented
160#2450C2214yescomplemented
161#2446C2214yescomplemented
162#2444C2214yes—
163#2435C2212yes—
164#2430C2214yescomplemented
165#2419C2214yescomplemented
166#2418C2214yes—
167#2414C2214yes—
168#2410C2214yes—
169#2409C2212yes—
170#2409C2214yescomplemented
171#2404C2212yes—
172#2398C2212yes—
173#2398C2214yescomplemented
174#2396C2214yescomplemented
175#2388C2212yes—
176C2×#393C2212yes—
177#2381C2211yescharacteristic, complemented
178#2379C2214yescomplemented
179#2378C2214yescomplemented
180#2375C2214yes—
181#2374C2214yescomplemented
182#2373C2214yescomplemented
183#2371C2211yescharacteristic, complemented
184#2364C2214yes—
185#2359C2214yescomplemented
186#2358C2214yes—
187#2353C2212yes—
188#2343C2214yescomplemented
189#2342C2214yes—
190#2341C2214yescomplemented
191Q8×C22⋊C4C2214yescomplemented
192#2337C2212yescomplemented
193#2337C2214yescomplemented
194#2335C2214yes—
195#2333C2214yescomplemented
196#2332C2214yescomplemented
197#2326C2212yes—
198C4×#126C2214yescomplemented
199C4×#124C2212yes—
200#2298C2211yescharacteristic
201#2276C2212yescomplemented
202#2275C2214yescomplemented
203C22×#41C2312yes—
204C23×Q8C2312yes—
205C23×D4C2311yescharacteristic
206#562—44no—
207Q82—44no—
208#548—48no—
209#541—44no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×#126C2314yes—
214C2×#126C2314yes—
215C2×#126C2314yes—
216C2×#125C2311yescharacteristic
217C2×#125C2314yes—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#120C2314yes—
240C2×#120C2314yes—
241#518—44no—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×#117C2311yescharacteristic
255C2×#117C2314yes—
256C2×#117C2311yescharacteristic
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2314yes—
259C22×C22⋊C4C2312yes—
260#401C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#399C2314yes—
276#399C2314yes—
277#399C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2312yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#397C2314yes—
291#397C2314yes—
292#397C2312yes—
293#397C2312yes—
294#397C2314yes—
295#397C2314yes—
296#397C2314yes—
297#397C2314yes—
298#397C2314yes—
299#397C2314yes—
300#397C2314yes—
301#397C2314yes—
302#397C2312yes—
303#397C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#396C2314yes—
312#396C2314yes—
313#396C2314yes—
314#396C2314yes—
315#396C2314yes—
316#396C2314yes—
317#395C2314yes—
318#395C2312yes—
319#395C2312yes—
320#395C2314yes—
321#395C2314yes—
322#394C2314yes—
323#394C2314yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#394C2314yes—
328#394C2314yes—
329#394C2314yes—
330#394C2314yes—
331#394C2312yes—
332#394C2314yes—
333#394C2314yes—
334#394C2314yes—
335#394C2314yes—
336#394C2314yes—
337#394C2314yes—
338#394C2314yes—
339#394C2314yes—
340#394C2314yes—
341#394C2314yes—
342#393C2312yes—
343#393C2314yes—
344#393C2312yes—
345#393C2314yes—
346#393C2314yes—
347#393C2314yes—
348#393C2312yes—
349#393C2314yes—
350#393C2312yes—
351#393C2312yes—
352#393C2314yes—
353#393C2314yes—
354#393C2314yes—
355#393C2314yes—
356#393C2312yes—
357#393C2314yes—
358#393C2314yes—
359#392C2312yes—
360#392C2312yes—
361#392C2314yes—
362#392C2312yes—
363#392C2314yes—
364#392C2314yes—
365#392C2314yes—
366#392C2314yes—
367#392C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2312yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2312yes—
384#390C2314yes—
385#390C2314yes—
386#390C2312yes—
387#390C2312yes—
388#390C2314yes—
389#390C2314yes—
390#390C2314yes—
391#390C2314yes—
392#390C2314yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
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#387C2314yes—
454#387C2314yes—
455#387C2314yes—
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#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#384C2312yes—
522#383C2314yes—
523#383C2314yes—
524#383C2312yes—
525#383C2314yes—
526#382C2312yes—
527#382C2314yes—
528#382C2314yes—
529#382C2314yes—
530#381C2314yes—
531#381C2314yes—
532#381C2314yes—
533#381C2314yes—
534#381C2314yes—
535#381C2312yes—
536#380C2314yes—
537#380C2314yes—
538#380C2314yes—
539#380C2314yes—
540#380C2314yes—
541#380C2314yes—
542#380C2314yes—
543#380C2314yes—
544#380C2314yes—
545#380C2312yes—
546#379C2314yes—
547#379C2314yes—
548#379C2314yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2312yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2312yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2312yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576C4×C22⋊C4C2314yes—
577#376C2311yescharacteristic
578#376C2314yes—
579#376C2312yes—
580#376C2314yes—
581C2×#95C2314yes—
582C2×#95C2312yes—
583C2×#95C2314yes—
584C43C2311yescharacteristic
585C25C2411yescharacteristic
586C25C2411yescharacteristic
587C2×#41—44no—
588C2×#41—48no—
589C22×Q8—44no—
590C22×Q8—48no—
591C22×Q8C2412yes—
592C22×Q8C2412yes—
593C22×Q8C2412yes—
594C22×Q8C2414yes—
595C22×Q8C2414yes—
596C22×D4—42no—
597C22×D4—44no—
598C22×D4C2412yes—
599C22×D4C2414yes—
600C22×D4C2412yes—
601C22×D4C2414yes—
602C22×D4C2414yes—
603C22×D4C2412yes—
604C22×D4C2414yes—
605C22×D4C2414yes—
606C22×D4C2414yes—
607C23×C4C2414yes—
608C23×C4C2412yes—
609C23×C4C2414yes—
610C23×C4C2412yes—
611C23×C4C2411yescharacteristic
612C23×C4C2414yes—
613C23×C4C2412yes—
614C23×C4C2412yes—
615C23×C4C2414yes—
616C23×C4C2414yes—
617C4⋊Q8—24no—
618C4⋊Q8—48no—
619C4⋊Q8—48no—
620#126—48no—
621#126—48no—
622#126—48no—
623#125—24no—
624#125—48no—
625#124—28no—
626#124—48no—
627#124—44no—
628#124—48no—
629#124—48no—
630#124—44no—
631#123—48no—
632#123—48no—
633#123—48no—
634#123—48no—
635C22⋊Q8—48no—
636C22⋊Q8—48no—
637C22⋊Q8—48no—
638C22⋊Q8—48no—
639C22⋊Q8—44no—
640C22⋊Q8—44no—
641#121—48no—
642#121—48no—
643#121—48no—
644#121—44no—
645#121—48no—
646#120—48no—
647#120—48no—
648C4×Q8—28no—
649C4×Q8—48no—
650C4×Q8—44no—
651C4×Q8—48no—
652C4×D4—28no—
653C4×D4—48no—
654C4×D4—44no—
655C4×D4—48no—
656C4×D4—48no—
657C4×D4—44no—
658C4×D4—44no—
659C4×D4—48no—
660#117—24no—
661#117—48no—
662#117—42no—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C22⋊C4—48no—
697C2×C22⋊C4—44no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2412yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2412yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C42C2411yescharacteristic
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2411yescharacteristic
767#95C2414yes—
768#95C2412yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2412yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2412yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2412yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821C24—24no—
822C24—41no—
823C24—41no—
824C24—42no—
825C24—44no—
826C24—44no—
827C24C2511yescharacteristic
828C24C2512yes—
829C24C2514yes—
830C24C2512yes—
831#41—816no—
832C2×Q8—24no—
833C2×Q8—24no—
834C2×Q8—24no—
835C2×Q8—28no—
836C2×Q8—28no—
837C2×Q8—44no—
838C2×Q8—42no—
839C2×Q8—42no—
840C2×Q8—44no—
841C2×Q8—44no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—44no—
845C2×Q8—816no—
846C2×D4—28no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—28no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—28no—
853C2×D4—42no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—416no—
873C22×C4—28no—
874C22×C4—22no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—28no—
878C22×C4—28no—
879C22×C4—42no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4C2514yes—
899C22×C4C2512yes—
900C22×C4C2512yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2511yescharacteristic
908C22×C4C2512yes—
909C22×C4C2514yes—
910C22×C4C2514yes—
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2512yes—
914C22×C4C2514yes—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—28no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—28no—
961C22⋊C4—42no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C42—22no—
998C42—28no—
999C42—28no—
1000C42—44no—
1001C42—41no—
1002C42—41no—
1003C42—44no—
1004C42—44no—
1005C42—44no—
1006C42—44no—
1007C42—44no—
1008C42—44no—
1009C42—44no—
1010C42—42no—
1011C42—42no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42H(5,𝔽2)14yes—
1016C23—22no—
1017C23—24no—
1018C23—22no—
1019C23—24no—
1020C23—21no—
1021C23—24no—
1022C23—22no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—22no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—22no—
1033C23—22no—
1034C23—24no—
1035C23—44no—
1036C23—44no—
1037C23—88no—
1038C23—162no—
1039C23—162no—
1040C23—164no—
1041C23#58514yes—
1042C23C2611yescharacteristic
1043Q8—216no—
1044Q8—84no—
1045Q8—84no—
1046Q8—88no—
1047Q8—164no—
1048D4—48no—
1049D4—416no—
1050D4—48no—
1051D4—84no—
1052D4—88no—
1053D4—88no—
1054D4—164no—
1055D4—164no—
1056D4—164no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—44no—
1100C2×C4—84no—
1101C2×C4—88no—
1102C2×C4—84no—
1103C2×C4—88no—
1104C2×C4—88no—
1105C2×C4—162no—
1106C2×C4—162no—
1107C2×C4—164no—
1108C2×C4—164no—
1109C2×C4C2×H(5,𝔽2)14yes—
1110C2×C4C2×H(5,𝔽2)12yes—
1111C2×C4#58518yes—
1112C22—24no—
1113C22—28no—
1114C22—42no—
1115C22—42no—
1116C22—44no—
1117C22—41no—
1118C22—42no—
1119C22—44no—
1120C22—44no—
1121C22—42no—
1122C22—44no—
1123C22—42no—
1124C22—42no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—164no—
1133C22—164no—
1134C22C22×H(5,𝔽2)11yescharacteristic
1135C22C2×#58512yes—
1136C22C2×#58514yes—
1137C4—22no—
1138C4—24no—
1139C4—28no—
1140C4—41no—
1141C4—44no—
1142C4—44no—
1143C4—42no—
1144C4—42no—
1145C4—44no—
1146C4—42no—
1147C4—44no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—44no—
1152C4—44no—
1153C4—44no—
1154C2—44no—
1155C2—84no—
1156C2—82no—
1157C2—81no—
1158C2#6282111yescharacteristic
1159C2#6282412yes—
1160C2#6282714yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52074C2semidirect
2. #51754C2semidirect
3. #51295C2semidirect
4. #51213C2semidirect
5. #51133C2semidirect
6. #51092C2semidirect
7. #50475C2semidirect
8. #50065C2semidirect
9. #50020C2semidirect
10. #49250C2semidirect
11. #49144C2semidirect
12. #48674C2semidirect
13. #48658C2semidirect
14. #36081C2semidirect
15. #35948C2semidirect
16. #35942C2semidirect
17. #35707C2semidirect
18. #35703C2semidirect
19. #35624C2semidirect
20. #35500C2semidirect
21. #35480C2semidirect
22. C2×#562C22semidirect
23. C2×Q82C22semidirect
28. #2799C22semidirect
29. #2798C22semidirect
30. #2798C22semidirect
31. #2781C22semidirect
32. #2781C22semidirect
34. #2762C22semidirect
36. #2754C22semidirect
37. #2754C22semidirect
38. #2753C22semidirect
39. #2752C22semidirect
41. #2751C22semidirect
42. #2746C22semidirect
44. #2741C22semidirect
45. #2737C22semidirect
47. #2732C22semidirect
49. #2728C22semidirect
52. #2713C22semidirect
54. #2710C22semidirect
57. #2700C22semidirect
58. #2698C22semidirect
60. #2690C22semidirect
61. #2688C22semidirect
65. #2680C22semidirect
67. #2676C22semidirect
73. #2646C22semidirect
74. #2640C22semidirect
75. #2640C22semidirect
77. #2637C22semidirect
78. #2634C22semidirect
80. #2630C22semidirect
83. #2606C22semidirect
84. #2602C22semidirect
87. #2597C22semidirect
89. #2593C22semidirect
90. #2592C22semidirect
91. #2592C22semidirect
92. #2589C22semidirect
93. #2577C22semidirect
94. #2574C22semidirect
95. #2572C22semidirect
96. #2572C22semidirect
97. #2570C22semidirect
98. #2569C22semidirect
102. #2560C22semidirect
103. #2559C22semidirect
105. #2554C22semidirect
107. #2547C22semidirect
112. #2532C22semidirect
113. #2531C22semidirect
114. #2531C22semidirect
115. #2530C22semidirect
116. #2529C22semidirect
117. #2527C22semidirect
118. #2527C22semidirect
119. #2525C22semidirect
120. #2524C22semidirect
121. #2522C22semidirect
122. #2520C22semidirect
124. #2515C22semidirect
125. #2515C22semidirect
127. #2510C22semidirect
129. #2493C22semidirect
130. #2492C22semidirect
131. #2492C22semidirect
132. #2492C22semidirect
135. #2491C22semidirect
136. #2490C22semidirect
138. #2488C22semidirect
142. #2477C22semidirect
145. #2469C22semidirect
146. #2468C22semidirect
148. #2467C22semidirect
151. #2462C22semidirect
156. #2459C22semidirect
158. #2458C22semidirect
159. #2456C22semidirect
160. #2450C22semidirect
161. #2446C22semidirect
164. #2430C22semidirect
165. #2419C22semidirect
170. #2409C22semidirect
173. #2398C22semidirect
174. #2396C22semidirect
177. #2381C22semidirect
178. #2379C22semidirect
179. #2378C22semidirect
181. #2374C22semidirect
182. #2373C22semidirect
183. #2371C22semidirect
185. #2359C22semidirect
188. #2343C22semidirect
190. #2341C22semidirect
191. Q8×C22⋊C4C22semidirect
192. #2337C22semidirect
193. #2337C22semidirect
195. #2333C22semidirect
196. #2332C22semidirect
198. C4×#126C22semidirect
201. #2276C22semidirect
202. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#520742
#517542
#512952
#512132
#511332
#510922
#504752
#500652
#500202
#492502
#491442
#486742
#486582
#360812
#359482
#359422
#357072
#357032
#356242
#355002
#354802