Finite Group Databasebeta

← #7992771

Subgroups — #7992771

Order 512.

4434 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51551C214yesmaximal, complemented
2#51549C214yesmaximal, complemented
3#51480C214yesmaximal, complemented
4#51346C214yesmaximal, complemented
5#51093C212yesmaximal, complemented
6#51087C212yesmaximal, complemented
7#50718C212yesmaximal, complemented
8#50716C212yesmaximal, complemented
9#47033C212yesmaximal, complemented
10#47032C212yesmaximal, complemented
11#46455C212yesmaximal, complemented
12#46452C212yesmaximal, complemented
13#42061C214yesmaximal, complemented
14#42061C214yesmaximal, complemented
15#41767C214yesmaximal, complemented
16#41753C214yesmaximal, complemented
17#41619C214yesmaximal, complemented
18#41609C214yesmaximal, complemented
19#37619C211yesmaximal, characteristic, complemented
20#37566C211yesmaximal, characteristic, complemented
21#37537C211yesmaximal, characteristic, complemented
22#37536C211yesmaximal, characteristic
23#34403C211yesmaximal, characteristic, complemented
24#34369C211yesmaximal, characteristic, complemented
25#34366C211yesmaximal, characteristic, complemented
26C2×#533C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C22×#124C2211yescharacteristic
29#2841C2214yes—
30#2837C2214yescomplemented
31#2837C2214yescomplemented
32#2820C2212yes—
33#2820C2212yes—
34#2819C2214yes—
35#2816C2212yes—
36#2816C2212yes—
37#2799C2214yescomplemented
38#2798C2214yescomplemented
39#2798C2214yescomplemented
40#2786C2214yes—
41#2786C2214yescomplemented
42#2784C2214yescomplemented
43#2781C2214yescomplemented
44#2780C2214yescomplemented
45#2779C2214yescomplemented
46#2775C2214yescomplemented
47#2772C2214yescomplemented
48#2770C2214yescomplemented
49#2761C2214yes—
50#2756C2214yescomplemented
51#2755C2214yescomplemented
52#2754C2214yescomplemented
53#2754C2214yescomplemented
54#2753C2214yescomplemented
55#2751C2214yes—
56#2750C2214yes—
57#2750C2214yescomplemented
58#2749C2214yescomplemented
59#2743C2214yes—
60#2740C2214yes—
61#2730C2214yes—
62#2730C2214yescomplemented
63#2716C2214yescomplemented
64#2716C2214yescomplemented
65#2716C2214yescomplemented
66#2716C2214yescomplemented
67#2715C2214yescomplemented
68#2715C2214yescomplemented
69#2712C2214yes—
70#2712C2214yescomplemented
71#2710C2214yes—
72#2710C2214yescomplemented
73#2709C2214yes—
74#2709C2214yes—
75#2706C2214yescomplemented
76#2705C2214yes—
77#2705C2214yescomplemented
78#2700C2214yescomplemented
79#2698C2214yescomplemented
80#2697C2214yes—
81#2695C2214yescomplemented
82#2685C2214yes—
83#2685C2214yes—
84#2684C2214yes—
85#2667C2212yes—
86#2666C2214yescomplemented
87#2666C2214yescomplemented
88#2665C2212yes—
89#2663C2214yescomplemented
90#2663C2214yescomplemented
91#2658C2212yes—
92#2658C2212yescomplemented
93#2657C2211yescharacteristic
94#2657C2211yescharacteristic
95#2651C2214yescomplemented
96#2651C2214yescomplemented
97#2649C2214yescomplemented
98#2649C2214yescomplemented
99#2640C2211yescharacteristic
100#2640C2212yes—
101#2640C2211yescharacteristic
102#2640C2212yescomplemented
103#2633C2214yescomplemented
104#2632C2212yes—
105#2632C2212yes—
106#2631C2214yes—
107#2626C2214yes—
108#2624C2214yes—
109#2617C2214yes—
110#2612C2214yescomplemented
111#2610C2214yescomplemented
112#2609C2214yes—
113#2609C2214yescomplemented
114#2608C2212yes—
115#2607C2212yes—
116#2607C2214yescomplemented
117#2607C2214yescomplemented
118#2606C2212yescomplemented
119#2605C2212yescomplemented
120#2603C2214yescomplemented
121#2601C2214yes—
122#2601C2214yes—
123#2601C2214yescomplemented
124#2596C2214yescomplemented
125#2589C2214yescomplemented
126#2589C2214yescomplemented
127#2588C2214yescomplemented
128#2580C2212yescomplemented
129#2580C2212yescomplemented
130#2579C2214yescomplemented
131#2560C2214yes—
132#2557C2214yes—
133#2557C2214yescomplemented
134#2554C2214yescomplemented
135#2553C2214yescomplemented
136#2553C2214yescomplemented
137#2548C2212yescomplemented
138#2546C2212yescomplemented
139#2545C2212yes—
140#2545C2212yes—
141#2544C2212yes—
142#2544C2214yes—
143#2544C2212yes—
144#2534C2214yes—
145#2530C2214yescomplemented
146#2529C2214yescomplemented
147#2521C2214yescomplemented
148#2521C2214yescomplemented
149#2521C2214yescomplemented
150#2520C2214yescomplemented
151#2516C2214yescomplemented
152#2516C2214yescomplemented
153#2492C2214yescomplemented
154#2492C2214yescomplemented
155#2482C2214yes—
156#2481C2214yescomplemented
157#2479C2214yes—
158#2478C2214yescomplemented
159#2477C2214yes—
160#2474C2214yescomplemented
161#2474C2214yescomplemented
162#2472C2214yes—
163#2471C2214yes—
164#2471C2214yescomplemented
165#2470C2214yescomplemented
166#2467C2214yes—
167#2467C2214yescomplemented
168#2461C2214yescomplemented
169#2459C2214yes—
170#2459C2214yescomplemented
171#2449C2214yescomplemented
172#2445C2214yes—
173#2439C2214yescomplemented
174#2439C2214yescomplemented
175#2436C2212yes—
176#2435C2211yescharacteristic
177#2435C2211yescharacteristic
178#2434C2211yescharacteristic
179#2434C2211yescharacteristic
180#2433C2212yes—
181#2432C2212yes—
182#2432C2212yes—
183#2418C2214yes—
184#2413C2214yescomplemented
185#2411C2214yes—
186#2404C2214yes—
187#2395C2214yescomplemented
188#2395C2214yescomplemented
189#2381C2212yescomplemented
190#2380C2212yescomplemented
191#2379C2214yes—
192#2378C2214yes—
193#2372C2214yes—
194#2372C2214yescomplemented
195#2370C2214yescomplemented
196#2356C2212yescomplemented
197#2356C2212yescomplemented
198#2352C2214yescomplemented
199#2352C2214yescomplemented
200#2347C2212yes—
201#2346C2212yes—
202#2342C2212yes—
203#2342C2212yes—
204#2342C2212yes—
205#2342C2212yes—
206#2337C2212yes—
207#2337C2212yes—
208#2337C2212yes—
209#2337C2212yes—
210#2333C2212yes—
211#2333C2212yes—
212#2333C2212yes—
213#2333C2212yes—
214#2332C2212yes—
215#2332C2212yes—
216#2331C2212yescomplemented
217#2331C2212yescomplemented
218#2320C2212yescomplemented
219#2320C2212yescomplemented
220#2311C2214yes—
221#2310C2212yes—
222#2308C2212yes—
223#2283C2211yescharacteristic
224#2283C2211yescharacteristic
225#2283C2211yescharacteristic
226#2283C2211yescharacteristic
227C22×#41C2312yes—
228C23×Q8C2311yescharacteristic
229C23×D4C2311yescharacteristic
230#533—28no—
231#532—28no—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×#127C2311yescharacteristic
240C2×#127C2312yes—
241C2×#127C2312yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125C2312yes—
247C2×#124—28no—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#124C2311yescharacteristic
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#124C2312yes—
255C2×#124C2314yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2311yescharacteristic
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×#121C2312yes—
273C2×#121C2312yes—
274C2×#120C2314yes—
275C2×#120C2314yes—
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2312yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C2×#117C2314yes—
289C22×C4⋊C4C2314yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C42C2311yescharacteristic
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2312yes—
362#395C2312yes—
363#395C2312yes—
364#395C2312yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#394C2312yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2312yes—
380#394C2312yes—
381#394C2312yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#390C2312yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2314yes—
445#390C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
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#388C2314yes—
496#388C2314yes—
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#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
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#385C2314yes—
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#383C2312yes—
568#383C2312yes—
569#383C2312yes—
570#383C2312yes—
571#383C2312yes—
572#383C2312yes—
573#382C2312yes—
574#382C2312yes—
575#382C2312yes—
576#382C2312yes—
577#382C2312yes—
578#382C2312yes—
579#382C2314yes—
580#382C2314yes—
581#381C2312yes—
582#381C2312yes—
583#381C2312yes—
584#381C2312yes—
585#381C2312yes—
586#381C2314yes—
587#381C2314yes—
588#381C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2312yes—
595#380C2312yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#379C2312yes—
600#379C2312yes—
601#379C2314yes—
602#379C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2311yescharacteristic
618C4×C22⋊C4C2311yescharacteristic
619C4×C22⋊C4C2311yescharacteristic
620C4×C22⋊C4C2311yescharacteristic
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2311yescharacteristic
630C4×C22⋊C4C2311yescharacteristic
631C4×C22⋊C4C2314yes—
632#376C2312yes—
633#376C2312yes—
634#376C2312yes—
635#376C2311yescharacteristic
636#376C2311yescharacteristic
637#376C2312yes—
638#376C2312yes—
639C25C2412yes—
640C2×#41—28no—
641C2×#41—82no—
642C2×#41—82no—
643C22×Q8—24no—
644C22×Q8—82no—
645C22×Q8C2412yes—
646C22×Q8C2411yescharacteristic
647C22×Q8C2411yescharacteristic
648C22×Q8C2411yescharacteristic
649C22×Q8C2411yescharacteristic
650C22×Q8C2412yes—
651C22×Q8C2412yes—
652C22×Q8C2414yes—
653C22×D4—24no—
654C22×D4—82no—
655C22×D4C2412yes—
656C22×D4C2412yes—
657C22×D4C2414yes—
658C22×D4C2412yes—
659C22×D4C2412yes—
660C22×D4C2411yescharacteristic
661C22×D4C2411yescharacteristic
662C22×D4C2414yes—
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2414yes—
666C23×C4C2412yes—
667C23×C4C2414yes—
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2414yes—
672C23×C4C2411yescharacteristic
673C23×C4C2411yescharacteristic
674C23×C4C2411yescharacteristic
675C4⋊Q8—24no—
676C4⋊Q8—24no—
677C4⋊Q8—24no—
678C4⋊Q8—82no—
679C4⋊Q8—82no—
680C4⋊Q8—82no—
681C4⋊Q8—82no—
682#127—24no—
683#127—82no—
684#127—82no—
685#126—84no—
686#126—84no—
687#126—84no—
688#126—84no—
689#125—28no—
690#124—28no—
691#124—24no—
692#124—24no—
693#124—24no—
694#124—24no—
695#124—28no—
696#124—28no—
697#124—84no—
698#124—84no—
699#124—82no—
700#124—82no—
701#124—82no—
702#124—82no—
703#124—82no—
704#124—82no—
705#123—84no—
706#123—84no—
707#123—84no—
708#123—84no—
709C22⋊Q8—28no—
710C22⋊Q8—24no—
711C22⋊Q8—24no—
712C22⋊Q8—84no—
713C22⋊Q8—84no—
714#121—28no—
715#121—28no—
716#120—84no—
717#120—84no—
718C4×Q8—24no—
719C4×Q8—24no—
720C4×Q8—28no—
721C4×D4—28no—
722C4×D4—28no—
723C4×D4—84no—
724C4×D4—84no—
725#117—28no—
726#117—82no—
727#117—84no—
728#117—84no—
729#117—84no—
730#117—82no—
731C2×C4⋊C4—84no—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—28no—
774C2×C22⋊C4—82no—
775C2×C22⋊C4—82no—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C42#4118yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2411yescharacteristic
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853C2×C42C2411yescharacteristic
854#95C2412yes—
855#95C2412yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2412yes—
865#95C2412yes—
866#95C2414yes—
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
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#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909C24—24no—
910C24—42no—
911C24—42no—
912C24—44no—
913C24—44no—
914C24C2512yes—
915C24C2512yes—
916C24C2514yes—
917C24C2511yescharacteristic
918#41—816no—
919C2×Q8—22no—
920C2×Q8—22no—
921C2×Q8—24no—
922C2×Q8—24no—
923C2×Q8—22no—
924C2×Q8—22no—
925C2×Q8—24no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—42no—
932C2×Q8—42no—
933C2×Q8—42no—
934C2×Q8—42no—
935C2×Q8—42no—
936C2×Q8—44no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×Q8—88no—
940C2×D4—28no—
941C2×D4—24no—
942C2×D4—24no—
943C2×D4—24no—
944C2×D4—22no—
945C2×D4—22no—
946C2×D4—24no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—88no—
972C22×C4—24no—
973C22×C4—28no—
974C22×C4—44no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
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×C4C2×#4114yes—
994C22×C4C2×#4114yes—
995C22×C4C2×#4114yes—
996C22×C4C2514yes—
997C22×C4C2514yes—
998C22×C4C2514yes—
999C22×C4C2514yes—
1000C22×C4C2514yes—
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2514yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2511yescharacteristic
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—24no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C22⋊C4—24no—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—24no—
1061C22⋊C4—24no—
1062C22⋊C4—24no—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
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—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
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—
1112C42—24no—
1113C42—24no—
1114C42—42no—
1115C42—42no—
1116C42—44no—
1117C42—44no—
1118C42—44no—
1119C42—44no—
1120C42—44no—
1121C42—44no—
1122C42—44no—
1123C42—44no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42C2×#4114yes—
1131C42C2×#4114yes—
1132C42C2×#4114yes—
1133C42C2×#4114yes—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—24no—
1140C23—24no—
1141C23—24no—
1142C23—24no—
1143C23—24no—
1144C23—24no—
1145C23—22no—
1146C23—22no—
1147C23—24no—
1148C23—22no—
1149C23—22no—
1150C23—24no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—48no—
1155C23—84no—
1156C23—84no—
1157C23—164no—
1158C23—164no—
1159C23C22×#4112yes—
1160C23C2611yescharacteristic
1161Q8—84no—
1162Q8—82no—
1163Q8—82no—
1164Q8—82no—
1165Q8—82no—
1166Q8—84no—
1167Q8—84no—
1168Q8—164no—
1169D4—84no—
1170D4—84no—
1171D4—82no—
1172D4—82no—
1173D4—84no—
1174D4—84no—
1175D4—88no—
1176D4—88no—
1177D4—88no—
1178D4—164no—
1179D4—164no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—44no—
1230C2×C4—44no—
1231C2×C4—44no—
1232C2×C4—416no—
1233C2×C4—48no—
1234C2×C4—88no—
1235C2×C4—88no—
1236C2×C4—164no—
1237C2×C4—164no—
1238C2×C4C22×#4112yes—
1239C2×C4C22×#4112yes—
1240C2×C4C22×#4112yes—
1241C2×C4C22×#4112yes—
1242C2×C4C22×#4112yes—
1243C2×C4C22×#4112yes—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—44no—
1248C22—44no—
1249C22—42no—
1250C22—42no—
1251C22—44no—
1252C22—42no—
1253C22—42no—
1254C22—44no—
1255C22—42no—
1256C22—42no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—168no—
1266C22C23×#4111yescharacteristic
1267C22H(7,𝔽2)12yes—
1268C22H(7,𝔽2)12yes—
1269C222−1+612yes—
1270C4—22no—
1271C4—22no—
1272C4—22no—
1273C4—22no—
1274C4—22no—
1275C4—22no—
1276C4—44no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—44no—
1285C4—44no—
1286C4—44no—
1287C4—44no—
1288C4—44no—
1289C4—44no—
1290C4—44no—
1291C2—42no—
1292C2—84no—
1293C2—82no—
1294C2—82no—
1295C2#6285511yescharacteristic
1296C2#6285511yescharacteristic
1297C2#6286011yescharacteristic
1298C2#6297414yes—
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. #51551C2semidirect
2. #51549C2semidirect
3. #51480C2semidirect
4. #51346C2semidirect
5. #51093C2semidirect
6. #51087C2semidirect
7. #50718C2semidirect
8. #50716C2semidirect
9. #47033C2semidirect
10. #47032C2semidirect
11. #46455C2semidirect
12. #46452C2semidirect
13. #42061C2semidirect
14. #42061C2semidirect
15. #41767C2semidirect
16. #41753C2semidirect
17. #41619C2semidirect
18. #41609C2semidirect
19. #37619C2semidirect
20. #37566C2semidirect
21. #37537C2semidirect
23. #34403C2semidirect
24. #34369C2semidirect
25. #34366C2semidirect
30. #2837C22semidirect
31. #2837C22semidirect
37. #2799C22semidirect
38. #2798C22semidirect
39. #2798C22semidirect
41. #2786C22semidirect
42. #2784C22semidirect
43. #2781C22semidirect
44. #2780C22semidirect
45. #2779C22semidirect
46. #2775C22semidirect
47. #2772C22semidirect
48. #2770C22semidirect
50. #2756C22semidirect
51. #2755C22semidirect
52. #2754C22semidirect
53. #2754C22semidirect
54. #2753C22semidirect
57. #2750C22semidirect
58. #2749C22semidirect
62. #2730C22semidirect
63. #2716C22semidirect
64. #2716C22semidirect
65. #2716C22semidirect
66. #2716C22semidirect
67. #2715C22semidirect
68. #2715C22semidirect
70. #2712C22semidirect
72. #2710C22semidirect
75. #2706C22semidirect
77. #2705C22semidirect
78. #2700C22semidirect
79. #2698C22semidirect
81. #2695C22semidirect
86. #2666C22semidirect
87. #2666C22semidirect
89. #2663C22semidirect
90. #2663C22semidirect
92. #2658C22semidirect
95. #2651C22semidirect
96. #2651C22semidirect
97. #2649C22semidirect
98. #2649C22semidirect
102. #2640C22semidirect
103. #2633C22semidirect
110. #2612C22semidirect
111. #2610C22semidirect
113. #2609C22semidirect
116. #2607C22semidirect
117. #2607C22semidirect
118. #2606C22semidirect
119. #2605C22semidirect
120. #2603C22semidirect
123. #2601C22semidirect
124. #2596C22semidirect
125. #2589C22semidirect
126. #2589C22semidirect
127. #2588C22semidirect
128. #2580C22semidirect
129. #2580C22semidirect
130. #2579C22semidirect
133. #2557C22semidirect
134. #2554C22semidirect
135. #2553C22semidirect
136. #2553C22semidirect
137. #2548C22semidirect
138. #2546C22semidirect
145. #2530C22semidirect
146. #2529C22semidirect
147. #2521C22semidirect
148. #2521C22semidirect
149. #2521C22semidirect
150. #2520C22semidirect
151. #2516C22semidirect
152. #2516C22semidirect
153. #2492C22semidirect
154. #2492C22semidirect
156. #2481C22semidirect
158. #2478C22semidirect
160. #2474C22semidirect
161. #2474C22semidirect
164. #2471C22semidirect
165. #2470C22semidirect
167. #2467C22semidirect
168. #2461C22semidirect
170. #2459C22semidirect
171. #2449C22semidirect
173. #2439C22semidirect
174. #2439C22semidirect
184. #2413C22semidirect
187. #2395C22semidirect
188. #2395C22semidirect
189. #2381C22semidirect
190. #2380C22semidirect
194. #2372C22semidirect
195. #2370C22semidirect
196. #2356C22semidirect
197. #2356C22semidirect
198. #2352C22semidirect
199. #2352C22semidirect
216. #2331C22semidirect
217. #2331C22semidirect
218. #2320C22semidirect
219. #2320C22semidirect

Maximal subgroups

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

subgroupindex
#515512
#515492
#514802
#513462
#510932
#510872
#507182
#507162
#470332
#470322
#464552
#464522
#420612
#417672
#417532
#416192
#416092
#376192
#375662
#375372
#375362
#344032
#343692
#343662