Finite Group Databasebeta

← #7643705

Subgroups — #7643705

Order 512.

4638 conjugacy classes of subgroups.

The subgroup lattice has 1237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41433C214yesmaximal, complemented
2#41432C214yesmaximal, complemented
3#40679C214yesmaximal, complemented
4#40678C214yesmaximal, complemented
5#40675C214yesmaximal, complemented
6#40674C214yesmaximal, complemented
7#40647C214yesmaximal, complemented
8#40646C214yesmaximal, complemented
9#37457C214yesmaximal, complemented
10#37456C214yesmaximal, complemented
11#36980C212yesmaximal, complemented
12#36977C211yesmaximal, characteristic, complemented
13#36976C211yesmaximal, characteristic, complemented
14#36730C212yesmaximal, complemented
15#36728C211yesmaximal, characteristic, complemented
16#36727C211yesmaximal, characteristic, complemented
17#35383C214yesmaximal, complemented
18#35382C214yesmaximal, complemented
19#35031C212yesmaximal, complemented
20#34578C211yesmaximal, characteristic, complemented
21#34575C211yesmaximal, characteristic, complemented
22#34218C212yesmaximal, complemented
23C2×#2318C211yesmaximal, characteristic, complemented
24C2×#525C2212yes—
25C22×C4×D4C2211yescharacteristic
26#2855C2212yes—
27#2854C2212yes—
28#2848C2212yes—
29#2847C2212yes—
30#2834C2214yescomplemented
31#2827C2214yes—
32#2827C2214yescomplemented
33#2827C2214yescomplemented
34#2826C2214yes—
35#2825C2214yes—
36#2824C2214yes—
37#2824C2214yescomplemented
38#2775C2214yescomplemented
39#2773C2214yescomplemented
40#2770C2214yescomplemented
41#2768C2214yescomplemented
42#2766C2214yescomplemented
43#2766C2214yescomplemented
44#2764C2214yescomplemented
45#2762C2214yescomplemented
46#2759C2214yescomplemented
47#2758C2214yescomplemented
48#2757C2214yescomplemented
49#2755C2214yescomplemented
50#2753C2214yescomplemented
51#2748C2214yescomplemented
52#2747C2214yescomplemented
53#2746C2214yescomplemented
54#2745C2214yescomplemented
55#2741C2214yescomplemented
56#2738C2214yescomplemented
57#2737C2214yescomplemented
58#2737C2214yescomplemented
59#2722C2214yescomplemented
60#2719C2214yescomplemented
61#2706C2214yescomplemented
62#2704C2214yescomplemented
63#2703C2214yescomplemented
64#2701C2214yescomplemented
65#2700C2214yescomplemented
66#2690C2214yescomplemented
67#2687C2214yescomplemented
68#2686C2214yescomplemented
69#2671C2214yescomplemented
70#2667C2214yescomplemented
71#2665C2214yescomplemented
72#2663C2214yescomplemented
73#2661C2214yescomplemented
74#2659C2211yescharacteristic
75#2659C2212yes—
76#2656C2211yescharacteristic
77#2653C2214yes—
78#2653C2214yescomplemented
79#2653C2214yescomplemented
80#2652C2214yescomplemented
81#2652C2214yescomplemented
82#2649C2214yes—
83#2648C2214yes—
84#2648C2214yes—
85#2646C2211yescharacteristic
86#2646C2211yescharacteristic
87#2639C2212yes—
88#2636C2214yes—
89#2635C2214yes—
90#2633C2214yescomplemented
91#2633C2214yescomplemented
92#2631C2214yes—
93#2630C2214yes—
94#2630C2214yescomplemented
95#2630C2214yescomplemented
96#2626C2214yes—
97#2622C2214yes—
98#2617C2214yes—
99#2613C2214yes—
100#2602C2214yes—
101#2602C2214yes—
102#2600C2214yes—
103#2600C2214yes—
104#2597C2214yescomplemented
105#2596C2214yescomplemented
106#2595C2214yescomplemented
107#2594C2214yescomplemented
108#2593C2214yescomplemented
109#2585C2214yescomplemented
110#2573C2214yescomplemented
111#2554C2214yescomplemented
112#2532C2214yescomplemented
113#2531C2214yescomplemented
114#2528C2214yescomplemented
115#2527C2214yescomplemented
116#2525C2214yescomplemented
117#2525C2214yescomplemented
118#2524C2214yescomplemented
119#2523C2214yescomplemented
120#2523C2214yescomplemented
121#2522C2214yescomplemented
122#2519C2214yescomplemented
123#2518C2214yes—
124#2518C2214yescomplemented
125#2516C2214yescomplemented
126#2510C2214yes—
127#2510C2214yes—
128#2510C2214yescomplemented
129#2505C2214yescomplemented
130#2494C2214yescomplemented
131#2493C2214yes—
132#2490C2214yescomplemented
133#2488C2214yes—
134#2485C2212yes—
135#2485C2212yes—
136#2480C2214yes—
137#2473C2214yes—
138#2473C2214yes—
139#2472C2214yes—
140#2467C2214yes—
141#2460C2214yescomplemented
142#2460C2214yescomplemented
143#2460C2214yescomplemented
144#2459C2214yes—
145#2459C2214yescomplemented
146#2458C2214yescomplemented
147#2458C2214yescomplemented
148#2456C2214yes—
149#2455C2214yescomplemented
150#2453C2214yescomplemented
151#2450C2214yes—
152#2450C2214yes—
153#2448C2214yescomplemented
154#2443C2214yes—
155#2443C2214yes—
156#2425C2214yes—
157#2425C2214yescomplemented
158#2424C2214yes—
159#2419C2214yes—
160#2419C2214yescomplemented
161#2418C2214yes—
162#2415C2212yes—
163#2415C2212yes—
164#2414C2212yes—
165#2414C2212yes—
166#2407C2212yes—
167#2407C2212yes—
168#2396C2214yescomplemented
169#2396C2214yescomplemented
170#2395C2214yescomplemented
171#2388C2214yescomplemented
172#2368C2214yescomplemented
173#2364C2214yescomplemented
174#2359C2214yescomplemented
175#2359C2214yescomplemented
176#2353C2214yescomplemented
177#2349C2214yescomplemented
178#2343C2214yescomplemented
179#2339C2214yescomplemented
180#2329C2212yes—
181#2329C2212yes—
182#2325C2212yes—
183#2325C2212yes—
184#2322C2214yes—
185#2321C2214yes—
186#2318C2214yes—
187#2318C2214yes—
188#2318C2214yes—
189#2318C2214yes—
190#2318C2214yes—
191C4×C22⋊Q8C2214yes—
192C4×#121C2214yes—
193C4×#120C2214yes—
194C4×#120C2214yes—
195C2×#388C2212yes—
196C2×#387C2212yes—
197C2×#386C2212yes—
198C2×#385C2212yes—
199C2×#383C2211yescharacteristic
200C2×#382C2211yescharacteristic
201#2280C2212yes—
202C2×#381C2211yescharacteristic
203C2×#380C2211yescharacteristic
204#2275C2214yes—
205C2×C4×C22⋊C4C2211yescharacteristic
206C22×#95C2211yescharacteristic
207C22×#41C2312yes—
208C23×D4C2311yescharacteristic
209C24×C4C2311yescharacteristic
210C24×C4C2312yes—
211C24×C4C2311yescharacteristic
212C2×#126C2314yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#124C2314yes—
216#525—216no—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2314yes—
233C2×#120C2314yes—
234C2×#120C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×D4—28no—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C22⋊C4C2311yescharacteristic
257C22×C22⋊C4C2311yescharacteristic
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C42C2311yescharacteristic
262C22×C42C2312yes—
263#401C2314yes—
264#401C2314yes—
265#401C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#399C2314yes—
282#399C2314yes—
283#399C2314yes—
284#399C2314yes—
285#399C2314yes—
286#399C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#394C2314yes—
339#394C2314yes—
340#394C2314yes—
341#394C2314yes—
342#394C2314yes—
343#394C2314yes—
344#394C2314yes—
345#394C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#393C2314yes—
361#393C2314yes—
362#393C2314yes—
363#393C2314yes—
364#393C2314yes—
365#393C2314yes—
366#393C2314yes—
367#392C2314yes—
368#392C2314yes—
369#392C2314yes—
370#392C2314yes—
371#392C2314yes—
372#392C2314yes—
373#392C2314yes—
374#392C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2312yes—
378#391C2312yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2314yes—
386#390C2312yes—
387#390C2312yes—
388#390C2314yes—
389#390C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
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#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
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#386C2314yes—
472#386C2314yes—
473#386C2314yes—
474#386C2314yes—
475#386C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
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#383C2314yes—
520#383C2314yes—
521#383C2314yes—
522#383C2314yes—
523#383C2314yes—
524#383C2314yes—
525#382C2314yes—
526#382C2314yes—
527#382C2314yes—
528#382C2314yes—
529#381C2314yes—
530#381C2314yes—
531#381C2314yes—
532#381C2314yes—
533#381C2314yes—
534#381C2314yes—
535#380C2314yes—
536#380C2314yes—
537#380C2314yes—
538#380C2312yes—
539#380C2312yes—
540#380C2312yes—
541#380C2312yes—
542#380C2312yes—
543#380C2312yes—
544#380C2312yes—
545#380C2312yes—
546#380C2314yes—
547#380C2314yes—
548#380C2314yes—
549#380C2314yes—
550#380C2314yes—
551#379C2314yes—
552#379C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
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⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575#376C2314yes—
576C2×#95C2314yes—
577C2×#95C2314yes—
578C2×#95C2312yes—
579C2×#95C2311yescharacteristic
580C2×#95C2311yescharacteristic
581C2×#95C2314yes—
582C2×#95C2311yescharacteristic
583C2×#95C2311yescharacteristic
584C2×#95C2312yes—
585C2×#95C2312yes—
586C2×#95C2312yes—
587C2×#95C2312yes—
588C25C2411yescharacteristic
589C25C2411yescharacteristic
590C2×#41—28no—
591C2×#41—82no—
592C2×#41—82no—
593C22×Q8C2412yes—
594C22×Q8C2414yes—
595C22×D4—24no—
596C22×D4—44no—
597C22×D4C2414yes—
598C22×D4C2414yes—
599C22×D4C2414yes—
600C22×D4C2412yes—
601C22×D4C2412yes—
602C22×D4C2412yes—
603C22×D4C2414yes—
604C22×D4C2414yes—
605C22×D4C2414yes—
606C23×C4—24no—
607C23×C4—44no—
608C23×C4—82no—
609C23×C4—82no—
610C23×C4—82no—
611C23×C4—82no—
612C23×C4#4118yes—
613C23×C4C2411yescharacteristic
614C23×C4C2412yes—
615C23×C4C2411yescharacteristic
616C23×C4C2412yes—
617C23×C4C2411yescharacteristic
618C23×C4C2412yes—
619C23×C4C2412yes—
620C23×C4C2414yes—
621C23×C4C2412yes—
622C23×C4C2412yes—
623C23×C4C2414yes—
624C23×C4C2414yes—
625C23×C4C2414yes—
626C23×C4C2414yes—
627C23×C4C2411yescharacteristic
628C23×C4C2412yes—
629C23×C4C2412yes—
630C23×C4C2411yescharacteristic
631#126—84no—
632#125—84no—
633#125—84no—
634#124—84no—
635#123—216no—
636#123—48no—
637#123—84no—
638#123—84no—
639#123—84no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—48no—
643C22⋊Q8—82no—
644C22⋊Q8—82no—
645#121—28no—
646#121—28no—
647#121—48no—
648#121—84no—
649#121—82no—
650#121—82no—
651#120—216no—
652#120—48no—
653C4×Q8—84no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—28no—
657C4×D4—28no—
658C4×D4—216no—
659C4×D4—216no—
660C4×D4—48no—
661C4×D4—48no—
662C4×D4—84no—
663C4×D4—84no—
664C4×D4—84no—
665C4×D4—84no—
666C4×D4—84no—
667#117—28no—
668#117—82no—
669#117—82no—
670C2×C4⋊C4—24no—
671C2×C4⋊C4—82no—
672C2×C4⋊C4—82no—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C22⋊C4—24no—
712C2×C22⋊C4—24no—
713C2×C22⋊C4—44no—
714C2×C22⋊C4—82no—
715C2×C22⋊C4—82no—
716C2×C22⋊C4C2412yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2411yescharacteristic
719C2×C22⋊C4C2411yescharacteristic
720C2×C22⋊C4C2411yescharacteristic
721C2×C22⋊C4C2411yescharacteristic
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×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C42—24no—
764C2×C42—82no—
765C2×C42C2414yes—
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
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—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832C24—24no—
833C24—22no—
834C24—24no—
835C24—42no—
836C24—41no—
837C24—41no—
838C24—41no—
839C24—42no—
840C24—41no—
841C24C2×#4114yes—
842C24C2511yescharacteristic
843C24C2511yescharacteristic
844C24C2514yes—
845C24C2512yes—
846C24C2511yescharacteristic
847#41—816no—
848C2×Q8—24no—
849C2×Q8—44no—
850C2×Q8—44no—
851C2×Q8—42no—
852C2×Q8—42no—
853C2×Q8—44no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—28no—
860C2×D4—28no—
861C2×D4—24no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—416no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—28no—
893C22×C4—42no—
894C22×C4—41no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—41no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—42no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—88no—
929C22×C4—88no—
930C22×C4—816no—
931C22×C4C2×#4114yes—
932C22×C4C2×#4114yes—
933C22×C4C2×#4118yes—
934C22×C4C2×#4118yes—
935C22×C4C2512yes—
936C22×C4C2514yes—
937C22×C4C2514yes—
938C22×C4C2514yes—
939C22×C4C2514yes—
940C22×C4C2514yes—
941C22×C4C2514yes—
942C22×C4C2514yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2514yes—
946C22×C4C2512yes—
947C22×C4C2514yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2511yescharacteristic
951C22×C4C2512yes—
952C22×C4C2511yescharacteristic
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—28no—
958C4⋊C4—28no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—28no—
994C22⋊C4—28no—
995C22⋊C4—28no—
996C22⋊C4—28no—
997C22⋊C4—28no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
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—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C42—24no—
1039C42—24no—
1040C42—28no—
1041C42—44no—
1042C42—44no—
1043C42—44no—
1044C42—44no—
1045C42—44no—
1046C42—44no—
1047C42—44no—
1048C42—44no—
1049C42—44no—
1050C42—44no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—28no—
1061C23—21no—
1062C23—21no—
1063C23—24no—
1064C23—24no—
1065C23—24no—
1066C23—22no—
1067C23—22no—
1068C23—21no—
1069C23—22no—
1070C23—22no—
1071C23—21no—
1072C23—24no—
1073C23—24no—
1074C23—24no—
1075C23—21no—
1076C23—24no—
1077C23—21no—
1078C23—44no—
1079C23—44no—
1080C23—48no—
1081C23—48no—
1082C23—44no—
1083C23—44no—
1084C23—44no—
1085C23—84no—
1086C23—84no—
1087C23C22×#4114yes—
1088C23C22×#4112yes—
1089C23#58514yes—
1090C23C2611yescharacteristic
1091Q8—84no—
1092Q8—88no—
1093D4—416no—
1094D4—48no—
1095D4—48no—
1096D4—416no—
1097D4—416no—
1098D4—84no—
1099D4—88no—
1100D4—164no—
1101D4—164no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—21no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—48no—
1154C2×C4—48no—
1155C2×C4—44no—
1156C2×C4—44no—
1157C2×C4—44no—
1158C2×C4—84no—
1159C2×C4—84no—
1160C2×C4—88no—
1161C2×C4—84no—
1162C2×C4—84no—
1163C2×C4—84no—
1164C2×C4—84no—
1165C2×C4—88no—
1166C2×C4—88no—
1167C2×C4—164no—
1168C2×C4—164no—
1169C2×C4C22×#4112yes—
1170C2×C4C22×#4114yes—
1171C2×C4C22×#4112yes—
1172C22—22no—
1173C22—22no—
1174C22—24no—
1175C22—24no—
1176C22—24no—
1177C22—24no—
1178C22—24no—
1179C22—416no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—41no—
1185C22—41no—
1186C22—44no—
1187C22—44no—
1188C22—41no—
1189C22—41no—
1190C22—44no—
1191C22—44no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—44no—
1196C22—44no—
1197C22—42no—
1198C22—41no—
1199C22—41no—
1200C22—44no—
1201C22—88no—
1202C22#345514yes—
1203C22C23×#4111yescharacteristic
1204C22C2×#58512yes—
1205C22H(7,𝔽2)12yes—
1206C22H(7,𝔽2)11yescharacteristic
1207C222−1+611yescharacteristic
1208C4—22no—
1209C4—24no—
1210C4—22no—
1211C4—42no—
1212C4—44no—
1213C4—41no—
1214C4—41no—
1215C4—44no—
1216C4—44no—
1217C4—44no—
1218C4—44no—
1219C4—44no—
1220C4—44no—
1221C4—44no—
1222C4—44no—
1223C4—44no—
1224C4—42no—
1225C4—44no—
1226C2—24no—
1227C2—44no—
1228C2—84no—
1229C2—81no—
1230C2—81no—
1231C2C2×#345511yescharacteristic
1232C2#6284411yescharacteristic
1233C2#6284511yescharacteristic
1234C2#6286712yes—
1235C2#6286812yes—
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. #41433C2semidirect
2. #41432C2semidirect
3. #40679C2semidirect
4. #40678C2semidirect
5. #40675C2semidirect
6. #40674C2semidirect
7. #40647C2semidirect
8. #40646C2semidirect
9. #37457C2semidirect
10. #37456C2semidirect
11. #36980C2semidirect
12. #36977C2semidirect
13. #36976C2semidirect
14. #36730C2semidirect
15. #36728C2semidirect
16. #36727C2semidirect
17. #35383C2semidirect
18. #35382C2semidirect
19. #35031C2semidirect
20. #34578C2semidirect
21. #34575C2semidirect
22. #34218C2semidirect
23. C2×#2318C2semidirect
30. #2834C22semidirect
32. #2827C22semidirect
33. #2827C22semidirect
37. #2824C22semidirect
38. #2775C22semidirect
39. #2773C22semidirect
40. #2770C22semidirect
41. #2768C22semidirect
42. #2766C22semidirect
43. #2766C22semidirect
44. #2764C22semidirect
45. #2762C22semidirect
46. #2759C22semidirect
47. #2758C22semidirect
48. #2757C22semidirect
49. #2755C22semidirect
50. #2753C22semidirect
51. #2748C22semidirect
52. #2747C22semidirect
53. #2746C22semidirect
54. #2745C22semidirect
55. #2741C22semidirect
56. #2738C22semidirect
57. #2737C22semidirect
58. #2737C22semidirect
59. #2722C22semidirect
60. #2719C22semidirect
61. #2706C22semidirect
62. #2704C22semidirect
63. #2703C22semidirect
64. #2701C22semidirect
65. #2700C22semidirect
66. #2690C22semidirect
67. #2687C22semidirect
68. #2686C22semidirect
69. #2671C22semidirect
70. #2667C22semidirect
71. #2665C22semidirect
72. #2663C22semidirect
73. #2661C22semidirect
78. #2653C22semidirect
79. #2653C22semidirect
80. #2652C22semidirect
81. #2652C22semidirect
90. #2633C22semidirect
91. #2633C22semidirect
94. #2630C22semidirect
95. #2630C22semidirect
104. #2597C22semidirect
105. #2596C22semidirect
106. #2595C22semidirect
107. #2594C22semidirect
108. #2593C22semidirect
109. #2585C22semidirect
110. #2573C22semidirect
111. #2554C22semidirect
112. #2532C22semidirect
113. #2531C22semidirect
114. #2528C22semidirect
115. #2527C22semidirect
116. #2525C22semidirect
117. #2525C22semidirect
118. #2524C22semidirect
119. #2523C22semidirect
120. #2523C22semidirect
121. #2522C22semidirect
122. #2519C22semidirect
124. #2518C22semidirect
125. #2516C22semidirect
128. #2510C22semidirect
129. #2505C22semidirect
130. #2494C22semidirect
132. #2490C22semidirect
141. #2460C22semidirect
142. #2460C22semidirect
143. #2460C22semidirect
145. #2459C22semidirect
146. #2458C22semidirect
147. #2458C22semidirect
149. #2455C22semidirect
150. #2453C22semidirect
153. #2448C22semidirect
157. #2425C22semidirect
160. #2419C22semidirect
168. #2396C22semidirect
169. #2396C22semidirect
170. #2395C22semidirect
171. #2388C22semidirect
172. #2368C22semidirect
173. #2364C22semidirect
174. #2359C22semidirect
175. #2359C22semidirect
176. #2353C22semidirect
177. #2349C22semidirect
178. #2343C22semidirect
179. #2339C22semidirect

Maximal subgroups

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

subgroupindex
#414332
#414322
#406792
#406782
#406752
#406742
#406472
#406462
#374572
#374562
#369802
#369772
#369762
#367302
#367282
#367272
#353832
#353822
#350312
#345782
#345752
#342182
C2×#23182