Finite Group Databasebeta

← #7710598

Subgroups — #7710598

Order 512.

4968 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59342C214yesmaximal, complemented
2#59341C214yesmaximal, complemented
3#46139C214yesmaximal, complemented
4#45980C214yesmaximal, complemented
5#39729C212yesmaximal, complemented
6#39345C212yesmaximal, complemented
7#37994C214yesmaximal, complemented
8#37993C214yesmaximal, complemented
9#37925C214yesmaximal, complemented
10#37924C214yesmaximal, complemented
11#37666C214yesmaximal, complemented
12#37562C211yesmaximal, characteristic, complemented
13#37556C211yesmaximal, characteristic, complemented
14#36731C212yesmaximal, complemented
15#36730C212yesmaximal, complemented
16#36624C211yesmaximal, characteristic, complemented
17#36621C211yesmaximal, characteristic, complemented
18#36530C212yesmaximal, complemented
19#36350C214yesmaximal, complemented
20#36339C212yesmaximal, complemented
21#35042C212yesmaximal, complemented
22#35004C212yesmaximal, complemented
23#34401C211yesmaximal, characteristic, complemented
24#34388C211yesmaximal, characteristic, complemented
25C2×#2283C211yesmaximal, characteristic, complemented
26C2×#539C2214yes—
27C2×#532C2211yescharacteristic
28C2×#529C2211yescharacteristic
29C2×#525C2212yes—
30C23×C42C2211yescharacteristic
31#2857C2212yes—
32#2856C2212yes—
33#2855C2211yescharacteristic
34#2854C2211yescharacteristic
35#2854C2212yes—
36#2854C2212yes—
37#2853C2212yes—
38#2852C2214yes—
39#2852C2214yes—
40#2851C2212yes—
41#2850C2212yes—
42#2850C2214yes—
43#2850C2214yes—
44#2849C2212yes—
45#2848C2211yescharacteristic
46#2847C2211yescharacteristic
47#2847C2212yes—
48#2847C2212yes—
49#2843C2214yescomplemented
50#2821C2212yescomplemented
51#2818C2212yescomplemented
52#2772C2214yescomplemented
53#2766C2214yescomplemented
54#2761C2214yescomplemented
55#2753C2214yescomplemented
56#2746C2214yes—
57#2745C2214yes—
58#2743C2214yes—
59#2743C2214yes—
60#2740C2214yes—
61#2740C2214yes—
62#2738C2214yes—
63#2737C2214yes—
64#2723C2214yescomplemented
65#2719C2214yescomplemented
66#2706C2214yescomplemented
67#2704C2214yes—
68#2703C2214yes—
69#2702C2214yes—
70#2701C2214yes—
71#2700C2214yes—
72#2699C2214yes—
73#2699C2214yes—
74#2698C2214yescomplemented
75#2692C2214yes—
76#2691C2214yes—
77#2690C2214yes—
78#2688C2214yes—
79#2688C2214yes—
80#2687C2214yes—
81#2686C2214yes—
82#2672C2214yes—
83#2671C2214yes—
84#2666C2214yescomplemented
85#2666C2214yescomplemented
86#2659C2212yes—
87#2656C2212yes—
88#2646C2212yes—
89#2639C2212yes—
90#2633C2212yescomplemented
91#2632C2212yescomplemented
92#2631C2212yescomplemented
93#2631C2212yescomplemented
94#2623C2214yes—
95#2618C2214yes—
96#2612C2214yescomplemented
97#2610C2214yescomplemented
98#2606C2212yescomplemented
99#2605C2214yescomplemented
100#2605C2212yescomplemented
101#2603C2214yescomplemented
102#2598C2214yescomplemented
103#2597C2214yescomplemented
104#2596C2214yescomplemented
105#2590C2214yescomplemented
106#2589C2214yescomplemented
107#2578C2214yes—
108#2576C2214yescomplemented
109#2574C2214yes—
110#2569C2212yes—
111#2559C2214yes—
112#2556C2214yescomplemented
113#2556C2214yescomplemented
114#2555C2214yes—
115#2554C2214yescomplemented
116#2554C2214yescomplemented
117#2553C2214yescomplemented
118#2549C2212yes—
119#2543C2212yes—
120#2543C2212yes—
121#2533C2214yescomplemented
122#2532C2214yescomplemented
123#2532C2214yescomplemented
124#2531C2214yes—
125#2531C2214yescomplemented
126#2531C2214yescomplemented
127#2530C2214yescomplemented
128#2529C2214yescomplemented
129#2527C2214yescomplemented
130#2527C2214yescomplemented
131#2526C2214yescomplemented
132#2526C2214yescomplemented
133#2522C2214yes—
134#2519C2214yescomplemented
135#2519C2214yescomplemented
136#2519C2214yescomplemented
137#2518C2214yes—
138#2518C2214yes—
139#2518C2214yescomplemented
140#2515C2214yescomplemented
141#2510C2214yes—
142#2489C2214yescomplemented
143#2488C2214yescomplemented
144#2479C2214yescomplemented
145#2478C2214yescomplemented
146#2476C2214yes—
147#2472C2214yes—
148#2468C2214yes—
149#2467C2214yes—
150#2467C2214yes—
151#2464C2214yes—
152#2461C2214yescomplemented
153#2461C2214yescomplemented
154#2460C2214yes—
155#2459C2214yes—
156#2457C2214yes—
157#2454C2214yes—
158#2450C2214yes—
159#2450C2214yes—
160#2444C2214yes—
161#2444C2214yes—
162#2438C2214yes—
163#2430C2214yes—
164#2427C2214yes—
165#2425C2214yes—
166#2424C2214yes—
167#2424C2214yes—
168#2418C2214yes—
169#2383C2214yescomplemented
170#2381C2212yescomplemented
171#2380C2212yescomplemented
172#2374C2214yes—
173#2373C2214yescomplemented
174#2372C2214yes—
175#2372C2214yescomplemented
176#2364C2212yes—
177#2364C2212yes—
178#2364C2214yes—
179#2363C2214yes—
180#2359C2214yes—
181#2353C2212yes—
182#2353C2214yescomplemented
183#2353C2214yescomplemented
184#2349C2212yes—
185#2347C2212yescomplemented
186#2343C2214yescomplemented
187#2343C2212yescomplemented
188#2339C2214yes—
189#2337C2212yescomplemented
190#2337C2214yescomplemented
191#2336C2212yescomplemented
192#2329C2212yes—
193#2325C2212yes—
194#2325C2212yes—
195#2325C2212yes—
196#2322C2214yes—
197#2320C2212yescomplemented
198#2318C2214yescomplemented
199#2318C2212yescomplemented
200C4×C22⋊Q8C2212yes—
201C4×#123C2212yes—
202C4×#121C2212yes—
203C4×#121C2214yes—
204C4×#121C2212yes—
205C4×#121C2212yes—
206C4×#121C2214yes—
207C4×#120C2212yes—
208#2297C2212yes—
209#2290C2214yes—
210#2290C2214yes—
211#2285C2211yescharacteristic
212#2283C2211yescharacteristic
213#2283C2214yes—
214#2283C2214yes—
215#2283C2214yes—
216#2283C2214yes—
217C2×#383C2211yescharacteristic
218C2×#383C2211yescharacteristic
219C2×#382C2211yescharacteristic
220C2×#382C2211yescharacteristic
221C2×#381C2212yes—
222C2×#380C2212yes—
223C2×C4×C4⋊C4C2212yes—
224C2×C4×C22⋊C4C2211yescharacteristic
225C2×C4×C22⋊C4C2211yescharacteristic
226C2×#376C2212yes—
227C22×#41C2312yes—
228C24×C4C2311yescharacteristic
229C24×C4C2311yescharacteristic
230C24×C4C2311yescharacteristic
231#539—416no—
232#532—28no—
233C2×C4⋊Q8C2311yescharacteristic
234C2×#127C2311yescharacteristic
235#529—28no—
236C2×#126C2312yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#125C2311yescharacteristic
241C2×#125C2314yes—
242C2×#125C2314yes—
243C2×#124C2311yescharacteristic
244C2×#124C2312yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247#525—48no—
248C2×#123C2314yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×#121C2312yes—
261C2×#121C2311yescharacteristic
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#120C2314yes—
273C2×#120C2312yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×#117C2312yes—
287C2×#117C2314yes—
288C2×#117C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C42—28no—
294C22×C42C2312yes—
295C22×C42C2312yes—
296C22×C42C2312yes—
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2312yes—
301C22×C42C2312yes—
302C22×C42C2312yes—
303C22×C42C2311yescharacteristic
304#401C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#398C2312yes—
322#398C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#397C2312yes—
337#397C2312yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2312yes—
364#394C2312yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#392C2314yes—
382#392C2314yes—
383#392C2312yes—
384#392C2312yes—
385#392C2314yes—
386#392C2314yes—
387#392C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2312yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#390C2312yes—
398#390C2314yes—
399#390C2314yes—
400#390C2312yes—
401#390C2314yes—
402#390C2312yes—
403#390C2314yes—
404#390C2314yes—
405#390C2314yes—
406#390C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2312yes—
412#389C2314yes—
413#389C2312yes—
414#389C2312yes—
415#389C2314yes—
416#389C2312yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
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#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
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#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
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#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2312yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2312yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2312yes—
535#385C2314yes—
536#385C2314yes—
537#385C2312yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#384C2312yes—
543#383C2312yes—
544#383C2312yes—
545#383C2312yes—
546#383C2312yes—
547#383C2314yes—
548#383C2312yes—
549#383C2312yes—
550#383C2312yes—
551#383C2314yes—
552#383C2312yes—
553#383C2312yes—
554#383C2312yes—
555#382C2312yes—
556#382C2312yes—
557#382C2314yes—
558#382C2312yes—
559#382C2314yes—
560#382C2314yes—
561#382C2314yes—
562#382C2314yes—
563#381C2312yes—
564#381C2314yes—
565#381C2312yes—
566#381C2312yes—
567#381C2314yes—
568#381C2314yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#381C2314yes—
573#380C2312yes—
574#380C2314yes—
575#380C2314yes—
576#380C2312yes—
577#380C2314yes—
578#380C2311yescharacteristic
579#380C2311yescharacteristic
580#380C2312yes—
581#380C2312yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#379C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2311yescharacteristic
599C4×C4⋊C4C2311yescharacteristic
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622#376C2312yes—
623#376C2314yes—
624#376C2314yes—
625#376C2312yes—
626#376C2314yes—
627#376C2314yes—
628#376C2314yes—
629C2×#95C2311yescharacteristic
630C2×#95C2314yes—
631C2×#95C2312yes—
632C2×#95C2312yes—
633C2×#95C2312yes—
634C2×#95C2311yescharacteristic
635C2×#95C2311yescharacteristic
636C2×#95C2312yes—
637C2×#95C2312yes—
638C2×#95C2312yes—
639C2×#95C2312yes—
640C2×#95C2311yescharacteristic
641C25C2411yescharacteristic
642C2×#41—28no—
643C2×#41—44no—
644C2×#41—44no—
645C22×Q8C2411yescharacteristic
646C22×Q8C2412yes—
647C22×Q8C2414yes—
648C22×D4C2412yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2411yescharacteristic
654C22×D4C2412yes—
655C22×D4C2412yes—
656C22×D4C2412yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C23×C4—24no—
660C23×C4—24no—
661C23×C4—24no—
662C23×C4—24no—
663C23×C4—44no—
664C23×C4—42no—
665C23×C4—44no—
666C23×C4C2411yescharacteristic
667C23×C4C2412yes—
668C23×C4C2412yes—
669C23×C4C2412yes—
670C23×C4C2412yes—
671C23×C4C2412yes—
672C23×C4C2412yes—
673C23×C4C2411yescharacteristic
674C23×C4C2411yescharacteristic
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2414yes—
681C23×C4C2411yescharacteristic
682C23×C4C2414yes—
683C23×C4C2414yes—
684C23×C4C2414yes—
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C4⋊Q8—24no—
688#127—24no—
689#126—28no—
690#126—48no—
691#126—48no—
692#126—48no—
693#125—24no—
694#125—48no—
695#125—48no—
696#124—24no—
697#124—28no—
698#124—48no—
699#124—48no—
700#123—28no—
701#123—216no—
702#123—28no—
703#123—48no—
704#123—48no—
705#123—48no—
706C22⋊Q8—24no—
707C22⋊Q8—44no—
708C22⋊Q8—48no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711C22⋊Q8—48no—
712#121—24no—
713#121—28no—
714#121—28no—
715#121—48no—
716#121—48no—
717#121—48no—
718#121—48no—
719#121—44no—
720#121—44no—
721#121—44no—
722#121—48no—
723#121—48no—
724#120—44no—
725#120—48no—
726C4×Q8—24no—
727C4×D4—28no—
728C4×D4—24no—
729C4×D4—28no—
730C4×D4—28no—
731C4×D4—48no—
732C4×D4—48no—
733C4×D4—48no—
734C4×D4—48no—
735C4×D4—48no—
736C4×D4—48no—
737C4×D4—48no—
738#117—28no—
739#117—48no—
740#117—44no—
741C2×C4⋊C4—28no—
742C2×C4⋊C4—44no—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C22⋊C4—44no—
783C2×C22⋊C4—44no—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C42—24no—
830C2×C42—24no—
831C2×C42—24no—
832C2×C42—28no—
833C2×C42—28no—
834C2×C42—28no—
835C2×C42—28no—
836C2×C42—44no—
837C2×C42—44no—
838C2×C42#4118yes—
839C2×C42C2412yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2414yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
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#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
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—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920C24—22no—
921C24—24no—
922C24—22no—
923C24—22no—
924C24—42no—
925C24C2512yes—
926C24C2514yes—
927C24C2512yes—
928C24C2511yescharacteristic
929#41—816no—
930C2×Q8—22no—
931C2×Q8—24no—
932C2×Q8—42no—
933C2×Q8—42no—
934C2×Q8—42no—
935C2×Q8—44no—
936C2×Q8—44no—
937C2×Q8—44no—
938C2×D4—24no—
939C2×D4—28no—
940C2×D4—24no—
941C2×D4—28no—
942C2×D4—28no—
943C2×D4—24no—
944C2×D4—28no—
945C2×D4—28no—
946C2×D4—28no—
947C2×D4—22no—
948C2×D4—24no—
949C2×D4—24no—
950C2×D4—24no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—42no—
957C2×D4—44no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—42no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—22no—
973C22×C4—22no—
974C22×C4—24no—
975C22×C4—22no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—28no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—416no—
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—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—416no—
1025C22×C4—416no—
1026C22×C4C2×#4114yes—
1027C22×C4C2×#4114yes—
1028C22×C4C2×#4114yes—
1029C22×C4H(5,𝔽2)14yes—
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2514yes—
1038C22×C4C2514yes—
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—22no—
1056C4⋊C4—24no—
1057C4⋊C4—22no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C22⋊C4—24no—
1091C22⋊C4—28no—
1092C22⋊C4—24no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—24no—
1098C22⋊C4—24no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—24no—
1102C22⋊C4—24no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
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—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—24no—
1142C42—28no—
1143C42—28no—
1144C42—44no—
1145C42—44no—
1146C42—44no—
1147C42—42no—
1148C42—42no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42C2×#4114yes—
1155C42C2×#4114yes—
1156C42C2×#4114yes—
1157C42C2×#4114yes—
1158C23—22no—
1159C23—22no—
1160C23—28no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—24no—
1169C23—22no—
1170C23—24no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—24no—
1177C23—24no—
1178C23—22no—
1179C23—48no—
1180C23—48no—
1181C23—44no—
1182C23—44no—
1183C23C22×#4112yes—
1184C23C2×H(5,𝔽2)12yes—
1185C23#58514yes—
1186C23#58512yes—
1187C23C2611yescharacteristic
1188Q8—82no—
1189Q8—84no—
1190Q8—164no—
1191D4—48no—
1192D4—416no—
1193D4—84no—
1194D4—84no—
1195D4—82no—
1196D4—84no—
1197D4—88no—
1198D4—88no—
1199D4—88no—
1200D4—88no—
1201D4—164no—
1202C2×C4—28no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—28no—
1216C2×C4—28no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—44no—
1255C2×C4—44no—
1256C2×C4—48no—
1257C2×C4—48no—
1258C2×C4—48no—
1259C2×C4—48no—
1260C2×C4—48no—
1261C2×C4—48no—
1262C2×C4—44no—
1263C2×C4—84no—
1264C2×C4—88no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—88no—
1270C2×C4—164no—
1271C2×C4—164no—
1272C2×C4C22×#4112yes—
1273C2×C4C22×#4112yes—
1274C2×C4C22×#4112yes—
1275C2×C4C22×#4112yes—
1276C2×C4C22×#4112yes—
1277C2×C4C22×#4112yes—
1278C2×C4C2×H(5,𝔽2)14yes—
1279C2×C4#58514yes—
1280C22—24no—
1281C22—22no—
1282C22—22no—
1283C22—24no—
1284C22—24no—
1285C22—24no—
1286C22—24no—
1287C22—416no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—42no—
1297C22—42no—
1298C22—44no—
1299C22—42no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22#349414yes—
1305C22C23×#4111yescharacteristic
1306C22C22×H(5,𝔽2)11yescharacteristic
1307C22C2×#58511yescharacteristic
1308C22C2×#58512yes—
1309C22C2×#58512yes—
1310C4—22no—
1311C4—22no—
1312C4—24no—
1313C4—24no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—22no—
1318C4—44no—
1319C4—44no—
1320C4—44no—
1321C4—44no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—44no—
1327C4—44no—
1328C4—44no—
1329C4—44no—
1330C4—44no—
1331C2—24no—
1332C2—44no—
1333C2—84no—
1334C2—82no—
1335C2#6275512yes—
1336C2C2×#349411yescharacteristic
1337C2#6281411yescharacteristic
1338C2#6281411yescharacteristic
1339C2#6283012yes—
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. #59342C2semidirect
2. #59341C2semidirect
3. #46139C2semidirect
4. #45980C2semidirect
5. #39729C2semidirect
6. #39345C2semidirect
7. #37994C2semidirect
8. #37993C2semidirect
9. #37925C2semidirect
10. #37924C2semidirect
11. #37666C2semidirect
12. #37562C2semidirect
13. #37556C2semidirect
14. #36731C2semidirect
15. #36730C2semidirect
16. #36624C2semidirect
17. #36621C2semidirect
18. #36530C2semidirect
19. #36350C2semidirect
20. #36339C2semidirect
21. #35042C2semidirect
22. #35004C2semidirect
23. #34401C2semidirect
24. #34388C2semidirect
25. C2×#2283C2semidirect
49. #2843C22semidirect
50. #2821C22semidirect
51. #2818C22semidirect
52. #2772C22semidirect
53. #2766C22semidirect
54. #2761C22semidirect
55. #2753C22semidirect
64. #2723C22semidirect
65. #2719C22semidirect
66. #2706C22semidirect
74. #2698C22semidirect
84. #2666C22semidirect
85. #2666C22semidirect
90. #2633C22semidirect
91. #2632C22semidirect
92. #2631C22semidirect
93. #2631C22semidirect
96. #2612C22semidirect
97. #2610C22semidirect
98. #2606C22semidirect
99. #2605C22semidirect
100. #2605C22semidirect
101. #2603C22semidirect
102. #2598C22semidirect
103. #2597C22semidirect
104. #2596C22semidirect
105. #2590C22semidirect
106. #2589C22semidirect
108. #2576C22semidirect
112. #2556C22semidirect
113. #2556C22semidirect
115. #2554C22semidirect
116. #2554C22semidirect
117. #2553C22semidirect
121. #2533C22semidirect
122. #2532C22semidirect
123. #2532C22semidirect
125. #2531C22semidirect
126. #2531C22semidirect
127. #2530C22semidirect
128. #2529C22semidirect
129. #2527C22semidirect
130. #2527C22semidirect
131. #2526C22semidirect
132. #2526C22semidirect
134. #2519C22semidirect
135. #2519C22semidirect
136. #2519C22semidirect
139. #2518C22semidirect
140. #2515C22semidirect
142. #2489C22semidirect
143. #2488C22semidirect
144. #2479C22semidirect
145. #2478C22semidirect
152. #2461C22semidirect
153. #2461C22semidirect
169. #2383C22semidirect
170. #2381C22semidirect
171. #2380C22semidirect
173. #2373C22semidirect
175. #2372C22semidirect
182. #2353C22semidirect
183. #2353C22semidirect
185. #2347C22semidirect
186. #2343C22semidirect
187. #2343C22semidirect
189. #2337C22semidirect
190. #2337C22semidirect
191. #2336C22semidirect
197. #2320C22semidirect
198. #2318C22semidirect
199. #2318C22semidirect

Maximal subgroups

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

subgroupindex
#593422
#593412
#461392
#459802
#397292
#393452
#379942
#379932
#379252
#379242
#376662
#375622
#375562
#367312
#367302
#366242
#366212
#365302
#363502
#363392
#350422
#350042
#344012
#343882
C2×#22832