Finite Group Databasebeta

← #7715626

Subgroups — #7715626

Order 512.

4766 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49772C214yesmaximal, complemented
2#49727C214yesmaximal, complemented
3#48266C214yesmaximal, complemented
4#48215C214yesmaximal, complemented
5#47671C214yesmaximal, complemented
6#47667C214yesmaximal, complemented
7#47191C214yesmaximal, complemented
8#47187C214yesmaximal, complemented
9#38215C212yesmaximal, complemented
10#38214C212yesmaximal, complemented
11#38205C212yesmaximal, complemented
12#38204C212yesmaximal, complemented
13#37892C212yesmaximal, complemented
14#37884C212yesmaximal, complemented
15#37711C212yesmaximal, complemented
16#37699C212yesmaximal, complemented
17#37522C211yesmaximal, characteristic, complemented
18#37520C211yesmaximal, characteristic, complemented
19#37380C211yesmaximal, characteristic, complemented
20#37283C211yesmaximal, characteristic, complemented
21#37268C212yesmaximal, complemented
22#35328C211yesmaximal, characteristic, complemented
23#35299C212yesmaximal, complemented
24#35280C211yesmaximal, characteristic, complemented
25#35260C212yesmaximal, complemented
26#34410C212yesmaximal, complemented
27#34065C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×#537C2212yes—
30C2×#533C2211yescharacteristic, complemented
31C2×#532C2211yescharacteristic, complemented
32C2×#525C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2863C2212yescomplemented
36#2860C2212yescomplemented
37#2857C2212yes—
38#2857C2212yescomplemented
39#2850C2212yes—
40#2850C2212yescomplemented
41#2848C2212yes—
42#2847C2212yes—
43#2839C2214yescomplemented
44#2837C2214yescomplemented
45#2803C2214yes—
46#2802C2214yescomplemented
47#2801C2214yescomplemented
48#2795C2214yes—
49#2793C2214yescomplemented
50#2790C2214yescomplemented
51#2787C2214yes—
52#2786C2214yes—
53#2778C2214yescomplemented
54#2773C2214yes—
55#2772C2214yes—
56#2768C2214yes—
57#2767C2214yescomplemented
58#2765C2214yes—
59#2762C2214yescomplemented
60#2756C2214yes—
61#2754C2214yes—
62#2750C2214yescomplemented
63#2749C2214yes—
64#2749C2214yes—
65#2747C2214yescomplemented
66#2741C2214yes—
67#2740C2214yes—
68#2740C2214yescomplemented
69#2738C2214yescomplemented
70#2735C2214yes—
71#2732C2214yes—
72#2730C2214yes—
73#2728C2214yes—
74#2728C2214yescomplemented
75#2723C2214yescomplemented
76#2722C2214yescomplemented
77#2718C2214yes—
78#2708C2214yes—
79#2708C2214yes—
80#2705C2214yes—
81#2703C2214yes—
82#2703C2214yes—
83#2701C2214yes—
84#2696C2214yes—
85#2691C2214yescomplemented
86#2688C2214yes—
87#2681C2214yescomplemented
88#2678C2214yes—
89#2678C2214yes—
90#2676C2214yes—
91#2671C2214yes—
92#2668C2214yes—
93#2652C2214yes—
94#2652C2214yes—
95#2647C2212yescomplemented
96#2640C2212yescomplemented
97#2636C2214yes—
98#2630C2214yes—
99#2629C2211yescharacteristic
100#2629C2211yescharacteristic
101#2629C2211yescharacteristic, complemented
102#2629C2211yescharacteristic, complemented
103#2628C2212yes—
104#2625C2212yes—
105#2625C2212yes—
106#2624C2212yes—
107#2624C2212yes—
108#2621C2211yescharacteristic
109#2621C2211yescharacteristic, complemented
110#2620C2212yes—
111#2619C2211yescharacteristic
112#2619C2211yescharacteristic, complemented
113#2609C2214yescomplemented
114#2606C2214yescomplemented
115#2596C2214yescomplemented
116#2591C2214yes—
117#2589C2214yescomplemented
118#2585C2214yescomplemented
119#2582C2214yescomplemented
120#2579C2214yescomplemented
121#2578C2214yes—
122#2560C2214yes—
123#2559C2214yes—
124#2554C2214yes—
125#2553C2214yescomplemented
126#2543C2214yes—
127#2543C2214yescomplemented
128#2538C2214yes—
129#2536C2214yescomplemented
130#2535C2214yes—
131#2532C2214yescomplemented
132#2531C2214yes—
133#2531C2214yes—
134#2531C2214yes—
135#2526C2214yescomplemented
136#2525C2214yes—
137#2522C2214yescomplemented
138#2512C2212yescomplemented
139#2511C2212yescomplemented
140#2509C2212yescomplemented
141#2508C2212yescomplemented
142#2505C2214yescomplemented
143#2498C2214yes—
144#2498C2214yes—
145#2495C2212yes—
146#2495C2214yescomplemented
147#2494C2212yes—
148#2493C2214yescomplemented
149#2490C2212yes—
150#2489C2212yes—
151#2488C2214yes—
152#2487C2212yes—
153#2486C2212yes—
154#2481C2214yes—
155#2481C2214yescomplemented
156#2479C2214yes—
157#2478C2214yescomplemented
158#2477C2214yes—
159#2477C2214yes—
160#2474C2214yes—
161#2472C2214yes—
162#2471C2214yes—
163#2470C2214yes—
164#2470C2214yescomplemented
165#2469C2214yescomplemented
166#2467C2214yescomplemented
167#2466C2214yescomplemented
168#2459C2214yes—
169#2458C2214yes—
170#2454C2212yescomplemented
171#2453C2212yescomplemented
172#2450C2214yescomplemented
173#2449C2214yes—
174#2448C2214yes—
175#2446C2212yescomplemented
176#2445C2212yescomplemented
177#2443C2214yes—
178#2438C2214yescomplemented
179#2429C2212yes—
180#2428C2212yes—
181#2425C2214yes—
182#2423C2212yes—
183#2422C2212yes—
184#2421C2214yescomplemented
185#2418C2214yes—
186#2417C2212yes—
187#2417C2214yes—
188#2417C2214yescomplemented
189#2416C2212yes—
190#2415C2212yes—
191#2414C2214yes—
192#2414C2212yes—
193#2407C2212yes—
194#2407C2212yes—
195#2377C2214yes—
196#2377C2214yes—
197#2364C2214yes—
198#2363C2214yes—
199#2363C2212yescomplemented
200#2362C2212yescomplemented
201#2361C2212yescomplemented
202#2360C2212yescomplemented
203#2345C2212yescomplemented
204#2344C2212yescomplemented
205#2341C2212yescomplemented
206#2339C2212yescomplemented
207#2333C2214yescomplemented
208#2332C2214yescomplemented
209#2331C2212yescomplemented
210#2329C2214yescomplemented
211#2326C2212yescomplemented
212#2324C2212yes—
213#2324C2212yes—
214#2324C2212yes—
215#2324C2212yes—
216#2324C2214yescomplemented
217#2323C2212yes—
218#2323C2212yes—
219#2323C2212yes—
220#2323C2212yes—
221#2322C2212yes—
222#2322C2212yes—
223#2321C2212yes—
224#2321C2212yes—
225#2316C2212yescomplemented
226#2314C2212yes—
227#2311C2212yes—
228#2311C2212yescomplemented
229C4×C22⋊Q8C2212yes—
230C4×#121C2212yes—
231#2297C2211yescharacteristic
232#2296C2211yescharacteristic
233#2295C2212yescomplemented
234#2293C2212yes—
235#2293C2212yes—
236#2293C2212yescomplemented
237#2290C2212yes—
238#2290C2212yes—
239C2×#384C2211yescharacteristic, complemented
240C2×#382C2211yescharacteristic, complemented
241#2280C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C22×#41C2312yes—
244C22×#41C2311yescharacteristic
245C24×C4C2311yescharacteristic
246#542—48no—
247#537—216no—
248#533—44no—
249#532—44no—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2311yescharacteristic
252C2×#127C2311yescharacteristic
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#124C2312yes—
259C2×#124C2314yes—
260#525—28no—
261C2×#123C2311yescharacteristic
262C2×#123C2311yescharacteristic
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#120C2311yescharacteristic
289C2×#120C2311yescharacteristic
290C2×#120C2314yes—
291C4×#41—44no—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×#117—44no—
307C2×#117C2312yes—
308C2×#117C2311yescharacteristic
309C2×#117C2312yes—
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2311yescharacteristic
317C2×#117C2314yes—
318C2×#117C2314yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2314yes—
323C22×C22⋊C4C2312yes—
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328#401C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#395C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#390C2314yes—
438#390C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2312yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2312yes—
493#388C2312yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2312yes—
568#386C2312yes—
569#386C2312yes—
570#386C2312yes—
571#386C2312yes—
572#386C2312yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#385C2312yes—
594#385C2312yes—
595#385C2312yes—
596#385C2312yes—
597#385C2312yes—
598#385C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#384C2312yes—
615#384C2314yes—
616#384C2311yescharacteristic
617#384C2311yescharacteristic
618#383C2314yes—
619#383C2314yes—
620#382C2312yes—
621#382C2314yes—
622#382C2311yescharacteristic
623#382C2311yescharacteristic
624#382C2314yes—
625#382C2314yes—
626#381C2312yes—
627#381C2314yes—
628#381C2314yes—
629#381C2314yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2314yes—
635#380C2314yes—
636#380C2312yes—
637#380C2312yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2312yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#379C2312yes—
651#379C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676#376C2312yes—
677#376C2314yes—
678C2×#95C2314yes—
679C2×#95C2314yes—
680C43C2312yes—
681C25C2411yescharacteristic
682C2×#41—28no—
683C2×#41—42no—
684C2×#41—42no—
685C2×#41—44no—
686C2×#41—44no—
687C2×#41#4118yes—
688C22×Q8C2412yes—
689C22×Q8C2414yes—
690C22×Q8C2411yescharacteristic
691C22×D4C2412yes—
692C22×D4C2414yes—
693C22×D4C2412yes—
694C22×D4C2412yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C22×D4C2411yescharacteristic
701C22×D4C2411yescharacteristic
702C22×D4C2411yescharacteristic
703C23×C4—24no—
704C23×C4—42no—
705C23×C4—42no—
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C23×C4C2411yescharacteristic
709C23×C4C2411yescharacteristic
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2411yescharacteristic
713C23×C4C2414yes—
714C23×C4C2412yes—
715C23×C4C2412yes—
716C23×C4C2414yes—
717C23×C4C2412yes—
718C23×C4C2414yes—
719C23×C4C2414yes—
720C23×C4C2414yes—
721C4⋊Q8—28no—
722C4⋊Q8—42no—
723#127—42no—
724#126—48no—
725#126—84no—
726#126—84no—
727#125—42no—
728#125—42no—
729#124—28no—
730#124—48no—
731#123—24no—
732#123—24no—
733#123—48no—
734#123—84no—
735#123—84no—
736#123—84no—
737C22⋊Q8—28no—
738C22⋊Q8—216no—
739C22⋊Q8—28no—
740C22⋊Q8—28no—
741C22⋊Q8—48no—
742C22⋊Q8—44no—
743C22⋊Q8—48no—
744C22⋊Q8—44no—
745C22⋊Q8—84no—
746C22⋊Q8—84no—
747#121—28no—
748#121—216no—
749#121—216no—
750#121—216no—
751#121—28no—
752#121—28no—
753#121—48no—
754#121—44no—
755#121—44no—
756#121—84no—
757#121—84no—
758#120—24no—
759#120—24no—
760#120—84no—
761C4×Q8—44no—
762C4×Q8—44no—
763C4×Q8—48no—
764C4×Q8—44no—
765C4×D4—28no—
766C4×D4—28no—
767C4×D4—48no—
768C4×D4—44no—
769C4×D4—44no—
770C4×D4—44no—
771C4×D4—44no—
772C4×D4—44no—
773C4×D4—84no—
774C4×D4—84no—
775#117—24no—
776#117—28no—
777#117—44no—
778#117—42no—
779#117—42no—
780#117—42no—
781#117—42no—
782#117—44no—
783#117—44no—
784#117—44no—
785#117—84no—
786#117—84no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—44no—
789C2×C4⋊C4—44no—
790C2×C4⋊C4—84no—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C22⋊C4—44no—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C42—24no—
898C2×C42—24no—
899C2×C42—24no—
900C2×C42—42no—
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2414yes—
913C2×C42C2411yescharacteristic
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2411yescharacteristic
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980C24—22no—
981C24—41no—
982C24—41no—
983C24—42no—
984C24—42no—
985C24C2512yes—
986C24C2514yes—
987C24C2511yescharacteristic
988C24C2511yescharacteristic
989C24C2511yescharacteristic
990#41—416no—
991#41—816no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—28no—
995C2×Q8—24no—
996C2×Q8—41no—
997C2×Q8—41no—
998C2×Q8—44no—
999C2×Q8—44no—
1000C2×Q8C2×#4114yes—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—28no—
1004C2×D4—28no—
1005C2×D4—28no—
1006C2×D4—24no—
1007C2×D4—24no—
1008C2×D4—24no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—41no—
1012C2×D4—41no—
1013C2×D4—41no—
1014C2×D4—41no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—42no—
1022C2×D4—42no—
1023C2×D4—44no—
1024C2×D4—42no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4C2×#4114yes—
1035C2×D4C2×#4114yes—
1036C2×D4C2×#4114yes—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—28no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—28no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—416no—
1080C22×C4C2×#4114yes—
1081C22×C4C2×#4114yes—
1082C22×C4C2×#4114yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—41no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C22⋊C4—22no—
1156C22⋊C4—22no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C42—24no—
1211C42—22no—
1212C42—24no—
1213C42—22no—
1214C42—22no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—41no—
1220C42—41no—
1221C42—42no—
1222C42—44no—
1223C42—42no—
1224C42—44no—
1225C42—42no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—42no—
1232C42H(5,𝔽2)14yes—
1233C23—21no—
1234C23—21no—
1235C23—21no—
1236C23—21no—
1237C23—21no—
1238C23—21no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—24no—
1247C23—22no—
1248C23—24no—
1249C23—22no—
1250C23—24no—
1251C23—24no—
1252C23—22no—
1253C23—22no—
1254C23—24no—
1255C23—22no—
1256C23—24no—
1257C23—24no—
1258C23—22no—
1259C23—44no—
1260C23—84no—
1261C23—84no—
1262C23—82no—
1263C23—82no—
1264C23C22×#4112yes—
1265C23C22×#4112yes—
1266C23C22×#4112yes—
1267C23C2611yescharacteristic
1268Q8—44no—
1269Q8—48no—
1270Q8—88no—
1271D4—44no—
1272D4—44no—
1273D4—44no—
1274D4—48no—
1275D4—88no—
1276D4—88no—
1277D4—84no—
1278D4—84no—
1279D4—88no—
1280D4—88no—
1281D4—164no—
1282D4—164no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—28no—
1292C2×C4—28no—
1293C2×C4—28no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—48no—
1346C2×C4—48no—
1347C2×C4—44no—
1348C2×C4—48no—
1349C2×C4—84no—
1350C2×C4—84no—
1351C2×C4—88no—
1352C2×C4—88no—
1353C2×C4—84no—
1354C2×C4—88no—
1355C2×C4—164no—
1356C2×C4—164no—
1357C2×C4C22×#4112yes—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C2×H(5,𝔽2)14yes—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4#58512yes—
1364C22—22no—
1365C22—22no—
1366C22—22no—
1367C22—24no—
1368C22—24no—
1369C22—24no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—41no—
1377C22—41no—
1378C22—41no—
1379C22—42no—
1380C22—44no—
1381C22—44no—
1382C22—42no—
1383C22—44no—
1384C22—42no—
1385C22—44no—
1386C22—44no—
1387C22—42no—
1388C22—42no—
1389C22—44no—
1390C22—42no—
1391C22—44no—
1392C22—42no—
1393C22—88no—
1394C22C23×#4111yescharacteristic
1395C22C22×H(5,𝔽2)11yescharacteristic
1396C22C2×#58511yescharacteristic
1397C22H(7,𝔽2)12yes—
1398C222−1+612yes—
1399C4—22no—
1400C4—22no—
1401C4—22no—
1402C4—24no—
1403C4—42no—
1404C4—44no—
1405C4—44no—
1406C4—44no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—44no—
1416C4—42no—
1417C4—44no—
1418C4—44no—
1419C4—42no—
1420C4#350514yes—
1421C2—42no—
1422C2—42no—
1423C2—42no—
1424C2—84no—
1425C2—82no—
1426C2C2×#350511yescharacteristic
1427C2#6285712yes—
1428C2#6287512yes—
1429C2#6288311yescharacteristic
1430C2#6289011yescharacteristic
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. #49772C2semidirect
2. #49727C2semidirect
3. #48266C2semidirect
4. #48215C2semidirect
5. #47671C2semidirect
6. #47667C2semidirect
7. #47191C2semidirect
8. #47187C2semidirect
9. #38215C2semidirect
10. #38214C2semidirect
11. #38205C2semidirect
12. #38204C2semidirect
13. #37892C2semidirect
14. #37884C2semidirect
15. #37711C2semidirect
16. #37699C2semidirect
17. #37522C2semidirect
18. #37520C2semidirect
19. #37380C2semidirect
20. #37283C2semidirect
21. #37268C2semidirect
22. #35328C2semidirect
23. #35299C2semidirect
24. #35280C2semidirect
25. #35260C2semidirect
26. #34410C2semidirect
27. #34065C2semidirect
30. C2×#533C22semidirect
31. C2×#532C22semidirect
35. #2863C22semidirect
36. #2860C22semidirect
38. #2857C22semidirect
40. #2850C22semidirect
43. #2839C22semidirect
44. #2837C22semidirect
46. #2802C22semidirect
47. #2801C22semidirect
49. #2793C22semidirect
50. #2790C22semidirect
53. #2778C22semidirect
57. #2767C22semidirect
59. #2762C22semidirect
62. #2750C22semidirect
65. #2747C22semidirect
68. #2740C22semidirect
69. #2738C22semidirect
74. #2728C22semidirect
75. #2723C22semidirect
76. #2722C22semidirect
85. #2691C22semidirect
87. #2681C22semidirect
95. #2647C22semidirect
96. #2640C22semidirect
101. #2629C22semidirect
102. #2629C22semidirect
109. #2621C22semidirect
112. #2619C22semidirect
113. #2609C22semidirect
114. #2606C22semidirect
115. #2596C22semidirect
117. #2589C22semidirect
118. #2585C22semidirect
119. #2582C22semidirect
120. #2579C22semidirect
125. #2553C22semidirect
127. #2543C22semidirect
129. #2536C22semidirect
131. #2532C22semidirect
135. #2526C22semidirect
137. #2522C22semidirect
138. #2512C22semidirect
139. #2511C22semidirect
140. #2509C22semidirect
141. #2508C22semidirect
142. #2505C22semidirect
146. #2495C22semidirect
148. #2493C22semidirect
155. #2481C22semidirect
157. #2478C22semidirect
164. #2470C22semidirect
165. #2469C22semidirect
166. #2467C22semidirect
167. #2466C22semidirect
170. #2454C22semidirect
171. #2453C22semidirect
172. #2450C22semidirect
175. #2446C22semidirect
176. #2445C22semidirect
178. #2438C22semidirect
184. #2421C22semidirect
188. #2417C22semidirect
199. #2363C22semidirect
200. #2362C22semidirect
201. #2361C22semidirect
202. #2360C22semidirect
203. #2345C22semidirect
204. #2344C22semidirect
205. #2341C22semidirect
206. #2339C22semidirect
207. #2333C22semidirect
208. #2332C22semidirect
209. #2331C22semidirect
210. #2329C22semidirect
211. #2326C22semidirect
216. #2324C22semidirect
225. #2316C22semidirect
228. #2311C22semidirect
233. #2295C22semidirect
236. #2293C22semidirect
239. C2×#384C22semidirect
240. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#497722
#497272
#482662
#482152
#476712
#476672
#471912
#471872
#382152
#382142
#382052
#382042
#378922
#378842
#377112
#376992
#375222
#375202
#373802
#372832
#372682
#353282
#352992
#352802
#352602
#344102
#340652