Finite Group Databasebeta

← #8757628

Subgroups — #8757628

Order 512.

4766 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58294C214yesmaximal, complemented
2#57519C214yesmaximal, complemented
3#57173C214yesmaximal, complemented
4#56370C214yesmaximal, complemented
5#54510C214yesmaximal, complemented
6#54265C214yesmaximal, complemented
7#52071C212yesmaximal, complemented
8#51903C212yesmaximal, complemented
9#51777C214yesmaximal, complemented
10#51733C214yesmaximal, complemented
11#47572C214yesmaximal, complemented
12#47567C212yesmaximal, complemented
13#47362C214yesmaximal, complemented
14#46458C212yesmaximal, complemented
15#46235C211yesmaximal, characteristic, complemented
16#46232C212yesmaximal, complemented
17#46232C211yesmaximal, characteristic, complemented
18#46230C212yesmaximal, complemented
19#45976C212yesmaximal, complemented
20#45974C212yesmaximal, complemented
21#45972C212yesmaximal, complemented
22#35327C211yesmaximal, characteristic, complemented
23#35189C212yesmaximal, complemented
24C2×#562C2212yes—
25C2×#562C2212yes—
26C2×#554C2212yescomplemented
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#529C2212yescomplemented
30C22×#124C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2851C2212yes—
33#2851C2212yescomplemented
34#2850C2212yes—
35#2850C2212yes—
36#2850C2212yes—
37#2850C2212yescomplemented
38#2844C2211yescharacteristic, complemented
39#2844C2211yescharacteristic, complemented
40#2841C2212yes—
41#2837C2214yescomplemented
42#2829C2214yescomplemented
43#2828C2214yescomplemented
44#2828C2214yescomplemented
45#2826C2214yescomplemented
46#2822C2211yescharacteristic, complemented
47#2820C2212yes—
48#2819C2212yes—
49#2819C2211yescharacteristic, complemented
50#2814C2214yescomplemented
51#2812C2212yes—
52#2803C2214yescomplemented
53#2800C2214yescomplemented
54#2797C2214yescomplemented
55#2795C2214yescomplemented
56#2795C2212yescomplemented
57#2794C2212yescomplemented
58#2793C2214yescomplemented
59#2792C2212yescomplemented
60#2786C2214yescomplemented
61#2781C2214yescomplemented
62#2777C2214yescomplemented
63#2764C2212yes—
64#2761C2214yes—
65#2761C2214yescomplemented
66#2757C2214yes—
67#2756C2214yes—
68#2752C2212yes—
69#2749C2214yescomplemented
70#2747C2214yes—
71#2742C2214yes—
72#2741C2214yescomplemented
73#2735C2212yes—
74#2732C2214yescomplemented
75#2730C2214yes—
76#2730C2214yes—
77#2730C2214yescomplemented
78#2730C2214yescomplemented
79#2729C2214yescomplemented
80#2720C2214yescomplemented
81#2717C2214yescomplemented
82#2714C2214yes—
83#2710C2214yes—
84#2709C2214yescomplemented
85#2707C2214yescomplemented
86#2707C2214yescomplemented
87#2706C2214yescomplemented
88#2704C2214yescomplemented
89#2703C2214yes—
90#2703C2214yes—
91#2703C2214yescomplemented
92#2702C2214yescomplemented
93#2700C2214yes—
94#2700C2214yescomplemented
95#2698C2214yescomplemented
96#2697C2214yes—
97#2696C2214yes—
98#2696C2214yescomplemented
99#2694C2214yes—
100#2693C2214yescomplemented
101#2692C2214yes—
102#2692C2214yescomplemented
103#2692C2214yescomplemented
104#2691C2214yes—
105#2690C2214yescomplemented
106#2688C2214yescomplemented
107#2686C2214yes—
108#2686C2214yescomplemented
109#2683C2214yescomplemented
110#2681C2214yescomplemented
111#2680C2214yescomplemented
112#2680C2212yescomplemented
113#2678C2214yes—
114#2676C2214yes—
115#2673C2214yes—
116#2673C2214yescomplemented
117#2673C2214yescomplemented
118#2672C2214yes—
119#2672C2214yes—
120#2672C2214yescomplemented
121#2672C2214yescomplemented
122#2670C2212yes—
123#2669C2214yes—
124#2667C2214yescomplemented
125#2657C2212yes—
126#2652C2214yescomplemented
127#2641C2212yes—
128#2632C2212yescomplemented
129#2631C2212yescomplemented
130#2630C2214yes—
131#2630C2214yescomplemented
132#2630C2214yescomplemented
133#2620C2212yes—
134#2620C2212yes—
135#2618C2214yescomplemented
136#2612C2214yescomplemented
137#2611C2212yes—
138#2610C2212yes—
139#2610C2214yescomplemented
140#2601C2214yes—
141#2601C2214yescomplemented
142#2600C2212yes—
143#2599C2212yes—
144#2598C2212yes—
145#2598C2214yescomplemented
146#2597C2214yes—
147#2596C2214yescomplemented
148#2587C2214yescomplemented
149#2586C2214yescomplemented
150#2582C2212yescomplemented
151#2556C2214yescomplemented
152#2545C2214yes—
153#2544C2214yes—
154#2539C2214yes—
155#2538C2212yes—
156#2538C2212yescomplemented
157#2537C2212yes—
158#2534C2214yes—
159#2534C2214yes—
160#2533C2214yescomplemented
161#2532C2214yescomplemented
162#2532C2214yescomplemented
163#2532C2214yescomplemented
164#2532C2214yescomplemented
165#2531C2214yescomplemented
166#2526C2214yescomplemented
167#2485C2214yescomplemented
168#2477C2214yescomplemented
169#2474C2214yescomplemented
170#2472C2214yes—
171#2470C2214yescomplemented
172#2470C2214yescomplemented
173#2464C2214yes—
174#2463C2214yescomplemented
175#2462C2214yescomplemented
176#2461C2214yes—
177#2461C2214yescomplemented
178#2461C2214yescomplemented
179#2458C2214yescomplemented
180#2457C2214yescomplemented
181#2456C2214yes—
182#2456C2214yes—
183#2456C2214yescomplemented
184#2449C2214yescomplemented
185#2445C2214yescomplemented
186#2443C2214yes—
187#2443C2214yescomplemented
188#2437C2214yes—
189#2437C2212yes—
190#2428C2214yes—
191#2426C2214yes—
192#2424C2214yes—
193#2421C2214yescomplemented
194#2418C2214yes—
195#2417C2214yescomplemented
196#2415C2212yes—
197#2415C2212yescomplemented
198#2414C2212yes—
199#2414C2212yescomplemented
200#2414C2214yescomplemented
201#2413C2214yescomplemented
202#2412C2214yes—
203#2410C2214yes—
204#2409C2214yes—
205#2407C2214yes—
206#2382C2212yescomplemented
207#2381C2212yescomplemented
208#2379C2212yes—
209#2379C2212yescomplemented
210#2372C2212yes—
211#2324C2214yes—
212#2323C2214yescomplemented
213#2321C2214yes—
214#2319C2214yes—
215#2310C2211yescharacteristic
216#2309C2211yescharacteristic
217#2285C2211yescharacteristic
218#2285C2212yescomplemented
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2311yescharacteristic
222#562—48no—
223#562—48no—
224#554—48no—
225#536—44no—
226#535—44no—
227C2×C4⋊Q8C2312yes—
228C2×#127C2312yes—
229C2×#127C2314yes—
230#529—48no—
231C2×#126C2314yes—
232C2×#125C2312yes—
233C2×#125C2312yes—
234C2×#125C2314yes—
235C2×#124—44no—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#124C2312yes—
242C2×#124C2314yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281C4×#41—44no—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2314yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C2×#117C2312yes—
301C22×C4⋊C4C2314yes—
302C22×C22⋊C4C2314yes—
303C22×C22⋊C4C2314yes—
304C22×C42C2312yes—
305C22×C42C2311yescharacteristic
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2312yes—
315#400C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2312yes—
321#399C2314yes—
322#399C2312yes—
323#398C2312yes—
324#398C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2312yes—
349#397C2312yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2312yes—
375#395C2312yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2312yes—
383#394C2312yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
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#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2312yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2312yes—
430#392C2312yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#390C2312yes—
445#390C2312yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2312yes—
455#390C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
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#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
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#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
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#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#384C2312yes—
581#384C2311yescharacteristic
582#384C2311yescharacteristic
583#384C2312yes—
584#383C2312yes—
585#383C2314yes—
586#383C2312yes—
587#382C2312yes—
588#382C2311yescharacteristic
589#382C2312yes—
590#382C2311yescharacteristic
591#382C2314yes—
592#381C2312yes—
593#381C2312yes—
594#381C2314yes—
595#381C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#379C2312yes—
610#379C2312yes—
611#379C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619#376C2314yes—
620#376C2312yes—
621#376C2312yes—
622C25C2412yes—
623C2×#41—24no—
624C2×#41—42no—
625C2×#41—42no—
626C22×Q8—42no—
627C22×Q8—42no—
628C22×Q8—42no—
629C22×Q8C2412yes—
630C22×Q8C2412yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2412yes—
634C22×Q8C2411yescharacteristic
635C22×D4—42no—
636C22×D4—42no—
637C22×D4—42no—
638C22×D4C2412yes—
639C22×D4C2411yescharacteristic
640C22×D4C2414yes—
641C22×D4C2412yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2412yes—
653C22×D4C2414yes—
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2414yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2414yes—
665C4⋊Q8—28no—
666#127—44no—
667#127—84no—
668#126—48no—
669#125—28no—
670#125—44no—
671#125—48no—
672#124—28no—
673#124—28no—
674#124—28no—
675#124—48no—
676#124—44no—
677#124—44no—
678#124—44no—
679#124—84no—
680#124—84no—
681#123—48no—
682#123—48no—
683#123—48no—
684#123—48no—
685#123—48no—
686#123—48no—
687#123—84no—
688#123—84no—
689#123—84no—
690C22⋊Q8—216no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—44no—
697C22⋊Q8—44no—
698C22⋊Q8—44no—
699C22⋊Q8—82no—
700C22⋊Q8—84no—
701C22⋊Q8—82no—
702C22⋊Q8—84no—
703#121—44no—
704#121—44no—
705#121—48no—
706#121—48no—
707#121—48no—
708#121—48no—
709#121—48no—
710#121—44no—
711#121—84no—
712#121—82no—
713#121—82no—
714#120—48no—
715#120—48no—
716#120—84no—
717C4×Q8—44no—
718C4×Q8—44no—
719C4×Q8—44no—
720C4×D4—44no—
721C4×D4—44no—
722C4×D4—44no—
723C4×D4—44no—
724C4×D4—44no—
725C4×D4—48no—
726C4×D4—48no—
727C4×D4—48no—
728C4×D4—84no—
729#117—44no—
730#117—42no—
731#117—42no—
732#117—42no—
733#117—48no—
734#117—82no—
735#117—82no—
736C2×C4⋊C4—48no—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
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×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C22⋊C4—48no—
783C2×C22⋊C4—84no—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C42—24no—
840C2×C42—28no—
841C2×C42C2412yes—
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2411yescharacteristic
856#95C2412yes—
857#95C2412yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2412yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
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#95C2412yes—
893#95C2414yes—
894#95C2412yes—
895#95C2414yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902C24—24no—
903C24—42no—
904C24—44no—
905C24—44no—
906C24—42no—
907C24C2514yes—
908C24C2514yes—
909C24C2512yes—
910C24C2511yescharacteristic
911#41—416no—
912C2×Q8—24no—
913C2×Q8—24no—
914C2×Q8—24no—
915C2×Q8—41no—
916C2×Q8—41no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—44no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—42no—
924C2×Q8—42no—
925C2×Q8—42no—
926C2×Q8—44no—
927C2×Q8—88no—
928C2×Q8H(5,𝔽2)14yes—
929C2×D4—24no—
930C2×D4—28no—
931C2×D4—24no—
932C2×D4—22no—
933C2×D4—24no—
934C2×D4—24no—
935C2×D4—24no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—41no—
939C2×D4—44no—
940C2×D4—41no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—44no—
948C2×D4—42no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—88no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—28no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4C2512yes—
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2512yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—41no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
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—42no—
1094C22⋊C4—42no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—42no—
1098C22⋊C4—44no—
1099C22⋊C4—42no—
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—
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—
1128C42—24no—
1129C42—22no—
1130C42—24no—
1131C42—24no—
1132C42—24no—
1133C42—24no—
1134C42—24no—
1135C42—44no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—44no—
1140C42—44no—
1141C42—44no—
1142C42H(5,𝔽2)14yes—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—22no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—24no—
1151C23—22no—
1152C23—22no—
1153C23—22no—
1154C23—24no—
1155C23—24no—
1156C23—22no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—24no—
1161C23—22no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—22no—
1167C23—22no—
1168C23—84no—
1169C23—88no—
1170C23—88no—
1171C23—162no—
1172C23—162no—
1173C23#58512yes—
1174C23C2611yescharacteristic
1175Q8—44no—
1176Q8—84no—
1177Q8—84no—
1178Q8—84no—
1179Q8—84no—
1180Q8—162no—
1181D4—48no—
1182D4—44no—
1183D4—48no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—88no—
1188D4—88no—
1189D4—88no—
1190D4—164no—
1191D4—164no—
1192D4—164no—
1193D4—162no—
1194D4—164no—
1195D4—164no—
1196D4—164no—
1197C2×C4—28no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—22no—
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—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—48no—
1248C2×C4—48no—
1249C2×C4—88no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—88no—
1254C2×C4—164no—
1255C2×C4—164no—
1256C2×C4—164no—
1257C2×C4C2×H(5,𝔽2)12yes—
1258C2×C4C2×H(5,𝔽2)14yes—
1259C2×C4C2×H(5,𝔽2)12yes—
1260C2×C4C2×H(5,𝔽2)14yes—
1261C22—24no—
1262C22—22no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—44no—
1267C22—42no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—42no—
1273C22—42no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—42no—
1278C22—42no—
1279C22—44no—
1280C22—44no—
1281C22—42no—
1282C22—42no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—168no—
1288C22C22×H(5,𝔽2)11yescharacteristic
1289C22C22×H(5,𝔽2)11yescharacteristic
1290C22C2×#58511yescharacteristic
1291C22H(7,𝔽2)12yes—
1292C222−1+612yes—
1293C4—22no—
1294C4—22no—
1295C4—24no—
1296C4—24no—
1297C4—42no—
1298C4—42no—
1299C4—44no—
1300C4—44no—
1301C4—42no—
1302C4—44no—
1303C4—44no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—44no—
1311C4—44no—
1312C2—42no—
1313C2—84no—
1314C2—82no—
1315C2—84no—
1316C2#6281811yescharacteristic
1317C2#6287512yes—
1318C2#6304811yescharacteristic
1319C2#6305012yes—
1320C2#6306611yescharacteristic
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. #58294C2semidirect
2. #57519C2semidirect
3. #57173C2semidirect
4. #56370C2semidirect
5. #54510C2semidirect
6. #54265C2semidirect
7. #52071C2semidirect
8. #51903C2semidirect
9. #51777C2semidirect
10. #51733C2semidirect
11. #47572C2semidirect
12. #47567C2semidirect
13. #47362C2semidirect
14. #46458C2semidirect
15. #46235C2semidirect
16. #46232C2semidirect
17. #46232C2semidirect
18. #46230C2semidirect
19. #45976C2semidirect
20. #45974C2semidirect
21. #45972C2semidirect
22. #35327C2semidirect
23. #35189C2semidirect
26. C2×#554C22semidirect
29. C2×#529C22semidirect
33. #2851C22semidirect
37. #2850C22semidirect
38. #2844C22semidirect
39. #2844C22semidirect
41. #2837C22semidirect
42. #2829C22semidirect
43. #2828C22semidirect
44. #2828C22semidirect
45. #2826C22semidirect
46. #2822C22semidirect
49. #2819C22semidirect
50. #2814C22semidirect
52. #2803C22semidirect
53. #2800C22semidirect
54. #2797C22semidirect
55. #2795C22semidirect
56. #2795C22semidirect
57. #2794C22semidirect
58. #2793C22semidirect
59. #2792C22semidirect
60. #2786C22semidirect
61. #2781C22semidirect
62. #2777C22semidirect
65. #2761C22semidirect
69. #2749C22semidirect
72. #2741C22semidirect
74. #2732C22semidirect
77. #2730C22semidirect
78. #2730C22semidirect
79. #2729C22semidirect
80. #2720C22semidirect
81. #2717C22semidirect
84. #2709C22semidirect
85. #2707C22semidirect
86. #2707C22semidirect
87. #2706C22semidirect
88. #2704C22semidirect
91. #2703C22semidirect
92. #2702C22semidirect
94. #2700C22semidirect
95. #2698C22semidirect
98. #2696C22semidirect
100. #2693C22semidirect
102. #2692C22semidirect
103. #2692C22semidirect
105. #2690C22semidirect
106. #2688C22semidirect
108. #2686C22semidirect
109. #2683C22semidirect
110. #2681C22semidirect
111. #2680C22semidirect
112. #2680C22semidirect
116. #2673C22semidirect
117. #2673C22semidirect
120. #2672C22semidirect
121. #2672C22semidirect
124. #2667C22semidirect
126. #2652C22semidirect
128. #2632C22semidirect
129. #2631C22semidirect
131. #2630C22semidirect
132. #2630C22semidirect
135. #2618C22semidirect
136. #2612C22semidirect
139. #2610C22semidirect
141. #2601C22semidirect
145. #2598C22semidirect
147. #2596C22semidirect
148. #2587C22semidirect
149. #2586C22semidirect
150. #2582C22semidirect
151. #2556C22semidirect
156. #2538C22semidirect
160. #2533C22semidirect
161. #2532C22semidirect
162. #2532C22semidirect
163. #2532C22semidirect
164. #2532C22semidirect
165. #2531C22semidirect
166. #2526C22semidirect
167. #2485C22semidirect
168. #2477C22semidirect
169. #2474C22semidirect
171. #2470C22semidirect
172. #2470C22semidirect
174. #2463C22semidirect
175. #2462C22semidirect
177. #2461C22semidirect
178. #2461C22semidirect
179. #2458C22semidirect
180. #2457C22semidirect
183. #2456C22semidirect
184. #2449C22semidirect
185. #2445C22semidirect
187. #2443C22semidirect
193. #2421C22semidirect
195. #2417C22semidirect
197. #2415C22semidirect
199. #2414C22semidirect
200. #2414C22semidirect
201. #2413C22semidirect
206. #2382C22semidirect
207. #2381C22semidirect
209. #2379C22semidirect
212. #2323C22semidirect
218. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#582942
#575192
#571732
#563702
#545102
#542652
#520712
#519032
#517772
#517332
#475722
#475672
#473622
#464582
#462352
#462322
#462302
#459762
#459742
#459722
#353272
#351892