Finite Group Databasebeta

← #8757638

Subgroups — #8757638

Order 512.

4798 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58866C214yesmaximal, complemented
2#57201C214yesmaximal, complemented
3#57172C214yesmaximal, complemented
4#56371C214yesmaximal, complemented
5#54785C214yesmaximal, complemented
6#54081C214yesmaximal, complemented
7#52076C212yesmaximal, complemented
8#51895C212yesmaximal, complemented
9#51878C214yesmaximal, complemented
10#51579C214yesmaximal, complemented
11#47662C214yesmaximal, complemented
12#47250C214yesmaximal, complemented
13#47032C212yesmaximal, complemented
14#46389C212yesmaximal, complemented
15#46233C212yesmaximal, complemented
16#46233C212yesmaximal, complemented
17#46231C212yesmaximal, complemented
18#46136C211yesmaximal, characteristic, complemented
19#45977C211yesmaximal, characteristic, complemented
20#45975C212yesmaximal, complemented
21#45973C212yesmaximal, complemented
22#35327C211yesmaximal, characteristic, complemented
23#35189C212yesmaximal, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×#563C2212yescomplemented
26C2×H(3,𝔽4)C2211yescharacteristic
27C2×#551C2212yescomplemented
28C2×#536C2211yescharacteristic, complemented
29C2×#535C2211yescharacteristic
30C2×#529C2212yescomplemented
31C22×#124C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic, complemented
33#2851C2212yescomplemented
34#2851C2212yescomplemented
35#2850C2212yes—
36#2850C2212yes—
37#2850C2212yescomplemented
38#2850C2212yescomplemented
39#2845C2212yescomplemented
40#2842C2212yescomplemented
41#2837C2214yescomplemented
42#2829C2214yescomplemented
43#2829C2214yescomplemented
44#2829C2214yescomplemented
45#2824C2214yescomplemented
46#2820C2212yes—
47#2820C2212yescomplemented
48#2819C2212yes—
49#2816C2212yes—
50#2813C2214yescomplemented
51#2808C2214yescomplemented
52#2800C2214yescomplemented
53#2800C2214yescomplemented
54#2790C2214yescomplemented
55#2790C2214yescomplemented
56#2781C2214yescomplemented
57#2780C2214yescomplemented
58#2761C2214yescomplemented
59#2755C2214yescomplemented
60#2754C2214yescomplemented
61#2750C2214yescomplemented
62#2748C2214yescomplemented
63#2748C2214yescomplemented
64#2741C2214yescomplemented
65#2741C2214yescomplemented
66#2733C2212yes—
67#2733C2212yescomplemented
68#2731C2212yes—
69#2731C2212yescomplemented
70#2730C2214yes—
71#2730C2214yescomplemented
72#2729C2214yescomplemented
73#2727C2214yescomplemented
74#2725C2214yescomplemented
75#2721C2214yescomplemented
76#2721C2214yescomplemented
77#2718C2214yescomplemented
78#2718C2214yescomplemented
79#2717C2212yescomplemented
80#2716C2214yescomplemented
81#2715C2214yescomplemented
82#2715C2214yescomplemented
83#2714C2214yescomplemented
84#2714C2214yescomplemented
85#2712C2214yes—
86#2711C2214yescomplemented
87#2709C2212yescomplemented
88#2707C2214yescomplemented
89#2706C2214yescomplemented
90#2705C2214yes—
91#2705C2214yescomplemented
92#2705C2214yescomplemented
93#2704C2214yescomplemented
94#2704C2214yescomplemented
95#2702C2214yescomplemented
96#2702C2214yescomplemented
97#2702C2214yescomplemented
98#2696C2214yescomplemented
99#2695C2214yescomplemented
100#2692C2214yescomplemented
101#2691C2214yes—
102#2691C2214yes—
103#2691C2214yescomplemented
104#2685C2214yes—
105#2685C2214yes—
106#2685C2214yes—
107#2685C2214yescomplemented
108#2685C2214yescomplemented
109#2685C2214yescomplemented
110#2685C2214yescomplemented
111#2684C2212yes—
112#2682C2214yes—
113#2681C2214yescomplemented
114#2678C2214yes—
115#2678C2214yescomplemented
116#2674C2214yescomplemented
117#2672C2214yescomplemented
118#2671C2214yescomplemented
119#2671C2214yescomplemented
120#2670C2214yes—
121#2669C2212yescomplemented
122#2668C2214yescomplemented
123#2664C2214yescomplemented
124#2662C2214yescomplemented
125#2654C2214yescomplemented
126#2630C2214yescomplemented
127#2630C2214yescomplemented
128#2630C2214yescomplemented
129#2626C2214yescomplemented
130#2620C2212yes—
131#2620C2212yescomplemented
132#2619C2214yes—
133#2609C2214yescomplemented
134#2609C2214yescomplemented
135#2608C2212yescomplemented
136#2601C2214yescomplemented
137#2601C2214yescomplemented
138#2601C2214yescomplemented
139#2601C2214yescomplemented
140#2601C2214yescomplemented
141#2589C2214yescomplemented
142#2589C2214yescomplemented
143#2582C2212yescomplemented
144#2558C2214yescomplemented
145#2554C2214yes—
146#2554C2214yescomplemented
147#2554C2214yescomplemented
148#2554C2214yescomplemented
149#2545C2214yescomplemented
150#2544C2214yescomplemented
151#2538C2212yescomplemented
152#2538C2212yescomplemented
153#2537C2212yes—
154#2534C2214yescomplemented
155#2534C2214yescomplemented
156#2522C2214yescomplemented
157#2520C2214yescomplemented
158#2520C2214yescomplemented
159#2519C2214yescomplemented
160#2519C2214yescomplemented
161#2490C2214yescomplemented
162#2485C2214yescomplemented
163#2480C2214yescomplemented
164#2480C2214yescomplemented
165#2479C2214yes—
166#2479C2214yescomplemented
167#2479C2214yescomplemented
168#2479C2214yescomplemented
169#2478C2214yescomplemented
170#2478C2214yescomplemented
171#2476C2214yescomplemented
172#2476C2214yescomplemented
173#2476C2214yescomplemented
174#2474C2214yescomplemented
175#2474C2214yescomplemented
176#2472C2214yes—
177#2469C2214yescomplemented
178#2463C2214yescomplemented
179#2461C2214yescomplemented
180#2456C2214yescomplemented
181#2454C2214yescomplemented
182#2452C2214yescomplemented
183#2448C2214yescomplemented
184#2439C2214yescomplemented
185#2437C2214yescomplemented
186#2436C2212yes—
187#2434C2212yescomplemented
188#2424C2214yes—
189#2424C2214yes—
190#2418C2214yescomplemented
191#2415C2212yescomplemented
192#2415C2212yescomplemented
193#2415C2214yescomplemented
194#2414C2212yes—
195#2414C2212yescomplemented
196#2411C2214yescomplemented
197#2410C2214yes—
198#2410C2214yescomplemented
199#2407C2214yescomplemented
200#2405C2212yes—
201#2405C2212yescomplemented
202#2403C2212yes—
203#2382C2212yescomplemented
204#2379C2211yescharacteristic
205#2379C2211yescharacteristic, complemented
206#2379C2212yescomplemented
207#2379C2212yescomplemented
208#2369C2212yescomplemented
209#2333C2212yes—
210#2332C2212yescomplemented
211#2324C2214yescomplemented
212#2323C2214yescomplemented
213#2312C2212yescomplemented
214#2310C2211yescharacteristic, complemented
215#2309C2211yescharacteristic
216#2309C2212yescomplemented
217#2285C2212yescomplemented
218#2285C2211yescharacteristic, complemented
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C23×D4C2312yes—
223#563—48no—
224#563—44no—
225H(3,𝔽4)—44no—
226#551—48no—
227#536—44no—
228#535—44no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×#127C2312yes—
233#529—48no—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2312yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#124—44no—
246C2×#124C2311yescharacteristic
247C2×#124C2312yes—
248C2×#124C2311yescharacteristic
249C2×#124C2312yes—
250C2×#124C2311yescharacteristic
251C2×#124C2311yescharacteristic
252C2×#124C2312yes—
253C2×#124C2314yes—
254C2×#124C2312yes—
255C2×#124C2314yes—
256C2×#124C2312yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2312yes—
260C2×#123C2312yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#120C2312yes—
284C2×#120C2312yes—
285C2×#120C2314yes—
286C2×#120C2314yes—
287C2×#120C2314yes—
288C2×#120C2314yes—
289C4×#41—44no—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2314yes—
302C2×#117C2312yes—
303C2×#117C2314yes—
304C2×#117C2314yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2314yes—
309C22×C22⋊C4C2314yes—
310C22×C42C2311yescharacteristic
311C22×C42C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
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#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#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#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2314yes—
426#392C2314yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
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#390C2314yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
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#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
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#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
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#386C2312yes—
556#386C2312yes—
557#386C2312yes—
558#386C2312yes—
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#385C2314yes—
581#385C2314yes—
582#384C2312yes—
583#384C2312yes—
584#384C2312yes—
585#382C2312yes—
586#382C2312yes—
587#382C2312yes—
588#382C2314yes—
589#382C2314yes—
590#381C2312yes—
591#381C2312yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#379C2312yes—
605#379C2312yes—
606#379C2312yes—
607#379C2314yes—
608#379C2312yes—
609#379C2314yes—
610#379C2314yes—
611#379C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2312yes—
623C25C2412yes—
624C25C2412yes—
625C2×#41—24no—
626C2×#41—42no—
627C2×#41—42no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C22×Q8C2411yescharacteristic
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2411yescharacteristic
637C22×D4—42no—
638C22×D4—42no—
639C22×D4—42no—
640C22×D4—44no—
641C22×D4—84no—
642C22×D4C2412yes—
643C22×D4C2411yescharacteristic
644C22×D4C2412yes—
645C22×D4C2411yescharacteristic
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2411yescharacteristic
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2412yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C23×C4C2411yescharacteristic
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2414yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2414yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C4⋊Q8—28no—
669C4⋊Q8—44no—
670C4⋊Q8—44no—
671#127—44no—
672#126—48no—
673#126—48no—
674#126—48no—
675#126—48no—
676#126—48no—
677#126—84no—
678#126—84no—
679#126—84no—
680#125—28no—
681#125—48no—
682#125—84no—
683#124—28no—
684#124—24no—
685#124—24no—
686#124—28no—
687#124—48no—
688#124—42no—
689#124—42no—
690#124—44no—
691#124—48no—
692#124—44no—
693#124—44no—
694#123—48no—
695#123—48no—
696#123—48no—
697#123—48no—
698#123—44no—
699#123—44no—
700#123—84no—
701C22⋊Q8—216no—
702C22⋊Q8—44no—
703C22⋊Q8—48no—
704C22⋊Q8—44no—
705C22⋊Q8—44no—
706C22⋊Q8—48no—
707C22⋊Q8—44no—
708C22⋊Q8—82no—
709C22⋊Q8—82no—
710#121—44no—
711#121—44no—
712#121—48no—
713#121—44no—
714#121—44no—
715#121—84no—
716#121—84no—
717#121—84no—
718#121—82no—
719#121—82no—
720#120—48no—
721#120—44no—
722#120—48no—
723#120—44no—
724#120—84no—
725#120—84no—
726C4×Q8—44no—
727C4×Q8—44no—
728C4×D4—44no—
729C4×D4—44no—
730C4×D4—44no—
731C4×D4—44no—
732C4×D4—48no—
733C4×D4—48no—
734#117—44no—
735#117—42no—
736#117—42no—
737#117—42no—
738#117—48no—
739#117—48no—
740#117—82no—
741#117—84no—
742#117—82no—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
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×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C22⋊C4—48no—
789C2×C22⋊C4—48no—
790C2×C22⋊C4—44no—
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⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C42—24no—
852C2×C42—28no—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2411yescharacteristic
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2411yescharacteristic
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909C24—24no—
910C24—42no—
911C24—42no—
912C24—44no—
913C24—44no—
914C24—44no—
915C24—42no—
916C24—42no—
917C24—44no—
918C24—42no—
919C24C2512yes—
920C24C2512yes—
921C24C2514yes—
922C24C2512yes—
923C24C2511yescharacteristic
924#41—416no—
925C2×Q8—24no—
926C2×Q8—22no—
927C2×Q8—22no—
928C2×Q8—24no—
929C2×Q8—41no—
930C2×Q8—41no—
931C2×Q8—41no—
932C2×Q8—41no—
933C2×Q8—42no—
934C2×Q8—42no—
935C2×Q8—41no—
936C2×Q8—41no—
937C2×Q8—42no—
938C2×Q8—42no—
939C2×Q8—42no—
940C2×Q8—42no—
941C2×Q8—42no—
942C2×Q8—88no—
943C2×Q8H(5,𝔽2)14yes—
944C2×D4—24no—
945C2×D4—28no—
946C2×D4—24no—
947C2×D4—22no—
948C2×D4—24no—
949C2×D4—22no—
950C2×D4—24no—
951C2×D4—22no—
952C2×D4—42no—
953C2×D4—41no—
954C2×D4—41no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—41no—
961C2×D4—41no—
962C2×D4—42no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—42no—
967C2×D4—41no—
968C2×D4—41no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—42no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—88no—
990C2×D4—816no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—24no—
999C22×C4—24no—
1000C22×C4—28no—
1001C22×C4—42no—
1002C22×C4—44no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—41no—
1110C22⋊C4—41no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—42no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4—42no—
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—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—44no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C42—24no—
1146C42—22no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—24no—
1151C42—24no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—42no—
1158C42—42no—
1159C42—44no—
1160C42—42no—
1161C42—42no—
1162C42H(5,𝔽2)14yes—
1163C23—21no—
1164C23—21no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—24no—
1169C23—24no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—24no—
1178C23—22no—
1179C23—22no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—22no—
1184C23—24no—
1185C23—22no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—22no—
1191C23—84no—
1192C23—84no—
1193C23—84no—
1194C23—84no—
1195C23—88no—
1196C23—88no—
1197C23—164no—
1198C23—162no—
1199C23—162no—
1200C23—164no—
1201C23#58512yes—
1202C23C2611yescharacteristic
1203Q8—44no—
1204Q8—84no—
1205Q8—82no—
1206Q8—82no—
1207Q8—84no—
1208Q8—162no—
1209D4—48no—
1210D4—44no—
1211D4—84no—
1212D4—82no—
1213D4—82no—
1214D4—84no—
1215D4—88no—
1216D4—88no—
1217D4—88no—
1218D4—88no—
1219D4—164no—
1220D4—164no—
1221D4—164no—
1222D4—162no—
1223D4—164no—
1224C2×C4—28no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—48no—
1276C2×C4—48no—
1277C2×C4—48no—
1278C2×C4—88no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—88no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4C2×H(5,𝔽2)12yes—
1286C2×C4C2×H(5,𝔽2)14yes—
1287C2×C4C2×H(5,𝔽2)12yes—
1288C2×C4C2×H(5,𝔽2)14yes—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—44no—
1297C22—42no—
1298C22—44no—
1299C22—44no—
1300C22—42no—
1301C22—42no—
1302C22—44no—
1303C22—44no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—44no—
1308C22—42no—
1309C22—44no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—168no—
1319C22—168no—
1320C22C22×H(5,𝔽2)11yescharacteristic
1321C22C22×H(5,𝔽2)11yescharacteristic
1322C22C2×#58511yescharacteristic
1323C22H(7,𝔽2)12yes—
1324C222−1+612yes—
1325C4—22no—
1326C4—22no—
1327C4—24no—
1328C4—24no—
1329C4—44no—
1330C4—44no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—44no—
1343C2—42no—
1344C2—82no—
1345C2—82no—
1346C2—84no—
1347C2—82no—
1348C2#6281811yescharacteristic
1349C2#6287512yes—
1350C2#6304611yescharacteristic
1351C2#6305212yes—
1352C2#6306411yescharacteristic
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. #58866C2semidirect
2. #57201C2semidirect
3. #57172C2semidirect
4. #56371C2semidirect
5. #54785C2semidirect
6. #54081C2semidirect
7. #52076C2semidirect
8. #51895C2semidirect
9. #51878C2semidirect
10. #51579C2semidirect
11. #47662C2semidirect
12. #47250C2semidirect
13. #47032C2semidirect
14. #46389C2semidirect
15. #46233C2semidirect
16. #46233C2semidirect
17. #46231C2semidirect
18. #46136C2semidirect
19. #45977C2semidirect
20. #45975C2semidirect
21. #45973C2semidirect
22. #35327C2semidirect
23. #35189C2semidirect
24. C2×#563C22semidirect
25. C2×#563C22semidirect
27. C2×#551C22semidirect
28. C2×#536C22semidirect
30. C2×#529C22semidirect
32. C2×C4×#41C22semidirect
33. #2851C22semidirect
34. #2851C22semidirect
37. #2850C22semidirect
38. #2850C22semidirect
39. #2845C22semidirect
40. #2842C22semidirect
41. #2837C22semidirect
42. #2829C22semidirect
43. #2829C22semidirect
44. #2829C22semidirect
45. #2824C22semidirect
47. #2820C22semidirect
50. #2813C22semidirect
51. #2808C22semidirect
52. #2800C22semidirect
53. #2800C22semidirect
54. #2790C22semidirect
55. #2790C22semidirect
56. #2781C22semidirect
57. #2780C22semidirect
58. #2761C22semidirect
59. #2755C22semidirect
60. #2754C22semidirect
61. #2750C22semidirect
62. #2748C22semidirect
63. #2748C22semidirect
64. #2741C22semidirect
65. #2741C22semidirect
67. #2733C22semidirect
69. #2731C22semidirect
71. #2730C22semidirect
72. #2729C22semidirect
73. #2727C22semidirect
74. #2725C22semidirect
75. #2721C22semidirect
76. #2721C22semidirect
77. #2718C22semidirect
78. #2718C22semidirect
79. #2717C22semidirect
80. #2716C22semidirect
81. #2715C22semidirect
82. #2715C22semidirect
83. #2714C22semidirect
84. #2714C22semidirect
86. #2711C22semidirect
87. #2709C22semidirect
88. #2707C22semidirect
89. #2706C22semidirect
91. #2705C22semidirect
92. #2705C22semidirect
93. #2704C22semidirect
94. #2704C22semidirect
95. #2702C22semidirect
96. #2702C22semidirect
97. #2702C22semidirect
98. #2696C22semidirect
99. #2695C22semidirect
100. #2692C22semidirect
103. #2691C22semidirect
107. #2685C22semidirect
108. #2685C22semidirect
109. #2685C22semidirect
110. #2685C22semidirect
113. #2681C22semidirect
115. #2678C22semidirect
116. #2674C22semidirect
117. #2672C22semidirect
118. #2671C22semidirect
119. #2671C22semidirect
121. #2669C22semidirect
122. #2668C22semidirect
123. #2664C22semidirect
124. #2662C22semidirect
125. #2654C22semidirect
126. #2630C22semidirect
127. #2630C22semidirect
128. #2630C22semidirect
129. #2626C22semidirect
131. #2620C22semidirect
133. #2609C22semidirect
134. #2609C22semidirect
135. #2608C22semidirect
136. #2601C22semidirect
137. #2601C22semidirect
138. #2601C22semidirect
139. #2601C22semidirect
140. #2601C22semidirect
141. #2589C22semidirect
142. #2589C22semidirect
143. #2582C22semidirect
144. #2558C22semidirect
146. #2554C22semidirect
147. #2554C22semidirect
148. #2554C22semidirect
149. #2545C22semidirect
150. #2544C22semidirect
151. #2538C22semidirect
152. #2538C22semidirect
154. #2534C22semidirect
155. #2534C22semidirect
156. #2522C22semidirect
157. #2520C22semidirect
158. #2520C22semidirect
159. #2519C22semidirect
160. #2519C22semidirect
161. #2490C22semidirect
162. #2485C22semidirect
163. #2480C22semidirect
164. #2480C22semidirect
166. #2479C22semidirect
167. #2479C22semidirect
168. #2479C22semidirect
169. #2478C22semidirect
170. #2478C22semidirect
171. #2476C22semidirect
172. #2476C22semidirect
173. #2476C22semidirect
174. #2474C22semidirect
175. #2474C22semidirect
177. #2469C22semidirect
178. #2463C22semidirect
179. #2461C22semidirect
180. #2456C22semidirect
181. #2454C22semidirect
182. #2452C22semidirect
183. #2448C22semidirect
184. #2439C22semidirect
185. #2437C22semidirect
187. #2434C22semidirect
190. #2418C22semidirect
191. #2415C22semidirect
192. #2415C22semidirect
193. #2415C22semidirect
195. #2414C22semidirect
196. #2411C22semidirect
198. #2410C22semidirect
199. #2407C22semidirect
201. #2405C22semidirect
203. #2382C22semidirect
205. #2379C22semidirect
206. #2379C22semidirect
207. #2379C22semidirect
208. #2369C22semidirect
210. #2332C22semidirect
211. #2324C22semidirect
212. #2323C22semidirect
213. #2312C22semidirect
214. #2310C22semidirect
216. #2309C22semidirect
217. #2285C22semidirect
218. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#588662
#572012
#571722
#563712
#547852
#540812
#520762
#518952
#518782
#515792
#476622
#472502
#470322
#463892
#462332
#462312
#461362
#459772
#459752
#459732
#353272
#351892