Finite Group Databasebeta

← #9912903

Subgroups — #9912903

Order 512.

4567 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58957C214yesmaximal, complemented
2#58537C214yesmaximal, complemented
3#58090C214yesmaximal, complemented
4#57495C214yesmaximal, complemented
5#57323C214yesmaximal, complemented
6#54913C214yesmaximal, complemented
7#54810C214yesmaximal, complemented
8#53726C212yesmaximal, complemented
9#53366C212yesmaximal, complemented
10#53173C214yesmaximal, complemented
11#51803C212yesmaximal, complemented
12#51326C212yesmaximal, complemented
13#51071C212yesmaximal, complemented
14#49059C212yesmaximal, complemented
15#48509C214yesmaximal, complemented
16#46237C211yesmaximal, characteristic, complemented
17#45956C212yesmaximal, complemented
18#45446C214yesmaximal, complemented
19#45442C212yesmaximal, complemented
20#38955C211yesmaximal, characteristic, complemented
21#37653C212yesmaximal, complemented
22#37374C212yesmaximal, complemented
23#37162C211yesmaximal, characteristic, complemented
24C2×#563C2211yescharacteristic
25C2×#563C2212yes—
26C2×H(3,𝔽4)C2211yescharacteristic
27C2×#554C2211yescharacteristic, complemented
28C2×#547C2211yescharacteristic
29C2×#536C2212yes—
30C2×#525C2212yes—
31C22×C22⋊Q8C2212yescomplemented
32#2863C2212yescomplemented
33#2862C2211yescharacteristic, complemented
34#2861C2212yes—
35#2849C2214yes—
36#2849C2212yescomplemented
37#2848C2214yescomplemented
38#2841C2214yescomplemented
39#2838C2214yescomplemented
40#2838C2214yescomplemented
41#2833C2212yescomplemented
42#2830C2214yescomplemented
43#2829C2214yescomplemented
44#2820C2212yes—
45#2817C2214yescomplemented
46#2814C2214yes—
47#2812C2214yes—
48#2811C2212yescomplemented
49#2808C2212yes—
50#2808C2212yescomplemented
51#2806C2212yescomplemented
52#2806C2212yescomplemented
53#2806C2212yescomplemented
54#2805C2214yescomplemented
55#2804C2211yescharacteristic
56#2804C2212yes—
57#2803C2214yes—
58#2801C2214yescomplemented
59#2793C2214yescomplemented
60#2790C2214yescomplemented
61#2788C2214yescomplemented
62#2778C2214yes—
63#2777C2214yescomplemented
64#2772C2214yescomplemented
65#2770C2214yescomplemented
66#2769C2212yescomplemented
67#2764C2214yescomplemented
68#2764C2214yescomplemented
69#2762C2214yescomplemented
70#2759C2214yescomplemented
71#2759C2214yescomplemented
72#2759C2214yescomplemented
73#2757C2214yescomplemented
74#2756C2214yes—
75#2754C2214yescomplemented
76#2752C2214yes—
77#2751C2214yes—
78#2749C2214yes—
79#2747C2214yescomplemented
80#2745C2214yescomplemented
81#2743C2214yescomplemented
82#2740C2214yescomplemented
83#2738C2214yescomplemented
84#2737C2214yes—
85#2737C2214yescomplemented
86#2736C2214yescomplemented
87#2734C2212yescomplemented
88#2733C2212yes—
89#2731C2212yes—
90#2729C2214yescomplemented
91#2729C2214yescomplemented
92#2729C2214yescomplemented
93#2728C2214yes—
94#2724C2211yescharacteristic
95#2724C2212yes—
96#2724C2212yes—
97#2723C2214yes—
98#2720C2214yescomplemented
99#2718C2214yescomplemented
100#2717C2212yes—
101#2717C2214yescomplemented
102#2716C2214yescomplemented
103#2713C2214yescomplemented
104#2710C2214yes—
105#2710C2214yes—
106#2708C2214yes—
107#2708C2214yes—
108#2702C2214yes—
109#2702C2214yescomplemented
110#2700C2214yes—
111#2700C2214yes—
112#2700C2214yescomplemented
113#2698C2214yescomplemented
114#2697C2212yes—
115#2697C2212yes—
116#2696C2214yes—
117#2692C2214yescomplemented
118#2690C2214yescomplemented
119#2689C2214yescomplemented
120#2689C2214yescomplemented
121#2687C2214yescomplemented
122#2687C2214yescomplemented
123#2686C2214yes—
124#2685C2214yes—
125#2684C2214yescomplemented
126#2684C2214yescomplemented
127#2683C2212yes—
128#2683C2214yescomplemented
129#2681C2214yes—
130#2680C2214yes—
131#2678C2214yes—
132#2677C2214yescomplemented
133#2677C2214yescomplemented
134#2677C2214yescomplemented
135#2676C2214yes—
136#2674C2214yes—
137#2674C2214yes—
138#2674C2214yescomplemented
139#2665C2214yescomplemented
140#2663C2214yescomplemented
141#2654C2214yescomplemented
142#2653C2214yes—
143#2651C2214yescomplemented
144#2650C2214yescomplemented
145#2640C2214yescomplemented
146#2634C2212yescomplemented
147#2631C2212yes—
148#2625C2214yescomplemented
149#2621C2212yescomplemented
150#2618C2212yescomplemented
151#2614C2212yescomplemented
152#2606C2214yescomplemented
153#2605C2214yescomplemented
154#2594C2214yescomplemented
155#2594C2214yescomplemented
156#2593C2212yes—
157#2586C2214yescomplemented
158#2585C2214yescomplemented
159#2578C2214yescomplemented
160#2563C2211yescharacteristic
161#2562C2212yescomplemented
162#2557C2214yes—
163#2556C2214yescomplemented
164#2551C2214yescomplemented
165#2546C2211yescharacteristic, complemented
166#2545C2212yes—
167#2539C2212yescomplemented
168#2534C2212yes—
169#2531C2214yes—
170#2529C2214yescomplemented
171#2527C2214yescomplemented
172#2526C2214yescomplemented
173#2523C2214yescomplemented
174#2521C2214yes—
175#2521C2214yescomplemented
176#2503C2212yescomplemented
177#2492C2214yescomplemented
178#2485C2214yes—
179#2481C2214yes—
180#2481C2214yes—
181#2481C2214yescomplemented
182#2480C2214yescomplemented
183#2480C2214yescomplemented
184#2478C2214yescomplemented
185#2474C2214yes—
186#2474C2214yescomplemented
187#2473C2214yescomplemented
188#2472C2214yes—
189#2467C2214yescomplemented
190#2463C2214yescomplemented
191#2461C2214yes—
192#2461C2214yes—
193#2459C2214yes—
194#2452C2214yescomplemented
195#2449C2214yes—
196#2447C2214yes—
197#2442C2214yescomplemented
198#2440C2214yescomplemented
199#2434C2214yescomplemented
200#2432C2212yes—
201#2420C2214yescomplemented
202#2418C2214yes—
203#2417C2214yescomplemented
204#2415C2214yescomplemented
205#2413C2212yescomplemented
206#2411C2212yescomplemented
207#2409C2214yes—
208#2406C2212yes—
209#2404C2212yes—
210#2378C2214yescomplemented
211#2375C2212yes—
212#2374C2212yes—
213#2344C2212yescomplemented
214#2336C2212yescomplemented
215#2322C2212yes—
216#2311C2212yes—
217C4×#124C2211yescharacteristic
218#2293C2211yescharacteristic, complemented
219C22×#41C2312yes—
220C23×Q8C2312yes—
221C24×C4C2312yes—
222#563—48no—
223#563—44no—
224H(3,𝔽4)—44no—
225#554—44no—
226#547—44no—
227#536—48no—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#125C2312yes—
239C2×#125C2312yes—
240C2×#125C2312yes—
241C2×#124C2311yescharacteristic
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248#525—48no—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2312yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2312yes—
256C2×#123C2312yes—
257C2×#123C2314yes—
258C2×#123C2312yes—
259C2×C22⋊Q8—48no—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#120C2312yes—
276C2×#120C2314yes—
277C2×#120C2312yes—
278C2×#120C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2312yes—
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×#117C2312yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294#401C2314yes—
295#401C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2312yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#399C2314yes—
313#399C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2312yes—
321#398C2312yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2312yes—
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#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
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#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
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#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2311yescharacteristic
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#390C2312yes—
446#390C2311yescharacteristic
447#390C2312yes—
448#390C2314yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#388C2314yes—
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#387C2314yes—
513#387C2314yes—
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#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2312yes—
543#386C2312yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2312yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#385C2312yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
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#384C2314yes—
579#383C2314yes—
580#383C2312yes—
581#383C2314yes—
582#383C2314yes—
583#382C2312yes—
584#382C2311yescharacteristic
585#382C2314yes—
586#381C2314yes—
587#381C2312yes—
588#381C2314yes—
589#381C2314yes—
590#381C2312yes—
591#381C2312yes—
592#381C2312yes—
593#381C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2312yes—
603#380C2314yes—
604#379C2314yes—
605#379C2314yes—
606#379C2314yes—
607#379C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2311yescharacteristic
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2312yes—
620#376C2314yes—
621C43C2311yescharacteristic
622C25C2412yes—
623C2×#41—28no—
624C2×#41—44no—
625C2×#41—82no—
626C22×Q8—44no—
627C22×Q8—44no—
628C22×Q8—82no—
629C22×Q8C2411yescharacteristic
630C22×Q8C2414yes—
631C22×Q8C2412yes—
632C22×Q8C2412yes—
633C22×Q8C2414yes—
634C22×Q8C2412yes—
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×D4C2411yescharacteristic
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2412yes—
644C22×D4C2414yes—
645C22×D4C2411yescharacteristic
646C23×C4—44no—
647C23×C4—44no—
648C23×C4—82no—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2414yes—
656C23×C4C2412yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C4⋊Q8—42no—
660C4⋊Q8—42no—
661C4⋊Q8—48no—
662C4⋊Q8—48no—
663C4⋊Q8—44no—
664C4⋊Q8—82no—
665C4⋊Q8—84no—
666#126—48no—
667#126—48no—
668#126—48no—
669#125—28no—
670#125—44no—
671#125—44no—
672#124—24no—
673#124—44no—
674#124—44no—
675#124—48no—
676#124—48no—
677#124—44no—
678#124—84no—
679#123—28no—
680#123—28no—
681#123—44no—
682#123—44no—
683#123—48no—
684#123—44no—
685#123—44no—
686#123—44no—
687#123—84no—
688#123—82no—
689C22⋊Q8—216no—
690C22⋊Q8—48no—
691C22⋊Q8—48no—
692C22⋊Q8—48no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697C22⋊Q8—48no—
698C22⋊Q8—44no—
699C22⋊Q8—44no—
700C22⋊Q8—48no—
701C22⋊Q8—84no—
702#121—48no—
703#121—44no—
704#120—28no—
705#120—44no—
706#120—48no—
707#120—82no—
708C4×Q8—42no—
709C4×D4—24no—
710C4×D4—44no—
711C4×D4—42no—
712C4×D4—48no—
713C4×D4—48no—
714#117—44no—
715#117—44no—
716#117—82no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—44no—
719C2×C4⋊C4—44no—
720C2×C4⋊C4—44no—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C22⋊C4—44no—
772C2×C22⋊C4—44no—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
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⋊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×C42C2411yescharacteristic
821C2×C42C2412yes—
822C2×C42C2411yescharacteristic
823C2×C42C2411yescharacteristic
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2412yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
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#95C2412yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890C24—24no—
891C24—42no—
892C24—44no—
893C24—42no—
894C24—44no—
895C24C2514yes—
896C24C2512yes—
897C24C2512yes—
898#41—816no—
899C2×Q8—28no—
900C2×Q8—24no—
901C2×Q8—22no—
902C2×Q8—41no—
903C2×Q8—44no—
904C2×Q8—44no—
905C2×Q8—42no—
906C2×Q8—44no—
907C2×Q8—44no—
908C2×Q8—41no—
909C2×Q8—44no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—42no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—42no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—816no—
924C2×D4—28no—
925C2×D4—24no—
926C2×D4—24no—
927C2×D4—22no—
928C2×D4—41no—
929C2×D4—42no—
930C2×D4—41no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—44no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—42no—
949C2×D4H(5,𝔽2)14yes—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—28no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—42no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—816no—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2511yescharacteristic
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2512yes—
996C22×C4C2511yescharacteristic
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—41no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—41no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4H(5,𝔽2)14yes—
1049C22⋊C4—24no—
1050C22⋊C4—24no—
1051C22⋊C4—24no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—28no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—42no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
1084C22⋊C4—44no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C42—22no—
1097C42—24no—
1098C42—22no—
1099C42—42no—
1100C42—44no—
1101C42—42no—
1102C42—44no—
1103C42—44no—
1104C42—44no—
1105C42—44no—
1106C42—41no—
1107C42—42no—
1108C42—42no—
1109C42—44no—
1110C42—42no—
1111C42—44no—
1112C23—22no—
1113C23—22no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—22no—
1118C23—24no—
1119C23—22no—
1120C23—24no—
1121C23—22no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—24no—
1126C23—24no—
1127C23—24no—
1128C23—48no—
1129C23—84no—
1130C23—88no—
1131C23—88no—
1132C23—84no—
1133C23C2×H(5,𝔽2)14yes—
1134C23C2611yescharacteristic
1135Q8—82no—
1136Q8—88no—
1137Q8—84no—
1138Q8—88no—
1139Q8—162no—
1140Q8—162no—
1141Q8—162no—
1142Q8—162no—
1143D4—44no—
1144D4—44no—
1145D4—88no—
1146D4—84no—
1147D4—84no—
1148D4—88no—
1149D4—164no—
1150D4—162no—
1151D4—162no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—48no—
1206C2×C4—48no—
1207C2×C4—48no—
1208C2×C4—48no—
1209C2×C4—84no—
1210C2×C4—88no—
1211C2×C4—84no—
1212C2×C4—84no—
1213C2×C4—88no—
1214C2×C4—164no—
1215C2×C4C2×H(5,𝔽2)12yes—
1216C2×C4C2×H(5,𝔽2)12yes—
1217C2×C4C2×H(5,𝔽2)14yes—
1218C22—28no—
1219C22—24no—
1220C22—44no—
1221C22—42no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—42no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—42no—
1232C22—44no—
1233C22—42no—
1234C22—44no—
1235C22—816no—
1236C22C22×H(5,𝔽2)11yescharacteristic
1237C22C22×H(5,𝔽2)11yescharacteristic
1238C22H(7,𝔽2)11yescharacteristic
1239C222−1+612yes—
1240C222−1+612yes—
1241C4—22no—
1242C4—24no—
1243C4—22no—
1244C4—44no—
1245C4—44no—
1246C4—42no—
1247C4—42no—
1248C4—44no—
1249C4—41no—
1250C4—44no—
1251C4—44no—
1252C4—44no—
1253C4—42no—
1254C4—44no—
1255C4—42no—
1256C4—42no—
1257C4—44no—
1258C4—42no—
1259C4—44no—
1260C4—42no—
1261C2—44no—
1262C2—82no—
1263C2—84no—
1264C2#6288611yescharacteristic
1265C2#6289211yescharacteristic
1266C2#6297812yes—
1267C2#6304811yescharacteristic
1268C2#6306312yes—
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. #58957C2semidirect
2. #58537C2semidirect
3. #58090C2semidirect
4. #57495C2semidirect
5. #57323C2semidirect
6. #54913C2semidirect
7. #54810C2semidirect
8. #53726C2semidirect
9. #53366C2semidirect
10. #53173C2semidirect
11. #51803C2semidirect
12. #51326C2semidirect
13. #51071C2semidirect
14. #49059C2semidirect
15. #48509C2semidirect
16. #46237C2semidirect
17. #45956C2semidirect
18. #45446C2semidirect
19. #45442C2semidirect
20. #38955C2semidirect
21. #37653C2semidirect
22. #37374C2semidirect
23. #37162C2semidirect
27. C2×#554C22semidirect
31. C22×C22⋊Q8C22semidirect
32. #2863C22semidirect
33. #2862C22semidirect
36. #2849C22semidirect
37. #2848C22semidirect
38. #2841C22semidirect
39. #2838C22semidirect
40. #2838C22semidirect
41. #2833C22semidirect
42. #2830C22semidirect
43. #2829C22semidirect
45. #2817C22semidirect
48. #2811C22semidirect
50. #2808C22semidirect
51. #2806C22semidirect
52. #2806C22semidirect
53. #2806C22semidirect
54. #2805C22semidirect
58. #2801C22semidirect
59. #2793C22semidirect
60. #2790C22semidirect
61. #2788C22semidirect
63. #2777C22semidirect
64. #2772C22semidirect
65. #2770C22semidirect
66. #2769C22semidirect
67. #2764C22semidirect
68. #2764C22semidirect
69. #2762C22semidirect
70. #2759C22semidirect
71. #2759C22semidirect
72. #2759C22semidirect
73. #2757C22semidirect
75. #2754C22semidirect
79. #2747C22semidirect
80. #2745C22semidirect
81. #2743C22semidirect
82. #2740C22semidirect
83. #2738C22semidirect
85. #2737C22semidirect
86. #2736C22semidirect
87. #2734C22semidirect
90. #2729C22semidirect
91. #2729C22semidirect
92. #2729C22semidirect
98. #2720C22semidirect
99. #2718C22semidirect
101. #2717C22semidirect
102. #2716C22semidirect
103. #2713C22semidirect
109. #2702C22semidirect
112. #2700C22semidirect
113. #2698C22semidirect
117. #2692C22semidirect
118. #2690C22semidirect
119. #2689C22semidirect
120. #2689C22semidirect
121. #2687C22semidirect
122. #2687C22semidirect
125. #2684C22semidirect
126. #2684C22semidirect
128. #2683C22semidirect
132. #2677C22semidirect
133. #2677C22semidirect
134. #2677C22semidirect
138. #2674C22semidirect
139. #2665C22semidirect
140. #2663C22semidirect
141. #2654C22semidirect
143. #2651C22semidirect
144. #2650C22semidirect
145. #2640C22semidirect
146. #2634C22semidirect
148. #2625C22semidirect
149. #2621C22semidirect
150. #2618C22semidirect
151. #2614C22semidirect
152. #2606C22semidirect
153. #2605C22semidirect
154. #2594C22semidirect
155. #2594C22semidirect
157. #2586C22semidirect
158. #2585C22semidirect
159. #2578C22semidirect
161. #2562C22semidirect
163. #2556C22semidirect
164. #2551C22semidirect
165. #2546C22semidirect
167. #2539C22semidirect
170. #2529C22semidirect
171. #2527C22semidirect
172. #2526C22semidirect
173. #2523C22semidirect
175. #2521C22semidirect
176. #2503C22semidirect
177. #2492C22semidirect
181. #2481C22semidirect
182. #2480C22semidirect
183. #2480C22semidirect
184. #2478C22semidirect
186. #2474C22semidirect
187. #2473C22semidirect
189. #2467C22semidirect
190. #2463C22semidirect
194. #2452C22semidirect
197. #2442C22semidirect
198. #2440C22semidirect
199. #2434C22semidirect
201. #2420C22semidirect
203. #2417C22semidirect
204. #2415C22semidirect
205. #2413C22semidirect
206. #2411C22semidirect
210. #2378C22semidirect
213. #2344C22semidirect
214. #2336C22semidirect
218. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#589572
#585372
#580902
#574952
#573232
#549132
#548102
#537262
#533662
#531732
#518032
#513262
#510712
#490592
#485092
#462372
#459562
#454462
#454422
#389552
#376532
#373742
#371622