Finite Group Databasebeta

← #8095586

Subgroups — #8095586

Order 512.

3839 conjugacy classes of subgroups.

The subgroup lattice has 1239 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53150C211yesmaximal, characteristic, complemented
2#53122C212yesmaximal
3#53121C211yesmaximal, characteristic, complemented
4#53075C211yesmaximal, characteristic, complemented
5#53030C211yesmaximal, characteristic, complemented
6#53028C212yesmaximal, complemented
7#52906C214yesmaximal, complemented
8#52882C214yesmaximal, complemented
9#52680C214yesmaximal, complemented
10#52660C214yesmaximal, complemented
11#46308C214yesmaximal
12#46245C214yesmaximal, complemented
13#46079C212yesmaximal, complemented
14#46069C212yesmaximal, complemented
15#45911C214yesmaximal, complemented
16#45859C214yesmaximal, complemented
17#45684C212yesmaximal, complemented
18#45671C212yesmaximal, complemented
19#35653C212yesmaximal, complemented
20#35652C212yesmaximal, complemented
21#35579C212yesmaximal, complemented
22#35336C211yesmaximal, characteristic, complemented
23#35323C211yesmaximal, characteristic, complemented
24#35204C212yesmaximal, complemented
25#35184C212yesmaximal, complemented
26#34920C212yesmaximal, complemented
27#34881C211yesmaximal, characteristic
28#2865C2214yes—
29#2864C2214yes—
30#2863C2214yes—
31#2863C2212yes—
32#2861C2214yes—
33#2859C2211yescharacteristic
34#2859C2211yescharacteristic
35#2857C2211yescharacteristic
36#2851C2212yes—
37#2851C2211yescharacteristic
38#2843C2214yes—
39#2841C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2839C2214yes—
43#2839C2214yes—
44#2839C2214yes—
45#2838C2214yes—
46#2838C2214yes—
47#2837C2214yes—
48#2836C2214yes—
49#2836C2214yes—
50#2836C2214yes—
51#2836C2214yes—
52#2836C2214yes—
53#2834C2214yes—
54#2833C2214yes—
55#2827C2214yes—
56#2822C2214yes—
57#2820C2214yes—
58#2802C2214yes—
59#2799C2214yes—
60#2793C2214yes—
61#2791C2214yes—
62#2786C2214yes—
63#2786C2214yes—
64#2777C2214yes—
65#2777C2214yes—
66#2777C2214yes—
67#2776C2214yes—
68#2776C2214yes—
69#2774C2214yes—
70#2773C2214yes—
71#2772C2214yes—
72#2771C2214yes—
73#2771C2214yes—
74#2770C2214yes—
75#2770C2214yes—
76#2769C2214yes—
77#2769C2214yes—
78#2768C2214yes—
79#2766C2214yes—
80#2766C2214yes—
81#2762C2214yes—
82#2762C2214yes—
83#2758C2214yes—
84#2758C2214yes—
85#2755C2214yes—
86#2743C2214yes—
87#2739C2214yes—
88#2739C2214yes—
89#2738C2214yes—
90#2730C2214yes—
91#2726C2214yes—
92#2721C2214yes—
93#2719C2214yes—
94#2717C2214yes—
95#2704C2214yes—
96#2694C2214yes—
97#2689C2214yes—
98#2655C2214yes—
99#2654C2214yes—
100#2654C2214yes—
101#2654C2214yes—
102#2647C2211yescharacteristic
103#2647C2211yescharacteristic
104#2647C2211yescharacteristic
105#2642C2211yescharacteristic
106#2629C2212yes—
107#2625C2212yes—
108#2596C2214yes—
109#2596C2214yes—
110#2596C2214yes—
111#2595C2214yes—
112#2594C2214yes—
113#2593C2212yes—
114#2590C2214yes—
115#2590C2214yes—
116#2590C2214yes—
117#2590C2214yes—
118#2590C2214yes—
119#2588C2214yes—
120#2588C2214yes—
121#2587C2214yes—
122#2587C2214yes—
123#2587C2214yes—
124#2585C2212yes—
125#2585C2214yes—
126#2585C2214yes—
127#2584C2212yes—
128#2581C2212yes—
129#2577C2214yes—
130#2577C2214yes—
131#2575C2214yes—
132#2573C2212yes—
133#2573C2214yes—
134#2570C2212yes—
135#2568C2212yes—
136#2565C2212yes—
137#2556C2214yes—
138#2554C2212yes—
139#2552C2212yes—
140#2552C2212yes—
141#2552C2212yes—
142#2550C2212yes—
143#2550C2212yes—
144#2547C2212yes—
145#2538C2212yes—
146#2533C2214yes—
147#2533C2214yes—
148#2531C2214yes—
149#2530C2214yes—
150#2529C2214yes—
151#2528C2214yes—
152#2528C2214yes—
153#2526C2214yes—
154#2525C2212yes—
155#2525C2214yes—
156#2525C2214yes—
157#2525C2214yes—
158#2522C2214yes—
159#2520C2214yes—
160#2516C2212yes—
161#2516C2214yes—
162#2514C2212yes—
163#2511C2212yes—
164#2511C2212yes—
165#2509C2214yes—
166#2509C2212yes—
167#2508C2212yes—
168#2508C2212yes—
169#2507C2212yes—
170#2507C2214yes—
171#2506C2212yes—
172#2503C2212yes—
173#2499C2212yes—
174#2495C2212yes—
175#2495C2212yes—
176#2495C2212yes—
177#2494C2214yes—
178#2494C2212yes—
179#2494C2212yes—
180#2489C2212yes—
181#2489C2212yes—
182#2489C2212yes—
183#2487C2212yes—
184#2485C2212yes—
185#2469C2212yes—
186#2462C2214yes—
187#2462C2214yes—
188#2458C2212yes—
189#2453C2214yes—
190#2453C2212yes—
191#2453C2212yes—
192#2451C2212yes—
193#2448C2214yes—
194#2446C2212yes—
195#2442C2212yes—
196#2442C2212yes—
197#2441C2212yes—
198#2441C2212yes—
199#2441C2212yes—
200#2440C2212yes—
201#2429C2212yes—
202#2423C2212yes—
203#2423C2212yes—
204#2423C2212yes—
205#2423C2214yes—
206#2417C2212yes—
207#2415C2212yes—
208#2402C2211yescharacteristic
209#2402C2214yes—
210#2399C2214yes—
211#2398C2211yescharacteristic
212#2396C2211yescharacteristic
213#2392C2211yescharacteristic
214#2382C2214yes—
215#2382C2214yes—
216#2379C2214yes—
217#2378C2214yes—
218#2330C2212yes—
219#2330C2211yescharacteristic
220#2327C2211yescharacteristic
221#2323C2212yes—
222#2323C2212yes—
223#2323C2212yes—
224#2314C2211yescharacteristic
225#2314C2211yescharacteristic
226#2314C2212yes—
227C4×C4⋊Q8C2212yes—
228C4×#125C2212yes—
229C4×#125C2212yes—
230C4×#125C2214yes—
231C4×#126C2212yes—
232C4×#123C2212yes—
233#2298C2212yes—
234#2295C2214yes—
235#2295C2212yes—
236#2295C2212yes—
237#2293C2211yescharacteristic
238#2293C2212yes—
239#2274C2212yes—
240C42×Q8C2211yescharacteristic
241C42×Q8C2212yes—
242C4×#117C2211yescharacteristic
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2311yescharacteristic
245C2×#126C2312yes—
246C2×#125C2314yes—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#125C2311yescharacteristic
251C2×#125C2312yes—
252C2×#125C2314yes—
253C2×#124C2314yes—
254C2×#123C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2314yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2312yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×#117C2311yescharacteristic
268C2×#117C2312yes—
269C2×#117C2311yescharacteristic
270C2×#117C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C42C2311yescharacteristic
273#401C2314yes—
274#401C2314yes—
275#401C2314yes—
276#400C2312yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2312yes—
287#400C2312yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2311yescharacteristic
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2311yescharacteristic
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2311yescharacteristic
360#398C2312yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2311yescharacteristic
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2312yes—
385#396C2314yes—
386#396C2314yes—
387#396C2312yes—
388#396C2314yes—
389#396C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2311yescharacteristic
396#395C2314yes—
397#394C2312yes—
398#394C2314yes—
399#394C2311yescharacteristic
400#394C2314yes—
401#394C2312yes—
402#393C2311yescharacteristic
403#393C2312yes—
404#392C2311yescharacteristic
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#390C2312yes—
421#390C2312yes—
422#390C2314yes—
423#390C2312yes—
424#389C2312yes—
425#389C2314yes—
426#389C2312yes—
427#389C2314yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2314yes—
433#389C2312yes—
434#389C2314yes—
435#389C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#388C2312yes—
473#388C2312yes—
474#388C2312yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2312yes—
480#388C2314yes—
481#388C2312yes—
482#388C2312yes—
483#388C2312yes—
484#388C2314yes—
485#388C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2312yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2314yes—
509#388C2314yes—
510#388C2312yes—
511#387C2312yes—
512#387C2312yes—
513#387C2312yes—
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#387C2312yes—
531#387C2314yes—
532#387C2312yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
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#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#386C2314yes—
579#386C2312yes—
580#386C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2312yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#384C2312yes—
590#384C2311yescharacteristic
591#384C2311yescharacteristic
592#384C2312yes—
593#384C2312yes—
594#384C2311yescharacteristic
595#384C2314yes—
596#383C2312yes—
597#383C2314yes—
598#383C2314yes—
599#383C2314yes—
600#383C2314yes—
601#383C2314yes—
602#382C2312yes—
603#382C2312yes—
604#382C2314yes—
605#382C2314yes—
606#382C2314yes—
607#382C2311yescharacteristic
608#382C2312yes—
609#382C2311yescharacteristic
610#382C2314yes—
611#382C2311yescharacteristic
612#382C2314yes—
613#381C2314yes—
614#381C2312yes—
615#381C2314yes—
616#380C2312yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2314yes—
621#380C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2314yes—
626#380C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666#376C2311yescharacteristic
667#376C2311yescharacteristic
668#376C2314yes—
669#376C2314yes—
670C43C2311yescharacteristic
671C43C2311yescharacteristic
672C43C2312yes—
673C43C2314yes—
674C22×Q8C2412yes—
675C22×Q8C2414yes—
676C22×Q8C2411yescharacteristic
677C22×D4C2412yes—
678C22×D4C2411yescharacteristic
679C23×C4C2412yes—
680C23×C4C2411yescharacteristic
681C23×C4C2414yes—
682C23×C4C2412yes—
683C4⋊Q8—44no—
684C4⋊Q8—42no—
685#126—44no—
686#125—44no—
687#125—42no—
688#125—44no—
689#125—44no—
690#125—48no—
691#125—48no—
692#125—48no—
693#124—48no—
694#123—44no—
695C22⋊Q8—48no—
696C22⋊Q8—44no—
697C22⋊Q8—44no—
698C22⋊Q8—44no—
699C4×Q8—28no—
700C4×Q8—42no—
701C4×Q8—44no—
702C4×Q8—44no—
703C4×Q8—48no—
704C4×Q8—44no—
705C4×D4—42no—
706C4×D4—44no—
707#117—24no—
708#117—28no—
709#117—42no—
710#117—44no—
711C2×C4⋊C4—44no—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C42—42no—
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2412yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838#95C2412yes—
839#95C2412yes—
840#95C2412yes—
841#95C2412yes—
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#95C2412yes—
855#95C2412yes—
856#95C2412yes—
857#95C2412yes—
858#95C2412yes—
859#95C2412yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
866#95C2414yes—
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2411yescharacteristic
883#95C2412yes—
884#95C2414yes—
885#95C2412yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2412yes—
890#95C2414yes—
891#95C2412yes—
892#95C2411yescharacteristic
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—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919C24C2512yes—
920C24C2511yescharacteristic
921C2×Q8—24no—
922C2×Q8—24no—
923C2×Q8—24no—
924C2×Q8—28no—
925C2×Q8—41no—
926C2×Q8—42no—
927C2×Q8—44no—
928C2×Q8—44no—
929C2×D4—24no—
930C2×D4—42no—
931C2×D4—41no—
932C2×D4—42no—
933C2×D4—42no—
934C22×C4—24no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4C2512yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2514yes—
950C22×C4C2514yes—
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2512yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2511yescharacteristic
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2511yescharacteristic
964C22×C4C2512yes—
965C22×C4C2514yes—
966C22×C4C2511yescharacteristic
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2511yescharacteristic
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—24no—
975C4⋊C4—28no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—44no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—44no—
992C4⋊C4—42no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—42no—
1000C4⋊C4—44no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—42no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—42no—
1007C4⋊C4—44no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
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—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—42no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C22⋊C4—24no—
1039C22⋊C4—24no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—44no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—44no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—44no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C42—22no—
1068C42—24no—
1069C42—28no—
1070C42—22no—
1071C42—22no—
1072C42—22no—
1073C42—22no—
1074C42—24no—
1075C42—24no—
1076C42—24no—
1077C42—28no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—44no—
1082C42—42no—
1083C42—44no—
1084C42—44no—
1085C42—42no—
1086C42—44no—
1087C42—42no—
1088C42—44no—
1089C42—42no—
1090C42—44no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—42no—
1095C422−1+414yes—
1096C23—21no—
1097C23—22no—
1098C23—22no—
1099C23—21no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—21no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23C2611yescharacteristic
1109Q8—44no—
1110Q8—48no—
1111Q8—88no—
1112D4—84no—
1113D4—82no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—44no—
1181C2×C4—48no—
1182C2×C4—84no—
1183C2×C4—164no—
1184C2×C4C2×2−1+414yes—
1185C2×C4C2×2−1+412yes—
1186C2×C4#58514yes—
1187C2×C4#58512yes—
1188C2×C4#58512yes—
1189C22—42no—
1190C22—41no—
1191C22—42no—
1192C22—41no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—41no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22C22×2−1+411yescharacteristic
1202C22C2×#58511yescharacteristic
1203C22C2×#58512yes—
1204C22C2×#58511yescharacteristic
1205C222−1+612yes—
1206C4—24no—
1207C4—24no—
1208C4—44no—
1209C4—41no—
1210C4—44no—
1211C4—41no—
1212C4—42no—
1213C4—42no—
1214C4—41no—
1215C4—44no—
1216C4—41no—
1217C4—42no—
1218C4—42no—
1219C4—42no—
1220C4—44no—
1221C4—44no—
1222C4—44no—
1223C4—41no—
1224C4—42no—
1225C4—44no—
1226C4—42no—
1227C4—42no—
1228C4—42no—
1229C4—44no—
1230C4#353114yes—
1231C2—82no—
1232C2—81no—
1233C2C2×#353111yescharacteristic
1234C2#6284011yescharacteristic
1235C2#6289011yescharacteristic
1236C2#6294012yes—
1237C2#6295612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53150C2semidirect
3. #53121C2semidirect
4. #53075C2semidirect
5. #53030C2semidirect
6. #53028C2semidirect
7. #52906C2semidirect
8. #52882C2semidirect
9. #52680C2semidirect
10. #52660C2semidirect
12. #46245C2semidirect
13. #46079C2semidirect
14. #46069C2semidirect
15. #45911C2semidirect
16. #45859C2semidirect
17. #45684C2semidirect
18. #45671C2semidirect
19. #35653C2semidirect
20. #35652C2semidirect
21. #35579C2semidirect
22. #35336C2semidirect
23. #35323C2semidirect
24. #35204C2semidirect
25. #35184C2semidirect
26. #34920C2semidirect

Maximal subgroups

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

subgroupindex
#531502
#531222
#531212
#530752
#530302
#530282
#529062
#528822
#526802
#526602
#463082
#462452
#460792
#460692
#459112
#458592
#456842
#456712
#356532
#356522
#355792
#353362
#353232
#352042
#351842
#349202
#348812