Finite Group Databasebeta

← #8115449

Subgroups — #8115449

Order 512.

4002 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58377C214yesmaximal, complemented
2#58326C214yesmaximal, complemented
3#56254C214yesmaximal, complemented
4#55845C214yesmaximal, complemented
5#55767C214yesmaximal
6#54219C214yesmaximal, complemented
7#53734C214yesmaximal, complemented
8#53605C214yesmaximal, complemented
9#53150C211yesmaximal, characteristic, complemented
10#53147C211yesmaximal, characteristic, complemented
11#53077C211yesmaximal, characteristic, complemented
12#53030C211yesmaximal, characteristic, complemented
13#45238C212yesmaximal, complemented
14#45177C212yesmaximal, complemented
15#42938C212yesmaximal, complemented
16#42863C212yesmaximal, complemented
17#42854C212yesmaximal, complemented
18#42675C212yesmaximal
19#39673C212yesmaximal, complemented
20#39553C212yesmaximal, complemented
21#37897C212yesmaximal, complemented
22#37865C212yesmaximal, complemented
23#37429C212yesmaximal, complemented
24#37395C212yesmaximal, complemented
25#35339C211yesmaximal, characteristic, complemented
26#35319C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic
28C2×#554C2212yes—
29C2×#552C2212yes—
30C2×#541C2211yescharacteristic
31C2×#541C2211yescharacteristic
32#2868C2211yescharacteristic
33#2864C2212yes—
34#2864C2212yes—
35#2859C2211yescharacteristic
36#2857C2212yes—
37#2841C2214yes—
38#2839C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2839C2214yes—
43#2839C2214yes—
44#2837C2214yes—
45#2836C2214yes—
46#2836C2214yes—
47#2833C2214yes—
48#2814C2214yes—
49#2809C2214yes—
50#2805C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2799C2214yes—
56#2798C2214yes—
57#2798C2214yes—
58#2796C2214yes—
59#2794C2214yes—
60#2794C2214yes—
61#2793C2214yes—
62#2793C2214yes—
63#2793C2214yes—
64#2793C2214yes—
65#2793C2214yes—
66#2792C2214yes—
67#2791C2214yes—
68#2791C2214yes—
69#2791C2214yes—
70#2791C2214yes—
71#2791C2214yes—
72#2791C2214yes—
73#2791C2214yes—
74#2790C2214yes—
75#2788C2214yes—
76#2787C2214yes—
77#2777C2214yes—
78#2774C2214yes—
79#2771C2214yes—
80#2768C2214yes—
81#2767C2214yes—
82#2758C2214yes—
83#2755C2214yes—
84#2755C2214yes—
85#2747C2214yes—
86#2747C2214yes—
87#2745C2214yes—
88#2744C2214yes—
89#2744C2214yes—
90#2743C2214yes—
91#2742C2214yes—
92#2741C2214yes—
93#2741C2214yes—
94#2739C2214yes—
95#2739C2214yes—
96#2738C2214yes—
97#2726C2214yes—
98#2725C2214yes—
99#2721C2214yes—
100#2720C2214yes—
101#2719C2214yes—
102#2719C2214yes—
103#2719C2214yes—
104#2719C2214yes—
105#2718C2214yes—
106#2718C2214yes—
107#2704C2214yes—
108#2702C2214yes—
109#2698C2214yes—
110#2698C2214yes—
111#2698C2214yes—
112#2689C2214yes—
113#2667C2214yes—
114#2666C2214yes—
115#2660C2212yes—
116#2655C2214yes—
117#2655C2214yes—
118#2655C2214yes—
119#2655C2212yes—
120#2654C2212yes—
121#2653C2212yes—
122#2652C2212yes—
123#2651C2212yes—
124#2650C2212yes—
125#2650C2214yes—
126#2649C2212yes—
127#2648C2212yes—
128#2647C2212yes—
129#2647C2211yescharacteristic
130#2647C2211yescharacteristic
131#2647C2211yescharacteristic
132#2647C2211yescharacteristic
133#2642C2211yescharacteristic
134#2642C2211yescharacteristic
135#2630C2214yes—
136#2625C2214yes—
137#2621C2212yes—
138#2621C2212yes—
139#2621C2212yes—
140#2597C2214yes—
141#2596C2214yes—
142#2596C2214yes—
143#2594C2214yes—
144#2590C2214yes—
145#2590C2214yes—
146#2588C2214yes—
147#2588C2214yes—
148#2586C2214yes—
149#2585C2214yes—
150#2585C2214yes—
151#2585C2214yes—
152#2585C2214yes—
153#2582C2212yes—
154#2581C2212yes—
155#2577C2214yes—
156#2575C2214yes—
157#2571C2212yes—
158#2570C2214yes—
159#2570C2214yes—
160#2570C2212yes—
161#2569C2214yes—
162#2569C2214yes—
163#2568C2212yes—
164#2565C2212yes—
165#2552C2214yes—
166#2552C2212yes—
167#2550C2212yes—
168#2519C2214yes—
169#2514C2212yes—
170#2511C2212yes—
171#2511C2212yes—
172#2511C2212yes—
173#2506C2214yes—
174#2506C2214yes—
175#2506C2214yes—
176#2503C2212yes—
177#2503C2212yes—
178#2502C2212yes—
179#2499C2212yes—
180#2496C2214yes—
181#2496C2214yes—
182#2489C2214yes—
183#2485C2214yes—
184#2478C2214yes—
185#2478C2214yes—
186#2468C2214yes—
187#2466C2214yes—
188#2453C2212yes—
189#2453C2212yes—
190#2451C2212yes—
191#2451C2212yes—
192#2446C2212yes—
193#2446C2212yes—
194#2446C2212yes—
195#2446C2212yes—
196#2442C2212yes—
197#2442C2212yes—
198#2441C2212yes—
199#2439C2212yes—
200#2438C2214yes—
201#2438C2214yes—
202#2429C2212yes—
203#2429C2212yes—
204#2429C2212yes—
205#2429C2212yes—
206#2423C2212yes—
207#2423C2212yes—
208#2423C2212yes—
209#2421C2212yes—
210#2419C2214yes—
211#2419C2214yes—
212#2417C2212yes—
213#2415C2212yes—
214#2415C2212yes—
215#2415C2212yes—
216#2402C2211yescharacteristic
217#2401C2212yes—
218#2398C2211yescharacteristic
219#2396C2211yescharacteristic
220#2395C2212yes—
221#2392C2211yescharacteristic
222#2362C2212yes—
223#2362C2212yes—
224#2362C2212yes—
225#2360C2212yes—
226#2351C2212yes—
227Q8×C4⋊C4C2212yes—
228#2327C2212yes—
229#2327C2212yes—
230#2327C2212yes—
231#2317C2212yes—
232#2317C2212yes—
233#2316C2212yes—
234#2314C2212yes—
235C4×C4⋊Q8C2212yes—
236#2298C2212yes—
237#2295C2211yescharacteristic
238#2293C2211yescharacteristic
239#2290C2212yes—
240#2285C2211yescharacteristic
241C2×#382C2211yescharacteristic
242C4×#117C2211yescharacteristic
243#554—48no—
244#552—48no—
245#541—44no—
246#541—44no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2311yescharacteristic
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#123C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2311yescharacteristic
281C2×#117C2312yes—
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2312yes—
285C2×#117C2312yes—
286C2×#117C2314yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C42C2311yescharacteristic
290#401C2314yes—
291#401C2312yes—
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#400C2312yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2312yes—
318#400C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2312yes—
334#400C2312yes—
335#400C2311yescharacteristic
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2311yescharacteristic
341#399C2312yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2311yescharacteristic
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2311yescharacteristic
402#397C2314yes—
403#397C2314yes—
404#397C2312yes—
405#397C2312yes—
406#397C2312yes—
407#397C2312yes—
408#397C2312yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2312yes—
416#396C2312yes—
417#396C2312yes—
418#396C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2311yescharacteristic
426#394C2314yes—
427#394C2312yes—
428#394C2314yes—
429#394C2314yes—
430#394C2312yes—
431#394C2311yescharacteristic
432#394C2312yes—
433#394C2312yes—
434#393C2312yes—
435#393C2314yes—
436#393C2311yescharacteristic
437#392C2311yescharacteristic
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#390C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2312yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2312yes—
514#388C2312yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2314yes—
527#388C2312yes—
528#388C2314yes—
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#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#386C2314yes—
597#386C2312yes—
598#386C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#384C2312yes—
611#384C2312yes—
612#384C2314yes—
613#384C2312yes—
614#384C2314yes—
615#384C2314yes—
616#384C2314yes—
617#384C2311yescharacteristic
618#384C2311yescharacteristic
619#384C2314yes—
620#383C2314yes—
621#382C2311yescharacteristic
622#382C2311yescharacteristic
623#382C2312yes—
624#382C2312yes—
625#382C2314yes—
626#382C2314yes—
627#382C2312yes—
628#382C2314yes—
629#382C2312yes—
630#382C2312yes—
631#382C2314yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672#376C2311yescharacteristic
673#376C2312yes—
674#376C2311yescharacteristic
675C2×#95C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C22×Q8C2412yes—
679C22×Q8C2412yes—
680C22×Q8C2411yescharacteristic
681C22×Q8C2414yes—
682C22×D4C2412yes—
683C22×D4C2411yescharacteristic
684C23×C4C2412yes—
685C23×C4C2411yescharacteristic
686C23×C4C2414yes—
687C23×C4C2412yes—
688C23×C4C2414yes—
689C4⋊Q8—28no—
690C4⋊Q8—44no—
691C4⋊Q8—44no—
692C4⋊Q8—42no—
693C4⋊Q8—42no—
694#126—48no—
695#126—48no—
696#126—48no—
697#125—42no—
698#125—42no—
699#125—44no—
700#125—48no—
701#125—48no—
702#125—48no—
703#125—48no—
704#123—48no—
705C22⋊Q8—28no—
706C22⋊Q8—28no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709C22⋊Q8—44no—
710C22⋊Q8—44no—
711C22⋊Q8—44no—
712C22⋊Q8—44no—
713C4×Q8—42no—
714C4×Q8—44no—
715C4×Q8—44no—
716C4×Q8—44no—
717C4×Q8—44no—
718C4×Q8—44no—
719C4×Q8—44no—
720C4×D4—28no—
721C4×D4—42no—
722C4×D4—48no—
723#117—24no—
724#117—28no—
725#117—42no—
726#117—48no—
727#117—44no—
728#117—44no—
729C2×C4⋊C4—28no—
730C2×C4⋊C4—44no—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C42—24no—
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838C2×C42C2412yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2411yescharacteristic
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2412yes—
859#95C2412yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2412yes—
864#95C2412yes—
865#95C2412yes—
866#95C2412yes—
867#95C2412yes—
868#95C2412yes—
869#95C2414yes—
870#95C2414yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2414yes—
885#95C2411yescharacteristic
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2412yes—
890#95C2414yes—
891#95C2411yescharacteristic
892#95C2412yes—
893#95C2412yes—
894#95C2411yescharacteristic
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2411yescharacteristic
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—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936C24C2512yes—
937C24C2511yescharacteristic
938C2×Q8—24no—
939C2×Q8—24no—
940C2×Q8—24no—
941C2×Q8—24no—
942C2×Q8—24no—
943C2×Q8—24no—
944C2×Q8—41no—
945C2×Q8—42no—
946C2×Q8—44no—
947C2×Q8—44no—
948C2×Q8—44no—
949C2×D4—24no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—41no—
953C2×D4—42no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—28no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4H(5,𝔽2)14yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2512yes—
976C22×C4C2511yescharacteristic
977C22×C4C2511yescharacteristic
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2511yescharacteristic
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—42no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—42no—
1039C4⋊C4—44no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—41no—
1045C4⋊C4—44no—
1046C4⋊C4—41no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—44no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—42no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C42—22no—
1093C42—22no—
1094C42—24no—
1095C42—24no—
1096C42—22no—
1097C42—24no—
1098C42—22no—
1099C42—22no—
1100C42—24no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—44no—
1106C42—44no—
1107C42—44no—
1108C42—44no—
1109C42—44no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C422−1+414yes—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23C2×H(5,𝔽2)12yes—
1128C23C2611yescharacteristic
1129Q8—48no—
1130Q8—48no—
1131Q8—82no—
1132Q8—164no—
1133D4—48no—
1134D4—82no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—28no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—48no—
1203C2×C4—84no—
1204C2×C4—88no—
1205C2×C4—164no—
1206C2×C4C2×H(5,𝔽2)12yes—
1207C2×C4C2×H(5,𝔽2)12yes—
1208C2×C4C2×2−1+414yes—
1209C2×C4C2×2−1+412yes—
1210C2×C4#58512yes—
1211C22—22no—
1212C22—24no—
1213C22—42no—
1214C22—41no—
1215C22—41no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22C22×H(5,𝔽2)11yescharacteristic
1224C22C22×2−1+411yescharacteristic
1225C22C2×#58511yescharacteristic
1226C222−1+612yes—
1227C222−1+612yes—
1228C4—22no—
1229C4—24no—
1230C4—42no—
1231C4—44no—
1232C4—44no—
1233C4—42no—
1234C4—42no—
1235C4—44no—
1236C4—44no—
1237C4—44no—
1238C4—44no—
1239C4—42no—
1240C4—42no—
1241C4—42no—
1242C4—42no—
1243C4—42no—
1244C4—42no—
1245C4—41no—
1246C4—41no—
1247C4—44no—
1248C4—44no—
1249C4—41no—
1250C4—42no—
1251C4—41no—
1252C4#355914yes—
1253C2—42no—
1254C2—82no—
1255C2C2×#355911yescharacteristic
1256C2#6288712yes—
1257C2#6288912yes—
1258C2#6289011yescharacteristic
1259C2#6289011yescharacteristic
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. #58377C2semidirect
2. #58326C2semidirect
3. #56254C2semidirect
4. #55845C2semidirect
6. #54219C2semidirect
7. #53734C2semidirect
8. #53605C2semidirect
9. #53150C2semidirect
10. #53147C2semidirect
11. #53077C2semidirect
12. #53030C2semidirect
13. #45238C2semidirect
14. #45177C2semidirect
15. #42938C2semidirect
16. #42863C2semidirect
17. #42854C2semidirect
19. #39673C2semidirect
20. #39553C2semidirect
21. #37897C2semidirect
22. #37865C2semidirect
23. #37429C2semidirect
24. #37395C2semidirect
25. #35339C2semidirect
26. #35319C2semidirect

Maximal subgroups

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

subgroupindex
#583772
#583262
#562542
#558452
#557672
#542192
#537342
#536052
#531502
#531472
#530772
#530302
#452382
#451772
#429382
#428632
#428542
#426752
#396732
#395532
#378972
#378652
#374292
#373952
#353392
#353192
#346402