Finite Group Databasebeta

← #8322109

Subgroups — #8322109

Order 512.

4316 conjugacy classes of subgroups.

The subgroup lattice has 1401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59281C212yesmaximal, complemented
2#59253C212yesmaximal, complemented
3#59031C212yesmaximal, complemented
4#58750C212yesmaximal, complemented
5#56121C214yesmaximal, complemented
6#56121C214yesmaximal, complemented
7#54337C214yesmaximal, complemented
8#53975C212yesmaximal, complemented
9#53034C212yesmaximal, complemented
10#52754C212yesmaximal, complemented
11#52246C211yesmaximal, characteristic, complemented
12#51044C214yesmaximal, complemented
13#49162C214yesmaximal, complemented
14#45626C212yesmaximal, complemented
15#45231C212yesmaximal, complemented
16#43727C212yesmaximal, complemented
17#42958C211yesmaximal, characteristic, complemented
18#42817C211yesmaximal, characteristic, complemented
19#42747C212yesmaximal, complemented
20#42543C212yesmaximal, complemented
21#40654C214yesmaximal, complemented
22#39880C212yesmaximal, complemented
23#39512C212yesmaximal, complemented
24#38100C212yesmaximal, complemented
25#37750C212yesmaximal, complemented
26#37565C211yesmaximal, characteristic, complemented
27#36031C211yesmaximal, characteristic, complemented
28#35693C211yesmaximal, characteristic
29#35619C211yesmaximal, characteristic, complemented
30C2×#554C2211yescharacteristic
31C2×#547C2211yescharacteristic
32C2×#536C2211yescharacteristic
33C2×#529C2212yes—
34C2×#520C2211yescharacteristic
35#2857C2212yes—
36#2851C2212yes—
37#2843C2212yes—
38#2843C2214yes—
39#2843C2212yes—
40#2841C2212yes—
41#2839C2214yes—
42#2839C2214yes—
43#2839C2214yes—
44#2835C2214yes—
45#2833C2214yes—
46#2833C2212yes—
47#2833C2214yes—
48#2811C2212yes—
49#2810C2214yes—
50#2805C2214yes—
51#2799C2212yes—
52#2799C2214yes—
53#2799C2214yes—
54#2794C2211yescharacteristic
55#2791C2214yes—
56#2791C2214yes—
57#2790C2212yes—
58#2790C2214yes—
59#2789C2211yescharacteristic
60#2788C2214yes—
61#2788C2214yes—
62#2782C2211yescharacteristic
63#2776C2214yes—
64#2776C2214yes—
65#2776C2214yes—
66#2776C2214yes—
67#2764C2214yes—
68#2764C2214yes—
69#2764C2212yes—
70#2764C2214yes—
71#2764C2214yes—
72#2760C2214yes—
73#2760C2212yes—
74#2758C2214yes—
75#2758C2214yes—
76#2758C2214yes—
77#2755C2214yes—
78#2755C2214yes—
79#2750C2214yes—
80#2750C2214yes—
81#2750C2214yes—
82#2747C2214yes—
83#2747C2214yes—
84#2747C2214yes—
85#2746C2212yes—
86#2745C2214yes—
87#2744C2212yes—
88#2744C2214yes—
89#2743C2214yes—
90#2739C2212yes—
91#2739C2214yes—
92#2739C2214yes—
93#2698C2214yes—
94#2695C2214yes—
95#2695C2214yes—
96#2693C2212yes—
97#2693C2214yes—
98#2689C2214yes—
99#2689C2214yes—
100#2689C2214yes—
101#2687C2214yes—
102#2687C2212yes—
103#2687C2214yes—
104#2687C2214yes—
105#2687C2214yes—
106#2680C2211yescharacteristic
107#2680C2214yes—
108#2667C2214yes—
109#2665C2214yes—
110#2665C2214yes—
111#2665C2214yes—
112#2665C2214yes—
113#2647C2212yes—
114#2646C2214yes—
115#2645C2214yes—
116#2642C2212yes—
117#2638C2214yes—
118#2638C2212yes—
119#2638C2214yes—
120#2629C2212yes—
121#2628C2211yescharacteristic
122#2628C2211yescharacteristic
123#2627C2214yes—
124#2627C2212yes—
125#2612C2212yes—
126#2612C2214yes—
127#2612C2212yes—
128#2607C2212yes—
129#2583C2212yes—
130#2581C2212yes—
131#2581C2211yescharacteristic
132#2579C2214yes—
133#2572C2214yes—
134#2572C2214yes—
135#2572C2212yes—
136#2570C2212yes—
137#2570C2212yes—
138#2570C2212yes—
139#2568C2212yes—
140#2568C2211yescharacteristic
141#2567C2211yescharacteristic
142#2565C2212yes—
143#2564C2212yes—
144#2563C2212yes—
145#2552C2212yes—
146#2550C2212yes—
147#2550C2212yes—
148#2536C2211yescharacteristic
149#2527C2214yes—
150#2527C2214yes—
151#2527C2214yes—
152#2527C2214yes—
153#2527C2214yes—
154#2514C2212yes—
155#2514C2212yes—
156#2514C2212yes—
157#2514C2212yes—
158#2511C2212yes—
159#2505C2214yes—
160#2505C2214yes—
161#2503C2212yes—
162#2503C2212yes—
163#2503C2212yes—
164#2503C2212yes—
165#2502C2212yes—
166#2502C2214yes—
167#2499C2212yes—
168#2499C2212yes—
169#2499C2214yes—
170#2493C2214yes—
171#2493C2214yes—
172#2493C2214yes—
173#2493C2214yes—
174#2493C2214yes—
175#2493C2214yes—
176#2492C2212yes—
177#2492C2212yes—
178#2489C2212yes—
179#2487C2212yes—
180#2486C2214yes—
181#2484C2214yes—
182#2470C2214yes—
183#2470C2214yes—
184#2470C2214yes—
185#2457C2214yes—
186#2457C2214yes—
187#2455C2214yes—
188#2453C2212yes—
189#2451C2212yes—
190#2451C2212yes—
191#2450C2214yes—
192#2450C2214yes—
193#2450C2214yes—
194#2447C2212yes—
195#2447C2212yes—
196#2447C2212yes—
197#2446C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2442C2212yes—
201#2442C2212yes—
202#2440C2212yes—
203#2439C2212yes—
204#2438C2214yes—
205#2438C2214yes—
206#2438C2214yes—
207#2429C2212yes—
208#2427C2212yes—
209#2422C2212yes—
210#2421C2212yes—
211#2420C2212yes—
212#2419C2214yes—
213#2419C2214yes—
214#2419C2214yes—
215#2419C2214yes—
216#2419C2214yes—
217#2417C2212yes—
218#2409C2212yes—
219#2407C2212yes—
220#2406C2212yes—
221#2406C2214yes—
222#2402C2212yes—
223#2401C2212yes—
224#2396C2211yescharacteristic
225C2×#400C2212yes—
226#2392C2211yescharacteristic
227#2388C2212yes—
228#2378C2214yes—
229#2361C2212yes—
230#2360C2212yes—
231#2360C2212yes—
232#2357C2211yescharacteristic
233#2357C2212yes—
234#2356C2212yes—
235#2353C2214yes—
236#2353C2214yes—
237#2352C2212yes—
238#2349C2211yescharacteristic
239#2349C2212yes—
240D4×C4⋊C4C2212yes—
241Q8×C22⋊C4C2212yes—
242#2339C2212yes—
243#2339C2214yes—
244#2331C2212yes—
245#2326C2212yes—
246#2322C2214yes—
247#2317C2211yescharacteristic
248#2313C2214yes—
249#2310C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×#123C2212yes—
252C4×#123C2212yes—
253#2297C2211yescharacteristic
254C2×#391C2211yescharacteristic
255C2×#389C2212yes—
256#2290C2212yes—
257#2285C2211yescharacteristic
258#2283C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2312yes—
261C23×Q8C2311yescharacteristic
262#554—44no—
263#547—44no—
264#536—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269#529—48no—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#124C2312yes—
274C2×#123C2314yes—
275C2×#123C2312yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2312yes—
279C2×#123C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×#121C2312yes—
291#520—44no—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2311yescharacteristic
311C2×#117C2312yes—
312C2×#117C2314yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2312yes—
319C22×C42C2311yescharacteristic
320C22×C42C2312yes—
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#401C2312yes—
325#401C2314yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2311yescharacteristic
368#400C2314yes—
369#400C2312yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#399C2312yes—
374#399C2312yes—
375#399C2311yescharacteristic
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2311yescharacteristic
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2312yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2312yes—
405#398C2312yes—
406#398C2312yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2311yescharacteristic
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2312yes—
417#397C2312yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2312yes—
426#396C2312yes—
427#396C2312yes—
428#396C2314yes—
429#396C2314yes—
430#395C2312yes—
431#395C2312yes—
432#395C2312yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2312yes—
440#395C2312yes—
441#395C2314yes—
442#395C2311yescharacteristic
443#394C2311yescharacteristic
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2312yes—
449#394C2312yes—
450#393C2314yes—
451#393C2314yes—
452#393C2311yescharacteristic
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2312yes—
457#393C2312yes—
458#393C2314yes—
459#392C2311yescharacteristic
460#392C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2314yes—
482#391C2312yes—
483#391C2314yes—
484#391C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2314yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#390C2312yes—
493#390C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#388C2312yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
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#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2312yes—
590#386C2314yes—
591#386C2312yes—
592#386C2314yes—
593#386C2312yes—
594#386C2314yes—
595#386C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#385C2312yes—
623#385C2312yes—
624#384C2312yes—
625#384C2312yes—
626#384C2312yes—
627#384C2311yescharacteristic
628#384C2311yescharacteristic
629#384C2314yes—
630#383C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2311yescharacteristic
640#382C2312yes—
641#382C2312yes—
642#382C2311yescharacteristic
643#382C2312yes—
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#382C2314yes—
647#381C2312yes—
648#381C2312yes—
649#381C2314yes—
650#381C2314yes—
651#381C2312yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2314yes—
660#381C2312yes—
661#381C2314yes—
662#381C2314yes—
663#381C2314yes—
664#381C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2312yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2312yes—
682#380C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709#376C2312yes—
710#376C2314yes—
711#376C2314yes—
712C2×#95C2312yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—44no—
720C2×#41—48no—
721C2×#41—42no—
722C22×Q8—24no—
723C22×Q8—42no—
724C22×Q8—42no—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2412yes—
731C22×Q8C2414yes—
732C22×D4C2412yes—
733C22×D4C2414yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2411yescharacteristic
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C4⋊Q8—44no—
752C4⋊Q8—42no—
753C4⋊Q8—42no—
754C4⋊Q8—44no—
755#126—48no—
756#125—44no—
757#125—44no—
758#124—28no—
759#123—44no—
760#123—48no—
761#123—44no—
762#123—48no—
763#123—48no—
764#123—48no—
765C22⋊Q8—48no—
766C22⋊Q8—44no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769C22⋊Q8—44no—
770C22⋊Q8—48no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—44no—
775#121—28no—
776C4×Q8—42no—
777C4×Q8—44no—
778C4×Q8—42no—
779C4×Q8—42no—
780C4×Q8—44no—
781C4×D4—24no—
782C4×D4—24no—
783C4×D4—28no—
784C4×D4—28no—
785C4×D4—44no—
786C4×D4—42no—
787C4×D4—48no—
788C4×D4—48no—
789C4×D4—44no—
790C4×D4—44no—
791C4×D4—48no—
792#117—42no—
793#117—42no—
794#117—44no—
795#117—48no—
796#117—42no—
797C2×C4⋊C4—44no—
798C2×C4⋊C4—42no—
799C2×C4⋊C4—44no—
800C2×C4⋊C4—48no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4—44no—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C42—24no—
901C2×C42—44no—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922#95C2414yes—
923#95C2412yes—
924#95C2412yes—
925#95C2411yescharacteristic
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2411yescharacteristic
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2411yescharacteristic
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2411yescharacteristic
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2512yes—
1009C24C2511yescharacteristic
1010C24C2512yes—
1011#41—416no—
1012#41—816no—
1013C2×Q8—22no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—22no—
1020C2×Q8—41no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—42no—
1025C2×Q8—44no—
1026C2×Q8—42no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—88no—
1032C2×D4—24no—
1033C2×D4—28no—
1034C2×D4—24no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—28no—
1038C2×D4—24no—
1039C2×D4—22no—
1040C2×D4—22no—
1041C2×D4—41no—
1042C2×D4—42no—
1043C2×D4—42no—
1044C2×D4—44no—
1045C2×D4H(5,𝔽2)14yes—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—28no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—28no—
1056C22×C4—28no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—42no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—42no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C42−1+414yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2514yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C4⋊C4—22no—
1112C4⋊C4—22no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—41no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—41no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—42no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—41no—
1196C22⋊C4—41no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C42—24no—
1209C42—24no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—42no—
1218C42—42no—
1219C42—44no—
1220C42—44no—
1221C42—42no—
1222C42—44no—
1223C42—42no—
1224C42—42no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C23—21no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—21no—
1235C23—22no—
1236C23—24no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—24no—
1241C23—22no—
1242C23C2×H(5,𝔽2)14yes—
1243C23C2×2−1+412yes—
1244C23#58514yes—
1245C23C2611yescharacteristic
1246Q8—48no—
1247Q8—44no—
1248Q8—84no—
1249Q8—82no—
1250Q8—84no—
1251Q8—162no—
1252Q8—164no—
1253D4—28no—
1254D4—48no—
1255D4—48no—
1256D4—416no—
1257D4—44no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—28no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—48no—
1328C2×C4—48no—
1329C2×C4—84no—
1330C2×C4—84no—
1331C2×C4—88no—
1332C2×C4—84no—
1333C2×C4—88no—
1334C2×C4—84no—
1335C2×C4—84no—
1336C2×C4—88no—
1337C2×C4—84no—
1338C2×C4—162no—
1339C2×C4—164no—
1340C2×C4C2×H(5,𝔽2)12yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4#58512yes—
1344C22—22no—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—24no—
1349C22—24no—
1350C22—24no—
1351C22—24no—
1352C22—42no—
1353C22—41no—
1354C22—42no—
1355C22—41no—
1356C22—42no—
1357C22—44no—
1358C22—44no—
1359C22—42no—
1360C22—42no—
1361C22C22×H(5,𝔽2)11yescharacteristic
1362C22C22×2−1+411yescharacteristic
1363C22C2×#58511yescharacteristic
1364C22C2×#58512yes—
1365C222−1+612yes—
1366C4—22no—
1367C4—42no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—44no—
1376C4—42no—
1377C4—41no—
1378C4—42no—
1379C4—42no—
1380C4—44no—
1381C4—41no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—44no—
1388C4—42no—
1389C4—44no—
1390C4—42no—
1391C4#353514yes—
1392C2—42no—
1393C2—44no—
1394C2—44no—
1395C2C2×#353511yescharacteristic
1396C2#6292812yes—
1397C2#6296412yes—
1398C2#6301711yescharacteristic
1399C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35693C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59281C2semidirect
2. #59253C2semidirect
3. #59031C2semidirect
4. #58750C2semidirect
5. #56121C2semidirect
6. #56121C2semidirect
7. #54337C2semidirect
8. #53975C2semidirect
9. #53034C2semidirect
10. #52754C2semidirect
11. #52246C2semidirect
12. #51044C2semidirect
13. #49162C2semidirect
14. #45626C2semidirect
15. #45231C2semidirect
16. #43727C2semidirect
17. #42958C2semidirect
18. #42817C2semidirect
19. #42747C2semidirect
20. #42543C2semidirect
21. #40654C2semidirect
22. #39880C2semidirect
23. #39512C2semidirect
24. #38100C2semidirect
25. #37750C2semidirect
26. #37565C2semidirect
27. #36031C2semidirect
29. #35619C2semidirect

Maximal subgroups

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

subgroupindex
#592812
#592532
#590312
#587502
#561212
#543372
#539752
#530342
#527542
#522462
#510442
#491622
#456262
#452312
#437272
#429582
#428172
#427472
#425432
#406542
#398802
#395122
#381002
#377502
#375652
#360312
#356932
#356192