Finite Group Databasebeta

← #7660809

Subgroups — #7660809

Order 512.

4796 conjugacy classes of subgroups.

The subgroup lattice has 1441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52290C211yesmaximal, characteristic, complemented
2C2×#2726C212yesmaximal, complemented
3#42823C212yesmaximal, complemented
4#42822C212yesmaximal, complemented
5#42489C212yesmaximal, complemented
6#42000C214yesmaximal, complemented
7#40619C214yesmaximal, complemented
8#40617C214yesmaximal, complemented
9#39979C212yesmaximal, complemented
10#39751C211yesmaximal, characteristic, complemented
11#39368C211yesmaximal, characteristic, complemented
12#39180C212yesmaximal, complemented
13#38447C212yesmaximal, complemented
14#38447C212yesmaximal, complemented
15#38441C214yesmaximal, complemented
16#37687C214yesmaximal, complemented
17#37313C212yesmaximal, complemented
18#37309C211yesmaximal, characteristic, complemented
19#37135C212yesmaximal, complemented
20#36751C214yesmaximal, complemented
21#36275C211yesmaximal, characteristic
22#36275C211yesmaximal, characteristic
23#36261C212yesmaximal, complemented
24D4×#125C212yesmaximal, complemented
25#35950C212yesmaximal, complemented
26#35858C212yesmaximal, complemented
27#35806C212yesmaximal
28#34260C212yesmaximal
29#34250C211yesmaximal, characteristic
30C2×#554C2211yescharacteristic
31C2×#554C2212yes—
32C2×#554C2211yescharacteristic
33C2×#544C2212yes—
34C22×#125C2214yes—
35C2×#520C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2859C2212yes—
39#2859C2212yes—
40#2857C2214yes—
41#2857C2211yescharacteristic
42#2857C2211yescharacteristic
43#2855C2212yes—
44#2855C2212yes—
45#2851C2214yes—
46#2845C2214yes—
47#2843C2214yes—
48#2841C2214yes—
49#2807C2214yes—
50#2806C2211yescharacteristic
51#2806C2212yes—
52#2806C2214yes—
53#2806C2212yes—
54#2805C2212yes—
55#2805C2211yescharacteristic
56#2802C2214yes—
57#2802C2214yes—
58#2802C2214yes—
59#2802C2214yes—
60#2792C2214yes—
61#2792C2214yes—
62#2792C2214yes—
63#2792C2214yes—
64#2791C2214yes—
65#2791C2212yes—
66#2788C2212yes—
67#2774C2214yes—
68#2774C2214yes—
69#2774C2212yes—
70#2774C2214yes—
71#2768C2212yes—
72#2768C2214yes—
73#2755C2214yes—
74#2755C2214yes—
75#2755C2214yes—
76#2734C2212yes—
77#2734C2211yescharacteristic
78#2729C2212yes—
79#2726C2214yes—
80#2726C2214yes—
81#2726C2212yes—
82#2726C2214yes—
83#2726C2214yes—
84#2726C2212yes—
85#2726C2212yes—
86#2726C2212yes—
87#2726C2211yescharacteristic
88#2726C2214yes—
89#2726C2214yes—
90#2726C2214yes—
91#2720C2214yes—
92#2720C2212yes—
93#2713C2214yes—
94#2713C2214yes—
95#2713C2214yes—
96#2704C2214yes—
97#2704C2214yes—
98#2704C2214yes—
99#2667C2214yes—
100#2666C2214yes—
101#2666C2214yes—
102#2666C2214yes—
103#2666C2214yes—
104#2660C2214yes—
105#2660C2212yes—
106#2659C2212yes—
107#2659C2214yes—
108#2647C2214yes—
109#2647C2212yes—
110#2646C2214yes—
111#2629C2214yes—
112#2629C2212yes—
113#2627C2214yes—
114#2627C2212yes—
115#2612C2214yes—
116#2606C2214yes—
117#2606C2214yes—
118#2584C2212yes—
119#2584C2212yes—
120#2584C2212yes—
121#2583C2214yes—
122#2583C2214yes—
123#2583C2214yes—
124#2582C2211yescharacteristic
125#2582C2212yes—
126#2582C2211yescharacteristic
127#2579C2214yes—
128#2570C2212yes—
129#2569C2214yes—
130#2567C2211yescharacteristic
131#2567C2211yescharacteristic
132#2565C2212yes—
133#2552C2212yes—
134#2552C2212yes—
135#2552C2214yes—
136#2552C2212yes—
137#2552C2212yes—
138#2552C2212yes—
139#2552C2212yes—
140#2551C2212yes—
141#2550C2214yes—
142#2550C2212yes—
143#2550C2212yes—
144#2550C2214yes—
145#2550C2212yes—
146#2550C2212yes—
147#2549C2214yes—
148#2549C2214yes—
149#2549C2214yes—
150#2549C2214yes—
151#2546C2212yes—
152#2508C2212yes—
153#2507C2212yes—
154#2507C2212yes—
155#2506C2212yes—
156#2506C2212yes—
157#2506C2212yes—
158#2506C2212yes—
159#2506C2212yes—
160#2505C2214yes—
161#2502C2214yes—
162#2487C2212yes—
163#2487C2212yes—
164#2473C2214yes—
165#2473C2214yes—
166#2473C2214yes—
167#2473C2214yes—
168#2473C2214yes—
169#2473C2214yes—
170#2473C2214yes—
171#2453C2212yes—
172#2453C2212yes—
173#2453C2212yes—
174#2451C2212yes—
175#2450C2214yes—
176#2449C2214yes—
177#2449C2214yes—
178#2449C2214yes—
179#2442C2214yes—
180#2442C2214yes—
181#2442C2214yes—
182#2442C2214yes—
183#2442C2212yes—
184#2441C2214yes—
185#2441C2212yes—
186#2441C2212yes—
187#2440C2214yes—
188#2440C2214yes—
189#2440C2214yes—
190#2440C2214yes—
191#2440C2212yes—
192#2438C2214yes—
193#2438C2214yes—
194#2438C2214yes—
195#2438C2214yes—
196#2438C2214yes—
197#2417C2212yes—
198#2417C2214yes—
199#2417C2212yes—
200#2402C2212yes—
201#2399C2212yes—
202#2396C2212yes—
203C2×#398C2214yes—
204C2×#398C2214yes—
205C2×#398C2214yes—
206#2356C2212yes—
207#2355C2212yes—
208#2353C2214yes—
209#2352C2214yes—
210#2351C2212yes—
211Q8×C4⋊C4C2212yes—
212#2349C2212yes—
213#2349C2212yes—
214#2349C2214yes—
215#2349C2212yes—
216D4×C4⋊C4C2211yescharacteristic
217D4×C4⋊C4C2212yes—
218D4×C4⋊C4C2212yes—
219D4×C4⋊C4C2212yes—
220D4×C4⋊C4C2212yes—
221D4×C4⋊C4C2212yes—
222D4×C4⋊C4C2211yescharacteristic
223D4×C4⋊C4C2212yes—
224D4×C4⋊C4C2214yes—
225#2345C2212yes—
226#2344C2212yes—
227#2343C2214yes—
228#2343C2214yes—
229#2339C2212yes—
230#2339C2212yes—
231#2330C2214yes—
232#2330C2214yes—
233#2329C2212yes—
234#2320C2212yes—
235#2318C2214yes—
236#2317C2212yes—
237#2317C2211yescharacteristic
238#2316C2212yes—
239#2316C2211yescharacteristic
240#2314C2212yes—
241#2313C2214yes—
242C4×C4⋊Q8C2212yes—
243C4×#125C2212yes—
244C4×C22⋊Q8C2211yescharacteristic
245C4×C22⋊Q8C2211yescharacteristic
246#2298C2212yes—
247#2296C2212yes—
248#2296C2211yescharacteristic
249#2295C2212yes—
250C2×#389C2212yes—
251C2×#389C2214yes—
252C2×#389C2212yes—
253C2×#389C2212yes—
254C2×#389C2211yescharacteristic
255#2290C2214yes—
256C2×#387C2214yes—
257#2275C2212yes—
258C42×D4C2212yes—
259C22×#41C2311yescharacteristic
260#554—44no—
261#554—44no—
262#554—48no—
263#544—48no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×#125—416no—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297#520—44no—
298#520Q8116yescomplemented
299C4×#41—44no—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×#117C2312yes—
320C2×#117C2311yescharacteristic
321C2×#117C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2314yes—
324C2×#117C2311yescharacteristic
325C2×#117C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2314yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2314yes—
334C22×C4⋊C4C2314yes—
335C22×C4⋊C4C2314yes—
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2314yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2311yescharacteristic
342C22×C42C2314yes—
343C22×C42C2312yes—
344C22×C42C2311yescharacteristic
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#399C2314yes—
364#399C2312yes—
365#399C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
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#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2312yes—
411#398C2312yes—
412#398C2312yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2312yes—
421#398C2312yes—
422#398C2312yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#396C2312yes—
427#396C2314yes—
428#396C2314yes—
429#396C2312yes—
430#396C2314yes—
431#396C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2312yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2312yes—
445#395C2312yes—
446#395C2312yes—
447#395C2312yes—
448#395C2314yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#393C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2311yescharacteristic
464#391C2311yescharacteristic
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2311yescharacteristic
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2311yescharacteristic
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2311yescharacteristic
548#389C2311yescharacteristic
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2311yescharacteristic
552#389C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
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#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2312yes—
631#385C2312yes—
632#384C2312yes—
633#384C2312yes—
634#384C2312yes—
635#384C2312yes—
636#384C2312yes—
637#384C2314yes—
638#384C2312yes—
639#384C2311yescharacteristic
640#384C2311yescharacteristic
641#384C2312yes—
642#384C2314yes—
643#384C2314yes—
644#384C2314yes—
645#383C2314yes—
646#383C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#382C2314yes—
654#382C2314yes—
655#382C2314yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2311yescharacteristic
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2311yescharacteristic
678#380C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709#376C2312yes—
710#376C2314yes—
711#376C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2312yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2312yes—
720C2×#41—24no—
721C2×#41—24no—
722C2×#41C2×Q818yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2414yes—
728C22×Q8C2412yes—
729C22×Q8C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C23×C4C2412yes—
733C23×C4C2414yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C4⋊Q8—48no—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—44no—
751C4⋊Q8—48no—
752#125—28no—
753#125—216no—
754#125—48no—
755#125—48no—
756#125—44no—
757#125—44no—
758#125—44no—
759#125—44no—
760#125—48no—
761#125—48no—
762#125—48no—
763#125—48no—
764#125—48no—
765#125—48no—
766C22⋊Q8—24no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—48no—
772C22⋊Q8—44no—
773C22⋊Q8—44no—
774C22⋊Q8—48no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—42no—
778C4×Q8—42no—
779C4×Q8—42no—
780C4×Q8—44no—
781C4×Q8—42no—
782C4×Q8—42no—
783C4×Q8—44no—
784C4×Q8C2×Q8116yes—
785C4×D4—24no—
786C4×D4—24no—
787C4×D4—28no—
788C4×D4—28no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—28no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—48no—
795C4×D4C2×Q8132yes—
796C4×D4C2×Q8116yes—
797#117—42no—
798#117—48no—
799#117—44no—
800#117—44no—
801#117—42no—
802#117C2×Q818yes—
803#117C2×Q8116yes—
804C2×C4⋊C4—28no—
805C2×C4⋊C4—44no—
806C2×C4⋊C4—48no—
807C2×C4⋊C4—42no—
808C2×C4⋊C4—48no—
809C2×C4⋊C4—48no—
810C2×C4⋊C4—48no—
811C2×C4⋊C4—48no—
812C2×C4⋊C4—48no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—48no—
818C2×C4⋊C4C2×Q8116yes—
819C2×C4⋊C4C2×Q818yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C42—42no—
932C2×C42—48no—
933C2×C42—44no—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029C24C2511yescharacteristic
1030C24C2512yes—
1031#41—232no—
1032C2×Q8—22no—
1033C2×Q8—22no—
1034C2×Q8—22no—
1035C2×Q8—22no—
1036C2×Q8—41no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—41no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—44no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×Q8—44no—
1051C2×Q8—42no—
1052C2×Q8C22×Q814yes—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4C22×Q818yes—
1056C2×D4C22×Q814yes—
1057C2×D4H(5,𝔽2)14yes—
1058C2×D42−1+414yes—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—28no—
1066C22×C4—28no—
1067C22×C4—28no—
1068C22×C4—28no—
1069C22×C4—28no—
1070C22×C4—28no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—44no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—44no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4C22×Q818yes—
1098C22×C4C22×Q814yes—
1099C22×C4C22×Q818yes—
1100C22×C4C22×Q8116yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2514yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2514yes—
1115C22×C4C2514yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2512yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—22no—
1142C4⋊C4—22no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—22no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—41no—
1154C4⋊C4—42no—
1155C4⋊C4—41no—
1156C4⋊C4—41no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—41no—
1188C4⋊C4—41no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—41no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4C22×Q814yes—
1217C4⋊C4C22×Q818yes—
1218C4⋊C4C22×Q8116yes—
1219C4⋊C4C22×Q818yes—
1220C4⋊C4C22×Q814yes—
1221C4⋊C4H(5,𝔽2)14yes—
1222C22⋊C4—28no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—24no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4C22×Q818yes—
1238C22⋊C4C22×Q8116yes—
1239C42—24no—
1240C42—28no—
1241C42—22no—
1242C42—22no—
1243C42—24no—
1244C42—24no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—41no—
1249C42—41no—
1250C42—42no—
1251C42—42no—
1252C42—42no—
1253C42—44no—
1254C42—44no—
1255C42—42no—
1256C42—44no—
1257C42—42no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—42no—
1262C42C22×Q8116yes—
1263C42C22×Q818yes—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—21no—
1269C23—21no—
1270C23—21no—
1271C23—21no—
1272C23—21no—
1273C23—21no—
1274C23C23×Q812yes—
1275C23C23×Q814yes—
1276C23C2×H(5,𝔽2)14yes—
1277C23C2×2−1+414yes—
1278C23C2611yescharacteristic
1279Q8—28no—
1280Q8—82no—
1281Q8—82no—
1282Q8—84no—
1283Q8—162no—
1284Q8—164no—
1285Q8—162no—
1286D4—216no—
1287D4#544116yescomplemented
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—216no—
1305C2×C4—28no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—416no—
1361C2×C4—48no—
1362C2×C4—416no—
1363C2×C4—48no—
1364C2×C4—48no—
1365C2×C4—82no—
1366C2×C4—82no—
1367C2×C4—88no—
1368C2×C4—88no—
1369C2×C4—88no—
1370C2×C4—88no—
1371C2×C4—162no—
1372C2×C4C23×Q814yes—
1373C2×C4C23×Q814yes—
1374C2×C4C23×Q818yes—
1375C2×C4C23×Q814yes—
1376C2×C4C23×Q812yes—
1377C2×C4C23×Q812yes—
1378C2×C4C2×H(5,𝔽2)14yes—
1379C2×C4C2×H(5,𝔽2)12yes—
1380C2×C4C2×H(5,𝔽2)12yes—
1381C2×C4C2×2−1+412yes—
1382C2×C4#58512yes—
1383C22—24no—
1384C22—24no—
1385C22—24no—
1386C22—24no—
1387C22—24no—
1388C22—24no—
1389C22—22no—
1390C22—22no—
1391C22—22no—
1392C22—41no—
1393C22—41no—
1394C22—41no—
1395C22—41no—
1396C22C2×#54418yes—
1397C22C24×Q811yescharacteristic
1398C22C22×H(5,𝔽2)11yescharacteristic
1399C22C22×H(5,𝔽2)11yescharacteristic
1400C22C22×2−1+411yescharacteristic
1401C22C2×#58511yescharacteristic
1402C222−1+611yescharacteristic
1403C222−1+611yescharacteristic
1404C4—24no—
1405C4—28no—
1406C4—24no—
1407C4—24no—
1408C4—22no—
1409C4—22no—
1410C4—22no—
1411C4—24no—
1412C4—44no—
1413C4—44no—
1414C4—42no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4—44no—
1420C4—41no—
1421C4—42no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—42no—
1426C4—44no—
1427C4—41no—
1428C4—44no—
1429C4—42no—
1430C4C2×#54414yes—
1431C2—28no—
1432C2—42no—
1433C2C22×#54411yescharacteristic
1434C2#6289811yescharacteristic
1435C2#6291411yescharacteristic
1436C2Q8×H(5,𝔽2)11yescharacteristic
1437C2#6300411yescharacteristic
1438C2#6301311yescharacteristic
1439C2#6306711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52290C2semidirect
2. C2×#2726C2semidirect
3. #42823C2semidirect
4. #42822C2semidirect
5. #42489C2semidirect
6. #42000C2semidirect
7. #40619C2semidirect
8. #40617C2semidirect
9. #39979C2semidirect
10. #39751C2semidirect
11. #39368C2semidirect
12. #39180C2semidirect
13. #38447C2semidirect
14. #38447C2semidirect
15. #38441C2semidirect
16. #37687C2semidirect
17. #37313C2semidirect
18. #37309C2semidirect
19. #37135C2semidirect
20. #36751C2semidirect
23. #36261C2semidirect
24. D4×#125C2semidirect
25. #35950C2semidirect
26. #35858C2semidirect
298. #520Q8semidirect
1287. D4#544semidirect

Maximal subgroups

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

subgroupindex
#522902
C2×#27262
#428232
#428222
#424892
#420002
#406192
#406172
#399792
#397512
#393682
#391802
#384472
#384412
#376872
#373132
#373092
#371352
#367512
#362752
#362612
D4×#1252
#359502
#358582
#358062
#342602
#342502