Finite Group Databasebeta

← #7901017

Subgroups — #7901017

Order 512.

4377 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59681C212yesmaximal, complemented
3#52287C211yesmaximal, characteristic, complemented
4#48843C214yesmaximal, complemented
5#47980C214yesmaximal, complemented
6#47975C214yesmaximal, complemented
7#46444C214yesmaximal, complemented
8#45794C212yesmaximal, complemented
9#45435C212yesmaximal, complemented
10#45426C212yesmaximal, complemented
11#44949C212yesmaximal, complemented
12#44894C214yesmaximal, complemented
13#42496C212yesmaximal
14#42496C212yesmaximal
15#40625C214yesmaximal, complemented
16#39749C211yesmaximal, characteristic, complemented
17#39711C212yesmaximal, complemented
18#39683C212yesmaximal, complemented
19#39637C211yesmaximal, characteristic, complemented
20#39370C212yesmaximal
21#39368C212yesmaximal, complemented
22#39181C212yesmaximal, complemented
23#37135C212yesmaximal, complemented
24#36477C211yesmaximal, characteristic
25#35952C212yesmaximal
26#35581C212yesmaximal
27#35177C211yesmaximal, characteristic
28#34489C212yesmaximal
29#34332C211yesmaximal, characteristic
30C2×Q82C2212yes—
31C2×#554C2211yescharacteristic
32C2×#544C2214yes—
33#2859C2212yes—
34#2859C2211yescharacteristic
35#2857C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2841C2214yes—
39#2841C2214yes—
40#2811C2211yescharacteristic
41#2809C2212yes—
42#2809C2212yes—
43#2806C2211yescharacteristic
44#2806C2212yes—
45#2806C2212yes—
46#2806C2211yescharacteristic
47#2806C2212yes—
48#2806C2212yes—
49#2805C2214yes—
50#2805C2212yes—
51#2805C2212yes—
52#2802C2214yes—
53#2802C2214yes—
54#2799C2214yes—
55#2799C2214yes—
56#2792C2214yes—
57#2792C2212yes—
58#2792C2212yes—
59#2792C2212yes—
60#2792C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2790C2214yes—
65#2790C2214yes—
66#2788C2214yes—
67#2788C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2755C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2734C2212yes—
75#2734C2212yes—
76#2734C2212yes—
77#2734C2211yescharacteristic
78#2734C2214yes—
79#2734C2214yes—
80#2729C2214yes—
81#2729C2214yes—
82#2729C2214yes—
83#2729C2214yes—
84#2726C2212yes—
85#2726C2212yes—
86#2713C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2704C2214yes—
91#2704C2214yes—
92#2677C2214yes—
93#2677C2214yes—
94#2665C2214yes—
95#2665C2214yes—
96#2665C2214yes—
97#2665C2214yes—
98#2660C2212yes—
99#2647C2212yes—
100#2647C2212yes—
101#2629C2214yes—
102#2627C2214yes—
103#2627C2214yes—
104#2608C2214yes—
105#2608C2214yes—
106#2590C2214yes—
107#2590C2214yes—
108#2590C2214yes—
109#2588C2214yes—
110#2588C2214yes—
111#2588C2214yes—
112#2587C2214yes—
113#2587C2214yes—
114#2586C2214yes—
115#2586C2214yes—
116#2585C2214yes—
117#2584C2214yes—
118#2584C2212yes—
119#2582C2212yes—
120#2581C2214yes—
121#2580C2212yes—
122#2574C2214yes—
123#2574C2214yes—
124#2574C2214yes—
125#2571C2212yes—
126#2570C2212yes—
127#2570C2212yes—
128#2570C2212yes—
129#2570C2212yes—
130#2569C2214yes—
131#2567C2212yes—
132#2567C2212yes—
133#2567C2211yescharacteristic
134#2566C2212yes—
135#2565C2214yes—
136#2563C2211yescharacteristic
137#2552C2212yes—
138#2551C2212yes—
139#2551C2212yes—
140#2551C2212yes—
141#2551C2214yes—
142#2551C2211yescharacteristic
143#2551C2214yes—
144#2551C2212yes—
145#2550C2214yes—
146#2549C2214yes—
147#2546C2212yes—
148#2546C2212yes—
149#2546C2214yes—
150#2546C2214yes—
151#2546C2212yes—
152#2546C2212yes—
153#2538C2211yescharacteristic
154#2538C2212yes—
155#2538C2211yescharacteristic
156#2538C2211yescharacteristic
157#2522C2214yes—
158#2520C2214yes—
159#2520C2214yes—
160#2511C2214yes—
161#2509C2212yes—
162#2509C2212yes—
163#2509C2214yes—
164#2509C2212yes—
165#2508C2212yes—
166#2507C2212yes—
167#2507C2212yes—
168#2507C2212yes—
169#2506C2212yes—
170#2506C2214yes—
171#2506C2214yes—
172#2506C2212yes—
173#2497C2212yes—
174#2497C2212yes—
175#2492C2212yes—
176#2465C2214yes—
177#2465C2214yes—
178#2465C2214yes—
179#2462C2214yes—
180#2462C2214yes—
181#2453C2214yes—
182#2452C2212yes—
183#2452C2212yes—
184#2452C2212yes—
185#2451C2214yes—
186#2451C2214yes—
187#2451C2214yes—
188#2451C2214yes—
189#2446C2214yes—
190#2442C2214yes—
191#2440C2214yes—
192#2440C2214yes—
193#2439C2214yes—
194#2439C2214yes—
195#2438C2214yes—
196#2438C2214yes—
197#2429C2212yes—
198#2429C2214yes—
199#2399C2212yes—
200#2399C2212yes—
201#2399C2212yes—
202#2396C2214yes—
203#2378C2214yes—
204#2378C2214yes—
205#2370C2212yes—
206#2370C2212yes—
207#2370C2212yes—
208#2370C2212yes—
209#2370C2212yes—
210#2369C2211yescharacteristic
211#2365C2212yes—
212#2365C2214yes—
213#2365C2212yes—
214#2362C2214yes—
215#2360C2214yes—
216#2360C2212yes—
217#2357C2212yes—
218#2357C2212yes—
219#2355C2212yes—
220#2355C2212yes—
221#2355C2212yes—
222#2355C2211yescharacteristic
223#2354C2212yes—
224Q8×C4⋊C4C2211yescharacteristic
225Q8×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2211yescharacteristic
227D4×C4⋊C4C2212yes—
228#2345C2212yes—
229#2344C2214yes—
230#2332C2214yes—
231#2332C2214yes—
232#2331C2212yes—
233#2331C2212yes—
234#2331C2212yes—
235#2330C2212yes—
236#2330C2212yes—
237#2330C2212yes—
238#2329C2214yes—
239#2323C2214yes—
240#2319C2212yes—
241#2319C2212yes—
242#2313C2214yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2211yescharacteristic
248C4×#125C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251#2295C2212yes—
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2295C2211yescharacteristic
255#2293C2212yes—
256C2×#389C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259Q82—48no—
260#554Q8116yescomplemented
261#544—416no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×#117C2314yes—
312C2×#117C2314yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C42C2312yes—
317#400C2314yes—
318#400C2314yes—
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#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#399C2314yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2312yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2312yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2312yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2312yes—
403#395C2314yes—
404#395C2314yes—
405#395C2312yes—
406#395C2314yes—
407#395C2312yes—
408#395C2312yes—
409#395C2312yes—
410#395C2312yes—
411#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2312yes—
415#395C2312yes—
416#395C2314yes—
417#395C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#391C2312yes—
424#391C2311yescharacteristic
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2311yescharacteristic
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2314yes—
449#391C2311yescharacteristic
450#391C2312yes—
451#391C2314yes—
452#391C2311yescharacteristic
453#391C2312yes—
454#391C2314yes—
455#391C2311yescharacteristic
456#391C2312yes—
457#391C2311yescharacteristic
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2314yes—
522#389C2312yes—
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2314yes—
536#389C2311yescharacteristic
537#389C2311yescharacteristic
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
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#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#384C2312yes—
625#384C2311yescharacteristic
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2312yes—
629#384C2314yes—
630#384C2312yes—
631#384C2314yes—
632#384C2311yescharacteristic
633#384C2312yes—
634#384C2312yes—
635#384C2312yes—
636#384C2311yescharacteristic
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#382C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709#376C2312yes—
710#376C2312yes—
711#376C2312yes—
712C2×#95C2314yes—
713C43C2312yes—
714C43C2311yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×D4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2412yes—
732C4⋊Q8—28no—
733C4⋊Q8—216no—
734C4⋊Q8—24no—
735C4⋊Q8—24no—
736C4⋊Q8—44no—
737C4⋊Q8—44no—
738C4⋊Q8—44no—
739C4⋊Q8—48no—
740C4⋊Q8—48no—
741C4⋊Q8—48no—
742C4⋊Q8—48no—
743C4⋊Q8—48no—
744C4⋊Q8—82no—
745C4⋊Q8—84no—
746C4⋊Q8—84no—
747C4⋊Q8C2×Q818yes—
748#125—28no—
749#125—48no—
750#125—48no—
751#125—48no—
752#125—48no—
753#125C2×Q8116yes—
754C22⋊Q8—28no—
755C22⋊Q8—48no—
756C22⋊Q8—48no—
757C22⋊Q8—48no—
758C22⋊Q8—82no—
759C22⋊Q8—84no—
760C22⋊Q8—82no—
761C22⋊Q8C2×Q8132yes—
762C22⋊Q8C2×Q8116yes—
763C4×Q8—24no—
764C4×Q8—42no—
765C4×Q8—42no—
766C4×Q8—44no—
767C4×Q8—44no—
768C4×Q8—48no—
769C4×Q8—48no—
770C4×Q8—44no—
771C4×Q8—44no—
772C4×Q8—82no—
773C4×Q8—82no—
774C4×Q8—84no—
775C4×Q8C2×Q818yes—
776C4×D4—24no—
777C4×D4—42no—
778C4×D4—44no—
779C4×D4C2×Q8116yes—
780C4×D4C2×Q818yes—
781#117—48no—
782#117—48no—
783C2×C4⋊C4—48no—
784C2×C4⋊C4—82no—
785C2×C4⋊C4C2×Q8116yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C42—82no—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999C24C2512yes—
1000C2×Q8—24no—
1001C2×Q8—28no—
1002C2×Q8—22no—
1003C2×Q8—24no—
1004C2×Q8—22no—
1005C2×Q8—42no—
1006C2×Q8—42no—
1007C2×Q8—41no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—42no—
1011C2×Q8—41no—
1012C2×Q8—42no—
1013C2×Q8—41no—
1014C2×Q8—42no—
1015C2×Q8—42no—
1016C2×Q8—44no—
1017C2×Q8—41no—
1018C2×Q8—41no—
1019C2×Q8—44no—
1020C2×Q8—42no—
1021C2×Q8—41no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8C22×Q814yes—
1031C2×Q8C22×Q818yes—
1032C2×Q8H(5,𝔽2)14yes—
1033C2×D4—22no—
1034C2×D4—22no—
1035C2×D4C22×Q814yes—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4C22×Q8116yes—
1050C22×C4C22×Q818yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—22no—
1092C4⋊C4—22no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—41no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—41no—
1161C4⋊C4—44no—
1162C4⋊C4C22×Q814yes—
1163C4⋊C4C22×Q8116yes—
1164C4⋊C4C22×Q818yes—
1165C4⋊C4C22×Q814yes—
1166C4⋊C4C22×Q818yes—
1167C4⋊C4C22×Q818yes—
1168C4⋊C4C22×Q8116yes—
1169C22⋊C4—28no—
1170C22⋊C4—24no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4C22×Q8116yes—
1181C22⋊C4C22×Q818yes—
1182C42—24no—
1183C42—28no—
1184C42—22no—
1185C42—24no—
1186C42—22no—
1187C42—24no—
1188C42—24no—
1189C42—24no—
1190C42—24no—
1191C42—41no—
1192C42—42no—
1193C42—42no—
1194C42—42no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—42no—
1199C42—42no—
1200C42—41no—
1201C42—41no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—42no—
1208C42—44no—
1209C42—44no—
1210C42—44no—
1211C42C22×Q818yes—
1212C42C22×Q814yes—
1213C422−1+414yes—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23C23×Q814yes—
1221C23C2611yescharacteristic
1222Q8—48no—
1223Q8—44no—
1224Q8—44no—
1225Q8—48no—
1226Q8—82no—
1227Q8—82no—
1228Q8—84no—
1229Q8—88no—
1230Q8—84no—
1231Q8—164no—
1232Q8—164no—
1233D4—28no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—416no—
1306C2×C4—48no—
1307C2×C4—84no—
1308C2×C4—84no—
1309C2×C4—164no—
1310C2×C4C23×Q814yes—
1311C2×C4C23×Q812yes—
1312C2×C4C23×Q814yes—
1313C2×C4C23×Q812yes—
1314C2×C4C23×Q814yes—
1315C2×C4C23×Q818yes—
1316C2×C4C23×Q812yes—
1317C2×C4C2×H(5,𝔽2)14yes—
1318C2×C4C2×H(5,𝔽2)12yes—
1319C2×C4C2×2−1+412yes—
1320C2×C4C2×2−1+412yes—
1321C2×C4C2×2−1+412yes—
1322C2×C4#58512yes—
1323C22—24no—
1324C22—24no—
1325C22—24no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22C24×Q811yescharacteristic
1331C22C22×H(5,𝔽2)11yescharacteristic
1332C22C22×2−1+411yescharacteristic
1333C22C2×#58511yescharacteristic
1334C22H(7,𝔽2)11yescharacteristic
1335C222−1+611yescharacteristic
1336C222−1+611yescharacteristic
1337C4—24no—
1338C4—28no—
1339C4—22no—
1340C4—22no—
1341C4—24no—
1342C4—24no—
1343C4—22no—
1344C4—22no—
1345C4—24no—
1346C4—22no—
1347C4—41no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—44no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—42no—
1357C4—44no—
1358C4—42no—
1359C4—44no—
1360C4—42no—
1361C4—42no—
1362C4—44no—
1363C4—44no—
1364C4#350214yes—
1365C2—44no—
1366C2C2×#350211yescharacteristic
1367C2#6285411yescharacteristic
1368C2#6287911yescharacteristic
1369C2#6290511yescharacteristic
1370C2#6291311yescharacteristic
1371C2Q8×H(5,𝔽2)11yescharacteristic
1372C2#6305311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59832C2semidirect
2. #59681C2semidirect
3. #52287C2semidirect
4. #48843C2semidirect
5. #47980C2semidirect
6. #47975C2semidirect
7. #46444C2semidirect
8. #45794C2semidirect
9. #45435C2semidirect
10. #45426C2semidirect
11. #44949C2semidirect
12. #44894C2semidirect
15. #40625C2semidirect
16. #39749C2semidirect
17. #39711C2semidirect
18. #39683C2semidirect
19. #39637C2semidirect
21. #39368C2semidirect
22. #39181C2semidirect
23. #37135C2semidirect
260. #554Q8semidirect

Maximal subgroups

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

subgroupindex
#598322
#596812
#522872
#488432
#479802
#479752
#464442
#457942
#454352
#454262
#449492
#448942
#424962
#406252
#397492
#397112
#396832
#396372
#393702
#393682
#391812
#371352
#364772
#359522
#355812
#351772
#344892
#343322