Finite Group Databasebeta

← #7727001

Subgroups — #7727001

Order 512.

6672 conjugacy classes of subgroups.

The subgroup lattice has 1485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C2×#3455C211yesmaximal, characteristic, complemented
3#52074C212yesmaximal, complemented
4#52073C212yesmaximal, complemented
5#52057C212yesmaximal, complemented
6#52009C212yesmaximal, complemented
7#47768C214yesmaximal, complemented
8#47716C214yesmaximal, complemented
9#44450C212yesmaximal, complemented
10#43892C212yesmaximal, complemented
11#43496C212yesmaximal, complemented
12#43004C212yesmaximal, complemented
13#39847C214yesmaximal, complemented
14#38365C214yesmaximal, complemented
15#38363C214yesmaximal, complemented
16#37763C212yesmaximal, complemented
17#37762C212yesmaximal, complemented
18#37698C212yesmaximal, complemented
19#37697C212yesmaximal, complemented
20#37557C211yesmaximal, characteristic, complemented
21#36963C214yesmaximal, complemented
22#36217C214yesmaximal, complemented
23#35450C214yesmaximal, complemented
24#35248C211yesmaximal, characteristic, complemented
25#35118C211yesmaximal, characteristic, complemented
26C2×#2599C211yesmaximal, characteristic, complemented
27#34388C211yesmaximal, characteristic, complemented
28#3522—216no—
29C2×#559C2211yescharacteristic, complemented
30C2×#559C2212yescomplemented
31C2×Q82C2211yescharacteristic, complemented
32C2×#554C2211yescharacteristic, complemented
33C2×#554C2212yescomplemented
34C2×#550C2211yescharacteristic, complemented
35C2×#548C2212yes—
36C2×#547C2214yes—
37C2×#547C2212yes—
38#3455—216no—
39C2×#542C2212yes—
40C2×#542C2212yes—
41C2×#542C2212yescomplemented
42C2×#542C2214yescomplemented
43C2×#541C2212yes—
44C2×#540C2212yes—
45C2×#539C2212yes—
46C2×#539C2212yes—
47C2×#538C2212yes—
48C2×#538C2212yes—
49C2×#533C2211yescharacteristic
50C2×#532C2212yes—
51C2×#532C2211yescharacteristic
52C2×#529C2211yescharacteristic
53C2×#529C2212yes—
54C2×#529C2214yes—
55C2×#529C2214yes—
56C2×#525C2212yes—
57C2×#520C2212yescomplemented
58C2×C4×#41C2212yes—
59C22×C4×Q8C2211yescharacteristic
60C22×#117C2211yescharacteristic
61#2855C2212yes—
62#2855C2212yes—
63#2855C2214yescomplemented
64#2853C2212yes—
65#2853C2214yescomplemented
66#2849C2212yes—
67#2821C2212yescomplemented
68#2821C2212yescomplemented
69#2732C2214yes—
70#2729C2214yes—
71#2729C2214yes—
72#2728C2214yes—
73#2723C2214yes—
74#2722C2214yescomplemented
75#2721C2214yes—
76#2720C2214yescomplemented
77#2719C2214yescomplemented
78#2718C2214yes—
79#2717C2214yescomplemented
80#2717C2214yescomplemented
81#2716C2214yes—
82#2716C2214yes—
83#2715C2214yes—
84#2715C2214yescomplemented
85#2713C2214yescomplemented
86#2713C2214yescomplemented
87#2712C2214yes—
88#2710C2214yes—
89#2710C2214yes—
90#2709C2214yescomplemented
91#2708C2214yes—
92#2708C2214yes—
93#2708C2214yescomplemented
94#2706C2214yes—
95#2700C2214yes—
96#2700C2214yescomplemented
97#2698C2214yescomplemented
98#2698C2214yescomplemented
99#2689C2214yescomplemented
100#2688C2214yes—
101#2688C2214yes—
102#2687C2214yescomplemented
103#2686C2214yes—
104#2686C2214yes—
105#2674C2214yes—
106#2674C2214yescomplemented
107#2673C2214yes—
108#2671C2214yes—
109#2659C2212yes—
110#2639C2212yes—
111#2638C2214yes—
112#2634C2212yescomplemented
113#2634C2212yescomplemented
114#2634C2212yescomplemented
115#2634C2212yescomplemented
116#2633C2212yescomplemented
117#2632C2212yescomplemented
118#2630C2214yes—
119#2627C2211yescharacteristic
120#2626C2211yescharacteristic
121#2618C2211yescharacteristic
122#2617C2211yescharacteristic
123#2611C2212yes—
124#2610C2212yes—
125#2609C2214yes—
126#2602C2214yes—
127#2601C2214yes—
128#2600C2214yes—
129#2599C2212yes—
130#2599C2212yes—
131#2599C2212yes—
132#2599C2212yes—
133#2599C2214yes—
134#2599C2212yes—
135#2599C2214yes—
136#2599C2214yescomplemented
137#2598C2212yes—
138#2581C2212yescomplemented
139#2581C2212yescomplemented
140#2579C2214yes—
141#2568C2212yescomplemented
142#2564C2214yes—
143#2564C2212yes—
144#2564C2212yes—
145#2557C2214yes—
146#2553C2214yescomplemented
147#2549C2214yescomplemented
148#2546C2212yescomplemented
149#2534C2214yes—
150#2521C2214yescomplemented
151#2503C2212yes—
152#2499C2214yescomplemented
153#2498C2214yes—
154#2498C2214yescomplemented
155#2491C2214yes—
156#2488C2214yes—
157#2488C2214yes—
158#2486C2214yes—
159#2485C2214yescomplemented
160#2484C2214yes—
161#2484C2214yescomplemented
162#2481C2214yes—
163#2478C2214yescomplemented
164#2474C2214yes—
165#2473C2214yescomplemented
166#2469C2214yes—
167#2469C2214yes—
168#2467C2214yes—
169#2466C2214yescomplemented
170#2462C2214yescomplemented
171#2462C2214yescomplemented
172#2460C2214yescomplemented
173#2459C2214yes—
174#2450C2214yescomplemented
175#2446C2214yescomplemented
176#2446C2214yescomplemented
177#2444C2214yes—
178#2444C2214yes—
179#2444C2214yes—
180#2444C2214yescomplemented
181#2443C2214yes—
182#2443C2214yes—
183#2443C2214yescomplemented
184#2440C2214yescomplemented
185#2438C2214yescomplemented
186#2434C2212yes—
187#2430C2214yes—
188#2425C2214yes—
189#2425C2214yes—
190#2424C2214yes—
191#2423C2214yescomplemented
192#2421C2214yescomplemented
193#2419C2214yes—
194#2419C2214yes—
195#2419C2214yes—
196#2419C2214yescomplemented
197#2419C2214yescomplemented
198#2419C2214yescomplemented
199#2419C2214yescomplemented
200#2419C2214yescomplemented
201#2418C2214yes—
202#2413C2214yes—
203#2406C2214yes—
204#2406C2214yescomplemented
205#2404C2214yes—
206C2×#398C2211yescharacteristic
207C2×#397C2211yescharacteristic
208C2×#395C2211yescharacteristic
209C2×#393C2211yescharacteristic
210#2381C2212yescomplemented
211#2380C2212yescomplemented
212#2364C2212yes—
213#2364C2212yes—
214#2353C2214yescomplemented
215#2349C2214yes—
216D4×C4⋊C4C2214yes—
217#2339C2214yes—
218#2339C2214yes—
219#2339C2214yes—
220#2337C2214yescomplemented
221#2327C2214yescomplemented
222#2325C2212yes—
223#2325C2212yes—
224#2325C2214yes—
225#2322C2212yes—
226#2322C2214yes—
227#2321C2212yes—
228#2318C2214yescomplemented
229C4×#123C2214yescomplemented
230C2×#388C2212yes—
231C2×#387C2212yes—
232C2×#387C2212yes—
233C2×#387C2214yescomplemented
234C2×#385C2212yes—
235#2283C2211yescharacteristic
236C2×#383C2211yescharacteristic
237C22×#41C2314yes—
238C22×#41C2312yes—
239C22×#41C2312yes—
240C23×Q8C2311yescharacteristic
241C24×C4C2311yescharacteristic
242#559—28no—
243#559—216no—
244Q82—28no—
245#554—28no—
246#554—216no—
247#550—28no—
248#548—216no—
249#547—232no—
250#547—216no—
251#542—216no—
252#542—216no—
253#542—232no—
254#542—216no—
255#541—216no—
256#540—216no—
257#539—216no—
258#539—216no—
259#538—216no—
260#538—216no—
261#533—28no—
262#532—216no—
263#532D4116yescomplemented
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2312yes—
272C2×#127C2311yescharacteristic
273#529—216no—
274#529—232no—
275#529—232no—
276#529—28no—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#125C2311yescharacteristic
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#124C2314yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296#525—216no—
297C2×#123C2312yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2312yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2311yescharacteristic
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2312yes—
322C2×#121C2311yescharacteristic
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2312yes—
330C2×#121C2314yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#120C2314yes—
334C2×#120C2312yes—
335#520—216no—
336C4×#41—216no—
337C2×C4×Q8—28no—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2314yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×#117—28no—
371C2×#117C2312yes—
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2314yes—
378C2×#117C2314yes—
379C22×C4⋊C4C2311yescharacteristic
380C22×C4⋊C4C2314yes—
381C22×C4⋊C4C2311yescharacteristic
382C22×C4⋊C4C2311yescharacteristic
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2312yes—
388C22×C22⋊C4C2311yescharacteristic
389C22×C22⋊C4C2311yescharacteristic
390C22×C22⋊C4C2312yes—
391C22×C22⋊C4C2312yes—
392C22×C42C2311yescharacteristic
393C22×C42C2314yes—
394C22×C42C2312yes—
395C22×C42C2311yescharacteristic
396#400C2312yes—
397#400C2312yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2312yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#399C2312yes—
410#399C2312yes—
411#399C2314yes—
412#399C2314yes—
413#399C2312yes—
414#399C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2312yes—
420#398C2314yes—
421#398C2312yes—
422#398C2312yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2312yes—
435#397C2312yes—
436#397C2314yes—
437#397C2312yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#395C2312yes—
458#395C2312yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2312yes—
464#395C2314yes—
465#395C2312yes—
466#395C2312yes—
467#395C2314yes—
468#395C2314yes—
469#394C2312yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#393C2312yes—
484#393C2312yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#393C2312yes—
489#393C2312yes—
490#393C2312yes—
491#393C2314yes—
492#392C2312yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#390C2314yes—
509#390C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
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#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2312yes—
587#386C2314yes—
588#386C2312yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#384C2314yes—
637#383C2312yes—
638#383C2312yes—
639#383C2312yes—
640#383C2312yes—
641#383C2312yes—
642#382C2314yes—
643#382C2312yes—
644#382C2314yes—
645#381C2314yes—
646#381C2312yes—
647#381C2314yes—
648#381C2312yes—
649#381C2314yes—
650#381C2314yes—
651#381C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2311yescharacteristic
662#380C2311yescharacteristic
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#379C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678#376C2312yes—
679C2×#95C2311yescharacteristic
680C2×#95C2311yescharacteristic
681C2×#95C2314yes—
682C2×#95C2312yes—
683C2×#95C2312yes—
684C2×#95C2312yes—
685C2×#95C2312yes—
686C2×#95C2314yes—
687C2×#95C2314yes—
688C2×#95C2312yes—
689C2×#95C2314yes—
690C2×#95C2312yes—
691C25C2411yescharacteristic
692C2×#41—28no—
693C2×#41—216no—
694C2×#41—44no—
695C2×#41—44no—
696C2×#41—48no—
697C2×#41—48no—
698C2×#41—48no—
699C2×#41C2×D4116yes—
700C22×Q8—24no—
701C22×Q8—44no—
702C22×Q8C2411yescharacteristic
703C22×Q8C2412yes—
704C22×Q8C2411yescharacteristic
705C22×Q8C2411yescharacteristic
706C22×Q8C2412yes—
707C22×Q8C2412yes—
708C22×Q8C2414yes—
709C22×Q8C2412yes—
710C22×D4C2412yes—
711C22×D4C2414yes—
712C22×D4C2414yes—
713C22×D4C2411yescharacteristic
714C22×D4C2414yes—
715C22×D4C2414yes—
716C22×D4C2414yes—
717C22×D4C2414yes—
718C22×D4C2412yes—
719C22×D4C2412yes—
720C22×D4C2412yes—
721C23×C4—24no—
722C23×C4—42no—
723C23×C4—42no—
724C23×C4C2412yes—
725C23×C4C2411yescharacteristic
726C23×C4C2412yes—
727C23×C4C2414yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2414yes—
745C4⋊Q8—216no—
746C4⋊Q8—28no—
747C4⋊Q8—28no—
748C4⋊Q8—24no—
749C4⋊Q8—24no—
750C4⋊Q8—48no—
751C4⋊Q8C2×D418yes—
752#127—28no—
753#127C2×D418yes—
754#126—216no—
755#126—216no—
756#126—216no—
757#126—216no—
758#126—216no—
759#126—28no—
760#125—216no—
761#125—216no—
762#125—28no—
763#125—24no—
764#125—28no—
765#124—28no—
766#124—28no—
767#124—216no—
768#124—216no—
769#124—216no—
770#124—216no—
771#124—24no—
772#124C2×D4116yes—
773#123—216no—
774#123—216no—
775#123—216no—
776#123—216no—
777#123—216no—
778#123—28no—
779#123—216no—
780#123—216no—
781#123—216no—
782#123—216no—
783#123—48no—
784#123—44no—
785#123—48no—
786C22⋊Q8—28no—
787C22⋊Q8—28no—
788C22⋊Q8—216no—
789C22⋊Q8—24no—
790C22⋊Q8—28no—
791C22⋊Q8—28no—
792C22⋊Q8—216no—
793C22⋊Q8—28no—
794C22⋊Q8—216no—
795C22⋊Q8—216no—
796C22⋊Q8—216no—
797C22⋊Q8—216no—
798#121—28no—
799#121—28no—
800#121—216no—
801#121—216no—
802#121—216no—
803#121—28no—
804#121—216no—
805#121—24no—
806#121—48no—
807#121C2×D4116yes—
808#121C2×D4116yes—
809#120—216no—
810#120—44no—
811C4×Q8—28no—
812C4×Q8—28no—
813C4×Q8—28no—
814C4×Q8—28no—
815C4×Q8—24no—
816C4×Q8—28no—
817C4×Q8—24no—
818C4×Q8—24no—
819C4×Q8—24no—
820C4×Q8—28no—
821C4×Q8—28no—
822C4×Q8—28no—
823C4×Q8—24no—
824C4×D4—216no—
825C4×D4—216no—
826C4×D4—28no—
827C4×D4—28no—
828C4×D4—28no—
829C4×D4—216no—
830C4×D4—28no—
831C4×D4—28no—
832C4×D4—216no—
833C4×D4—216no—
834C4×D4—216no—
835C4×D4—28no—
836C4×D4—28no—
837C4×D4—216no—
838C4×D4—24no—
839C4×D4—48no—
840C4×D4—48no—
841C4×D4C2×D4116yes—
842C4×D4C2×D4116yes—
843#117—28no—
844#117—216no—
845#117—216no—
846#117—28no—
847#117—28no—
848#117—28no—
849#117—28no—
850#117—28no—
851C2×C4⋊C4—24no—
852C2×C4⋊C4—24no—
853C2×C4⋊C4—24no—
854C2×C4⋊C4—28no—
855C2×C4⋊C4—216no—
856C2×C4⋊C4—28no—
857C2×C4⋊C4—44no—
858C2×C4⋊C4—48no—
859C2×C4⋊C4—44no—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C22⋊C4—24no—
913C2×C22⋊C4—24no—
914C2×C22⋊C4—44no—
915C2×C22⋊C4—44no—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C42—24no—
962C2×C42—28no—
963C2×C42—216no—
964C2×C42C2×D418yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2414yes—
968C2×C42C2412yes—
969C2×C42C2414yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2412yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034C24—22no—
1035C24—22no—
1036C24—22no—
1037C24—42no—
1038C24—42no—
1039C24C2512yes—
1040C24C2512yes—
1041C24C2514yes—
1042C24C2511yescharacteristic
1043#41—432no—
1044#41—432no—
1045#41—832no—
1046C2×Q8—22no—
1047C2×Q8—22no—
1048C2×Q8—24no—
1049C2×Q8—22no—
1050C2×Q8—24no—
1051C2×Q8—24no—
1052C2×Q8—28no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×Q8—42no—
1059C2×Q8—42no—
1060C2×Q8—44no—
1061C2×Q8—42no—
1062C2×Q8—42no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8—416no—
1066C2×Q8C22×D418yes—
1067C2×D4—28no—
1068C2×D4—28no—
1069C2×D4—28no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—28no—
1075C2×D4—28no—
1076C2×D4—22no—
1077C2×D4—28no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—42no—
1082C2×D4—42no—
1083C2×D4—44no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4C22×D4116yes—
1095C2×D4C22×D418yes—
1096C2×D4C22×D418yes—
1097C2×D4C22×D418yes—
1098C22×C4—22no—
1099C22×C4—22no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—22no—
1103C22×C4—28no—
1104C22×C4—24no—
1105C22×C4—22no—
1106C22×C4—24no—
1107C22×C4—22no—
1108C22×C4—22no—
1109C22×C4—22no—
1110C22×C4—28no—
1111C22×C4—28no—
1112C22×C4—28no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—28no—
1120C22×C4—28no—
1121C22×C4—42no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—42no—
1141C22×C4—42no—
1142C22×C4—42no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—416no—
1153C22×C4C22×D414yes—
1154C22×C4C22×D414yes—
1155C22×C4C22×D4116yes—
1156C22×C4C22×D414yes—
1157C22×C4C2514yes—
1158C22×C4C2514yes—
1159C22×C4C2514yes—
1160C22×C4C2514yes—
1161C22×C4C2512yes—
1162C22×C4C2514yes—
1163C22×C4C2512yes—
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2514yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C22×C4C2511yescharacteristic
1178C22×C4C2514yes—
1179C22×C4C2512yes—
1180C4⋊C4—24no—
1181C4⋊C4—22no—
1182C4⋊C4—28no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—24no—
1190C4⋊C4—22no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—28no—
1198C4⋊C4—28no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—28no—
1202C4⋊C4—24no—
1203C4⋊C4—28no—
1204C4⋊C4—28no—
1205C4⋊C4—28no—
1206C4⋊C4—28no—
1207C4⋊C4—24no—
1208C4⋊C4—24no—
1209C4⋊C4—28no—
1210C4⋊C4—24no—
1211C4⋊C4—28no—
1212C4⋊C4—28no—
1213C4⋊C4—28no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C4⋊C4—42no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4C22×D418yes—
1231C4⋊C4C22×D418yes—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—28no—
1235C22⋊C4—28no—
1236C22⋊C4—24no—
1237C22⋊C4—28no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—28no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—24no—
1250C22⋊C4—28no—
1251C22⋊C4—28no—
1252C22⋊C4—24no—
1253C22⋊C4—28no—
1254C22⋊C4—24no—
1255C22⋊C4—28no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4C22×D4116yes—
1276C22⋊C4C22×D4116yes—
1277C42—24no—
1278C42—24no—
1279C42—24no—
1280C42—28no—
1281C42—24no—
1282C42—24no—
1283C42—28no—
1284C42—28no—
1285C42—24no—
1286C42—28no—
1287C42—24no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C42C22×D414yes—
1292C42C22×D414yes—
1293C42C22×D414yes—
1294C42C22×D414yes—
1295C23—22no—
1296C23—22no—
1297C23—24no—
1298C23—24no—
1299C23—24no—
1300C23—24no—
1301C23—24no—
1302C23—24no—
1303C23—22no—
1304C23—22no—
1305C23—24no—
1306C23—22no—
1307C23—24no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—24no—
1312C23—24no—
1313C23—48no—
1314C23—44no—
1315C23—82no—
1316C23—82no—
1317C23—84no—
1318C23C23×D418yes—
1319C23C23×D412yes—
1320C23#58512yes—
1321C23#58512yes—
1322C23C2611yescharacteristic
1323Q8—28no—
1324Q8—48no—
1325Q8—48no—
1326Q8—44no—
1327Q8—44no—
1328Q8—84no—
1329Q8—84no—
1330Q8—88no—
1331D4—232no—
1332D4—48no—
1333D4—48no—
1334D4—48no—
1335D4—416no—
1336D4—44no—
1337D4—48no—
1338D4—88no—
1339D4—88no—
1340D4—88no—
1341D4—164no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—28no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—44no—
1397C2×C4—44no—
1398C2×C4—416no—
1399C2×C4—48no—
1400C2×C4—416no—
1401C2×C4—48no—
1402C2×C4—48no—
1403C2×C4—48no—
1404C2×C4—44no—
1405C2×C4—48no—
1406C2×C4—88no—
1407C2×C4—82no—
1408C2×C4—88no—
1409C2×C4—82no—
1410C2×C4—88no—
1411C2×C4—84no—
1412C2×C4—84no—
1413C2×C4—88no—
1414C2×C4—88no—
1415C2×C4—164no—
1416C2×C4C23×D412yes—
1417C2×C4C23×D412yes—
1418C2×C4C23×D412yes—
1419C2×C4C23×D418yes—
1420C2×C4C23×D412yes—
1421C2×C4C23×D412yes—
1422C2×C4C23×D412yes—
1423C2×C4#58514yes—
1424C22—22no—
1425C22—22no—
1426C22—24no—
1427C22—24no—
1428C22—28no—
1429C22—28no—
1430C22—28no—
1431C22—44no—
1432C22—44no—
1433C22—44no—
1434C22—44no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—44no—
1442C22—44no—
1443C22—44no—
1444C22—44no—
1445C22—88no—
1446C22#348514yes—
1447C22C24×D411yescharacteristic
1448C22C2×#58511yescharacteristic
1449C22C2×#58511yescharacteristic
1450C22C2×#58512yes—
1451C222−1+612yes—
1452C4—22no—
1453C4—22no—
1454C4—28no—
1455C4—22no—
1456C4—24no—
1457C4—22no—
1458C4—22no—
1459C4—22no—
1460C4—42no—
1461C4—42no—
1462C4—42no—
1463C4—42no—
1464C4—42no—
1465C4—42no—
1466C4—42no—
1467C4—44no—
1468C4—42no—
1469C4—44no—
1470C4—42no—
1471C4—44no—
1472C4—44no—
1473C4—44no—
1474C4—44no—
1475C2—24no—
1476C2—48no—
1477C2—82no—
1478C2—82no—
1479C2C2×#348511yescharacteristic
1480C2#6281111yescharacteristic
1481C2#6285911yescharacteristic
1482C2#6290712yes—
1483C2#6296412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3522C2semidirect
2. C2×#3455C2semidirect
3. #52074C2semidirect
4. #52073C2semidirect
5. #52057C2semidirect
6. #52009C2semidirect
7. #47768C2semidirect
8. #47716C2semidirect
9. #44450C2semidirect
10. #43892C2semidirect
11. #43496C2semidirect
12. #43004C2semidirect
13. #39847C2semidirect
14. #38365C2semidirect
15. #38363C2semidirect
16. #37763C2semidirect
17. #37762C2semidirect
18. #37698C2semidirect
19. #37697C2semidirect
20. #37557C2semidirect
21. #36963C2semidirect
22. #36217C2semidirect
23. #35450C2semidirect
24. #35248C2semidirect
25. #35118C2semidirect
26. C2×#2599C2semidirect
27. #34388C2semidirect
29. C2×#559C22semidirect
30. C2×#559C22semidirect
31. C2×Q82C22semidirect
32. C2×#554C22semidirect
33. C2×#554C22semidirect
34. C2×#550C22semidirect
41. C2×#542C22semidirect
42. C2×#542C22semidirect
57. C2×#520C22semidirect
63. #2855C22semidirect
65. #2853C22semidirect
67. #2821C22semidirect
68. #2821C22semidirect
74. #2722C22semidirect
76. #2720C22semidirect
77. #2719C22semidirect
79. #2717C22semidirect
80. #2717C22semidirect
84. #2715C22semidirect
85. #2713C22semidirect
86. #2713C22semidirect
90. #2709C22semidirect
93. #2708C22semidirect
96. #2700C22semidirect
97. #2698C22semidirect
98. #2698C22semidirect
99. #2689C22semidirect
102. #2687C22semidirect
106. #2674C22semidirect
112. #2634C22semidirect
113. #2634C22semidirect
114. #2634C22semidirect
115. #2634C22semidirect
116. #2633C22semidirect
117. #2632C22semidirect
136. #2599C22semidirect
138. #2581C22semidirect
139. #2581C22semidirect
141. #2568C22semidirect
146. #2553C22semidirect
147. #2549C22semidirect
148. #2546C22semidirect
150. #2521C22semidirect
152. #2499C22semidirect
154. #2498C22semidirect
159. #2485C22semidirect
161. #2484C22semidirect
163. #2478C22semidirect
165. #2473C22semidirect
169. #2466C22semidirect
170. #2462C22semidirect
171. #2462C22semidirect
172. #2460C22semidirect
174. #2450C22semidirect
175. #2446C22semidirect
176. #2446C22semidirect
180. #2444C22semidirect
183. #2443C22semidirect
184. #2440C22semidirect
185. #2438C22semidirect
191. #2423C22semidirect
192. #2421C22semidirect
196. #2419C22semidirect
197. #2419C22semidirect
198. #2419C22semidirect
199. #2419C22semidirect
200. #2419C22semidirect
204. #2406C22semidirect
210. #2381C22semidirect
211. #2380C22semidirect
214. #2353C22semidirect
220. #2337C22semidirect
221. #2327C22semidirect
228. #2318C22semidirect
229. C4×#123C22semidirect
233. C2×#387C22semidirect
263. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C2×#34552
#520742
#520732
#520572
#520092
#477682
#477162
#444502
#438922
#434962
#430042
#398472
#383652
#383632
#377632
#377622
#376982
#376972
#375572
#369632
#362172
#354502
#352482
#351182
C2×#25992
#343882