Finite Group Databasebeta

← #7683722

Subgroups — #7683722

Order 512.

6892 conjugacy classes of subgroups.

The subgroup lattice has 1491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C212yesmaximal, complemented
2#59586C212yesmaximal, complemented
3#59418C212yesmaximal, complemented
4#59317C212yesmaximal, complemented
5#59178C214yesmaximal, complemented
6#59163C214yesmaximal, complemented
7#59161C214yesmaximal, complemented
8#59140C214yesmaximal, complemented
9#59066C212yesmaximal, complemented
10#45432C211yesmaximal, characteristic, complemented
11#45412C212yesmaximal, complemented
12#45387C211yesmaximal, characteristic, complemented
13#45334C211yesmaximal, characteristic, complemented
14#44996C212yesmaximal, complemented
15#44948C211yesmaximal, characteristic, complemented
16#44635C214yesmaximal, complemented
17#44579C214yesmaximal, complemented
18#44382C214yesmaximal, complemented
19#44160C214yesmaximal, complemented
20#35637C212yesmaximal, complemented
21#35625C212yesmaximal, complemented
22#35521C212yesmaximal, complemented
23#34880C211yesmaximal, characteristic, complemented
24#34720C212yesmaximal, complemented
25#34295C212yesmaximal, complemented
26#34281C211yesmaximal, characteristic, complemented
27#34208C211yesmaximal, characteristic, complemented
28#3515—232no—
29C2×#557C2212yes—
30C2×#554C2212yes—
31C2×#554C2212yes—
32C2×#553C2214yes—
33C2×#552C2214yes—
34C2×#552C2214yes—
35C2×#552C2214yes—
36C2×#552C2212yes—
37C2×#552C2212yes—
38C2×#550C2212yes—
39C2×#547C2212yes—
40C2×#547C2212yes—
41C2×#547C2212yes—
42C2×#541C2212yes—
43C2×#541C2211yescharacteristic
44C2×#539C2214yes—
45C2×#539C2214yes—
46C2×#533C2212yes—
47C2×#532C2211yescharacteristic
48C2×#529C2214yes—
49C2×#529C2212yes—
50C22×#125C2214yes—
51C2×#520C2212yes—
52C2×#520C2212yes—
53C2×C4×#41C2212yes—
54#2723C2214yes—
55#2721C2214yes—
56#2719C2214yes—
57#2719C2214yes—
58#2719C2214yes—
59#2707C2214yes—
60#2707C2214yes—
61#2707C2214yes—
62#2706C2214yes—
63#2705C2214yes—
64#2705C2214yes—
65#2703C2214yes—
66#2696C2214yes—
67#2696C2214yes—
68#2694C2214yes—
69#2692C2214yes—
70#2690C2214yes—
71#2687C2214yes—
72#2683C2214yes—
73#2681C2214yes—
74#2673C2214yes—
75#2673C2214yes—
76#2671C2214yes—
77#2671C2214yes—
78#2611C2214yes—
79#2611C2214yes—
80#2604C2214yes—
81#2603C2214yes—
82#2601C2214yes—
83#2601C2214yes—
84#2581C2212yes—
85#2565C2214yes—
86#2562C2214yes—
87#2560C2214yes—
88#2560C2214yes—
89#2558C2214yes—
90#2558C2214yes—
91#2556C2212yes—
92#2556C2214yes—
93#2555C2212yes—
94#2554C2212yes—
95#2553C2212yes—
96#2550C2212yes—
97#2546C2212yes—
98#2542C2212yes—
99#2538C2212yes—
100#2538C2212yes—
101#2536C2212yes—
102#2535C2212yes—
103#2521C2212yes—
104#2519C2212yes—
105#2519C2214yes—
106#2519C2214yes—
107#2506C2214yes—
108#2492C2212yes—
109#2490C2214yes—
110#2489C2214yes—
111#2489C2214yes—
112#2489C2212yes—
113#2488C2214yes—
114#2487C2212yes—
115#2486C2212yes—
116#2481C2214yes—
117#2481C2214yes—
118#2481C2214yes—
119#2481C2214yes—
120#2477C2214yes—
121#2477C2214yes—
122#2476C2214yes—
123#2475C2214yes—
124#2475C2214yes—
125#2473C2214yes—
126#2473C2214yes—
127#2471C2214yes—
128#2471C2214yes—
129#2470C2214yes—
130#2467C2214yes—
131#2466C2214yes—
132#2464C2212yes—
133#2463C2214yes—
134#2462C2214yes—
135#2462C2214yes—
136#2461C2214yes—
137#2461C2214yes—
138#2461C2212yes—
139#2460C2214yes—
140#2460C2214yes—
141#2457C2214yes—
142#2457C2214yes—
143#2456C2214yes—
144#2456C2214yes—
145#2454C2212yes—
146#2452C2212yes—
147#2449C2214yes—
148#2449C2214yes—
149#2446C2212yes—
150#2446C2212yes—
151#2445C2214yes—
152#2443C2214yes—
153#2443C2214yes—
154#2443C2214yes—
155#2443C2214yes—
156#2442C2214yes—
157#2442C2214yes—
158#2442C2212yes—
159#2441C2214yes—
160#2439C2212yes—
161#2438C2214yes—
162#2432C2212yes—
163#2432C2212yes—
164#2429C2212yes—
165#2429C2212yes—
166#2428C2214yes—
167#2427C2212yes—
168#2427C2212yes—
169#2426C2214yes—
170#2425C2214yes—
171#2422C2214yes—
172#2421C2212yes—
173#2421C2212yes—
174#2417C2214yes—
175#2417C2214yes—
176#2417C2212yes—
177#2415C2212yes—
178#2407C2212yes—
179#2407C2212yes—
180#2407C2212yes—
181#2407C2212yes—
182#2399C2211yescharacteristic
183#2398C2214yes—
184#2397C2211yescharacteristic
185#2392C2211yescharacteristic
186#2392C2211yescharacteristic
187#2392C2214yes—
188#2373C2214yes—
189#2373C2214yes—
190#2371C2214yes—
191#2370C2214yes—
192#2366C2214yes—
193#2366C2212yes—
194#2364C2214yes—
195#2364C2214yes—
196#2363C2214yes—
197#2363C2212yes—
198#2361C2214yes—
199#2361C2212yes—
200#2360C2214yes—
201#2359C2214yes—
202#2352C2214yes—
203#2352C2214yes—
204#2352C2214yes—
205#2352C2214yes—
206#2352C2212yes—
207#2351C2212yes—
208D4×C4⋊C4C2214yes—
209#2341C2212yes—
210#2341C2212yes—
211#2330C2211yescharacteristic
212#2328C2211yescharacteristic
213#2328C2214yes—
214#2328C2211yescharacteristic
215#2327C2211yescharacteristic
216#2327C2211yescharacteristic
217#2327C2211yescharacteristic
218#2324C2214yes—
219#2324C2212yes—
220#2323C2212yes—
221#2323C2212yes—
222#2314C2211yescharacteristic
223#2311C2212yes—
224C4×C4⋊Q8C2211yescharacteristic
225C4×#125C2211yescharacteristic
226C4×#124C2212yes—
227C4×#124C2212yes—
228C4×#124C2212yes—
229C4×C22⋊Q8C2214yes—
230C4×C22⋊Q8C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×#121C2214yes—
233C4×#121C2212yes—
234C4×#121C2212yes—
235#2295C2212yes—
236#2293C2211yescharacteristic
237#2290C2214yes—
238#2290C2214yes—
239#2290C2212yes—
240C2×#382C2211yescharacteristic
241#2276C2212yes—
242C42×D4C2211yescharacteristic
243C4×#117C2211yescharacteristic
244C22×#41C2312yes—
245C22×#41C2312yes—
246C22×#41C2312yes—
247#557—216no—
248#554—216no—
249#554—216no—
250#553—232no—
251#552—232no—
252#552—216no—
253#552—232no—
254#552—232no—
255#552—216no—
256#550—216no—
257#547—216no—
258#547—216no—
259#547—216no—
260#541—216no—
261#541D4116yescomplemented
262#539—232no—
263#539—232no—
264#533—216no—
265#532—28no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2314yes—
272C2×#127C2311yescharacteristic
273#529—232no—
274#529—216no—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2312yes—
279C2×#126C2312yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#125—232no—
283C2×#125C2314yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#125C2312yes—
293C2×#125C2314yes—
294C2×#125C2311yescharacteristic
295C2×#125C2314yes—
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2312yes—
303C2×#123C2312yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2312yes—
326C2×#121C2312yes—
327C2×#121C2314yes—
328C2×#121C2312yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2312yes—
336#520—216no—
337#520—216no—
338C4×#41—216no—
339C2×C4×Q8C2314yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2314yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2311yescharacteristic
372C2×#117C2312yes—
373C2×#117C2314yes—
374C2×#117C2314yes—
375C2×#117C2314yes—
376C2×#117C2312yes—
377C2×#117C2314yes—
378C2×#117C2314yes—
379C2×#117C2314yes—
380C2×#117C2311yescharacteristic
381C2×#117C2311yescharacteristic
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2314yes—
384C22×C4⋊C4C2314yes—
385C22×C4⋊C4C2314yes—
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2314yes—
389C22×C4⋊C4C2314yes—
390C22×C42C2314yes—
391C22×C42C2312yes—
392C22×C42C2311yescharacteristic
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#399C2314yes—
403#399C2314yes—
404#399C2314yes—
405#399C2312yes—
406#399C2312yes—
407#399C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2311yescharacteristic
419#398C2311yescharacteristic
420#398C2312yes—
421#398C2312yes—
422#398C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2311yescharacteristic
428#397C2311yescharacteristic
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2312yes—
438#396C2314yes—
439#396C2314yes—
440#396C2312yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2312yes—
448#395C2312yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2312yes—
457#394C2314yes—
458#394C2311yescharacteristic
459#394C2311yescharacteristic
460#394C2312yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#392C2314yes—
469#392C2314yes—
470#392C2311yescharacteristic
471#392C2311yescharacteristic
472#392C2312yes—
473#392C2312yes—
474#392C2314yes—
475#392C2314yes—
476#392C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2314yes—
487#390C2314yes—
488#390C2314yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2314yes—
494#390C2314yes—
495#390C2314yes—
496#390C2314yes—
497#390C2312yes—
498#390C2314yes—
499#390C2312yes—
500#390C2314yes—
501#390C2312yes—
502#390C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#388C2312yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2312yes—
552#388C2312yes—
553#388C2314yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
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#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#386C2312yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2312yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2314yes—
610#386C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2312yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#384C2311yescharacteristic
630#384C2314yes—
631#382C2311yescharacteristic
632#382C2314yes—
633#382C2311yescharacteristic
634#382C2311yescharacteristic
635#382C2314yes—
636#382C2314yes—
637#382C2312yes—
638#382C2312yes—
639#381C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2314yes—
655#380C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693#376C2311yescharacteristic
694#376C2311yescharacteristic
695#376C2314yes—
696#376C2314yes—
697C2×#95C2314yes—
698C43C2311yescharacteristic
699C43C2311yescharacteristic
700C2×#41—28no—
701C2×#41—28no—
702C2×#41—28no—
703C2×#41—28no—
704C2×#41—28no—
705C2×#41—28no—
706C2×#41—44no—
707C2×#41—44no—
708C2×#41—44no—
709C22×Q8C2412yes—
710C22×Q8C2412yes—
711C22×Q8C2412yes—
712C22×Q8C2414yes—
713C22×D4C2412yes—
714C22×D4C2414yes—
715C22×D4C2414yes—
716C22×D4C2414yes—
717C22×D4C2412yes—
718C22×D4C2412yes—
719C22×D4C2412yes—
720C22×D4C2414yes—
721C22×D4C2414yes—
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C22×D4C2411yescharacteristic
725C22×D4C2414yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2414yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C23×C4C2412yes—
733C23×C4C2411yescharacteristic
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C4⋊Q8—28no—
742C4⋊Q8—28no—
743C4⋊Q8—28no—
744C4⋊Q8—24no—
745C4⋊Q8C2×D418yes—
746#127—216no—
747#127#4118yes—
748#126—28no—
749#126—216no—
750#126—216no—
751#126—216no—
752#126—28no—
753#126—216no—
754#126C2×D4132yes—
755#125—28no—
756#125—216no—
757#125—216no—
758#125—216no—
759#125—216no—
760#125—216no—
761#125—216no—
762#125—216no—
763#125—216no—
764#125—28no—
765#125—216no—
766#125C2×D4132yes—
767#125C2×D418yes—
768#124—28no—
769#124—28no—
770#124—44no—
771#123—28no—
772#123—216no—
773#123—216no—
774#123—216no—
775#123—216no—
776#123—216no—
777#123—28no—
778#123—216no—
779#123—216no—
780#123—216no—
781#123—48no—
782C22⋊Q8—28no—
783C22⋊Q8—28no—
784C22⋊Q8—28no—
785C22⋊Q8—216no—
786C22⋊Q8—216no—
787C22⋊Q8—28no—
788C22⋊Q8—216no—
789C22⋊Q8—216no—
790C22⋊Q8—216no—
791C22⋊Q8—28no—
792C22⋊Q8—216no—
793C22⋊Q8—48no—
794C22⋊Q8—48no—
795C22⋊Q8—44no—
796C22⋊Q8—44no—
797C22⋊Q8C2×D4116yes—
798#121—216no—
799#121—28no—
800#121—28no—
801#121—216no—
802#121—216no—
803#121—216no—
804#121—216no—
805#121—28no—
806#121—216no—
807#121—44no—
808C4×Q8—28no—
809C4×Q8—28no—
810C4×Q8—216no—
811C4×Q8—28no—
812C4×Q8—28no—
813C4×Q8—28no—
814C4×Q8—216no—
815C4×Q8—28no—
816C4×Q8—44no—
817C4×Q8C2×D4116yes—
818C4×D4—216no—
819C4×D4—216no—
820C4×D4—28no—
821C4×D4—28no—
822C4×D4—28no—
823C4×D4—216no—
824C4×D4—216no—
825C4×D4—28no—
826C4×D4—216no—
827C4×D4—216no—
828C4×D4—216no—
829C4×D4—28no—
830C4×D4—216no—
831C4×D4—28no—
832C4×D4—216no—
833C4×D4—28no—
834C4×D4—28no—
835C4×D4—42no—
836C4×D4—42no—
837C4×D4—48no—
838C4×D4—48no—
839C4×D4—48no—
840C4×D4—44no—
841#117—28no—
842#117—216no—
843#117—216no—
844#117—216no—
845#117—216no—
846#117—28no—
847#117—216no—
848#117—216no—
849#117—42no—
850#117C2×D418yes—
851C2×C4⋊C4—28no—
852C2×C4⋊C4—216no—
853C2×C4⋊C4—216no—
854C2×C4⋊C4—28no—
855C2×C4⋊C4—216no—
856C2×C4⋊C4—216no—
857C2×C4⋊C4—216no—
858C2×C4⋊C4—216no—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2411yescharacteristic
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2411yescharacteristic
942C2×C22⋊C4C2411yescharacteristic
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C42—216no—
968C2×C42—28no—
969C2×C42—24no—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2414yes—
982C2×C42C2411yescharacteristic
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2411yescharacteristic
993C2×C42C2414yes—
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2411yescharacteristic
1018#95C2411yescharacteristic
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2411yescharacteristic
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2411yescharacteristic
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045C24C2512yes—
1046C24C2512yes—
1047C24C2511yescharacteristic
1048C24C2514yes—
1049#41—432no—
1050#41—432no—
1051#41—432no—
1052C2×Q8—24no—
1053C2×Q8—24no—
1054C2×Q8—28no—
1055C2×Q8—24no—
1056C2×Q8—24no—
1057C2×Q8—24no—
1058C2×Q8—24no—
1059C2×Q8—24no—
1060C2×Q8—42no—
1061C2×Q8—44no—
1062C2×Q8—44no—
1063C2×Q8C22×D418yes—
1064C2×D4—24no—
1065C2×D4—28no—
1066C2×D4—28no—
1067C2×D4—28no—
1068C2×D4—28no—
1069C2×D4—24no—
1070C2×D4—28no—
1071C2×D4—28no—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—28no—
1075C2×D4—24no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—44no—
1080C2×D4—41no—
1081C2×D4—42no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—41no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4C2×#4118yes—
1100C2×D4C2×#41116yes—
1101C22×C4—22no—
1102C22×C4—22no—
1103C22×C4—28no—
1104C22×C4—28no—
1105C22×C4—28no—
1106C22×C4—28no—
1107C22×C4—28no—
1108C22×C4—28no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—28no—
1112C22×C4—28no—
1113C22×C4—24no—
1114C22×C4—24no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—28no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—28no—
1121C22×C4—24no—
1122C22×C4—28no—
1123C22×C4—28no—
1124C22×C4—28no—
1125C22×C4—24no—
1126C22×C4—42no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—42no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—42no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—42no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—42no—
1144C22×C4—44no—
1145C22×C4C22×D414yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2514yes—
1148C22×C4C2511yescharacteristic
1149C22×C4C2512yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2514yes—
1153C22×C4C2514yes—
1154C22×C4C2512yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2514yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2514yes—
1164C22×C4C2514yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C4⋊C4—24no—
1170C4⋊C4—28no—
1171C4⋊C4—28no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—28no—
1181C4⋊C4—24no—
1182C4⋊C4—28no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—24no—
1190C4⋊C4—28no—
1191C4⋊C4—28no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—28no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—28no—
1198C4⋊C4—28no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—28no—
1202C4⋊C4—24no—
1203C4⋊C4—24no—
1204C4⋊C4—28no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4C22×D418yes—
1220C4⋊C4C22×D4116yes—
1221C4⋊C4C22×D418yes—
1222C4⋊C4C22×D4116yes—
1223C4⋊C4C22×D4116yes—
1224C4⋊C4C22×D4116yes—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—28no—
1235C22⋊C4—28no—
1236C22⋊C4—28no—
1237C22⋊C4—28no—
1238C22⋊C4—24no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—24no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—28no—
1249C22⋊C4—24no—
1250C22⋊C4—24no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—42no—
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—42no—
1274C22⋊C4—42no—
1275C22⋊C4C22×D4116yes—
1276C22⋊C4C22×D418yes—
1277C42—24no—
1278C42—28no—
1279C42—24no—
1280C42—28no—
1281C42—24no—
1282C42—28no—
1283C42—28no—
1284C42—28no—
1285C42—24no—
1286C42—24no—
1287C42—22no—
1288C42—28no—
1289C42—22no—
1290C42—22no—
1291C42—42no—
1292C42—42no—
1293C42—42no—
1294C42—44no—
1295C42—44no—
1296C42—44no—
1297C42—44no—
1298C42—42no—
1299C42C22×D414yes—
1300C42C22×D4116yes—
1301C42C22×D414yes—
1302C42C2×#4114yes—
1303C23—24no—
1304C23—21no—
1305C23—24no—
1306C23—24no—
1307C23—21no—
1308C23—22no—
1309C23—24no—
1310C23—24no—
1311C23—24no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23—22no—
1327C23C23×D412yes—
1328C23C22×#4118yes—
1329C23C2611yescharacteristic
1330Q8—216no—
1331Q8—48no—
1332Q8—48no—
1333Q8—88no—
1334D4—216no—
1335D4—416no—
1336D4—48no—
1337D4—416no—
1338D4—416no—
1339D4—416no—
1340D4—44no—
1341D4—84no—
1342D4—84no—
1343D4—88no—
1344D4—88no—
1345D4—84no—
1346D4—82no—
1347C2×C4—22no—
1348C2×C4—21no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—28no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—48no—
1404C2×C4—416no—
1405C2×C4—416no—
1406C2×C4—416no—
1407C2×C4—416no—
1408C2×C4—48no—
1409C2×C4—48no—
1410C2×C4—84no—
1411C2×C4—88no—
1412C2×C4—84no—
1413C2×C4—88no—
1414C2×C4—88no—
1415C2×C4—88no—
1416C2×C4—88no—
1417C2×C4C23×D414yes—
1418C2×C4C23×D414yes—
1419C2×C4C23×D418yes—
1420C2×C4C23×D418yes—
1421C2×C4C23×D412yes—
1422C2×C4C23×D412yes—
1423C2×C4C22×#4114yes—
1424C2×C4C22×#4112yes—
1425C2×C4#58514yes—
1426C2×C4#58512yes—
1427C22—28no—
1428C22—28no—
1429C22—24no—
1430C22—22no—
1431C22—28no—
1432C22—42no—
1433C22—44no—
1434C22—44no—
1435C22—44no—
1436C22—41no—
1437C22—41no—
1438C22—44no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22C24×D411yescharacteristic
1454C22C23×#4111yescharacteristic
1455C22C2×#58512yes—
1456C22C2×#58511yescharacteristic
1457C222−1+612yes—
1458C4—24no—
1459C4—24no—
1460C4—24no—
1461C4—28no—
1462C4—24no—
1463C4—22no—
1464C4—28no—
1465C4—42no—
1466C4—44no—
1467C4—44no—
1468C4—42no—
1469C4—44no—
1470C4—42no—
1471C4—42no—
1472C4—41no—
1473C4—44no—
1474C4—41no—
1475C4—41no—
1476C4—41no—
1477C4—42no—
1478C4—42no—
1479C4—44no—
1480C4D4×#4114yes—
1481C2—48no—
1482C2—42no—
1483C2—82no—
1484C2—82no—
1485C2C2×D4×#4111yescharacteristic
1486C2#6284011yescharacteristic
1487C2#6289011yescharacteristic
1488C2#6299112yes—
1489C2#6300212yes—
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×#3515C2semidirect
2. #59586C2semidirect
3. #59418C2semidirect
4. #59317C2semidirect
5. #59178C2semidirect
6. #59163C2semidirect
7. #59161C2semidirect
8. #59140C2semidirect
9. #59066C2semidirect
10. #45432C2semidirect
11. #45412C2semidirect
12. #45387C2semidirect
13. #45334C2semidirect
14. #44996C2semidirect
15. #44948C2semidirect
16. #44635C2semidirect
17. #44579C2semidirect
18. #44382C2semidirect
19. #44160C2semidirect
20. #35637C2semidirect
21. #35625C2semidirect
22. #35521C2semidirect
23. #34880C2semidirect
24. #34720C2semidirect
25. #34295C2semidirect
26. #34281C2semidirect
27. #34208C2semidirect
261. #541D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
#595862
#594182
#593172
#591782
#591632
#591612
#591402
#590662
#454322
#454122
#453872
#453342
#449962
#449482
#446352
#445792
#443822
#441602
#356372
#356252
#355212
#348802
#347202
#342952
#342812
#342082