Finite Group Databasebeta

← #7848982

Subgroups — #7848982

Order 512.

4628 conjugacy classes of subgroups.

The subgroup lattice has 1451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59951C212yesmaximal, complemented
2#59871C212yesmaximal, complemented
3#59714C212yesmaximal, complemented
4#59694C212yesmaximal, complemented
5#59642C212yesmaximal, complemented
6#52280C211yesmaximal, characteristic
7#52049C214yesmaximal, complemented
8#50146C214yesmaximal, complemented
9#49133C214yesmaximal, complemented
10#47777C214yesmaximal, complemented
11#46285C212yesmaximal, complemented
12#45345C212yesmaximal, complemented
13#45238C212yesmaximal, complemented
14#45217C212yesmaximal, complemented
15#44978C212yesmaximal, complemented
16#44195C214yesmaximal, complemented
17#43386C214yesmaximal, complemented
18#42911C212yesmaximal, complemented
19#39830C212yesmaximal, complemented
20#39640C211yesmaximal, characteristic, complemented
21#39632C211yesmaximal, characteristic, complemented
22#39574C212yesmaximal, complemented
23#37324C211yesmaximal, characteristic, complemented
24#36481C211yesmaximal, characteristic, complemented
25#36473C211yesmaximal, characteristic, complemented
26#35686C212yesmaximal, complemented
27#35671C212yesmaximal, complemented
28#34481C212yesmaximal, complemented
29#34276C211yesmaximal, characteristic, complemented
30C2×#556C2212yes—
31C2×#552C2212yes—
32C2×#541C2212yes—
33C2×#536C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#519C2211yescharacteristic
36#2863C2212yes—
37#2860C2212yes—
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2821C2214yes—
41#2808C2211yescharacteristic
42#2808C2212yes—
43#2807C2214yes—
44#2807C2214yes—
45#2806C2211yescharacteristic
46#2806C2212yes—
47#2806C2212yes—
48#2806C2212yes—
49#2805C2212yes—
50#2805C2212yes—
51#2804C2212yes—
52#2803C2212yes—
53#2802C2214yes—
54#2798C2214yes—
55#2798C2214yes—
56#2796C2214yes—
57#2794C2214yes—
58#2790C2214yes—
59#2788C2214yes—
60#2781C2212yes—
61#2775C2212yes—
62#2774C2214yes—
63#2772C2214yes—
64#2771C2214yes—
65#2770C2214yes—
66#2769C2214yes—
67#2758C2214yes—
68#2756C2212yes—
69#2741C2214yes—
70#2733C2211yescharacteristic
71#2731C2214yes—
72#2730C2212yes—
73#2727C2211yescharacteristic
74#2727C2212yes—
75#2727C2214yes—
76#2721C2214yes—
77#2721C2214yes—
78#2721C2214yes—
79#2719C2214yes—
80#2718C2214yes—
81#2718C2214yes—
82#2718C2214yes—
83#2718C2214yes—
84#2718C2214yes—
85#2716C2214yes—
86#2714C2212yes—
87#2710C2214yes—
88#2710C2214yes—
89#2702C2214yes—
90#2694C2214yes—
91#2662C2214yes—
92#2646C2212yes—
93#2646C2212yes—
94#2633C2214yes—
95#2632C2214yes—
96#2616C2212yes—
97#2611C2214yes—
98#2607C2214yes—
99#2606C2214yes—
100#2606C2214yes—
101#2604C2214yes—
102#2604C2214yes—
103#2604C2214yes—
104#2602C2214yes—
105#2601C2214yes—
106#2599C2214yes—
107#2596C2214yes—
108#2593C2214yes—
109#2589C2214yes—
110#2589C2214yes—
111#2588C2214yes—
112#2587C2214yes—
113#2587C2214yes—
114#2585C2214yes—
115#2584C2214yes—
116#2584C2214yes—
117#2582C2214yes—
118#2582C2214yes—
119#2580C2214yes—
120#2570C2214yes—
121#2568C2212yes—
122#2567C2214yes—
123#2554C2214yes—
124#2552C2211yescharacteristic
125#2552C2214yes—
126#2552C2214yes—
127#2551C2211yescharacteristic
128#2546C2212yes—
129#2546C2211yescharacteristic
130#2542C2212yes—
131#2542C2211yescharacteristic
132#2542C2212yes—
133#2533C2214yes—
134#2532C2214yes—
135#2532C2214yes—
136#2529C2214yes—
137#2529C2214yes—
138#2522C2214yes—
139#2521C2214yes—
140#2519C2214yes—
141#2515C2214yes—
142#2511C2212yes—
143#2511C2212yes—
144#2507C2212yes—
145#2507C2214yes—
146#2507C2214yes—
147#2505C2214yes—
148#2502C2212yes—
149#2502C2212yes—
150#2496C2212yes—
151#2496C2212yes—
152#2492C2212yes—
153#2492C2212yes—
154#2492C2212yes—
155#2492C2212yes—
156#2492C2212yes—
157#2491C2212yes—
158#2486C2212yes—
159#2479C2214yes—
160#2479C2214yes—
161#2478C2214yes—
162#2478C2214yes—
163#2475C2214yes—
164#2469C2214yes—
165#2469C2214yes—
166#2468C2214yes—
167#2466C2214yes—
168#2466C2214yes—
169#2462C2214yes—
170#2458C2214yes—
171#2458C2214yes—
172#2455C2214yes—
173#2455C2214yes—
174#2453C2212yes—
175#2450C2214yes—
176#2446C2212yes—
177#2446C2212yes—
178#2441C2212yes—
179#2441C2212yes—
180#2441C2214yes—
181#2434C2212yes—
182#2429C2212yes—
183#2429C2212yes—
184#2429C2212yes—
185#2429C2212yes—
186#2429C2212yes—
187#2423C2212yes—
188#2423C2212yes—
189#2423C2212yes—
190#2417C2212yes—
191#2415C2212yes—
192#2415C2212yes—
193#2415C2212yes—
194#2415C2212yes—
195#2409C2212yes—
196#2395C2212yes—
197#2392C2212yes—
198#2392C2214yes—
199#2388C2212yes—
200#2383C2214yes—
201#2383C2214yes—
202#2373C2214yes—
203#2370C2212yes—
204#2369C2214yes—
205#2367C2214yes—
206#2367C2214yes—
207#2365C2211yescharacteristic
208#2365C2212yes—
209#2365C2211yescharacteristic
210#2365C2214yes—
211#2362C2212yes—
212#2362C2212yes—
213#2362C2212yes—
214#2360C2212yes—
215#2360C2212yes—
216#2360C2212yes—
217#2360C2212yes—
218#2360C2212yes—
219#2359C2214yes—
220#2359C2214yes—
221#2354C2211yescharacteristic
222Q8×C4⋊C4C2212yes—
223Q8×C4⋊C4C2214yes—
224Q8×C4⋊C4C2211yescharacteristic
225D4×C4⋊C4C2212yes—
226D4×C4⋊C4C2212yes—
227#2347C2212yes—
228#2347C2212yes—
229#2347C2212yes—
230#2334C2214yes—
231#2334C2214yes—
232#2329C2212yes—
233#2327C2212yes—
234#2326C2212yes—
235#2326C2214yes—
236#2325C2212yes—
237#2323C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2320C2214yes—
241#2317C2211yescharacteristic
242#2317C2212yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2212yes—
248C4×#126C2212yes—
249C4×#124C2212yes—
250C4×#124C2212yes—
251C4×C22⋊Q8C2211yescharacteristic
252C4×#121C2211yescharacteristic
253#2297C2211yescharacteristic
254#2295C2212yes—
255#2295C2212yes—
256C2×#391C2211yescharacteristic
257#2293C2212yes—
258C4×#117C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#556—216no—
262#552—48no—
263#541—48no—
264#536—28no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×#126C2312yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#124C2314yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×#121C2311yescharacteristic
302#520—44no—
303#519—44no—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2311yescharacteristic
331C2×#117C2314yes—
332C2×#117C2314yes—
333C2×#117C2311yescharacteristic
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C42C2311yescharacteristic
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2312yes—
362#399C2314yes—
363#399C2314yes—
364#398C2314yes—
365#398C2314yes—
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#398C2312yes—
386#398C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2312yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2312yes—
403#396C2314yes—
404#396C2312yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2312yes—
420#394C2312yes—
421#394C2312yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#393C2312yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#392C2312yes—
435#392C2312yes—
436#392C2312yes—
437#392C2312yes—
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2314yes—
459#391C2314yes—
460#391C2311yescharacteristic
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#390C2312yes—
466#390C2314yes—
467#390C2312yes—
468#390C2311yescharacteristic
469#390C2312yes—
470#390C2312yes—
471#390C2311yescharacteristic
472#390C2312yes—
473#390C2314yes—
474#390C2311yescharacteristic
475#389C2311yescharacteristic
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2311yescharacteristic
525#389C2312yes—
526#389C2314yes—
527#388C2312yes—
528#388C2312yes—
529#388C2312yes—
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#388C2312yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2312yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2312yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2312yes—
572#388C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
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#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2312yes—
617#386C2312yes—
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#385C2314yes—
637#385C2312yes—
638#384C2312yes—
639#384C2312yes—
640#384C2312yes—
641#384C2312yes—
642#384C2312yes—
643#384C2314yes—
644#384C2314yes—
645#384C2314yes—
646#384C2314yes—
647#384C2311yescharacteristic
648#384C2311yescharacteristic
649#383C2312yes—
650#383C2314yes—
651#383C2314yes—
652#383C2314yes—
653#382C2314yes—
654#382C2312yes—
655#382C2312yes—
656#382C2314yes—
657#381C2314yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2311yescharacteristic
667#380C2311yescharacteristic
668#380C2314yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2311yescharacteristic
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2314yes—
712#376C2312yes—
713#376C2314yes—
714C2×#95C2312yes—
715C2×#95C2312yes—
716C43C2312yes—
717C43C2312yes—
718C2×#41—24no—
719C2×#41—42no—
720C2×#41—42no—
721C22×Q8—24no—
722C22×Q8—42no—
723C22×Q8—42no—
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C4⋊Q8—28no—
747C4⋊Q8—28no—
748C4⋊Q8—28no—
749C4⋊Q8—28no—
750C4⋊Q8—42no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753C4⋊Q8—44no—
754#126—28no—
755#126—216no—
756#126—216no—
757#126—48no—
758#126—48no—
759#126—48no—
760#126—84no—
761#125—28no—
762#125—48no—
763#125—48no—
764#125—48no—
765#124—28no—
766#124—216no—
767#124—28no—
768#123—216no—
769#123—48no—
770#123—84no—
771C22⋊Q8—24no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—28no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—82no—
782#121—24no—
783C4×Q8—28no—
784C4×Q8—28no—
785C4×Q8—216no—
786C4×Q8—42no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—84no—
794C4×Q8—84no—
795C4×Q8—82no—
796C4×Q8—82no—
797C4×D4—28no—
798C4×D4—48no—
799C4×D4—44no—
800C4×D4—42no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—84no—
804C4×D4—84no—
805#117—28no—
806#117—24no—
807#117—28no—
808#117—42no—
809#117—44no—
810#117—48no—
811#117—48no—
812#117#4118yes—
813C2×C4⋊C4—42no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C42—42no—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2414yes—
940C2×C42C2411yescharacteristic
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2411yescharacteristic
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024C24C2512yes—
1025C24C2512yes—
1026C24C2511yescharacteristic
1027#41—416no—
1028C2×Q8—24no—
1029C2×Q8—28no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—24no—
1035C2×Q8—28no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—42no—
1040C2×Q8—41no—
1041C2×Q8—41no—
1042C2×Q8—41no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—41no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—416no—
1049C2×Q82−1+414yes—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—22no—
1056C2×D4—41no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—41no—
1065C2×D4—42no—
1066C2×D4—41no—
1067C2×D4—42no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4C2×#4114yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—22no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—41no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—41no—
1155C4⋊C4—41no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—41no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—41no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—41no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4C2×#4114yes—
1189C4⋊C4C2×#4114yes—
1190C4⋊C4H(5,𝔽2)14yes—
1191C4⋊C42−1+414yes—
1192C22⋊C4—24no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—24no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—28no—
1201C22⋊C4—28no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4C2×#4118yes—
1234C42—28no—
1235C42—24no—
1236C42—28no—
1237C42—28no—
1238C42—24no—
1239C42—24no—
1240C42—24no—
1241C42—28no—
1242C42—24no—
1243C42—24no—
1244C42—24no—
1245C42—24no—
1246C42—22no—
1247C42—22no—
1248C42—24no—
1249C42—41no—
1250C42—41no—
1251C42—42no—
1252C42—42no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—42no—
1260C42—42no—
1261C42—44no—
1262C42—44no—
1263C42C2×#4118yes—
1264C23—21no—
1265C23—21no—
1266C23—21no—
1267C23—21no—
1268C23—21no—
1269C23—21no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23C22×#4112yes—
1285C23C2611yescharacteristic
1286Q8—44no—
1287Q8—416no—
1288Q8—48no—
1289Q8—44no—
1290Q8—48no—
1291Q8—48no—
1292Q8—84no—
1293D4—48no—
1294D4—48no—
1295D4—44no—
1296D4—48no—
1297D4—82no—
1298D4—84no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—28no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—48no—
1368C2×C4—48no—
1369C2×C4—48no—
1370C2×C4—82no—
1371C2×C4—82no—
1372C2×C4—88no—
1373C2×C4—162no—
1374C2×C4—164no—
1375C2×C4C22×#4114yes—
1376C2×C4C22×#4112yes—
1377C2×C4C22×#4114yes—
1378C2×C4C22×#4112yes—
1379C2×C4C2×H(5,𝔽2)14yes—
1380C2×C4C2×H(5,𝔽2)12yes—
1381C2×C4C2×2−1+412yes—
1382C2×C4C2×2−1+412yes—
1383C2×C4C2×2−1+414yes—
1384C2×C4C2×2−1+414yes—
1385C2×C4#58512yes—
1386C22—22no—
1387C22—22no—
1388C22—22no—
1389C22—41no—
1390C22—41no—
1391C22—41no—
1392C22—41no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22C23×#4111yescharacteristic
1408C22C22×H(5,𝔽2)11yescharacteristic
1409C22C22×2−1+411yescharacteristic
1410C22C22×2−1+411yescharacteristic
1411C22C2×#58511yescharacteristic
1412C22H(7,𝔽2)11yescharacteristic
1413C222−1+611yescharacteristic
1414C4—24no—
1415C4—24no—
1416C4—24no—
1417C4—22no—
1418C4—24no—
1419C4—22no—
1420C4—24no—
1421C4—22no—
1422C4—44no—
1423C4—42no—
1424C4—42no—
1425C4—42no—
1426C4—44no—
1427C4—44no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—44no—
1432C4—44no—
1433C4—42no—
1434C4—42no—
1435C4—41no—
1436C4—44no—
1437C4—42no—
1438C4—41no—
1439C4#350614yes—
1440C2—42no—
1441C2—82no—
1442C2—82no—
1443C2C2×#350611yescharacteristic
1444C2#6290211yescharacteristic
1445C2#6293211yescharacteristic
1446C2#6300011yescharacteristic
1447C2#6300111yescharacteristic
1448C2#6303711yescharacteristic
1449C2#6305211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52280C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59951C2semidirect
2. #59871C2semidirect
3. #59714C2semidirect
4. #59694C2semidirect
5. #59642C2semidirect
7. #52049C2semidirect
8. #50146C2semidirect
9. #49133C2semidirect
10. #47777C2semidirect
11. #46285C2semidirect
12. #45345C2semidirect
13. #45238C2semidirect
14. #45217C2semidirect
15. #44978C2semidirect
16. #44195C2semidirect
17. #43386C2semidirect
18. #42911C2semidirect
19. #39830C2semidirect
20. #39640C2semidirect
21. #39632C2semidirect
22. #39574C2semidirect
23. #37324C2semidirect
24. #36481C2semidirect
25. #36473C2semidirect
26. #35686C2semidirect
27. #35671C2semidirect
28. #34481C2semidirect
29. #34276C2semidirect

Maximal subgroups

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

subgroupindex
#599512
#598712
#597142
#596942
#596422
#522802
#520492
#501462
#491332
#477772
#462852
#453452
#452382
#452172
#449782
#441952
#433862
#429112
#398302
#396402
#396322
#395742
#373242
#364812
#364732
#356862
#356712
#344812
#342762