Finite Group Databasebeta

← #7895405

Subgroups — #7895405

Order 512.

4725 conjugacy classes of subgroups.

The subgroup lattice has 1496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59856C212yesmaximal, complemented
2#59823C211yesmaximal, characteristic, complemented
3#52160C211yesmaximal, characteristic, complemented
4#50798C214yesmaximal, complemented
5#49478C214yesmaximal, complemented
6#48372C214yesmaximal, complemented
7#46877C214yesmaximal, complemented
8#46315C212yesmaximal, complemented
9#45356C212yesmaximal, complemented
10#45196C212yesmaximal, complemented
11#44977C212yesmaximal, complemented
12#43285C214yesmaximal, complemented
13#42855C214yesmaximal, complemented
14#42690C212yesmaximal, complemented
15#42620C212yesmaximal, complemented
16#40198C212yesmaximal, complemented
17#39710C212yesmaximal, complemented
18#39637C211yesmaximal, characteristic, complemented
19#39373C211yesmaximal, characteristic, complemented
20#39259C212yesmaximal, complemented
21#38780C212yesmaximal, complemented
22#38042C212yesmaximal, complemented
23#37220C212yesmaximal, complemented
24#36468C211yesmaximal, characteristic, complemented
25#35699C212yesmaximal, complemented
26#35635C212yesmaximal, complemented
27#35206C211yesmaximal, characteristic, complemented
28#34464C212yesmaximal, complemented
29#34316C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×#553C2212yes—
32C2×#547C2211yescharacteristic
33C2×#541C2212yes—
34C2×#529C2212yes—
35#2859C2211yescharacteristic
36#2855C2212yes—
37#2854C2212yes—
38#2854C2212yes—
39#2851C2212yes—
40#2829C2214yes—
41#2829C2214yes—
42#2809C2212yes—
43#2806C2212yes—
44#2805C2212yes—
45#2802C2214yes—
46#2800C2214yes—
47#2786C2214yes—
48#2786C2214yes—
49#2780C2214yes—
50#2780C2214yes—
51#2779C2214yes—
52#2779C2214yes—
53#2777C2214yes—
54#2773C2214yes—
55#2772C2214yes—
56#2756C2214yes—
57#2753C2214yes—
58#2753C2214yes—
59#2747C2214yes—
60#2741C2214yes—
61#2740C2214yes—
62#2740C2214yes—
63#2733C2211yescharacteristic
64#2732C2211yescharacteristic
65#2732C2214yes—
66#2732C2212yes—
67#2732C2214yes—
68#2732C2212yes—
69#2730C2212yes—
70#2727C2211yescharacteristic
71#2727C2212yes—
72#2727C2214yes—
73#2727C2212yes—
74#2726C2212yes—
75#2726C2212yes—
76#2726C2212yes—
77#2725C2214yes—
78#2725C2214yes—
79#2721C2214yes—
80#2721C2212yes—
81#2714C2214yes—
82#2714C2212yes—
83#2707C2214yes—
84#2705C2212yes—
85#2705C2214yes—
86#2699C2214yes—
87#2695C2214yes—
88#2694C2214yes—
89#2694C2214yes—
90#2694C2212yes—
91#2694C2214yes—
92#2682C2211yescharacteristic
93#2673C2212yes—
94#2672C2214yes—
95#2671C2214yes—
96#2667C2214yes—
97#2654C2214yes—
98#2652C2214yes—
99#2652C2214yes—
100#2648C2214yes—
101#2648C2214yes—
102#2647C2212yes—
103#2629C2212yes—
104#2624C2212yes—
105#2624C2214yes—
106#2602C2214yes—
107#2601C2214yes—
108#2596C2214yes—
109#2590C2214yes—
110#2587C2214yes—
111#2587C2214yes—
112#2585C2214yes—
113#2585C2214yes—
114#2584C2212yes—
115#2579C2214yes—
116#2569C2214yes—
117#2568C2211yescharacteristic
118#2562C2214yes—
119#2562C2212yes—
120#2559C2214yes—
121#2559C2214yes—
122#2558C2214yes—
123#2556C2214yes—
124#2554C2214yes—
125#2553C2214yes—
126#2552C2212yes—
127#2552C2211yescharacteristic
128#2547C2211yescharacteristic
129#2542C2212yes—
130#2540C2212yes—
131#2540C2212yes—
132#2538C2214yes—
133#2538C2212yes—
134#2538C2211yescharacteristic
135#2537C2211yescharacteristic
136#2537C2211yescharacteristic
137#2536C2212yes—
138#2535C2212yes—
139#2522C2214yes—
140#2522C2214yes—
141#2522C2214yes—
142#2522C2214yes—
143#2521C2214yes—
144#2519C2214yes—
145#2519C2214yes—
146#2519C2214yes—
147#2515C2214yes—
148#2512C2214yes—
149#2511C2212yes—
150#2507C2212yes—
151#2506C2212yes—
152#2506C2214yes—
153#2497C2212yes—
154#2496C2214yes—
155#2496C2212yes—
156#2496C2212yes—
157#2495C2212yes—
158#2490C2214yes—
159#2490C2214yes—
160#2489C2212yes—
161#2487C2214yes—
162#2487C2212yes—
163#2485C2212yes—
164#2485C2212yes—
165#2485C2212yes—
166#2476C2214yes—
167#2475C2214yes—
168#2470C2214yes—
169#2468C2214yes—
170#2467C2214yes—
171#2467C2214yes—
172#2466C2214yes—
173#2460C2214yes—
174#2456C2214yes—
175#2456C2214yes—
176#2454C2214yes—
177#2454C2214yes—
178#2453C2214yes—
179#2449C2214yes—
180#2447C2212yes—
181#2428C2212yes—
182#2426C2212yes—
183#2426C2212yes—
184#2425C2214yes—
185#2425C2214yes—
186#2423C2212yes—
187#2423C2212yes—
188#2417C2212yes—
189#2417C2212yes—
190#2417C2212yes—
191#2417C2212yes—
192#2417C2212yes—
193#2416C2212yes—
194#2416C2214yes—
195#2416C2212yes—
196#2415C2212yes—
197#2415C2212yes—
198#2415C2212yes—
199#2407C2214yes—
200#2407C2214yes—
201#2397C2212yes—
202#2392C2214yes—
203#2392C2212yes—
204#2392C2212yes—
205#2382C2214yes—
206#2378C2214yes—
207#2374C2214yes—
208#2370C2212yes—
209#2366C2212yes—
210#2365C2211yescharacteristic
211#2364C2214yes—
212#2363C2212yes—
213#2362C2212yes—
214#2362C2212yes—
215#2360C2214yes—
216#2360C2212yes—
217#2354C2211yescharacteristic
218#2354C2211yescharacteristic
219#2354C2211yescharacteristic
220#2352C2214yes—
221#2352C2212yes—
222#2351C2212yes—
223D4×C4⋊C4C2212yes—
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227#2345C2212yes—
228#2345C2212yes—
229#2344C2212yes—
230#2341C2212yes—
231#2336C2214yes—
232#2335C2214yes—
233#2333C2214yes—
234#2331C2212yes—
235#2329C2214yes—
236#2326C2212yes—
237#2324C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2323C2214yes—
241#2320C2212yes—
242#2318C2214yes—
243#2316C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×#121C2212yes—
251C4×#121C2212yes—
252#2297C2212yes—
253#2295C2211yescharacteristic
254#2293C2211yescharacteristic
255C2×#389C2212yes—
256#2290C2212yes—
257#2274C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260#554—216no—
261#553—48no—
262#547—28no—
263#541—48no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×#127C2311yescharacteristic
267#529—48no—
268C2×#126C2312yes—
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2312yes—
286C2×#123C2312yes—
287C2×#123C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2314yes—
344C22×C42C2312yes—
345C22×C42C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2312yes—
360#399C2312yes—
361#399C2312yes—
362#399C2312yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2312yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2312yes—
413#396C2312yes—
414#396C2312yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#395C2314yes—
421#394C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2312yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#392C2312yes—
444#392C2314yes—
445#392C2314yes—
446#392C2312yes—
447#392C2312yes—
448#392C2312yes—
449#392C2314yes—
450#392C2312yes—
451#392C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2314yes—
461#391C2311yescharacteristic
462#391C2311yescharacteristic
463#390C2311yescharacteristic
464#390C2312yes—
465#390C2311yescharacteristic
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2312yes—
471#390C2312yes—
472#390C2314yes—
473#390C2314yes—
474#390C2311yescharacteristic
475#390C2312yes—
476#390C2314yes—
477#390C2314yes—
478#390C2314yes—
479#390C2314yes—
480#390C2314yes—
481#390C2311yescharacteristic
482#390C2314yes—
483#390C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2311yescharacteristic
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2311yescharacteristic
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2312yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2312yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2314yes—
560#388C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
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#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2314yes—
602#386C2312yes—
603#386C2314yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2312yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2312yes—
637#384C2311yescharacteristic
638#384C2311yescharacteristic
639#384C2311yescharacteristic
640#384C2312yes—
641#384C2311yescharacteristic
642#384C2311yescharacteristic
643#384C2314yes—
644#383C2314yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#382C2312yes—
649#381C2314yes—
650#381C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2312yes—
656#380C2312yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2314yes—
675#380C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714#376C2312yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C2×#41—28no—
718C2×#41—82no—
719C2×#41—82no—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2414yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2414yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C4⋊Q8—24no—
749C4⋊Q8#4118yes—
750#127—24no—
751#126—44no—
752#126—44no—
753#126—48no—
754#126—48no—
755#126—48no—
756#126—84no—
757#125—216no—
758#125—28no—
759#125—44no—
760#125—48no—
761#125—48no—
762#125—82no—
763#125—84no—
764#124—44no—
765#124—44no—
766#123—216no—
767#123—44no—
768#123—48no—
769#123—44no—
770#123—84no—
771C22⋊Q8—28no—
772C22⋊Q8—216no—
773C22⋊Q8—216no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—82no—
782#121—28no—
783#121—28no—
784#121—28no—
785#121—44no—
786#121—48no—
787#121—44no—
788#121—44no—
789#121—82no—
790#121—84no—
791#121—84no—
792C4×Q8—28no—
793C4×Q8—24no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—82no—
797C4×Q8—82no—
798C4×D4—216no—
799C4×D4—24no—
800C4×D4—24no—
801C4×D4—28no—
802C4×D4—28no—
803C4×D4—24no—
804C4×D4—42no—
805C4×D4—42no—
806C4×D4—42no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—44no—
810C4×D4—44no—
811C4×D4—48no—
812C4×D4—82no—
813C4×D4—84no—
814C4×D4—84no—
815C4×D4—84no—
816#117—28no—
817#117—44no—
818#117—44no—
819#117—44no—
820#117—84no—
821#117—82no—
822C2×C4⋊C4—28no—
823C2×C4⋊C4—28no—
824C2×C4⋊C4—28no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4—84no—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C42—44no—
951C2×C42—82no—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2411yescharacteristic
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2412yes—
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2411yescharacteristic
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030C24C2512yes—
1031C24C2512yes—
1032C24C2512yes—
1033C24C2512yes—
1034#41—816no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—41no—
1042C2×Q8—41no—
1043C2×Q8C2×#4118yes—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—28no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—22no—
1051C2×D4—22no—
1052C2×D4—28no—
1053C2×D4—22no—
1054C2×D4—24no—
1055C2×D4—22no—
1056C2×D4—22no—
1057C2×D4—41no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—41no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—41no—
1067C2×D4—41no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—41no—
1072C2×D4—41no—
1073C2×D4—42no—
1074C2×D4—42no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D42−1+414yes—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—28no—
1095C22×C4—28no—
1096C22×C4—28no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—42no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—42no—
1114C22×C4—42no—
1115C22×C4—42no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2514yes—
1129C22×C4C2514yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2514yes—
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C4⋊C4—22no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—22no—
1150C4⋊C4—24no—
1151C4⋊C4—28no—
1152C4⋊C4—28no—
1153C4⋊C4—28no—
1154C4⋊C4—22no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—24no—
1162C4⋊C4—22no—
1163C4⋊C4—28no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—41no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—41no—
1186C4⋊C4—41no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—41no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—41no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4C2×#4118yes—
1212C4⋊C4C2×#4118yes—
1213C22⋊C4—28no—
1214C22⋊C4—24no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—42no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—42no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
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—42no—
1267C42—28no—
1268C42—24no—
1269C42—24no—
1270C42—22no—
1271C42—22no—
1272C42—24no—
1273C42—42no—
1274C42—42no—
1275C42—41no—
1276C42—42no—
1277C42—42no—
1278C42—42no—
1279C42—41no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42—44no—
1287C42—44no—
1288C42—44no—
1289C42—41no—
1290C42C2×#4114yes—
1291C42H(5,𝔽2)14yes—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—22no—
1300C23—22no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—22no—
1305C23—22no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—22no—
1313C23—22no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—22no—
1318C23—22no—
1319C23C2×2−1+414yes—
1320C23C2611yescharacteristic
1321Q8—48no—
1322Q8—48no—
1323Q8—82no—
1324D4—44no—
1325D4—48no—
1326D4—48no—
1327D4—44no—
1328D4—48no—
1329D4—48no—
1330D4—44no—
1331D4—82no—
1332D4—88no—
1333D4—84no—
1334D4—88no—
1335D4—84no—
1336D4—164no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—21no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—21no—
1397C2×C4—22no—
1398C2×C4—24no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—48no—
1404C2×C4—48no—
1405C2×C4—48no—
1406C2×C4—48no—
1407C2×C4—88no—
1408C2×C4—88no—
1409C2×C4—84no—
1410C2×C4—84no—
1411C2×C4—88no—
1412C2×C4—84no—
1413C2×C4—84no—
1414C2×C4—164no—
1415C2×C4C22×#4112yes—
1416C2×C4C22×#4112yes—
1417C2×C4C22×#4118yes—
1418C2×C4C22×#4112yes—
1419C2×C4C2×H(5,𝔽2)12yes—
1420C2×C4C2×H(5,𝔽2)12yes—
1421C2×C4C2×H(5,𝔽2)12yes—
1422C2×C4C2×2−1+412yes—
1423C2×C4#58512yes—
1424C22—24no—
1425C22—24no—
1426C22—24no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
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—
1452C22C23×#4111yescharacteristic
1453C22C22×H(5,𝔽2)11yescharacteristic
1454C22C22×2−1+411yescharacteristic
1455C22C2×#58511yescharacteristic
1456C22H(7,𝔽2)11yescharacteristic
1457C22H(7,𝔽2)11yescharacteristic
1458C222−1+611yescharacteristic
1459C4—22no—
1460C4—22no—
1461C4—28no—
1462C4—22no—
1463C4—22no—
1464C4—22no—
1465C4—42no—
1466C4—42no—
1467C4—42no—
1468C4—44no—
1469C4—41no—
1470C4—44no—
1471C4—42no—
1472C4—42no—
1473C4—44no—
1474C4—42no—
1475C4—42no—
1476C4—42no—
1477C4—44no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—44no—
1483C4#351714yes—
1484C2—44no—
1485C2—82no—
1486C2—82no—
1487C2—82no—
1488C2C2×#351711yescharacteristic
1489C2#6284611yescharacteristic
1490C2#6287811yescharacteristic
1491C2#6290211yescharacteristic
1492C2#6294411yescharacteristic
1493C2#6299811yescharacteristic
1494C2#6304711yescharacteristic
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. #59856C2semidirect
2. #59823C2semidirect
3. #52160C2semidirect
4. #50798C2semidirect
5. #49478C2semidirect
6. #48372C2semidirect
7. #46877C2semidirect
8. #46315C2semidirect
9. #45356C2semidirect
10. #45196C2semidirect
11. #44977C2semidirect
12. #43285C2semidirect
13. #42855C2semidirect
14. #42690C2semidirect
15. #42620C2semidirect
16. #40198C2semidirect
17. #39710C2semidirect
18. #39637C2semidirect
19. #39373C2semidirect
20. #39259C2semidirect
21. #38780C2semidirect
22. #38042C2semidirect
23. #37220C2semidirect
24. #36468C2semidirect
25. #35699C2semidirect
26. #35635C2semidirect
27. #35206C2semidirect
28. #34464C2semidirect
29. #34316C2semidirect

Maximal subgroups

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

subgroupindex
#598562
#598232
#521602
#507982
#494782
#483722
#468772
#463152
#453562
#451962
#449772
#432852
#428552
#426902
#426202
#401982
#397102
#396372
#393732
#392592
#387802
#380422
#372202
#364682
#356992
#356352
#352062
#344642
#343162