Finite Group Databasebeta

← #8125442

Subgroups — #8125442

Order 512.

4617 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58031C214yesmaximal, complemented
2#57972C214yesmaximal, complemented
3#57759C214yesmaximal, complemented
4#57511C214yesmaximal, complemented
5#53017C212yesmaximal, complemented
6#52976C212yesmaximal, complemented
7#47655C214yesmaximal, complemented
8#47000C214yesmaximal, complemented
9#46952C214yesmaximal, complemented
10#46402C214yesmaximal, complemented
11#45253C212yesmaximal, complemented
12#44873C212yesmaximal, complemented
13#40171C212yesmaximal, complemented
14#39938C212yesmaximal, complemented
15#39602C212yesmaximal, complemented
16#39567C212yesmaximal, complemented
17#38996C212yesmaximal, complemented
18#38907C212yesmaximal, complemented
19#37851C212yesmaximal, complemented
20#37839C212yesmaximal, complemented
21#37428C211yesmaximal, characteristic, complemented
22#37318C211yesmaximal, characteristic, complemented
23#35333C211yesmaximal, characteristic, complemented
24#35259C211yesmaximal, characteristic, complemented
25#35081C211yesmaximal, characteristic, complemented
26#35020C211yesmaximal, characteristic, complemented
27#34742C211yesmaximal, characteristic, complemented
28C2×#547C2212yes—
29C2×#540C2211yescharacteristic, complemented
30C22×#125C2211yescharacteristic, complemented
31C2×#525C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2856C2211yescharacteristic
34#2854C2212yescomplemented
35#2851C2211yescharacteristic
36#2851C2211yescharacteristic
37#2851C2211yescharacteristic
38#2851C2212yes—
39#2851C2211yescharacteristic, complemented
40#2851C2211yescharacteristic, complemented
41#2847C2212yes—
42#2841C2214yes—
43#2837C2214yescomplemented
44#2831C2214yescomplemented
45#2831C2214yescomplemented
46#2827C2214yescomplemented
47#2826C2214yescomplemented
48#2822C2214yescomplemented
49#2813C2214yes—
50#2807C2214yes—
51#2798C2214yescomplemented
52#2797C2214yes—
53#2796C2214yescomplemented
54#2794C2214yescomplemented
55#2790C2214yescomplemented
56#2784C2214yes—
57#2782C2214yescomplemented
58#2780C2214yes—
59#2774C2214yescomplemented
60#2774C2214yescomplemented
61#2772C2214yescomplemented
62#2771C2214yescomplemented
63#2769C2214yescomplemented
64#2767C2214yescomplemented
65#2764C2214yes—
66#2763C2214yes—
67#2752C2214yescomplemented
68#2751C2214yescomplemented
69#2750C2214yes—
70#2749C2214yes—
71#2748C2214yes—
72#2743C2214yes—
73#2743C2214yes—
74#2743C2214yescomplemented
75#2741C2214yes—
76#2740C2214yes—
77#2738C2214yescomplemented
78#2737C2214yes—
79#2720C2214yescomplemented
80#2711C2214yes—
81#2708C2214yes—
82#2708C2214yes—
83#2708C2214yescomplemented
84#2707C2214yes—
85#2707C2214yes—
86#2706C2214yes—
87#2706C2214yes—
88#2706C2214yes—
89#2706C2214yes—
90#2706C2214yescomplemented
91#2703C2214yes—
92#2701C2214yes—
93#2701C2214yescomplemented
94#2696C2214yes—
95#2694C2214yes—
96#2694C2214yes—
97#2694C2214yescomplemented
98#2694C2214yescomplemented
99#2693C2214yes—
100#2693C2214yes—
101#2692C2214yes—
102#2690C2214yescomplemented
103#2690C2214yescomplemented
104#2682C2214yes—
105#2680C2214yescomplemented
106#2654C2214yescomplemented
107#2652C2214yescomplemented
108#2648C2214yes—
109#2646C2214yes—
110#2638C2214yescomplemented
111#2629C2212yes—
112#2629C2212yescomplemented
113#2629C2211yescharacteristic, complemented
114#2628C2212yes—
115#2624C2212yes—
116#2623C2214yescomplemented
117#2619C2211yescharacteristic, complemented
118#2615C2212yes—
119#2609C2214yes—
120#2602C2214yes—
121#2598C2214yes—
122#2579C2214yes—
123#2579C2214yescomplemented
124#2575C2214yes—
125#2575C2214yescomplemented
126#2574C2214yescomplemented
127#2571C2212yescomplemented
128#2571C2212yescomplemented
129#2569C2214yes—
130#2569C2214yes—
131#2566C2214yes—
132#2566C2212yescomplemented
133#2565C2214yescomplemented
134#2563C2212yes—
135#2558C2214yes—
136#2550C2212yescomplemented
137#2550C2212yescomplemented
138#2550C2212yescomplemented
139#2539C2214yes—
140#2535C2212yes—
141#2534C2214yes—
142#2523C2214yescomplemented
143#2515C2214yescomplemented
144#2513C2212yescomplemented
145#2509C2212yescomplemented
146#2506C2212yescomplemented
147#2506C2212yescomplemented
148#2505C2214yescomplemented
149#2504C2212yescomplemented
150#2501C2212yes—
151#2498C2214yes—
152#2497C2212yes—
153#2497C2212yes—
154#2497C2212yes—
155#2495C2212yescomplemented
156#2495C2212yescomplemented
157#2490C2212yes—
158#2490C2212yes—
159#2490C2212yescomplemented
160#2488C2214yes—
161#2488C2214yescomplemented
162#2487C2212yes—
163#2486C2212yes—
164#2477C2214yes—
165#2475C2214yescomplemented
166#2471C2214yescomplemented
167#2464C2214yes—
168#2458C2214yescomplemented
169#2456C2214yes—
170#2456C2214yescomplemented
171#2455C2214yes—
172#2454C2214yes—
173#2454C2212yescomplemented
174#2454C2212yescomplemented
175#2452C2212yescomplemented
176#2450C2214yes—
177#2445C2212yescomplemented
178#2444C2214yes—
179#2442C2212yes—
180#2442C2212yes—
181#2442C2212yes—
182#2442C2212yes—
183#2442C2212yes—
184#2441C2214yes—
185#2441C2212yescomplemented
186#2430C2214yes—
187#2430C2214yes—
188#2428C2212yes—
189#2424C2214yes—
190#2423C2212yes—
191#2422C2214yes—
192#2422C2212yes—
193#2422C2212yescomplemented
194#2421C2212yes—
195#2420C2212yes—
196#2420C2212yes—
197#2420C2212yes—
198#2419C2214yes—
199#2419C2212yes—
200#2419C2212yes—
201#2419C2214yescomplemented
202#2418C2212yes—
203#2418C2212yes—
204#2416C2212yes—
205#2414C2212yes—
206#2413C2214yescomplemented
207#2411C2214yes—
208#2407C2214yes—
209#2406C2214yes—
210#2404C2214yes—
211#2395C2212yes—
212#2395C2212yes—
213#2370C2212yescomplemented
214#2363C2212yescomplemented
215#2361C2212yes—
216#2352C2212yes—
217#2349C2212yescomplemented
218#2344C2212yes—
219#2344C2212yescomplemented
220#2335C2214yes—
221#2333C2214yes—
222#2324C2214yes—
223#2324C2212yes—
224#2324C2212yes—
225#2318C2214yes—
226#2317C2212yescomplemented
227#2315C2214yes—
228#2314C2212yes—
229#2314C2211yescharacteristic, complemented
230#2311C2212yes—
231#2311C2214yes—
232C4×#123C2212yes—
233C4×#123C2212yes—
234C4×#121C2212yes—
235C4×#121C2212yescomplemented
236#2297C2211yescharacteristic
237#2296C2211yescharacteristic
238#2285C2211yescharacteristic
239#2285C2211yescharacteristic, complemented
240#2280C2211yescharacteristic
241C2×#380C2212yes—
242C2×C4×C22⋊C4C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2314yes—
245C24×C4C2311yescharacteristic
246#547—48no—
247#540—44no—
248C2×C4⋊Q8C2312yes—
249C2×#127C2311yescharacteristic
250C2×#125—44no—
251C2×#125C2314yes—
252C2×#125C2312yes—
253C2×#125C2311yescharacteristic
254C2×#125C2311yescharacteristic
255C2×#125C2311yescharacteristic
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259#525—44no—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2312yes—
263C2×#123C2311yescharacteristic
264C2×#123C2311yescharacteristic
265C2×#123C2312yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2314yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#120C2311yescharacteristic
287C2×#120C2311yescharacteristic
288C2×#120C2314yes—
289C4×#41—44no—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×#117C2311yescharacteristic
303C2×#117C2311yescharacteristic
304C2×#117C2312yes—
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2314yes—
309C2×#117C2314yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2312yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2312yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#397C2312yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2312yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2312yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2312yes—
420#394C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2312yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#390C2314yes—
447#390C2314yes—
448#390C2312yes—
449#390C2312yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2311yescharacteristic
462#390C2311yescharacteristic
463#390C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2312yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2312yes—
513#388C2312yes—
514#388C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2312yes—
542#387C2312yes—
543#386C2312yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2312yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2312yes—
562#386C2314yes—
563#386C2314yes—
564#386C2312yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2314yes—
596#385C2312yes—
597#385C2314yes—
598#385C2312yes—
599#385C2312yes—
600#384C2314yes—
601#384C2312yes—
602#384C2312yes—
603#384C2311yescharacteristic
604#384C2312yes—
605#383C2314yes—
606#383C2314yes—
607#382C2314yes—
608#382C2314yes—
609#382C2312yes—
610#382C2312yes—
611#382C2311yescharacteristic
612#382C2311yescharacteristic
613#382C2314yes—
614#382C2314yes—
615#382C2312yes—
616#382C2311yescharacteristic
617#382C2312yes—
618#381C2314yes—
619#381C2314yes—
620#381C2314yes—
621#381C2314yes—
622#381C2314yes—
623#381C2312yes—
624#381C2312yes—
625#381C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2314yes—
634#380C2312yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2312yes—
643#380C2314yes—
644#380C2314yes—
645#380C2312yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#379C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C2×#95C2314yes—
677C2×#95C2314yes—
678C2×#95C2312yes—
679C25C2411yescharacteristic
680C2×#41—24no—
681C2×#41—24no—
682C2×#41—42no—
683C2×#41—48no—
684C2×#41—48no—
685C2×#41—84no—
686C22×Q8C2411yescharacteristic
687C22×Q8C2414yes—
688C22×D4C2412yes—
689C22×D4C2411yescharacteristic
690C22×D4C2411yescharacteristic
691C22×D4C2411yescharacteristic
692C22×D4C2412yes—
693C22×D4C2412yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C23×C4—24no—
701C23×C4—42no—
702C23×C4—42no—
703C23×C4C2412yes—
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2411yescharacteristic
713C23×C4C2412yes—
714C23×C4C2412yes—
715C23×C4C2412yes—
716C23×C4C2414yes—
717C23×C4C2414yes—
718C23×C4C2414yes—
719C4⋊Q8—44no—
720#127—42no—
721#125—42no—
722#125—42no—
723#125—44no—
724#125—48no—
725#125—44no—
726#125—42no—
727#125—84no—
728#125—84no—
729#123—48no—
730#123—48no—
731#123—44no—
732#123—44no—
733#123—42no—
734#123—48no—
735#123—48no—
736#123—42no—
737#123—84no—
738#123—84no—
739#123—84no—
740#123—84no—
741#123—84no—
742C22⋊Q8—48no—
743C22⋊Q8—44no—
744C22⋊Q8—84no—
745#121—28no—
746#121—28no—
747#121—48no—
748#121—44no—
749#121—48no—
750#121—44no—
751#121—44no—
752#121—44no—
753#121—48no—
754#121—84no—
755#120—42no—
756#120—42no—
757#120—84no—
758C4×Q8—44no—
759C4×D4—28no—
760C4×D4—44no—
761C4×D4—44no—
762C4×D4—44no—
763C4×D4—44no—
764C4×D4—44no—
765C4×D4—48no—
766C4×D4—44no—
767C4×D4—44no—
768C4×D4—84no—
769C4×D4—84no—
770#117—24no—
771#117—24no—
772#117—42no—
773#117—42no—
774#117—42no—
775#117—44no—
776#117—84no—
777#117—84no—
778C2×C4⋊C4—28no—
779C2×C4⋊C4—44no—
780C2×C4⋊C4—44no—
781C2×C4⋊C4—48no—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C22⋊C4—44no—
836C2×C22⋊C4—48no—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2411yescharacteristic
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C42—24no—
892C2×C42—42no—
893C2×C42—42no—
894C2×C42—42no—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972C24—22no—
973C24—24no—
974C24—41no—
975C24—42no—
976C24—41no—
977C24C2514yes—
978C24C2511yescharacteristic
979C24C2511yescharacteristic
980C24C2511yescharacteristic
981C24C2512yes—
982#41—416no—
983#41—832no—
984C2×Q8—22no—
985C2×Q8—22no—
986C2×Q8—41no—
987C2×Q8—44no—
988C2×Q8—44no—
989C2×Q8—44no—
990C2×D4—24no—
991C2×D4—22no—
992C2×D4—22no—
993C2×D4—22no—
994C2×D4—22no—
995C2×D4—24no—
996C2×D4—28no—
997C2×D4—28no—
998C2×D4—28no—
999C2×D4—24no—
1000C2×D4—28no—
1001C2×D4—22no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—22no—
1005C2×D4—24no—
1006C2×D4—41no—
1007C2×D4—41no—
1008C2×D4—41no—
1009C2×D4—42no—
1010C2×D4—42no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—42no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—28no—
1031C22×C4—24no—
1032C22×C4—22no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—22no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—22no—
1039C22×C4—24no—
1040C22×C4—22no—
1041C22×C4—24no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—41no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—88no—
1073C22×C4H(5,𝔽2)14yes—
1074C22×C42−1+414yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—28no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—22no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—42no—
1168C22⋊C4—42no—
1169C22⋊C4—41no—
1170C22⋊C4—41no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C42—22no—
1205C42—22no—
1206C42—24no—
1207C42—22no—
1208C42—22no—
1209C42—24no—
1210C42—24no—
1211C42—24no—
1212C42—41no—
1213C42—41no—
1214C42—42no—
1215C42—42no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C23—28no—
1223C23—22no—
1224C23—21no—
1225C23—22no—
1226C23—21no—
1227C23—22no—
1228C23—21no—
1229C23—22no—
1230C23—22no—
1231C23—21no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—24no—
1238C23—21no—
1239C23—24no—
1240C23—21no—
1241C23—24no—
1242C23—24no—
1243C23—22no—
1244C23—24no—
1245C23—21no—
1246C23—22no—
1247C23—24no—
1248C23—24no—
1249C23—82no—
1250C23—82no—
1251C23—84no—
1252C23—84no—
1253C23C2×H(5,𝔽2)12yes—
1254C23C2×2−1+412yes—
1255C23#58514yes—
1256C23C2611yescharacteristic
1257Q8—44no—
1258Q8—88no—
1259D4—44no—
1260D4—44no—
1261D4—44no—
1262D4—48no—
1263D4—48no—
1264D4—88no—
1265D4—84no—
1266D4—88no—
1267D4—88no—
1268D4—88no—
1269D4—88no—
1270D4—164no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—28no—
1276C2×C4—28no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—21no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—416no—
1335C2×C4—48no—
1336C2×C4—44no—
1337C2×C4—84no—
1338C2×C4—84no—
1339C2×C4—88no—
1340C2×C4—82no—
1341C2×C4—88no—
1342C2×C4—84no—
1343C2×C4—84no—
1344C2×C4—84no—
1345C2×C4—88no—
1346C2×C4—164no—
1347C2×C4—164no—
1348C2×C4C2×H(5,𝔽2)12yes—
1349C2×C4C2×H(5,𝔽2)12yes—
1350C2×C4C2×2−1+412yes—
1351C2×C4C2×2−1+412yes—
1352C2×C4#58512yes—
1353C22—22no—
1354C22—22no—
1355C22—22no—
1356C22—24no—
1357C22—22no—
1358C22—24no—
1359C22—24no—
1360C22—24no—
1361C22—42no—
1362C22—41no—
1363C22—41no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—41no—
1371C22—44no—
1372C22—44no—
1373C22—41no—
1374C22—44no—
1375C22—41no—
1376C22—44no—
1377C22—42no—
1378C22—44no—
1379C22—44no—
1380C22—42no—
1381C22—44no—
1382C22—88no—
1383C22C22×H(5,𝔽2)11yescharacteristic
1384C22C22×2−1+411yescharacteristic
1385C22C2×#58511yescharacteristic
1386C22C2×#58512yes—
1387C22H(7,𝔽2)12yes—
1388C4—22no—
1389C4—22no—
1390C4—42no—
1391C4—41no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4—44no—
1396C4—44no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—44no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—44no—
1406C4—42no—
1407C4—44no—
1408C4—44no—
1409C4#353514yes—
1410C2—42no—
1411C2—42no—
1412C2—44no—
1413C2—81no—
1414C2—84no—
1415C2C2×#353511yescharacteristic
1416C2#6282511yescharacteristic
1417C2#6288111yescharacteristic
1418C2#6292412yes—
1419C2#6294112yes—
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. #58031C2semidirect
2. #57972C2semidirect
3. #57759C2semidirect
4. #57511C2semidirect
5. #53017C2semidirect
6. #52976C2semidirect
7. #47655C2semidirect
8. #47000C2semidirect
9. #46952C2semidirect
10. #46402C2semidirect
11. #45253C2semidirect
12. #44873C2semidirect
13. #40171C2semidirect
14. #39938C2semidirect
15. #39602C2semidirect
16. #39567C2semidirect
17. #38996C2semidirect
18. #38907C2semidirect
19. #37851C2semidirect
20. #37839C2semidirect
21. #37428C2semidirect
22. #37318C2semidirect
23. #35333C2semidirect
24. #35259C2semidirect
25. #35081C2semidirect
26. #35020C2semidirect
27. #34742C2semidirect
29. C2×#540C22semidirect
30. C22×#125C22semidirect
34. #2854C22semidirect
39. #2851C22semidirect
40. #2851C22semidirect
43. #2837C22semidirect
44. #2831C22semidirect
45. #2831C22semidirect
46. #2827C22semidirect
47. #2826C22semidirect
48. #2822C22semidirect
51. #2798C22semidirect
53. #2796C22semidirect
54. #2794C22semidirect
55. #2790C22semidirect
57. #2782C22semidirect
59. #2774C22semidirect
60. #2774C22semidirect
61. #2772C22semidirect
62. #2771C22semidirect
63. #2769C22semidirect
64. #2767C22semidirect
67. #2752C22semidirect
68. #2751C22semidirect
74. #2743C22semidirect
77. #2738C22semidirect
79. #2720C22semidirect
83. #2708C22semidirect
90. #2706C22semidirect
93. #2701C22semidirect
97. #2694C22semidirect
98. #2694C22semidirect
102. #2690C22semidirect
103. #2690C22semidirect
105. #2680C22semidirect
106. #2654C22semidirect
107. #2652C22semidirect
110. #2638C22semidirect
112. #2629C22semidirect
113. #2629C22semidirect
116. #2623C22semidirect
117. #2619C22semidirect
123. #2579C22semidirect
125. #2575C22semidirect
126. #2574C22semidirect
127. #2571C22semidirect
128. #2571C22semidirect
132. #2566C22semidirect
133. #2565C22semidirect
136. #2550C22semidirect
137. #2550C22semidirect
138. #2550C22semidirect
142. #2523C22semidirect
143. #2515C22semidirect
144. #2513C22semidirect
145. #2509C22semidirect
146. #2506C22semidirect
147. #2506C22semidirect
148. #2505C22semidirect
149. #2504C22semidirect
155. #2495C22semidirect
156. #2495C22semidirect
159. #2490C22semidirect
161. #2488C22semidirect
165. #2475C22semidirect
166. #2471C22semidirect
168. #2458C22semidirect
170. #2456C22semidirect
173. #2454C22semidirect
174. #2454C22semidirect
175. #2452C22semidirect
177. #2445C22semidirect
185. #2441C22semidirect
193. #2422C22semidirect
201. #2419C22semidirect
206. #2413C22semidirect
213. #2370C22semidirect
214. #2363C22semidirect
217. #2349C22semidirect
219. #2344C22semidirect
226. #2317C22semidirect
229. #2314C22semidirect
235. C4×#121C22semidirect
239. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#580312
#579722
#577592
#575112
#530172
#529762
#476552
#470002
#469522
#464022
#452532
#448732
#401712
#399382
#396022
#395672
#389962
#389072
#378512
#378392
#374282
#373182
#353332
#352592
#350812
#350202
#347422