Finite Group Databasebeta

← #7893278

Subgroups — #7893278

Order 512.

4583 conjugacy classes of subgroups.

The subgroup lattice has 1446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#59119C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic, complemented
4#50596C214yesmaximal, complemented
5#50071C214yesmaximal, complemented
6#49454C214yesmaximal, complemented
7#47360C214yesmaximal, complemented
8#46097C212yesmaximal, complemented
9#45222C212yesmaximal, complemented
10#45142C212yesmaximal, complemented
11#45055C214yesmaximal, complemented
12#44875C212yesmaximal, complemented
13#42707C212yesmaximal, complemented
14#42513C212yesmaximal, complemented
15#41559C214yesmaximal, complemented
16#40078C212yesmaximal, complemented
17#39629C211yesmaximal, characteristic, complemented
18#39621C211yesmaximal, characteristic, complemented
19#38782C212yesmaximal, complemented
20#38467C212yesmaximal, complemented
21#38104C212yesmaximal, complemented
22#37767C212yesmaximal, complemented
23#37167C212yesmaximal, complemented
24#36415C211yesmaximal, characteristic
25#36044C212yesmaximal, complemented
26#35636C212yesmaximal, complemented
27#35206C211yesmaximal, characteristic, complemented
28#34463C212yesmaximal, complemented
29#34332C211yesmaximal, characteristic, complemented
30C2×#556C2212yes—
31C2×#555C2211yescharacteristic
32C2×#554C2211yescharacteristic
33C2×#547C2211yescharacteristic
34C2×#542C2212yes—
35C2×#529C2212yes—
36#2862C2211yescharacteristic
37#2857C2212yes—
38#2855C2212yes—
39#2851C2212yes—
40#2850C2212yes—
41#2838C2214yes—
42#2838C2214yes—
43#2811C2212yes—
44#2808C2211yescharacteristic
45#2808C2211yescharacteristic
46#2806C2212yes—
47#2806C2212yes—
48#2806C2212yes—
49#2806C2212yes—
50#2805C2212yes—
51#2805C2212yes—
52#2804C2211yescharacteristic
53#2800C2214yes—
54#2796C2212yes—
55#2796C2212yes—
56#2796C2214yes—
57#2794C2212yes—
58#2794C2214yes—
59#2780C2214yes—
60#2775C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2773C2214yes—
64#2773C2214yes—
65#2768C2214yes—
66#2766C2214yes—
67#2766C2214yes—
68#2757C2214yes—
69#2754C2214yes—
70#2754C2214yes—
71#2751C2212yes—
72#2751C2212yes—
73#2734C2212yes—
74#2732C2214yes—
75#2730C2214yes—
76#2730C2214yes—
77#2727C2212yes—
78#2727C2212yes—
79#2724C2214yes—
80#2724C2211yescharacteristic
81#2723C2214yes—
82#2723C2214yes—
83#2723C2214yes—
84#2720C2214yes—
85#2717C2214yes—
86#2717C2214yes—
87#2715C2214yes—
88#2709C2212yes—
89#2706C2214yes—
90#2701C2214yes—
91#2698C2214yes—
92#2698C2214yes—
93#2698C2214yes—
94#2695C2214yes—
95#2680C2214yes—
96#2674C2214yes—
97#2660C2212yes—
98#2652C2214yes—
99#2652C2214yes—
100#2651C2214yes—
101#2650C2214yes—
102#2650C2214yes—
103#2648C2214yes—
104#2647C2212yes—
105#2637C2214yes—
106#2629C2212yes—
107#2602C2214yes—
108#2595C2214yes—
109#2589C2214yes—
110#2587C2214yes—
111#2586C2214yes—
112#2581C2212yes—
113#2570C2214yes—
114#2568C2211yescharacteristic
115#2564C2214yes—
116#2563C2211yescharacteristic
117#2560C2214yes—
118#2557C2214yes—
119#2557C2214yes—
120#2557C2214yes—
121#2556C2214yes—
122#2554C2214yes—
123#2553C2214yes—
124#2553C2214yes—
125#2552C2211yescharacteristic
126#2551C2212yes—
127#2550C2212yes—
128#2550C2212yes—
129#2548C2212yes—
130#2547C2211yescharacteristic
131#2547C2211yescharacteristic
132#2542C2212yes—
133#2538C2212yes—
134#2538C2211yescharacteristic
135#2535C2212yes—
136#2535C2212yes—
137#2531C2214yes—
138#2530C2214yes—
139#2521C2214yes—
140#2521C2214yes—
141#2521C2214yes—
142#2520C2214yes—
143#2520C2214yes—
144#2520C2214yes—
145#2517C2214yes—
146#2515C2214yes—
147#2515C2214yes—
148#2512C2214yes—
149#2511C2212yes—
150#2510C2214yes—
151#2508C2214yes—
152#2507C2214yes—
153#2502C2212yes—
154#2499C2212yes—
155#2499C2214yes—
156#2499C2212yes—
157#2498C2214yes—
158#2496C2212yes—
159#2496C2214yes—
160#2495C2212yes—
161#2494C2212yes—
162#2492C2212yes—
163#2489C2212yes—
164#2489C2212yes—
165#2489C2212yes—
166#2489C2212yes—
167#2488C2214yes—
168#2481C2214yes—
169#2481C2214yes—
170#2478C2214yes—
171#2478C2214yes—
172#2474C2214yes—
173#2465C2214yes—
174#2461C2214yes—
175#2451C2212yes—
176#2451C2214yes—
177#2451C2212yes—
178#2449C2214yes—
179#2448C2214yes—
180#2447C2214yes—
181#2447C2212yes—
182#2443C2214yes—
183#2441C2212yes—
184#2441C2212yes—
185#2441C2212yes—
186#2440C2212yes—
187#2440C2214yes—
188#2432C2214yes—
189#2431C2212yes—
190#2427C2212yes—
191#2427C2212yes—
192#2423C2212yes—
193#2422C2212yes—
194#2421C2214yes—
195#2421C2214yes—
196#2421C2212yes—
197#2420C2212yes—
198#2415C2212yes—
199#2415C2212yes—
200#2413C2214yes—
201#2406C2214yes—
202#2401C2214yes—
203#2398C2212yes—
204#2398C2212yes—
205#2395C2212yes—
206#2383C2214yes—
207#2379C2214yes—
208#2373C2214yes—
209#2370C2212yes—
210#2369C2211yescharacteristic
211#2363C2212yes—
212#2363C2212yes—
213#2362C2212yes—
214#2360C2212yes—
215#2360C2214yes—
216#2360C2212yes—
217#2355C2214yes—
218#2355C2212yes—
219#2354C2212yes—
220#2352C2212yes—
221#2352C2212yes—
222#2351C2212yes—
223Q8×C4⋊C4C2211yescharacteristic
224Q8×C4⋊C4C2212yes—
225D4×C4⋊C4C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227#2347C2212yes—
228#2346C2212yes—
229#2345C2212yes—
230#2344C2214yes—
231#2337C2214yes—
232#2334C2214yes—
233#2334C2214yes—
234#2331C2212yes—
235#2331C2214yes—
236#2330C2212yes—
237#2329C2214yes—
238#2327C2212yes—
239#2326C2212yes—
240#2323C2212yes—
241#2320C2214yes—
242#2320C2212yes—
243#2317C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×#123C2212yes—
250#2297C2212yes—
251#2296C2212yes—
252#2295C2211yescharacteristic
253#2295C2211yescharacteristic
254C2×#389C2212yes—
255#2290C2212yes—
256#2290C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260#556—216no—
261#555—44no—
262#554—28no—
263#547—44no—
264#542—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×#127C2311yescharacteristic
272#529—48no—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#124C2314yes—
284C2×#124C2314yes—
285C2×#124C2312yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2314yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2314yes—
328C2×#117C2312yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2314yes—
332C22×C4⋊C4C2312yes—
333C22×C42C2312yes—
334C22×C42C2312yes—
335#401C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#399C2314yes—
354#399C2312yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#397C2314yes—
377#397C2312yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2312yes—
428#394C2314yes—
429#394C2312yes—
430#394C2312yes—
431#394C2312yes—
432#394C2314yes—
433#393C2312yes—
434#393C2314yes—
435#393C2314yes—
436#393C2312yes—
437#393C2312yes—
438#393C2312yes—
439#392C2314yes—
440#392C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2312yes—
461#391C2311yescharacteristic
462#391C2312yes—
463#391C2312yes—
464#391C2311yescharacteristic
465#391C2314yes—
466#391C2311yescharacteristic
467#391C2311yescharacteristic
468#390C2314yes—
469#390C2311yescharacteristic
470#390C2312yes—
471#390C2311yescharacteristic
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2314yes—
477#390C2314yes—
478#390C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2311yescharacteristic
508#389C2314yes—
509#389C2311yescharacteristic
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2312yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2312yes—
548#388C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#386C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2312yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2312yes—
609#386C2314yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
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#385C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2312yes—
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#384C2314yes—
635#384C2314yes—
636#384C2312yes—
637#384C2312yes—
638#384C2312yes—
639#383C2314yes—
640#383C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#382C2314yes—
645#382C2314yes—
646#382C2314yes—
647#382C2314yes—
648#382C2312yes—
649#382C2312yes—
650#382C2314yes—
651#382C2312yes—
652#382C2314yes—
653#381C2314yes—
654#381C2314yes—
655#381C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2312yes—
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2312yes—
669#380C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2314yes—
715#376C2312yes—
716C2×#95C2314yes—
717C43C2311yescharacteristic
718C2×#41—44no—
719C2×#41—44no—
720C2×#41—82no—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×D4C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C22×D4C2414yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2414yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C4⋊Q8—24no—
746C4⋊Q8—44no—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749C4⋊Q8—48no—
750C4⋊Q8#4118yescomplemented
751#127—42no—
752#126—216no—
753#126—216no—
754#126—48no—
755#126—48no—
756#126—84no—
757#125—28no—
758#125—44no—
759#125—82no—
760#124—216no—
761#124—28no—
762#124—48no—
763#124—48no—
764#124—82no—
765#123—48no—
766#123—48no—
767#123—48no—
768#123—44no—
769#123—84no—
770C22⋊Q8—216no—
771C22⋊Q8—28no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—48no—
775C22⋊Q8—44no—
776C22⋊Q8—44no—
777C22⋊Q8—44no—
778C22⋊Q8—84no—
779C22⋊Q8—82no—
780C22⋊Q8—84no—
781#121—28no—
782#121—28no—
783#121—44no—
784C4×Q8—216no—
785C4×Q8—24no—
786C4×Q8—28no—
787C4×Q8—24no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×Q8—82no—
792C4×D4—28no—
793C4×D4—24no—
794C4×D4—28no—
795C4×D4—24no—
796C4×D4—28no—
797C4×D4—28no—
798C4×D4—24no—
799C4×D4—42no—
800C4×D4—42no—
801C4×D4—48no—
802#117—28no—
803#117—28no—
804#117—44no—
805#117—48no—
806#117—44no—
807#117—44no—
808C2×C4⋊C4—28no—
809C2×C4⋊C4—48no—
810C2×C4⋊C4—44no—
811C2×C4⋊C4—82no—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C42—44no—
922C2×C42—82no—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2414yes—
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019C24C2512yes—
1020C24C2512yes—
1021C24C2512yes—
1022#41—816no—
1023C2×Q8—22no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—22no—
1028C2×Q8—24no—
1029C2×Q8—42no—
1030C2×Q8—41no—
1031C2×Q8—42no—
1032C2×Q8—41no—
1033C2×Q8—42no—
1034C2×Q8—41no—
1035C2×Q8—42no—
1036C2×Q8—41no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8—42no—
1042C2×Q8—42no—
1043C2×Q8C2×#4118yes—
1044C2×D4—28no—
1045C2×D4—28no—
1046C2×D4—22no—
1047C2×D4—24no—
1048C2×D4—22no—
1049C2×D4—24no—
1050C2×D4—22no—
1051C2×D4—22no—
1052C2×D4—41no—
1053C2×D4—41no—
1054C2×D4—41no—
1055C2×D4—44no—
1056C2×D4—41no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4H(5,𝔽2)14yes—
1065C22×C4—24no—
1066C22×C4—28no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—28no—
1076C22×C4—24no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—42no—
1088C22×C4—44no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2514yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C4⋊C4—22no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—22no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—22no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—22no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—41no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—41no—
1153C4⋊C4—41no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—41no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—41no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4C2×#4118yes—
1185C4⋊C4C2×#4118yes—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—24no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—28no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—44no—
1219C22⋊C4—42no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C42—28no—
1231C42—28no—
1232C42—24no—
1233C42—28no—
1234C42—24no—
1235C42—24no—
1236C42—22no—
1237C42—24no—
1238C42—22no—
1239C42—42no—
1240C42—42no—
1241C42—41no—
1242C42—42no—
1243C42—42no—
1244C42—42no—
1245C42—44no—
1246C42—44no—
1247C42—41no—
1248C42—41no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42C2×#4114yes—
1256C422−1+414yes—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23C2×H(5,𝔽2)14yes—
1278C23C2611yescharacteristic
1279Q8—48no—
1280Q8—44no—
1281Q8—48no—
1282Q8—82no—
1283Q8—84no—
1284Q8—162no—
1285Q8—164no—
1286D4—28no—
1287D4—44no—
1288D4—84no—
1289D4—82no—
1290D4—84no—
1291D4—88no—
1292D4—88no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—24no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—24no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—48no—
1363C2×C4—48no—
1364C2×C4—48no—
1365C2×C4—48no—
1366C2×C4—88no—
1367C2×C4—84no—
1368C2×C4—88no—
1369C2×C4—84no—
1370C2×C4—84no—
1371C2×C4—88no—
1372C2×C4C22×#4112yes—
1373C2×C4C22×#4118yes—
1374C2×C4C22×#4112yes—
1375C2×C4C22×#4112yes—
1376C2×C4C2×H(5,𝔽2)12yes—
1377C2×C4C2×2−1+412yes—
1378C2×C4C2×2−1+412yes—
1379C2×C4C2×2−1+412yes—
1380C2×C4#58512yes—
1381C22—24no—
1382C22—24no—
1383C22—24no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22C23×#4111yescharacteristic
1403C22C22×H(5,𝔽2)11yescharacteristic
1404C22C22×2−1+411yescharacteristic
1405C22C2×#58511yescharacteristic
1406C22H(7,𝔽2)11yescharacteristic
1407C222−1+611yescharacteristic
1408C222−1+611yescharacteristic
1409C4—28no—
1410C4—22no—
1411C4—22no—
1412C4—22no—
1413C4—22no—
1414C4—22no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—44no—
1422C4—41no—
1423C4—44no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—42no—
1430C4—44no—
1431C4—44no—
1432C4—42no—
1433C4—42no—
1434C4#352214yes—
1435C2—44no—
1436C2—82no—
1437C2—82no—
1438C2C2×#352211yescharacteristic
1439C2#6285111yescharacteristic
1440C2#6287911yescharacteristic
1441C2#6289611yescharacteristic
1442C2#6295911yescharacteristic
1443C2#6299111yescharacteristic
1444C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36415C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59119C2semidirect
3. #52273C2semidirect
4. #50596C2semidirect
5. #50071C2semidirect
6. #49454C2semidirect
7. #47360C2semidirect
8. #46097C2semidirect
9. #45222C2semidirect
10. #45142C2semidirect
11. #45055C2semidirect
12. #44875C2semidirect
13. #42707C2semidirect
14. #42513C2semidirect
15. #41559C2semidirect
16. #40078C2semidirect
17. #39629C2semidirect
18. #39621C2semidirect
19. #38782C2semidirect
20. #38467C2semidirect
21. #38104C2semidirect
22. #37767C2semidirect
23. #37167C2semidirect
25. #36044C2semidirect
26. #35636C2semidirect
27. #35206C2semidirect
28. #34463C2semidirect
29. #34332C2semidirect
750. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598212
#591192
#522732
#505962
#500712
#494542
#473602
#460972
#452222
#451422
#450552
#448752
#427072
#425132
#415592
#400782
#396292
#396212
#387822
#384672
#381042
#377672
#371672
#364152
#360442
#356362
#352062
#344632
#343322