Finite Group Databasebeta

← #7715047

Subgroups — #7715047

Order 512.

4716 conjugacy classes of subgroups.

The subgroup lattice has 1413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51997C214yesmaximal, complemented
2#51955C214yesmaximal, complemented
3#51856C214yesmaximal, complemented
4#51701C214yesmaximal, complemented
5#46698C214yesmaximal, complemented
6#46686C214yesmaximal, complemented
7#46682C214yesmaximal, complemented
8#46580C214yesmaximal, complemented
9#39509C212yesmaximal, complemented
10#39505C212yesmaximal, complemented
11#39387C212yesmaximal, complemented
12#39374C212yesmaximal, complemented
13#39275C212yesmaximal, complemented
14#39274C212yesmaximal, complemented
15#39259C212yesmaximal, complemented
16#39258C212yesmaximal, complemented
17#37516C212yesmaximal, complemented
18#37375C211yesmaximal, characteristic, complemented
19#37282C212yesmaximal, complemented
20#37270C211yesmaximal, characteristic
21#35332C211yesmaximal, characteristic, complemented
22#35283C211yesmaximal, characteristic, complemented
23#35260C212yesmaximal, complemented
24#35258C212yesmaximal, complemented
25#34423C211yesmaximal, characteristic, complemented
26#34421C211yesmaximal, characteristic, complemented
27#34065C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×#542C2212yescomplemented
30C2×#541C2211yescharacteristic
31C2×#540C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2868C2211yescharacteristic, complemented
36#2862C2211yescharacteristic, complemented
37#2859C2211yescharacteristic, complemented
38#2858C2211yescharacteristic, complemented
39#2857C2212yes—
40#2855C2212yescomplemented
41#2854C2212yescomplemented
42#2850C2212yes—
43#2848C2212yes—
44#2847C2212yes—
45#2826C2214yes—
46#2824C2214yes—
47#2810C2214yescomplemented
48#2808C2214yes—
49#2805C2214yescomplemented
50#2803C2214yes—
51#2798C2214yes—
52#2795C2214yes—
53#2795C2214yescomplemented
54#2794C2214yescomplemented
55#2784C2214yes—
56#2782C2214yescomplemented
57#2781C2214yes—
58#2780C2214yescomplemented
59#2779C2214yes—
60#2779C2214yes—
61#2772C2214yescomplemented
62#2771C2214yescomplemented
63#2753C2214yes—
64#2751C2214yes—
65#2751C2214yes—
66#2751C2214yescomplemented
67#2750C2214yes—
68#2747C2214yescomplemented
69#2743C2214yes—
70#2731C2214yes—
71#2731C2214yescomplemented
72#2730C2214yes—
73#2730C2214yescomplemented
74#2727C2214yes—
75#2720C2214yes—
76#2718C2214yes—
77#2715C2214yes—
78#2711C2214yes—
79#2710C2214yes—
80#2710C2214yes—
81#2710C2214yescomplemented
82#2709C2214yes—
83#2705C2214yes—
84#2705C2214yescomplemented
85#2703C2214yes—
86#2696C2214yes—
87#2691C2214yes—
88#2689C2214yescomplemented
89#2689C2214yescomplemented
90#2685C2214yes—
91#2685C2214yes—
92#2684C2214yes—
93#2673C2214yes—
94#2669C2214yes—
95#2665C2214yescomplemented
96#2662C2214yescomplemented
97#2650C2214yescomplemented
98#2648C2214yescomplemented
99#2647C2211yescharacteristic, complemented
100#2647C2211yescharacteristic, complemented
101#2642C2211yescharacteristic, complemented
102#2641C2211yescharacteristic, complemented
103#2628C2212yes—
104#2628C2212yes—
105#2628C2212yescomplemented
106#2625C2212yes—
107#2624C2212yes—
108#2620C2212yes—
109#2620C2212yes—
110#2620C2212yescomplemented
111#2616C2212yes—
112#2615C2212yes—
113#2601C2214yes—
114#2600C2214yescomplemented
115#2596C2214yes—
116#2596C2214yes—
117#2596C2214yescomplemented
118#2596C2214yescomplemented
119#2595C2214yes—
120#2595C2214yes—
121#2589C2214yescomplemented
122#2569C2214yescomplemented
123#2562C2212yes—
124#2562C2212yes—
125#2559C2214yes—
126#2559C2214yes—
127#2558C2214yescomplemented
128#2558C2214yescomplemented
129#2554C2214yes—
130#2548C2214yes—
131#2544C2214yes—
132#2542C2212yes—
133#2541C2212yes—
134#2538C2212yes—
135#2538C2214yescomplemented
136#2537C2212yes—
137#2536C2212yes—
138#2535C2212yes—
139#2521C2214yes—
140#2521C2214yescomplemented
141#2516C2214yescomplemented
142#2512C2214yescomplemented
143#2511C2214yescomplemented
144#2511C2214yescomplemented
145#2500C2214yes—
146#2497C2212yes—
147#2497C2214yescomplemented
148#2497C2212yescomplemented
149#2496C2212yes—
150#2496C2212yescomplemented
151#2492C2212yes—
152#2492C2214yes—
153#2492C2212yescomplemented
154#2491C2214yes—
155#2491C2212yes—
156#2491C2212yescomplemented
157#2488C2214yes—
158#2488C2214yescomplemented
159#2481C2214yes—
160#2479C2214yes—
161#2477C2214yes—
162#2474C2214yes—
163#2472C2214yes—
164#2470C2214yes—
165#2470C2214yescomplemented
166#2469C2214yes—
167#2469C2214yescomplemented
168#2469C2214yescomplemented
169#2468C2214yescomplemented
170#2467C2214yes—
171#2467C2214yes—
172#2465C2214yescomplemented
173#2463C2214yes—
174#2461C2214yes—
175#2459C2214yes—
176#2459C2214yes—
177#2459C2214yescomplemented
178#2457C2214yes—
179#2455C2214yescomplemented
180#2451C2214yescomplemented
181#2449C2214yes—
182#2445C2214yes—
183#2444C2214yes—
184#2439C2214yescomplemented
185#2427C2212yes—
186#2427C2212yescomplemented
187#2426C2212yes—
188#2426C2212yescomplemented
189#2423C2214yes—
190#2421C2212yes—
191#2421C2212yescomplemented
192#2420C2212yes—
193#2420C2212yescomplemented
194#2418C2214yes—
195#2382C2214yescomplemented
196#2376C2214yescomplemented
197#2370C2212yescomplemented
198#2370C2212yescomplemented
199#2370C2214yescomplemented
200#2366C2212yescomplemented
201#2365C2212yescomplemented
202#2359C2214yescomplemented
203#2355C2212yescomplemented
204#2354C2212yescomplemented
205#2351C2212yescomplemented
206#2349C2212yescomplemented
207#2334C2214yes—
208#2334C2214yes—
209#2331C2212yescomplemented
210#2326C2212yescomplemented
211#2325C2214yes—
212#2324C2212yes—
213#2324C2212yes—
214#2324C2212yes—
215#2324C2214yes—
216#2324C2212yes—
217#2323C2212yes—
218#2323C2212yes—
219#2323C2212yes—
220#2323C2212yes—
221#2322C2212yes—
222#2322C2212yes—
223#2321C2212yes—
224#2321C2212yes—
225#2314C2212yes—
226#2314C2211yescharacteristic
227#2314C2211yescharacteristic
228#2314C2212yescomplemented
229C4×C4⋊Q8C2212yescomplemented
230C4×#124C2212yescomplemented
231C4×C22⋊Q8C2212yes—
232C4×C22⋊Q8C2212yescomplemented
233C4×#121C2212yes—
234C4×#121C2212yescomplemented
235#2297C2211yescharacteristic
236#2296C2211yescharacteristic
237#2293C2212yes—
238#2293C2212yes—
239#2290C2212yes—
240#2290C2212yes—
241#2280C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C24×C4C2311yescharacteristic
245#542—48no—
246#542—48no—
247#541—28no—
248#540—28no—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2314yes—
253C2×#127C2311yescharacteristic
254C2×#127C2314yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2311yescharacteristic
261C2×#125C2311yescharacteristic
262C2×#125C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#124C2314yes—
269#525—28no—
270C2×#123C2312yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#120C2312yes—
293C2×#120C2314yes—
294C4×#41—44no—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×#117—44no—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2311yescharacteristic
319C2×#117C2314yes—
320C2×#117C2311yescharacteristic
321C22×C4⋊C4C2312yes—
322C22×C22⋊C4C2312yes—
323C22×C42C2311yescharacteristic
324C22×C42C2312yes—
325C22×C42C2311yescharacteristic
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#391C2314yes—
423#391C2311yescharacteristic
424#391C2311yescharacteristic
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2312yes—
444#390C2314yes—
445#390C2312yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2312yes—
493#388C2312yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#386C2312yes—
567#386C2314yes—
568#386C2312yes—
569#386C2312yes—
570#386C2312yes—
571#386C2312yes—
572#386C2312yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2312yes—
594#385C2312yes—
595#385C2312yes—
596#385C2312yes—
597#385C2312yes—
598#385C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#384C2312yes—
609#384C2311yescharacteristic
610#384C2311yescharacteristic
611#384C2312yes—
612#384C2314yes—
613#384C2314yes—
614#382C2312yes—
615#382C2311yescharacteristic
616#382C2311yescharacteristic
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#381C2311yescharacteristic
621#381C2311yescharacteristic
622#381C2314yes—
623#381C2314yes—
624#381C2314yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#379C2311yescharacteristic
644#379C2311yescharacteristic
645#379C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676#376C2311yescharacteristic
677#376C2311yescharacteristic
678C2×#95C2314yes—
679C43C2311yescharacteristic
680C43C2311yescharacteristic
681C25C2411yescharacteristic
682C2×#41—24no—
683C2×#41—42no—
684C2×#41—42no—
685C22×Q8C2412yes—
686C22×Q8C2411yescharacteristic
687C22×Q8C2414yes—
688C22×Q8C2414yes—
689C22×D4C2412yes—
690C22×D4C2412yes—
691C22×D4C2411yescharacteristic
692C22×D4C2414yes—
693C22×D4C2412yes—
694C22×D4C2412yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C23×C4—24no—
701C23×C4—42no—
702C23×C4—42no—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C23×C4C2411yescharacteristic
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C23×C4C2412yes—
709C23×C4C2414yes—
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2412yes—
715C4⋊Q8—24no—
716C4⋊Q8—28no—
717C4⋊Q8—44no—
718C4⋊Q8—84no—
719#127—24no—
720#127—84no—
721#126—216no—
722#126—48no—
723#126—48no—
724#126—84no—
725#126—84no—
726#125—216no—
727#125—24no—
728#125—24no—
729#124—28no—
730#124—44no—
731#124—48no—
732#124—48no—
733#124—84no—
734#124—84no—
735#123—216no—
736#123—28no—
737#123—48no—
738#123—48no—
739#123—84no—
740C22⋊Q8—28no—
741C22⋊Q8—28no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—44no—
745C22⋊Q8—44no—
746C22⋊Q8—44no—
747C22⋊Q8—44no—
748C22⋊Q8—84no—
749#121—28no—
750#121—28no—
751#121—216no—
752#121—44no—
753#121—44no—
754#121—44no—
755#121—44no—
756#121—84no—
757#120—28no—
758#120—84no—
759C4×Q8—28no—
760C4×Q8—44no—
761C4×Q8—44no—
762C4×Q8—44no—
763C4×Q8—84no—
764C4×D4—28no—
765C4×D4—28no—
766C4×D4—28no—
767C4×D4—44no—
768C4×D4—44no—
769C4×D4—44no—
770C4×D4—44no—
771C4×D4—44no—
772C4×D4—84no—
773C4×D4—84no—
774C4×D4—84no—
775#117—28no—
776#117—28no—
777#117—44no—
778#117—42no—
779#117—42no—
780#117—44no—
781#117—44no—
782#117—84no—
783#117#4118yes—
784C2×C4⋊C4—44no—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C22⋊C4—44no—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2411yescharacteristic
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C42—24no—
894C2×C42—42no—
895C2×C42—44no—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
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—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976C24—22no—
977C24—41no—
978C24—41no—
979C24—42no—
980C24—42no—
981C24C2512yes—
982C24C2514yes—
983C24C2512yes—
984C24C2511yescharacteristic
985#41—416no—
986C2×Q8—24no—
987C2×Q8—22no—
988C2×Q8—24no—
989C2×Q8—28no—
990C2×Q8—24no—
991C2×Q8—41no—
992C2×Q8—41no—
993C2×Q8—44no—
994C2×Q8—44no—
995C2×Q8—44no—
996C2×Q8—44no—
997C2×Q8—44no—
998C2×D4—24no—
999C2×D4—28no—
1000C2×D4—24no—
1001C2×D4—22no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—28no—
1005C2×D4—24no—
1006C2×D4—24no—
1007C2×D4—41no—
1008C2×D4—42no—
1009C2×D4—41no—
1010C2×D4—42no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—42no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—24no—
1043C22×C4—41no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—41no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—416no—
1067C22×C4C2×#4114yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—41no—
1117C4⋊C4—41no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4C2×#4118yes—
1140C22⋊C4—28no—
1141C22⋊C4—24no—
1142C22⋊C4—24no—
1143C22⋊C4—28no—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—28no—
1147C22⋊C4—24no—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—44no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—41no—
1164C22⋊C4—41no—
1165C22⋊C4—41no—
1166C22⋊C4—41no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
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—42no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4C2×#4118yes—
1198C42—28no—
1199C42—22no—
1200C42—24no—
1201C42—24no—
1202C42—24no—
1203C42—22no—
1204C42—22no—
1205C42—41no—
1206C42—41no—
1207C42—42no—
1208C42—42no—
1209C42—42no—
1210C42—42no—
1211C42—44no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—42no—
1218C42—44no—
1219C42—44no—
1220C42—42no—
1221C42C2×#4114yes—
1222C42C2×#4114yes—
1223C42H(5,𝔽2)14yes—
1224C23—21no—
1225C23—21no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—24no—
1231C23—22no—
1232C23—24no—
1233C23—22no—
1234C23—24no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—24no—
1240C23—24no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—24no—
1247C23—24no—
1248C23—22no—
1249C23—44no—
1250C23—84no—
1251C23—84no—
1252C23—82no—
1253C23—82no—
1254C23C22×#4112yes—
1255C23C2611yescharacteristic
1256Q8—44no—
1257Q8—48no—
1258Q8—88no—
1259Q8—164no—
1260D4—44no—
1261D4—48no—
1262D4—48no—
1263D4—84no—
1264D4—88no—
1265D4—84no—
1266D4—88no—
1267D4—88no—
1268D4—164no—
1269D4—164no—
1270D4—164no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—28no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—48no—
1331C2×C4—44no—
1332C2×C4—48no—
1333C2×C4—48no—
1334C2×C4—88no—
1335C2×C4—84no—
1336C2×C4—84no—
1337C2×C4—84no—
1338C2×C4—84no—
1339C2×C4—164no—
1340C2×C4—164no—
1341C2×C4C22×#4114yes—
1342C2×C4C22×#4114yes—
1343C2×C4C22×#4112yes—
1344C2×C4C22×#4112yes—
1345C2×C4C2×H(5,𝔽2)14yes—
1346C2×C4C2×H(5,𝔽2)12yes—
1347C2×C4#58512yes—
1348C22—22no—
1349C22—24no—
1350C22—42no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—42no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—44no—
1365C22—44no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—44no—
1370C22—42no—
1371C22—44no—
1372C22—42no—
1373C22—42no—
1374C22—88no—
1375C22C23×#4111yescharacteristic
1376C22C22×H(5,𝔽2)11yescharacteristic
1377C22C2×#58511yescharacteristic
1378C22H(7,𝔽2)12yes—
1379C222−1+612yes—
1380C4—22no—
1381C4—24no—
1382C4—24no—
1383C4—24no—
1384C4—42no—
1385C4—42no—
1386C4—44no—
1387C4—44no—
1388C4—44no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4—44no—
1396C4—41no—
1397C4—44no—
1398C4—44no—
1399C4—41no—
1400C4—41no—
1401C4—41no—
1402C4#350614yes—
1403C2—42no—
1404C2—82no—
1405C2—84no—
1406C2—82no—
1407C2C2×#350611yescharacteristic
1408C2#6285712yes—
1409C2#6287812yes—
1410C2#6288311yescharacteristic
1411C2#6289011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37270C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51997C2semidirect
2. #51955C2semidirect
3. #51856C2semidirect
4. #51701C2semidirect
5. #46698C2semidirect
6. #46686C2semidirect
7. #46682C2semidirect
8. #46580C2semidirect
9. #39509C2semidirect
10. #39505C2semidirect
11. #39387C2semidirect
12. #39374C2semidirect
13. #39275C2semidirect
14. #39274C2semidirect
15. #39259C2semidirect
16. #39258C2semidirect
17. #37516C2semidirect
18. #37375C2semidirect
19. #37282C2semidirect
21. #35332C2semidirect
22. #35283C2semidirect
23. #35260C2semidirect
24. #35258C2semidirect
25. #34423C2semidirect
26. #34421C2semidirect
27. #34065C2semidirect
29. C2×#542C22semidirect
35. #2868C22semidirect
36. #2862C22semidirect
37. #2859C22semidirect
38. #2858C22semidirect
40. #2855C22semidirect
41. #2854C22semidirect
47. #2810C22semidirect
49. #2805C22semidirect
53. #2795C22semidirect
54. #2794C22semidirect
56. #2782C22semidirect
58. #2780C22semidirect
61. #2772C22semidirect
62. #2771C22semidirect
66. #2751C22semidirect
68. #2747C22semidirect
71. #2731C22semidirect
73. #2730C22semidirect
81. #2710C22semidirect
84. #2705C22semidirect
88. #2689C22semidirect
89. #2689C22semidirect
95. #2665C22semidirect
96. #2662C22semidirect
97. #2650C22semidirect
98. #2648C22semidirect
99. #2647C22semidirect
100. #2647C22semidirect
101. #2642C22semidirect
102. #2641C22semidirect
105. #2628C22semidirect
110. #2620C22semidirect
114. #2600C22semidirect
117. #2596C22semidirect
118. #2596C22semidirect
121. #2589C22semidirect
122. #2569C22semidirect
127. #2558C22semidirect
128. #2558C22semidirect
135. #2538C22semidirect
140. #2521C22semidirect
141. #2516C22semidirect
142. #2512C22semidirect
143. #2511C22semidirect
144. #2511C22semidirect
147. #2497C22semidirect
148. #2497C22semidirect
150. #2496C22semidirect
153. #2492C22semidirect
156. #2491C22semidirect
158. #2488C22semidirect
165. #2470C22semidirect
167. #2469C22semidirect
168. #2469C22semidirect
169. #2468C22semidirect
172. #2465C22semidirect
177. #2459C22semidirect
179. #2455C22semidirect
180. #2451C22semidirect
184. #2439C22semidirect
186. #2427C22semidirect
188. #2426C22semidirect
191. #2421C22semidirect
193. #2420C22semidirect
195. #2382C22semidirect
196. #2376C22semidirect
197. #2370C22semidirect
198. #2370C22semidirect
199. #2370C22semidirect
200. #2366C22semidirect
201. #2365C22semidirect
202. #2359C22semidirect
203. #2355C22semidirect
204. #2354C22semidirect
205. #2351C22semidirect
206. #2349C22semidirect
209. #2331C22semidirect
210. #2326C22semidirect
228. #2314C22semidirect
229. C4×C4⋊Q8C22semidirect
230. C4×#124C22semidirect
232. C4×C22⋊Q8C22semidirect
234. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#519972
#519552
#518562
#517012
#466982
#466862
#466822
#465802
#395092
#395052
#393872
#393742
#392752
#392742
#392592
#392582
#375162
#373752
#372822
#372702
#353322
#352832
#352602
#352582
#344232
#344212
#340652