Finite Group Databasebeta

← #7713307

Subgroups — #7713307

Order 512.

4458 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48804C214yesmaximal, complemented
2#47925C214yesmaximal, complemented
3#47923C214yesmaximal, complemented
4#47892C214yesmaximal, complemented
5#47196C211yesmaximal, characteristic, complemented
6#47009C214yesmaximal, complemented
7#46999C211yesmaximal, characteristic, complemented
8#46998C211yesmaximal, characteristic, complemented
9#46838C211yesmaximal, characteristic, complemented
10#46837C211yesmaximal, characteristic, complemented
11#46401C214yesmaximal, complemented
12#46388C211yesmaximal, characteristic, complemented
13#46386C211yesmaximal, characteristic
14#46385C211yesmaximal, characteristic
15#40348C214yesmaximal, complemented
16#40324C214yesmaximal, complemented
17#38752C214yesmaximal, complemented
18#38745C214yesmaximal, complemented
19#37480C211yesmaximal, characteristic, complemented
20#37441C211yesmaximal, characteristic, complemented
21#36984C214yesmaximal, complemented
22#35084C211yesmaximal, characteristic, complemented
23#35062C211yesmaximal, characteristic
24#35055C214yesmaximal, complemented
25#34370C211yesmaximal, characteristic, complemented
26#34357C211yesmaximal, characteristic, complemented
27#34057C211yesmaximal, characteristic, complemented
28C22×#123C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31#2855C2212yescomplemented
32#2855C2214yescomplemented
33#2853C2212yes—
34#2853C2214yescomplemented
35#2849C2212yes—
36#2848C2212yescomplemented
37#2842C2211yescharacteristic
38#2842C2211yescharacteristic
39#2840C2211yescharacteristic
40#2840C2211yescharacteristic
41#2814C2214yes—
42#2809C2214yescomplemented
43#2804C2214yescomplemented
44#2796C2214yescomplemented
45#2787C2214yescomplemented
46#2783C2214yescomplemented
47#2779C2214yescomplemented
48#2776C2214yescomplemented
49#2774C2214yescomplemented
50#2774C2214yescomplemented
51#2773C2214yescomplemented
52#2772C2214yescomplemented
53#2771C2214yescomplemented
54#2766C2214yescomplemented
55#2765C2214yescomplemented
56#2764C2214yescomplemented
57#2763C2214yescomplemented
58#2762C2214yescomplemented
59#2759C2214yescomplemented
60#2759C2214yescomplemented
61#2758C2214yescomplemented
62#2758C2214yescomplemented
63#2751C2214yes—
64#2750C2214yes—
65#2746C2214yes—
66#2745C2214yescomplemented
67#2745C2214yescomplemented
68#2745C2214yescomplemented
69#2745C2214yescomplemented
70#2744C2214yescomplemented
71#2743C2214yes—
72#2743C2214yes—
73#2743C2214yescomplemented
74#2739C2214yescomplemented
75#2739C2214yescomplemented
76#2738C2214yescomplemented
77#2738C2214yescomplemented
78#2737C2214yes—
79#2737C2214yescomplemented
80#2736C2214yescomplemented
81#2729C2214yescomplemented
82#2696C2214yes—
83#2695C2214yescomplemented
84#2693C2214yes—
85#2689C2214yescomplemented
86#2687C2214yes—
87#2687C2214yescomplemented
88#2684C2214yes—
89#2674C2214yescomplemented
90#2665C2214yescomplemented
91#2665C2214yescomplemented
92#2663C2214yes—
93#2653C2214yescomplemented
94#2652C2214yescomplemented
95#2638C2214yes—
96#2630C2214yes—
97#2628C2214yescomplemented
98#2627C2212yescomplemented
99#2626C2212yescomplemented
100#2623C2212yescomplemented
101#2614C2212yescomplemented
102#2607C2214yescomplemented
103#2606C2214yescomplemented
104#2602C2214yes—
105#2599C2214yescomplemented
106#2599C2214yescomplemented
107#2596C2214yescomplemented
108#2590C2214yescomplemented
109#2588C2214yescomplemented
110#2588C2214yescomplemented
111#2587C2214yescomplemented
112#2587C2214yescomplemented
113#2583C2212yescomplemented
114#2583C2212yescomplemented
115#2581C2214yescomplemented
116#2579C2212yes—
117#2577C2214yescomplemented
118#2577C2214yescomplemented
119#2576C2214yescomplemented
120#2576C2214yescomplemented
121#2575C2214yescomplemented
122#2573C2214yescomplemented
123#2572C2214yes—
124#2572C2214yescomplemented
125#2564C2214yescomplemented
126#2561C2212yescomplemented
127#2561C2212yescomplemented
128#2561C2214yescomplemented
129#2557C2214yes—
130#2553C2214yes—
131#2549C2214yescomplemented
132#2534C2214yes—
133#2534C2212yes—
134#2533C2214yescomplemented
135#2532C2214yescomplemented
136#2532C2214yescomplemented
137#2530C2214yescomplemented
138#2528C2214yescomplemented
139#2527C2214yescomplemented
140#2527C2214yescomplemented
141#2527C2214yescomplemented
142#2527C2214yescomplemented
143#2521C2214yescomplemented
144#2515C2214yescomplemented
145#2515C2214yescomplemented
146#2493C2214yescomplemented
147#2488C2214yescomplemented
148#2486C2212yescomplemented
149#2483C2211yescharacteristic
150#2483C2211yescharacteristic
151#2483C2211yescharacteristic
152#2483C2211yescharacteristic
153#2483C2211yescharacteristic
154#2482C2214yescomplemented
155#2480C2214yescomplemented
156#2477C2214yes—
157#2477C2214yescomplemented
158#2472C2214yes—
159#2470C2214yes—
160#2470C2214yescomplemented
161#2466C2214yescomplemented
162#2465C2214yescomplemented
163#2465C2214yescomplemented
164#2458C2214yes—
165#2458C2214yescomplemented
166#2458C2214yescomplemented
167#2457C2214yes—
168#2447C2214yescomplemented
169#2446C2214yescomplemented
170#2439C2214yescomplemented
171#2439C2214yescomplemented
172#2439C2214yescomplemented
173#2418C2214yes—
174#2415C2214yes—
175#2413C2212yes—
176#2413C2212yescomplemented
177#2413C2212yescomplemented
178#2411C2212yes—
179#2409C2212yescomplemented
180#2405C2211yescharacteristic
181#2405C2211yescharacteristic
182#2405C2211yescharacteristic
183#2405C2211yescharacteristic
184#2405C2211yescharacteristic
185#2405C2211yescharacteristic
186#2403C2211yescharacteristic
187#2378C2214yescomplemented
188#2376C2214yescomplemented
189#2374C2214yescomplemented
190#2362C2214yescomplemented
191#2345C2212yescomplemented
192#2345C2212yescomplemented
193#2345C2212yescomplemented
194#2344C2212yescomplemented
195#2344C2212yescomplemented
196#2342C2212yescomplemented
197#2342C2212yescomplemented
198Q8×C22⋊C4C2212yescomplemented
199#2337C2214yescomplemented
200#2335C2214yes—
201#2335C2214yes—
202#2334C2214yescomplemented
203#2332C2214yescomplemented
204#2323C2214yescomplemented
205#2322C2212yes—
206#2322C2212yescomplemented
207#2322C2212yescomplemented
208#2321C2212yes—
209#2318C2214yes—
210#2318C2214yescomplemented
211#2315C2212yescomplemented
212#2313C2212yescomplemented
213#2312C2211yescharacteristic
214#2312C2211yescharacteristic
215#2312C2211yescharacteristic
216#2312C2211yescharacteristic
217#2312C2211yescharacteristic
218#2312C2211yescharacteristic
219#2312C2211yescharacteristic
220#2312C2211yescharacteristic
221#2309C2211yescharacteristic
222#2308C2211yescharacteristic
223#2308C2211yescharacteristic
224#2308C2211yescharacteristic
225C4×C22⋊Q8C2214yescomplemented
226#2290C2214yes—
227#2290C2214yescomplemented
228#2290C2214yescomplemented
229#2283C2212yescomplemented
230#2280C2211yescharacteristic
231#2280C2211yescharacteristic
232#2280C2211yescharacteristic
233#2280C2211yescharacteristic
234C2×C4×C22⋊C4C2212yescomplemented
235C23×Q8C2311yescharacteristic
236C23×D4C2311yescharacteristic
237C23×D4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240C2×C4⋊Q8C2314yes—
241C2×#126C2314yes—
242C2×#124C2314yes—
243C2×#123—28no—
244C2×#123C2312yes—
245C2×#123C2312yes—
246C2×#123C2312yes—
247C2×#123C2312yes—
248C2×#123C2312yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×#123C2312yes—
252C2×#123C2314yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×C22⋊Q8—28no—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×#120C2312yes—
264C2×#120C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2314yes—
267C2×C4×D4—28no—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2314yes—
273C2×#117C2312yes—
274C2×#117C2312yes—
275C2×#117C2312yes—
276C2×#117C2312yes—
277C2×#117C2314yes—
278C2×#117C2312yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C42C2311yescharacteristic
296C22×C42C2314yes—
297#401C2314yes—
298#401C2314yes—
299#401C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#392C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#390C2314yes—
408#390C2314yes—
409#390C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2312yes—
522#386C2312yes—
523#386C2312yes—
524#386C2314yes—
525#386C2314yes—
526#386C2312yes—
527#386C2312yes—
528#386C2312yes—
529#386C2312yes—
530#386C2312yes—
531#386C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2312yes—
539#385C2312yes—
540#385C2314yes—
541#385C2312yes—
542#385C2314yes—
543#385C2312yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2312yes—
548#385C2312yes—
549#385C2314yes—
550#385C2312yes—
551#385C2312yes—
552#385C2312yes—
553#385C2312yes—
554#385C2312yes—
555#385C2312yes—
556#385C2312yes—
557#385C2314yes—
558#385C2314yes—
559#385C2312yes—
560#385C2312yes—
561#385C2312yes—
562#385C2314yes—
563#383C2314yes—
564#383C2314yes—
565#383C2314yes—
566#383C2314yes—
567#383C2314yes—
568#382C2314yes—
569#382C2314yes—
570#382C2314yes—
571#382C2314yes—
572#381C2312yes—
573#381C2314yes—
574#381C2314yes—
575#381C2312yes—
576#381C2312yes—
577#381C2312yes—
578#381C2312yes—
579#381C2312yes—
580#381C2312yes—
581#381C2312yes—
582#381C2312yes—
583#381C2312yes—
584#381C2312yes—
585#381C2312yes—
586#381C2312yes—
587#381C2314yes—
588#381C2312yes—
589#381C2312yes—
590#381C2312yes—
591#381C2312yes—
592#381C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2312yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2312yes—
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2314yes—
608#380C2312yes—
609#380C2312yes—
610#380C2312yes—
611#380C2312yes—
612#380C2314yes—
613#379C2312yes—
614#379C2312yes—
615#379C2312yes—
616#379C2312yes—
617#379C2312yes—
618#379C2311yescharacteristic
619#379C2311yescharacteristic
620#379C2311yescharacteristic
621#379C2311yescharacteristic
622#379C2311yescharacteristic
623#379C2311yescharacteristic
624#379C2312yes—
625#379C2311yescharacteristic
626#379C2311yescharacteristic
627#379C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2312yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658#376C2314yes—
659#376C2314yes—
660C2×#95C2314yes—
661C25C2411yescharacteristic
662C25C2411yescharacteristic
663C25C2411yescharacteristic
664C22×Q8—24no—
665C22×Q8—82no—
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×Q8C2414yes—
669C22×Q8C2414yes—
670C22×D4—24no—
671C22×D4—24no—
672C22×D4—44no—
673C22×D4—82no—
674C22×D4C2412yes—
675C22×D4C2412yes—
676C22×D4C2414yes—
677C22×D4C2412yes—
678C22×D4C2412yes—
679C23×C4—24no—
680C23×C4—82no—
681C23×C4—82no—
682C23×C4#4118yes—
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2414yes—
692C23×C4C2411yescharacteristic
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C4⋊Q8—84no—
705#126—48no—
706#124—48no—
707#123—28no—
708#123—28no—
709#123—28no—
710#123—28no—
711#123—44no—
712#123—44no—
713#123—44no—
714#123—84no—
715#123—82no—
716#123—82no—
717#123—82no—
718C22⋊Q8—28no—
719C22⋊Q8—28no—
720C22⋊Q8—28no—
721C22⋊Q8—28no—
722C22⋊Q8—48no—
723C22⋊Q8—84no—
724C22⋊Q8—84no—
725#120—44no—
726#120—82no—
727C4×Q8—84no—
728C4×Q8—84no—
729C4×D4—28no—
730C4×D4—28no—
731C4×D4—28no—
732C4×D4—28no—
733C4×D4—48no—
734#117—82no—
735#117—82no—
736#117—84no—
737#117—82no—
738#117—82no—
739#117—82no—
740C2×C4⋊C4—24no—
741C2×C4⋊C4—24no—
742C2×C4⋊C4—24no—
743C2×C4⋊C4—24no—
744C2×C4⋊C4—24no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C22⋊C4—24no—
789C2×C22⋊C4—24no—
790C2×C22⋊C4—24no—
791C2×C22⋊C4—24no—
792C2×C22⋊C4—24no—
793C2×C22⋊C4—24no—
794C2×C22⋊C4—24no—
795C2×C22⋊C4—44no—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—82no—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C42—24no—
856C2×C42—84no—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932C24—22no—
933C24—24no—
934C24—22no—
935C24—42no—
936C24—42no—
937C24—42no—
938C24—42no—
939C24—42no—
940C24—42no—
941C24—42no—
942C24—42no—
943C24C2×#4114yes—
944C24C2512yes—
945C24C2511yescharacteristic
946C24C2511yescharacteristic
947C24C2511yescharacteristic
948C24C2512yes—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—44no—
952C2×Q8—44no—
953C2×Q8—44no—
954C2×Q8—44no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—44no—
959C2×Q8—88no—
960C2×D4—24no—
961C2×D4—24no—
962C2×D4—24no—
963C2×D4—24no—
964C2×D4—24no—
965C2×D4—24no—
966C2×D4—28no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—44no—
970C2×D4—42no—
971C2×D4—42no—
972C2×D4—42no—
973C2×D4—42no—
974C2×D4—44no—
975C2×D4—416no—
976C2×D4—88no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—28no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—88no—
1017C22×C4—88no—
1018C22×C4C2×#4114yes—
1019C22×C4C2×#4114yes—
1020C22×C4C2×#4114yes—
1021C22×C4C2×#4114yes—
1022C22×C4C2×#4114yes—
1023C22×C4C2×#4114yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C22⋊C4—24no—
1089C22⋊C4—24no—
1090C22⋊C4—24no—
1091C22⋊C4—24no—
1092C22⋊C4—24no—
1093C22⋊C4—24no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—24no—
1103C22⋊C4—24no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—44no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
1114C22⋊C4—42no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—44no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—42no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C42—24no—
1146C42—24no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C23—28no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—24no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—24no—
1174C23—22no—
1175C23—24no—
1176C23—22no—
1177C23—22no—
1178C23—24no—
1179C23—44no—
1180C23—44no—
1181C23—44no—
1182C23—44no—
1183C23—82no—
1184C23—82no—
1185C23—88no—
1186C23—82no—
1187C23—82no—
1188C23—88no—
1189C23—164no—
1190C23C22×#4112yes—
1191C23C22×#4112yes—
1192C23C22×#4112yes—
1193C23#58514yes—
1194C23C2611yescharacteristic
1195Q8—48no—
1196Q8—84no—
1197Q8—88no—
1198Q8—164no—
1199D4—48no—
1200D4—48no—
1201D4—88no—
1202D4—84no—
1203D4—84no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—44no—
1255C2×C4—44no—
1256C2×C4—44no—
1257C2×C4—44no—
1258C2×C4—44no—
1259C2×C4—44no—
1260C2×C4—48no—
1261C2×C4—44no—
1262C2×C4—44no—
1263C2×C4—84no—
1264C2×C4—82no—
1265C2×C4—82no—
1266C2×C4—82no—
1267C2×C4—82no—
1268C2×C4—82no—
1269C2×C4—88no—
1270C2×C4—82no—
1271C2×C4—82no—
1272C2×C4—82no—
1273C2×C4—88no—
1274C2×C4—88no—
1275C2×C4C22×#4112yes—
1276C2×C4C22×#4112yes—
1277C2×C4C22×#4112yes—
1278C2×C4C22×#4112yes—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—24no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—28no—
1290C22—42no—
1291C22—42no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—44no—
1300C22—44no—
1301C22—88no—
1302C22—88no—
1303C22—164no—
1304C22C23×#4111yescharacteristic
1305C22C2×#58512yes—
1306C22H(7,𝔽2)12yes—
1307C222−1+612yes—
1308C4—22no—
1309C4—22no—
1310C4—22no—
1311C4—22no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—44no—
1324C4—44no—
1325C4—44no—
1326C4—44no—
1327C4—44no—
1328C4—44no—
1329C4—44no—
1330C2—42no—
1331C2—44no—
1332C2—42no—
1333C2—42no—
1334C2—82no—
1335C2#6281411yescharacteristic
1336C2#6284411yescharacteristic
1337C2#6286011yescharacteristic
1338C2#6286914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2403C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48804C2semidirect
2. #47925C2semidirect
3. #47923C2semidirect
4. #47892C2semidirect
5. #47196C2semidirect
6. #47009C2semidirect
7. #46999C2semidirect
8. #46998C2semidirect
9. #46838C2semidirect
10. #46837C2semidirect
11. #46401C2semidirect
12. #46388C2semidirect
15. #40348C2semidirect
16. #40324C2semidirect
17. #38752C2semidirect
18. #38745C2semidirect
19. #37480C2semidirect
20. #37441C2semidirect
21. #36984C2semidirect
22. #35084C2semidirect
24. #35055C2semidirect
25. #34370C2semidirect
26. #34357C2semidirect
27. #34057C2semidirect
31. #2855C22semidirect
32. #2855C22semidirect
34. #2853C22semidirect
36. #2848C22semidirect
42. #2809C22semidirect
43. #2804C22semidirect
44. #2796C22semidirect
45. #2787C22semidirect
46. #2783C22semidirect
47. #2779C22semidirect
48. #2776C22semidirect
49. #2774C22semidirect
50. #2774C22semidirect
51. #2773C22semidirect
52. #2772C22semidirect
53. #2771C22semidirect
54. #2766C22semidirect
55. #2765C22semidirect
56. #2764C22semidirect
57. #2763C22semidirect
58. #2762C22semidirect
59. #2759C22semidirect
60. #2759C22semidirect
61. #2758C22semidirect
62. #2758C22semidirect
66. #2745C22semidirect
67. #2745C22semidirect
68. #2745C22semidirect
69. #2745C22semidirect
70. #2744C22semidirect
73. #2743C22semidirect
74. #2739C22semidirect
75. #2739C22semidirect
76. #2738C22semidirect
77. #2738C22semidirect
79. #2737C22semidirect
80. #2736C22semidirect
81. #2729C22semidirect
83. #2695C22semidirect
85. #2689C22semidirect
87. #2687C22semidirect
89. #2674C22semidirect
90. #2665C22semidirect
91. #2665C22semidirect
93. #2653C22semidirect
94. #2652C22semidirect
97. #2628C22semidirect
98. #2627C22semidirect
99. #2626C22semidirect
100. #2623C22semidirect
101. #2614C22semidirect
102. #2607C22semidirect
103. #2606C22semidirect
105. #2599C22semidirect
106. #2599C22semidirect
107. #2596C22semidirect
108. #2590C22semidirect
109. #2588C22semidirect
110. #2588C22semidirect
111. #2587C22semidirect
112. #2587C22semidirect
113. #2583C22semidirect
114. #2583C22semidirect
115. #2581C22semidirect
117. #2577C22semidirect
118. #2577C22semidirect
119. #2576C22semidirect
120. #2576C22semidirect
121. #2575C22semidirect
122. #2573C22semidirect
124. #2572C22semidirect
125. #2564C22semidirect
126. #2561C22semidirect
127. #2561C22semidirect
128. #2561C22semidirect
131. #2549C22semidirect
134. #2533C22semidirect
135. #2532C22semidirect
136. #2532C22semidirect
137. #2530C22semidirect
138. #2528C22semidirect
139. #2527C22semidirect
140. #2527C22semidirect
141. #2527C22semidirect
142. #2527C22semidirect
143. #2521C22semidirect
144. #2515C22semidirect
145. #2515C22semidirect
146. #2493C22semidirect
147. #2488C22semidirect
148. #2486C22semidirect
154. #2482C22semidirect
155. #2480C22semidirect
157. #2477C22semidirect
160. #2470C22semidirect
161. #2466C22semidirect
162. #2465C22semidirect
163. #2465C22semidirect
165. #2458C22semidirect
166. #2458C22semidirect
168. #2447C22semidirect
169. #2446C22semidirect
170. #2439C22semidirect
171. #2439C22semidirect
172. #2439C22semidirect
176. #2413C22semidirect
177. #2413C22semidirect
179. #2409C22semidirect
187. #2378C22semidirect
188. #2376C22semidirect
189. #2374C22semidirect
190. #2362C22semidirect
191. #2345C22semidirect
192. #2345C22semidirect
193. #2345C22semidirect
194. #2344C22semidirect
195. #2344C22semidirect
196. #2342C22semidirect
197. #2342C22semidirect
198. Q8×C22⋊C4C22semidirect
199. #2337C22semidirect
202. #2334C22semidirect
203. #2332C22semidirect
204. #2323C22semidirect
206. #2322C22semidirect
207. #2322C22semidirect
210. #2318C22semidirect
211. #2315C22semidirect
212. #2313C22semidirect
225. C4×C22⋊Q8C22semidirect
227. #2290C22semidirect
228. #2290C22semidirect
229. #2283C22semidirect
234. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#488042
#479252
#479232
#478922
#471962
#470092
#469992
#469982
#468382
#468372
#464012
#463882
#463862
#463852
#403482
#403242
#387522
#387452
#374802
#374412
#369842
#350842
#350622
#350552
#343702
#343572
#340572