Finite Group Databasebeta

← #7660778

Subgroups — #7660778

Order 512.

4428 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52305C212yesmaximal, complemented
2#52281C211yesmaximal, characteristic
3#42640C212yesmaximal, complemented
4#42558C212yesmaximal, complemented
5#42436C212yesmaximal, complemented
6#42290C214yesmaximal, complemented
7#41727C214yesmaximal, complemented
8#41636C214yesmaximal, complemented
9#40309C214yesmaximal
10#40189C212yesmaximal, complemented
11#39701C212yesmaximal, complemented
12#39614C211yesmaximal, characteristic
13#39447C212yesmaximal, complemented
14#39427C214yesmaximal, complemented
15#39407C212yesmaximal, complemented
16#39368C211yesmaximal, characteristic, complemented
17#37342C212yesmaximal, complemented
18#37323C211yesmaximal, characteristic, complemented
19#37153C212yesmaximal, complemented
20#37052C214yesmaximal, complemented
21#36565C212yesmaximal, complemented
22#36491C212yesmaximal, complemented
23#36459C211yesmaximal, characteristic
24#36450C211yesmaximal, characteristic, complemented
25#36006C212yesmaximal, complemented
26#36006C212yesmaximal, complemented
27#35819C212yesmaximal, complemented
28#34317C212yesmaximal, complemented
29#34272C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×#544C2211yescharacteristic
32C2×#544C2212yes—
33C2×#541C2214yes—
34#2866C2214yes—
35#2863C2212yes—
36#2863C2212yes—
37#2862C2214yes—
38#2860C2212yes—
39#2859C2212yes—
40#2857C2211yescharacteristic
41#2857C2211yescharacteristic
42#2839C2214yes—
43#2838C2214yes—
44#2817C2214yes—
45#2810C2212yes—
46#2809C2212yes—
47#2808C2211yescharacteristic
48#2805C2211yescharacteristic
49#2805C2212yes—
50#2799C2214yes—
51#2796C2214yes—
52#2792C2214yes—
53#2786C2212yes—
54#2777C2212yes—
55#2775C2214yes—
56#2773C2212yes—
57#2770C2212yes—
58#2770C2214yes—
59#2767C2214yes—
60#2767C2214yes—
61#2767C2214yes—
62#2762C2214yes—
63#2758C2214yes—
64#2754C2214yes—
65#2747C2214yes—
66#2745C2214yes—
67#2737C2214yes—
68#2734C2212yes—
69#2727C2211yescharacteristic
70#2726C2212yes—
71#2726C2212yes—
72#2726C2212yes—
73#2726C2211yescharacteristic
74#2723C2212yes—
75#2723C2214yes—
76#2721C2214yes—
77#2719C2214yes—
78#2719C2214yes—
79#2719C2214yes—
80#2719C2214yes—
81#2716C2214yes—
82#2716C2214yes—
83#2713C2214yes—
84#2713C2214yes—
85#2713C2214yes—
86#2711C2212yes—
87#2704C2214yes—
88#2698C2214yes—
89#2690C2214yes—
90#2690C2214yes—
91#2690C2214yes—
92#2689C2214yes—
93#2683C2212yes—
94#2677C2214yes—
95#2666C2214yes—
96#2666C2214yes—
97#2659C2212yes—
98#2655C2214yes—
99#2650C2214yes—
100#2650C2214yes—
101#2650C2214yes—
102#2638C2214yes—
103#2637C2214yes—
104#2634C2214yes—
105#2628C2214yes—
106#2628C2212yes—
107#2627C2212yes—
108#2625C2212yes—
109#2625C2212yes—
110#2621C2214yes—
111#2605C2214yes—
112#2596C2214yes—
113#2595C2214yes—
114#2595C2214yes—
115#2590C2214yes—
116#2589C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2586C2214yes—
121#2577C2214yes—
122#2568C2211yescharacteristic
123#2563C2211yescharacteristic
124#2560C2214yes—
125#2560C2214yes—
126#2560C2214yes—
127#2556C2214yes—
128#2552C2211yescharacteristic
129#2552C2211yescharacteristic
130#2551C2212yes—
131#2551C2212yes—
132#2550C2214yes—
133#2550C2214yes—
134#2550C2214yes—
135#2550C2212yes—
136#2546C2212yes—
137#2532C2214yes—
138#2530C2214yes—
139#2530C2214yes—
140#2528C2214yes—
141#2525C2214yes—
142#2524C2214yes—
143#2524C2214yes—
144#2522C2214yes—
145#2520C2214yes—
146#2520C2214yes—
147#2519C2214yes—
148#2519C2214yes—
149#2519C2214yes—
150#2514C2212yes—
151#2511C2212yes—
152#2511C2212yes—
153#2509C2212yes—
154#2506C2212yes—
155#2506C2212yes—
156#2506C2212yes—
157#2506C2212yes—
158#2499C2212yes—
159#2496C2212yes—
160#2496C2212yes—
161#2496C2212yes—
162#2495C2212yes—
163#2494C2212yes—
164#2492C2214yes—
165#2492C2212yes—
166#2492C2212yes—
167#2490C2212yes—
168#2489C2212yes—
169#2489C2214yes—
170#2489C2214yes—
171#2489C2212yes—
172#2485C2212yes—
173#2479C2214yes—
174#2478C2214yes—
175#2462C2214yes—
176#2462C2214yes—
177#2453C2214yes—
178#2453C2212yes—
179#2451C2214yes—
180#2451C2212yes—
181#2451C2212yes—
182#2451C2212yes—
183#2451C2212yes—
184#2446C2212yes—
185#2442C2212yes—
186#2440C2212yes—
187#2440C2212yes—
188#2440C2212yes—
189#2438C2214yes—
190#2429C2212yes—
191#2423C2212yes—
192#2417C2214yes—
193#2417C2212yes—
194#2417C2212yes—
195#2415C2214yes—
196#2402C2214yes—
197#2402C2214yes—
198#2402C2214yes—
199#2396C2212yes—
200#2395C2212yes—
201#2395C2212yes—
202#2370C2214yes—
203#2370C2212yes—
204#2370C2212yes—
205#2369C2212yes—
206#2369C2211yescharacteristic
207#2369C2212yes—
208#2369C2212yes—
209#2368C2214yes—
210#2365C2212yes—
211#2365C2211yescharacteristic
212#2362C2214yes—
213#2362C2214yes—
214#2362C2212yes—
215#2362C2212yes—
216#2362C2212yes—
217#2360C2214yes—
218#2357C2214yes—
219#2355C2212yes—
220#2355C2212yes—
221#2355C2211yescharacteristic
222#2355C2212yes—
223#2354C2212yes—
224#2354C2211yescharacteristic
225#2347C2212yes—
226#2346C2212yes—
227#2344C2212yes—
228#2344C2212yes—
229#2336C2214yes—
230#2332C2214yes—
231#2332C2214yes—
232#2331C2212yes—
233#2330C2212yes—
234#2325C2212yes—
235#2323C2212yes—
236#2323C2212yes—
237#2317C2211yescharacteristic
238C4×C4⋊Q8C2212yes—
239C4×C4⋊Q8C2212yes—
240C4×#125C2214yes—
241C4×#125C2214yes—
242C4×#125C2212yes—
243C4×#125C2212yes—
244C4×#125C2212yes—
245C4×#125C2212yes—
246C4×#125C2214yes—
247C4×#126C2212yes—
248C4×C22⋊Q8C2211yescharacteristic
249C4×#121C2211yescharacteristic
250#2296C2211yescharacteristic
251#2293C2214yes—
252#2293C2212yes—
253C2×#389C2211yescharacteristic
254#2274C2211yescharacteristic
255#2274C2212yes—
256#2274C2211yescharacteristic
257C42×Q8C2212yes—
258C4×#117C2211yescharacteristic
259#554—216no—
260#544—28no—
261#544—48no—
262#541—416no—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×#126C2312yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2312yes—
310C2×#117C2311yescharacteristic
311C2×#117C2311yescharacteristic
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2314yes—
315C2×#117C2314yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
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#400C2312yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#399C2314yes—
350#399C2312yes—
351#399C2314yes—
352#399C2312yes—
353#399C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
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#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#397C2312yes—
400#396C2314yes—
401#396C2312yes—
402#396C2314yes—
403#396C2312yes—
404#396C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2312yes—
419#394C2312yes—
420#394C2312yes—
421#394C2314yes—
422#394C2312yes—
423#394C2312yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#390C2312yes—
459#390C2314yes—
460#390C2312yes—
461#390C2311yescharacteristic
462#390C2312yes—
463#390C2312yes—
464#389C2311yescharacteristic
465#389C2311yescharacteristic
466#389C2312yes—
467#389C2311yescharacteristic
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2311yescharacteristic
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2311yescharacteristic
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2311yescharacteristic
498#389C2314yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
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#388C2312yes—
533#388C2312yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#385C2314yes—
608#385C2312yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2312yes—
615#384C2312yes—
616#384C2312yes—
617#384C2311yescharacteristic
618#384C2311yescharacteristic
619#384C2312yes—
620#384C2312yes—
621#383C2312yes—
622#383C2314yes—
623#383C2314yes—
624#383C2314yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2314yes—
629#382C2312yes—
630#382C2314yes—
631#382C2314yes—
632#382C2314yes—
633#382C2314yes—
634#382C2314yes—
635#382C2312yes—
636#381C2314yes—
637#381C2314yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2311yescharacteristic
647#380C2314yes—
648#380C2314yes—
649#380C2311yescharacteristic
650#380C2314yes—
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710#376C2312yes—
711#376C2314yes—
712C2×#95C2312yes—
713C43C2312yes—
714C43C2312yes—
715C43C2314yes—
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C22×Q8C2414yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2411yescharacteristic
726C23×C4C2411yescharacteristic
727C23×C4C2414yes—
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2412yes—
731C4⋊Q8—28no—
732C4⋊Q8—28no—
733C4⋊Q8—28no—
734C4⋊Q8—42no—
735C4⋊Q8—44no—
736C4⋊Q8—48no—
737C4⋊Q8—48no—
738C4⋊Q8—42no—
739C4⋊Q8—48no—
740#126—28no—
741#126—48no—
742#126—48no—
743#126—48no—
744#125—28no—
745#125—28no—
746#125—216no—
747#125—28no—
748#125—216no—
749#125—28no—
750#125—28no—
751#125—48no—
752#125—48no—
753#125—48no—
754#125—48no—
755C22⋊Q8—216no—
756C22⋊Q8—216no—
757C22⋊Q8—28no—
758C22⋊Q8—216no—
759C22⋊Q8—28no—
760C22⋊Q8—24no—
761C22⋊Q8—48no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766#121—24no—
767C4×Q8—28no—
768C4×Q8—28no—
769C4×Q8—42no—
770C4×Q8—48no—
771C4×Q8—48no—
772C4×Q8—44no—
773C4×D4—216no—
774C4×D4—28no—
775C4×D4—42no—
776#117—24no—
777#117—24no—
778#117—24no—
779#117—28no—
780#117—42no—
781#117—44no—
782#117—48no—
783#117—48no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—42no—
786C2×C4⋊C4—44no—
787C2×C4⋊C4#4118yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C42—42no—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2411yescharacteristic
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2414yes—
926C2×C42C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
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#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24C2512yes—
1004C24C2511yescharacteristic
1005C2×Q8—24no—
1006C2×Q8—28no—
1007C2×Q8—28no—
1008C2×Q8—22no—
1009C2×Q8—24no—
1010C2×Q8—24no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—41no—
1014C2×Q8—41no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—42no—
1018C2×Q8—44no—
1019C2×Q8—42no—
1020C2×Q8—44no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—22no—
1026C2×D4—42no—
1027C2×D4—41no—
1028C2×D4—41no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—28no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—44no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4C2×#4114yes—
1049C22×C4C2×#4118yes—
1050C22×C4C2512yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2511yescharacteristic
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—41no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—41no—
1134C4⋊C4—41no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4C2×#4118yes—
1151C4⋊C4C2×#4118yes—
1152C4⋊C4H(5,𝔽2)14yes—
1153C4⋊C42−1+414yes—
1154C4⋊C42−1+414yes—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—28no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—42no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C42—24no—
1184C42—24no—
1185C42—28no—
1186C42—24no—
1187C42—28no—
1188C42—24no—
1189C42—24no—
1190C42—24no—
1191C42—28no—
1192C42—24no—
1193C42—28no—
1194C42—24no—
1195C42—24no—
1196C42—22no—
1197C42—22no—
1198C42—24no—
1199C42—24no—
1200C42—41no—
1201C42—41no—
1202C42—44no—
1203C42—42no—
1204C42—42no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—42no—
1209C42—42no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23C22×#4112yes—
1229C23C2611yescharacteristic
1230Q8—48no—
1231Q8—88no—
1232Q8—88no—
1233Q8—82no—
1234Q8—162no—
1235Q8—164no—
1236D4—48no—
1237D4—82no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—24no—
1252C2×C4—28no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—48no—
1311C2×C4—48no—
1312C2×C4—88no—
1313C2×C4—82no—
1314C2×C4—82no—
1315C2×C4—162no—
1316C2×C4C22×#4112yes—
1317C2×C4C22×#4118yes—
1318C2×C4C22×#4112yes—
1319C2×C4C2×H(5,𝔽2)14yes—
1320C2×C4C2×H(5,𝔽2)12yes—
1321C2×C4C2×2−1+414yes—
1322C2×C4C2×2−1+412yes—
1323C2×C4C2×2−1+414yes—
1324C2×C4C2×2−1+412yes—
1325C2×C4#58512yes—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22C23×#4111yescharacteristic
1341C22C22×H(5,𝔽2)11yescharacteristic
1342C22C22×2−1+411yescharacteristic
1343C22C22×2−1+411yescharacteristic
1344C22C2×#58511yescharacteristic
1345C222−1+611yescharacteristic
1346C222−1+611yescharacteristic
1347C4—28no—
1348C4—24no—
1349C4—24no—
1350C4—24no—
1351C4—22no—
1352C4—22no—
1353C4—22no—
1354C4—44no—
1355C4—42no—
1356C4—42no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—44no—
1362C4—42no—
1363C4—42no—
1364C4—41no—
1365C4—44no—
1366C4—42no—
1367C4—44no—
1368C4—42no—
1369C4—42no—
1370C4—41no—
1371C4—42no—
1372C4—44no—
1373C4#346114yes—
1374C2—42no—
1375C2—82no—
1376C2C2×#346111yescharacteristic
1377C2#6293111yescharacteristic
1378C2#6293211yescharacteristic
1379C2#6298411yescharacteristic
1380C2#6299811yescharacteristic
1381C2#6303711yescharacteristic
1382C2#6306711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52305C2semidirect
3. #42640C2semidirect
4. #42558C2semidirect
5. #42436C2semidirect
6. #42290C2semidirect
7. #41727C2semidirect
8. #41636C2semidirect
10. #40189C2semidirect
11. #39701C2semidirect
13. #39447C2semidirect
14. #39427C2semidirect
15. #39407C2semidirect
16. #39368C2semidirect
17. #37342C2semidirect
18. #37323C2semidirect
19. #37153C2semidirect
20. #37052C2semidirect
21. #36565C2semidirect
22. #36491C2semidirect
24. #36450C2semidirect
25. #36006C2semidirect
26. #36006C2semidirect
27. #35819C2semidirect
28. #34317C2semidirect
29. #34272C2semidirect

Maximal subgroups

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

subgroupindex
#523052
#522812
#426402
#425582
#424362
#422902
#417272
#416362
#403092
#401892
#397012
#396142
#394472
#394272
#394072
#393682
#373422
#373232
#371532
#370522
#365652
#364912
#364592
#364502
#360062
#358192
#343172
#342722