Finite Group Databasebeta

← #7713152

Subgroups — #7713152

Order 512.

4414 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49098C214yesmaximal, complemented
2#49062C214yesmaximal, complemented
3#48259C214yesmaximal, complemented
4#48219C214yesmaximal, complemented
5#47294C214yesmaximal, complemented
6#47109C214yesmaximal, complemented
7#46944C214yesmaximal, complemented
8#46590C214yesmaximal, complemented
9#39676C212yesmaximal, complemented
10#39640C212yesmaximal, complemented
11#39542C212yesmaximal, complemented
12#39508C212yesmaximal, complemented
13#37956C212yesmaximal, complemented
14#37932C212yesmaximal
15#37881C212yesmaximal
16#37880C212yesmaximal, complemented
17#37460C212yesmaximal, complemented
18#36979C212yesmaximal, complemented
19#36966C212yesmaximal
20#35033C211yesmaximal, characteristic, complemented
21#35015C211yesmaximal, characteristic, complemented
22#35015C211yesmaximal, characteristic, complemented
23#35014C211yesmaximal, characteristic, complemented
24#35014C211yesmaximal, characteristic, complemented
25#35002C211yesmaximal, characteristic, complemented
26#34433C212yesmaximal, complemented
27C2×#2337C211yesmaximal, characteristic
28C2×#543C2212yes—
29C22×#124C2211yescharacteristic
30#2857C2212yes—
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2855C2212yes—
36#2855C2212yes—
37#2851C2212yes—
38#2848C2212yes—
39#2848C2212yes—
40#2836C2214yescomplemented
41#2831C2214yescomplemented
42#2806C2214yescomplemented
43#2805C2214yescomplemented
44#2799C2214yescomplemented
45#2798C2214yescomplemented
46#2793C2214yescomplemented
47#2788C2214yescomplemented
48#2787C2214yescomplemented
49#2787C2214yescomplemented
50#2781C2214yes—
51#2779C2214yes—
52#2776C2214yescomplemented
53#2776C2214yescomplemented
54#2774C2214yescomplemented
55#2774C2214yescomplemented
56#2771C2214yescomplemented
57#2770C2214yescomplemented
58#2769C2214yescomplemented
59#2769C2214yescomplemented
60#2765C2214yescomplemented
61#2762C2214yescomplemented
62#2762C2214yescomplemented
63#2759C2214yescomplemented
64#2758C2214yescomplemented
65#2758C2214yescomplemented
66#2755C2214yescomplemented
67#2750C2214yes—
68#2747C2214yescomplemented
69#2745C2214yescomplemented
70#2745C2214yescomplemented
71#2743C2214yes—
72#2741C2214yes—
73#2739C2214yescomplemented
74#2716C2214yescomplemented
75#2713C2214yescomplemented
76#2713C2214yescomplemented
77#2702C2214yes—
78#2700C2214yes—
79#2700C2214yes—
80#2700C2214yes—
81#2700C2214yes—
82#2695C2214yes—
83#2690C2214yescomplemented
84#2689C2214yescomplemented
85#2687C2214yes—
86#2674C2214yes—
87#2674C2214yes—
88#2674C2214yes—
89#2674C2214yes—
90#2664C2214yescomplemented
91#2659C2212yes—
92#2659C2212yes—
93#2654C2214yescomplemented
94#2650C2214yescomplemented
95#2646C2212yes—
96#2646C2212yes—
97#2646C2212yes—
98#2646C2212yes—
99#2637C2214yescomplemented
100#2627C2212yes—
101#2627C2212yes—
102#2626C2212yes—
103#2626C2212yes—
104#2626C2212yes—
105#2626C2212yes—
106#2609C2214yes—
107#2608C2214yescomplemented
108#2607C2214yescomplemented
109#2599C2214yescomplemented
110#2599C2214yescomplemented
111#2596C2214yescomplemented
112#2594C2214yescomplemented
113#2590C2214yescomplemented
114#2590C2214yescomplemented
115#2589C2214yescomplemented
116#2589C2214yescomplemented
117#2588C2214yescomplemented
118#2588C2214yescomplemented
119#2588C2214yescomplemented
120#2587C2214yescomplemented
121#2587C2214yescomplemented
122#2577C2214yescomplemented
123#2575C2214yescomplemented
124#2568C2214yescomplemented
125#2561C2214yes—
126#2553C2214yes—
127#2550C2214yescomplemented
128#2549C2214yescomplemented
129#2549C2214yescomplemented
130#2546C2214yescomplemented
131#2525C2214yescomplemented
132#2520C2214yescomplemented
133#2519C2214yescomplemented
134#2515C2214yescomplemented
135#2511C2214yescomplemented
136#2511C2212yescomplemented
137#2511C2212yescomplemented
138#2507C2212yescomplemented
139#2507C2212yescomplemented
140#2505C2214yes—
141#2505C2214yes—
142#2505C2214yes—
143#2498C2214yes—
144#2497C2212yescomplemented
145#2497C2212yescomplemented
146#2493C2214yes—
147#2493C2214yes—
148#2493C2214yescomplemented
149#2492C2212yescomplemented
150#2492C2212yescomplemented
151#2488C2214yes—
152#2484C2214yescomplemented
153#2483C2214yes—
154#2481C2214yes—
155#2480C2214yes—
156#2480C2214yes—
157#2478C2214yescomplemented
158#2477C2214yes—
159#2475C2214yescomplemented
160#2473C2214yes—
161#2473C2214yescomplemented
162#2470C2214yes—
163#2469C2214yescomplemented
164#2469C2214yescomplemented
165#2465C2214yescomplemented
166#2451C2212yescomplemented
167#2451C2212yescomplemented
168#2451C2214yescomplemented
169#2446C2212yescomplemented
170#2446C2212yescomplemented
171#2446C2214yescomplemented
172#2441C2212yescomplemented
173#2441C2212yescomplemented
174#2440C2212yescomplemented
175#2440C2212yescomplemented
176#2440C2212yescomplemented
177#2440C2212yescomplemented
178#2439C2212yescomplemented
179#2439C2212yescomplemented
180#2438C2214yescomplemented
181#2434C2214yes—
182#2429C2212yescomplemented
183#2429C2212yescomplemented
184#2423C2212yescomplemented
185#2423C2212yescomplemented
186#2413C2214yes—
187#2405C2214yes—
188#2378C2214yescomplemented
189#2378C2214yescomplemented
190#2368C2214yes—
191#2362C2214yescomplemented
192#2362C2214yescomplemented
193#2360C2214yes—
194#2342C2214yes—
195#2342C2214yes—
196#2337C2214yes—
197#2337C2214yes—
198#2337C2214yes—
199#2337C2214yes—
200#2332C2214yescomplemented
201#2332C2214yescomplemented
202#2329C2212yes—
203#2329C2212yes—
204#2329C2212yes—
205#2329C2212yes—
206#2329C2212yes—
207#2329C2212yes—
208#2323C2214yescomplemented
209#2323C2214yescomplemented
210#2315C2212yes—
211#2313C2212yes—
212#2313C2212yes—
213#2312C2212yes—
214#2312C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C4×C22⋊Q8C2212yes—
218C4×C22⋊Q8C2212yes—
219C2×#391C2211yescharacteristic
220C2×#391C2211yescharacteristic
221C2×#388C2211yescharacteristic
222C2×#388C2211yescharacteristic
223C2×#388C2211yescharacteristic
224C2×#388C2211yescharacteristic
225C2×#386C2211yescharacteristic
226C2×#386C2211yescharacteristic
227C2×#385C2211yescharacteristic
228C2×#385C2211yescharacteristic
229C2×#383C2211yescharacteristic
230#2280C2212yes—
231C2×#380C2212yes—
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×D4C2311yescharacteristic
237C24×C4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239#543—216no—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2312yes—
250C2×#125C2314yes—
251C2×#124—28no—
252C2×#124C2314yes—
253C2×#124C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2312yes—
277C2×#117C2312yes—
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2311yescharacteristic
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2311yescharacteristic
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300#401C2314yes—
301#401C2314yes—
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#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
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#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2312yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#389C2312yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
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#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#384C2311yescharacteristic
573#384C2311yescharacteristic
574#384C2311yescharacteristic
575#384C2312yes—
576#384C2311yescharacteristic
577#383C2314yes—
578#383C2314yes—
579#383C2314yes—
580#383C2314yes—
581#382C2314yes—
582#382C2314yes—
583#382C2312yes—
584#382C2314yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#381C2314yes—
589#381C2314yes—
590#381C2314yes—
591#381C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2312yes—
600#380C2314yes—
601#380C2312yes—
602#380C2314yes—
603#380C2314yes—
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2314yes—
608#380C2314yes—
609#380C2312yes—
610#380C2312yes—
611#380C2312yes—
612#380C2312yes—
613#379C2314yes—
614#379C2314yes—
615#379C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2312yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2312yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2312yes—
647C2×#95C2311yescharacteristic
648C2×#95C2311yescharacteristic
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2311yescharacteristic
652C2×#95C2311yescharacteristic
653C2×#95C2311yescharacteristic
654C2×#95C2314yes—
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C25C2411yescharacteristic
661C25C2411yescharacteristic
662C22×Q8—24no—
663C22×Q8—81no—
664C22×Q8—81no—
665C22×Q8C2414yes—
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2412yes—
670C22×Q8C2414yes—
671C22×D4—24no—
672C22×D4—81no—
673C22×D4—81no—
674C22×D4C2414yes—
675C23×C4—24no—
676C23×C4—24no—
677C23×C4—81no—
678C23×C4—81no—
679C23×C4—81no—
680C23×C4—81no—
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2414yes—
688C23×C4C2414yes—
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C4⋊Q8—81no—
701C4⋊Q8—81no—
702C4⋊Q8—82no—
703C4⋊Q8—81no—
704C4⋊Q8—81no—
705C4⋊Q8—84no—
706C4⋊Q8—84no—
707#126—84no—
708#126—84no—
709#125—82no—
710#125—84no—
711#124—216no—
712#124—216no—
713#123—84no—
714#123—84no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—216no—
718C22⋊Q8—28no—
719C22⋊Q8—28no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—82no—
725C22⋊Q8—82no—
726C22⋊Q8—82no—
727C22⋊Q8—82no—
728C4×Q8—82no—
729C4×Q8—82no—
730C4×Q8—82no—
731C4×Q8—82no—
732C4×Q8—84no—
733#117—82no—
734#117—84no—
735#117—84no—
736#117—82no—
737C2×C4⋊C4—24no—
738C2×C4⋊C4—24no—
739C2×C4⋊C4—81no—
740C2×C4⋊C4—81no—
741C2×C4⋊C4—82no—
742C2×C4⋊C4—82no—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C22⋊C4—24no—
801C2×C22⋊C4—216no—
802C2×C22⋊C4—24no—
803C2×C22⋊C4—24no—
804C2×C22⋊C4—24no—
805C2×C22⋊C4—24no—
806C2×C22⋊C4—81no—
807C2×C22⋊C4—81no—
808C2×C22⋊C4—81no—
809C2×C22⋊C4—81no—
810C2×C22⋊C4#4118yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C42—24no—
844C2×C42—81no—
845C2×C42—81no—
846C2×C42—81no—
847C2×C42—81no—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2412yes—
869C2×C42C2414yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
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—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938C24—22no—
939C24—22no—
940C24—22no—
941C24—22no—
942C24—22no—
943C24—41no—
944C24—41no—
945C24—41no—
946C24—41no—
947C24—41no—
948C24—41no—
949C24—41no—
950C24—41no—
951C24C2×#4114yes—
952C24C2512yes—
953C24C2512yes—
954C24C2511yescharacteristic
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—28no—
958C2×Q8—28no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—44no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×Q8—88no—
974C2×D4—28no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—88no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—22no—
983C22×C4—28no—
984C22×C4—28no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—41no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—41no—
1005C22×C4—41no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—41no—
1013C22×C4—41no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—44no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—41no—
1029C22×C4—44no—
1030C22×C4—41no—
1031C22×C4—88no—
1032C22×C4—88no—
1033C22×C4C2×#4114yes—
1034C22×C4C2×#4114yes—
1035C22×C42−1+414yes—
1036C22×C42−1+414yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—24no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4C2×#4118yes—
1149C22⋊C4C2×#4118yes—
1150C42—24no—
1151C42—24no—
1152C42—42no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—42no—
1157C42—41no—
1158C42—41no—
1159C42—41no—
1160C42—41no—
1161C42—42no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—28no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—44no—
1191C23—44no—
1192C23—44no—
1193C23—44no—
1194C23—44no—
1195C23—82no—
1196C23—82no—
1197C23—82no—
1198C23—82no—
1199C23—82no—
1200C23—82no—
1201C23—82no—
1202C23—82no—
1203C23C22×#4114yes—
1204C23C22×#4112yes—
1205C23C2×2−1+412yes—
1206C23C2×2−1+412yes—
1207C23C2611yescharacteristic
1208Q8—88no—
1209Q8—84no—
1210Q8—84no—
1211Q8—84no—
1212Q8—84no—
1213Q8—88no—
1214D4—88no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—44no—
1281C2×C4—44no—
1282C2×C4—44no—
1283C2×C4—44no—
1284C2×C4—48no—
1285C2×C4—48no—
1286C2×C4—44no—
1287C2×C4—44no—
1288C2×C4—44no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—88no—
1292C2×C4—88no—
1293C2×C4—82no—
1294C2×C4—82no—
1295C2×C4—82no—
1296C2×C4—82no—
1297C2×C4—82no—
1298C2×C4—82no—
1299C2×C4C22×#4112yes—
1300C2×C4C22×#4112yes—
1301C2×C4C22×#4114yes—
1302C2×C4C2×2−1+412yes—
1303C2×C4C2×2−1+412yes—
1304C2×C4C2×2−1+412yes—
1305C2×C4C2×2−1+412yes—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—24no—
1313C22—24no—
1314C22—24no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—88no—
1327C22—88no—
1328C22#350914yes—
1329C22C23×#4111yescharacteristic
1330C22C22×2−1+411yescharacteristic
1331C22C22×2−1+411yescharacteristic
1332C22H(7,𝔽2)11yescharacteristic
1333C22H(7,𝔽2)11yescharacteristic
1334C22H(7,𝔽2)11yescharacteristic
1335C222−1+611yescharacteristic
1336C4—24no—
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—22no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—44no—
1348C4—44no—
1349C4—44no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—44no—
1355C4—44no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—42no—
1360C2—24no—
1361C2—44no—
1362C2—82no—
1363C2C2×#350911yescharacteristic
1364C2#6284611yescharacteristic
1365C2#6284711yescharacteristic
1366C2#6286411yescharacteristic
1367C2#6286411yescharacteristic
1368C2#6287911yescharacteristic
1369C2#6287911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #49098C2semidirect
2. #49062C2semidirect
3. #48259C2semidirect
4. #48219C2semidirect
5. #47294C2semidirect
6. #47109C2semidirect
7. #46944C2semidirect
8. #46590C2semidirect
9. #39676C2semidirect
10. #39640C2semidirect
11. #39542C2semidirect
12. #39508C2semidirect
13. #37956C2semidirect
16. #37880C2semidirect
17. #37460C2semidirect
18. #36979C2semidirect
20. #35033C2semidirect
21. #35015C2semidirect
22. #35015C2semidirect
23. #35014C2semidirect
24. #35014C2semidirect
25. #35002C2semidirect
26. #34433C2semidirect
40. #2836C22semidirect
41. #2831C22semidirect
42. #2806C22semidirect
43. #2805C22semidirect
44. #2799C22semidirect
45. #2798C22semidirect
46. #2793C22semidirect
47. #2788C22semidirect
48. #2787C22semidirect
49. #2787C22semidirect
52. #2776C22semidirect
53. #2776C22semidirect
54. #2774C22semidirect
55. #2774C22semidirect
56. #2771C22semidirect
57. #2770C22semidirect
58. #2769C22semidirect
59. #2769C22semidirect
60. #2765C22semidirect
61. #2762C22semidirect
62. #2762C22semidirect
63. #2759C22semidirect
64. #2758C22semidirect
65. #2758C22semidirect
66. #2755C22semidirect
68. #2747C22semidirect
69. #2745C22semidirect
70. #2745C22semidirect
73. #2739C22semidirect
74. #2716C22semidirect
75. #2713C22semidirect
76. #2713C22semidirect
83. #2690C22semidirect
84. #2689C22semidirect
90. #2664C22semidirect
93. #2654C22semidirect
94. #2650C22semidirect
99. #2637C22semidirect
107. #2608C22semidirect
108. #2607C22semidirect
109. #2599C22semidirect
110. #2599C22semidirect
111. #2596C22semidirect
112. #2594C22semidirect
113. #2590C22semidirect
114. #2590C22semidirect
115. #2589C22semidirect
116. #2589C22semidirect
117. #2588C22semidirect
118. #2588C22semidirect
119. #2588C22semidirect
120. #2587C22semidirect
121. #2587C22semidirect
122. #2577C22semidirect
123. #2575C22semidirect
124. #2568C22semidirect
127. #2550C22semidirect
128. #2549C22semidirect
129. #2549C22semidirect
130. #2546C22semidirect
131. #2525C22semidirect
132. #2520C22semidirect
133. #2519C22semidirect
134. #2515C22semidirect
135. #2511C22semidirect
136. #2511C22semidirect
137. #2511C22semidirect
138. #2507C22semidirect
139. #2507C22semidirect
144. #2497C22semidirect
145. #2497C22semidirect
148. #2493C22semidirect
149. #2492C22semidirect
150. #2492C22semidirect
152. #2484C22semidirect
157. #2478C22semidirect
159. #2475C22semidirect
161. #2473C22semidirect
163. #2469C22semidirect
164. #2469C22semidirect
165. #2465C22semidirect
166. #2451C22semidirect
167. #2451C22semidirect
168. #2451C22semidirect
169. #2446C22semidirect
170. #2446C22semidirect
171. #2446C22semidirect
172. #2441C22semidirect
173. #2441C22semidirect
174. #2440C22semidirect
175. #2440C22semidirect
176. #2440C22semidirect
177. #2440C22semidirect
178. #2439C22semidirect
179. #2439C22semidirect
180. #2438C22semidirect
182. #2429C22semidirect
183. #2429C22semidirect
184. #2423C22semidirect
185. #2423C22semidirect
188. #2378C22semidirect
189. #2378C22semidirect
191. #2362C22semidirect
192. #2362C22semidirect
200. #2332C22semidirect
201. #2332C22semidirect
208. #2323C22semidirect
209. #2323C22semidirect

Maximal subgroups

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

subgroupindex
#490982
#490622
#482592
#482192
#472942
#471092
#469442
#465902
#396762
#396402
#395422
#395082
#379562
#379322
#378812
#378802
#374602
#369792
#369662
#350332
#350152
#350142
#350022
#344332
C2×#23372