Finite Group Databasebeta

← #7715914

Subgroups — #7715914

Order 512.

4482 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50429C214yesmaximal, complemented
2#50409C214yesmaximal, complemented
3#49251C214yesmaximal, complemented
4#49223C214yesmaximal, complemented
5#44825C214yesmaximal, complemented
6#44804C214yesmaximal, complemented
7#44372C214yesmaximal, complemented
8#43993C214yesmaximal, complemented
9#39676C212yesmaximal, complemented
10#39640C212yesmaximal, complemented
11#37958C212yesmaximal, complemented
12#37934C212yesmaximal, complemented
13#37932C212yesmaximal
14#37881C212yesmaximal
15#36966C212yesmaximal
16#36760C212yesmaximal, complemented
17#36204C212yesmaximal, complemented
18#36167C212yesmaximal, complemented
19#35315C212yesmaximal, complemented
20#35120C211yesmaximal, characteristic, complemented
21#35120C211yesmaximal, characteristic, complemented
22#35012C211yesmaximal, characteristic, complemented
23#35012C211yesmaximal, characteristic, complemented
24#35002C211yesmaximal, characteristic, complemented
25#34578C211yesmaximal, characteristic, complemented
26#34433C212yesmaximal, complemented
27C2×#2372C211yesmaximal, characteristic
28C2×#543C2212yes—
29C22×#124C2211yescharacteristic
30#2857C2212yes—
31#2857C2212yes—
32#2855C2212yes—
33#2855C2212yes—
34#2855C2212yes—
35#2855C2212yes—
36#2851C2212yes—
37#2851C2212yes—
38#2848C2212yes—
39#2848C2212yes—
40#2806C2214yescomplemented
41#2805C2214yescomplemented
42#2799C2214yescomplemented
43#2798C2214yescomplemented
44#2783C2214yescomplemented
45#2783C2214yescomplemented
46#2781C2214yes—
47#2779C2214yes—
48#2777C2214yescomplemented
49#2775C2214yescomplemented
50#2774C2214yescomplemented
51#2774C2214yescomplemented
52#2772C2214yescomplemented
53#2765C2214yescomplemented
54#2764C2214yescomplemented
55#2759C2214yescomplemented
56#2755C2214yescomplemented
57#2754C2214yescomplemented
58#2750C2214yes—
59#2744C2214yescomplemented
60#2743C2214yes—
61#2741C2214yes—
62#2738C2214yescomplemented
63#2725C2214yescomplemented
64#2725C2214yescomplemented
65#2721C2214yescomplemented
66#2716C2214yescomplemented
67#2713C2214yescomplemented
68#2713C2214yescomplemented
69#2702C2214yes—
70#2700C2214yes—
71#2700C2214yes—
72#2700C2214yes—
73#2700C2214yes—
74#2695C2214yes—
75#2687C2214yes—
76#2674C2214yes—
77#2674C2214yes—
78#2674C2214yes—
79#2674C2214yes—
80#2667C2214yescomplemented
81#2665C2214yescomplemented
82#2659C2211yescharacteristic
83#2659C2211yescharacteristic
84#2659C2211yescharacteristic
85#2659C2211yescharacteristic
86#2659C2212yes—
87#2647C2212yescomplemented
88#2646C2212yes—
89#2646C2212yes—
90#2646C2212yes—
91#2645C2212yescomplemented
92#2645C2212yescomplemented
93#2642C2212yescomplemented
94#2626C2212yes—
95#2626C2212yes—
96#2626C2212yes—
97#2626C2212yes—
98#2612C2214yescomplemented
99#2612C2214yescomplemented
100#2612C2214yescomplemented
101#2612C2214yescomplemented
102#2611C2214yescomplemented
103#2609C2214yes—
104#2606C2214yescomplemented
105#2606C2214yescomplemented
106#2605C2214yescomplemented
107#2605C2214yescomplemented
108#2604C2214yescomplemented
109#2594C2214yescomplemented
110#2588C2214yescomplemented
111#2577C2214yescomplemented
112#2574C2214yescomplemented
113#2574C2214yescomplemented
114#2573C2214yescomplemented
115#2573C2214yescomplemented
116#2568C2214yescomplemented
117#2561C2214yes—
118#2556C2214yescomplemented
119#2556C2214yescomplemented
120#2553C2214yes—
121#2550C2214yescomplemented
122#2549C2214yescomplemented
123#2549C2214yescomplemented
124#2546C2214yescomplemented
125#2533C2214yescomplemented
126#2533C2214yescomplemented
127#2532C2214yescomplemented
128#2530C2214yescomplemented
129#2528C2214yescomplemented
130#2528C2214yescomplemented
131#2527C2214yescomplemented
132#2527C2214yescomplemented
133#2523C2214yescomplemented
134#2522C2214yescomplemented
135#2522C2214yescomplemented
136#2520C2214yescomplemented
137#2511C2214yescomplemented
138#2505C2214yes—
139#2505C2214yes—
140#2505C2214yes—
141#2503C2212yescomplemented
142#2499C2212yescomplemented
143#2498C2214yes—
144#2496C2212yescomplemented
145#2495C2212yescomplemented
146#2494C2212yescomplemented
147#2494C2212yescomplemented
148#2493C2214yes—
149#2493C2214yes—
150#2493C2214yescomplemented
151#2492C2212yescomplemented
152#2489C2212yescomplemented
153#2488C2214yes—
154#2483C2214yes—
155#2481C2214yes—
156#2480C2214yes—
157#2480C2214yes—
158#2477C2214yes—
159#2475C2214yescomplemented
160#2473C2214yes—
161#2470C2214yes—
162#2469C2214yescomplemented
163#2465C2214yescomplemented
164#2465C2214yescomplemented
165#2451C2214yescomplemented
166#2446C2214yescomplemented
167#2442C2212yescomplemented
168#2440C2214yescomplemented
169#2440C2214yescomplemented
170#2439C2212yescomplemented
171#2434C2214yes—
172#2421C2212yescomplemented
173#2421C2212yescomplemented
174#2413C2214yes—
175#2405C2214yes—
176#2396C2214yescomplemented
177#2396C2214yescomplemented
178#2378C2214yescomplemented
179#2378C2214yescomplemented
180#2373C2214yescomplemented
181#2372C2214yes—
182#2372C2214yes—
183#2372C2214yes—
184#2372C2214yes—
185#2368C2214yes—
186#2362C2214yescomplemented
187#2362C2214yescomplemented
188#2362C2212yescomplemented
189#2360C2214yes—
190#2360C2212yescomplemented
191#2347C2212yescomplemented
192#2344C2212yescomplemented
193#2343C2214yescomplemented
194#2342C2214yes—
195#2342C2214yes—
196#2332C2214yescomplemented
197#2332C2214yescomplemented
198#2330C2212yescomplemented
199#2329C2212yes—
200#2329C2212yes—
201#2329C2212yes—
202#2329C2212yes—
203#2329C2212yes—
204#2329C2212yes—
205#2327C2212yescomplemented
206#2323C2214yescomplemented
207#2323C2214yescomplemented
208#2320C2212yescomplemented
209#2320C2212yescomplemented
210#2315C2212yes—
211#2312C2212yes—
212#2312C2212yes—
213C4×C22⋊Q8C2212yes—
214C4×C22⋊Q8C2212yes—
215C4×C22⋊Q8C2212yes—
216C4×C22⋊Q8C2212yes—
217C2×#391C2211yescharacteristic
218C2×#391C2211yescharacteristic
219C2×#388C2211yescharacteristic
220C2×#388C2211yescharacteristic
221C2×#388C2211yescharacteristic
222C2×#388C2211yescharacteristic
223C2×#386C2211yescharacteristic
224C2×#386C2211yescharacteristic
225#2283C2212yes—
226#2283C2212yes—
227#2280C2212yes—
228C2×#380C2212yes—
229C2×C4×C22⋊C4C2211yescharacteristic
230C2×C4×C22⋊C4C2211yescharacteristic
231C2×C4×C22⋊C4C2211yescharacteristic
232C2×C4×C22⋊C4C2211yescharacteristic
233C2×#376C2211yescharacteristic
234C2×#376C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×D4C2311yescharacteristic
237C24×C4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239#543—216no—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#125C2314yes—
249C2×#124—28no—
250C2×#124C2314yes—
251C2×#124C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2312yes—
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C2×#117C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2314yes—
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
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#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
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#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2314yes—
399#391C2314yes—
400#391C2312yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2314yes—
414#391C2312yes—
415#391C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2312yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2312yes—
433#389C2312yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
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#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#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#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#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#384C2312yes—
559#384C2312yes—
560#383C2314yes—
561#383C2314yes—
562#383C2314yes—
563#383C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2312yes—
567#382C2312yes—
568#382C2314yes—
569#382C2312yes—
570#382C2312yes—
571#382C2312yes—
572#382C2312yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#380C2312yes—
581#380C2312yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2314yes—
587#380C2312yes—
588#380C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2312yes—
593#380C2312yes—
594#380C2314yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2312yes—
599#380C2312yes—
600#380C2312yes—
601#379C2314yes—
602#379C2314yes—
603#379C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2312yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2312yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2312yes—
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2314yes—
639#376C2312yes—
640#376C2312yes—
641#376C2314yes—
642#376C2314yes—
643#376C2314yes—
644#376C2314yes—
645#376C2312yes—
646#376C2312yes—
647C2×#95C2311yescharacteristic
648C2×#95C2311yescharacteristic
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2311yescharacteristic
652C2×#95C2314yes—
653C2×#95C2311yescharacteristic
654C2×#95C2311yescharacteristic
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—42no—
678C23×C4—42no—
679C23×C4—81no—
680C23×C4—81no—
681C23×C4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2414yes—
692C23×C4C2414yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C4⋊Q8—44no—
701C4⋊Q8—82no—
702C4⋊Q8—84no—
703C4⋊Q8—84no—
704#126—48no—
705#126—84no—
706#125—44no—
707#125—82no—
708#125—84no—
709#124—216no—
710#124—216no—
711#123—84no—
712#123—84no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—216no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—44no—
723C22⋊Q8—44no—
724C22⋊Q8—82no—
725C22⋊Q8—82no—
726C4×Q8—44no—
727C4×Q8—44no—
728C4×Q8—82no—
729C4×Q8—82no—
730C4×Q8—84no—
731#117—44no—
732#117—48no—
733#117—82no—
734#117—84no—
735C2×C4⋊C4—44no—
736C2×C4⋊C4—81no—
737C2×C4⋊C4—82no—
738C2×C4⋊C4—81no—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C22⋊C4—24no—
793C2×C22⋊C4—216no—
794C2×C22⋊C4—24no—
795C2×C22⋊C4—24no—
796C2×C22⋊C4—24no—
797C2×C22⋊C4—24no—
798C2×C22⋊C4—42no—
799C2×C22⋊C4—42no—
800C2×C22⋊C4—81no—
801C2×C22⋊C4—81no—
802C2×C22⋊C4#4118yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
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×C42—24no—
836C2×C42—24no—
837C2×C42—24no—
838C2×C42—42no—
839C2×C42—42no—
840C2×C42—81no—
841C2×C42—81no—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2414yes—
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
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—
936C24—22no—
937C24—22no—
938C24—22no—
939C24—22no—
940C24—22no—
941C24—41no—
942C24—41no—
943C24—41no—
944C24—41no—
945C24—41no—
946C24—41no—
947C24—41no—
948C24—41no—
949C24C2×#4114yes—
950C24C2512yes—
951C24C2512yes—
952C24C2511yescharacteristic
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—28no—
956C2×Q8—28no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—44no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—88no—
972C2×D4—28no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—88no—
976C22×C4—22no—
977C22×C4—22no—
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—24no—
990C22×C4—24no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4—42no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—42no—
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—41no—
1020C22×C4—41no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—88no—
1030C22×C4—88no—
1031C22×C4C2×#4114yes—
1032C22×C4C2×#4114yes—
1033C22×C42−1+414yes—
1034C22×C42−1+414yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2514yes—
1048C22×C4C2514yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2511yescharacteristic
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
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—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—24no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
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⋊C4C2×#41116yes—
1144C42—24no—
1145C42—24no—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—24no—
1151C42—24no—
1152C42—28no—
1153C42—42no—
1154C42—42no—
1155C42—42no—
1156C42—42no—
1157C42—42no—
1158C42—42no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—28no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—44no—
1187C23—44no—
1188C23—44no—
1189C23—44no—
1190C23—44no—
1191C23—82no—
1192C23—82no—
1193C23—82no—
1194C23—82no—
1195C23—82no—
1196C23—82no—
1197C23—82no—
1198C23—82no—
1199C23C22×#4114yes—
1200C23C22×#4112yes—
1201C23C2×2−1+412yes—
1202C23C2×2−1+412yes—
1203C23C2611yescharacteristic
1204Q8—84no—
1205Q8—84no—
1206Q8—88no—
1207Q8—84no—
1208Q8—84no—
1209Q8—88no—
1210D4—88no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—44no—
1278C2×C4—44no—
1279C2×C4—44no—
1280C2×C4—44no—
1281C2×C4—48no—
1282C2×C4—48no—
1283C2×C4—44no—
1284C2×C4—44no—
1285C2×C4—44no—
1286C2×C4—44no—
1287C2×C4—44no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—88no—
1291C2×C4—88no—
1292C2×C4—82no—
1293C2×C4—82no—
1294C2×C4—82no—
1295C2×C4—82no—
1296C2×C4C22×#4114yes—
1297C2×C4C22×#4114yes—
1298C2×C4C2×2−1+414yes—
1299C2×C4C2×2−1+414yes—
1300C2×C4#58512yes—
1301C2×C4#58512yes—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—24no—
1309C22—24no—
1310C22—24no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—88no—
1323C22—88no—
1324C22#350914yes—
1325C22C23×#4111yescharacteristic
1326C22C22×2−1+411yescharacteristic
1327C22C22×2−1+411yescharacteristic
1328C22C2×#58511yescharacteristic
1329C22C2×#58511yescharacteristic
1330C22H(7,𝔽2)11yescharacteristic
1331C22H(7,𝔽2)11yescharacteristic
1332C4—24no—
1333C4—24no—
1334C4—22no—
1335C4—22no—
1336C4—24no—
1337C4—24no—
1338C4—44no—
1339C4—44no—
1340C4—41no—
1341C4—41no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4—41no—
1347C4—41no—
1348C4—44no—
1349C4—44no—
1350C4—44no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C2—24no—
1357C2—44no—
1358C2—82no—
1359C2#6278111yescharacteristic
1360C2C2×#350911yescharacteristic
1361C2#6284611yescharacteristic
1362C2#6290311yescharacteristic
1363C2#6290311yescharacteristic
1364C2#6292911yescharacteristic
1365C2#6292911yescharacteristic
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. #50429C2semidirect
2. #50409C2semidirect
3. #49251C2semidirect
4. #49223C2semidirect
5. #44825C2semidirect
6. #44804C2semidirect
7. #44372C2semidirect
8. #43993C2semidirect
9. #39676C2semidirect
10. #39640C2semidirect
11. #37958C2semidirect
12. #37934C2semidirect
16. #36760C2semidirect
17. #36204C2semidirect
18. #36167C2semidirect
19. #35315C2semidirect
20. #35120C2semidirect
21. #35120C2semidirect
22. #35012C2semidirect
23. #35012C2semidirect
24. #35002C2semidirect
25. #34578C2semidirect
26. #34433C2semidirect
40. #2806C22semidirect
41. #2805C22semidirect
42. #2799C22semidirect
43. #2798C22semidirect
44. #2783C22semidirect
45. #2783C22semidirect
48. #2777C22semidirect
49. #2775C22semidirect
50. #2774C22semidirect
51. #2774C22semidirect
52. #2772C22semidirect
53. #2765C22semidirect
54. #2764C22semidirect
55. #2759C22semidirect
56. #2755C22semidirect
57. #2754C22semidirect
59. #2744C22semidirect
62. #2738C22semidirect
63. #2725C22semidirect
64. #2725C22semidirect
65. #2721C22semidirect
66. #2716C22semidirect
67. #2713C22semidirect
68. #2713C22semidirect
80. #2667C22semidirect
81. #2665C22semidirect
87. #2647C22semidirect
91. #2645C22semidirect
92. #2645C22semidirect
93. #2642C22semidirect
98. #2612C22semidirect
99. #2612C22semidirect
100. #2612C22semidirect
101. #2612C22semidirect
102. #2611C22semidirect
104. #2606C22semidirect
105. #2606C22semidirect
106. #2605C22semidirect
107. #2605C22semidirect
108. #2604C22semidirect
109. #2594C22semidirect
110. #2588C22semidirect
111. #2577C22semidirect
112. #2574C22semidirect
113. #2574C22semidirect
114. #2573C22semidirect
115. #2573C22semidirect
116. #2568C22semidirect
118. #2556C22semidirect
119. #2556C22semidirect
121. #2550C22semidirect
122. #2549C22semidirect
123. #2549C22semidirect
124. #2546C22semidirect
125. #2533C22semidirect
126. #2533C22semidirect
127. #2532C22semidirect
128. #2530C22semidirect
129. #2528C22semidirect
130. #2528C22semidirect
131. #2527C22semidirect
132. #2527C22semidirect
133. #2523C22semidirect
134. #2522C22semidirect
135. #2522C22semidirect
136. #2520C22semidirect
137. #2511C22semidirect
141. #2503C22semidirect
142. #2499C22semidirect
144. #2496C22semidirect
145. #2495C22semidirect
146. #2494C22semidirect
147. #2494C22semidirect
150. #2493C22semidirect
151. #2492C22semidirect
152. #2489C22semidirect
159. #2475C22semidirect
162. #2469C22semidirect
163. #2465C22semidirect
164. #2465C22semidirect
165. #2451C22semidirect
166. #2446C22semidirect
167. #2442C22semidirect
168. #2440C22semidirect
169. #2440C22semidirect
170. #2439C22semidirect
172. #2421C22semidirect
173. #2421C22semidirect
176. #2396C22semidirect
177. #2396C22semidirect
178. #2378C22semidirect
179. #2378C22semidirect
180. #2373C22semidirect
186. #2362C22semidirect
187. #2362C22semidirect
188. #2362C22semidirect
190. #2360C22semidirect
191. #2347C22semidirect
192. #2344C22semidirect
193. #2343C22semidirect
196. #2332C22semidirect
197. #2332C22semidirect
198. #2330C22semidirect
205. #2327C22semidirect
206. #2323C22semidirect
207. #2323C22semidirect
208. #2320C22semidirect
209. #2320C22semidirect

Maximal subgroups

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

subgroupindex
#504292
#504092
#492512
#492232
#448252
#448042
#443722
#439932
#396762
#396402
#379582
#379342
#379322
#378812
#369662
#367602
#362042
#361672
#353152
#351202
#350122
#350022
#345782
#344332
C2×#23722