Finite Group Databasebeta

← #7681877

Subgroups — #7681877

Order 512.

4877 conjugacy classes of subgroups.

The subgroup lattice has 1351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59571C214yesmaximal, complemented
2#59529C214yesmaximal, complemented
3#59473C214yesmaximal, complemented
4#59373C214yesmaximal, complemented
5#43820C214yesmaximal, complemented
6#43781C214yesmaximal, complemented
7#43369C214yesmaximal, complemented
8#43366C214yesmaximal, complemented
9#39750C211yesmaximal, characteristic, complemented
10#39611C211yesmaximal, characteristic, complemented
11#38930C212yesmaximal, complemented
12#38926C212yesmaximal, complemented
13#38926C212yesmaximal, complemented
14#37962C212yesmaximal, complemented
15#37764C212yesmaximal, complemented
16#36492C212yesmaximal, complemented
17#36196C211yesmaximal, characteristic, complemented
18#36149C211yesmaximal, characteristic, complemented
19#35553C212yesmaximal, complemented
20#35552C212yesmaximal, complemented
21#35337C211yesmaximal, characteristic, complemented
22#35304C212yesmaximal, complemented
23#34917C212yesmaximal, complemented
24#34333C212yesmaximal, complemented
25#34222C212yesmaximal, complemented
26#34123C211yesmaximal, characteristic, complemented
27C4×#540C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#540C2211yescharacteristic
30C2×#532C2212yes—
31C2×C4×#41C2211yescharacteristic
32#2862C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2851C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2799C2214yes—
40#2765C2214yes—
41#2765C2214yes—
42#2762C2214yes—
43#2759C2214yes—
44#2755C2214yes—
45#2750C2214yes—
46#2750C2214yes—
47#2745C2214yes—
48#2744C2214yes—
49#2744C2214yes—
50#2743C2214yes—
51#2743C2214yes—
52#2740C2214yes—
53#2738C2214yes—
54#2738C2214yes—
55#2732C2214yes—
56#2717C2214yes—
57#2708C2214yes—
58#2695C2214yes—
59#2695C2214yes—
60#2686C2214yes—
61#2683C2214yes—
62#2671C2214yes—
63#2660C2212yes—
64#2660C2212yes—
65#2647C2211yescharacteristic
66#2647C2211yescharacteristic
67#2647C2212yes—
68#2647C2212yes—
69#2628C2212yes—
70#2612C2214yes—
71#2612C2214yes—
72#2606C2214yes—
73#2605C2214yes—
74#2604C2214yes—
75#2589C2214yes—
76#2589C2214yes—
77#2588C2214yes—
78#2588C2214yes—
79#2588C2214yes—
80#2578C2214yes—
81#2577C2214yes—
82#2577C2214yes—
83#2576C2214yes—
84#2576C2214yes—
85#2575C2214yes—
86#2573C2214yes—
87#2571C2212yes—
88#2570C2212yes—
89#2570C2212yes—
90#2569C2214yes—
91#2566C2212yes—
92#2566C2212yes—
93#2563C2212yes—
94#2562C2212yes—
95#2562C2212yes—
96#2560C2214yes—
97#2560C2214yes—
98#2559C2214yes—
99#2549C2214yes—
100#2542C2212yes—
101#2537C2212yes—
102#2536C2214yes—
103#2535C2212yes—
104#2535C2212yes—
105#2533C2214yes—
106#2530C2214yes—
107#2528C2214yes—
108#2526C2214yes—
109#2520C2214yes—
110#2518C2214yes—
111#2517C2214yes—
112#2515C2214yes—
113#2503C2214yes—
114#2497C2212yes—
115#2497C2212yes—
116#2496C2212yes—
117#2496C2212yes—
118#2494C2212yes—
119#2494C2212yes—
120#2493C2214yes—
121#2493C2214yes—
122#2493C2214yes—
123#2488C2214yes—
124#2477C2214yes—
125#2477C2214yes—
126#2477C2214yes—
127#2471C2214yes—
128#2468C2214yes—
129#2468C2214yes—
130#2467C2214yes—
131#2466C2214yes—
132#2466C2214yes—
133#2465C2214yes—
134#2463C2214yes—
135#2463C2214yes—
136#2457C2214yes—
137#2450C2214yes—
138#2449C2214yes—
139#2449C2214yes—
140#2447C2214yes—
141#2444C2214yes—
142#2443C2214yes—
143#2438C2214yes—
144#2438C2214yes—
145#2430C2214yes—
146#2427C2214yes—
147#2422C2212yes—
148#2422C2212yes—
149#2421C2214yes—
150#2421C2214yes—
151#2420C2212yes—
152#2420C2212yes—
153#2420C2212yes—
154#2420C2212yes—
155#2419C2214yes—
156#2419C2214yes—
157#2419C2214yes—
158#2417C2214yes—
159#2407C2214yes—
160#2407C2214yes—
161#2406C2214yes—
162#2401C2214yes—
163#2392C2214yes—
164#2373C2214yes—
165#2372C2214yes—
166#2372C2214yes—
167#2370C2212yes—
168#2370C2212yes—
169#2368C2214yes—
170#2368C2214yes—
171#2365C2212yes—
172#2364C2214yes—
173#2364C2214yes—
174#2361C2214yes—
175#2360C2214yes—
176#2356C2212yes—
177#2355C2212yes—
178#2353C2214yes—
179#2353C2214yes—
180#2353C2212yes—
181#2353C2212yes—
182#2352C2214yes—
183#2349C2212yes—
184#2349C2212yes—
185#2349C2212yes—
186D4×C4⋊C4C2212yes—
187#2346C2212yes—
188#2345C2214yes—
189#2343C2212yes—
190#2343C2212yes—
191#2339C2214yes—
192#2339C2212yes—
193#2339C2214yes—
194#2339C2214yes—
195#2335C2214yes—
196#2333C2214yes—
197#2331C2212yes—
198#2331C2212yes—
199#2331C2212yes—
200#2330C2212yes—
201#2330C2211yescharacteristic
202#2329C2214yes—
203#2329C2214yes—
204#2328C2211yescharacteristic
205#2328C2212yes—
206#2324C2212yes—
207#2319C2212yes—
208#2319C2212yes—
209#2319C2212yes—
210#2314C2211yescharacteristic
211#2314C2211yescharacteristic
212#2314C2211yescharacteristic
213C4×#127C2211yescharacteristic
214C4×#125C2212yes—
215C4×#125C2211yescharacteristic
216C4×C22⋊Q8C2214yes—
217C4×#123C2214yes—
218C4×#123C2214yes—
219C4×#121C2212yes—
220C4×#121C2212yes—
221C4×#121C2212yes—
222C4×#121C2214yes—
223C4×#121C2212yes—
224C4×#121C2212yes—
225#2295C2211yescharacteristic
226#2295C2211yescharacteristic
227#2290C2212yes—
228#2290C2212yes—
229#2290C2214yes—
230C2×#387C2214yes—
231#2285C2212yes—
232#2283C2211yescharacteristic
233#2283C2212yes—
234#2283C2212yes—
235#2283C2212yes—
236#2275C2212yes—
237#2275C2212yes—
238C42×D4C2212yes—
239C42×D4C2211yescharacteristic
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×#376C2212yes—
243C22×#41C2311yescharacteristic
244C22×#41C2314yes—
245#554—216no—
246#540—28no—
247#532—216no—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×#127C2311yescharacteristic
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2312yes—
254C2×#125C2311yescharacteristic
255C2×#125C2312yes—
256C2×#124C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×#121C2312yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C4×#41—28no—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2311yescharacteristic
277C2×C4×D4C2312yes—
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2312yes—
300C2×#117C2311yescharacteristic
301C2×#117C2314yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2314yes—
304C22×C42C2311yescharacteristic
305C22×C42C2312yes—
306C22×C42C2312yes—
307C22×C42C2312yes—
308C22×C42C2314yes—
309#401C2314yes—
310#401C2314yes—
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#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#392C2314yes—
380#392C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2312yes—
394#391C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2312yes—
398#390C2314yes—
399#390C2312yes—
400#390C2312yes—
401#390C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2314yes—
408#389C2314yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2312yes—
418#389C2314yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2312yes—
426#388C2312yes—
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#388C2312yes—
447#388C2312yes—
448#388C2312yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2312yes—
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#387C2312yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2312yes—
492#387C2312yes—
493#387C2312yes—
494#387C2312yes—
495#387C2312yes—
496#387C2312yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#386C2312yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2312yes—
516#386C2312yes—
517#386C2312yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2312yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2312yes—
542#385C2312yes—
543#385C2312yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#384C2311yescharacteristic
548#384C2311yescharacteristic
549#384C2312yes—
550#384C2311yescharacteristic
551#384C2312yes—
552#384C2312yes—
553#383C2314yes—
554#383C2311yescharacteristic
555#383C2312yes—
556#383C2314yes—
557#383C2311yescharacteristic
558#383C2312yes—
559#382C2311yescharacteristic
560#382C2312yes—
561#382C2314yes—
562#382C2312yes—
563#382C2311yescharacteristic
564#382C2311yescharacteristic
565#382C2312yes—
566#382C2312yes—
567#382C2314yes—
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#381C2312yes—
581#381C2312yes—
582#381C2314yes—
583#381C2311yescharacteristic
584#381C2311yescharacteristic
585#381C2314yes—
586#380C2312yes—
587#380C2312yes—
588#380C2312yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2314yes—
604#380C2312yes—
605#380C2312yes—
606#380C2312yes—
607#380C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2311yescharacteristic
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2311yescharacteristic
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2314yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2312yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2312yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657#376C2312yes—
658#376C2311yescharacteristic
659#376C2311yescharacteristic
660#376C2312yes—
661#376C2312yes—
662#376C2312yes—
663#376C2312yes—
664#376C2314yes—
665#376C2312yes—
666#376C2312yes—
667#376C2314yes—
668C2×#95C2312yes—
669C2×#95C2314yes—
670C2×#95C2314yes—
671C2×#95C2312yes—
672C2×#95C2314yes—
673C2×#95C2312yes—
674C2×#95C2312yes—
675C2×#95C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C2×#41—24no—
679C2×#41—216no—
680C2×#41—44no—
681C2×#41—48no—
682C2×#41—84no—
683C22×Q8C2414yes—
684C22×Q8C2414yes—
685C22×Q8C2411yescharacteristic
686C22×D4C2411yescharacteristic
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2412yes—
690C22×D4C2412yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C23×C4C2411yescharacteristic
694C23×C4C2412yes—
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2412yes—
708C23×C4C2414yes—
709C23×C4C2412yes—
710C4⋊Q8—28no—
711C4⋊Q8—28no—
712#127#4118yescomplemented
713#126—48no—
714#126—84no—
715#125—24no—
716#125—28no—
717#125—28no—
718#124—216no—
719#123—216no—
720#123—48no—
721#123—84no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—84no—
726C22⋊Q8—84no—
727C22⋊Q8—84no—
728C22⋊Q8—84no—
729#121—28no—
730#121—28no—
731#121—216no—
732#121—216no—
733#121—28no—
734#121—48no—
735C4×Q8—24no—
736C4×Q8—84no—
737C4×Q8#4118yescomplemented
738C4×D4—28no—
739C4×D4—28no—
740C4×D4—216no—
741C4×D4—28no—
742C4×D4—28no—
743C4×D4—24no—
744C4×D4—24no—
745C4×D4—28no—
746C4×D4—28no—
747C4×D4—28no—
748C4×D4—28no—
749C4×D4—28no—
750C4×D4—48no—
751C4×D4—48no—
752C4×D4—44no—
753C4×D4—44no—
754C4×D4—84no—
755C4×D4—84no—
756C4×D4—84no—
757C4×D4—84no—
758#117—28no—
759#117—24no—
760#117—24no—
761#117—24no—
762#117—84no—
763C2×C4⋊C4—216no—
764C2×C4⋊C4—84no—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C42—24no—
851C2×C42—28no—
852C2×C42—28no—
853C2×C42—28no—
854C2×C42—84no—
855C2×C42C2412yes—
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2412yes—
865C2×C42C2411yescharacteristic
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2411yescharacteristic
882C2×C42C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
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#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2411yescharacteristic
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2411yescharacteristic
929#95C2411yescharacteristic
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958C24C2511yescharacteristic
959C24C2514yes—
960C24C2512yes—
961#41—416no—
962#41—832no—
963C2×Q8—28no—
964C2×Q8—28no—
965C2×Q8—42no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8C2×#4114yes—
971C2×D4—24no—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—24no—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—22no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4C2×#4118yes—
990C2×D4C2×#41116yes—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—28no—
995C22×C4—28no—
996C22×C4—28no—
997C22×C4—24no—
998C22×C4—22no—
999C22×C4—24no—
1000C22×C4—22no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—22no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—22no—
1007C22×C4—24no—
1008C22×C4—22no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—28no—
1013C22×C4—24no—
1014C22×C4—28no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—44no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—22no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—28no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4C2×#4118yes—
1110C4⋊C4C2×#4114yes—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—28no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—24no—
1129C22⋊C4—28no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
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—42no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C42—22no—
1150C42—24no—
1151C42—22no—
1152C42—24no—
1153C42—24no—
1154C42—22no—
1155C42—24no—
1156C42—24no—
1157C42—22no—
1158C42—24no—
1159C42—24no—
1160C42—24no—
1161C42—22no—
1162C42—42no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—42no—
1168C42—44no—
1169C42—42no—
1170C42—44no—
1171C42—42no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42C2×#4114yes—
1176C42C2×#4114yes—
1177C42C2×#4118yes—
1178C422−1+414yes—
1179C23—24no—
1180C23—22no—
1181C23—22no—
1182C23—24no—
1183C23—22no—
1184C23—24no—
1185C23—22no—
1186C23—24no—
1187C23—22no—
1188C23—24no—
1189C23—24no—
1190C23—22no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—22no—
1195C23—22no—
1196C23C22×#4118yes—
1197C23#58514yes—
1198C23C2611yescharacteristic
1199Q8—44no—
1200Q8—88no—
1201Q8—88no—
1202D4—28no—
1203D4—216no—
1204D4—416no—
1205D4—48no—
1206D4—416no—
1207D4—416no—
1208D4—88no—
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—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—21no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—48no—
1269C2×C4—48no—
1270C2×C4—48no—
1271C2×C4—44no—
1272C2×C4—48no—
1273C2×C4—44no—
1274C2×C4—84no—
1275C2×C4—88no—
1276C2×C4—82no—
1277C2×C4—88no—
1278C2×C4—84no—
1279C2×C4—88no—
1280C2×C4—84no—
1281C2×C4—88no—
1282C2×C4—88no—
1283C2×C4—88no—
1284C2×C4—88no—
1285C2×C4C22×#4114yes—
1286C2×C4C22×#4112yes—
1287C2×C4C22×#4114yes—
1288C2×C4C22×#4114yes—
1289C2×C4C22×#4112yes—
1290C2×C4C22×#4112yes—
1291C2×C4C22×#4112yes—
1292C2×C4C2×2−1+414yes—
1293C2×C4C2×2−1+412yes—
1294C22—24no—
1295C22—28no—
1296C22—28no—
1297C22—24no—
1298C22—24no—
1299C22—28no—
1300C22—42no—
1301C22—44no—
1302C22—44no—
1303C22—42no—
1304C22—44no—
1305C22—42no—
1306C22—44no—
1307C22—42no—
1308C22—42no—
1309C22—41no—
1310C22—41no—
1311C22—42no—
1312C22—41no—
1313C22C23×#4111yescharacteristic
1314C22C23×#4111yescharacteristic
1315C22C22×2−1+411yescharacteristic
1316C22C2×#58512yes—
1317C22H(7,𝔽2)12yes—
1318C4—24no—
1319C4—24no—
1320C4—22no—
1321C4—22no—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—44no—
1328C4—44no—
1329C4—44no—
1330C4—41no—
1331C4—44no—
1332C4—41no—
1333C4—44no—
1334C4—44no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—41no—
1341C4#348214yes—
1342C2—44no—
1343C2—48no—
1344C2—81no—
1345C2C2×#348211yescharacteristic
1346C2#6281411yescharacteristic
1347C2#6285811yescharacteristic
1348C2#6295812yes—
1349C2#6299012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59571C2semidirect
2. #59529C2semidirect
3. #59473C2semidirect
4. #59373C2semidirect
5. #43820C2semidirect
6. #43781C2semidirect
7. #43369C2semidirect
8. #43366C2semidirect
9. #39750C2semidirect
10. #39611C2semidirect
11. #38930C2semidirect
12. #38926C2semidirect
13. #38926C2semidirect
14. #37962C2semidirect
15. #37764C2semidirect
16. #36492C2semidirect
17. #36196C2semidirect
18. #36149C2semidirect
19. #35553C2semidirect
20. #35552C2semidirect
21. #35337C2semidirect
22. #35304C2semidirect
23. #34917C2semidirect
24. #34333C2semidirect
25. #34222C2semidirect
26. #34123C2semidirect
27. C4×#540C2semidirect
712. #127#41semidirect
737. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#595712
#595292
#594732
#593732
#438202
#437812
#433692
#433662
#397502
#396112
#389302
#389262
#379622
#377642
#364922
#361962
#361492
#355532
#355522
#353372
#353042
#349172
#343332
#342222
#341232
C4×#5402