Finite Group Databasebeta

← #8157342

Subgroups — #8157342

Order 512.

4010 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59254C212yesmaximal, complemented
2#59240C212yesmaximal, complemented
3#58034C214yesmaximal, complemented
4#57691C214yesmaximal, complemented
5#56826C214yesmaximal, complemented
6#54312C214yesmaximal, complemented
7#53131C212yesmaximal, complemented
8#52961C212yesmaximal, complemented
9#52349C214yesmaximal, complemented
10#45280C212yesmaximal, complemented
11#44904C212yesmaximal, complemented
12#42932C212yesmaximal, complemented
13#42623C212yesmaximal, complemented
14#42597C212yesmaximal, complemented
15#42461C212yesmaximal, complemented
16#40757C214yesmaximal, complemented
17#39797C212yesmaximal
18#39751C211yesmaximal, characteristic, complemented
19#39639C212yesmaximal, complemented
20#39631C211yesmaximal, characteristic
21#38100C212yesmaximal, complemented
22#37882C212yesmaximal, complemented
23#37466C212yesmaximal, complemented
24#36763C212yesmaximal
25#36586C211yesmaximal, characteristic
26#36564C211yesmaximal, characteristic, complemented
27#35104C211yesmaximal, characteristic, complemented
28C2×#2507C211yesmaximal, characteristic, complemented
29#34584C211yesmaximal, characteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2212yes—
33#2851C2212yes—
34#2850C2212yes—
35#2843C2214yes—
36#2839C2214yes—
37#2839C2214yes—
38#2839C2214yes—
39#2836C2214yes—
40#2836C2214yes—
41#2836C2214yes—
42#2834C2214yes—
43#2833C2214yes—
44#2833C2214yes—
45#2831C2214yes—
46#2822C2214yes—
47#2809C2214yes—
48#2809C2214yes—
49#2807C2214yes—
50#2805C2212yes—
51#2805C2212yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2799C2214yes—
56#2794C2214yes—
57#2794C2214yes—
58#2791C2214yes—
59#2791C2214yes—
60#2790C2214yes—
61#2790C2214yes—
62#2789C2214yes—
63#2788C2214yes—
64#2788C2214yes—
65#2783C2214yes—
66#2777C2214yes—
67#2772C2214yes—
68#2767C2214yes—
69#2767C2214yes—
70#2766C2214yes—
71#2766C2214yes—
72#2764C2214yes—
73#2762C2214yes—
74#2762C2214yes—
75#2758C2214yes—
76#2755C2214yes—
77#2755C2214yes—
78#2754C2214yes—
79#2751C2214yes—
80#2739C2214yes—
81#2738C2214yes—
82#2732C2212yes—
83#2726C2212yes—
84#2726C2214yes—
85#2725C2214yes—
86#2722C2214yes—
87#2721C2214yes—
88#2721C2214yes—
89#2721C2214yes—
90#2720C2214yes—
91#2719C2214yes—
92#2716C2214yes—
93#2715C2214yes—
94#2715C2214yes—
95#2704C2214yes—
96#2698C2214yes—
97#2666C2214yes—
98#2666C2214yes—
99#2659C2212yes—
100#2655C2212yes—
101#2655C2214yes—
102#2655C2214yes—
103#2655C2214yes—
104#2654C2212yes—
105#2651C2212yes—
106#2650C2212yes—
107#2647C2212yes—
108#2647C2212yes—
109#2646C2211yescharacteristic
110#2646C2212yes—
111#2643C2212yes—
112#2639C2211yescharacteristic
113#2637C2214yes—
114#2634C2214yes—
115#2629C2212yes—
116#2629C2212yes—
117#2627C2211yescharacteristic
118#2627C2212yes—
119#2627C2212yes—
120#2625C2214yes—
121#2623C2212yes—
122#2618C2211yescharacteristic
123#2611C2214yes—
124#2606C2214yes—
125#2605C2214yes—
126#2604C2214yes—
127#2601C2214yes—
128#2596C2214yes—
129#2588C2214yes—
130#2586C2214yes—
131#2584C2212yes—
132#2582C2214yes—
133#2579C2214yes—
134#2571C2212yes—
135#2571C2211yescharacteristic
136#2570C2212yes—
137#2570C2212yes—
138#2570C2212yes—
139#2570C2212yes—
140#2567C2211yescharacteristic
141#2552C2214yes—
142#2552C2212yes—
143#2551C2211yescharacteristic
144#2550C2212yes—
145#2550C2212yes—
146#2550C2212yes—
147#2549C2214yes—
148#2547C2211yescharacteristic
149#2533C2214yes—
150#2528C2214yes—
151#2524C2214yes—
152#2514C2212yes—
153#2511C2214yes—
154#2510C2214yes—
155#2509C2212yes—
156#2509C2212yes—
157#2508C2212yes—
158#2508C2212yes—
159#2507C2212yes—
160#2507C2214yes—
161#2507C2214yes—
162#2507C2212yes—
163#2507C2212yes—
164#2507C2212yes—
165#2507C2212yes—
166#2507C2212yes—
167#2507C2212yes—
168#2506C2212yes—
169#2506C2212yes—
170#2506C2212yes—
171#2506C2212yes—
172#2505C2214yes—
173#2502C2214yes—
174#2497C2212yes—
175#2496C2212yes—
176#2496C2212yes—
177#2496C2212yes—
178#2495C2212yes—
179#2494C2212yes—
180#2494C2212yes—
181#2494C2212yes—
182#2493C2214yes—
183#2493C2214yes—
184#2488C2214yes—
185#2487C2212yes—
186#2487C2212yes—
187#2487C2212yes—
188#2481C2214yes—
189#2481C2214yes—
190#2481C2214yes—
191#2478C2214yes—
192#2475C2214yes—
193#2473C2214yes—
194#2473C2214yes—
195#2473C2214yes—
196#2469C2214yes—
197#2462C2214yes—
198#2453C2214yes—
199#2451C2212yes—
200#2450C2214yes—
201#2449C2214yes—
202#2448C2212yes—
203#2446C2214yes—
204#2442C2214yes—
205#2442C2212yes—
206#2442C2212yes—
207#2442C2212yes—
208#2440C2212yes—
209#2440C2212yes—
210#2439C2212yes—
211#2439C2212yes—
212#2419C2214yes—
213#2402C2212yes—
214#2401C2212yes—
215#2396C2212yes—
216#2395C2212yes—
217C2×#398C2212yes—
218C2×#398C2212yes—
219#2370C2212yes—
220#2369C2212yes—
221#2369C2211yescharacteristic
222#2365C2212yes—
223#2365C2211yescharacteristic
224#2360C2214yes—
225#2354C2211yescharacteristic
226#2352C2214yes—
227#2352C2212yes—
228Q8×C4⋊C4C2211yescharacteristic
229D4×C4⋊C4C2212yes—
230#2347C2212yes—
231#2347C2212yes—
232#2345C2212yes—
233#2345C2212yes—
234#2344C2212yes—
235#2331C2212yes—
236#2330C2212yes—
237#2329C2212yes—
238#2329C2212yes—
239#2329C2212yes—
240#2325C2212yes—
241#2317C2212yes—
242#2314C2212yes—
243C4×C22⋊Q8C2211yescharacteristic
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×#123C2212yes—
247C4×#121C2211yescharacteristic
248C2×#389C2211yescharacteristic
249C2×#389C2211yescharacteristic
250C2×#389C2212yes—
251C2×#389C2211yescharacteristic
252C2×#389C2211yescharacteristic
253#2290C2212yes—
254C2×#387C2212yes—
255C2×#384C2211yescharacteristic
256#2283C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#124C2312yes—
273C2×#123C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2311yescharacteristic
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2311yescharacteristic
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2314yes—
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2312yes—
307#401C2314yes—
308#401C2314yes—
309#401C2314yes—
310#401C2312yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#400C2314yes—
344#400C2312yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#399C2312yes—
353#399C2312yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2312yes—
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2314yes—
417#397C2312yes—
418#397C2312yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#396C2312yes—
428#396C2312yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2312yes—
438#394C2312yes—
439#394C2312yes—
440#393C2314yes—
441#393C2314yes—
442#393C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2311yescharacteristic
459#391C2314yes—
460#390C2312yes—
461#390C2311yescharacteristic
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2311yescharacteristic
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2312yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2312yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2312yes—
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#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#386C2312yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2312yes—
600#386C2312yes—
601#386C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2312yes—
615#385C2314yes—
616#385C2312yes—
617#385C2312yes—
618#385C2312yes—
619#385C2314yes—
620#384C2312yes—
621#384C2312yes—
622#384C2311yescharacteristic
623#384C2311yescharacteristic
624#384C2312yes—
625#384C2312yes—
626#384C2314yes—
627#384C2314yes—
628#384C2312yes—
629#384C2314yes—
630#383C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#382C2314yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#382C2314yes—
643#382C2314yes—
644#381C2314yes—
645#381C2312yes—
646#381C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650#380C2312yes—
651#380C2311yescharacteristic
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2314yes—
663#380C2311yescharacteristic
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703#376C2312yes—
704#376C2314yes—
705C2×#95C2312yes—
706C2×#95C2311yescharacteristic
707C2×#95C2311yescharacteristic
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C22×Q8C2411yescharacteristic
713C22×Q8C2412yes—
714C22×Q8C2414yes—
715C22×Q8C2412yes—
716C22×D4C2412yes—
717C22×D4C2411yescharacteristic
718C23×C4C2411yescharacteristic
719C23×C4C2412yes—
720C23×C4C2412yes—
721C23×C4C2411yescharacteristic
722C23×C4C2412yes—
723C23×C4C2411yescharacteristic
724C23×C4C2412yes—
725C23×C4C2411yescharacteristic
726C23×C4C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2414yes—
730C23×C4C2411yescharacteristic
731C4⋊Q8—28no—
732C4⋊Q8—42no—
733C4⋊Q8—42no—
734C4⋊Q8—82no—
735#126—84no—
736#126—84no—
737#126—84no—
738#125—44no—
739#125—44no—
740#125—84no—
741#125—84no—
742#125—84no—
743#125—84no—
744#124—82no—
745#123—44no—
746C22⋊Q8—24no—
747C22⋊Q8—28no—
748C22⋊Q8—44no—
749C22⋊Q8—48no—
750C22⋊Q8—84no—
751#121—24no—
752C4×Q8—42no—
753C4×Q8—82no—
754C4×Q8—82no—
755C4×Q8—84no—
756C4×D4—28no—
757C4×D4—42no—
758C4×D4—48no—
759#117—28no—
760#117—44no—
761#117—84no—
762C2×C4⋊C4—24no—
763C2×C4⋊C4—24no—
764C2×C4⋊C4—24no—
765C2×C4⋊C4—24no—
766C2×C4⋊C4—42no—
767C2×C4⋊C4—44no—
768C2×C4⋊C4—44no—
769C2×C4⋊C4—42no—
770C2×C4⋊C4—82no—
771C2×C4⋊C4—82no—
772C2×C4⋊C4—82no—
773C2×C4⋊C4—82no—
774C2×C4⋊C4—82no—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C42—24no—
880C2×C42—42no—
881C2×C42—42no—
882C2×C42—82no—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2411yescharacteristic
887C2×C42C2412yes—
888C2×C42C2411yescharacteristic
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
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#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989C24C2512yes—
990C24C2511yescharacteristic
991C2×Q8—22no—
992C2×Q8—24no—
993C2×Q8—28no—
994C2×Q8—41no—
995C2×Q8—41no—
996C2×Q8—42no—
997C2×Q8—44no—
998C2×Q8—44no—
999C2×Q8—42no—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—42no—
1003C2×D4—24no—
1004C2×D4—24no—
1005C2×D4—24no—
1006C2×D4—22no—
1007C2×D4—41no—
1008C2×D4—41no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—24no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—22no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—42no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—41no—
1039C22×C4—41no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—41no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C42−1+414yes—
1047C22×C42−1+414yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
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⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—41no—
1116C4⋊C4—44no—
1117C4⋊C4—41no—
1118C4⋊C4—42no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—41no—
1154C4⋊C42−1+414yes—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—24no—
1160C22⋊C4—28no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—42no—
1166C22⋊C4—44no—
1167C22⋊C4—42no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C42—24no—
1180C42—24no—
1181C42—28no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—22no—
1186C42—22no—
1187C42—24no—
1188C42—41no—
1189C42—41no—
1190C42—42no—
1191C42—42no—
1192C42—42no—
1193C42—42no—
1194C42—42no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—44no—
1201C42—44no—
1202C42—44no—
1203C23—21no—
1204C23—21no—
1205C23—21no—
1206C23—21no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23C2×2−1+412yes—
1215C23C2×2−1+412yes—
1216C23#58512yes—
1217C23C2611yescharacteristic
1218Q8—44no—
1219Q8—84no—
1220Q8—88no—
1221Q8—162no—
1222D4—48no—
1223D4—82no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—28no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
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—22no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—24no—
1299C2×C4—44no—
1300C2×C4—48no—
1301C2×C4—44no—
1302C2×C4—44no—
1303C2×C4—44no—
1304C2×C4—48no—
1305C2×C4—82no—
1306C2×C4—84no—
1307C2×C4—84no—
1308C2×C4—82no—
1309C2×C4—84no—
1310C2×C4—88no—
1311C2×C4C2×2−1+412yes—
1312C2×C4C2×2−1+414yes—
1313C2×C4C2×2−1+412yes—
1314C2×C4C2×2−1+412yes—
1315C2×C4C2×2−1+412yes—
1316C2×C4C2×2−1+412yes—
1317C2×C4#58512yes—
1318C22—22no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—42no—
1329C22—42no—
1330C22—42no—
1331C22#355514yes—
1332C22C22×2−1+411yescharacteristic
1333C22C22×2−1+411yescharacteristic
1334C22C22×2−1+411yescharacteristic
1335C22C2×#58511yescharacteristic
1336C22C2×#58511yescharacteristic
1337C22H(7,𝔽2)11yescharacteristic
1338C22H(7,𝔽2)11yescharacteristic
1339C4—22no—
1340C4—22no—
1341C4—22no—
1342C4—24no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—42no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—42no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4—42no—
1356C4—41no—
1357C4—44no—
1358C4—44no—
1359C4—41no—
1360C4—44no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4#356314yes—
1366C2—24no—
1367C2—82no—
1368C2C2×#356311yescharacteristic
1369C2C2×#355511yescharacteristic
1370C2#6288111yescharacteristic
1371C2#6290211yescharacteristic
1372C2#6293511yescharacteristic
1373C2#6294311yescharacteristic
1374C2#6294811yescharacteristic
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. #59254C2semidirect
2. #59240C2semidirect
3. #58034C2semidirect
4. #57691C2semidirect
5. #56826C2semidirect
6. #54312C2semidirect
7. #53131C2semidirect
8. #52961C2semidirect
9. #52349C2semidirect
10. #45280C2semidirect
11. #44904C2semidirect
12. #42932C2semidirect
13. #42623C2semidirect
14. #42597C2semidirect
15. #42461C2semidirect
16. #40757C2semidirect
18. #39751C2semidirect
19. #39639C2semidirect
21. #38100C2semidirect
22. #37882C2semidirect
23. #37466C2semidirect
26. #36564C2semidirect
27. #35104C2semidirect
28. C2×#2507C2semidirect

Maximal subgroups

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

subgroupindex
#592542
#592402
#580342
#576912
#568262
#543122
#531312
#529612
#523492
#452802
#449042
#429322
#426232
#425972
#424612
#407572
#397972
#397512
#396392
#396312
#381002
#378822
#374662
#367632
#365862
#365642
#351042
C2×#25072
#345842