Finite Group Databasebeta

← #7895510

Subgroups — #7895510

Order 512.

4427 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59962C212yesmaximal, complemented
2#59823C211yesmaximal, characteristic, complemented
3#52274C211yesmaximal, characteristic, complemented
4#51172C214yesmaximal, complemented
5#49486C214yesmaximal, complemented
6#48381C214yesmaximal, complemented
7#46872C214yesmaximal, complemented
8#46098C212yesmaximal, complemented
9#45357C212yesmaximal, complemented
10#45202C212yesmaximal, complemented
11#45007C212yesmaximal, complemented
12#43271C214yesmaximal, complemented
13#42852C214yesmaximal, complemented
14#42687C212yesmaximal, complemented
15#42626C212yesmaximal, complemented
16#39756C211yesmaximal, characteristic, complemented
17#39637C211yesmaximal, characteristic, complemented
18#39217C212yesmaximal, complemented
19#38821C212yesmaximal, complemented
20#38484C212yesmaximal, complemented
21#38238C212yesmaximal, complemented
22#38226C212yesmaximal, complemented
23#37220C212yesmaximal, complemented
24#36416C211yesmaximal, characteristic, complemented
25#35865C212yesmaximal
26#35612C212yesmaximal, complemented
27#35197C211yesmaximal, characteristic
28#34489C212yesmaximal, complemented
29#34334C211yesmaximal, characteristic, complemented
30C2×#554C2212yes—
31C2×D4×Q8C2211yescharacteristic
32#2860C2212yes—
33#2859C2211yescharacteristic
34#2854C2212yes—
35#2851C2212yes—
36#2850C2212yes—
37#2831C2214yes—
38#2831C2214yes—
39#2809C2211yescharacteristic
40#2809C2212yes—
41#2808C2212yes—
42#2808C2212yes—
43#2808C2214yes—
44#2806C2211yescharacteristic
45#2806C2212yes—
46#2805C2211yescharacteristic
47#2805C2212yes—
48#2802C2212yes—
49#2802C2214yes—
50#2800C2214yes—
51#2799C2212yes—
52#2798C2214yes—
53#2791C2212yes—
54#2791C2214yes—
55#2786C2214yes—
56#2781C2214yes—
57#2781C2214yes—
58#2779C2214yes—
59#2779C2214yes—
60#2774C2214yes—
61#2774C2212yes—
62#2755C2214yes—
63#2755C2212yes—
64#2754C2214yes—
65#2747C2214yes—
66#2744C2214yes—
67#2743C2214yes—
68#2743C2214yes—
69#2739C2214yes—
70#2732C2212yes—
71#2732C2214yes—
72#2732C2214yes—
73#2732C2212yes—
74#2727C2212yes—
75#2727C2212yes—
76#2726C2212yes—
77#2726C2211yescharacteristic
78#2725C2214yes—
79#2725C2214yes—
80#2722C2214yes—
81#2713C2212yes—
82#2707C2214yes—
83#2704C2214yes—
84#2700C2214yes—
85#2695C2214yes—
86#2694C2214yes—
87#2692C2214yes—
88#2692C2214yes—
89#2690C2214yes—
90#2689C2214yes—
91#2689C2214yes—
92#2687C2214yes—
93#2664C2214yes—
94#2654C2214yes—
95#2650C2214yes—
96#2650C2214yes—
97#2648C2214yes—
98#2648C2214yes—
99#2647C2212yes—
100#2644C2212yes—
101#2641C2212yes—
102#2625C2214yes—
103#2609C2214yes—
104#2608C2214yes—
105#2601C2214yes—
106#2589C2214yes—
107#2588C2214yes—
108#2587C2214yes—
109#2587C2214yes—
110#2585C2214yes—
111#2584C2212yes—
112#2580C2212yes—
113#2580C2212yes—
114#2571C2211yescharacteristic
115#2571C2211yescharacteristic
116#2569C2214yes—
117#2566C2212yes—
118#2562C2214yes—
119#2560C2214yes—
120#2559C2214yes—
121#2556C2214yes—
122#2554C2214yes—
123#2553C2214yes—
124#2553C2214yes—
125#2552C2212yes—
126#2552C2211yescharacteristic
127#2550C2212yes—
128#2550C2212yes—
129#2548C2211yescharacteristic
130#2542C2212yes—
131#2541C2211yescharacteristic
132#2538C2211yescharacteristic
133#2538C2214yes—
134#2538C2212yes—
135#2522C2214yes—
136#2519C2214yes—
137#2519C2214yes—
138#2513C2212yes—
139#2513C2212yes—
140#2513C2212yes—
141#2513C2212yes—
142#2512C2212yes—
143#2512C2212yes—
144#2512C2212yes—
145#2511C2214yes—
146#2509C2214yes—
147#2509C2212yes—
148#2509C2212yes—
149#2509C2212yes—
150#2508C2214yes—
151#2508C2212yes—
152#2508C2212yes—
153#2507C2212yes—
154#2506C2212yes—
155#2506C2212yes—
156#2498C2214yes—
157#2498C2214yes—
158#2497C2214yes—
159#2489C2214yes—
160#2485C2214yes—
161#2481C2214yes—
162#2479C2214yes—
163#2477C2214yes—
164#2476C2214yes—
165#2475C2214yes—
166#2474C2214yes—
167#2466C2214yes—
168#2466C2214yes—
169#2466C2214yes—
170#2457C2214yes—
171#2457C2214yes—
172#2454C2212yes—
173#2454C2212yes—
174#2454C2212yes—
175#2454C2212yes—
176#2453C2214yes—
177#2452C2212yes—
178#2452C2212yes—
179#2449C2214yes—
180#2449C2214yes—
181#2445C2212yes—
182#2445C2212yes—
183#2445C2212yes—
184#2444C2214yes—
185#2441C2212yes—
186#2441C2214yes—
187#2439C2212yes—
188#2438C2214yes—
189#2427C2212yes—
190#2425C2214yes—
191#2420C2212yes—
192#2419C2214yes—
193#2417C2214yes—
194#2415C2214yes—
195#2413C2214yes—
196#2409C2214yes—
197#2409C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2399C2212yes—
201#2392C2214yes—
202#2378C2214yes—
203#2378C2214yes—
204#2370C2212yes—
205#2370C2212yes—
206#2370C2212yes—
207#2370C2212yes—
208#2369C2212yes—
209#2368C2214yes—
210#2366C2212yes—
211#2366C2212yes—
212#2366C2212yes—
213#2365C2211yescharacteristic
214#2362C2214yes—
215#2360C2212yes—
216#2359C2214yes—
217#2357C2212yes—
218#2357C2212yes—
219#2355C2211yescharacteristic
220#2355C2212yes—
221#2354C2212yes—
222#2354C2211yescharacteristic
223#2354C2211yescharacteristic
224#2349C2212yes—
225D4×C4⋊C4C2212yes—
226D4×C4⋊C4C2211yescharacteristic
227#2344C2214yes—
228Q8×C22⋊C4C2212yes—
229#2334C2214yes—
230#2332C2214yes—
231#2332C2214yes—
232#2331C2212yes—
233#2331C2212yes—
234#2330C2212yes—
235#2330C2212yes—
236#2329C2214yes—
237#2328C2212yes—
238#2323C2214yes—
239#2319C2212yes—
240#2319C2212yes—
241#2319C2212yes—
242#2313C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×C22⋊Q8C2212yes—
249#2296C2212yes—
250#2295C2212yes—
251#2295C2211yescharacteristic
252#2295C2212yes—
253#2295C2211yescharacteristic
254C2×#391C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C23×Q8C2312yes—
260#554—216no—
261D4×Q8—28no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×#127C2311yescharacteristic
266C2×#127C2312yes—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#124C2312yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×#117C2312yes—
312C2×#117C2314yes—
313C2×#117C2314yes—
314C2×#117C2314yes—
315C2×#117C2312yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2312yes—
318C22×C42C2312yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2312yes—
359#398C2312yes—
360#398C2312yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#395C2312yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2312yes—
408#395C2312yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#392C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2311yescharacteristic
443#391C2312yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2311yescharacteristic
472#389C2312yes—
473#389C2311yescharacteristic
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2311yescharacteristic
506#389C2314yes—
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2311yescharacteristic
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2312yes—
556#387C2312yes—
557#387C2314yes—
558#387C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2312yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2314yes—
597#387C2312yes—
598#387C2312yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#384C2311yescharacteristic
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2311yescharacteristic
633#384C2314yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#382C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2312yes—
709#376C2312yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C43C2312yes—
713C43C2311yescharacteristic
714C22×Q8—28no—
715C22×Q8—82no—
716C22×Q8—82no—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C23×C4C2412yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2412yes—
736C4⋊Q8—28no—
737C4⋊Q8—42no—
738C4⋊Q8#4118yes—
739#127—28no—
740#127—24no—
741#126—48no—
742#126—84no—
743#126—84no—
744#126—84no—
745#125—28no—
746#125—28no—
747#125—28no—
748#125—44no—
749#125—82no—
750#125—84no—
751#125—84no—
752#124—82no—
753#123—48no—
754#123—84no—
755#123—84no—
756C22⋊Q8—28no—
757C22⋊Q8—216no—
758C22⋊Q8—216no—
759C22⋊Q8—216no—
760C22⋊Q8—216no—
761C22⋊Q8—82no—
762C22⋊Q8—84no—
763C22⋊Q8—84no—
764C22⋊Q8—84no—
765#121—82no—
766#121—82no—
767C4×Q8—24no—
768C4×Q8—28no—
769C4×Q8—24no—
770C4×Q8—82no—
771C4×Q8—82no—
772C4×D4—24no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—28no—
777C4×D4—24no—
778C4×D4—28no—
779C4×D4—24no—
780C4×D4—44no—
781C4×D4—84no—
782C4×D4—82no—
783C4×D4—84no—
784C4×D4—84no—
785#117—44no—
786#117—84no—
787#117—82no—
788#117—84no—
789#117—84no—
790C2×C4⋊C4—216no—
791C2×C4⋊C4—82no—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C42—82no—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2411yescharacteristic
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24C2514yes—
1004C24C2512yes—
1005C2×Q8—22no—
1006C2×Q8—24no—
1007C2×Q8—28no—
1008C2×Q8—22no—
1009C2×Q8—42no—
1010C2×Q8—42no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—41no—
1014C2×Q8—42no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—41no—
1018C2×Q8—42no—
1019C2×Q8—816no—
1020C2×Q8C2×#4118yes—
1021C2×D4—28no—
1022C2×D4—28no—
1023C2×D4—22no—
1024C2×D4—24no—
1025C2×D4—22no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—24no—
1029C2×D4—24no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C2×D4—42no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—42no—
1037C2×D4—44no—
1038C2×D42−1+414yes—
1039C22×C4—24no—
1040C22×C4—28no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—28no—
1044C22×C4—28no—
1045C22×C4—28no—
1046C22×C4—28no—
1047C22×C4—24no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2511yescharacteristic
1085C22×C4C2514yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—22no—
1105C4⋊C4—22no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—41no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—41no—
1133C4⋊C4—44no—
1134C4⋊C4—41no—
1135C4⋊C4—41no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—41no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4C2×#4118yes—
1165C4⋊C4C2×#4118yes—
1166C22⋊C4—24no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—28no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C42—24no—
1201C42—24no—
1202C42—24no—
1203C42—22no—
1204C42—24no—
1205C42—24no—
1206C42—24no—
1207C42—22no—
1208C42—41no—
1209C42—42no—
1210C42—42no—
1211C42—42no—
1212C42—44no—
1213C42—44no—
1214C42—42no—
1215C42—42no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—41no—
1220C42—44no—
1221C42—44no—
1222C42—41no—
1223C42—42no—
1224C42—44no—
1225C42—44no—
1226C42—42no—
1227C42C2×#4114yes—
1228C422−1+414yes—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—24no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23C2×2−1+414yes—
1243C23C2611yescharacteristic
1244Q8—48no—
1245Q8—44no—
1246Q8—84no—
1247Q8—82no—
1248Q8—88no—
1249D4—28no—
1250D4—48no—
1251D4—48no—
1252D4—84no—
1253D4—88no—
1254D4—88no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—48no—
1328C2×C4—48no—
1329C2×C4—88no—
1330C2×C4—88no—
1331C2×C4—88no—
1332C2×C4—84no—
1333C2×C4—88no—
1334C2×C4—88no—
1335C2×C4C22×#4112yes—
1336C2×C4C22×#4112yes—
1337C2×C4C22×#4118yes—
1338C2×C4C22×#4112yes—
1339C2×C4C2×2−1+412yes—
1340C2×C4C2×2−1+412yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4C2×2−1+412yes—
1343C2×C4#58512yes—
1344C22—24no—
1345C22—24no—
1346C22—24no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22C23×#4111yescharacteristic
1359C22C22×2−1+411yescharacteristic
1360C22C22×2−1+411yescharacteristic
1361C22C2×#58511yescharacteristic
1362C22H(7,𝔽2)11yescharacteristic
1363C22H(7,𝔽2)11yescharacteristic
1364C22H(7,𝔽2)11yescharacteristic
1365C4—22no—
1366C4—22no—
1367C4—28no—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—41no—
1376C4—44no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—44no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4#352314yes—
1392C2—44no—
1393C2—84no—
1394C2C2×#352311yescharacteristic
1395C2#6284611yescharacteristic
1396C2#6288111yescharacteristic
1397C2#6292611yescharacteristic
1398C2#6294811yescharacteristic
1399C2#6300611yescharacteristic
1400C2#6305411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59962C2semidirect
2. #59823C2semidirect
3. #52274C2semidirect
4. #51172C2semidirect
5. #49486C2semidirect
6. #48381C2semidirect
7. #46872C2semidirect
8. #46098C2semidirect
9. #45357C2semidirect
10. #45202C2semidirect
11. #45007C2semidirect
12. #43271C2semidirect
13. #42852C2semidirect
14. #42687C2semidirect
15. #42626C2semidirect
16. #39756C2semidirect
17. #39637C2semidirect
18. #39217C2semidirect
19. #38821C2semidirect
20. #38484C2semidirect
21. #38238C2semidirect
22. #38226C2semidirect
23. #37220C2semidirect
24. #36416C2semidirect
26. #35612C2semidirect
28. #34489C2semidirect
29. #34334C2semidirect

Maximal subgroups

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

subgroupindex
#599622
#598232
#522742
#511722
#494862
#483812
#468722
#460982
#453572
#452022
#450072
#432712
#428522
#426872
#426262
#397562
#396372
#392172
#388212
#384842
#382382
#382262
#372202
#364162
#358652
#356122
#351972
#344892
#343342