Finite Group Databasebeta

← #7743588

Subgroups — #7743588

Order 512.

4432 conjugacy classes of subgroups.

The subgroup lattice has 1433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51196C212yesmaximal, complemented
2#51054C212yesmaximal, complemented
3#50879C212yesmaximal, complemented
4#50676C212yesmaximal, complemented
5#50192C214yesmaximal, complemented
6#48881C214yesmaximal, complemented
7#48879C214yesmaximal, complemented
8#48804C214yesmaximal, complemented
9#45461C214yesmaximal, complemented
10#45460C214yesmaximal, complemented
11#39562C212yesmaximal, complemented
12#39545C212yesmaximal, complemented
13#39076C212yesmaximal, complemented
14#39044C212yesmaximal, complemented
15#38265C212yesmaximal, complemented
16#38201C212yesmaximal, complemented
17#37974C212yesmaximal, complemented
18#37938C212yesmaximal, complemented
19#37480C211yesmaximal, characteristic, complemented
20#37445C211yesmaximal, characteristic
21#37366C212yesmaximal, complemented
22#37364C212yesmaximal, complemented
23#35599C212yesmaximal, complemented
24#35590C212yesmaximal, complemented
25#35227C211yesmaximal, characteristic, complemented
26#35227C211yesmaximal, characteristic, complemented
27#34391C211yesmaximal, characteristic, complemented
28#34342C211yesmaximal, characteristic, complemented
29#34178C211yesmaximal, characteristic, complemented
30C2×#525C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33#2864C2212yescomplemented
34#2860C2212yescomplemented
35#2857C2212yescomplemented
36#2855C2212yescomplemented
37#2849C2212yes—
38#2849C2214yes—
39#2849C2212yes—
40#2842C2212yes—
41#2840C2212yes—
42#2812C2214yes—
43#2809C2214yescomplemented
44#2808C2214yescomplemented
45#2802C2214yescomplemented
46#2798C2214yescomplemented
47#2796C2214yescomplemented
48#2794C2214yescomplemented
49#2787C2214yescomplemented
50#2777C2214yescomplemented
51#2774C2214yescomplemented
52#2773C2214yescomplemented
53#2771C2214yes—
54#2764C2214yes—
55#2762C2214yescomplemented
56#2760C2214yes—
57#2758C2214yescomplemented
58#2758C2214yescomplemented
59#2754C2214yescomplemented
60#2752C2214yes—
61#2751C2214yes—
62#2751C2214yes—
63#2751C2214yescomplemented
64#2745C2214yes—
65#2745C2214yes—
66#2745C2214yescomplemented
67#2743C2214yes—
68#2743C2214yes—
69#2743C2214yes—
70#2743C2214yes—
71#2743C2214yescomplemented
72#2742C2214yescomplemented
73#2741C2214yescomplemented
74#2739C2214yes—
75#2739C2214yes—
76#2738C2214yescomplemented
77#2737C2214yes—
78#2737C2214yes—
79#2730C2214yescomplemented
80#2721C2214yescomplemented
81#2705C2214yes—
82#2705C2214yes—
83#2696C2214yes—
84#2696C2214yes—
85#2695C2214yes—
86#2695C2214yes—
87#2689C2214yescomplemented
88#2689C2214yescomplemented
89#2687C2214yes—
90#2687C2214yes—
91#2665C2214yes—
92#2665C2212yes—
93#2665C2212yes—
94#2663C2212yes—
95#2661C2212yes—
96#2647C2212yescomplemented
97#2645C2212yescomplemented
98#2638C2212yes—
99#2635C2212yes—
100#2628C2212yes—
101#2628C2212yes—
102#2628C2212yescomplemented
103#2625C2211yescharacteristic
104#2624C2211yescharacteristic
105#2624C2212yescomplemented
106#2623C2214yes—
107#2623C2214yes—
108#2616C2211yescharacteristic
109#2615C2211yescharacteristic
110#2611C2214yes—
111#2610C2214yes—
112#2607C2214yes—
113#2607C2214yescomplemented
114#2605C2214yescomplemented
115#2604C2214yescomplemented
116#2602C2214yes—
117#2599C2214yes—
118#2598C2214yes—
119#2597C2214yescomplemented
120#2594C2214yescomplemented
121#2590C2214yescomplemented
122#2577C2214yescomplemented
123#2575C2214yescomplemented
124#2573C2214yes—
125#2573C2214yes—
126#2572C2214yes—
127#2572C2214yes—
128#2564C2214yescomplemented
129#2558C2214yes—
130#2558C2214yes—
131#2557C2214yes—
132#2557C2214yes—
133#2556C2214yescomplemented
134#2533C2214yescomplemented
135#2533C2214yescomplemented
136#2532C2214yescomplemented
137#2532C2214yescomplemented
138#2530C2214yescomplemented
139#2528C2214yescomplemented
140#2527C2214yes—
141#2527C2214yes—
142#2526C2214yes—
143#2526C2214yes—
144#2521C2214yescomplemented
145#2516C2214yescomplemented
146#2514C2212yescomplemented
147#2513C2212yescomplemented
148#2511C2214yescomplemented
149#2509C2212yescomplemented
150#2509C2212yescomplemented
151#2507C2212yescomplemented
152#2506C2212yescomplemented
153#2504C2211yescharacteristic
154#2504C2212yes—
155#2504C2211yescharacteristic
156#2503C2212yes—
157#2503C2212yes—
158#2502C2211yescharacteristic
159#2502C2212yes—
160#2502C2211yescharacteristic
161#2501C2212yes—
162#2501C2212yes—
163#2497C2212yescomplemented
164#2496C2212yescomplemented
165#2495C2212yescomplemented
166#2495C2212yescomplemented
167#2493C2214yescomplemented
168#2492C2212yescomplemented
169#2491C2212yescomplemented
170#2487C2212yes—
171#2487C2212yes—
172#2487C2212yes—
173#2487C2212yes—
174#2486C2212yes—
175#2486C2214yes—
176#2486C2212yes—
177#2485C2212yes—
178#2479C2214yes—
179#2479C2214yes—
180#2477C2214yes—
181#2477C2214yes—
182#2467C2214yescomplemented
183#2458C2214yes—
184#2458C2214yes—
185#2457C2214yes—
186#2457C2214yes—
187#2453C2214yescomplemented
188#2452C2212yescomplemented
189#2451C2212yescomplemented
190#2447C2214yescomplemented
191#2439C2212yes—
192#2439C2212yes—
193#2439C2212yes—
194#2439C2212yes—
195#2423C2214yescomplemented
196#2421C2212yescomplemented
197#2420C2212yescomplemented
198#2415C2212yes—
199#2414C2212yes—
200#2407C2212yes—
201#2378C2211yescharacteristic
202#2378C2212yes—
203#2378C2211yescharacteristic
204#2377C2211yescharacteristic
205#2377C2212yes—
206#2377C2211yescharacteristic
207#2376C2212yes—
208#2376C2212yes—
209#2375C2212yes—
210#2375C2212yes—
211#2375C2214yes—
212#2363C2212yes—
213#2362C2212yes—
214#2357C2212yes—
215#2353C2212yes—
216#2347C2211yescharacteristic
217#2346C2211yescharacteristic
218#2345C2212yes—
219#2345C2212yes—
220#2345C2212yes—
221#2345C2212yes—
222#2344C2212yes—
223#2344C2212yes—
224#2344C2214yes—
225#2341C2211yescharacteristic
226#2339C2211yescharacteristic
227#2335C2214yes—
228#2331C2212yescomplemented
229#2324C2212yes—
230#2323C2212yes—
231#2323C2212yescomplemented
232#2319C2212yes—
233#2319C2212yescomplemented
234#2318C2212yes—
235#2317C2212yes—
236#2317C2212yes—
237#2316C2212yes—
238#2314C2212yescomplemented
239#2313C2212yes—
240#2313C2212yes—
241#2311C2212yes—
242#2311C2212yes—
243C4×C4⋊Q8C2212yescomplemented
244C4×#121C2212yescomplemented
245#2298C2212yes—
246#2297C2212yes—
247#2295C2212yescomplemented
248#2293C2212yes—
249#2293C2212yes—
250#2290C2212yes—
251#2290C2212yes—
252#2283C2212yescomplemented
253#2280C2211yescharacteristic
254#2280C2211yescharacteristic
255#2280C2211yescharacteristic
256#2280C2211yescharacteristic
257#2280C2214yes—
258#2274C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C24×C4C2312yes—
262C24×C4C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#125C2314yes—
268C2×#124C2314yes—
269#525—28no—
270#525—28no—
271C2×#123C2312yes—
272C2×#123C2312yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×C22⋊Q8C2311yescharacteristic
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×#121C2311yescharacteristic
285C2×#121C2311yescharacteristic
286C2×#121C2311yescharacteristic
287C2×#121C2311yescharacteristic
288C2×#121C2312yes—
289C2×#120C2312yes—
290C2×#120C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2314yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×#117C2311yescharacteristic
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C2×#117C2314yes—
307C2×#117C2314yes—
308C22×C4⋊C4—28no—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C42C2312yes—
317#401C2314yes—
318#401C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2312yes—
352#399C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2312yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2312yes—
389#395C2314yes—
390#395C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2312yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2312yes—
412#393C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2312yes—
416#392C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#390C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2314yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#390C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#388C2314yes—
482#388C2314yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
488#388C2312yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2312yes—
507#388C2314yes—
508#388C2312yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2312yes—
521#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2312yes—
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#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2314yes—
570#387C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2312yes—
578#386C2312yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2312yes—
585#386C2312yes—
586#386C2312yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2312yes—
591#386C2312yes—
592#386C2312yes—
593#386C2312yes—
594#386C2312yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2312yes—
607#385C2312yes—
608#385C2312yes—
609#385C2312yes—
610#385C2314yes—
611#385C2312yes—
612#385C2312yes—
613#384C2312yes—
614#384C2312yes—
615#384C2314yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#383C2314yes—
620#383C2312yes—
621#382C2312yes—
622#382C2314yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#381C2311yescharacteristic
628#381C2311yescharacteristic
629#381C2312yes—
630#381C2314yes—
631#381C2314yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2312yes—
636#381C2312yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2312yes—
641#381C2314yes—
642#381C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2311yescharacteristic
654#380C2311yescharacteristic
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2311yescharacteristic
659#380C2311yescharacteristic
660#380C2312yes—
661#380C2311yescharacteristic
662#380C2311yescharacteristic
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2311yescharacteristic
669#380C2311yescharacteristic
670#379C2311yescharacteristic
671#379C2312yes—
672#379C2312yes—
673#379C2311yescharacteristic
674#379C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2311yescharacteristic
708C4×C22⋊C4C2311yescharacteristic
709#376C2312yes—
710#376C2312yes—
711#376C2314yes—
712#376C2314yes—
713C2×#95C2312yes—
714C43C2312yes—
715C25C2411yescharacteristic
716C2×#41—24no—
717C2×#41—24no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×Q8C2414yes—
723C22×Q8C2414yes—
724C22×D4C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2411yescharacteristic
732C22×D4C2414yes—
733C23×C4—28no—
734C23×C4—44no—
735C23×C4—84no—
736C23×C4#4118yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C4⋊Q8—44no—
753C4⋊Q8—44no—
754#126—84no—
755#126—84no—
756#125—84no—
757#124—84no—
758#123—28no—
759#123—28no—
760#123—84no—
761#123—84no—
762#123—84no—
763#123—84no—
764C22⋊Q8—24no—
765C22⋊Q8—24no—
766C22⋊Q8—24no—
767C22⋊Q8—24no—
768C22⋊Q8—44no—
769C22⋊Q8—84no—
770C22⋊Q8—84no—
771#121—24no—
772#121—24no—
773#121—24no—
774#121—24no—
775#121—44no—
776#120—28no—
777#120—28no—
778C4×Q8—44no—
779C4×Q8—84no—
780C4×D4—28no—
781C4×D4—28no—
782C4×D4—28no—
783C4×D4—28no—
784C4×D4—44no—
785C4×D4—84no—
786#117—24no—
787#117—24no—
788#117—44no—
789#117—44no—
790#117—44no—
791#117—44no—
792#117—44no—
793#117—84no—
794#117—84no—
795C2×C4⋊C4—28no—
796C2×C4⋊C4—28no—
797C2×C4⋊C4—28no—
798C2×C4⋊C4—24no—
799C2×C4⋊C4—24no—
800C2×C4⋊C4—28no—
801C2×C4⋊C4—28no—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2411yescharacteristic
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C42—44no—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931#95C2411yescharacteristic
932#95C2412yes—
933#95C2414yes—
934#95C2411yescharacteristic
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2411yescharacteristic
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24—42no—
1004C24—42no—
1005C24—41no—
1006C24—41no—
1007C24C2×#4114yes—
1008C24C2512yes—
1009C24C2512yes—
1010C24C2511yescharacteristic
1011C24C2511yescharacteristic
1012C24C2511yescharacteristic
1013#41—88no—
1014#41—88no—
1015C2×Q8—22no—
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—44no—
1019C2×Q8—44no—
1020C2×Q8—44no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×D4—24no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—24no—
1029C2×D4—24no—
1030C2×D4—24no—
1031C2×D4—22no—
1032C2×D4—22no—
1033C2×D4—24no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—42no—
1037C2×D4—44no—
1038C2×D4—42no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C2×D4—42no—
1042C2×D4—42no—
1043C2×D4—44no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—44no—
1047C2×D4—42no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—24no—
1053C22×C4—28no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—416no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—816no—
1080C22×C4C2×#4114yes—
1081C22×C4C2×#4114yes—
1082C22×C4C2×#4114yes—
1083C22×C4C2×#4114yes—
1084C22×C4C2×#4114yes—
1085C22×C4C2×#4114yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—41no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—41no—
1179C22⋊C4—42no—
1180C22⋊C4—42no—
1181C22⋊C4—42no—
1182C22⋊C4—44no—
1183C22⋊C4—41no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—41no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—42no—
1224C42—42no—
1225C42—44no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—42no—
1236C42—44no—
1237C42—42no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—21no—
1245C23—21no—
1246C23—21no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—24no—
1255C23—22no—
1256C23—24no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—44no—
1263C23—44no—
1264C23—44no—
1265C23—48no—
1266C23—48no—
1267C23C22×#4112yes—
1268C23C22×#4112yes—
1269C23C22×#4112yes—
1270C23C2611yescharacteristic
1271Q8—44no—
1272Q8—82no—
1273Q8—88no—
1274Q8—164no—
1275D4—44no—
1276D4—82no—
1277D4—84no—
1278D4—84no—
1279D4—84no—
1280D4—84no—
1281D4—84no—
1282D4—84no—
1283D4—88no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—28no—
1288C2×C4—28no—
1289C2×C4—28no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—44no—
1349C2×C4—44no—
1350C2×C4—44no—
1351C2×C4—416no—
1352C2×C4—48no—
1353C2×C4—84no—
1354C2×C4—84no—
1355C2×C4—88no—
1356C2×C4—84no—
1357C2×C4—84no—
1358C2×C4—84no—
1359C2×C4—164no—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4112yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4112yes—
1364C2×C4#58514yes—
1365C22—22no—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22—22no—
1370C22—22no—
1371C22—22no—
1372C22—22no—
1373C22—22no—
1374C22—416no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—44no—
1386C22—42no—
1387C22—44no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22C23×#4111yescharacteristic
1394C22C2×#58512yes—
1395C22H(7,𝔽2)12yes—
1396C222−1+611yescharacteristic
1397C222−1+611yescharacteristic
1398C4—22no—
1399C4—22no—
1400C4—22no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—44no—
1411C4—44no—
1412C4—44no—
1413C4—42no—
1414C4—44no—
1415C4—44no—
1416C4—44no—
1417C4—42no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4#349114yes—
1422C2—42no—
1423C2—42no—
1424C2—42no—
1425C2—82no—
1426C2—82no—
1427C2C2×#349111yescharacteristic
1428C2#6285511yescharacteristic
1429C2#6286011yescharacteristic
1430C2#6304312yes—
1431C2#6304312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37445C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51196C2semidirect
2. #51054C2semidirect
3. #50879C2semidirect
4. #50676C2semidirect
5. #50192C2semidirect
6. #48881C2semidirect
7. #48879C2semidirect
8. #48804C2semidirect
9. #45461C2semidirect
10. #45460C2semidirect
11. #39562C2semidirect
12. #39545C2semidirect
13. #39076C2semidirect
14. #39044C2semidirect
15. #38265C2semidirect
16. #38201C2semidirect
17. #37974C2semidirect
18. #37938C2semidirect
19. #37480C2semidirect
21. #37366C2semidirect
22. #37364C2semidirect
23. #35599C2semidirect
24. #35590C2semidirect
25. #35227C2semidirect
26. #35227C2semidirect
27. #34391C2semidirect
28. #34342C2semidirect
29. #34178C2semidirect
33. #2864C22semidirect
34. #2860C22semidirect
35. #2857C22semidirect
36. #2855C22semidirect
43. #2809C22semidirect
44. #2808C22semidirect
45. #2802C22semidirect
46. #2798C22semidirect
47. #2796C22semidirect
48. #2794C22semidirect
49. #2787C22semidirect
50. #2777C22semidirect
51. #2774C22semidirect
52. #2773C22semidirect
55. #2762C22semidirect
57. #2758C22semidirect
58. #2758C22semidirect
59. #2754C22semidirect
63. #2751C22semidirect
66. #2745C22semidirect
71. #2743C22semidirect
72. #2742C22semidirect
73. #2741C22semidirect
76. #2738C22semidirect
79. #2730C22semidirect
80. #2721C22semidirect
87. #2689C22semidirect
88. #2689C22semidirect
96. #2647C22semidirect
97. #2645C22semidirect
102. #2628C22semidirect
105. #2624C22semidirect
113. #2607C22semidirect
114. #2605C22semidirect
115. #2604C22semidirect
119. #2597C22semidirect
120. #2594C22semidirect
121. #2590C22semidirect
122. #2577C22semidirect
123. #2575C22semidirect
128. #2564C22semidirect
133. #2556C22semidirect
134. #2533C22semidirect
135. #2533C22semidirect
136. #2532C22semidirect
137. #2532C22semidirect
138. #2530C22semidirect
139. #2528C22semidirect
144. #2521C22semidirect
145. #2516C22semidirect
146. #2514C22semidirect
147. #2513C22semidirect
148. #2511C22semidirect
149. #2509C22semidirect
150. #2509C22semidirect
151. #2507C22semidirect
152. #2506C22semidirect
163. #2497C22semidirect
164. #2496C22semidirect
165. #2495C22semidirect
166. #2495C22semidirect
167. #2493C22semidirect
168. #2492C22semidirect
169. #2491C22semidirect
182. #2467C22semidirect
187. #2453C22semidirect
188. #2452C22semidirect
189. #2451C22semidirect
190. #2447C22semidirect
195. #2423C22semidirect
196. #2421C22semidirect
197. #2420C22semidirect
228. #2331C22semidirect
231. #2323C22semidirect
233. #2319C22semidirect
238. #2314C22semidirect
243. C4×C4⋊Q8C22semidirect
244. C4×#121C22semidirect
247. #2295C22semidirect
252. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#511962
#510542
#508792
#506762
#501922
#488812
#488792
#488042
#454612
#454602
#395622
#395452
#390762
#390442
#382652
#382012
#379742
#379382
#374802
#374452
#373662
#373642
#355992
#355902
#352272
#343912
#343422
#341782