Finite Group Databasebeta

← #7732510

Subgroups — #7732510

Order 512.

4254 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48915C214yesmaximal, complemented
2#48048C214yesmaximal, complemented
3#47765C214yesmaximal, complemented
4#47759C214yesmaximal, complemented
5#45391C212yesmaximal, complemented
6#45366C212yesmaximal, complemented
7#45150C212yesmaximal, complemented
8#44962C212yesmaximal, complemented
9#40322C214yesmaximal, complemented
10#40023C212yesmaximal, complemented
11#40022C212yesmaximal, complemented
12#39803C212yesmaximal, complemented
13#39802C212yesmaximal, complemented
14#39769C212yesmaximal, complemented
15#39766C212yesmaximal, complemented
16#38706C214yesmaximal, complemented
17#37540C211yesmaximal, characteristic, complemented
18#37019C212yesmaximal, complemented
19#37013C212yesmaximal, complemented
20#36485C212yesmaximal, complemented
21#36421C212yesmaximal, complemented
22#35506C212yesmaximal, complemented
23#35501C212yesmaximal, complemented
24#35341C211yesmaximal, characteristic
25#35298C211yesmaximal, characteristic
26#34912C211yesmaximal, characteristic, complemented
27#34402C211yesmaximal, characteristic
28#34239C211yesmaximal, characteristic, complemented
29#34085C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C22×#125C2211yescharacteristic
33#2868C2211yescharacteristic
34#2866C2214yes—
35#2865C2214yes—
36#2862C2211yescharacteristic
37#2861C2212yes—
38#2861C2212yes—
39#2858C2211yescharacteristic
40#2858C2211yescharacteristic
41#2822C2214yes—
42#2796C2214yes—
43#2796C2214yes—
44#2794C2214yes—
45#2794C2214yes—
46#2794C2214yes—
47#2794C2214yes—
48#2793C2214yes—
49#2790C2214yes—
50#2789C2214yes—
51#2786C2214yes—
52#2777C2214yes—
53#2772C2214yes—
54#2767C2214yes—
55#2765C2214yes—
56#2762C2214yes—
57#2761C2214yes—
58#2758C2214yes—
59#2751C2214yes—
60#2751C2214yes—
61#2751C2214yes—
62#2750C2214yes—
63#2747C2214yes—
64#2747C2214yes—
65#2746C2214yes—
66#2745C2214yes—
67#2744C2214yes—
68#2743C2214yes—
69#2743C2214yes—
70#2742C2214yes—
71#2740C2214yes—
72#2740C2214yes—
73#2739C2214yes—
74#2739C2214yes—
75#2738C2214yes—
76#2737C2214yes—
77#2729C2214yes—
78#2722C2214yes—
79#2716C2214yes—
80#2715C2214yes—
81#2700C2214yes—
82#2660C2212yes—
83#2654C2214yes—
84#2650C2214yes—
85#2642C2212yes—
86#2642C2212yes—
87#2641C2212yes—
88#2634C2214yes—
89#2627C2212yes—
90#2627C2212yes—
91#2620C2214yes—
92#2609C2214yes—
93#2608C2211yescharacteristic
94#2608C2211yescharacteristic
95#2607C2211yescharacteristic
96#2607C2211yescharacteristic
97#2606C2212yes—
98#2605C2214yes—
99#2605C2212yes—
100#2601C2214yes—
101#2601C2214yes—
102#2596C2214yes—
103#2595C2214yes—
104#2595C2214yes—
105#2594C2214yes—
106#2594C2214yes—
107#2592C2212yes—
108#2592C2212yes—
109#2591C2214yes—
110#2591C2212yes—
111#2591C2212yes—
112#2588C2214yes—
113#2587C2214yes—
114#2582C2212yes—
115#2581C2212yes—
116#2580C2212yes—
117#2577C2214yes—
118#2577C2214yes—
119#2576C2214yes—
120#2575C2214yes—
121#2574C2214yes—
122#2572C2214yes—
123#2570C2214yes—
124#2570C2214yes—
125#2570C2212yes—
126#2569C2214yes—
127#2568C2212yes—
128#2568C2212yes—
129#2566C2212yes—
130#2566C2212yes—
131#2565C2212yes—
132#2565C2212yes—
133#2562C2212yes—
134#2562C2212yes—
135#2562C2214yes—
136#2560C2214yes—
137#2550C2212yes—
138#2545C2212yes—
139#2545C2212yes—
140#2538C2212yes—
141#2532C2214yes—
142#2530C2214yes—
143#2530C2214yes—
144#2529C2214yes—
145#2529C2214yes—
146#2528C2214yes—
147#2527C2214yes—
148#2526C2214yes—
149#2525C2214yes—
150#2524C2214yes—
151#2522C2214yes—
152#2522C2214yes—
153#2521C2214yes—
154#2519C2214yes—
155#2516C2214yes—
156#2516C2214yes—
157#2516C2214yes—
158#2515C2214yes—
159#2514C2212yes—
160#2514C2212yes—
161#2513C2212yes—
162#2513C2212yes—
163#2512C2212yes—
164#2512C2212yes—
165#2511C2214yes—
166#2511C2212yes—
167#2511C2212yes—
168#2511C2214yes—
169#2505C2214yes—
170#2503C2211yescharacteristic
171#2503C2211yescharacteristic
172#2502C2211yescharacteristic
173#2502C2211yescharacteristic
174#2500C2212yes—
175#2500C2212yes—
176#2493C2214yes—
177#2484C2212yes—
178#2484C2212yes—
179#2479C2214yes—
180#2477C2214yes—
181#2475C2214yes—
182#2474C2214yes—
183#2448C2212yes—
184#2448C2212yes—
185#2447C2212yes—
186#2447C2212yes—
187#2446C2212yes—
188#2446C2212yes—
189#2446C2212yes—
190#2446C2212yes—
191#2441C2212yes—
192#2439C2212yes—
193#2438C2214yes—
194#2432C2212yes—
195#2432C2212yes—
196#2396C2212yes—
197#2396C2212yes—
198#2377C2212yes—
199#2377C2212yes—
200#2371C2214yes—
201#2370C2212yes—
202#2370C2212yes—
203#2367C2212yes—
204#2367C2212yes—
205#2367C2212yes—
206#2367C2212yes—
207#2365C2212yes—
208#2365C2212yes—
209#2357C2212yes—
210#2356C2212yes—
211#2355C2212yes—
212#2354C2212yes—
213#2353C2214yes—
214#2345C2212yes—
215#2344C2214yes—
216#2344C2212yes—
217#2341C2212yes—
218#2339C2212yes—
219#2336C2214yes—
220#2336C2212yes—
221#2336C2212yes—
222#2334C2214yes—
223#2333C2212yes—
224#2333C2212yes—
225#2332C2214yes—
226#2332C2214yes—
227#2331C2212yes—
228#2328C2212yes—
229#2327C2212yes—
230#2327C2212yes—
231#2326C2214yes—
232#2323C2212yes—
233#2323C2212yes—
234#2318C2214yes—
235#2313C2212yes—
236#2311C2212yes—
237#2311C2212yes—
238C4×C4⋊Q8C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#125C2212yes—
242C4×#126C2214yes—
243#2298C2212yes—
244#2298C2212yes—
245#2298C2214yes—
246#2295C2212yes—
247#2295C2211yescharacteristic
248#2295C2211yescharacteristic
249#2295C2212yes—
250#2295C2212yes—
251#2295C2212yes—
252#2283C2211yescharacteristic
253#2283C2211yescharacteristic
254#2274C2212yes—
255C42×Q8C2211yescharacteristic
256C42×Q8C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C22×#41C2312yes—
260#533—28no—
261#532—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×#127C2311yescharacteristic
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125—28no—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2314yes—
304C2×#117C2312yes—
305C2×#117C2314yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2312yes—
310C22×C42C2311yescharacteristic
311#401C2314yes—
312#401C2314yes—
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#400C2312yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2312yes—
344#399C2312yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2312yes—
383#396C2312yes—
384#396C2314yes—
385#396C2312yes—
386#396C2312yes—
387#396C2314yes—
388#396C2314yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2312yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#393C2314yes—
403#393C2312yes—
404#393C2314yes—
405#393C2314yes—
406#393C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
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#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#387C2312yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
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#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
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#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2314yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2312yes—
602#385C2312yes—
603#385C2312yes—
604#385C2312yes—
605#384C2312yes—
606#384C2312yes—
607#384C2312yes—
608#384C2312yes—
609#384C2312yes—
610#384C2314yes—
611#383C2314yes—
612#383C2314yes—
613#383C2312yes—
614#383C2314yes—
615#383C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2314yes—
624#382C2314yes—
625#382C2314yes—
626#381C2314yes—
627#381C2312yes—
628#381C2314yes—
629#381C2314yes—
630#381C2314yes—
631#381C2312yes—
632#381C2312yes—
633#381C2311yescharacteristic
634#381C2311yescharacteristic
635#381C2312yes—
636#381C2312yes—
637#381C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2311yescharacteristic
648#380C2311yescharacteristic
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2311yescharacteristic
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2311yescharacteristic
701#376C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2314yes—
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708C2×#95C2314yes—
709C43C2312yes—
710C43C2311yescharacteristic
711C43C2311yescharacteristic
712C43C2311yescharacteristic
713C43C2311yescharacteristic
714C43C2312yes—
715C2×#41—28no—
716C2×#41—44no—
717C2×#41—44no—
718C22×Q8C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2414yes—
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C4⋊Q8—24no—
737C4⋊Q8—24no—
738C4⋊Q8—24no—
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—44no—
742#127—24no—
743#126—48no—
744#126—48no—
745#125—28no—
746#125—28no—
747#125—28no—
748#125—28no—
749#125—28no—
750#125—44no—
751#124—28no—
752#124—48no—
753#124—44no—
754#124—44no—
755C22⋊Q8—24no—
756C22⋊Q8—24no—
757C22⋊Q8—28no—
758C22⋊Q8—48no—
759#121—28no—
760#121—28no—
761C4×Q8—28no—
762C4×Q8—24no—
763C4×Q8—24no—
764C4×Q8—44no—
765C4×Q8—44no—
766C4×Q8—44no—
767C4×Q8—44no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—44no—
773C4×D4—44no—
774#117—28no—
775#117—44no—
776#117—48no—
777#117—48no—
778#117—44no—
779C2×C4⋊C4—24no—
780C2×C4⋊C4—28no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—24no—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C42#4118yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995C24C2514yes—
996C24C2511yescharacteristic
997#41—816no—
998C2×Q8—22no—
999C2×Q8—22no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—24no—
1007C2×Q8—42no—
1008C2×Q8—42no—
1009C2×Q8—44no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—42no—
1013C2×D4—28no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—44no—
1020C2×D4—42no—
1021C2×D4—42no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—28no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4C2×#4114yes—
1043C22×C4C2×#4114yes—
1044C22×C4C2×#4114yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C22⋊C4—24no—
1136C22⋊C4—24no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—24no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—41no—
1149C22⋊C4—41no—
1150C22⋊C4—41no—
1151C22⋊C4—41no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C42—24no—
1171C42—24no—
1172C42—28no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—24no—
1177C42—24no—
1178C42—24no—
1179C42—24no—
1180C42—42no—
1181C42—42no—
1182C42—41no—
1183C42—41no—
1184C42—41no—
1185C42—41no—
1186C42—41no—
1187C42—44no—
1188C42—41no—
1189C42—41no—
1190C42—41no—
1191C42—44no—
1192C42—42no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42—42no—
1200C42—44no—
1201C42—42no—
1202C42C2×#4114yes—
1203C42C2×#4114yes—
1204C42C2×#4114yes—
1205C42C2×#4114yes—
1206C23—22no—
1207C23—22no—
1208C23—21no—
1209C23—21no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23C22×#4112yes—
1218C23C2611yescharacteristic
1219Q8—44no—
1220Q8—44no—
1221Q8—48no—
1222Q8—84no—
1223Q8—84no—
1224Q8—84no—
1225D4—48no—
1226D4—84no—
1227D4—84no—
1228D4—88no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—28no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—44no—
1296C2×C4—44no—
1297C2×C4—48no—
1298C2×C4—88no—
1299C2×C4—84no—
1300C2×C4—88no—
1301C2×C4—164no—
1302C2×C4C22×#4112yes—
1303C2×C4C22×#4112yes—
1304C2×C4C22×#4112yes—
1305C2×C4C22×#4112yes—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4112yes—
1308C2×C4#58514yes—
1309C2×C4#58514yes—
1310C22—22no—
1311C22—22no—
1312C22—22no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22C23×#4111yescharacteristic
1323C22C2×#58512yes—
1324C22C2×#58512yes—
1325C222−1+611yescharacteristic
1326C222−1+611yescharacteristic
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—24no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—44no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4#351014yes—
1354C2—42no—
1355C2—84no—
1356C2C2×#351011yescharacteristic
1357C2#6281511yescharacteristic
1358C2#6286011yescharacteristic
1359C2#6293912yes—
1360C2#6297112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48915C2semidirect
2. #48048C2semidirect
3. #47765C2semidirect
4. #47759C2semidirect
5. #45391C2semidirect
6. #45366C2semidirect
7. #45150C2semidirect
8. #44962C2semidirect
9. #40322C2semidirect
10. #40023C2semidirect
11. #40022C2semidirect
12. #39803C2semidirect
13. #39802C2semidirect
14. #39769C2semidirect
15. #39766C2semidirect
16. #38706C2semidirect
17. #37540C2semidirect
18. #37019C2semidirect
19. #37013C2semidirect
20. #36485C2semidirect
21. #36421C2semidirect
22. #35506C2semidirect
23. #35501C2semidirect
26. #34912C2semidirect
28. #34239C2semidirect
29. #34085C2semidirect

Maximal subgroups

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

subgroupindex
#489152
#480482
#477652
#477592
#453912
#453662
#451502
#449622
#403222
#400232
#400222
#398032
#398022
#397692
#397662
#387062
#375402
#370192
#370132
#364852
#364212
#355062
#355012
#353412
#352982
#349122
#344022
#342392
#340852