Finite Group Databasebeta

← #7658006

Subgroups — #7658006

Order 512.

4512 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42134C214yesmaximal, complemented
2#42126C214yesmaximal, complemented
3#41915C214yesmaximal, complemented
4#41912C214yesmaximal, complemented
5#41594C214yesmaximal, complemented
6#41581C214yesmaximal, complemented
7#39809C212yesmaximal, complemented
8#39740C211yesmaximal, characteristic, complemented
9#39719C212yesmaximal, complemented
10#39674C212yesmaximal, complemented
11#39622C211yesmaximal, characteristic, complemented
12#37798C212yesmaximal
13#37793C212yesmaximal, complemented
14#37630C212yesmaximal, complemented
15#37581C212yesmaximal, complemented
16#37572C212yesmaximal, complemented
17#36602C211yesmaximal, characteristic, complemented
18#36574C211yesmaximal, characteristic, complemented
19#36140C212yesmaximal, complemented
20#35878C214yesmaximal, complemented
21#35872C214yesmaximal, complemented
22#35332C211yesmaximal, characteristic
23#35300C212yesmaximal, complemented
24#34631C212yesmaximal, complemented
25#34629C211yesmaximal, characteristic, complemented
26#34322C212yesmaximal, complemented
27#34145C211yesmaximal, characteristic, complemented
28C2×#556C2212yes—
29C2×#541C2211yescharacteristic
30C2×#540C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#533C2212yes—
33C2×#529C2212yes—
34#2861C2212yes—
35#2859C2211yescharacteristic
36#2859C2212yes—
37#2858C2211yescharacteristic
38#2855C2212yes—
39#2854C2212yes—
40#2850C2212yes—
41#2839C2214yes—
42#2839C2214yes—
43#2838C2214yes—
44#2837C2214yes—
45#2832C2214yes—
46#2831C2214yes—
47#2807C2214yes—
48#2806C2214yes—
49#2798C2214yes—
50#2792C2214yes—
51#2788C2214yes—
52#2773C2214yes—
53#2771C2214yes—
54#2768C2214yes—
55#2768C2214yes—
56#2763C2214yes—
57#2732C2214yes—
58#2729C2214yes—
59#2728C2214yes—
60#2727C2214yes—
61#2726C2214yes—
62#2723C2214yes—
63#2719C2214yes—
64#2718C2214yes—
65#2716C2214yes—
66#2708C2214yes—
67#2701C2214yes—
68#2698C2214yes—
69#2695C2214yes—
70#2689C2214yes—
71#2665C2214yes—
72#2664C2214yes—
73#2664C2214yes—
74#2663C2214yes—
75#2663C2214yes—
76#2663C2214yes—
77#2660C2212yes—
78#2658C2212yes—
79#2655C2214yes—
80#2655C2214yes—
81#2655C2214yes—
82#2654C2214yes—
83#2653C2214yes—
84#2653C2214yes—
85#2652C2214yes—
86#2652C2214yes—
87#2650C2214yes—
88#2649C2214yes—
89#2647C2211yescharacteristic
90#2647C2214yes—
91#2645C2212yes—
92#2645C2214yes—
93#2645C2212yes—
94#2644C2212yes—
95#2642C2211yescharacteristic
96#2642C2211yescharacteristic
97#2642C2212yes—
98#2641C2211yescharacteristic
99#2640C2212yes—
100#2629C2211yescharacteristic
101#2625C2212yes—
102#2621C2212yes—
103#2621C2211yescharacteristic
104#2620C2212yes—
105#2620C2212yes—
106#2597C2214yes—
107#2596C2214yes—
108#2596C2214yes—
109#2594C2214yes—
110#2593C2214yes—
111#2592C2212yes—
112#2592C2212yes—
113#2589C2214yes—
114#2589C2214yes—
115#2587C2214yes—
116#2586C2214yes—
117#2584C2214yes—
118#2583C2214yes—
119#2582C2212yes—
120#2581C2212yes—
121#2580C2212yes—
122#2576C2214yes—
123#2575C2214yes—
124#2568C2212yes—
125#2560C2214yes—
126#2559C2214yes—
127#2559C2214yes—
128#2558C2214yes—
129#2558C2214yes—
130#2558C2214yes—
131#2556C2214yes—
132#2552C2212yes—
133#2550C2212yes—
134#2550C2212yes—
135#2546C2212yes—
136#2545C2212yes—
137#2544C2212yes—
138#2530C2214yes—
139#2529C2214yes—
140#2527C2214yes—
141#2526C2214yes—
142#2519C2214yes—
143#2519C2214yes—
144#2511C2214yes—
145#2509C2214yes—
146#2509C2214yes—
147#2508C2214yes—
148#2507C2214yes—
149#2488C2214yes—
150#2479C2214yes—
151#2479C2214yes—
152#2478C2214yes—
153#2478C2214yes—
154#2477C2214yes—
155#2477C2214yes—
156#2475C2214yes—
157#2475C2214yes—
158#2475C2214yes—
159#2473C2214yes—
160#2470C2214yes—
161#2470C2214yes—
162#2470C2214yes—
163#2469C2214yes—
164#2462C2214yes—
165#2458C2214yes—
166#2454C2212yes—
167#2453C2214yes—
168#2453C2212yes—
169#2453C2212yes—
170#2453C2212yes—
171#2452C2212yes—
172#2451C2212yes—
173#2449C2214yes—
174#2448C2212yes—
175#2447C2212yes—
176#2446C2212yes—
177#2446C2212yes—
178#2446C2212yes—
179#2445C2212yes—
180#2443C2214yes—
181#2422C2214yes—
182#2413C2214yes—
183#2413C2214yes—
184#2402C2214yes—
185#2401C2214yes—
186#2396C2214yes—
187#2396C2214yes—
188#2395C2214yes—
189#2395C2214yes—
190#2374C2214yes—
191#2373C2214yes—
192#2373C2214yes—
193#2370C2212yes—
194#2370C2214yes—
195#2370C2212yes—
196#2369C2212yes—
197#2368C2212yes—
198#2368C2212yes—
199#2367C2212yes—
200#2367C2212yes—
201#2365C2212yes—
202#2365C2212yes—
203#2362C2214yes—
204#2360C2214yes—
205#2360C2212yes—
206#2360C2212yes—
207#2359C2214yes—
208#2355C2212yes—
209#2351C2212yes—
210#2351C2212yes—
211D4×C4⋊C4C2212yes—
212#2346C2214yes—
213#2334C2214yes—
214#2334C2214yes—
215#2330C2212yes—
216#2326C2212yes—
217#2326C2212yes—
218#2324C2212yes—
219#2323C2214yes—
220#2323C2212yes—
221C4×C4⋊Q8C2212yes—
222C4×C4⋊Q8C2211yescharacteristic
223C4×C4⋊Q8C2212yes—
224C4×#125C2211yescharacteristic
225C4×#124C2212yes—
226C4×#124C2212yes—
227C4×#124C2212yes—
228C4×C22⋊Q8C2212yes—
229#2296C2212yes—
230#2295C2212yes—
231#2295C2212yes—
232#2295C2211yescharacteristic
233#2295C2212yes—
234#2295C2212yes—
235#2295C2211yescharacteristic
236#2293C2212yes—
237#2274C2214yes—
238C42×Q8C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2212yes—
242C2×C4×C4⋊C4C2211yescharacteristic
243#556—216no—
244#541—44no—
245#540—44no—
246#533—28no—
247#533—48no—
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×#127C2311yescharacteristic
256#529—48no—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#125C2311yescharacteristic
262C2×#125C2312yes—
263C2×#125C2314yes—
264C2×#125C2311yescharacteristic
265C2×#125C2311yescharacteristic
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2311yescharacteristic
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×#121C2312yes—
286C2×#121C2314yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×#117C2312yes—
304C2×#117C2314yes—
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2314yes—
308C2×#117C2314yes—
309C2×#117C2314yes—
310C22×C4⋊C4C2314yes—
311C22×C4⋊C4C2312yes—
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314#401C2314yes—
315#401C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#397C2314yes—
372#397C2314yes—
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#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2312yes—
450#390C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
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#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2312yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2312yes—
594#385C2312yes—
595#385C2312yes—
596#385C2312yes—
597#385C2314yes—
598#384C2311yescharacteristic
599#384C2312yes—
600#384C2312yes—
601#384C2314yes—
602#382C2311yescharacteristic
603#382C2314yes—
604#382C2314yes—
605#382C2312yes—
606#382C2312yes—
607#382C2314yes—
608#382C2314yes—
609#381C2314yes—
610#381C2314yes—
611#380C2312yes—
612#380C2314yes—
613#380C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2311yescharacteristic
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668#376C2311yescharacteristic
669#376C2312yes—
670#376C2314yes—
671#376C2314yes—
672#376C2312yes—
673#376C2311yescharacteristic
674C2×#95C2311yescharacteristic
675C2×#95C2311yescharacteristic
676C43C2311yescharacteristic
677C43C2312yes—
678C43C2312yes—
679C43C2311yescharacteristic
680C22×Q8C2412yes—
681C22×Q8C2412yes—
682C22×Q8C2411yescharacteristic
683C22×Q8C2412yes—
684C22×Q8C2414yes—
685C22×Q8C2411yescharacteristic
686C22×D4C2412yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2414yes—
693C23×C4C2414yes—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2414yes—
697C4⋊Q8—24no—
698C4⋊Q8—24no—
699C4⋊Q8—28no—
700C4⋊Q8—24no—
701C4⋊Q8—44no—
702C4⋊Q8—44no—
703C4⋊Q8—42no—
704#127—42no—
705#126—216no—
706#126—216no—
707#126—48no—
708#126—48no—
709#125—28no—
710#125—24no—
711#125—48no—
712#125—44no—
713#125—48no—
714#125—42no—
715#125—42no—
716#125—48no—
717#124—28no—
718#124—28no—
719#124—28no—
720#124—44no—
721#123—48no—
722#123—48no—
723#123—48no—
724#123—48no—
725C22⋊Q8—24no—
726C22⋊Q8—216no—
727C22⋊Q8—28no—
728C22⋊Q8—28no—
729C22⋊Q8—24no—
730C22⋊Q8—28no—
731C22⋊Q8—48no—
732C22⋊Q8—48no—
733#121—28no—
734#121—48no—
735C4×Q8—28no—
736C4×Q8—24no—
737C4×Q8—28no—
738C4×Q8—28no—
739C4×Q8—44no—
740C4×Q8—44no—
741C4×Q8—48no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×Q8—44no—
745C4×Q8—44no—
746C4×Q8#4118yes—
747C4×D4—28no—
748C4×D4—44no—
749C4×D4—44no—
750C4×D4—48no—
751#117—24no—
752#117—216no—
753#117—28no—
754#117—24no—
755#117—48no—
756#117—48no—
757#117—48no—
758C2×C4⋊C4—48no—
759C2×C4⋊C4—44no—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C42—28no—
855C2×C42—24no—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2411yescharacteristic
859C2×C42C2412yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2412yes—
865C2×C42C2411yescharacteristic
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2412yes—
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2412yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960C24C2514yes—
961C24C2511yescharacteristic
962C2×Q8—22no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8—42no—
975C2×Q8—42no—
976C2×Q8—44no—
977C2×Q8C2×#4114yes—
978C2×D4—28no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—24no—
990C22×C4—24no—
991C22×C4—22no—
992C22×C4—28no—
993C22×C4—24no—
994C22×C4—22no—
995C22×C4—28no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4—42no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4H(5,𝔽2)14yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2514yes—
1022C22×C4C2514yes—
1023C22×C4C2512yes—
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2512yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2511yescharacteristic
1034C4⋊C4—28no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—22no—
1045C4⋊C4—28no—
1046C4⋊C4—24no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—28no—
1052C4⋊C4—24no—
1053C4⋊C4—28no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—24no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4C2×#4118yes—
1096C4⋊C4C2×#4114yes—
1097C22⋊C4—24no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—24no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C42—22no—
1129C42—22no—
1130C42—22no—
1131C42—24no—
1132C42—28no—
1133C42—28no—
1134C42—24no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—22no—
1139C42—22no—
1140C42—22no—
1141C42—24no—
1142C42—24no—
1143C42—42no—
1144C42—42no—
1145C42—44no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—44no—
1150C42—42no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—42no—
1156C42—42no—
1157C42—42no—
1158C42—42no—
1159C42—44no—
1160C42C2×#4114yes—
1161C42C2×#4118yes—
1162C422−1+414yes—
1163C23—21no—
1164C23—21no—
1165C23—22no—
1166C23—22no—
1167C23—24no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—24no—
1173C23—24no—
1174C23C2×H(5,𝔽2)12yes—
1175C23C2611yescharacteristic
1176Q8—44no—
1177Q8—44no—
1178Q8—48no—
1179Q8—48no—
1180Q8—84no—
1181Q8—88no—
1182D4—48no—
1183D4—88no—
1184D4—164no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—28no—
1198C2×C4—24no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—48no—
1248C2×C4—416no—
1249C2×C4—44no—
1250C2×C4—82no—
1251C2×C4—88no—
1252C2×C4—84no—
1253C2×C4—164no—
1254C2×C4C22×#4112yes—
1255C2×C4C22×#4114yes—
1256C2×C4C22×#4112yes—
1257C2×C4C22×#4114yes—
1258C2×C4C22×#4112yes—
1259C2×C4C2×H(5,𝔽2)12yes—
1260C2×C4C2×H(5,𝔽2)12yes—
1261C2×C4C2×2−1+414yes—
1262C2×C4C2×2−1+412yes—
1263C2×C4#58514yes—
1264C22—22no—
1265C22—24no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22C23×#4111yescharacteristic
1277C22C22×H(5,𝔽2)11yescharacteristic
1278C22C22×2−1+411yescharacteristic
1279C22C2×#58512yes—
1280C222−1+612yes—
1281C4—22no—
1282C4—22no—
1283C4—24no—
1284C4—24no—
1285C4—22no—
1286C4—24no—
1287C4—24no—
1288C4—44no—
1289C4—44no—
1290C4—41no—
1291C4—42no—
1292C4—44no—
1293C4—41no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—44no—
1298C4—42no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—44no—
1303C4—42no—
1304C4—44no—
1305C4#352214yes—
1306C2—42no—
1307C2—84no—
1308C2#6268611yescharacteristic
1309C2C2×#352211yescharacteristic
1310C2#6286111yescharacteristic
1311C2#6295412yes—
1312C2#6295612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#540C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42134C2semidirect
2. #42126C2semidirect
3. #41915C2semidirect
4. #41912C2semidirect
5. #41594C2semidirect
6. #41581C2semidirect
7. #39809C2semidirect
8. #39740C2semidirect
9. #39719C2semidirect
10. #39674C2semidirect
11. #39622C2semidirect
13. #37793C2semidirect
14. #37630C2semidirect
15. #37581C2semidirect
16. #37572C2semidirect
17. #36602C2semidirect
18. #36574C2semidirect
19. #36140C2semidirect
20. #35878C2semidirect
21. #35872C2semidirect
23. #35300C2semidirect
24. #34631C2semidirect
25. #34629C2semidirect
26. #34322C2semidirect
27. #34145C2semidirect

Maximal subgroups

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

subgroupindex
#421342
#421262
#419152
#419122
#415942
#415812
#398092
#397402
#397192
#396742
#396222
#377982
#377932
#376302
#375812
#375722
#366022
#365742
#361402
#358782
#358722
#353322
#353002
#346312
#346292
#343222
#341452