Finite Group Databasebeta

← #7652272

Subgroups — #7652272

Order 512.

4548 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42941C211yesmaximal, characteristic, complemented
2#42937C211yesmaximal, characteristic
3#42851C212yesmaximal, complemented
4#42850C212yesmaximal, complemented
5#42818C211yesmaximal, characteristic, complemented
6#42807C211yesmaximal, characteristic
7#42292C214yesmaximal, complemented
8#42287C214yesmaximal, complemented
9#42245C214yesmaximal, complemented
10#42213C214yesmaximal, complemented
11#40257C214yesmaximal
12#40201C212yesmaximal, complemented
13#39913C212yesmaximal, complemented
14#39703C214yesmaximal, complemented
15#39663C212yesmaximal, complemented
16#39593C212yesmaximal, complemented
17#38887C214yesmaximal, complemented
18#38748C214yesmaximal, complemented
19#35671C212yesmaximal, complemented
20#35671C212yesmaximal, complemented
21#35670C212yesmaximal, complemented
22#35324C211yesmaximal, characteristic, complemented
23#35217C212yesmaximal, complemented
24#34951C212yesmaximal, complemented
25#34881C211yesmaximal, characteristic
26#34311C212yesmaximal, complemented
27#34209C211yesmaximal, characteristic, complemented
28C2×D4×Q8C2212yes—
29C2×#541C2212yes—
30C22×C4⋊Q8C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2212yes—
33C2×#519C2211yescharacteristic
34#2866C2214yes—
35#2864C2211yescharacteristic
36#2863C2214yes—
37#2862C2211yescharacteristic
38#2855C2212yes—
39#2841C2212yes—
40#2839C2214yes—
41#2833C2212yes—
42#2832C2212yes—
43#2831C2214yes—
44#2817C2212yes—
45#2810C2214yes—
46#2809C2212yes—
47#2806C2214yes—
48#2806C2214yes—
49#2805C2214yes—
50#2802C2214yes—
51#2799C2212yes—
52#2794C2214yes—
53#2791C2214yes—
54#2791C2214yes—
55#2788C2214yes—
56#2787C2214yes—
57#2781C2214yes—
58#2777C2214yes—
59#2776C2214yes—
60#2774C2214yes—
61#2771C2212yes—
62#2771C2212yes—
63#2768C2214yes—
64#2765C2214yes—
65#2764C2212yes—
66#2759C2214yes—
67#2752C2212yes—
68#2751C2214yes—
69#2740C2214yes—
70#2739C2214yes—
71#2738C2214yes—
72#2734C2212yes—
73#2734C2214yes—
74#2734C2214yes—
75#2729C2214yes—
76#2729C2214yes—
77#2729C2214yes—
78#2728C2212yes—
79#2721C2214yes—
80#2694C2214yes—
81#2667C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2655C2214yes—
86#2655C2214yes—
87#2655C2214yes—
88#2654C2214yes—
89#2654C2214yes—
90#2650C2214yes—
91#2650C2214yes—
92#2649C2214yes—
93#2645C2212yes—
94#2638C2214yes—
95#2628C2211yescharacteristic
96#2627C2214yes—
97#2621C2211yescharacteristic
98#2611C2214yes—
99#2611C2214yes—
100#2607C2212yes—
101#2604C2214yes—
102#2604C2214yes—
103#2601C2214yes—
104#2601C2214yes—
105#2600C2212yes—
106#2596C2214yes—
107#2594C2214yes—
108#2594C2214yes—
109#2593C2212yes—
110#2590C2214yes—
111#2590C2214yes—
112#2589C2214yes—
113#2589C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2586C2212yes—
117#2586C2214yes—
118#2586C2212yes—
119#2585C2214yes—
120#2585C2212yes—
121#2585C2214yes—
122#2585C2214yes—
123#2584C2214yes—
124#2584C2214yes—
125#2583C2214yes—
126#2582C2212yes—
127#2579C2214yes—
128#2575C2214yes—
129#2573C2212yes—
130#2568C2212yes—
131#2565C2212yes—
132#2565C2212yes—
133#2554C2212yes—
134#2552C2212yes—
135#2546C2212yes—
136#2546C2212yes—
137#2546C2212yes—
138#2533C2214yes—
139#2532C2214yes—
140#2528C2214yes—
141#2527C2214yes—
142#2525C2212yes—
143#2516C2212yes—
144#2514C2212yes—
145#2511C2212yes—
146#2511C2212yes—
147#2509C2214yes—
148#2509C2212yes—
149#2499C2212yes—
150#2499C2212yes—
151#2495C2212yes—
152#2492C2212yes—
153#2479C2214yes—
154#2479C2214yes—
155#2478C2214yes—
156#2478C2214yes—
157#2478C2214yes—
158#2478C2214yes—
159#2475C2214yes—
160#2475C2214yes—
161#2469C2214yes—
162#2469C2212yes—
163#2469C2214yes—
164#2462C2214yes—
165#2462C2214yes—
166#2462C2214yes—
167#2462C2214yes—
168#2462C2214yes—
169#2462C2214yes—
170#2458C2212yes—
171#2453C2212yes—
172#2453C2212yes—
173#2453C2214yes—
174#2451C2212yes—
175#2446C2212yes—
176#2446C2212yes—
177#2446C2212yes—
178#2446C2212yes—
179#2446C2212yes—
180#2441C2212yes—
181#2441C2212yes—
182#2434C2212yes—
183#2434C2212yes—
184#2434C2212yes—
185#2434C2212yes—
186#2429C2212yes—
187#2429C2212yes—
188#2429C2212yes—
189#2423C2212yes—
190#2423C2212yes—
191#2421C2212yes—
192#2415C2212yes—
193#2415C2212yes—
194#2409C2212yes—
195#2409C2212yes—
196#2402C2214yes—
197#2402C2214yes—
198#2402C2211yescharacteristic
199#2398C2211yescharacteristic
200#2396C2211yescharacteristic
201#2392C2211yescharacteristic
202#2365C2214yes—
203#2365C2212yes—
204#2365C2214yes—
205#2365C2214yes—
206#2362C2214yes—
207#2362C2212yes—
208#2362C2214yes—
209#2362C2212yes—
210#2354C2214yes—
211#2354C2212yes—
212Q8×C4⋊C4C2212yes—
213#2344C2214yes—
214#2344C2214yes—
215Q8×C22⋊C4C2212yes—
216Q8×C22⋊C4C2212yes—
217#2336C2214yes—
218#2336C2214yes—
219#2334C2214yes—
220#2331C2211yescharacteristic
221#2327C2211yescharacteristic
222#2327C2212yes—
223#2327C2212yes—
224#2323C2214yes—
225#2323C2214yes—
226#2323C2212yes—
227#2323C2212yes—
228#2323C2212yes—
229#2322C2214yes—
230#2310C2211yescharacteristic
231#2310C2211yescharacteristic
232C4×C4⋊Q8C2214yes—
233C4×C4⋊Q8C2212yes—
234C4×C4⋊Q8C2212yes—
235C4×C4⋊Q8C2212yes—
236C4×C4⋊Q8C2212yes—
237C4×#125C2214yes—
238C4×#126C2212yes—
239C4×#123C2212yes—
240#2298C2212yes—
241#2295C2212yes—
242#2295C2212yes—
243#2295C2214yes—
244#2293C2212yes—
245#2293C2214yes—
246#2293C2211yescharacteristic
247#2285C2211yescharacteristic
248C42×Q8C2212yes—
249C42×Q8C2211yescharacteristic
250C4×#117C2211yescharacteristic
251C23×Q8C2311yescharacteristic
252C23×Q8C2312yes—
253C23×Q8C2311yescharacteristic
254D4×Q8—216no—
255#541—48no—
256C2×C4⋊Q8—28no—
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2314yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×#126C2312yes—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#125C2314yes—
270C2×#125C2312yes—
271C2×#125C2314yes—
272C2×#125C2314yes—
273C2×#123C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281#519—44no—
282#519—44no—
283#519—48no—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2311yescharacteristic
302C2×#117C2311yescharacteristic
303C2×#117C2312yes—
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2314yes—
308C2×#117C2314yes—
309C2×#117C2314yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C22×C4⋊C4C2314yes—
313C22×C42C2311yescharacteristic
314#401C2314yes—
315#401C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2311yescharacteristic
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2312yes—
343#399C2312yes—
344#399C2311yescharacteristic
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2311yescharacteristic
368#398C2312yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#397C2311yescharacteristic
383#397C2312yes—
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2312yes—
393#397C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2312yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2311yescharacteristic
412#395C2314yes—
413#395C2314yes—
414#394C2311yescharacteristic
415#394C2314yes—
416#394C2312yes—
417#394C2314yes—
418#394C2312yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2312yes—
423#393C2312yes—
424#393C2311yescharacteristic
425#392C2311yescharacteristic
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2312yes—
455#391C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2312yes—
506#388C2312yes—
507#388C2312yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2312yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2312yes—
528#388C2312yes—
529#388C2312yes—
530#388C2312yes—
531#388C2314yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2314yes—
539#388C2314yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2312yes—
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#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2314yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#384C2312yes—
623#384C2312yes—
624#384C2312yes—
625#384C2314yes—
626#383C2312yes—
627#383C2314yes—
628#383C2314yes—
629#382C2314yes—
630#382C2311yescharacteristic
631#382C2312yes—
632#382C2314yes—
633#382C2311yescharacteristic
634#381C2312yes—
635#381C2312yes—
636#381C2312yes—
637#381C2312yes—
638#381C2312yes—
639#381C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2312yes—
643#380C2314yes—
644#380C2312yes—
645#380C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688#376C2311yescharacteristic
689#376C2311yescharacteristic
690#376C2314yes—
691#376C2314yes—
692C43C2311yescharacteristic
693C43C2314yes—
694C43C2311yescharacteristic
695C43C2312yes—
696C22×Q8—28no—
697C22×Q8—24no—
698C22×Q8—42no—
699C22×Q8—42no—
700C22×Q8—44no—
701C22×Q8—42no—
702C22×Q8—42no—
703C22×Q8—44no—
704C22×Q8#4118yes—
705C22×Q8C2412yes—
706C22×Q8C2412yes—
707C22×Q8C2411yescharacteristic
708C22×Q8C2412yes—
709C22×Q8C2414yes—
710C22×Q8C2412yes—
711C22×Q8C2412yes—
712C22×Q8C2412yes—
713C22×D4C2412yes—
714C22×D4C2411yescharacteristic
715C23×C4C2412yes—
716C23×C4C2412yes—
717C23×C4C2411yescharacteristic
718C23×C4C2412yes—
719C23×C4C2414yes—
720C23×C4C2412yes—
721C4⋊Q8—28no—
722C4⋊Q8—28no—
723C4⋊Q8—216no—
724C4⋊Q8—28no—
725C4⋊Q8—216no—
726C4⋊Q8—42no—
727C4⋊Q8—42no—
728C4⋊Q8—44no—
729C4⋊Q8—44no—
730#126—28no—
731#126—48no—
732#126—48no—
733#125—216no—
734#125—44no—
735#125—48no—
736#125—48no—
737#123—28no—
738C22⋊Q8—28no—
739C22⋊Q8—216no—
740C22⋊Q8—28no—
741C22⋊Q8—216no—
742C22⋊Q8—44no—
743C22⋊Q8—44no—
744C22⋊Q8—44no—
745C4×Q8—28no—
746C4×Q8—28no—
747C4×Q8—28no—
748C4×Q8—28no—
749C4×Q8—28no—
750C4×Q8—42no—
751C4×Q8—48no—
752C4×Q8—48no—
753C4×Q8—48no—
754C4×Q8—48no—
755C4×Q8—44no—
756C4×Q8—44no—
757C4×Q8—44no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×D4—28no—
761C4×D4—216no—
762C4×D4—42no—
763#117—24no—
764#117—28no—
765#117—42no—
766#117—48no—
767#117—48no—
768#117—48no—
769#117—48no—
770#117—42no—
771#117—44no—
772#117—42no—
773C2×C4⋊C4—216no—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2411yescharacteristic
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C42—24no—
871C2×C42C2414yes—
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2411yescharacteristic
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2411yescharacteristic
934#95C2414yes—
935#95C2414yes—
936#95C2411yescharacteristic
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2411yescharacteristic
970#95C2411yescharacteristic
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982C24C2512yes—
983C24C2511yescharacteristic
984C2×Q8—28no—
985C2×Q8—24no—
986C2×Q8—24no—
987C2×Q8—24no—
988C2×Q8—24no—
989C2×Q8—24no—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—24no—
995C2×Q8—42no—
996C2×Q8—44no—
997C2×Q8—42no—
998C2×Q8—41no—
999C2×Q8—42no—
1000C2×Q8—44no—
1001C2×Q8—42no—
1002C2×Q8—42no—
1003C2×Q8—44no—
1004C2×Q8—416no—
1005C2×Q8—416no—
1006C2×Q8—432no—
1007C2×Q8C2×#4118yes—
1008C2×Q8C2×#4118yes—
1009C2×D4—24no—
1010C2×D4—24no—
1011C2×D4—42no—
1012C2×D4—41no—
1013C2×D4—42no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—28no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4C2×#4114yes—
1031C22×C4C2×#4118yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C4⋊C4—28no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—28no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—41no—
1102C4⋊C4—41no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—41no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—41no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C42−1+418yes—
1124C22⋊C4—28no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—28no—
1128C22⋊C4—24no—
1129C22⋊C4—24no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—24no—
1136C22⋊C4—24no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
1144C22⋊C4—41no—
1145C22⋊C4—41no—
1146C22⋊C4—42no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C42—22no—
1154C42—24no—
1155C42—22no—
1156C42—28no—
1157C42—24no—
1158C42—22no—
1159C42—24no—
1160C42—28no—
1161C42—28no—
1162C42—28no—
1163C42—24no—
1164C42—24no—
1165C42—24no—
1166C42—28no—
1167C42—24no—
1168C42—22no—
1169C42—22no—
1170C42—24no—
1171C42—42no—
1172C42—42no—
1173C42—42no—
1174C42—44no—
1175C42—44no—
1176C42—42no—
1177C42—44no—
1178C42—44no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42H(5,𝔽2)14yes—
1186C23—21no—
1187C23—22no—
1188C23—21no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23C22×#4112yes—
1198C23C2611yescharacteristic
1199Q8—216no—
1200Q8—48no—
1201Q8—44no—
1202Q8—48no—
1203Q8—416no—
1204Q8—48no—
1205Q8—48no—
1206Q8—162no—
1207D4—48no—
1208D4—82no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—28no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—48no—
1273C2×C4—48no—
1274C2×C4—416no—
1275C2×C4—48no—
1276C2×C4—48no—
1277C2×C4C22×#4112yes—
1278C2×C4C22×#4118yes—
1279C2×C4C22×#4112yes—
1280C2×C4C2×H(5,𝔽2)14yes—
1281C2×C4C2×H(5,𝔽2)12yes—
1282C2×C4C2×2−1+414yes—
1283C2×C4C2×2−1+414yes—
1284C2×C4C2×2−1+414yes—
1285C2×C4#58512yes—
1286C22—24no—
1287C22—22no—
1288C22—41no—
1289C22—41no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22C23×#4111yescharacteristic
1299C22C22×H(5,𝔽2)11yescharacteristic
1300C22C22×2−1+412yes—
1301C22C2×#58511yescharacteristic
1302C222−1+612yes—
1303C4—24no—
1304C4—24no—
1305C4—24no—
1306C4—22no—
1307C4—28no—
1308C4—24no—
1309C4—42no—
1310C4—44no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—42no—
1315C4—41no—
1316C4—44no—
1317C4—41no—
1318C4—44no—
1319C4—42no—
1320C4—44no—
1321C4—42no—
1322C4—44no—
1323C4—42no—
1324C4—42no—
1325C4—44no—
1326C4—44no—
1327C4#345914yes—
1328C2—42no—
1329C2—82no—
1330C2C2×#345911yescharacteristic
1331C2#6283711yescharacteristic
1332C2#6289111yescharacteristic
1333C2#6294612yes—
1334C2#6299812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42941C2semidirect
3. #42851C2semidirect
4. #42850C2semidirect
5. #42818C2semidirect
7. #42292C2semidirect
8. #42287C2semidirect
9. #42245C2semidirect
10. #42213C2semidirect
12. #40201C2semidirect
13. #39913C2semidirect
14. #39703C2semidirect
15. #39663C2semidirect
16. #39593C2semidirect
17. #38887C2semidirect
18. #38748C2semidirect
19. #35671C2semidirect
20. #35671C2semidirect
21. #35670C2semidirect
22. #35324C2semidirect
23. #35217C2semidirect
24. #34951C2semidirect
26. #34311C2semidirect
27. #34209C2semidirect

Maximal subgroups

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

subgroupindex
#429412
#429372
#428512
#428502
#428182
#428072
#422922
#422872
#422452
#422132
#402572
#402012
#399132
#397032
#396632
#395932
#388872
#387482
#356712
#356702
#353242
#352172
#349512
#348812
#343112
#342092