Finite Group Databasebeta

← #8095380

Subgroups — #8095380

Order 512.

4171 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53147C211yesmaximal, characteristic, complemented
2#53146C211yesmaximal, characteristic, complemented
3#53136C212yesmaximal
4#53077C211yesmaximal, characteristic, complemented
5#53032C211yesmaximal, characteristic, complemented
6#53013C212yesmaximal, complemented
7#52814C214yesmaximal, complemented
8#52812C214yesmaximal, complemented
9#52805C214yesmaximal, complemented
10#52804C214yesmaximal, complemented
11#46095C214yesmaximal, complemented
12#46079C212yesmaximal, complemented
13#46009C214yesmaximal, complemented
14#46002C212yesmaximal, complemented
15#45934C214yesmaximal
16#45851C214yesmaximal, complemented
17#45671C212yesmaximal, complemented
18#45503C212yesmaximal, complemented
19#35671C212yesmaximal, complemented
20#35671C212yesmaximal, complemented
21#35670C212yesmaximal, complemented
22#35323C211yesmaximal, characteristic, complemented
23#35319C211yesmaximal, characteristic, complemented
24#35209C212yesmaximal, complemented
25#35204C212yesmaximal, complemented
26#34951C212yesmaximal, complemented
27#34881C211yesmaximal, characteristic
28C2×#541C2212yes—
29C2×#541C2211yescharacteristic
30C2×#541C2211yescharacteristic
31C2×#519C2212yes—
32#2868C2211yescharacteristic
33#2865C2214yes—
34#2864C2214yes—
35#2863C2212yes—
36#2860C2214yes—
37#2859C2214yes—
38#2859C2211yescharacteristic
39#2857C2212yes—
40#2857C2211yescharacteristic
41#2851C2211yescharacteristic
42#2845C2214yes—
43#2844C2214yes—
44#2843C2214yes—
45#2841C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2839C2214yes—
51#2838C2214yes—
52#2838C2214yes—
53#2837C2214yes—
54#2836C2214yes—
55#2836C2214yes—
56#2836C2214yes—
57#2836C2214yes—
58#2836C2214yes—
59#2835C2214yes—
60#2830C2214yes—
61#2827C2214yes—
62#2807C2214yes—
63#2807C2214yes—
64#2802C2214yes—
65#2802C2214yes—
66#2802C2214yes—
67#2802C2214yes—
68#2802C2214yes—
69#2798C2214yes—
70#2797C2214yes—
71#2796C2214yes—
72#2794C2214yes—
73#2792C2214yes—
74#2792C2214yes—
75#2792C2214yes—
76#2792C2214yes—
77#2792C2214yes—
78#2792C2214yes—
79#2791C2214yes—
80#2791C2214yes—
81#2790C2214yes—
82#2790C2214yes—
83#2790C2214yes—
84#2790C2214yes—
85#2786C2214yes—
86#2783C2214yes—
87#2782C2214yes—
88#2777C2214yes—
89#2776C2214yes—
90#2773C2214yes—
91#2772C2214yes—
92#2768C2214yes—
93#2766C2214yes—
94#2763C2214yes—
95#2755C2214yes—
96#2754C2214yes—
97#2748C2214yes—
98#2742C2214yes—
99#2739C2214yes—
100#2721C2214yes—
101#2694C2214yes—
102#2664C2214yes—
103#2664C2214yes—
104#2655C2214yes—
105#2654C2214yes—
106#2647C2211yescharacteristic
107#2642C2211yescharacteristic
108#2642C2211yescharacteristic
109#2642C2211yescharacteristic
110#2625C2212yes—
111#2621C2212yes—
112#2611C2214yes—
113#2611C2214yes—
114#2604C2214yes—
115#2604C2214yes—
116#2601C2214yes—
117#2601C2214yes—
118#2596C2214yes—
119#2593C2212yes—
120#2590C2214yes—
121#2590C2214yes—
122#2585C2212yes—
123#2585C2214yes—
124#2585C2214yes—
125#2584C2214yes—
126#2584C2214yes—
127#2582C2212yes—
128#2577C2214yes—
129#2573C2212yes—
130#2568C2212yes—
131#2565C2212yes—
132#2565C2212yes—
133#2554C2212yes—
134#2552C2212yes—
135#2552C2212yes—
136#2546C2212yes—
137#2546C2212yes—
138#2546C2212yes—
139#2546C2212yes—
140#2542C2212yes—
141#2538C2212yes—
142#2533C2214yes—
143#2530C2214yes—
144#2529C2214yes—
145#2528C2214yes—
146#2525C2212yes—
147#2519C2214yes—
148#2519C2214yes—
149#2516C2212yes—
150#2512C2214yes—
151#2511C2212yes—
152#2511C2212yes—
153#2511C2212yes—
154#2509C2214yes—
155#2508C2212yes—
156#2506C2214yes—
157#2506C2214yes—
158#2506C2214yes—
159#2499C2212yes—
160#2499C2212yes—
161#2496C2214yes—
162#2496C2214yes—
163#2494C2212yes—
164#2489C2212yes—
165#2489C2212yes—
166#2489C2212yes—
167#2479C2214yes—
168#2479C2214yes—
169#2478C2214yes—
170#2478C2214yes—
171#2478C2214yes—
172#2478C2214yes—
173#2475C2214yes—
174#2475C2214yes—
175#2469C2214yes—
176#2469C2212yes—
177#2469C2214yes—
178#2462C2214yes—
179#2462C2214yes—
180#2462C2214yes—
181#2462C2214yes—
182#2462C2214yes—
183#2462C2214yes—
184#2458C2212yes—
185#2453C2214yes—
186#2453C2212yes—
187#2453C2212yes—
188#2453C2212yes—
189#2446C2212yes—
190#2446C2212yes—
191#2446C2212yes—
192#2446C2212yes—
193#2446C2212yes—
194#2441C2212yes—
195#2441C2212yes—
196#2434C2212yes—
197#2434C2212yes—
198#2434C2212yes—
199#2434C2212yes—
200#2429C2212yes—
201#2429C2212yes—
202#2429C2212yes—
203#2429C2212yes—
204#2429C2212yes—
205#2423C2212yes—
206#2423C2212yes—
207#2423C2212yes—
208#2415C2212yes—
209#2415C2212yes—
210#2409C2212yes—
211#2409C2212yes—
212#2402C2211yescharacteristic
213#2402C2214yes—
214#2402C2214yes—
215#2398C2211yescharacteristic
216#2396C2211yescharacteristic
217#2392C2211yescharacteristic
218#2383C2214yes—
219#2382C2214yes—
220#2382C2214yes—
221#2376C2214yes—
222#2330C2211yescharacteristic
223#2327C2211yescharacteristic
224#2327C2212yes—
225#2323C2212yes—
226#2323C2212yes—
227#2323C2212yes—
228C4×C4⋊Q8C2212yes—
229C4×C4⋊Q8C2212yes—
230C4×C4⋊Q8C2212yes—
231C4×#125C2214yes—
232C4×#126C2212yes—
233C4×#123C2212yes—
234#2298C2212yes—
235#2295C2214yes—
236#2295C2212yes—
237#2295C2212yes—
238#2293C2211yescharacteristic
239#2293C2212yes—
240C42×Q8C2211yescharacteristic
241C42×Q8C2212yes—
242C4×#117C2211yescharacteristic
243C23×Q8C2312yes—
244#541—48no—
245#541—44no—
246#541—44no—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2312yes—
255C2×#126C2312yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#125C2314yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2311yescharacteristic
265C2×#125C2311yescharacteristic
266C2×#125C2311yescharacteristic
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#123C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277#519—48no—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2314yes—
288C2×C4×Q8C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×#117C2312yes—
292C2×#117C2311yescharacteristic
293C2×#117C2314yes—
294C2×#117C2314yes—
295C2×#117C2311yescharacteristic
296C2×#117C2312yes—
297C22×C42C2311yescharacteristic
298#401C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2312yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2311yescharacteristic
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#399C2314yes—
332#399C2311yescharacteristic
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
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#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2311yescharacteristic
373#398C2314yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2311yescharacteristic
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2311yescharacteristic
420#394C2311yescharacteristic
421#394C2314yes—
422#394C2312yes—
423#394C2314yes—
424#394C2312yes—
425#393C2314yes—
426#393C2314yes—
427#393C2311yescharacteristic
428#393C2312yes—
429#392C2311yescharacteristic
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#390C2314yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
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#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2312yes—
536#388C2314yes—
537#388C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2312yes—
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#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
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#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2312yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#384C2312yes—
615#384C2312yes—
616#384C2312yes—
617#384C2311yescharacteristic
618#384C2314yes—
619#384C2314yes—
620#384C2314yes—
621#384C2314yes—
622#383C2312yes—
623#383C2314yes—
624#382C2314yes—
625#382C2311yescharacteristic
626#382C2312yes—
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#382C2314yes—
631#381C2312yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670#376C2311yescharacteristic
671#376C2314yes—
672#376C2314yes—
673#376C2311yescharacteristic
674C43C2311yescharacteristic
675C43C2314yes—
676C43C2311yescharacteristic
677C43C2312yes—
678C22×Q8—44no—
679C22×Q8—44no—
680C22×Q8—44no—
681C22×Q8C2412yes—
682C22×Q8C2412yes—
683C22×Q8C2412yes—
684C22×Q8C2411yescharacteristic
685C22×Q8C2414yes—
686C22×D4C2412yes—
687C22×D4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2414yes—
692C4⋊Q8—42no—
693C4⋊Q8—44no—
694C4⋊Q8—44no—
695C4⋊Q8—44no—
696C4⋊Q8—44no—
697C4⋊Q8—44no—
698C4⋊Q8—42no—
699C4⋊Q8—42no—
700#126—28no—
701#126—48no—
702#126—48no—
703#126—48no—
704#126—48no—
705#125—216no—
706#125—42no—
707#125—44no—
708#125—42no—
709#125—42no—
710#125—48no—
711#125—48no—
712#125—48no—
713#125—48no—
714#123—28no—
715C22⋊Q8—44no—
716C22⋊Q8—44no—
717C22⋊Q8—44no—
718C22⋊Q8—44no—
719C22⋊Q8—44no—
720C22⋊Q8—44no—
721C22⋊Q8—44no—
722C4×Q8—28no—
723C4×Q8—28no—
724C4×Q8—28no—
725C4×Q8—28no—
726C4×Q8—42no—
727C4×Q8—48no—
728C4×Q8—48no—
729C4×Q8—44no—
730C4×Q8—44no—
731C4×Q8—44no—
732C4×Q8—44no—
733C4×D4—42no—
734C4×D4—44no—
735#117—28no—
736#117—24no—
737#117—42no—
738#117—48no—
739#117—48no—
740#117—44no—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C42—42no—
842C2×C42C2411yescharacteristic
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2411yescharacteristic
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2411yescharacteristic
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2411yescharacteristic
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2411yescharacteristic
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2414yes—
917#95C2414yes—
918#95C2411yescharacteristic
919#95C2411yescharacteristic
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946C24C2511yescharacteristic
947C24C2512yes—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—44no—
959C2×Q8—41no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—432no—
963C2×D4—24no—
964C2×D4—42no—
965C2×D4—41no—
966C2×D4—42no—
967C2×D4—42no—
968C22×C4—24no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2514yes—
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2511yescharacteristic
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—28no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—42no—
1038C4⋊C4—44no—
1039C4⋊C4—42no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—41no—
1046C4⋊C4—42no—
1047C4⋊C4—41no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C42−1+418yes—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—24no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—24no—
1083C22⋊C4—24no—
1084C22⋊C4—24no—
1085C22⋊C4—42no—
1086C22⋊C4—44no—
1087C22⋊C4—42no—
1088C22⋊C4—44no—
1089C22⋊C4—42no—
1090C22⋊C4—44no—
1091C22⋊C4—42no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—44no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C42—24no—
1106C42—22no—
1107C42—28no—
1108C42—28no—
1109C42—28no—
1110C42—24no—
1111C42—24no—
1112C42—24no—
1113C42—28no—
1114C42—24no—
1115C42—22no—
1116C42—22no—
1117C42—22no—
1118C42—22no—
1119C42—24no—
1120C42—24no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C42—44no—
1125C42—42no—
1126C42—44no—
1127C42—42no—
1128C42—44no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C42H(5,𝔽2)14yes—
1134C23—21no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—21no—
1140C23—22no—
1141C23—22no—
1142C23—21no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23C2611yescharacteristic
1147Q8—44no—
1148Q8—416no—
1149Q8—48no—
1150Q8—48no—
1151Q8—48no—
1152D4—84no—
1153D4—82no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—21no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—416no—
1219C2×C4—44no—
1220C2×C4—48no—
1221C2×C4—84no—
1222C2×C4C2×H(5,𝔽2)14yes—
1223C2×C4C2×H(5,𝔽2)12yes—
1224C2×C4C2×2−1+414yes—
1225C2×C4C2×2−1+414yes—
1226C2×C4C2×2−1+414yes—
1227C2×C4#58512yes—
1228C2×C4#58512yes—
1229C22—42no—
1230C22—41no—
1231C22—42no—
1232C22—41no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—41no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22C22×H(5,𝔽2)11yescharacteristic
1242C22C22×2−1+412yes—
1243C22C2×#58511yescharacteristic
1244C22C2×#58511yescharacteristic
1245C222−1+612yes—
1246C4—24no—
1247C4—24no—
1248C4—24no—
1249C4—24no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—42no—
1254C4—44no—
1255C4—41no—
1256C4—42no—
1257C4—42no—
1258C4—44no—
1259C4—44no—
1260C4—42no—
1261C4—44no—
1262C4—41no—
1263C4—44no—
1264C4—44no—
1265C4—42no—
1266C4—44no—
1267C4—42no—
1268C4—44no—
1269C4—42no—
1270C4#352914yes—
1271C2—82no—
1272C2—81no—
1273C2C2×#352911yescharacteristic
1274C2#6283711yescharacteristic
1275C2#6289011yescharacteristic
1276C2#6294612yes—
1277C2#6295012yes—
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. #53147C2semidirect
2. #53146C2semidirect
4. #53077C2semidirect
5. #53032C2semidirect
6. #53013C2semidirect
7. #52814C2semidirect
8. #52812C2semidirect
9. #52805C2semidirect
10. #52804C2semidirect
11. #46095C2semidirect
12. #46079C2semidirect
13. #46009C2semidirect
14. #46002C2semidirect
16. #45851C2semidirect
17. #45671C2semidirect
18. #45503C2semidirect
19. #35671C2semidirect
20. #35671C2semidirect
21. #35670C2semidirect
22. #35323C2semidirect
23. #35319C2semidirect
24. #35209C2semidirect
25. #35204C2semidirect
26. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#531472
#531462
#531362
#530772
#530322
#530132
#528142
#528122
#528052
#528042
#460952
#460792
#460092
#460022
#459342
#458512
#456712
#455032
#356712
#356702
#353232
#353192
#352092
#352042
#349512
#348812