Finite Group Databasebeta

← #8096610

Subgroups — #8096610

Order 512.

3881 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53140C212yesmaximal, complemented
2#53050C212yesmaximal
3#53028C212yesmaximal, complemented
4#52784C214yesmaximal, complemented
5#52709C214yesmaximal
6#52458C214yesmaximal, complemented
7#52306C211yesmaximal, characteristic
8#52272C212yesmaximal
9#46344C212yesmaximal, complemented
10#46283C212yesmaximal, complemented
11#46218C214yesmaximal, complemented
12#46157C211yesmaximal, characteristic, complemented
13#46051C212yesmaximal, complemented
14#46051C212yesmaximal, complemented
15#46023C211yesmaximal, characteristic
16#46006C211yesmaximal, characteristic, complemented
17#45963C212yesmaximal
18#45941C212yesmaximal, complemented
19#45883C214yesmaximal, complemented
20#45859C214yesmaximal, complemented
21#36554C212yesmaximal, complemented
22#36497C211yesmaximal, characteristic, complemented
23#36408C212yesmaximal, complemented
24#36313C211yesmaximal, characteristic, complemented
25#36299C211yesmaximal, characteristic
26#36286C212yesmaximal, complemented
27#35843C212yesmaximal, complemented
28#35789C212yesmaximal, complemented
29#35726C212yesmaximal
30#2864C2214yes—
31#2864C2212yes—
32#2863C2212yes—
33#2863C2212yes—
34#2863C2214yes—
35#2863C2214yes—
36#2863C2212yes—
37#2863C2212yes—
38#2862C2211yescharacteristic
39#2862C2212yes—
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2844C2212yes—
43#2843C2214yes—
44#2839C2214yes—
45#2839C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2838C2214yes—
49#2836C2214yes—
50#2836C2214yes—
51#2831C2214yes—
52#2831C2214yes—
53#2831C2214yes—
54#2831C2214yes—
55#2831C2214yes—
56#2831C2214yes—
57#2830C2214yes—
58#2822C2212yes—
59#2820C2212yes—
60#2810C2212yes—
61#2809C2211yescharacteristic
62#2808C2212yes—
63#2806C2212yes—
64#2806C2214yes—
65#2805C2212yes—
66#2802C2214yes—
67#2800C2214yes—
68#2799C2214yes—
69#2799C2214yes—
70#2798C2214yes—
71#2793C2214yes—
72#2791C2214yes—
73#2783C2214yes—
74#2777C2214yes—
75#2776C2214yes—
76#2775C2212yes—
77#2775C2214yes—
78#2775C2214yes—
79#2775C2212yes—
80#2774C2214yes—
81#2772C2214yes—
82#2772C2214yes—
83#2769C2214yes—
84#2769C2212yes—
85#2769C2214yes—
86#2767C2214yes—
87#2766C2214yes—
88#2762C2214yes—
89#2762C2214yes—
90#2762C2214yes—
91#2759C2214yes—
92#2759C2214yes—
93#2758C2214yes—
94#2758C2214yes—
95#2758C2214yes—
96#2755C2214yes—
97#2755C2214yes—
98#2754C2214yes—
99#2734C2211yescharacteristic
100#2734C2212yes—
101#2731C2212yes—
102#2727C2211yescharacteristic
103#2727C2211yescharacteristic
104#2726C2212yes—
105#2721C2212yes—
106#2721C2212yes—
107#2719C2214yes—
108#2716C2214yes—
109#2716C2214yes—
110#2713C2214yes—
111#2713C2214yes—
112#2665C2214yes—
113#2652C2214yes—
114#2652C2214yes—
115#2629C2212yes—
116#2625C2212yes—
117#2621C2212yes—
118#2608C2214yes—
119#2605C2214yes—
120#2605C2214yes—
121#2590C2214yes—
122#2590C2214yes—
123#2589C2214yes—
124#2589C2214yes—
125#2588C2214yes—
126#2588C2214yes—
127#2588C2214yes—
128#2586C2214yes—
129#2585C2214yes—
130#2585C2214yes—
131#2585C2214yes—
132#2584C2212yes—
133#2582C2211yescharacteristic
134#2581C2212yes—
135#2581C2212yes—
136#2577C2214yes—
137#2574C2214yes—
138#2573C2214yes—
139#2570C2212yes—
140#2570C2212yes—
141#2570C2212yes—
142#2570C2212yes—
143#2568C2212yes—
144#2568C2212yes—
145#2568C2211yescharacteristic
146#2567C2212yes—
147#2552C2211yescharacteristic
148#2551C2212yes—
149#2551C2211yescharacteristic
150#2550C2212yes—
151#2546C2211yescharacteristic
152#2538C2211yescharacteristic
153#2533C2214yes—
154#2533C2214yes—
155#2528C2214yes—
156#2528C2214yes—
157#2524C2214yes—
158#2524C2214yes—
159#2524C2214yes—
160#2523C2214yes—
161#2523C2214yes—
162#2522C2214yes—
163#2520C2214yes—
164#2520C2214yes—
165#2520C2214yes—
166#2517C2214yes—
167#2515C2214yes—
168#2515C2214yes—
169#2514C2212yes—
170#2514C2212yes—
171#2514C2212yes—
172#2511C2212yes—
173#2511C2212yes—
174#2511C2214yes—
175#2509C2212yes—
176#2509C2212yes—
177#2508C2212yes—
178#2508C2212yes—
179#2507C2212yes—
180#2506C2212yes—
181#2499C2212yes—
182#2499C2212yes—
183#2495C2212yes—
184#2495C2212yes—
185#2492C2212yes—
186#2492C2212yes—
187#2489C2212yes—
188#2478C2214yes—
189#2475C2214yes—
190#2462C2214yes—
191#2460C2214yes—
192#2453C2212yes—
193#2453C2212yes—
194#2453C2214yes—
195#2453C2212yes—
196#2451C2212yes—
197#2451C2212yes—
198#2451C2214yes—
199#2447C2212yes—
200#2446C2214yes—
201#2446C2212yes—
202#2446C2212yes—
203#2446C2212yes—
204#2439C2212yes—
205#2439C2214yes—
206#2439C2212yes—
207#2439C2212yes—
208#2429C2212yes—
209#2429C2212yes—
210#2423C2212yes—
211#2421C2212yes—
212#2421C2212yes—
213#2415C2212yes—
214#2401C2214yes—
215#2398C2214yes—
216#2396C2214yes—
217#2396C2212yes—
218#2396C2212yes—
219#2395C2212yes—
220#2382C2214yes—
221#2382C2212yes—
222#2382C2212yes—
223#2382C2212yes—
224#2381C2214yes—
225#2381C2214yes—
226#2370C2212yes—
227#2369C2212yes—
228#2365C2211yescharacteristic
229#2365C2211yescharacteristic
230#2365C2212yes—
231#2365C2212yes—
232#2360C2212yes—
233#2360C2212yes—
234#2360C2212yes—
235#2356C2212yes—
236#2356C2212yes—
237#2355C2212yes—
238#2355C2211yescharacteristic
239#2355C2211yescharacteristic
240#2355C2211yescharacteristic
241D4×C4⋊C4C2211yescharacteristic
242#2345C2212yes—
243#2344C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×#125C2211yescharacteristic
247C4×#125C2211yescharacteristic
248C4×#126C2214yes—
249C4×#126C2212yes—
250C4×#126C2212yes—
251C4×#124C2211yescharacteristic
252#2298C2214yes—
253#2295C2214yes—
254#2295C2212yes—
255#2293C2212yes—
256#2274C2212yes—
257C42×Q8C2212yes—
258C42×Q8C2211yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2314yes—
267C2×#126C2312yes—
268C2×#126C2312yes—
269C2×#125C2311yescharacteristic
270C2×#125C2311yescharacteristic
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2311yescharacteristic
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×#117C2314yes—
292C2×#117C2312yes—
293C2×#117C2312yes—
294C22×C4⋊C4C2312yes—
295#401C2314yes—
296#401C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
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#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#399C2314yes—
335#399C2312yes—
336#399C2312yes—
337#399C2312yes—
338#398C2314yes—
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#398C2312yes—
362#398C2312yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2312yes—
369#398C2312yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2312yes—
377#397C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2312yes—
386#397C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2312yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2312yes—
397#396C2312yes—
398#396C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2312yes—
409#395C2314yes—
410#395C2312yes—
411#394C2314yes—
412#394C2312yes—
413#394C2312yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2312yes—
418#393C2312yes—
419#393C2314yes—
420#393C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2314yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#390C2312yes—
462#390C2311yescharacteristic
463#389C2311yescharacteristic
464#389C2311yescharacteristic
465#389C2311yescharacteristic
466#389C2311yescharacteristic
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#388C2312yes—
516#388C2312yes—
517#388C2314yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#388C2312yes—
522#388C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2312yes—
538#387C2314yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2314yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#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#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
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#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#384C2312yes—
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2311yescharacteristic
624#384C2311yescharacteristic
625#384C2311yescharacteristic
626#383C2314yes—
627#383C2312yes—
628#383C2312yes—
629#383C2314yes—
630#383C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#382C2311yescharacteristic
637#382C2311yescharacteristic
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2314yes—
651#382C2314yes—
652#382C2311yescharacteristic
653#382C2314yes—
654#381C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706#376C2314yes—
707#376C2314yes—
708C43C2312yes—
709C43C2314yes—
710C43C2311yescharacteristic
711C43C2312yes—
712C22×Q8C2411yescharacteristic
713C22×Q8C2412yes—
714C22×Q8C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2414yes—
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×D4C2411yescharacteristic
720C23×C4C2412yes—
721C23×C4C2414yes—
722C4⋊Q8—28no—
723C4⋊Q8—44no—
724C4⋊Q8—42no—
725C4⋊Q8—44no—
726C4⋊Q8—44no—
727C4⋊Q8—42no—
728C4⋊Q8—48no—
729C4⋊Q8—44no—
730#126—28no—
731#126—44no—
732#125—24no—
733#125—44no—
734#125—44no—
735#125—44no—
736#125—42no—
737#125—48no—
738#124—42no—
739C22⋊Q8—44no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C4×Q8—24no—
743C4×Q8—28no—
744C4×Q8—44no—
745C4×Q8—42no—
746C4×Q8—48no—
747C4×Q8—44no—
748C4×Q8—42no—
749C4×Q8—44no—
750C4×Q8—44no—
751C4×Q8—42no—
752C4×D4—44no—
753C4×D4—42no—
754#117—44no—
755#117—48no—
756#117—44no—
757C2×C4⋊C4—28no—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2411yescharacteristic
862C2×C42C2412yes—
863C2×C42C2411yescharacteristic
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2411yescharacteristic
888C2×C42C2414yes—
889C2×C42C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2414yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2414yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977C24C2512yes—
978C2×Q8—22no—
979C2×Q8—24no—
980C2×Q8—28no—
981C2×Q8—22no—
982C2×Q8—24no—
983C2×Q8—24no—
984C2×Q8—22no—
985C2×Q8—24no—
986C2×Q8—22no—
987C2×Q8—41no—
988C2×Q8—44no—
989C2×Q8—42no—
990C2×Q8—44no—
991C2×Q8—42no—
992C2×Q8—42no—
993C2×Q8—41no—
994C2×Q8—42no—
995C2×Q8—42no—
996C2×Q8—44no—
997C2×Q8—44no—
998C2×Q8—44no—
999C2×D4—22no—
1000C2×D4—41no—
1001C2×D4—41no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—28no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2512yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—22no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—28no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—22no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—28no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—24no—
1059C4⋊C4—22no—
1060C4⋊C4—24no—
1061C4⋊C4—42no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—42no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C42−1+414yes—
1114C4⋊C42−1+414yes—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—44no—
1126C22⋊C4—42no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C42—22no—
1136C42—24no—
1137C42—24no—
1138C42—28no—
1139C42—22no—
1140C42—24no—
1141C42—24no—
1142C42—24no—
1143C42—24no—
1144C42—24no—
1145C42—24no—
1146C42—22no—
1147C42—24no—
1148C42—22no—
1149C42—24no—
1150C42—22no—
1151C42—22no—
1152C42—41no—
1153C42—44no—
1154C42—42no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—42no—
1161C42—42no—
1162C42—44no—
1163C42—44no—
1164C42—44no—
1165C42—42no—
1166C42—42no—
1167C42—44no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23C2611yescharacteristic
1176Q8—44no—
1177Q8—48no—
1178Q8—88no—
1179Q8—82no—
1180Q8—84no—
1181Q8—84no—
1182Q8—164no—
1183D4—44no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—48no—
1261C2×C4—88no—
1262C2×C4C2×2−1+412yes—
1263C2×C4C2×2−1+414yes—
1264C2×C4C2×2−1+414yes—
1265C2×C4C2×2−1+412yes—
1266C2×C4#58512yes—
1267C2×C4#58512yes—
1268C2×C4#58512yes—
1269C2×C4#58512yes—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22C22×2−1+411yescharacteristic
1278C22C22×2−1+411yescharacteristic
1279C22C2×#58511yescharacteristic
1280C22C2×#58511yescharacteristic
1281C22C2×#58511yescharacteristic
1282C22C2×#58511yescharacteristic
1283C222−1+611yescharacteristic
1284C4—24no—
1285C4—24no—
1286C4—22no—
1287C4—22no—
1288C4—22no—
1289C4—41no—
1290C4—41no—
1291C4—42no—
1292C4—44no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—41no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C4—44no—
1309C4—44no—
1310C4—42no—
1311C4#353114yes—
1312C2—82no—
1313C2C2×#353111yescharacteristic
1314C2#6290711yescharacteristic
1315C2#6294711yescharacteristic
1316C2#6296411yescharacteristic
1317C2#6302511yescharacteristic
1318C2#6302511yescharacteristic
1319C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53140C2semidirect
3. #53028C2semidirect
4. #52784C2semidirect
6. #52458C2semidirect
9. #46344C2semidirect
10. #46283C2semidirect
11. #46218C2semidirect
12. #46157C2semidirect
13. #46051C2semidirect
14. #46051C2semidirect
16. #46006C2semidirect
18. #45941C2semidirect
19. #45883C2semidirect
20. #45859C2semidirect
21. #36554C2semidirect
22. #36497C2semidirect
23. #36408C2semidirect
24. #36313C2semidirect
26. #36286C2semidirect
27. #35843C2semidirect
28. #35789C2semidirect

Maximal subgroups

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

subgroupindex
#531402
#530502
#530282
#527842
#527092
#524582
#523062
#522722
#463442
#462832
#462182
#461572
#460512
#460232
#460062
#459632
#459412
#458832
#458592
#365542
#364972
#364082
#363132
#362992
#362862
#358432
#357892
#357262