Finite Group Databasebeta

← #8110413

Subgroups — #8110413

Order 512.

3958 conjugacy classes of subgroups.

The subgroup lattice has 1393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59868C212yesmaximal
2#59867C212yesmaximal
3#53383C214yesmaximal, complemented
4#53368C212yesmaximal, complemented
5#53358C212yesmaximal, complemented
6#46344C212yesmaximal, complemented
7#46344C212yesmaximal, complemented
8#46169C214yesmaximal
9#45859C214yesmaximal, complemented
10#40215C212yesmaximal, complemented
11#40189C212yesmaximal, complemented
12#39752C211yesmaximal, characteristic
13#39751C211yesmaximal, characteristic
14#39748C212yesmaximal
15#39640C211yesmaximal, characteristic
16#39639C211yesmaximal, characteristic
17#39636C212yesmaximal
18#38395C214yesmaximal
19#38243C212yesmaximal, complemented
20#38229C212yesmaximal, complemented
21#38066C212yesmaximal
22#38057C212yesmaximal
23#37401C212yesmaximal, complemented
24#37344C212yesmaximal, complemented
25#37163C212yesmaximal, complemented
26#37163C212yesmaximal, complemented
27#36979C212yesmaximal
28#36979C212yesmaximal
29#36635C211yesmaximal, characteristic
30#36635C211yesmaximal, characteristic
31C2×#2863C211yesmaximal, characteristic
32#2864C2212yes—
33#2864C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2863C2212yes—
40#2863C2212yes—
41#2863C2212yes—
42#2863C2212yes—
43#2863C2211yescharacteristic
44#2863C2211yescharacteristic
45#2863C2212yes—
46#2863C2212yes—
47#2862C2211yescharacteristic
48#2862C2211yescharacteristic
49#2859C2211yescharacteristic
50#2859C2211yescharacteristic
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2211yescharacteristic
54#2857C2211yescharacteristic
55#2855C2211yescharacteristic
56#2855C2212yes—
57#2855C2211yescharacteristic
58#2855C2212yes—
59#2855C2212yes—
60#2851C2212yes—
61#2851C2212yes—
62#2839C2214yes—
63#2839C2214yes—
64#2810C2214yes—
65#2809C2212yes—
66#2809C2212yes—
67#2806C2212yes—
68#2806C2212yes—
69#2805C2212yes—
70#2805C2212yes—
71#2802C2214yes—
72#2802C2214yes—
73#2802C2214yes—
74#2799C2214yes—
75#2799C2214yes—
76#2799C2214yes—
77#2791C2214yes—
78#2791C2214yes—
79#2776C2214yes—
80#2776C2214yes—
81#2776C2214yes—
82#2776C2214yes—
83#2776C2214yes—
84#2776C2214yes—
85#2774C2214yes—
86#2774C2214yes—
87#2774C2214yes—
88#2769C2214yes—
89#2769C2214yes—
90#2769C2214yes—
91#2769C2214yes—
92#2769C2214yes—
93#2769C2214yes—
94#2767C2214yes—
95#2767C2214yes—
96#2767C2214yes—
97#2767C2214yes—
98#2767C2214yes—
99#2767C2214yes—
100#2766C2214yes—
101#2766C2214yes—
102#2762C2214yes—
103#2762C2214yes—
104#2762C2214yes—
105#2762C2214yes—
106#2762C2214yes—
107#2762C2214yes—
108#2762C2214yes—
109#2762C2214yes—
110#2758C2214yes—
111#2758C2214yes—
112#2758C2214yes—
113#2758C2214yes—
114#2758C2214yes—
115#2758C2214yes—
116#2755C2214yes—
117#2755C2214yes—
118#2755C2214yes—
119#2755C2214yes—
120#2755C2214yes—
121#2726C2214yes—
122#2726C2212yes—
123#2726C2212yes—
124#2719C2214yes—
125#2719C2214yes—
126#2719C2214yes—
127#2719C2214yes—
128#2719C2214yes—
129#2719C2214yes—
130#2713C2214yes—
131#2713C2214yes—
132#2659C2212yes—
133#2659C2212yes—
134#2655C2214yes—
135#2655C2214yes—
136#2647C2212yes—
137#2646C2212yes—
138#2646C2212yes—
139#2645C2212yes—
140#2645C2212yes—
141#2642C2212yes—
142#2590C2214yes—
143#2588C2214yes—
144#2588C2214yes—
145#2585C2214yes—
146#2585C2214yes—
147#2585C2214yes—
148#2584C2212yes—
149#2584C2212yes—
150#2583C2214yes—
151#2582C2212yes—
152#2582C2212yes—
153#2581C2212yes—
154#2581C2212yes—
155#2569C2214yes—
156#2569C2214yes—
157#2569C2214yes—
158#2568C2212yes—
159#2568C2212yes—
160#2565C2212yes—
161#2552C2212yes—
162#2550C2212yes—
163#2546C2212yes—
164#2533C2214yes—
165#2533C2214yes—
166#2528C2214yes—
167#2528C2214yes—
168#2520C2214yes—
169#2520C2214yes—
170#2514C2212yes—
171#2514C2212yes—
172#2511C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2511C2212yes—
176#2509C2214yes—
177#2509C2214yes—
178#2509C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2506C2212yes—
182#2506C2212yes—
183#2506C2212yes—
184#2505C2214yes—
185#2505C2214yes—
186#2505C2214yes—
187#2505C2214yes—
188#2505C2214yes—
189#2505C2214yes—
190#2502C2212yes—
191#2493C2214yes—
192#2493C2214yes—
193#2493C2214yes—
194#2493C2214yes—
195#2473C2214yes—
196#2473C2214yes—
197#2462C2214yes—
198#2453C2212yes—
199#2453C2212yes—
200#2453C2212yes—
201#2453C2212yes—
202#2453C2212yes—
203#2453C2214yes—
204#2451C2212yes—
205#2446C2212yes—
206#2446C2212yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2446C2212yes—
211#2442C2214yes—
212#2442C2214yes—
213#2442C2212yes—
214#2442C2212yes—
215#2434C2212yes—
216#2382C2214yes—
217#2382C2214yes—
218#2370C2212yes—
219#2368C2214yes—
220#2365C2212yes—
221#2360C2212yes—
222#2360C2212yes—
223#2355C2212yes—
224#2351C2212yes—
225#2345C2214yes—
226#2345C2212yes—
227Q8×C22⋊C4C2212yes—
228#2336C2214yes—
229#2336C2214yes—
230#2330C2212yes—
231#2329C2212yes—
232#2329C2212yes—
233#2329C2212yes—
234#2329C2212yes—
235#2327C2212yes—
236#2320C2212yes—
237#2320C2212yes—
238C4×C4⋊Q8C2211yescharacteristic
239C4×C4⋊Q8C2211yescharacteristic
240C4×C4⋊Q8C2211yescharacteristic
241C4×C4⋊Q8C2211yescharacteristic
242C4×#125C2212yes—
243C4×#125C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2211yescharacteristic
246C4×C22⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249#2295C2212yes—
250#2295C2212yes—
251#2295C2211yescharacteristic
252#2295C2212yes—
253#2295C2211yescharacteristic
254C2×#391C2211yescharacteristic
255C2×#391C2211yescharacteristic
256C2×#391C2211yescharacteristic
257C2×#389C2211yescharacteristic
258C2×#389C2211yescharacteristic
259C2×#389C2211yescharacteristic
260C2×#387C2212yes—
261C2×#387C2212yes—
262C2×#387C2212yes—
263#2283C2212yes—
264#2283C2212yes—
265C2×#383C2212yes—
266C2×C43C2211yescharacteristic
267C23×Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2311yescharacteristic
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309#401C2314yes—
310#401C2314yes—
311#401C2314yes—
312#401C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#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#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#391C2312yes—
406#391C2311yescharacteristic
407#391C2312yes—
408#391C2312yes—
409#391C2311yescharacteristic
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2311yescharacteristic
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2311yescharacteristic
437#391C2312yes—
438#391C2311yescharacteristic
439#391C2312yes—
440#391C2312yes—
441#391C2311yescharacteristic
442#391C2312yes—
443#391C2312yes—
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2311yescharacteristic
463#389C2312yes—
464#389C2312yes—
465#389C2311yescharacteristic
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2311yescharacteristic
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2311yescharacteristic
502#389C2312yes—
503#389C2311yescharacteristic
504#389C2314yes—
505#389C2311yescharacteristic
506#389C2312yes—
507#389C2312yes—
508#389C2311yescharacteristic
509#389C2311yescharacteristic
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
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#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2314yes—
590#387C2312yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2312yes—
609#387C2314yes—
610#387C2312yes—
611#387C2312yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2312yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#384C2311yescharacteristic
636#384C2311yescharacteristic
637#384C2311yescharacteristic
638#384C2311yescharacteristic
639#384C2312yes—
640#384C2312yes—
641#383C2314yes—
642#383C2314yes—
643#383C2314yes—
644#383C2314yes—
645#383C2312yes—
646#383C2314yes—
647#383C2314yes—
648#383C2314yes—
649#383C2314yes—
650#383C2314yes—
651#383C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2312yes—
655#382C2314yes—
656#382C2314yes—
657#382C2314yes—
658#382C2314yes—
659#382C2312yes—
660#382C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#382C2314yes—
665#382C2314yes—
666#382C2314yes—
667#382C2314yes—
668#381C2312yes—
669#381C2314yes—
670#381C2312yes—
671#380C2314yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2311yescharacteristic
679#380C2312yes—
680#380C2311yescharacteristic
681#380C2312yes—
682#380C2312yes—
683#380C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714#376C2312yes—
715#376C2312yes—
716#376C2314yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C2×#95C2312yes—
720C2×#95C2312yes—
721C2×#95C2312yes—
722C2×#95C2312yes—
723C2×#95C2312yes—
724C2×#95C2312yes—
725C2×#95C2312yes—
726C43C2311yescharacteristic
727C43C2311yescharacteristic
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C22×Q8—24no—
735C22×Q8—42no—
736C22×Q8—42no—
737C22×Q8C2412yes—
738C22×Q8C2412yes—
739C22×Q8C2411yescharacteristic
740C22×Q8C2412yes—
741C22×Q8C2411yescharacteristic
742C22×Q8C2412yes—
743C22×Q8C2412yes—
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C4⋊Q8—42no—
756C4⋊Q8—42no—
757C4⋊Q8—42no—
758C4⋊Q8—42no—
759C4⋊Q8—44no—
760C4⋊Q8—44no—
761#125—44no—
762#125—44no—
763#125—44no—
764#125—44no—
765#125—48no—
766#125—48no—
767#125—48no—
768#125—48no—
769C22⋊Q8—28no—
770C22⋊Q8—28no—
771C22⋊Q8—24no—
772C22⋊Q8—24no—
773C22⋊Q8—28no—
774C4×Q8—42no—
775C4×Q8—44no—
776C4×Q8—42no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—44no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—42no—
786C2×C4⋊C4—42no—
787C2×C4⋊C4—44no—
788C2×C4⋊C4—44no—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C42—24no—
873C2×C42—24no—
874C2×C42—24no—
875C2×C42—42no—
876C2×C42—42no—
877C2×C42—42no—
878C2×C42—42no—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2411yescharacteristic
883C2×C42C2411yescharacteristic
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2412yes—
887C2×C42C2411yescharacteristic
888C2×C42C2411yescharacteristic
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
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#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013C24C2511yescharacteristic
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—24no—
1017C2×Q8—22no—
1018C2×Q8—22no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—41no—
1026C2×Q8—42no—
1027C2×Q8—41no—
1028C2×Q8—42no—
1029C2×Q8—41no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—41no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—88no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C42−1+414yes—
1067C22×C42−1+414yes—
1068C22×C42−1+414yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2514yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—41no—
1132C4⋊C4—42no—
1133C4⋊C4—41no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—41no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—41no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C42—22no—
1183C42—22no—
1184C42—22no—
1185C42—22no—
1186C42—22no—
1187C42—22no—
1188C42—22no—
1189C42—22no—
1190C42—22no—
1191C42—22no—
1192C42—22no—
1193C42—22no—
1194C42—22no—
1195C42—22no—
1196C42—22no—
1197C42—22no—
1198C42—22no—
1199C42—22no—
1200C42—22no—
1201C42—22no—
1202C42—24no—
1203C42—24no—
1204C42—24no—
1205C42—24no—
1206C42—41no—
1207C42—41no—
1208C42—41no—
1209C42—41no—
1210C42—41no—
1211C42—41no—
1212C42—41no—
1213C42—41no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C23—21no—
1225C23—21no—
1226C23—21no—
1227C23—21no—
1228C23C2×2−1+412yes—
1229C23C2×2−1+412yes—
1230C23C2×2−1+412yes—
1231C23C2611yescharacteristic
1232Q8—48no—
1233Q8—48no—
1234Q8—82no—
1235Q8—84no—
1236Q8—82no—
1237Q8—84no—
1238Q8—84no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—28no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—44no—
1321C2×C4—44no—
1322C2×C4—44no—
1323C2×C4—44no—
1324C2×C4—44no—
1325C2×C4—44no—
1326C2×C4—84no—
1327C2×C4—84no—
1328C2×C4—84no—
1329C2×C4—84no—
1330C2×C4C2×2−1+412yes—
1331C2×C4C2×2−1+412yes—
1332C2×C4C2×2−1+412yes—
1333C2×C4C2×2−1+412yes—
1334C2×C4C2×2−1+412yes—
1335C2×C4C2×2−1+412yes—
1336C2×C4#58512yes—
1337C2×C4#58512yes—
1338C2×C4#58512yes—
1339C2×C4#58512yes—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—22no—
1344C22—22no—
1345C22—22no—
1346C22#355614yes—
1347C22C22×2−1+411yescharacteristic
1348C22C22×2−1+411yescharacteristic
1349C22C22×2−1+411yescharacteristic
1350C22C2×#58511yescharacteristic
1351C22C2×#58511yescharacteristic
1352C22C2×#58511yescharacteristic
1353C22C2×#58511yescharacteristic
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—22no—
1361C4—44no—
1362C4—44no—
1363C4—42no—
1364C4—42no—
1365C4—41no—
1366C4—44no—
1367C4—41no—
1368C4—41no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—44no—
1375C4—44no—
1376C4—41no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4—44no—
1381C4—41no—
1382C4—41no—
1383C4#356414yes—
1384C2—24no—
1385C2C2×#356411yescharacteristic
1386C2#6275211yescharacteristic
1387C2C2×#355611yescharacteristic
1388C2#6282311yescharacteristic
1389C2#6282311yescharacteristic
1390C2#6283111yescharacteristic
1391C2#6283811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #53383C2semidirect
4. #53368C2semidirect
5. #53358C2semidirect
6. #46344C2semidirect
7. #46344C2semidirect
9. #45859C2semidirect
10. #40215C2semidirect
11. #40189C2semidirect
19. #38243C2semidirect
20. #38229C2semidirect
23. #37401C2semidirect
24. #37344C2semidirect
25. #37163C2semidirect
26. #37163C2semidirect

Maximal subgroups

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

subgroupindex
#598682
#598672
#533832
#533682
#533582
#463442
#461692
#458592
#402152
#401892
#397522
#397512
#397482
#396402
#396392
#396362
#383952
#382432
#382292
#380662
#380572
#374012
#373442
#371632
#369792
#366352
C2×#28632