Finite Group Databasebeta

← #7645491

Subgroups — #7645491

Order 512.

4174 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42185C214yesmaximal, complemented
2#42183C214yesmaximal, complemented
3#42004C214yesmaximal, complemented
4#42002C214yesmaximal, complemented
5#39750C212yesmaximal, complemented
6#39749C212yesmaximal, complemented
7#39622C212yesmaximal, complemented
8#39621C212yesmaximal, complemented
9#39177C212yesmaximal, complemented
10#39177C212yesmaximal, complemented
11#39176C212yesmaximal, complemented
12#39176C212yesmaximal, complemented
13#37623C212yesmaximal
14#37561C211yesmaximal, characteristic
15#37561C211yesmaximal, characteristic
16#37194C214yesmaximal
17#36752C212yesmaximal
18#36751C212yesmaximal
19#35403C214yesmaximal
20#35239C211yesmaximal, characteristic
21#35239C211yesmaximal, characteristic
22#35235C212yesmaximal
23#35132C212yesmaximal
24#35015C212yesmaximal
25#35013C212yesmaximal
26#34966C212yesmaximal
27#34187C211yesmaximal, characteristic
28C2×#2355C211yesmaximal, characteristic
29#34059C211yesmaximal, characteristic
30C22×C4×Q8C2211yescharacteristic
31#2864C2212yes—
32#2864C2212yes—
33#2862C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2855C2214yes—
38#2855C2214yes—
39#2851C2212yes—
40#2851C2212yes—
41#2845C2212yes—
42#2845C2212yes—
43#2844C2212yes—
44#2844C2212yes—
45#2843C2214yes—
46#2843C2214yes—
47#2811C2214yes—
48#2809C2214yes—
49#2809C2214yes—
50#2809C2214yes—
51#2806C2214yes—
52#2806C2214yes—
53#2806C2214yes—
54#2806C2214yes—
55#2806C2214yes—
56#2806C2214yes—
57#2806C2214yes—
58#2805C2214yes—
59#2802C2214yes—
60#2802C2214yes—
61#2799C2214yes—
62#2799C2214yes—
63#2799C2214yes—
64#2799C2214yes—
65#2799C2214yes—
66#2799C2214yes—
67#2792C2214yes—
68#2792C2214yes—
69#2791C2214yes—
70#2791C2214yes—
71#2774C2214yes—
72#2774C2214yes—
73#2755C2214yes—
74#2755C2214yes—
75#2734C2214yes—
76#2726C2214yes—
77#2713C2214yes—
78#2713C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2666C2214yes—
86#2666C2214yes—
87#2660C2214yes—
88#2660C2212yes—
89#2660C2212yes—
90#2660C2212yes—
91#2660C2212yes—
92#2659C2212yes—
93#2659C2212yes—
94#2647C2212yes—
95#2647C2212yes—
96#2647C2212yes—
97#2647C2212yes—
98#2647C2214yes—
99#2646C2212yes—
100#2646C2212yes—
101#2627C2214yes—
102#2627C2214yes—
103#2612C2214yes—
104#2612C2214yes—
105#2606C2214yes—
106#2606C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2590C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2588C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2586C2214yes—
121#2585C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2585C2214yes—
125#2571C2211yescharacteristic
126#2571C2212yes—
127#2571C2211yescharacteristic
128#2570C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2570C2212yes—
132#2570C2212yes—
133#2570C2212yes—
134#2570C2212yes—
135#2570C2212yes—
136#2570C2212yes—
137#2570C2212yes—
138#2569C2214yes—
139#2552C2211yescharacteristic
140#2552C2212yes—
141#2552C2211yescharacteristic
142#2552C2212yes—
143#2552C2211yescharacteristic
144#2552C2211yescharacteristic
145#2551C2211yescharacteristic
146#2551C2212yes—
147#2551C2211yescharacteristic
148#2550C2212yes—
149#2550C2212yes—
150#2550C2212yes—
151#2550C2212yes—
152#2550C2212yes—
153#2550C2212yes—
154#2550C2212yes—
155#2550C2212yes—
156#2550C2212yes—
157#2550C2212yes—
158#2549C2214yes—
159#2520C2214yes—
160#2520C2214yes—
161#2520C2214yes—
162#2520C2214yes—
163#2511C2214yes—
164#2511C2214yes—
165#2507C2214yes—
166#2507C2214yes—
167#2462C2214yes—
168#2462C2214yes—
169#2462C2214yes—
170#2462C2214yes—
171#2451C2214yes—
172#2451C2214yes—
173#2446C2214yes—
174#2446C2214yes—
175#2442C2212yes—
176#2442C2212yes—
177#2442C2214yes—
178#2442C2212yes—
179#2442C2212yes—
180#2440C2212yes—
181#2440C2212yes—
182#2440C2214yes—
183#2440C2212yes—
184#2440C2212yes—
185#2438C2214yes—
186#2438C2214yes—
187#2438C2214yes—
188#2438C2214yes—
189#2438C2214yes—
190#2438C2214yes—
191#2438C2214yes—
192#2438C2214yes—
193#2402C2214yes—
194#2399C2214yes—
195#2356C2214yes—
196#2356C2214yes—
197#2355C2212yes—
198#2355C2212yes—
199#2355C2212yes—
200#2355C2212yes—
201#2355C2212yes—
202#2355C2212yes—
203#2355C2214yes—
204#2355C2214yes—
205#2355C2212yes—
206#2355C2212yes—
207#2331C2212yes—
208#2331C2212yes—
209#2331C2212yes—
210#2331C2212yes—
211#2330C2212yes—
212#2330C2212yes—
213#2330C2212yes—
214#2330C2212yes—
215#2329C2214yes—
216#2329C2214yes—
217#2320C2212yes—
218#2320C2212yes—
219#2320C2212yes—
220#2320C2212yes—
221#2316C2211yescharacteristic
222#2316C2211yescharacteristic
223#2313C2212yes—
224#2313C2211yescharacteristic
225#2313C2211yescharacteristic
226#2313C2212yes—
227#2313C2212yes—
228#2310C2212yes—
229#2310C2212yes—
230C4×C4⋊Q8C2212yes—
231C4×C4⋊Q8C2212yes—
232C4×#125C2212yes—
233C4×#125C2212yes—
234C4×C22⋊Q8C2214yes—
235C4×C22⋊Q8C2214yes—
236#2295C2212yes—
237#2295C2212yes—
238#2295C2212yes—
239#2295C2212yes—
240C2×#391C2212yes—
241C2×#387C2212yes—
242C2×#387C2212yes—
243#2285C2211yescharacteristic
244#2285C2211yescharacteristic
245C2×#384C2211yescharacteristic
246#2283C2212yes—
247#2283C2211yescharacteristic
248#2283C2211yescharacteristic
249#2283C2212yes—
250#2283C2212yes—
251C2×#382C2211yescharacteristic
252C2×#382C2211yescharacteristic
253#2274C2212yes—
254C4×#117C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C23×Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C4×Q8Q8116yescomplemented
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2314yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×#117C2312yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C2×#117C2312yes—
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C42C2312yes—
299C22×C42C2312yes—
300C22×C42C2312yes—
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
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#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
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#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#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2312yes—
501#387C2312yes—
502#387C2312yes—
503#387C2312yes—
504#387C2312yes—
505#387C2312yes—
506#387C2312yes—
507#387C2312yes—
508#387C2312yes—
509#387C2312yes—
510#387C2312yes—
511#387C2312yes—
512#387C2312yes—
513#387C2312yes—
514#387C2312yes—
515#387C2312yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
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#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#384C2312yes—
581#384C2312yes—
582#384C2312yes—
583#384C2312yes—
584#384C2312yes—
585#384C2312yes—
586#384C2311yescharacteristic
587#384C2312yes—
588#384C2311yescharacteristic
589#384C2314yes—
590#384C2311yescharacteristic
591#384C2312yes—
592#384C2311yescharacteristic
593#384C2314yes—
594#383C2312yes—
595#383C2312yes—
596#383C2312yes—
597#383C2312yes—
598#383C2314yes—
599#383C2314yes—
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2311yescharacteristic
604#382C2311yescharacteristic
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2312yes—
609#382C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2311yescharacteristic
618#382C2311yescharacteristic
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2314yes—
626#381C2312yes—
627#381C2312yes—
628#381C2314yes—
629#381C2312yes—
630#381C2314yes—
631#381C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2311yescharacteristic
636#380C2311yescharacteristic
637#380C2311yescharacteristic
638#380C2311yescharacteristic
639#380C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2312yes—
645#380C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696#376C2312yes—
697#376C2312yes—
698#376C2312yes—
699#376C2312yes—
700#376C2312yes—
701#376C2312yes—
702#376C2314yes—
703#376C2314yes—
704C2×#95C2312yes—
705C2×#95C2312yes—
706C2×#95C2312yes—
707C2×#95C2312yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C43C2312yes—
712C43C2312yes—
713C22×Q8—42no—
714C22×Q8—42no—
715C22×Q8C2×Q818yes—
716C22×Q8C2414yes—
717C22×Q8C2414yes—
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C23×C4C2412yes—
723C23×C4C2411yescharacteristic
724C23×C4C2411yescharacteristic
725C23×C4C2411yescharacteristic
726C23×C4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C4⋊Q8—28no—
734C4⋊Q8—44no—
735C4⋊Q8—44no—
736C4⋊Q8—44no—
737C4⋊Q8—82no—
738C4⋊Q8—82no—
739C4⋊Q8—84no—
740#125—28no—
741#125—44no—
742#125—44no—
743#125—44no—
744#125—82no—
745#125—82no—
746#125—84no—
747C22⋊Q8—48no—
748C22⋊Q8—48no—
749C22⋊Q8—48no—
750C22⋊Q8—48no—
751C4×Q8—84no—
752C4×Q8—84no—
753C4×Q8C2×Q8116yes—
754C4×Q8C2×Q8116yes—
755C4×Q8C2×Q8116yes—
756C4×Q8C2×Q8116yes—
757#117—44no—
758#117—44no—
759#117—44no—
760#117—44no—
761C2×C4⋊C4—24no—
762C2×C4⋊C4—42no—
763C2×C4⋊C4—42no—
764C2×C4⋊C4—42no—
765C2×C4⋊C4—44no—
766C2×C4⋊C4—82no—
767C2×C4⋊C4C2×Q818yes—
768C2×C4⋊C4C2×Q818yes—
769C2×C4⋊C4C2×Q818yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C42—44no—
861C2×C42—82no—
862C2×C42—82no—
863C2×C42C2×Q818yes—
864C2×C42C2×Q818yes—
865C2×C42C2×Q818yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988C24C2511yescharacteristic
989C2×Q8—28no—
990C2×Q8—416no—
991C2×Q8—42no—
992C2×Q8—42no—
993C2×Q8—42no—
994C2×Q8—42no—
995C2×Q8—44no—
996C2×Q8—44no—
997C2×Q8—44no—
998C2×Q8—44no—
999C2×Q8—44no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—44no—
1003C2×Q8—44no—
1004C2×Q8—44no—
1005C2×Q8—44no—
1006C2×Q8C22×Q818yes—
1007C2×Q8C22×Q818yes—
1008C22×C4—22no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—42no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4C22×Q814yes—
1035C22×C4C22×Q814yes—
1036C22×C4C22×Q814yes—
1037C22×C4C22×Q814yes—
1038C22×C4C22×Q814yes—
1039C22×C4C22×Q814yes—
1040C22×C4C22×Q814yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C4⋊C4—24no—
1070C4⋊C4—22no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—22no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—41no—
1094C4⋊C4—41no—
1095C4⋊C4—41no—
1096C4⋊C4—41no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
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—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—41no—
1133C4⋊C4—41no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4C22×Q818yes—
1147C4⋊C4C22×Q818yes—
1148C4⋊C4C22×Q818yes—
1149C4⋊C4C22×Q818yes—
1150C4⋊C4C22×Q818yes—
1151C4⋊C4C22×Q818yes—
1152C4⋊C42−1+414yes—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—28no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—28no—
1159C42—24no—
1160C42—24no—
1161C42—24no—
1162C42—24no—
1163C42—44no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—42no—
1168C42—42no—
1169C42—42no—
1170C42—42no—
1171C42—44no—
1172C42—42no—
1173C42—42no—
1174C42—44no—
1175C42—44no—
1176C42—44no—
1177C42—42no—
1178C42—42no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—42no—
1183C42—42no—
1184C42—44no—
1185C42C22×Q818yes—
1186C42C22×Q818yes—
1187C42C22×Q814yes—
1188C42C22×Q814yes—
1189C42C22×Q818yes—
1190C42C22×Q814yes—
1191C42C22×Q814yes—
1192C42C22×Q818yes—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23C23×Q812yes—
1198C23#58512yes—
1199C23#58512yes—
1200C23C2611yescharacteristic
1201Q8—48no—
1202Q8—48no—
1203Q8—88no—
1204Q8—88no—
1205Q8—164no—
1206Q8—164no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—28no—
1228C2×C4—28no—
1229C2×C4—28no—
1230C2×C4—28no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—44no—
1283C2×C4—44no—
1284C2×C4—44no—
1285C2×C4—48no—
1286C2×C4—84no—
1287C2×C4—84no—
1288C2×C4—84no—
1289C2×C4C23×Q812yes—
1290C2×C4C23×Q814yes—
1291C2×C4C23×Q812yes—
1292C2×C4C23×Q812yes—
1293C2×C4C23×Q814yes—
1294C2×C4C23×Q814yes—
1295C2×C4C23×Q812yes—
1296C2×C4C23×Q812yes—
1297C2×C4C23×Q814yes—
1298C2×C4C23×Q812yes—
1299C2×C4C2×2−1+414yes—
1300C2×C4C2×2−1+412yes—
1301C2×C4#58512yes—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22#345814yes—
1309C22C24×Q811yescharacteristic
1310C22C22×2−1+411yescharacteristic
1311C22C2×#58511yescharacteristic
1312C22C2×#58511yescharacteristic
1313C22C2×#58511yescharacteristic
1314C22H(7,𝔽2)11yescharacteristic
1315C222−1+611yescharacteristic
1316C4—22no—
1317C4—24no—
1318C4—22no—
1319C4—22no—
1320C4—24no—
1321C4—24no—
1322C4—22no—
1323C4—22no—
1324C4—24no—
1325C4—24no—
1326C4—42no—
1327C4—42no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—44no—
1335C4—44no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—42no—
1343C4#350214yes—
1344C2—24no—
1345C2C2×#345811yescharacteristic
1346C2C2×#350211yescharacteristic
1347C2#6285411yescharacteristic
1348C2#6294811yescharacteristic
1349C2#6294911yescharacteristic
1350C2#6296411yescharacteristic
1351C2#6296511yescharacteristic
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
1. #42185C2semidirect
2. #42183C2semidirect
3. #42004C2semidirect
4. #42002C2semidirect
5. #39750C2semidirect
6. #39749C2semidirect
7. #39622C2semidirect
8. #39621C2semidirect
9. #39177C2semidirect
10. #39177C2semidirect
11. #39176C2semidirect
12. #39176C2semidirect
278. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#421852
#421832
#420042
#420022
#397502
#397492
#396222
#396212
#391772
#391762
#376232
#375612
#371942
#367522
#367512
#354032
#352392
#352352
#351322
#350152
#350132
#349662
#341872
C2×#23552
#340592