Finite Group Databasebeta

← #7695632

Subgroups — #7695632

Order 512.

4811 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59923C212yesmaximal, complemented
2#59918C214yesmaximal, complemented
3#59871C211yesmaximal, characteristic, complemented
4#59668C212yesmaximal, complemented
5#52287C211yesmaximal, characteristic, complemented
6C2×#2806C212yesmaximal, complemented
7#45364C212yesmaximal, complemented
8#44950C212yesmaximal, complemented
9#44950C212yesmaximal, complemented
10#43553C214yesmaximal, complemented
11#43126C214yesmaximal, complemented
12#43126C214yesmaximal, complemented
13#39626C212yesmaximal, complemented
14#39624C212yesmaximal, complemented
15#39624C214yesmaximal, complemented
16#39623C212yesmaximal, complemented
17#39622C212yesmaximal, complemented
18#39621C211yesmaximal, characteristic, complemented
19#39621C211yesmaximal, characteristic, complemented
20#39620C214yesmaximal, complemented
21#36276C211yesmaximal, characteristic
22#36261C212yesmaximal
23#35950C212yesmaximal
24#35950C212yesmaximal
25#35928C212yesmaximal
26#34334C212yesmaximal
27#34334C211yesmaximal, characteristic
28#34333C212yesmaximal
29#34332C211yesmaximal, characteristic
30C2×#554C2212yes—
31C2×#554C2212yes—
32C2×#554C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36#2862C2211yescharacteristic
37#2859C2212yes—
38#2857C2214yes—
39#2857C2212yes—
40#2811C2212yes—
41#2811C2214yes—
42#2811C2211yescharacteristic
43#2811C2212yes—
44#2806C2214yes—
45#2806C2214yes—
46#2806C2211yescharacteristic
47#2806C2212yes—
48#2806C2214yes—
49#2806C2214yes—
50#2806C2214yes—
51#2806C2211yescharacteristic
52#2806C2214yes—
53#2806C2214yes—
54#2806C2214yes—
55#2806C2212yes—
56#2806C2212yes—
57#2806C2214yes—
58#2806C2212yes—
59#2806C2212yes—
60#2806C2212yes—
61#2806C2212yes—
62#2806C2214yes—
63#2806C2214yes—
64#2806C2214yes—
65#2806C2212yes—
66#2792C2212yes—
67#2792C2214yes—
68#2792C2214yes—
69#2792C2214yes—
70#2792C2214yes—
71#2792C2214yes—
72#2792C2212yes—
73#2792C2212yes—
74#2792C2214yes—
75#2792C2214yes—
76#2734C2212yes—
77#2734C2212yes—
78#2734C2214yes—
79#2734C2211yescharacteristic
80#2734C2214yes—
81#2734C2212yes—
82#2660C2212yes—
83#2660C2212yes—
84#2660C2212yes—
85#2659C2214yes—
86#2659C2214yes—
87#2659C2214yes—
88#2586C2214yes—
89#2586C2214yes—
90#2586C2214yes—
91#2586C2214yes—
92#2586C2214yes—
93#2586C2214yes—
94#2586C2214yes—
95#2584C2212yes—
96#2584C2212yes—
97#2584C2212yes—
98#2584C2212yes—
99#2584C2212yes—
100#2583C2214yes—
101#2583C2214yes—
102#2583C2214yes—
103#2583C2214yes—
104#2583C2214yes—
105#2582C2214yes—
106#2582C2214yes—
107#2582C2214yes—
108#2567C2214yes—
109#2567C2212yes—
110#2567C2214yes—
111#2567C2212yes—
112#2567C2211yescharacteristic
113#2567C2214yes—
114#2552C2212yes—
115#2552C2212yes—
116#2552C2212yes—
117#2552C2212yes—
118#2552C2212yes—
119#2551C2214yes—
120#2551C2212yes—
121#2551C2212yes—
122#2551C2212yes—
123#2550C2212yes—
124#2550C2212yes—
125#2550C2212yes—
126#2550C2212yes—
127#2550C2212yes—
128#2550C2212yes—
129#2550C2212yes—
130#2550C2212yes—
131#2550C2212yes—
132#2550C2212yes—
133#2549C2214yes—
134#2549C2214yes—
135#2549C2214yes—
136#2549C2214yes—
137#2549C2214yes—
138#2549C2214yes—
139#2549C2214yes—
140#2549C2214yes—
141#2549C2214yes—
142#2549C2214yes—
143#2546C2211yescharacteristic
144#2546C2212yes—
145#2546C2212yes—
146#2507C2214yes—
147#2507C2214yes—
148#2507C2214yes—
149#2507C2214yes—
150#2507C2214yes—
151#2507C2214yes—
152#2507C2214yes—
153#2507C2214yes—
154#2502C2212yes—
155#2502C2214yes—
156#2502C2214yes—
157#2451C2214yes—
158#2451C2214yes—
159#2451C2214yes—
160#2451C2214yes—
161#2451C2214yes—
162#2451C2214yes—
163#2451C2214yes—
164#2451C2214yes—
165#2451C2214yes—
166#2440C2214yes—
167#2440C2214yes—
168#2440C2214yes—
169#2440C2214yes—
170#2440C2214yes—
171#2440C2214yes—
172#2440C2214yes—
173#2440C2214yes—
174#2434C2214yes—
175#2434C2212yes—
176#2399C2212yes—
177#2399C2212yes—
178#2399C2212yes—
179C2×#398C2214yes—
180C2×#398C2214yes—
181C2×#395C2214yes—
182#2370C2212yes—
183#2370C2212yes—
184#2370C2212yes—
185#2369C2214yes—
186#2369C2212yes—
187#2369C2212yes—
188#2369C2211yescharacteristic
189#2369C2212yes—
190#2368C2214yes—
191#2368C2214yes—
192#2368C2214yes—
193#2368C2214yes—
194#2368C2214yes—
195#2365C2212yes—
196#2365C2212yes—
197#2365C2211yescharacteristic
198#2360C2214yes—
199#2360C2214yes—
200#2360C2212yes—
201#2360C2214yes—
202#2360C2212yes—
203#2355C2212yes—
204#2355C2212yes—
205#2355C2211yescharacteristic
206Q8×C4⋊C4C2212yes—
207Q8×C4⋊C4C2211yescharacteristic
208#2349C2212yes—
209#2349C2212yes—
210#2349C2212yes—
211#2349C2212yes—
212#2349C2212yes—
213D4×C4⋊C4C2212yes—
214D4×C4⋊C4C2211yescharacteristic
215D4×C4⋊C4C2212yes—
216D4×C4⋊C4C2212yes—
217D4×C4⋊C4C2211yescharacteristic
218#2345C2212yes—
219#2345C2214yes—
220Q8×C22⋊C4C2214yes—
221Q8×C22⋊C4C2212yes—
222#2331C2212yes—
223#2331C2212yes—
224#2331C2212yes—
225#2331C2212yes—
226#2330C2212yes—
227#2330C2212yes—
228#2329C2214yes—
229#2329C2214yes—
230#2329C2214yes—
231#2329C2214yes—
232#2329C2214yes—
233#2329C2214yes—
234C4×C4⋊Q8C2212yes—
235C4×C4⋊Q8C2212yes—
236C4×C4⋊Q8C2211yescharacteristic
237C4×C4⋊Q8C2211yescharacteristic
238C4×C4⋊Q8C2211yescharacteristic
239C4×#125C2212yes—
240C4×C22⋊Q8C2214yes—
241C4×C22⋊Q8C2214yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244#2295C2211yescharacteristic
245#2295C2212yes—
246#2295C2211yescharacteristic
247#2295C2212yes—
248C2×#391C2212yes—
249C2×#391C2214yes—
250C2×#391C2212yes—
251C2×#389C2214yes—
252C2×#389C2212yes—
253C2×#387C2214yes—
254#2275C2212yes—
255#2275C2212yes—
256#2275C2212yes—
257C42×D4C2211yescharacteristic
258C42×D4C2212yes—
259C23×Q8C2312yes—
260C23×Q8C2312yes—
261#554—48no—
262#554—44no—
263#554—48no—
264#554Q8116yescomplemented
265D4×Q8—44no—
266D4×Q8Q8116yescomplemented
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2311yescharacteristic
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C22×C4⋊C4C2314yes—
326C22×C4⋊C4C2314yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2314yes—
329C22×C4⋊C4C2314yes—
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2314yes—
333C22×C4⋊C4C2312yes—
334C22×C42C2314yes—
335C22×C42C2312yes—
336#398C2312yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#395C2312yes—
385#395C2312yes—
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#395C2314yes—
401#395C2312yes—
402#395C2312yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2312yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2312yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2312yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2312yes—
426#391C2312yes—
427#391C2311yescharacteristic
428#391C2312yes—
429#391C2312yes—
430#391C2311yescharacteristic
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2311yescharacteristic
468#391C2312yes—
469#391C2314yes—
470#391C2312yes—
471#391C2312yes—
472#391C2311yescharacteristic
473#391C2312yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2311yescharacteristic
480#391C2311yescharacteristic
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2311yescharacteristic
551#389C2312yes—
552#389C2314yes—
553#389C2312yes—
554#389C2312yes—
555#389C2311yescharacteristic
556#389C2312yes—
557#389C2314yes—
558#389C2311yescharacteristic
559#389C2311yescharacteristic
560#389C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
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#387C2312yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2312yes—
602#387C2312yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2311yescharacteristic
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2312yes—
627#384C2314yes—
628#384C2314yes—
629#384C2314yes—
630#384C2314yes—
631#384C2312yes—
632#384C2312yes—
633#384C2314yes—
634#384C2314yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708C2×#95C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2312yes—
717C43C2311yescharacteristic
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8—82no—
721C22×Q8—82no—
722C22×Q8—82no—
723C22×Q8C2×Q8116yescomplemented
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2414yes—
730C22×Q8C2414yes—
731C22×Q8C2412yes—
732C22×Q8C2414yes—
733C22×Q8C2412yes—
734C22×Q8C2411yescharacteristic
735C22×Q8C2414yes—
736C22×Q8C2412yes—
737C22×Q8C2411yescharacteristic
738C22×D4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C4⋊Q8—44no—
749C4⋊Q8—42no—
750C4⋊Q8—44no—
751C4⋊Q8—44no—
752C4⋊Q8—42no—
753C4⋊Q8—42no—
754C4⋊Q8—44no—
755C4⋊Q8—48no—
756C4⋊Q8—84no—
757C4⋊Q8—82no—
758C4⋊Q8—84no—
759C4⋊Q8—84no—
760C4⋊Q8—84no—
761C4⋊Q8C2×Q8116yescomplemented
762C4⋊Q8C2×Q818yescomplemented
763C4⋊Q8C2×Q818yescomplemented
764#125—44no—
765#125—44no—
766#125—44no—
767#125—44no—
768#125—44no—
769#125C2×Q8116yescomplemented
770C22⋊Q8—44no—
771C22⋊Q8—48no—
772C22⋊Q8—48no—
773C22⋊Q8—48no—
774C22⋊Q8—48no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—44no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8C2×Q8132yescomplemented
781C22⋊Q8C2×Q8116yescomplemented
782C22⋊Q8C2×Q8132yescomplemented
783C22⋊Q8C2×Q8116yescomplemented
784C4×Q8—42no—
785C4×Q8—42no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—84no—
790C4×Q8—82no—
791C4×Q8—84no—
792C4×Q8—82no—
793C4×Q8—82no—
794C4×Q8—84no—
795C4×Q8C2×Q818yescomplemented
796C4×Q8C2×Q818yescomplemented
797C4×D4—28no—
798C4×D4—24no—
799C4×D4—28no—
800C4×D4—28no—
801C4×D4—28no—
802C4×D4C2×Q8116yes—
803C4×D4C2×Q818yes—
804C4×D4C2×Q8116yes—
805C4×D4C2×Q818yes—
806C2×C4⋊C4—48no—
807C2×C4⋊C4—44no—
808C2×C4⋊C4—48no—
809C2×C4⋊C4—48no—
810C2×C4⋊C4—84no—
811C2×C4⋊C4—82no—
812C2×C4⋊C4—82no—
813C2×C4⋊C4—84no—
814C2×C4⋊C4C2×Q8116yescomplemented
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2411yescharacteristic
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2411yescharacteristic
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C42—82no—
916C2×C42—84no—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2412yes—
948C2×C42C2411yescharacteristic
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
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—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022C24C2512yes—
1023C2×Q8—22no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—41no—
1027C2×Q8—42no—
1028C2×Q8—41no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—42no—
1034C2×Q8—41no—
1035C2×Q8—41no—
1036C2×Q8—41no—
1037C2×Q8—41no—
1038C2×Q8—41no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—42no—
1044C2×Q8—41no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—44no—
1053C2×Q8—44no—
1054C2×Q8—44no—
1055C2×Q8—42no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×Q8—42no—
1060C2×Q8—816no—
1061C2×Q8—816no—
1062C2×Q8C22×Q814yes—
1063C2×Q8C22×Q814yes—
1064C2×Q8C22×Q818yes—
1065C2×Q8C22×Q8116yes—
1066C2×Q8C22×Q818yes—
1067C2×D4C22×Q814yes—
1068C2×D4C22×Q814yes—
1069C2×D4H(5,𝔽2)14yes—
1070C22×C4—24no—
1071C22×C4—28no—
1072C22×C4—28no—
1073C22×C4—28no—
1074C22×C4—28no—
1075C22×C4—24no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—42no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4C22×Q8116yes—
1094C22×C4C22×Q818yes—
1095C22×C4C22×Q8116yes—
1096C22×C4C22×Q818yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2514yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2514yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—41no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—41no—
1168C4⋊C4—42no—
1169C4⋊C4—41no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—41no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4C22×Q814yes—
1204C4⋊C4C22×Q8116yes—
1205C4⋊C4C22×Q818yes—
1206C4⋊C4C22×Q814yes—
1207C4⋊C4C22×Q818yes—
1208C4⋊C4C22×Q814yes—
1209C4⋊C4C22×Q818yes—
1210C4⋊C4C22×Q818yes—
1211C4⋊C4C22×Q814yes—
1212C4⋊C4C22×Q818yes—
1213C4⋊C4C22×Q8116yes—
1214C4⋊C4C22×Q818yes—
1215C4⋊C4C22×Q8116yes—
1216C22⋊C4—28no—
1217C22⋊C4—24no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4C22×Q8116yes—
1222C22⋊C4C22×Q818yes—
1223C22⋊C4C22×Q8116yes—
1224C22⋊C4C22×Q818yes—
1225C42—24no—
1226C42—24no—
1227C42—24no—
1228C42—24no—
1229C42—22no—
1230C42—22no—
1231C42—42no—
1232C42—41no—
1233C42—42no—
1234C42—44no—
1235C42—44no—
1236C42—42no—
1237C42—42no—
1238C42—44no—
1239C42—44no—
1240C42—42no—
1241C42—41no—
1242C42—44no—
1243C42—44no—
1244C42—42no—
1245C42—44no—
1246C42—41no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C42—44no—
1252C42—42no—
1253C42C22×Q818yes—
1254C42C22×Q818yes—
1255C42C22×Q814yes—
1256C42C22×Q814yes—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23C23×Q814yes—
1262C23C23×Q814yes—
1263C23C2×H(5,𝔽2)14yes—
1264C23C2611yescharacteristic
1265Q8—44no—
1266Q8—48no—
1267Q8—416no—
1268Q8—48no—
1269Q8—44no—
1270Q8—44no—
1271Q8—82no—
1272Q8—84no—
1273Q8—84no—
1274Q8—84no—
1275Q8—88no—
1276Q8—164no—
1277Q8—162no—
1278Q8—164no—
1279D4Q82116yes—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—21no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—21no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—416no—
1349C2×C4—48no—
1350C2×C4—416no—
1351C2×C4—48no—
1352C2×C4—48no—
1353C2×C4—88no—
1354C2×C4—88no—
1355C2×C4—88no—
1356C2×C4—88no—
1357C2×C4C23×Q812yes—
1358C2×C4C23×Q814yes—
1359C2×C4C23×Q814yes—
1360C2×C4C23×Q812yes—
1361C2×C4C23×Q814yes—
1362C2×C4C23×Q812yes—
1363C2×C4C23×Q814yes—
1364C2×C4C23×Q812yes—
1365C2×C4C23×Q814yes—
1366C2×C4C23×Q818yes—
1367C2×C4C23×Q818yes—
1368C2×C4C23×Q814yes—
1369C2×C4C23×Q812yes—
1370C2×C4C23×Q812yes—
1371C2×C4C2×H(5,𝔽2)12yes—
1372C2×C4#58512yes—
1373C22—24no—
1374C22—24no—
1375C22—24no—
1376C22—24no—
1377C22—24no—
1378C22—24no—
1379C22C2×Q8218yes—
1380C22C24×Q811yescharacteristic
1381C22C24×Q811yescharacteristic
1382C22C22×H(5,𝔽2)11yescharacteristic
1383C22C2×#58511yescharacteristic
1384C22H(7,𝔽2)11yescharacteristic
1385C22H(7,𝔽2)11yescharacteristic
1386C222−1+611yescharacteristic
1387C4—24no—
1388C4—28no—
1389C4—22no—
1390C4—22no—
1391C4—24no—
1392C4—24no—
1393C4—22no—
1394C4—28no—
1395C4—24no—
1396C4—22no—
1397C4—24no—
1398C4—24no—
1399C4—22no—
1400C4—42no—
1401C4—42no—
1402C4—44no—
1403C4—44no—
1404C4—42no—
1405C4—42no—
1406C4—41no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—44no—
1411C4—44no—
1412C4—42no—
1413C4—42no—
1414C4C2×Q8214yes—
1415C2—28no—
1416C2C22×Q8211yescharacteristic
1417C2#6284311yescharacteristic
1418C2#6285411yescharacteristic
1419C2#6289611yescharacteristic
1420C2#6298911yescharacteristic
1421C2#6300411yescharacteristic
1422C2#6304911yescharacteristic
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. #59923C2semidirect
2. #59918C2semidirect
3. #59871C2semidirect
4. #59668C2semidirect
5. #52287C2semidirect
6. C2×#2806C2semidirect
7. #45364C2semidirect
8. #44950C2semidirect
9. #44950C2semidirect
10. #43553C2semidirect
11. #43126C2semidirect
12. #43126C2semidirect
13. #39626C2semidirect
14. #39624C2semidirect
15. #39624C2semidirect
16. #39623C2semidirect
17. #39622C2semidirect
18. #39621C2semidirect
19. #39621C2semidirect
20. #39620C2semidirect
264. #554Q8semidirect
266. D4×Q8Q8semidirect
723. C22×Q8C2×Q8semidirect
761. C4⋊Q8C2×Q8semidirect
762. C4⋊Q8C2×Q8semidirect
763. C4⋊Q8C2×Q8semidirect
769. #125C2×Q8semidirect
780. C22⋊Q8C2×Q8semidirect
781. C22⋊Q8C2×Q8semidirect
782. C22⋊Q8C2×Q8semidirect
783. C22⋊Q8C2×Q8semidirect
795. C4×Q8C2×Q8semidirect
796. C4×Q8C2×Q8semidirect
814. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599232
#599182
#598712
#596682
#522872
C2×#28062
#453642
#449502
#435532
#431262
#396262
#396242
#396232
#396222
#396212
#396202
#362762
#362612
#359502
#359282
#343342
#343332
#343322