Finite Group Databasebeta

← #7655460

Subgroups — #7655460

Order 512.

4656 conjugacy classes of subgroups.

The subgroup lattice has 1383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42823C212yesmaximal, complemented
2#42819C212yesmaximal, complemented
3#40621C214yesmaximal, complemented
4#40617C214yesmaximal, complemented
5#39986C212yesmaximal, complemented
6#39982C212yesmaximal, complemented
7#39979C212yesmaximal, complemented
8#39975C212yesmaximal, complemented
9#38449C214yesmaximal, complemented
10#38447C214yesmaximal, complemented
11#38442C214yesmaximal, complemented
12#38441C214yesmaximal, complemented
13#37567C211yesmaximal, characteristic, complemented
14#37562C212yesmaximal, complemented
15#36275C212yesmaximal
16#36261C212yesmaximal, complemented
17#36239C212yesmaximal, complemented
18#36219C212yesmaximal
19#35950C212yesmaximal, complemented
20#35858C212yesmaximal, complemented
21#35304C212yesmaximal, complemented
22#35235C212yesmaximal, complemented
23#35202C211yesmaximal, characteristic, complemented
24#35104C211yesmaximal, characteristic, complemented
25#34966C211yesmaximal, characteristic, complemented
26C2×#2606C212yesmaximal, complemented
27#34195C211yesmaximal, characteristic
28#34123C211yesmaximal, characteristic
29C4⋊C4×#41C211yesmaximal, characteristic
30C2×#554C2212yes—
31C2×#554C2212yes—
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2864C2212yes—
36#2859C2212yes—
37#2857C2212yes—
38#2857C2214yes—
39#2855C2214yes—
40#2855C2214yes—
41#2851C2212yes—
42#2851C2214yes—
43#2843C2214yes—
44#2843C2214yes—
45#2841C2214yes—
46#2807C2214yes—
47#2805C2214yes—
48#2802C2214yes—
49#2802C2214yes—
50#2802C2214yes—
51#2792C2214yes—
52#2792C2214yes—
53#2792C2214yes—
54#2791C2214yes—
55#2791C2214yes—
56#2790C2214yes—
57#2788C2214yes—
58#2774C2214yes—
59#2774C2214yes—
60#2768C2214yes—
61#2768C2214yes—
62#2755C2214yes—
63#2734C2214yes—
64#2726C2214yes—
65#2726C2214yes—
66#2720C2214yes—
67#2713C2214yes—
68#2704C2214yes—
69#2677C2214yes—
70#2667C2212yes—
71#2667C2212yes—
72#2667C2212yes—
73#2666C2214yes—
74#2666C2214yes—
75#2666C2214yes—
76#2666C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2665C2212yes—
81#2660C2212yes—
82#2660C2214yes—
83#2659C2214yes—
84#2647C2212yes—
85#2647C2214yes—
86#2646C2214yes—
87#2627C2214yes—
88#2612C2214yes—
89#2612C2214yes—
90#2606C2212yes—
91#2606C2212yes—
92#2606C2214yes—
93#2606C2214yes—
94#2606C2211yescharacteristic
95#2606C2214yes—
96#2606C2214yes—
97#2606C2214yes—
98#2606C2214yes—
99#2606C2212yes—
100#2606C2212yes—
101#2606C2212yes—
102#2606C2211yescharacteristic
103#2605C2212yes—
104#2605C2212yes—
105#2605C2211yescharacteristic
106#2605C2211yescharacteristic
107#2605C2212yes—
108#2584C2212yes—
109#2584C2212yes—
110#2584C2212yes—
111#2583C2214yes—
112#2583C2214yes—
113#2583C2214yes—
114#2582C2212yes—
115#2581C2212yes—
116#2579C2214yes—
117#2570C2212yes—
118#2570C2212yes—
119#2570C2212yes—
120#2570C2212yes—
121#2570C2214yes—
122#2569C2214yes—
123#2569C2214yes—
124#2569C2214yes—
125#2567C2212yes—
126#2565C2212yes—
127#2564C2214yes—
128#2552C2212yes—
129#2552C2212yes—
130#2552C2212yes—
131#2552C2212yes—
132#2551C2212yes—
133#2550C2212yes—
134#2550C2212yes—
135#2550C2212yes—
136#2550C2212yes—
137#2550C2214yes—
138#2550C2212yes—
139#2549C2214yes—
140#2549C2214yes—
141#2549C2214yes—
142#2549C2214yes—
143#2546C2212yes—
144#2509C2212yes—
145#2508C2212yes—
146#2508C2212yes—
147#2507C2212yes—
148#2507C2212yes—
149#2507C2212yes—
150#2506C2212yes—
151#2506C2212yes—
152#2505C2214yes—
153#2505C2214yes—
154#2505C2214yes—
155#2502C2214yes—
156#2487C2214yes—
157#2473C2214yes—
158#2473C2214yes—
159#2473C2214yes—
160#2473C2214yes—
161#2473C2214yes—
162#2453C2212yes—
163#2453C2212yes—
164#2453C2212yes—
165#2451C2212yes—
166#2450C2214yes—
167#2449C2214yes—
168#2449C2214yes—
169#2449C2214yes—
170#2442C2214yes—
171#2442C2212yes—
172#2441C2214yes—
173#2441C2212yes—
174#2441C2212yes—
175#2441C2212yes—
176#2440C2214yes—
177#2440C2214yes—
178#2440C2214yes—
179#2440C2214yes—
180#2440C2212yes—
181#2439C2212yes—
182#2438C2212yes—
183#2438C2212yes—
184#2438C2214yes—
185#2438C2214yes—
186#2438C2214yes—
187#2438C2214yes—
188#2417C2214yes—
189#2402C2212yes—
190#2399C2212yes—
191C2×#398C2214yes—
192C2×#398C2214yes—
193#2356C2211yescharacteristic
194#2356C2211yescharacteristic
195#2356C2211yescharacteristic
196#2356C2211yescharacteristic
197#2353C2212yes—
198#2353C2212yes—
199#2353C2212yes—
200#2353C2212yes—
201#2351C2212yes—
202Q8×C4⋊C4C2212yes—
203#2349C2211yescharacteristic
204#2349C2212yes—
205#2349C2214yes—
206#2349C2212yes—
207#2349C2211yescharacteristic
208#2349C2212yes—
209#2349C2211yescharacteristic
210#2349C2211yescharacteristic
211D4×C4⋊C4C2212yes—
212D4×C4⋊C4C2212yes—
213D4×C4⋊C4C2212yes—
214D4×C4⋊C4C2212yes—
215D4×C4⋊C4C2214yes—
216D4×C4⋊C4C2212yes—
217#2347C2212yes—
218#2346C2212yes—
219#2343C2214yes—
220#2343C2214yes—
221#2339C2212yes—
222#2339C2212yes—
223#2331C2214yes—
224#2331C2214yes—
225#2330C2214yes—
226#2330C2214yes—
227#2330C2214yes—
228#2329C2214yes—
229#2320C2212yes—
230#2318C2214yes—
231C4×C4⋊Q8C2212yes—
232C4×#125C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235#2296C2211yescharacteristic
236#2296C2212yes—
237#2296C2212yes—
238#2296C2211yescharacteristic
239#2295C2212yes—
240C2×#389C2214yes—
241C2×#389C2214yes—
242#2290C2214yes—
243C2×#387C2214yes—
244C2×#387C2214yes—
245#2285C2211yescharacteristic
246#2285C2212yes—
247#2283C2211yescharacteristic
248#2283C2211yescharacteristic
249#2283C2212yes—
250#2283C2211yescharacteristic
251#2283C2212yes—
252C2×#383C2212yes—
253#2275C2212yes—
254C42×D4C2212yes—
255C4×#117C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2212yes—
258C2×#376C2212yes—
259C22×#41C2311yescharacteristic
260#554—48no—
261#554—48no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C4×#41—44no—
285C4×#41—44no—
286C4×#41Q8116yescomplemented
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2311yescharacteristic
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2314yes—
317C22×C4⋊C4C2314yes—
318C22×C4⋊C4C2314yes—
319C22×C4⋊C4C2314yes—
320C22×C42C2311yescharacteristic
321C22×C42C2314yes—
322C22×C42C2312yes—
323C22×C42C2312yes—
324C22×C42C2311yescharacteristic
325C22×C42C2312yes—
326C22×C42C2311yescharacteristic
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
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#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2312yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2312yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2312yes—
417#395C2314yes—
418#395C2312yes—
419#395C2312yes—
420#395C2314yes—
421#395C2314yes—
422#393C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#387C2312yes—
510#387C2312yes—
511#387C2312yes—
512#387C2312yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2312yes—
533#387C2312yes—
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#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#385C2312yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2312yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2312yes—
588#385C2312yes—
589#384C2312yes—
590#384C2312yes—
591#384C2312yes—
592#384C2312yes—
593#384C2312yes—
594#384C2314yes—
595#384C2314yes—
596#384C2314yes—
597#384C2314yes—
598#384C2312yes—
599#383C2314yes—
600#383C2312yes—
601#383C2312yes—
602#383C2312yes—
603#383C2314yes—
604#383C2311yescharacteristic
605#383C2311yescharacteristic
606#383C2312yes—
607#383C2312yes—
608#383C2312yes—
609#382C2312yes—
610#382C2312yes—
611#382C2312yes—
612#382C2311yescharacteristic
613#382C2311yescharacteristic
614#382C2314yes—
615#382C2312yes—
616#382C2314yes—
617#382C2312yes—
618#382C2314yes—
619#382C2314yes—
620#382C2311yescharacteristic
621#382C2314yes—
622#382C2311yescharacteristic
623#381C2312yes—
624#381C2312yes—
625#381C2314yes—
626#381C2314yes—
627#381C2311yescharacteristic
628#381C2311yescharacteristic
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2312yes—
639#380C2314yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649C4×C4⋊C4C2311yescharacteristic
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694#376C2312yes—
695#376C2312yes—
696#376C2312yes—
697#376C2314yes—
698#376C2312yes—
699#376C2312yes—
700#376C2311yescharacteristic
701#376C2311yescharacteristic
702#376C2312yes—
703#376C2312yes—
704#376C2314yes—
705C2×#95C2314yes—
706C2×#95C2312yes—
707C2×#95C2312yes—
708C2×#95C2314yes—
709C2×#95C2314yes—
710C2×#95C2312yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C2×#95C2314yes—
716C43C2312yes—
717C2×#41—24no—
718C2×#41—24no—
719C2×#41C2×Q818yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2414yes—
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2412yes—
730C23×C4C2411yescharacteristic
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2414yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2412yes—
741C4⋊Q8—48no—
742C4⋊Q8—44no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—48no—
746#125—48no—
747#125—44no—
748#125—44no—
749#125—44no—
750#125—44no—
751#125—44no—
752#125—48no—
753#125—48no—
754C22⋊Q8—48no—
755C22⋊Q8—48no—
756C22⋊Q8—48no—
757C22⋊Q8—48no—
758C22⋊Q8—48no—
759C22⋊Q8—48no—
760C22⋊Q8—44no—
761C22⋊Q8—44no—
762C22⋊Q8—48no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×Q8—44no—
766C4×Q8—44no—
767C4×Q8C2×Q818yes—
768C4×Q8C2×Q818yes—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—28no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—48no—
776C4×D4—48no—
777C4×D4C2×Q8116yes—
778C4×D4C2×Q8116yes—
779C4×D4C2×Q818yes—
780C4×D4C2×Q818yes—
781#117—44no—
782#117—44no—
783#117—44no—
784#117—42no—
785#117—42no—
786#117C2×Q8116yes—
787#117C2×Q818yes—
788C2×C4⋊C4—48no—
789C2×C4⋊C4—44no—
790C2×C4⋊C4—48no—
791C2×C4⋊C4—48no—
792C2×C4⋊C4—48no—
793C2×C4⋊C4—48no—
794C2×C4⋊C4—48no—
795C2×C4⋊C4—48no—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C42—42no—
892C2×C42—42no—
893C2×C42—48no—
894C2×C42—44no—
895C2×C42—44no—
896C2×C42C2×Q8116yes—
897C2×C42C2×Q818yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929#95C2412yes—
930#95C2412yes—
931#95C2411yescharacteristic
932#95C2411yescharacteristic
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2411yescharacteristic
937#95C2411yescharacteristic
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2411yescharacteristic
969#95C2411yescharacteristic
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2411yescharacteristic
974#95C2411yescharacteristic
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011C24C2511yescharacteristic
1012C24C2512yes—
1013#41—232no—
1014C2×Q8—22no—
1015C2×Q8—22no—
1016C2×Q8—24no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—42no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8C22×Q814yes—
1029C2×D4—24no—
1030C2×D4—24no—
1031C2×D4C22×Q818yes—
1032C2×D4C22×Q814yes—
1033C2×D4H(5,𝔽2)14yes—
1034C2×D42−1+414yes—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—28no—
1040C22×C4—28no—
1041C22×C4—28no—
1042C22×C4—28no—
1043C22×C4—28no—
1044C22×C4—28no—
1045C22×C4—28no—
1046C22×C4—28no—
1047C22×C4—24no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4C22×Q818yes—
1068C22×C4C22×Q814yes—
1069C22×C4C22×Q814yes—
1070C22×C4C22×Q814yes—
1071C22×C4C22×Q818yes—
1072C22×C4C22×Q818yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4C22×Q818yes—
1175C4⋊C4C22×Q818yes—
1176C4⋊C4C22×Q814yes—
1177C4⋊C4C22×Q814yes—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—28no—
1184C22⋊C4—24no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4C22×Q818yes—
1193C22⋊C4C22×Q818yes—
1194C22⋊C4C22×Q818yes—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—24no—
1202C42—28no—
1203C42—41no—
1204C42—41no—
1205C42—44no—
1206C42—44no—
1207C42—41no—
1208C42—41no—
1209C42—42no—
1210C42—42no—
1211C42—44no—
1212C42—44no—
1213C42—42no—
1214C42—44no—
1215C42—42no—
1216C42—44no—
1217C42—42no—
1218C42—44no—
1219C42C22×Q814yes—
1220C42C22×Q818yes—
1221C42C22×Q814yes—
1222C42C22×Q818yes—
1223C42C22×Q818yes—
1224C42C22×Q814yes—
1225C42C22×Q814yes—
1226C23—24no—
1227C23—24no—
1228C23—21no—
1229C23—21no—
1230C23—22no—
1231C23—22no—
1232C23C23×Q812yes—
1233C23C23×Q814yes—
1234C23C2×H(5,𝔽2)14yes—
1235C23C2×2−1+414yes—
1236C23C2611yescharacteristic
1237Q8—28no—
1238Q8—84no—
1239Q8—84no—
1240Q8—164no—
1241Q8—164no—
1242D4—216no—
1243D4#544116yes—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—216no—
1259C2×C4—28no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—48no—
1309C2×C4—48no—
1310C2×C4—44no—
1311C2×C4—44no—
1312C2×C4—416no—
1313C2×C4—416no—
1314C2×C4—84no—
1315C2×C4—88no—
1316C2×C4—88no—
1317C2×C4—88no—
1318C2×C4—88no—
1319C2×C4—84no—
1320C2×C4C23×Q812yes—
1321C2×C4C23×Q812yes—
1322C2×C4C23×Q812yes—
1323C2×C4C23×Q814yes—
1324C2×C4C23×Q814yes—
1325C2×C4C23×Q812yes—
1326C2×C4C23×Q812yes—
1327C2×C4C23×Q814yes—
1328C2×C4C23×Q812yes—
1329C2×C4C2×H(5,𝔽2)12yes—
1330C2×C4C2×2−1+412yes—
1331C2×C4#58514yes—
1332C2×C4#58514yes—
1333C22—28no—
1334C22—28no—
1335C22—24no—
1336C22—24no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—42no—
1341C22—42no—
1342C22C2×#54418yes—
1343C22C24×Q811yescharacteristic
1344C22C22×H(5,𝔽2)11yescharacteristic
1345C22C22×2−1+411yescharacteristic
1346C22C2×#58512yes—
1347C22C2×#58512yes—
1348C4—24no—
1349C4—24no—
1350C4—22no—
1351C4—22no—
1352C4—24no—
1353C4—22no—
1354C4—24no—
1355C4—22no—
1356C4—22no—
1357C4—24no—
1358C4—44no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—44no—
1365C4—42no—
1366C4—44no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—44no—
1372C4—44no—
1373C4—42no—
1374C4C2×#54414yes—
1375C2—28no—
1376C2—42no—
1377C2C22×#54411yescharacteristic
1378C2#6281311yescharacteristic
1379C2#6281311yescharacteristic
1380C2#6301812yes—
1381C2#6302312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42823C2semidirect
2. #42819C2semidirect
3. #40621C2semidirect
4. #40617C2semidirect
5. #39986C2semidirect
6. #39982C2semidirect
7. #39979C2semidirect
8. #39975C2semidirect
9. #38449C2semidirect
10. #38447C2semidirect
11. #38442C2semidirect
12. #38441C2semidirect
13. #37567C2semidirect
14. #37562C2semidirect
16. #36261C2semidirect
17. #36239C2semidirect
19. #35950C2semidirect
20. #35858C2semidirect
21. #35304C2semidirect
22. #35235C2semidirect
23. #35202C2semidirect
24. #35104C2semidirect
25. #34966C2semidirect
26. C2×#2606C2semidirect
286. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#428232
#428192
#406212
#406172
#399862
#399822
#399792
#399752
#384492
#384472
#384422
#384412
#375672
#375622
#362752
#362612
#362392
#362192
#359502
#358582
#353042
#352352
#352022
#351042
#349662
C2×#26062
#341952
#341232
C4⋊C4×#412