Finite Group Databasebeta

← #7658046

Subgroups — #7658046

Order 512.

4223 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41584C214yesmaximal, complemented
2#41575C214yesmaximal, complemented
3#41568C214yesmaximal, complemented
4#41554C214yesmaximal, complemented
5#41536C214yesmaximal, complemented
6#41532C214yesmaximal
7#39638C211yesmaximal, characteristic, complemented
8#39629C211yesmaximal, characteristic, complemented
9#38927C212yesmaximal, complemented
10#38075C212yesmaximal, complemented
11#38069C212yesmaximal, complemented
12#37897C211yesmaximal, characteristic, complemented
13#37894C211yesmaximal, characteristic, complemented
14#37888C211yesmaximal, characteristic, complemented
15#37883C211yesmaximal, characteristic, complemented
16#37580C212yesmaximal, complemented
17#37509C212yesmaximal, complemented
18#37503C212yesmaximal, complemented
19#36375C212yesmaximal
20#36191C211yesmaximal, characteristic, complemented
21#36181C211yesmaximal, characteristic, complemented
22#36068C214yesmaximal, complemented
23#36023C214yesmaximal, complemented
24#35337C211yesmaximal, characteristic, complemented
25#35315C211yesmaximal, characteristic, complemented
26#35315C211yesmaximal, characteristic, complemented
27#34638C211yesmaximal, characteristic, complemented
28#34629C211yesmaximal, characteristic, complemented
29C2×#2647C211yesmaximal, characteristic, complemented
30#34314C212yesmaximal, complemented
31#34123C211yesmaximal, characteristic
32C2×#552C2212yes—
33C2×C4×#41C2211yescharacteristic
34#2862C2211yescharacteristic
35#2859C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2855C2212yes—
39#2855C2212yes—
40#2851C2211yescharacteristic
41#2851C2212yes—
42#2851C2211yescharacteristic
43#2839C2214yes—
44#2839C2214yes—
45#2838C2214yes—
46#2835C2214yes—
47#2833C2214yes—
48#2827C2214yes—
49#2806C2214yes—
50#2805C2214yes—
51#2802C2214yes—
52#2793C2214yes—
53#2791C2214yes—
54#2781C2214yes—
55#2774C2214yes—
56#2774C2214yes—
57#2772C2214yes—
58#2770C2214yes—
59#2770C2214yes—
60#2769C2214yes—
61#2768C2214yes—
62#2767C2214yes—
63#2767C2214yes—
64#2766C2214yes—
65#2766C2214yes—
66#2765C2214yes—
67#2764C2214yes—
68#2758C2214yes—
69#2747C2214yes—
70#2745C2214yes—
71#2744C2214yes—
72#2741C2214yes—
73#2666C2214yes—
74#2666C2214yes—
75#2655C2214yes—
76#2655C2214yes—
77#2655C2214yes—
78#2655C2214yes—
79#2655C2214yes—
80#2654C2214yes—
81#2653C2214yes—
82#2652C2214yes—
83#2652C2214yes—
84#2650C2214yes—
85#2647C2211yescharacteristic
86#2647C2211yescharacteristic
87#2647C2211yescharacteristic
88#2647C2211yescharacteristic
89#2647C2211yescharacteristic
90#2647C2212yes—
91#2647C2212yes—
92#2647C2214yes—
93#2647C2211yescharacteristic
94#2647C2214yes—
95#2647C2212yes—
96#2647C2212yes—
97#2647C2211yescharacteristic
98#2646C2214yes—
99#2646C2214yes—
100#2645C2212yes—
101#2645C2212yes—
102#2645C2212yes—
103#2642C2211yescharacteristic
104#2629C2211yescharacteristic
105#2628C2212yes—
106#2627C2214yes—
107#2625C2212yes—
108#2623C2214yes—
109#2621C2211yescharacteristic
110#2596C2214yes—
111#2596C2214yes—
112#2589C2214yes—
113#2589C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2588C2214yes—
117#2585C2214yes—
118#2585C2214yes—
119#2584C2212yes—
120#2581C2212yes—
121#2575C2214yes—
122#2574C2214yes—
123#2570C2212yes—
124#2569C2214yes—
125#2565C2212yes—
126#2533C2214yes—
127#2533C2214yes—
128#2533C2214yes—
129#2528C2214yes—
130#2528C2214yes—
131#2528C2214yes—
132#2525C2214yes—
133#2524C2214yes—
134#2524C2214yes—
135#2524C2214yes—
136#2524C2214yes—
137#2524C2214yes—
138#2520C2214yes—
139#2520C2214yes—
140#2520C2214yes—
141#2520C2214yes—
142#2515C2214yes—
143#2514C2212yes—
144#2514C2214yes—
145#2511C2212yes—
146#2510C2214yes—
147#2509C2214yes—
148#2509C2212yes—
149#2508C2212yes—
150#2508C2212yes—
151#2507C2212yes—
152#2506C2214yes—
153#2505C2214yes—
154#2505C2214yes—
155#2503C2214yes—
156#2503C2212yes—
157#2499C2212yes—
158#2497C2212yes—
159#2496C2214yes—
160#2495C2212yes—
161#2493C2214yes—
162#2493C2214yes—
163#2493C2214yes—
164#2493C2214yes—
165#2488C2214yes—
166#2486C2212yes—
167#2486C2214yes—
168#2485C2212yes—
169#2484C2214yes—
170#2484C2214yes—
171#2478C2214yes—
172#2475C2214yes—
173#2466C2214yes—
174#2462C2214yes—
175#2451C2212yes—
176#2451C2212yes—
177#2450C2214yes—
178#2440C2212yes—
179#2439C2212yes—
180#2438C2214yes—
181#2423C2212yes—
182#2421C2212yes—
183#2419C2214yes—
184#2417C2212yes—
185#2415C2212yes—
186#2413C2214yes—
187#2406C2214yes—
188#2402C2214yes—
189#2402C2214yes—
190#2402C2214yes—
191#2401C2214yes—
192C2×#400C2214yes—
193C2×#398C2214yes—
194#2373C2214yes—
195#2370C2212yes—
196#2370C2214yes—
197#2368C2214yes—
198#2362C2212yes—
199#2360C2212yes—
200#2359C2214yes—
201#2359C2214yes—
202#2356C2212yes—
203#2353C2212yes—
204#2353C2212yes—
205#2352C2212yes—
206#2351C2212yes—
207#2349C2212yes—
208#2347C2212yes—
209#2346C2212yes—
210#2344C2212yes—
211#2344C2214yes—
212#2344C2214yes—
213#2343C2214yes—
214#2343C2212yes—
215#2343C2212yes—
216#2339C2212yes—
217#2336C2214yes—
218#2334C2214yes—
219#2331C2212yes—
220#2330C2211yescharacteristic
221#2330C2211yescharacteristic
222#2327C2211yescharacteristic
223#2327C2211yescharacteristic
224#2322C2214yes—
225#2320C2212yes—
226#2320C2212yes—
227#2314C2211yescharacteristic
228#2314C2211yescharacteristic
229C4×C4⋊Q8C2211yescharacteristic
230C4×#125C2212yes—
231C4×#125C2211yescharacteristic
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235#2296C2212yes—
236#2296C2212yes—
237#2295C2212yes—
238#2295C2211yescharacteristic
239#2295C2211yescharacteristic
240C2×#389C2212yes—
241C2×#389C2212yes—
242#2290C2211yescharacteristic
243#2290C2211yescharacteristic
244#2290C2211yescharacteristic
245#2290C2211yescharacteristic
246#2285C2211yescharacteristic
247#2285C2211yescharacteristic
248C2×#384C2211yescharacteristic
249#2283C2211yescharacteristic
250#2283C2211yescharacteristic
251#2283C2211yescharacteristic
252C2×#382C2211yescharacteristic
253#2274C2214yes—
254C42×D4C2211yescharacteristic
255C42×D4C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C2×#376C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C22×#41C2311yescharacteristic
260#552—216no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×#126C2314yes—
264C2×#125C2312yes—
265C2×#125C2311yescharacteristic
266C2×#125C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C4×#41—28no—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C2×#117C2314yes—
291C2×#117C2311yescharacteristic
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2311yescharacteristic
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2314yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2312yes—
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308#401C2314yes—
309#401C2314yes—
310#401C2314yes—
311#401C2314yes—
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#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#399C2314yes—
355#399C2314yes—
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#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#394C2314yes—
409#394C2314yes—
410#393C2314yes—
411#393C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2312yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2312yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
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#387C2312yes—
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#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#386C2312yes—
556#386C2314yes—
557#386C2312yes—
558#386C2312yes—
559#386C2312yes—
560#386C2314yes—
561#385C2312yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2312yes—
569#385C2314yes—
570#385C2314yes—
571#385C2312yes—
572#385C2312yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#384C2311yescharacteristic
581#384C2312yes—
582#384C2311yescharacteristic
583#384C2311yescharacteristic
584#384C2312yes—
585#384C2314yes—
586#383C2314yes—
587#383C2314yes—
588#383C2314yes—
589#383C2312yes—
590#383C2312yes—
591#383C2312yes—
592#383C2314yes—
593#383C2314yes—
594#382C2312yes—
595#382C2311yescharacteristic
596#382C2312yes—
597#382C2311yescharacteristic
598#382C2311yescharacteristic
599#382C2312yes—
600#382C2314yes—
601#382C2314yes—
602#382C2314yes—
603#382C2314yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2314yes—
609#382C2314yes—
610#381C2312yes—
611#381C2314yes—
612#381C2312yes—
613#381C2312yes—
614#381C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2312yes—
622#380C2312yes—
623#380C2314yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2314yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2311yescharacteristic
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2311yescharacteristic
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2311yescharacteristic
676C4×C22⋊C4C2311yescharacteristic
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2311yescharacteristic
679C4×C22⋊C4C2311yescharacteristic
680C4×C22⋊C4C2311yescharacteristic
681C4×C22⋊C4C2311yescharacteristic
682#376C2311yescharacteristic
683#376C2311yescharacteristic
684#376C2311yescharacteristic
685#376C2311yescharacteristic
686#376C2311yescharacteristic
687#376C2312yes—
688#376C2312yes—
689#376C2314yes—
690#376C2312yes—
691#376C2312yes—
692#376C2311yescharacteristic
693#376C2311yescharacteristic
694#376C2311yescharacteristic
695C2×#95C2314yes—
696C2×#95C2312yes—
697C2×#95C2312yes—
698C2×#95C2314yes—
699C2×#95C2312yes—
700C2×#95C2312yes—
701C2×#95C2314yes—
702C43C2311yescharacteristic
703C43C2311yescharacteristic
704C2×#41—24no—
705C2×#41—44no—
706C22×Q8C2412yes—
707C22×Q8C2411yescharacteristic
708C22×Q8C2414yes—
709C22×D4C2411yescharacteristic
710C22×D4C2411yescharacteristic
711C22×D4C2411yescharacteristic
712C23×C4C2414yes—
713C23×C4C2411yescharacteristic
714C23×C4C2411yescharacteristic
715C23×C4C2412yes—
716C23×C4C2411yescharacteristic
717C23×C4C2411yescharacteristic
718C23×C4C2414yes—
719C23×C4C2412yes—
720C23×C4C2411yescharacteristic
721C23×C4C2411yescharacteristic
722C23×C4C2411yescharacteristic
723C23×C4C2411yescharacteristic
724C23×C4C2411yescharacteristic
725C23×C4C2412yes—
726C23×C4C2412yes—
727C4⋊Q8—24no—
728C4⋊Q8—44no—
729#126—216no—
730#125—216no—
731#125—28no—
732#125—24no—
733#123—216no—
734#123—48no—
735C22⋊Q8—28no—
736C22⋊Q8—28no—
737C22⋊Q8—48no—
738C22⋊Q8—44no—
739C4×Q8—24no—
740C4×Q8—24no—
741C4×Q8—28no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×D4—24no—
745C4×D4—24no—
746C4×D4—24no—
747C4×D4—24no—
748C4×D4—24no—
749C4×D4—44no—
750C4×D4—44no—
751C4×D4#4118yes—
752#117—28no—
753#117—24no—
754#117—24no—
755#117—24no—
756#117—216no—
757#117—24no—
758#117—42no—
759#117—48no—
760#117—44no—
761C2×C4⋊C4—28no—
762C2×C4⋊C4—44no—
763C2×C4⋊C4—48no—
764C2×C4⋊C4—48no—
765C2×C4⋊C4—48no—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2411yescharacteristic
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2411yescharacteristic
850C2×C22⋊C4C2411yescharacteristic
851C2×C42—24no—
852C2×C42—24no—
853C2×C42—24no—
854C2×C42—24no—
855C2×C42—24no—
856C2×C42—42no—
857C2×C42—42no—
858C2×C42C2414yes—
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2414yes—
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2411yescharacteristic
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894#95C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979C24C2511yescharacteristic
980C24C2511yescharacteristic
981C24C2511yescharacteristic
982#41—416no—
983C2×Q8—22no—
984C2×Q8—24no—
985C2×Q8—24no—
986C2×Q8—24no—
987C2×Q8—42no—
988C2×Q8—44no—
989C2×Q8—44no—
990C2×Q8—44no—
991C2×D4—24no—
992C2×D4—22no—
993C2×D4—22no—
994C2×D4—24no—
995C2×D4—42no—
996C2×D4C2×#4114yes—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—28no—
1004C22×C4—28no—
1005C22×C4—24no—
1006C22×C4—28no—
1007C22×C4—24no—
1008C22×C4—22no—
1009C22×C4—22no—
1010C22×C4—24no—
1011C22×C4—28no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—24no—
1015C22×C4—22no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—24no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—44no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4C2×#4114yes—
1035C22×C4C2×#4114yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2514yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2514yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—28no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
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⋊C4C2×#4114yes—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—24no—
1131C22⋊C4—28no—
1132C22⋊C4—24no—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—24no—
1136C22⋊C4—44no—
1137C22⋊C4—42no—
1138C22⋊C4—44no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—44no—
1142C22⋊C4—42no—
1143C22⋊C4—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4C2×#4114yes—
1148C22⋊C4C2×#4114yes—
1149C42—22no—
1150C42—22no—
1151C42—22no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—22no—
1156C42—22no—
1157C42—22no—
1158C42—28no—
1159C42—28no—
1160C42—24no—
1161C42—24no—
1162C42—22no—
1163C42—22no—
1164C42—22no—
1165C42—22no—
1166C42—22no—
1167C42—22no—
1168C42—22no—
1169C42—42no—
1170C42—42no—
1171C42—42no—
1172C42—42no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—44no—
1183C42C2×#4114yes—
1184C422−1+414yes—
1185C23—21no—
1186C23—21no—
1187C23—22no—
1188C23—21no—
1189C23—21no—
1190C23—22no—
1191C23—22no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—22no—
1196C23—22no—
1197C23C22×#4112yes—
1198C23C22×#4112yes—
1199C23#58514yes—
1200C23C2611yescharacteristic
1201Q8—44no—
1202Q8—48no—
1203Q8—164no—
1204D4—28no—
1205D4—44no—
1206D4—44no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—28no—
1216C2×C4—28no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—24no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—21no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—48no—
1278C2×C4—44no—
1279C2×C4—44no—
1280C2×C4—416no—
1281C2×C4—44no—
1282C2×C4—44no—
1283C2×C4—82no—
1284C2×C4—84no—
1285C2×C4—82no—
1286C2×C4—82no—
1287C2×C4—84no—
1288C2×C4—88no—
1289C2×C4—84no—
1290C2×C4C22×#4112yes—
1291C2×C4C22×#4112yes—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4112yes—
1294C2×C4C22×#4112yes—
1295C2×C4C2×2−1+414yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4#58512yes—
1298C22—22no—
1299C22—22no—
1300C22—24no—
1301C22—24no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—42no—
1306C22—42no—
1307C22—41no—
1308C22—41no—
1309C22—42no—
1310C22—42no—
1311C22—41no—
1312C22#345514yes—
1313C22C23×#4111yescharacteristic
1314C22C22×2−1+411yescharacteristic
1315C22C2×#58511yescharacteristic
1316C22C2×#58512yes—
1317C222−1+612yes—
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—24no—
1322C4—22no—
1323C4—41no—
1324C4—44no—
1325C4—44no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4—42no—
1337C4—44no—
1338C4—44no—
1339C4—42no—
1340C4—44no—
1341C4—44no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4#351514yes—
1346C2—24no—
1347C2—42no—
1348C2—81no—
1349C2C2×#345511yescharacteristic
1350C2C2×#351511yescharacteristic
1351C2#6286111yescharacteristic
1352C2#6292812yes—
1353C2#6294012yes—
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. #41584C2semidirect
2. #41575C2semidirect
3. #41568C2semidirect
4. #41554C2semidirect
5. #41536C2semidirect
7. #39638C2semidirect
8. #39629C2semidirect
9. #38927C2semidirect
10. #38075C2semidirect
11. #38069C2semidirect
12. #37897C2semidirect
13. #37894C2semidirect
14. #37888C2semidirect
15. #37883C2semidirect
16. #37580C2semidirect
17. #37509C2semidirect
18. #37503C2semidirect
20. #36191C2semidirect
21. #36181C2semidirect
22. #36068C2semidirect
23. #36023C2semidirect
24. #35337C2semidirect
25. #35315C2semidirect
26. #35315C2semidirect
27. #34638C2semidirect
28. #34629C2semidirect
29. C2×#2647C2semidirect
30. #34314C2semidirect

Maximal subgroups

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

subgroupindex
#415842
#415752
#415682
#415542
#415362
#415322
#396382
#396292
#389272
#380752
#380692
#378972
#378942
#378882
#378832
#375802
#375092
#375032
#363752
#361912
#361812
#360682
#360232
#353372
#353152
#346382
#346292
C2×#26472
#343142
#341232