Finite Group Databasebeta

← #7683816

Subgroups — #7683816

Order 512.

4344 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59927C214yesmaximal, complemented
2#59712C214yesmaximal
3#59671C212yesmaximal, complemented
4#59669C214yesmaximal, complemented
5#59612C214yesmaximal
6#59464C212yesmaximal, complemented
7#59245C212yesmaximal
8#59154C212yesmaximal
9#45435C211yesmaximal, characteristic, complemented
10#45409C212yesmaximal
11#45395C211yesmaximal, characteristic, complemented
12#45277C211yesmaximal, characteristic, complemented
13#45190C212yesmaximal
14#45164C211yesmaximal, characteristic, complemented
15#44753C214yesmaximal, complemented
16#44701C214yesmaximal
17#44667C214yesmaximal, complemented
18#44625C214yesmaximal
19#35643C212yesmaximal, complemented
20#35582C212yesmaximal, complemented
21#35577C212yesmaximal
22#34951C212yesmaximal, complemented
23#34882C211yesmaximal, characteristic
24#34336C212yesmaximal, complemented
25#34286C212yesmaximal
26#34281C211yesmaximal, characteristic
27#34217C211yesmaximal, characteristic
28C2×#557C2212yes—
29C2×#541C2211yescharacteristic
30C22×#125C2211yescharacteristic
31#2806C2214yes—
32#2805C2214yes—
33#2805C2214yes—
34#2805C2214yes—
35#2802C2214yes—
36#2792C2214yes—
37#2792C2214yes—
38#2791C2214yes—
39#2788C2214yes—
40#2788C2214yes—
41#2788C2214yes—
42#2774C2214yes—
43#2774C2214yes—
44#2774C2214yes—
45#2774C2214yes—
46#2768C2214yes—
47#2755C2214yes—
48#2742C2214yes—
49#2734C2214yes—
50#2726C2214yes—
51#2726C2214yes—
52#2713C2214yes—
53#2713C2214yes—
54#2704C2214yes—
55#2612C2214yes—
56#2612C2214yes—
57#2606C2214yes—
58#2605C2214yes—
59#2605C2214yes—
60#2605C2214yes—
61#2590C2214yes—
62#2590C2214yes—
63#2590C2214yes—
64#2588C2214yes—
65#2588C2214yes—
66#2588C2214yes—
67#2588C2214yes—
68#2588C2214yes—
69#2588C2214yes—
70#2588C2214yes—
71#2588C2214yes—
72#2588C2214yes—
73#2587C2214yes—
74#2586C2214yes—
75#2586C2214yes—
76#2586C2212yes—
77#2586C2214yes—
78#2586C2214yes—
79#2585C2212yes—
80#2585C2214yes—
81#2585C2214yes—
82#2585C2214yes—
83#2585C2214yes—
84#2584C2212yes—
85#2582C2212yes—
86#2582C2212yes—
87#2581C2212yes—
88#2574C2212yes—
89#2574C2214yes—
90#2574C2214yes—
91#2574C2214yes—
92#2571C2212yes—
93#2570C2214yes—
94#2570C2212yes—
95#2568C2212yes—
96#2568C2212yes—
97#2567C2212yes—
98#2565C2212yes—
99#2556C2212yes—
100#2552C2212yes—
101#2551C2214yes—
102#2551C2212yes—
103#2551C2212yes—
104#2550C2212yes—
105#2550C2214yes—
106#2550C2214yes—
107#2550C2214yes—
108#2550C2212yes—
109#2546C2212yes—
110#2522C2212yes—
111#2520C2214yes—
112#2520C2214yes—
113#2520C2214yes—
114#2520C2212yes—
115#2511C2214yes—
116#2511C2214yes—
117#2511C2214yes—
118#2511C2214yes—
119#2509C2212yes—
120#2509C2212yes—
121#2509C2212yes—
122#2509C2214yes—
123#2509C2212yes—
124#2508C2214yes—
125#2508C2212yes—
126#2508C2214yes—
127#2507C2214yes—
128#2506C2214yes—
129#2506C2214yes—
130#2506C2212yes—
131#2497C2214yes—
132#2497C2214yes—
133#2492C2214yes—
134#2492C2214yes—
135#2492C2214yes—
136#2473C2214yes—
137#2473C2214yes—
138#2465C2212yes—
139#2465C2214yes—
140#2462C2214yes—
141#2462C2212yes—
142#2462C2214yes—
143#2462C2214yes—
144#2453C2212yes—
145#2453C2212yes—
146#2453C2212yes—
147#2451C2212yes—
148#2451C2214yes—
149#2451C2212yes—
150#2451C2212yes—
151#2446C2214yes—
152#2446C2214yes—
153#2446C2214yes—
154#2442C2212yes—
155#2440C2214yes—
156#2440C2212yes—
157#2439C2212yes—
158#2439C2212yes—
159#2402C2214yes—
160#2402C2214yes—
161#2399C2211yescharacteristic
162#2399C2211yescharacteristic
163#2396C2211yescharacteristic
164#2396C2211yescharacteristic
165#2373C2214yes—
166#2373C2214yes—
167#2373C2214yes—
168#2373C2214yes—
169#2371C2214yes—
170#2371C2214yes—
171#2370C2212yes—
172#2370C2214yes—
173#2370C2214yes—
174#2370C2214yes—
175#2370C2214yes—
176#2370C2214yes—
177#2370C2212yes—
178#2370C2212yes—
179#2370C2212yes—
180#2370C2214yes—
181#2370C2214yes—
182#2369C2214yes—
183#2369C2212yes—
184#2369C2214yes—
185#2369C2214yes—
186#2365C2212yes—
187#2365C2212yes—
188#2362C2212yes—
189#2362C2212yes—
190#2360C2214yes—
191#2360C2212yes—
192#2360C2212yes—
193#2355C2212yes—
194#2355C2214yes—
195#2351C2212yes—
196#2351C2212yes—
197Q8×C4⋊C4C2212yes—
198#2345C2214yes—
199#2345C2214yes—
200#2336C2214yes—
201#2334C2214yes—
202#2331C2212yes—
203#2331C2214yes—
204#2331C2212yes—
205#2330C2211yescharacteristic
206#2330C2214yes—
207#2330C2211yescharacteristic
208#2330C2211yescharacteristic
209#2330C2211yescharacteristic
210#2330C2211yescharacteristic
211#2327C2211yescharacteristic
212#2323C2212yes—
213#2320C2212yes—
214#2316C2212yes—
215#2314C2211yescharacteristic
216C4×C4⋊Q8C2214yes—
217C4×C4⋊Q8C2211yescharacteristic
218C4×C4⋊Q8C2212yes—
219C4×#125C2214yes—
220C4×#125C2214yes—
221C4×#125C2211yescharacteristic
222C4×#125C2212yes—
223C4×#125C2212yes—
224C4×#125C2212yes—
225C4×#125C2212yes—
226C4×#126C2214yes—
227C4×C22⋊Q8C2212yes—
228C4×C22⋊Q8C2212yes—
229#2298C2212yes—
230#2295C2214yes—
231#2295C2214yes—
232#2295C2212yes—
233#2295C2211yescharacteristic
234#2295C2212yes—
235#2295C2212yes—
236#2285C2211yescharacteristic
237#2276C2212yes—
238#2276C2212yes—
239#2274C2212yes—
240C42×Q8C2212yes—
241C42×Q8C2211yescharacteristic
242C4×#117C2211yescharacteristic
243#557—216no—
244#541Q8116yescomplemented
245C2×C4⋊Q8C2314yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2314yes—
251C2×C4⋊Q8C2314yes—
252C2×C4⋊Q8C2311yescharacteristic
253C2×#126C2314yes—
254C2×#125—28no—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2311yescharacteristic
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#125C2311yescharacteristic
264C2×#125C2314yes—
265C2×#125C2311yescharacteristic
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×#117C2311yescharacteristic
283C2×#117C2312yes—
284C2×#117C2311yescharacteristic
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2314yes—
287C22×C42C2311yescharacteristic
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2311yescharacteristic
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2311yescharacteristic
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#399C2311yescharacteristic
313#399C2311yescharacteristic
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2312yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2312yes—
328#398C2312yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2312yes—
341#398C2312yes—
342#398C2312yes—
343#398C2314yes—
344#396C2312yes—
345#396C2314yes—
346#396C2314yes—
347#396C2312yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2312yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2311yescharacteristic
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2312yes—
363#395C2314yes—
364#395C2314yes—
365#395C2312yes—
366#395C2311yescharacteristic
367#395C2312yes—
368#393C2311yescharacteristic
369#393C2314yes—
370#393C2314yes—
371#393C2311yescharacteristic
372#391C2312yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2312yes—
377#391C2312yes—
378#391C2314yes—
379#391C2312yes—
380#391C2312yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2312yes—
386#391C2314yes—
387#391C2312yes—
388#391C2314yes—
389#391C2314yes—
390#391C2312yes—
391#391C2314yes—
392#391C2314yes—
393#391C2312yes—
394#391C2312yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2314yes—
413#389C2312yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2314yes—
431#389C2314yes—
432#389C2312yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#388C2312yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2312yes—
477#388C2312yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2312yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2312yes—
486#387C2312yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2312yes—
491#387C2312yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2312yes—
496#387C2314yes—
497#387C2312yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2312yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2312yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2312yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2312yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2312yes—
535#387C2314yes—
536#387C2312yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2312yes—
544#387C2312yes—
545#387C2314yes—
546#387C2312yes—
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#387C2312yes—
563#385C2314yes—
564#385C2314yes—
565#385C2312yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2312yes—
570#384C2312yes—
571#384C2311yescharacteristic
572#384C2314yes—
573#384C2314yes—
574#384C2311yescharacteristic
575#384C2311yescharacteristic
576#384C2314yes—
577#383C2314yes—
578#382C2312yes—
579#382C2312yes—
580#382C2311yescharacteristic
581#382C2314yes—
582#382C2314yes—
583#382C2312yes—
584#382C2312yes—
585#382C2312yes—
586#382C2314yes—
587#382C2314yes—
588#382C2314yes—
589#380C2312yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2312yes—
594#380C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2312yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2311yescharacteristic
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666#376C2312yes—
667#376C2311yescharacteristic
668#376C2311yescharacteristic
669#376C2314yes—
670#376C2314yes—
671#376C2314yes—
672#376C2314yes—
673C43C2314yes—
674C43C2311yescharacteristic
675C43C2311yescharacteristic
676C43C2312yes—
677C22×Q8C2411yescharacteristic
678C22×Q8C2412yes—
679C22×Q8C2412yes—
680C22×Q8C2414yes—
681C22×Q8C2414yes—
682C22×Q8C2411yescharacteristic
683C22×Q8C2414yes—
684C23×C4C2411yescharacteristic
685C23×C4C2414yes—
686C23×C4C2412yes—
687C4⋊Q8—216no—
688C4⋊Q8—28no—
689C4⋊Q8—44no—
690C4⋊Q8—44no—
691C4⋊Q8—48no—
692C4⋊Q8—48no—
693C4⋊Q8—48no—
694C4⋊Q8C2×Q818yes—
695#126C2×Q8132yes—
696#125—28no—
697#125—216no—
698#125—216no—
699#125—28no—
700#125—216no—
701#125—24no—
702#125—44no—
703#125—48no—
704#125C2×Q818yes—
705#125C2×Q8132yes—
706#125#4118yes—
707C22⋊Q8—48no—
708C22⋊Q8—44no—
709C22⋊Q8C2×Q8116yes—
710C4×Q8—28no—
711C4×Q8—216no—
712C4×Q8—28no—
713C4×Q8—28no—
714C4×Q8—28no—
715C4×Q8—42no—
716C4×Q8—42no—
717C4×Q8—44no—
718C4×Q8—44no—
719C4×Q8—48no—
720C4×Q8—44no—
721C4×Q8—44no—
722C4×Q8C2×Q8116yes—
723#117—42no—
724#117—44no—
725#117C2×Q818yes—
726C2×C4⋊C4—28no—
727C2×C4⋊C4—216no—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2414yes—
814C2×C42—24no—
815C2×C42C2411yescharacteristic
816C2×C42C2411yescharacteristic
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2411yescharacteristic
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2412yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2414yes—
852C2×C42C2411yescharacteristic
853#95C2412yes—
854#95C2412yes—
855#95C2414yes—
856#95C2412yes—
857#95C2412yes—
858#95C2414yes—
859#95C2414yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2412yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2412yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2412yes—
886#95C2414yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2412yes—
894#95C2412yes—
895#95C2411yescharacteristic
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2411yescharacteristic
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2411yescharacteristic
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2411yescharacteristic
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934C24C2511yescharacteristic
935C2×Q8—24no—
936C2×Q8—24no—
937C2×Q8—28no—
938C2×Q8—24no—
939C2×Q8—24no—
940C2×Q8—28no—
941C2×Q8—41no—
942C2×Q8—41no—
943C2×Q8—44no—
944C2×Q8—42no—
945C2×Q8—44no—
946C2×Q8—44no—
947C2×Q8—44no—
948C2×Q8—42no—
949C2×Q8—42no—
950C2×Q8—44no—
951C2×Q8—44no—
952C2×Q8—44no—
953C2×Q8C22×Q818yes—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—24no—
957C22×C4—28no—
958C22×C4—42no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—42no—
962C22×C4C22×Q814yes—
963C22×C4C2512yes—
964C22×C4C2511yescharacteristic
965C22×C4C2512yes—
966C22×C4C2511yescharacteristic
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2514yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2511yescharacteristic
985C22×C4C2514yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2511yescharacteristic
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—42no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—42no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—42no—
1035C4⋊C4—41no—
1036C4⋊C4—42no—
1037C4⋊C4—41no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—44no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—42no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4C22×Q818yes—
1058C4⋊C4C22×Q818yes—
1059C4⋊C4C22×Q8116yes—
1060C4⋊C4C22×Q8116yes—
1061C4⋊C4C22×Q8116yes—
1062C4⋊C4C22×Q8116yes—
1063C4⋊C4C2×#4118yes—
1064C4⋊C4C2×#41116yes—
1065C22⋊C4—24no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—42no—
1073C22⋊C4C22×Q818yes—
1074C22⋊C4C22×Q8116yes—
1075C42—24no—
1076C42—22no—
1077C42—28no—
1078C42—28no—
1079C42—24no—
1080C42—28no—
1081C42—24no—
1082C42—22no—
1083C42—22no—
1084C42—24no—
1085C42—24no—
1086C42—24no—
1087C42—44no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—42no—
1096C42—44no—
1097C42—42no—
1098C42—44no—
1099C42—42no—
1100C42—44no—
1101C42—44no—
1102C42—44no—
1103C42—44no—
1104C42—44no—
1105C42—42no—
1106C42—44no—
1107C42—44no—
1108C42—44no—
1109C42C22×Q814yes—
1110C42C22×Q814yes—
1111C42C22×Q8116yes—
1112C42C2×#4114yes—
1113C23—21no—
1114C23—22no—
1115C23—21no—
1116C23—22no—
1117C23C23×Q812yes—
1118C23C2611yescharacteristic
1119Q8—216no—
1120Q8—44no—
1121Q8—88no—
1122Q8—84no—
1123Q8—88no—
1124Q8—82no—
1125Q8—164no—
1126C2×C4—24no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—28no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—84no—
1191C2×C4—88no—
1192C2×C4C23×Q814yes—
1193C2×C4C23×Q814yes—
1194C2×C4C23×Q818yes—
1195C2×C4C23×Q818yes—
1196C2×C4C23×Q812yes—
1197C2×C4C23×Q812yes—
1198C2×C4C22×#4114yes—
1199C2×C4C22×#4118yes—
1200C2×C4C22×#4112yes—
1201C2×C4#58514yes—
1202C2×C4#58512yes—
1203C22—24no—
1204C22—22no—
1205C22—42no—
1206C22—41no—
1207C22—41no—
1208C22C24×Q811yescharacteristic
1209C22C23×#4111yescharacteristic
1210C22C2×#58512yes—
1211C22C2×#58511yescharacteristic
1212C222−1+612yes—
1213C4—24no—
1214C4—24no—
1215C4—28no—
1216C4—28no—
1217C4—24no—
1218C4—24no—
1219C4—22no—
1220C4—28no—
1221C4—42no—
1222C4—42no—
1223C4—42no—
1224C4—44no—
1225C4—44no—
1226C4—42no—
1227C4—42no—
1228C4—41no—
1229C4—41no—
1230C4—44no—
1231C4—44no—
1232C4—42no—
1233C4—41no—
1234C4—42no—
1235C4—44no—
1236C4—41no—
1237C4—42no—
1238C4Q8×#4114yes—
1239C2—42no—
1240C2C2×Q8×#4111yescharacteristic
1241C2#6282911yescharacteristic
1242C2#6289011yescharacteristic
1243C2#6300412yes—
1244C2#6300912yes—
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. #59927C2semidirect
3. #59671C2semidirect
4. #59669C2semidirect
6. #59464C2semidirect
9. #45435C2semidirect
11. #45395C2semidirect
12. #45277C2semidirect
14. #45164C2semidirect
15. #44753C2semidirect
17. #44667C2semidirect
19. #35643C2semidirect
20. #35582C2semidirect
22. #34951C2semidirect
24. #34336C2semidirect
244. #541Q8semidirect

Maximal subgroups

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

subgroupindex
#599272
#597122
#596712
#596692
#596122
#594642
#592452
#591542
#454352
#454092
#453952
#452772
#451902
#451642
#447532
#447012
#446672
#446252
#356432
#355822
#355772
#349512
#348822
#343362
#342862
#342812
#342172