Finite Group Databasebeta

← #7711492

Subgroups — #7711492

Order 512.

4222 conjugacy classes of subgroups.

The subgroup lattice has 1269 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59923C212yesmaximal
2#59866C212yesmaximal
3#59661C214yesmaximal
4#46313C212yesmaximal, complemented
5#46283C212yesmaximal, complemented
6#46283C212yesmaximal, complemented
7#46283C212yesmaximal, complemented
8#39715C214yesmaximal, complemented
9#39703C212yesmaximal, complemented
10#39701C212yesmaximal, complemented
11#39677C212yesmaximal
12#39676C212yesmaximal
13#39636C212yesmaximal
14#39620C212yesmaximal
15#38451C214yesmaximal, complemented
16#38447C212yesmaximal
17#38446C212yesmaximal
18#37562C212yesmaximal
19#37196C212yesmaximal, complemented
20#37195C212yesmaximal, complemented
21#36635C211yesmaximal, characteristic
22C2×#2863C211yesmaximal, characteristic
23#36283C214yesmaximal, complemented
24#36282C214yesmaximal
25#35221C214yesmaximal, complemented
26#34389C212yesmaximal
27C4×#533C211yesmaximal, characteristic
28C2×#533C2211yescharacteristic
29#2864C2212yes—
30#2864C2214yes—
31#2863C2212yes—
32#2863C2212yes—
33#2863C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2863C2212yes—
40#2863C2212yes—
41#2863C2214yes—
42#2862C2211yescharacteristic
43#2859C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2855C2212yes—
47#2855C2212yes—
48#2851C2212yes—
49#2843C2214yes—
50#2843C2214yes—
51#2811C2212yes—
52#2809C2212yes—
53#2806C2214yes—
54#2806C2212yes—
55#2806C2212yes—
56#2806C2212yes—
57#2806C2212yes—
58#2806C2214yes—
59#2806C2214yes—
60#2806C2212yes—
61#2805C2212yes—
62#2805C2212yes—
63#2805C2212yes—
64#2802C2214yes—
65#2802C2214yes—
66#2802C2214yes—
67#2799C2214yes—
68#2799C2214yes—
69#2799C2214yes—
70#2792C2214yes—
71#2792C2214yes—
72#2792C2214yes—
73#2791C2214yes—
74#2774C2214yes—
75#2755C2214yes—
76#2755C2214yes—
77#2755C2214yes—
78#2734C2212yes—
79#2734C2212yes—
80#2734C2212yes—
81#2734C2214yes—
82#2726C2212yes—
83#2726C2212yes—
84#2726C2214yes—
85#2726C2212yes—
86#2713C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2713C2214yes—
91#2666C2214yes—
92#2666C2214yes—
93#2666C2214yes—
94#2666C2214yes—
95#2666C2214yes—
96#2666C2214yes—
97#2659C2212yes—
98#2659C2212yes—
99#2646C2212yes—
100#2646C2212yes—
101#2612C2214yes—
102#2612C2214yes—
103#2606C2214yes—
104#2606C2214yes—
105#2606C2214yes—
106#2605C2214yes—
107#2605C2214yes—
108#2605C2214yes—
109#2590C2214yes—
110#2590C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2590C2214yes—
115#2588C2214yes—
116#2588C2214yes—
117#2588C2214yes—
118#2588C2214yes—
119#2586C2214yes—
120#2586C2214yes—
121#2586C2214yes—
122#2586C2214yes—
123#2586C2214yes—
124#2586C2214yes—
125#2585C2214yes—
126#2585C2214yes—
127#2585C2214yes—
128#2585C2214yes—
129#2585C2214yes—
130#2585C2214yes—
131#2584C2214yes—
132#2583C2214yes—
133#2583C2214yes—
134#2581C2214yes—
135#2569C2214yes—
136#2565C2214yes—
137#2550C2214yes—
138#2550C2214yes—
139#2550C2214yes—
140#2549C2214yes—
141#2549C2214yes—
142#2549C2214yes—
143#2520C2214yes—
144#2520C2214yes—
145#2520C2214yes—
146#2520C2214yes—
147#2511C2214yes—
148#2509C2214yes—
149#2507C2214yes—
150#2505C2214yes—
151#2505C2214yes—
152#2473C2214yes—
153#2473C2214yes—
154#2473C2214yes—
155#2473C2214yes—
156#2462C2214yes—
157#2462C2214yes—
158#2462C2214yes—
159#2462C2214yes—
160#2453C2214yes—
161#2453C2214yes—
162#2453C2214yes—
163#2451C2214yes—
164#2451C2214yes—
165#2451C2214yes—
166#2451C2214yes—
167#2440C2214yes—
168#2438C2214yes—
169#2438C2214yes—
170#2434C2214yes—
171#2381C2214yes—
172#2381C2214yes—
173#2370C2214yes—
174#2370C2214yes—
175#2369C2214yes—
176#2368C2214yes—
177#2368C2214yes—
178#2368C2214yes—
179#2368C2214yes—
180#2365C2214yes—
181#2360C2214yes—
182#2356C2214yes—
183#2356C2214yes—
184#2345C2214yes—
185#2343C2214yes—
186#2343C2214yes—
187#2336C2214yes—
188#2336C2214yes—
189#2331C2214yes—
190#2330C2214yes—
191#2329C2212yes—
192#2329C2212yes—
193#2329C2212yes—
194#2329C2212yes—
195#2320C2214yes—
196#2320C2214yes—
197C4×C4⋊Q8C2211yescharacteristic
198C4×C4⋊Q8C2211yescharacteristic
199C4×C4⋊Q8C2211yescharacteristic
200C4×C4⋊Q8C2211yescharacteristic
201C4×C4⋊Q8C2211yescharacteristic
202C4×C4⋊Q8C2211yescharacteristic
203C4×#125C2212yes—
204C4×#125C2212yes—
205C4×#125C2212yes—
206C4×#125C2214yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C4×C22⋊Q8C2212yes—
210C4×C22⋊Q8C2212yes—
211C4×C22⋊Q8C2212yes—
212C4×C22⋊Q8C2212yes—
213#2296C2212yes—
214#2295C2212yes—
215#2295C2212yes—
216#2295C2212yes—
217#2295C2212yes—
218#2295C2214yes—
219C2×#391C2211yescharacteristic
220C2×#391C2211yescharacteristic
221C2×#391C2211yescharacteristic
222C2×#389C2211yescharacteristic
223C2×#389C2211yescharacteristic
224C2×#389C2211yescharacteristic
225C2×#387C2212yes—
226C2×#387C2212yes—
227C2×#387C2212yes—
228#2285C2211yescharacteristic
229#2283C2212yes—
230C2×#383C2212yes—
231C42×Q8C2212yes—
232C42×Q8C2212yes—
233C4×#117C2212yes—
234C2×C43C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236#533Q8116yescomplemented
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×#125C2314yes—
245C2×#125C2312yes—
246C2×#125C2314yes—
247C2×#125C2314yes—
248C2×#125C2314yes—
249C2×#125C2312yes—
250C2×C22⋊Q8C2312yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#395C2314yes—
358#395C2314yes—
359#395C2314yes—
360#391C2312yes—
361#391C2312yes—
362#391C2312yes—
363#391C2312yes—
364#391C2312yes—
365#391C2312yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2312yes—
378#391C2314yes—
379#391C2312yes—
380#391C2312yes—
381#391C2312yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2312yes—
387#391C2314yes—
388#391C2312yes—
389#391C2314yes—
390#391C2314yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2314yes—
412#389C2312yes—
413#389C2314yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
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#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#384C2311yescharacteristic
567#384C2311yescharacteristic
568#384C2311yescharacteristic
569#384C2311yescharacteristic
570#384C2314yes—
571#383C2314yes—
572#383C2314yes—
573#383C2314yes—
574#383C2314yes—
575#383C2314yes—
576#383C2314yes—
577#383C2314yes—
578#382C2312yes—
579#382C2314yes—
580#382C2312yes—
581#382C2314yes—
582#382C2312yes—
583#382C2312yes—
584#382C2314yes—
585#382C2314yes—
586#381C2314yes—
587#380C2312yes—
588#380C2314yes—
589#380C2314yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
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⋊C4C2314yes—
629C4×C4⋊C4C2312yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
637#376C2314yes—
638#376C2314yes—
639#376C2314yes—
640#376C2314yes—
641C2×#95C2312yes—
642C2×#95C2312yes—
643C2×#95C2312yes—
644C2×#95C2312yes—
645C2×#95C2312yes—
646C2×#95C2312yes—
647C2×#95C2312yes—
648C2×#95C2312yes—
649C2×#95C2312yes—
650C43C2311yescharacteristic
651C43C2311yescharacteristic
652C43C2314yes—
653C43C2311yescharacteristic
654C43C2311yescharacteristic
655C43C2311yescharacteristic
656C43C2311yescharacteristic
657C43C2311yescharacteristic
658C43C2311yescharacteristic
659C22×Q8—42no—
660C22×Q8—42no—
661C22×Q8—42no—
662C22×Q8C2412yes—
663C22×Q8C2412yes—
664C22×Q8C2412yes—
665C22×Q8C2412yes—
666C22×Q8C2414yes—
667C22×Q8C2414yes—
668C22×Q8C2412yes—
669C22×Q8C2412yes—
670C23×C4C2411yescharacteristic
671C23×C4C2411yescharacteristic
672C23×C4C2411yescharacteristic
673C23×C4C2411yescharacteristic
674C23×C4C2412yes—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2411yescharacteristic
679C23×C4C2411yescharacteristic
680C23×C4C2411yescharacteristic
681C4⋊Q8—42no—
682C4⋊Q8—42no—
683C4⋊Q8—48no—
684C4⋊Q8—48no—
685C4⋊Q8—48no—
686C4⋊Q8C2×Q818yescomplemented
687C4⋊Q8C2×Q818yescomplemented
688#125—44no—
689#125—48no—
690#125—48no—
691#125—48no—
692#125—48no—
693#125C2×Q8116yescomplemented
694C22⋊Q8—28no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697C22⋊Q8—44no—
698C22⋊Q8C2×Q8116yes—
699C22⋊Q8C2×Q8116yes—
700C4×Q8—44no—
701C4×Q8—44no—
702C4×Q8—44no—
703C4×Q8—44no—
704C4×Q8—44no—
705C4×Q8—44no—
706C4×Q8—48no—
707C4×Q8C2×Q8116yescomplemented
708C4×Q8C2×Q8116yescomplemented
709#117—44no—
710#117C2×Q8116yes—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—44no—
713C2×C4⋊C4—42no—
714C2×C4⋊C4—42no—
715C2×C4⋊C4—44no—
716C2×C4⋊C4—42no—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C42—24no—
792C2×C42—42no—
793C2×C42—42no—
794C2×C42—42no—
795C2×C42—42no—
796C2×C42—42no—
797C2×C42C2×Q818yes—
798C2×C42C2414yes—
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828C2×C42C2411yescharacteristic
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2411yescharacteristic
837C2×C42C2414yes—
838C2×C42C2411yescharacteristic
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912C24C2511yescharacteristic
913C2×Q8—24no—
914C2×Q8—24no—
915C2×Q8—24no—
916C2×Q8—24no—
917C2×Q8—42no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—42no—
922C2×Q8—42no—
923C2×Q8—44no—
924C2×Q8—42no—
925C2×Q8—44no—
926C2×Q8—42no—
927C2×Q8—44no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8—42no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—88no—
936C2×Q8C22×Q818yes—
937C2×Q8C22×Q818yes—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4C22×Q814yes—
968C22×C4C22×Q814yes—
969C22×C4C22×Q814yes—
970C22×C42−1+414yes—
971C22×C4C2514yes—
972C22×C4C2511yescharacteristic
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2514yes—
979C22×C4C2511yescharacteristic
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2511yescharacteristic
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—24no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—44no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—42no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4C22×Q818yes—
1062C4⋊C4C22×Q818yes—
1063C4⋊C4C22×Q8116yes—
1064C4⋊C4C22×Q8116yes—
1065C4⋊C4C22×Q818yes—
1066C4⋊C4C22×Q818yes—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4C22×Q8116yes—
1071C42—22no—
1072C42—22no—
1073C42—22no—
1074C42—22no—
1075C42—22no—
1076C42—22no—
1077C42—22no—
1078C42—22no—
1079C42—22no—
1080C42—22no—
1081C42—22no—
1082C42—22no—
1083C42—28no—
1084C42—41no—
1085C42—41no—
1086C42—41no—
1087C42—41no—
1088C42—41no—
1089C42—41no—
1090C42—41no—
1091C42—41no—
1092C42—41no—
1093C42—41no—
1094C42—41no—
1095C42—41no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42—44no—
1100C42—44no—
1101C42—44no—
1102C42—44no—
1103C42—44no—
1104C42—44no—
1105C42—44no—
1106C42—44no—
1107C42—44no—
1108C42—44no—
1109C42—44no—
1110C42C22×Q814yes—
1111C42C22×Q814yes—
1112C42C22×Q814yes—
1113C42C22×Q814yes—
1114C42C22×Q8116yes—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23C23×Q812yes—
1120C23C2×2−1+412yes—
1121C23#58512yes—
1122C23C2611yescharacteristic
1123Q8—48no—
1124Q8—48no—
1125Q8—84no—
1126Q8—84no—
1127Q8—84no—
1128Q8—84no—
1129Q8—88no—
1130Q8—164no—
1131C2×C4—28no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—24no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—28no—
1161C2×C4—21no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—44no—
1198C2×C4—44no—
1199C2×C4—44no—
1200C2×C4—44no—
1201C2×C4—44no—
1202C2×C4—84no—
1203C2×C4—84no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4C23×Q812yes—
1207C2×C4C23×Q812yes—
1208C2×C4C23×Q812yes—
1209C2×C4C23×Q812yes—
1210C2×C4C23×Q812yes—
1211C2×C4C23×Q812yes—
1212C2×C4C23×Q818yes—
1213C2×C4C23×Q818yes—
1214C2×C4C2×2−1+412yes—
1215C2×C4C2×2−1+412yes—
1216C2×C4#58512yes—
1217C2×C4#58512yes—
1218C2×C4#58512yes—
1219C2×C4#58512yes—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22#350214yes—
1227C22C24×Q811yescharacteristic
1228C22C22×2−1+411yescharacteristic
1229C22C2×#58511yescharacteristic
1230C22C2×#58511yescharacteristic
1231C22C2×#58511yescharacteristic
1232C22C2×#58511yescharacteristic
1233C22C2×#58511yescharacteristic
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—28no—
1243C4—28no—
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—44no—
1249C4—41no—
1250C4—44no—
1251C4—41no—
1252C4—44no—
1253C4—44no—
1254C4—44no—
1255C4—44no—
1256C4—44no—
1257C4—44no—
1258C4—44no—
1259C4—44no—
1260C2—24no—
1261C2#6275211yescharacteristic
1262C2#6275511yescharacteristic
1263C2C2×#350211yescharacteristic
1264C2#6281311yescharacteristic
1265C2#6281311yescharacteristic
1266C2#6282311yescharacteristic
1267C2#6282611yescharacteristic
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
4. #46313C2semidirect
5. #46283C2semidirect
6. #46283C2semidirect
7. #46283C2semidirect
8. #39715C2semidirect
9. #39703C2semidirect
10. #39701C2semidirect
15. #38451C2semidirect
19. #37196C2semidirect
20. #37195C2semidirect
23. #36283C2semidirect
25. #35221C2semidirect
236. #533Q8semidirect
686. C4⋊Q8C2×Q8semidirect
687. C4⋊Q8C2×Q8semidirect
693. #125C2×Q8semidirect
707. C4×Q8C2×Q8semidirect
708. C4×Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599232
#598662
#596612
#463132
#462832
#397152
#397032
#397012
#396772
#396762
#396362
#396202
#384512
#384472
#384462
#375622
#371962
#371952
#366352
C2×#28632
#362832
#362822
#352212
#343892
C4×#5332