Finite Group Databasebeta

← #7710326

Subgroups — #7710326

Order 512.

4242 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59669C212yesmaximal, complemented
2#59447C212yesmaximal, complemented
3#59284C214yesmaximal
4#46157C211yesmaximal, characteristic, complemented
5C4⋊#564C211yesmaximal, characteristic, complemented
6#46145C212yesmaximal
7C22⋊#564C212yesmaximal
8#46022C211yesmaximal, characteristic, complemented
9#46006C211yesmaximal, characteristic, complemented
10#40466C214yesmaximal, complemented
11#40107C212yesmaximal, complemented
12#40082C212yesmaximal, complemented
13#40024C212yesmaximal, complemented
14#39979C212yesmaximal, complemented
15#38809C212yesmaximal, complemented
16#38790C212yesmaximal, complemented
17#38610C214yesmaximal
18#38465C212yesmaximal
19#38447C212yesmaximal
20#37603C212yesmaximal, complemented
21#37062C214yesmaximal, complemented
22#36640C211yesmaximal, characteristic
23#36635C211yesmaximal, characteristic
24#36571C212yesmaximal
25#36199C212yesmaximal
26#36199C212yesmaximal
27#36193C212yesmaximal
28#35239C212yesmaximal
29#35087C212yesmaximal
30#34530C212yesmaximal, complemented
31C2×C4×#125C211yesmaximal, characteristic
32C2×#564C2212yes—
33C22×#125C2211yescharacteristic
34#2864C2212yes—
35#2864C2212yes—
36#2864C2212yes—
37#2863C2212yes—
38#2863C2212yes—
39#2862C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2212yes—
48#2855C2212yes—
49#2855C2212yes—
50#2855C2212yes—
51#2855C2212yes—
52#2851C2212yes—
53#2851C2212yes—
54#2851C2212yes—
55#2851C2212yes—
56#2851C2212yes—
57#2851C2212yes—
58#2844C2212yes—
59#2822C2212yes—
60#2822C2212yes—
61#2822C2212yes—
62#2810C2212yes—
63#2809C2212yes—
64#2805C2212yes—
65#2805C2212yes—
66#2802C2214yes—
67#2802C2214yes—
68#2794C2214yes—
69#2792C2214yes—
70#2789C2214yes—
71#2776C2214yes—
72#2776C2214yes—
73#2774C2214yes—
74#2774C2214yes—
75#2774C2214yes—
76#2769C2214yes—
77#2767C2214yes—
78#2766C2214yes—
79#2766C2214yes—
80#2766C2214yes—
81#2766C2214yes—
82#2762C2214yes—
83#2762C2214yes—
84#2734C2212yes—
85#2726C2214yes—
86#2726C2214yes—
87#2726C2212yes—
88#2726C2212yes—
89#2726C2212yes—
90#2719C2214yes—
91#2719C2214yes—
92#2719C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2713C2214yes—
98#2666C2214yes—
99#2666C2214yes—
100#2666C2214yes—
101#2666C2214yes—
102#2655C2214yes—
103#2655C2214yes—
104#2655C2214yes—
105#2655C2214yes—
106#2612C2214yes—
107#2606C2214yes—
108#2606C2214yes—
109#2590C2214yes—
110#2588C2214yes—
111#2588C2214yes—
112#2585C2214yes—
113#2583C2214yes—
114#2571C2212yes—
115#2570C2212yes—
116#2570C2212yes—
117#2570C2212yes—
118#2570C2212yes—
119#2567C2212yes—
120#2565C2212yes—
121#2565C2212yes—
122#2565C2212yes—
123#2552C2212yes—
124#2552C2212yes—
125#2552C2212yes—
126#2551C2212yes—
127#2550C2214yes—
128#2550C2212yes—
129#2550C2212yes—
130#2550C2212yes—
131#2533C2214yes—
132#2533C2214yes—
133#2528C2214yes—
134#2528C2214yes—
135#2528C2214yes—
136#2528C2214yes—
137#2524C2214yes—
138#2524C2214yes—
139#2524C2214yes—
140#2524C2214yes—
141#2524C2214yes—
142#2524C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2520C2214yes—
146#2520C2214yes—
147#2520C2214yes—
148#2520C2214yes—
149#2514C2212yes—
150#2514C2212yes—
151#2514C2214yes—
152#2514C2212yes—
153#2514C2212yes—
154#2511C2212yes—
155#2511C2212yes—
156#2511C2212yes—
157#2511C2212yes—
158#2509C2212yes—
159#2508C2212yes—
160#2508C2212yes—
161#2508C2214yes—
162#2507C2212yes—
163#2507C2212yes—
164#2506C2212yes—
165#2506C2212yes—
166#2506C2212yes—
167#2506C2212yes—
168#2506C2212yes—
169#2505C2214yes—
170#2493C2214yes—
171#2493C2214yes—
172#2493C2214yes—
173#2493C2214yes—
174#2484C2214yes—
175#2484C2214yes—
176#2473C2214yes—
177#2473C2214yes—
178#2473C2214yes—
179#2473C2214yes—
180#2473C2214yes—
181#2462C2214yes—
182#2453C2212yes—
183#2453C2212yes—
184#2453C2212yes—
185#2451C2212yes—
186#2446C2212yes—
187#2446C2212yes—
188#2446C2214yes—
189#2442C2214yes—
190#2442C2214yes—
191#2440C2214yes—
192#2438C2214yes—
193#2438C2214yes—
194#2438C2214yes—
195#2438C2214yes—
196#2382C2212yes—
197#2382C2212yes—
198#2382C2212yes—
199#2371C2214yes—
200#2371C2214yes—
201#2371C2214yes—
202#2370C2214yes—
203#2370C2212yes—
204#2370C2212yes—
205#2370C2212yes—
206#2370C2214yes—
207#2370C2214yes—
208#2369C2212yes—
209#2368C2214yes—
210#2356C2212yes—
211#2356C2212yes—
212#2355C2212yes—
213#2351C2212yes—
214#2344C2214yes—
215#2343C2214yes—
216#2343C2214yes—
217#2336C2214yes—
218#2336C2214yes—
219#2336C2214yes—
220#2336C2214yes—
221#2331C2214yes—
222#2330C2214yes—
223#2330C2214yes—
224#2330C2214yes—
225C4×C4⋊Q8C2211yescharacteristic
226C4×C4⋊Q8C2211yescharacteristic
227C4×#125C2212yes—
228C4×#125C2212yes—
229C4×#125C2212yes—
230C4×#125C2212yes—
231C4×#125C2212yes—
232C4×#125C2212yes—
233C4×#125C2212yes—
234C4×#125C2212yes—
235C4×#125C2211yescharacteristic
236C4×#125C2211yescharacteristic
237C4×#125C2211yescharacteristic
238C4×#125C2211yescharacteristic
239C4×#125C2211yescharacteristic
240C4×#125C2211yescharacteristic
241C4×#125C2212yes—
242C4×#125C2211yescharacteristic
243C4×#125C2211yescharacteristic
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×C22⋊Q8C2212yes—
247C4×C22⋊Q8C2212yes—
248#2296C2212yes—
249#2296C2212yes—
250#2295C2212yes—
251#2295C2212yes—
252C2×#389C2211yescharacteristic
253C2×#389C2211yescharacteristic
254C2×#387C2212yes—
255C2×#387C2212yes—
256#2285C2211yescharacteristic
257#2285C2211yescharacteristic
258#2285C2212yes—
259#2283C2212yes—
260#2283C2212yes—
261C2×#382C2211yescharacteristic
262C2×C4×C4⋊C4C2212yes—
263C2×C4×C4⋊C4C2212yes—
264C2×C4×C4⋊C4C2211yescharacteristic
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×C43C2211yescharacteristic
267#564—216no—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×#125—28no—
273C2×#125C2311yescharacteristic
274C2×#125C2311yescharacteristic
275C2×#125C2311yescharacteristic
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2314yes—
291C2×#125C2311yescharacteristic
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×#117C2312yes—
300C2×#117C2314yes—
301C2×#117C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2312yes—
318C22×C42C2311yescharacteristic
319#401C2314yes—
320#401C2314yes—
321#401C2314yes—
322#401C2314yes—
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#400C2314yes—
355#398C2314yes—
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#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#389C2311yescharacteristic
421#389C2312yes—
422#389C2311yescharacteristic
423#389C2312yes—
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2311yescharacteristic
428#389C2311yescharacteristic
429#389C2312yes—
430#389C2312yes—
431#389C2311yescharacteristic
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#387C2312yes—
494#387C2312yes—
495#387C2312yes—
496#387C2312yes—
497#387C2312yes—
498#387C2312yes—
499#387C2312yes—
500#387C2312yes—
501#387C2312yes—
502#387C2312yes—
503#387C2312yes—
504#387C2312yes—
505#387C2312yes—
506#387C2312yes—
507#387C2312yes—
508#387C2312yes—
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#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#384C2311yescharacteristic
602#384C2311yescharacteristic
603#384C2311yescharacteristic
604#384C2312yes—
605#384C2312yes—
606#384C2311yescharacteristic
607#384C2312yes—
608#384C2311yescharacteristic
609#384C2314yes—
610#384C2311yescharacteristic
611#383C2314yes—
612#383C2314yes—
613#383C2314yes—
614#383C2314yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#382C2311yescharacteristic
620#382C2311yescharacteristic
621#382C2312yes—
622#382C2312yes—
623#382C2311yescharacteristic
624#382C2311yescharacteristic
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2314yes—
634#382C2314yes—
635#382C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2312yes—
640#382C2312yes—
641#382C2314yes—
642#382C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718#376C2314yes—
719#376C2314yes—
720#376C2314yes—
721#376C2314yes—
722C2×#95C2312yes—
723C2×#95C2312yes—
724C2×#95C2312yes—
725C2×#95C2312yes—
726C2×#95C2312yes—
727C2×#95C2312yes—
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C22×Q8C2412yes—
737C22×Q8C2412yes—
738C22×Q8C2414yes—
739C23×C4C2411yescharacteristic
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C4⋊Q8—44no—
751C4⋊Q8—42no—
752C4⋊Q8—42no—
753C4⋊Q8—48no—
754#125—24no—
755#125—24no—
756#125—28no—
757#125—28no—
758#125—216no—
759#125—216no—
760#125—216no—
761#125—216no—
762#125—216no—
763#125—216no—
764#125—24no—
765#125—28no—
766#125—28no—
767#125—28no—
768#125—44no—
769#125—44no—
770#125—44no—
771#125—48no—
772#125#4118yes—
773C22⋊Q8—28no—
774C22⋊Q8—48no—
775C22⋊Q8—44no—
776C4×Q8—28no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780#117—28no—
781#117—44no—
782#117—48no—
783C2×C4⋊C4—28no—
784C2×C4⋊C4—24no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—28no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—44no—
789C2×C4⋊C4—42no—
790C2×C4⋊C4—42no—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C42—24no—
881C2×C42—28no—
882C2×C42—24no—
883C2×C42—24no—
884C2×C42—24no—
885C2×C42—42no—
886C2×C42—44no—
887C2×C42—42no—
888C2×C42—42no—
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2411yescharacteristic
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021C24C2511yescharacteristic
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—24no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—22no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—41no—
1055C22×C4—42no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C42−1+414yes—
1063C22×C42−1+414yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2514yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—22no—
1103C4⋊C4—22no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—28no—
1138C4⋊C4—24no—
1139C4⋊C4—42no—
1140C4⋊C4—41no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—42no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4C2×#4114yes—
1176C4⋊C4C2×#4114yes—
1177C4⋊C4C2×#4118yes—
1178C4⋊C4C2×#4118yes—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C42—22no—
1184C42—22no—
1185C42—22no—
1186C42—28no—
1187C42—28no—
1188C42—22no—
1189C42—22no—
1190C42—22no—
1191C42—22no—
1192C42—22no—
1193C42—24no—
1194C42—22no—
1195C42—22no—
1196C42—22no—
1197C42—22no—
1198C42—24no—
1199C42—22no—
1200C42—22no—
1201C42—24no—
1202C42—24no—
1203C42—28no—
1204C42—28no—
1205C42—22no—
1206C42—24no—
1207C42—24no—
1208C42—22no—
1209C42—22no—
1210C42—22no—
1211C42—41no—
1212C42—42no—
1213C42—41no—
1214C42—41no—
1215C42—41no—
1216C42—41no—
1217C42—42no—
1218C42—41no—
1219C42—41no—
1220C42—41no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42C2×#4114yes—
1230C422−1+414yes—
1231C23—21no—
1232C23—21no—
1233C23—21no—
1234C23—21no—
1235C23C2×2−1+412yes—
1236C23C2×2−1+412yes—
1237C23#58512yes—
1238C23C2611yescharacteristic
1239Q8—48no—
1240Q8—84no—
1241Q8—164no—
1242C2×C4—28no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—28no—
1266C2×C4—28no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—44no—
1322C2×C4—44no—
1323C2×C4—48no—
1324C2×C4—48no—
1325C2×C4—44no—
1326C2×C4—44no—
1327C2×C4—48no—
1328C2×C4—84no—
1329C2×C4C22×#4114yes—
1330C2×C4C22×#4114yes—
1331C2×C4C22×#4112yes—
1332C2×C4C22×#4112yes—
1333C2×C4C22×#4112yes—
1334C2×C4C2×2−1+412yes—
1335C2×C4C2×2−1+412yes—
1336C2×C4C2×2−1+412yes—
1337C2×C4C2×2−1+412yes—
1338C2×C4C2×2−1+412yes—
1339C2×C4C2×2−1+412yes—
1340C2×C4C2×2−1+412yes—
1341C2×C4#58512yes—
1342C2×C4#58512yes—
1343C22—22no—
1344C22—22no—
1345C22—22no—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22#356314yes—
1350C22C23×#4111yescharacteristic
1351C22C22×2−1+411yescharacteristic
1352C22C22×2−1+411yescharacteristic
1353C22C22×2−1+411yescharacteristic
1354C22C2×#58511yescharacteristic
1355C22C2×#58511yescharacteristic
1356C22C2×#58511yescharacteristic
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—22no—
1364C4—24no—
1365C4—24no—
1366C4—22no—
1367C4—22no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—44no—
1372C4—44no—
1373C4—44no—
1374C4—44no—
1375C4—41no—
1376C4—41no—
1377C4—42no—
1378C4—42no—
1379C4—41no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C4—44no—
1384C4—44no—
1385C4—41no—
1386C4#356314yes—
1387C2—24no—
1388C2C2×#356311yescharacteristic
1389C2C2×#356311yescharacteristic
1390C2#6278811yescharacteristic
1391C2#6280511yescharacteristic
1392C2#6280511yescharacteristic
1393C2#6282811yescharacteristic
1394C2#6283711yescharacteristic
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. #59669C2semidirect
2. #59447C2semidirect
4. #46157C2semidirect
5. C4⋊#564C2semidirect
8. #46022C2semidirect
9. #46006C2semidirect
10. #40466C2semidirect
11. #40107C2semidirect
12. #40082C2semidirect
13. #40024C2semidirect
14. #39979C2semidirect
15. #38809C2semidirect
16. #38790C2semidirect
20. #37603C2semidirect
21. #37062C2semidirect
30. #34530C2semidirect

Maximal subgroups

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

subgroupindex
#596692
#594472
#592842
#461572
C4⋊#5642
#461452
C22⋊#5642
#460222
#460062
#404662
#401072
#400822
#400242
#399792
#388092
#387902
#386102
#384652
#384472
#376032
#370622
#366402
#366352
#365712
#361992
#361932
#352392
#350872
#345302
C2×C4×#1252