Finite Group Databasebeta

← #7709816

Subgroups — #7709816

Order 512.

4334 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59495C214yesmaximal, complemented
2#59254C212yesmaximal, complemented
3#59209C212yesmaximal, complemented
4#46191C212yesmaximal, complemented
5#46190C212yesmaximal, complemented
6#45959C212yesmaximal, complemented
7#45946C212yesmaximal, complemented
8#40202C212yesmaximal, complemented
9#40178C212yesmaximal, complemented
10#39751C211yesmaximal, characteristic, complemented
11#39631C211yesmaximal, characteristic
12#39496C211yesmaximal, characteristic, complemented
13#39376C211yesmaximal, characteristic
14#38809C212yesmaximal, complemented
15#38788C212yesmaximal, complemented
16#38731C214yesmaximal, complemented
17#38600C214yesmaximal, complemented
18#37935C212yesmaximal, complemented
19#37763C212yesmaximal
20#37466C212yesmaximal, complemented
21#37110C214yesmaximal, complemented
22#36635C211yesmaximal, characteristic, complemented
23C2×#2864C211yesmaximal, characteristic, complemented
24#36567C212yesmaximal, complemented
25#36171C212yesmaximal, complemented
26#36171C212yesmaximal, complemented
27#36165C212yesmaximal, complemented
28#35142C212yesmaximal, complemented
29#35132C212yesmaximal, complemented
30#34427C212yesmaximal
31C4×#529C211yesmaximal, characteristic
32C2×#539C2212yes—
33C2×#529C2211yescharacteristic
34#2864C2212yes—
35#2864C2212yes—
36#2864C2212yes—
37#2864C2212yes—
38#2864C2212yes—
39#2864C2212yes—
40#2864C2212yes—
41#2864C2212yes—
42#2864C2212yes—
43#2864C2212yes—
44#2863C2212yes—
45#2863C2212yes—
46#2862C2211yescharacteristic
47#2859C2211yescharacteristic
48#2859C2212yes—
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2855C2212yes—
52#2855C2212yes—
53#2851C2212yes—
54#2851C2212yes—
55#2851C2212yes—
56#2839C2214yes—
57#2833C2214yes—
58#2810C2214yes—
59#2807C2214yes—
60#2806C2212yes—
61#2805C2212yes—
62#2805C2212yes—
63#2805C2212yes—
64#2802C2214yes—
65#2802C2214yes—
66#2789C2214yes—
67#2787C2214yes—
68#2787C2214yes—
69#2776C2214yes—
70#2770C2214yes—
71#2769C2214yes—
72#2767C2214yes—
73#2767C2214yes—
74#2767C2214yes—
75#2767C2214yes—
76#2766C2214yes—
77#2766C2214yes—
78#2758C2214yes—
79#2755C2214yes—
80#2739C2214yes—
81#2738C2214yes—
82#2738C2214yes—
83#2738C2214yes—
84#2732C2212yes—
85#2726C2212yes—
86#2726C2212yes—
87#2724C2212yes—
88#2722C2214yes—
89#2719C2214yes—
90#2717C2214yes—
91#2698C2214yes—
92#2690C2214yes—
93#2689C2214yes—
94#2666C2214yes—
95#2666C2214yes—
96#2659C2212yes—
97#2655C2214yes—
98#2655C2214yes—
99#2652C2214yes—
100#2646C2212yes—
101#2634C2214yes—
102#2627C2212yes—
103#2627C2212yes—
104#2612C2214yes—
105#2612C2214yes—
106#2611C2214yes—
107#2606C2214yes—
108#2590C2214yes—
109#2590C2214yes—
110#2585C2214yes—
111#2585C2214yes—
112#2584C2212yes—
113#2584C2212yes—
114#2575C2214yes—
115#2575C2214yes—
116#2571C2212yes—
117#2571C2212yes—
118#2570C2212yes—
119#2570C2212yes—
120#2550C2212yes—
121#2550C2212yes—
122#2533C2214yes—
123#2533C2214yes—
124#2530C2214yes—
125#2528C2214yes—
126#2528C2214yes—
127#2528C2214yes—
128#2524C2214yes—
129#2524C2214yes—
130#2524C2214yes—
131#2517C2214yes—
132#2517C2214yes—
133#2509C2212yes—
134#2509C2212yes—
135#2509C2212yes—
136#2508C2212yes—
137#2508C2214yes—
138#2508C2214yes—
139#2508C2212yes—
140#2508C2212yes—
141#2507C2212yes—
142#2507C2212yes—
143#2507C2212yes—
144#2506C2212yes—
145#2506C2212yes—
146#2506C2212yes—
147#2505C2214yes—
148#2505C2214yes—
149#2505C2214yes—
150#2505C2214yes—
151#2497C2212yes—
152#2496C2212yes—
153#2495C2212yes—
154#2495C2212yes—
155#2495C2212yes—
156#2494C2212yes—
157#2494C2212yes—
158#2494C2212yes—
159#2493C2214yes—
160#2493C2214yes—
161#2493C2214yes—
162#2493C2214yes—
163#2487C2212yes—
164#2487C2212yes—
165#2486C2212yes—
166#2486C2214yes—
167#2486C2212yes—
168#2484C2214yes—
169#2478C2214yes—
170#2475C2214yes—
171#2475C2214yes—
172#2473C2214yes—
173#2462C2214yes—
174#2462C2214yes—
175#2462C2214yes—
176#2449C2214yes—
177#2442C2212yes—
178#2442C2212yes—
179#2442C2212yes—
180#2442C2212yes—
181#2442C2212yes—
182#2442C2212yes—
183#2442C2214yes—
184#2440C2212yes—
185#2440C2212yes—
186#2438C2214yes—
187#2438C2214yes—
188#2438C2214yes—
189#2421C2214yes—
190#2419C2214yes—
191#2419C2214yes—
192#2419C2214yes—
193#2419C2214yes—
194#2382C2214yes—
195#2376C2214yes—
196#2370C2212yes—
197#2370C2212yes—
198#2370C2214yes—
199#2370C2214yes—
200#2359C2214yes—
201#2359C2214yes—
202#2359C2214yes—
203#2352C2214yes—
204#2349C2214yes—
205#2349C2214yes—
206D4×C4⋊C4C2212yes—
207D4×C4⋊C4C2212yes—
208#2345C2212yes—
209#2345C2212yes—
210#2344C2212yes—
211#2344C2212yes—
212#2343C2214yes—
213#2343C2214yes—
214#2336C2214yes—
215#2334C2214yes—
216#2334C2214yes—
217#2329C2212yes—
218#2329C2214yes—
219#2329C2214yes—
220#2325C2212yes—
221#2323C2214yes—
222#2316C2212yes—
223C4×C4⋊Q8C2211yescharacteristic
224C4×C4⋊Q8C2211yescharacteristic
225C4×#125C2212yes—
226C4×#125C2212yes—
227C4×#125C2212yes—
228C4×#125C2211yescharacteristic
229C4×#125C2211yescharacteristic
230C4×#126C2212yes—
231C4×#126C2212yes—
232C4×#124C2211yescharacteristic
233C4×#124C2211yescharacteristic
234C4×C22⋊Q8C2212yes—
235C4×C22⋊Q8C2212yes—
236C4×C22⋊Q8C2211yescharacteristic
237C4×C22⋊Q8C2211yescharacteristic
238C4×#123C2212yes—
239C4×#123C2212yes—
240C4×#121C2211yescharacteristic
241C4×#121C2211yescharacteristic
242#2298C2212yes—
243#2295C2212yes—
244#2295C2212yes—
245#2295C2211yescharacteristic
246#2293C2211yescharacteristic
247C2×#389C2211yescharacteristic
248C2×#389C2211yescharacteristic
249C2×#389C2211yescharacteristic
250C2×#389C2211yescharacteristic
251#2290C2212yes—
252C2×#387C2212yes—
253C2×#387C2212yes—
254C2×#387C2212yes—
255C2×#387C2212yes—
256#2283C2212yes—
257#2283C2211yescharacteristic
258#2283C2212yes—
259C2×#382C2211yescharacteristic
260C2×#382C2211yescharacteristic
261C2×#382C2212yes—
262C42×Q8C2211yescharacteristic
263C42×D4C2212yes—
264C42×D4C2211yescharacteristic
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267#539—216no—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270#529—28no—
271C2×#126C2312yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2311yescharacteristic
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#124C2311yescharacteristic
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×#121C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2311yescharacteristic
303C2×#117C2312yes—
304C2×#117C2314yes—
305C2×#117C2314yes—
306C2×#117C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C42C2311yescharacteristic
318C22×C42C2312yes—
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325#401C2314yes—
326#401C2314yes—
327#401C2314yes—
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#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2314yes—
360#399C2314yes—
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#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2311yescharacteristic
408#391C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2311yescharacteristic
425#389C2311yescharacteristic
426#389C2311yescharacteristic
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#388C2312yes—
486#388C2312yes—
487#388C2312yes—
488#388C2312yes—
489#388C2312yes—
490#388C2312yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2312yes—
499#388C2312yes—
500#387C2312yes—
501#387C2312yes—
502#387C2312yes—
503#387C2312yes—
504#387C2312yes—
505#387C2312yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2312yes—
513#387C2312yes—
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#386C2314yes—
578#386C2314yes—
579#386C2312yes—
580#386C2312yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
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#385C2312yes—
602#385C2312yes—
603#384C2311yescharacteristic
604#384C2311yescharacteristic
605#384C2312yes—
606#384C2312yes—
607#383C2312yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#382C2311yescharacteristic
617#382C2311yescharacteristic
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2314yes—
623#382C2314yes—
624#382C2312yes—
625#382C2314yes—
626#382C2314yes—
627#382C2314yes—
628#382C2314yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2314yes—
635#381C2314yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2312yes—
642#380C2311yescharacteristic
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2311yescharacteristic
660#380C2312yes—
661#380C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2314yes—
714#376C2314yes—
715#376C2312yes—
716#376C2312yes—
717C2×#95C2312yes—
718C2×#95C2314yes—
719C2×#95C2312yes—
720C2×#95C2314yes—
721C2×#95C2312yes—
722C2×#95C2312yes—
723C2×#95C2312yes—
724C2×#95C2312yes—
725C2×#95C2312yes—
726C2×#95C2312yes—
727C43C2311yescharacteristic
728C43C2311yescharacteristic
729C43C2312yes—
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C22×Q8C2411yescharacteristic
737C22×Q8C2412yes—
738C22×Q8C2412yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2411yescharacteristic
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2411yescharacteristic
757C4⋊Q8—42no—
758C4⋊Q8—42no—
759#126—28no—
760#126—216no—
761#125—24no—
762#125—216no—
763#125—28no—
764#125—48no—
765#125—44no—
766#125—44no—
767#125—48no—
768#124—24no—
769#123—28no—
770#123—216no—
771#123—216no—
772C22⋊Q8—24no—
773C22⋊Q8—28no—
774C22⋊Q8—216no—
775C22⋊Q8—44no—
776C22⋊Q8—48no—
777#121#4118yes—
778C4×Q8—24no—
779C4×Q8—42no—
780C4×Q8—44no—
781C4×Q8—42no—
782C4×Q8—44no—
783C4×D4—24no—
784C4×D4—28no—
785C4×D4—216no—
786C4×D4—28no—
787C4×D4—42no—
788C4×D4—42no—
789C4×D4—44no—
790C4×D4—48no—
791#117—28no—
792#117—44no—
793#117—48no—
794#117—48no—
795C2×C4⋊C4—28no—
796C2×C4⋊C4—24no—
797C2×C4⋊C4—24no—
798C2×C4⋊C4—42no—
799C2×C4⋊C4—42no—
800C2×C4⋊C4—44no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4—44no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4—44no—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C42—24no—
897C2×C42—24no—
898C2×C42—24no—
899C2×C42—28no—
900C2×C42—42no—
901C2×C42—42no—
902C2×C42—42no—
903C2×C42—42no—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
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#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
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—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027C24C2512yes—
1028C24C2511yescharacteristic
1029C2×Q8—22no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—41no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—42no—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—41no—
1041C2×D4—41no—
1042C2×D4C2×#4118yes—
1043C2×D4C2×#4114yes—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—24no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—28no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—41no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—41no—
1074C22×C4—41no—
1075C22×C4—41no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4C2×#4114yes—
1091C22×C42−1+414yes—
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—22no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—41no—
1164C4⋊C4—41no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—41no—
1168C4⋊C4—41no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4C2×#4114yes—
1191C22⋊C4—24no—
1192C22⋊C4—28no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—24no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—28no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—42no—
1206C22⋊C4—44no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4C2×#4118yes—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—22no—
1216C42—24no—
1217C42—28no—
1218C42—22no—
1219C42—22no—
1220C42—22no—
1221C42—22no—
1222C42—24no—
1223C42—24no—
1224C42—22no—
1225C42—22no—
1226C42—22no—
1227C42—24no—
1228C42—24no—
1229C42—22no—
1230C42—22no—
1231C42—22no—
1232C42—22no—
1233C42—22no—
1234C42—22no—
1235C42—28no—
1236C42—24no—
1237C42—41no—
1238C42—41no—
1239C42—41no—
1240C42—41no—
1241C42—41no—
1242C42—41no—
1243C42—41no—
1244C42—41no—
1245C42—41no—
1246C42—41no—
1247C42—42no—
1248C42—44no—
1249C42—44no—
1250C42—44no—
1251C42—42no—
1252C42—44no—
1253C42—44no—
1254C42—42no—
1255C42—44no—
1256C422−1+414yes—
1257C23—21no—
1258C23—21no—
1259C23—21no—
1260C23—21no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23C22×#4114yes—
1268C23C22×#4112yes—
1269C23C2×2−1+412yes—
1270C23#58512yes—
1271C23C2611yescharacteristic
1272Q8—44no—
1273Q8—84no—
1274Q8—84no—
1275D4—216no—
1276D4—44no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—28no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—21no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—24no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—24no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—44no—
1355C2×C4—44no—
1356C2×C4—44no—
1357C2×C4—48no—
1358C2×C4—44no—
1359C2×C4—44no—
1360C2×C4—44no—
1361C2×C4—48no—
1362C2×C4—48no—
1363C2×C4—84no—
1364C2×C4—84no—
1365C2×C4—88no—
1366C2×C4—84no—
1367C2×C4—84no—
1368C2×C4—164no—
1369C2×C4C22×#4114yes—
1370C2×C4C22×#4112yes—
1371C2×C4C22×#4112yes—
1372C2×C4C2×2−1+412yes—
1373C2×C4C2×2−1+412yes—
1374C2×C4C2×2−1+412yes—
1375C2×C4C2×2−1+412yes—
1376C2×C4C2×2−1+412yes—
1377C2×C4#58512yes—
1378C2×C4#58512yes—
1379C2×C4#58512yes—
1380C22—22no—
1381C22—22no—
1382C22—22no—
1383C22—22no—
1384C22—22no—
1385C22—22no—
1386C22—24no—
1387C22—24no—
1388C22—24no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22#351514yes—
1394C22C23×#4111yescharacteristic
1395C22C22×2−1+411yescharacteristic
1396C22C22×2−1+411yescharacteristic
1397C22C2×#58511yescharacteristic
1398C22C2×#58511yescharacteristic
1399C22C2×#58511yescharacteristic
1400C22C2×#58511yescharacteristic
1401C4—22no—
1402C4—22no—
1403C4—24no—
1404C4—22no—
1405C4—22no—
1406C4—22no—
1407C4—22no—
1408C4—22no—
1409C4—42no—
1410C4—44no—
1411C4—41no—
1412C4—42no—
1413C4—41no—
1414C4—41no—
1415C4—44no—
1416C4—44no—
1417C4—44no—
1418C4—42no—
1419C4—44no—
1420C4—41no—
1421C4—42no—
1422C4—42no—
1423C4—41no—
1424C4—44no—
1425C4—44no—
1426C4—42no—
1427C4—41no—
1428C4—44no—
1429C4#356314yes—
1430C2—24no—
1431C2—44no—
1432C2C2×#356311yescharacteristic
1433C2#6275211yescharacteristic
1434C2C2×#351511yescharacteristic
1435C2#6278111yescharacteristic
1436C2#6280511yescharacteristic
1437C2#6282911yescharacteristic
1438C2#6283111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59495C2semidirect
2. #59254C2semidirect
3. #59209C2semidirect
4. #46191C2semidirect
5. #46190C2semidirect
6. #45959C2semidirect
7. #45946C2semidirect
8. #40202C2semidirect
9. #40178C2semidirect
10. #39751C2semidirect
12. #39496C2semidirect
14. #38809C2semidirect
15. #38788C2semidirect
16. #38731C2semidirect
17. #38600C2semidirect
18. #37935C2semidirect
20. #37466C2semidirect
21. #37110C2semidirect
22. #36635C2semidirect
23. C2×#2864C2semidirect
24. #36567C2semidirect
25. #36171C2semidirect
26. #36171C2semidirect
27. #36165C2semidirect
28. #35142C2semidirect
29. #35132C2semidirect

Maximal subgroups

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

subgroupindex
#594952
#592542
#592092
#461912
#461902
#459592
#459462
#402022
#401782
#397512
#396312
#394962
#393762
#388092
#387882
#387312
#386002
#379352
#377632
#374662
#371102
#366352
C2×#28642
#365672
#361712
#361652
#351422
#351322
#344272
C4×#5292