Finite Group Databasebeta

← #7712644

Subgroups — #7712644

Order 512.

4582 conjugacy classes of subgroups.

The subgroup lattice has 1472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59319C214yesmaximal, complemented
2#59149C214yesmaximal, complemented
3#46155C212yesmaximal, complemented
4#46154C212yesmaximal, complemented
5#46009C212yesmaximal, complemented
6#46008C212yesmaximal, complemented
7#39707C214yesmaximal, complemented
8#39706C214yesmaximal, complemented
9#39636C212yesmaximal, complemented
10#39627C212yesmaximal
11#39620C212yesmaximal, complemented
12#39610C212yesmaximal
13#39176C212yesmaximal, complemented
14#38960C212yesmaximal, complemented
15#38099C212yesmaximal, complemented
16#38098C212yesmaximal, complemented
17#37561C211yesmaximal, characteristic, complemented
18#37561C211yesmaximal, characteristic, complemented
19#37312C212yesmaximal, complemented
20#37312C212yesmaximal, complemented
21#36645C211yesmaximal, characteristic, complemented
22C2×#2864C211yesmaximal, characteristic, complemented
23#36497C212yesmaximal, complemented
24#36387C212yesmaximal, complemented
25#36363C212yesmaximal, complemented
26#36261C212yesmaximal, complemented
27#35282C212yesmaximal, complemented
28#35265C212yesmaximal, complemented
29#34382C211yesmaximal, characteristic
30#34382C211yesmaximal, characteristic
31C4×#529C211yesmaximal, characteristic
32C2×#554C2214yes—
33C2×#533C2212yes—
34C2×#529C2211yescharacteristic
35#2868C2211yescharacteristic
36#2868C2211yescharacteristic
37#2864C2212yes—
38#2864C2212yes—
39#2864C2212yes—
40#2864C2212yes—
41#2864C2212yes—
42#2864C2212yes—
43#2864C2212yes—
44#2864C2212yes—
45#2864C2212yes—
46#2862C2212yes—
47#2859C2212yes—
48#2859C2211yescharacteristic
49#2859C2211yescharacteristic
50#2859C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2851C2212yes—
57#2845C2212yes—
58#2845C2212yes—
59#2844C2212yes—
60#2844C2212yes—
61#2807C2214yes—
62#2806C2214yes—
63#2806C2214yes—
64#2802C2214yes—
65#2802C2214yes—
66#2799C2214yes—
67#2792C2214yes—
68#2792C2214yes—
69#2792C2214yes—
70#2792C2214yes—
71#2791C2214yes—
72#2791C2214yes—
73#2790C2214yes—
74#2790C2214yes—
75#2788C2214yes—
76#2780C2214yes—
77#2774C2214yes—
78#2755C2214yes—
79#2734C2214yes—
80#2734C2214yes—
81#2729C2214yes—
82#2729C2214yes—
83#2729C2214yes—
84#2720C2214yes—
85#2720C2214yes—
86#2713C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2704C2214yes—
90#2692C2214yes—
91#2677C2214yes—
92#2677C2214yes—
93#2666C2214yes—
94#2666C2214yes—
95#2660C2212yes—
96#2660C2212yes—
97#2659C2212yes—
98#2659C2212yes—
99#2647C2212yes—
100#2647C2212yes—
101#2647C2212yes—
102#2647C2212yes—
103#2646C2212yes—
104#2646C2212yes—
105#2629C2212yes—
106#2628C2212yes—
107#2590C2214yes—
108#2589C2214yes—
109#2588C2214yes—
110#2588C2214yes—
111#2587C2214yes—
112#2587C2214yes—
113#2586C2214yes—
114#2586C2214yes—
115#2585C2214yes—
116#2585C2214yes—
117#2585C2214yes—
118#2584C2214yes—
119#2583C2214yes—
120#2583C2214yes—
121#2579C2214yes—
122#2574C2214yes—
123#2574C2214yes—
124#2570C2212yes—
125#2570C2212yes—
126#2570C2212yes—
127#2570C2212yes—
128#2564C2214yes—
129#2564C2214yes—
130#2556C2214yes—
131#2552C2212yes—
132#2552C2212yes—
133#2551C2212yes—
134#2551C2212yes—
135#2550C2212yes—
136#2550C2212yes—
137#2550C2214yes—
138#2550C2212yes—
139#2550C2212yes—
140#2549C2214yes—
141#2549C2214yes—
142#2549C2214yes—
143#2522C2214yes—
144#2522C2214yes—
145#2520C2214yes—
146#2520C2214yes—
147#2520C2214yes—
148#2509C2214yes—
149#2508C2214yes—
150#2507C2214yes—
151#2506C2214yes—
152#2505C2214yes—
153#2505C2214yes—
154#2505C2214yes—
155#2473C2214yes—
156#2473C2214yes—
157#2473C2214yes—
158#2465C2214yes—
159#2465C2214yes—
160#2465C2214yes—
161#2462C2214yes—
162#2462C2214yes—
163#2462C2214yes—
164#2462C2214yes—
165#2453C2214yes—
166#2451C2214yes—
167#2450C2214yes—
168#2450C2214yes—
169#2449C2214yes—
170#2449C2214yes—
171#2446C2214yes—
172#2442C2212yes—
173#2442C2212yes—
174#2441C2212yes—
175#2441C2212yes—
176#2440C2212yes—
177#2440C2212yes—
178#2440C2214yes—
179#2440C2212yes—
180#2440C2212yes—
181#2440C2212yes—
182#2440C2212yes—
183#2439C2212yes—
184#2439C2212yes—
185#2438C2214yes—
186#2438C2214yes—
187#2423C2214yes—
188#2417C2214yes—
189#2382C2212yes—
190#2382C2212yes—
191#2379C2212yes—
192#2379C2212yes—
193#2370C2214yes—
194#2368C2214yes—
195#2368C2214yes—
196#2365C2214yes—
197#2360C2214yes—
198#2359C2214yes—
199#2359C2214yes—
200#2355C2212yes—
201#2355C2212yes—
202#2352C2212yes—
203#2352C2212yes—
204#2352C2212yes—
205#2352C2212yes—
206#2349C2214yes—
207D4×C4⋊C4C2212yes—
208D4×C4⋊C4C2212yes—
209#2345C2214yes—
210#2334C2214yes—
211#2334C2214yes—
212#2331C2212yes—
213#2330C2212yes—
214#2329C2212yes—
215#2329C2212yes—
216#2325C2212yes—
217#2325C2212yes—
218#2317C2212yes—
219#2317C2212yes—
220#2317C2212yes—
221#2316C2212yes—
222#2314C2212yes—
223#2314C2212yes—
224C4×C4⋊Q8C2212yes—
225C4×C4⋊Q8C2212yes—
226C4×C4⋊Q8C2212yes—
227C4×C4⋊Q8C2212yes—
228C4×C4⋊Q8C2212yes—
229C4×#125C2212yes—
230C4×#125C2211yescharacteristic
231C4×#125C2211yescharacteristic
232C4×#126C2212yes—
233C4×#126C2212yes—
234C4×#124C2211yescharacteristic
235C4×#124C2211yescharacteristic
236C4×C22⋊Q8C2211yescharacteristic
237C4×C22⋊Q8C2211yescharacteristic
238C4×#123C2212yes—
239C4×#123C2212yes—
240C4×#121C2211yescharacteristic
241C4×#121C2211yescharacteristic
242#2298C2212yes—
243#2296C2212yes—
244#2295C2211yescharacteristic
245#2293C2211yescharacteristic
246C2×#389C2212yes—
247C2×#389C2211yescharacteristic
248C2×#389C2211yescharacteristic
249C2×#389C2211yescharacteristic
250C2×#389C2211yescharacteristic
251#2290C2212yes—
252C2×#387C2212yes—
253C2×#387C2212yes—
254C2×#387C2212yes—
255C2×#387C2212yes—
256#2285C2211yescharacteristic
257#2285C2211yescharacteristic
258#2285C2212yes—
259#2283C2211yescharacteristic
260C2×#382C2211yescharacteristic
261C2×#382C2211yescharacteristic
262C42×Q8C2211yescharacteristic
263C42×D4C2211yescharacteristic
264C42×D4C2212yes—
265C4×#117C2212yes—
266C2×C43C2211yescharacteristic
267#554—416no—
268#533—48no—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2314yes—
279#529Q8116yescomplemented
280C2×#126C2312yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2311yescharacteristic
289C2×#124C2311yescharacteristic
290C2×#123C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2311yescharacteristic
301C2×#121C2311yescharacteristic
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C2×#117C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2314yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2311yescharacteristic
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
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#399C2314yes—
357#399C2314yes—
358#399C2314yes—
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#398C2314yes—
392#398C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#389C2312yes—
442#389C2312yes—
443#389C2311yescharacteristic
444#389C2311yescharacteristic
445#389C2311yescharacteristic
446#389C2311yescharacteristic
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2312yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
522#388C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2314yes—
530#387C2314yes—
531#387C2312yes—
532#387C2312yes—
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#386C2314yes—
584#386C2312yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
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#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2312yes—
613#384C2312yes—
614#384C2312yes—
615#384C2312yes—
616#384C2312yes—
617#384C2312yes—
618#384C2311yescharacteristic
619#384C2311yescharacteristic
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2312yes—
625#384C2314yes—
626#384C2312yes—
627#384C2312yes—
628#383C2312yes—
629#382C2312yes—
630#382C2311yescharacteristic
631#382C2311yescharacteristic
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#382C2312yes—
649#381C2312yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2311yescharacteristic
666#380C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717#376C2312yes—
718#376C2312yes—
719C2×#95C2312yes—
720C2×#95C2312yes—
721C2×#95C2312yes—
722C2×#95C2312yes—
723C2×#95C2312yes—
724C2×#95C2314yes—
725C2×#95C2312yes—
726C2×#95C2312yes—
727C2×#95C2312yes—
728C43C2311yescharacteristic
729C43C2311yescharacteristic
730C43C2312yes—
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C22×Q8C2414yes—
738C22×Q8C2414yes—
739C22×Q8C2414yes—
740C22×Q8C2414yes—
741C22×Q8C2411yescharacteristic
742C22×D4C2412yes—
743C22×D4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2414yes—
757C23×C4C2411yescharacteristic
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C4⋊Q8—44no—
761C4⋊Q8—44no—
762C4⋊Q8—44no—
763C4⋊Q8—44no—
764C4⋊Q8—44no—
765C4⋊Q8—44no—
766C4⋊Q8—44no—
767C4⋊Q8—44no—
768C4⋊Q8—48no—
769C4⋊Q8—48no—
770#126C2×Q8116yes—
771#125—44no—
772#125—44no—
773#125—44no—
774#125—44no—
775#125—48no—
776#125—48no—
777#125—48no—
778#125C2×Q818yes—
779#124C2×Q818yes—
780#123C2×Q8116yes—
781C22⋊Q8—216no—
782C22⋊Q8—48no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790C22⋊Q8C2×Q818yes—
791#121C2×Q818yes—
792C4×Q8—42no—
793C4×Q8—42no—
794C4×Q8—48no—
795C4×Q8—48no—
796C4×Q8—48no—
797C4×Q8C2×Q818yes—
798C4×D4—28no—
799C4×D4—28no—
800C4×D4—42no—
801C4×D4—42no—
802C4×D4—48no—
803C4×D4—48no—
804C4×D4C2×Q818yes—
805C4×D4C2×Q8116yes—
806#117—44no—
807#117—44no—
808#117—44no—
809#117—44no—
810#117—44no—
811#117C2×Q8116yes—
812C2×C4⋊C4—28no—
813C2×C4⋊C4—28no—
814C2×C4⋊C4—42no—
815C2×C4⋊C4—42no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4—42no—
819C2×C4⋊C4—42no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4—44no—
822C2×C4⋊C4—48no—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C42—24no—
923C2×C42—24no—
924C2×C42—44no—
925C2×C42—42no—
926C2×C42—42no—
927C2×C42—42no—
928C2×C42—42no—
929C2×C42C2×Q818yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971C2×C42C2412yes—
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
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#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043C24C2512yes—
1044C24C2511yescharacteristic
1045C2×Q8—28no—
1046C2×Q8—28no—
1047C2×Q8—41no—
1048C2×Q8—41no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—44no—
1052C2×Q8—44no—
1053C2×Q8—44no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×Q8C22×Q814yes—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4C22×Q818yes—
1065C2×D4C22×Q814yes—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—24no—
1071C22×C4—24no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—41no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—41no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4C22×Q814yes—
1109C22×C4C22×Q814yes—
1110C22×C4C22×Q818yes—
1111C22×C4C22×Q814yes—
1112C22×C4H(5,𝔽2)14yes—
1113C22×C42−1+414yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2514yes—
1117C22×C4C2514yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2514yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2514yes—
1124C22×C4C2514yes—
1125C22×C4C2514yes—
1126C22×C4C2514yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C4⋊C4—28no—
1144C4⋊C4—28no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—41no—
1182C4⋊C4—41no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—41no—
1186C4⋊C4—41no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4C22×Q818yes—
1216C4⋊C4C22×Q818yes—
1217C4⋊C4C22×Q814yes—
1218C4⋊C4C22×Q818yes—
1219C4⋊C4C22×Q814yes—
1220C4⋊C4C22×Q818yes—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4C22×Q818yes—
1238C22⋊C4C22×Q818yes—
1239C22⋊C4C22×Q818yes—
1240C22⋊C4C22×Q818yes—
1241C22⋊C4C22×Q818yes—
1242C42—22no—
1243C42—22no—
1244C42—22no—
1245C42—22no—
1246C42—24no—
1247C42—22no—
1248C42—22no—
1249C42—22no—
1250C42—22no—
1251C42—24no—
1252C42—22no—
1253C42—22no—
1254C42—22no—
1255C42—22no—
1256C42—24no—
1257C42—22no—
1258C42—22no—
1259C42—22no—
1260C42—22no—
1261C42—24no—
1262C42—41no—
1263C42—41no—
1264C42—41no—
1265C42—41no—
1266C42—42no—
1267C42—42no—
1268C42—41no—
1269C42—41no—
1270C42—41no—
1271C42—41no—
1272C42—44no—
1273C42—44no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42—44no—
1278C42—42no—
1279C42—42no—
1280C42—44no—
1281C42—44no—
1282C42C22×Q814yes—
1283C42C22×Q814yes—
1284C42C22×Q814yes—
1285C42C22×Q814yes—
1286C42C22×Q818yes—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23C23×Q814yes—
1298C23C23×Q812yes—
1299C23C2×H(5,𝔽2)12yes—
1300C23C2×2−1+412yes—
1301C23C2611yescharacteristic
1302Q8—44no—
1303Q8—88no—
1304Q8—88no—
1305Q8—88no—
1306Q8—164no—
1307D4—216no—
1308D4—44no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—22no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—22no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—28no—
1338C2×C4—28no—
1339C2×C4—216no—
1340C2×C4—21no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—44no—
1383C2×C4—44no—
1384C2×C4—44no—
1385C2×C4—44no—
1386C2×C4—44no—
1387C2×C4—84no—
1388C2×C4—84no—
1389C2×C4—84no—
1390C2×C4—84no—
1391C2×C4—84no—
1392C2×C4—84no—
1393C2×C4—88no—
1394C2×C4—164no—
1395C2×C4C23×Q812yes—
1396C2×C4C23×Q812yes—
1397C2×C4C23×Q812yes—
1398C2×C4C23×Q812yes—
1399C2×C4C23×Q812yes—
1400C2×C4C23×Q814yes—
1401C2×C4C23×Q814yes—
1402C2×C4C23×Q814yes—
1403C2×C4C23×Q812yes—
1404C2×C4C2×H(5,𝔽2)12yes—
1405C2×C4C2×H(5,𝔽2)12yes—
1406C2×C4C2×2−1+412yes—
1407C2×C4C2×2−1+412yes—
1408C2×C4#58512yes—
1409C2×C4#58512yes—
1410C2×C4#58512yes—
1411C2×C4#58512yes—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—24no—
1419C22—24no—
1420C22—24no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22#350314yes—
1426C22C24×Q811yescharacteristic
1427C22C22×H(5,𝔽2)11yescharacteristic
1428C22C22×2−1+411yescharacteristic
1429C22C2×#58511yescharacteristic
1430C22C2×#58511yescharacteristic
1431C22C2×#58511yescharacteristic
1432C22C2×#58511yescharacteristic
1433C4—22no—
1434C4—22no—
1435C4—22no—
1436C4—22no—
1437C4—24no—
1438C4—24no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—24no—
1443C4—22no—
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—41no—
1448C4—44no—
1449C4—44no—
1450C4—42no—
1451C4—44no—
1452C4—42no—
1453C4—41no—
1454C4—44no—
1455C4—44no—
1456C4—42no—
1457C4—44no—
1458C4—44no—
1459C4—42no—
1460C4—44no—
1461C4#350414yes—
1462C2—24no—
1463C2—44no—
1464C2#6274811yescharacteristic
1465C2#6275211yescharacteristic
1466C2C2×#350311yescharacteristic
1467C2C2×#350411yescharacteristic
1468C2#6281311yescharacteristic
1469C2#6282211yescharacteristic
1470C2#6282311yescharacteristic
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. #59319C2semidirect
2. #59149C2semidirect
3. #46155C2semidirect
4. #46154C2semidirect
5. #46009C2semidirect
6. #46008C2semidirect
7. #39707C2semidirect
8. #39706C2semidirect
9. #39636C2semidirect
11. #39620C2semidirect
13. #39176C2semidirect
14. #38960C2semidirect
15. #38099C2semidirect
16. #38098C2semidirect
17. #37561C2semidirect
18. #37561C2semidirect
19. #37312C2semidirect
20. #37312C2semidirect
21. #36645C2semidirect
22. C2×#2864C2semidirect
23. #36497C2semidirect
24. #36387C2semidirect
25. #36363C2semidirect
26. #36261C2semidirect
27. #35282C2semidirect
28. #35265C2semidirect
279. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#593192
#591492
#461552
#461542
#460092
#460082
#397072
#397062
#396362
#396272
#396202
#396102
#391762
#389602
#380992
#380982
#375612
#373122
#366452
C2×#28642
#364972
#363872
#363632
#362612
#352822
#352652
#343822
C4×#5292