Finite Group Databasebeta

← #7711064

Subgroups — #7711064

Order 512.

4708 conjugacy classes of subgroups.

The subgroup lattice has 1486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59909C212yesmaximal, complemented
2#59833C212yesmaximal, complemented
3#59461C212yesmaximal, complemented
4#59460C212yesmaximal, complemented
5#45796C214yesmaximal, complemented
6#45793C212yesmaximal, complemented
7#45792C212yesmaximal, complemented
8#39981C212yesmaximal, complemented
9#39980C212yesmaximal, complemented
10#39710C212yesmaximal, complemented
11#39708C212yesmaximal, complemented
12#39696C214yesmaximal, complemented
13#39673C212yesmaximal, complemented
14#39672C212yesmaximal, complemented
15#39629C211yesmaximal, characteristic, complemented
16#39628C211yesmaximal, characteristic, complemented
17#39612C211yesmaximal, characteristic, complemented
18#39611C211yesmaximal, characteristic, complemented
19#38453C212yesmaximal, complemented
20#38452C212yesmaximal, complemented
21#37567C212yesmaximal, complemented
22#37137C212yesmaximal, complemented
23#37136C212yesmaximal, complemented
24#36635C211yesmaximal, characteristic, complemented
25#36635C211yesmaximal, characteristic, complemented
26#36431C212yesmaximal, complemented
27#36281C214yesmaximal, complemented
28#36219C212yesmaximal, complemented
29#35018C214yesmaximal, complemented
30#34402C212yesmaximal
31C4×#532C211yesmaximal, characteristic
32C2×#557C2212yes—
33C2×#554C2212yes—
34C2×#532C2211yescharacteristic
35C2×C4×#41C2212yes—
36#2864C2212yes—
37#2864C2212yes—
38#2863C2212yes—
39#2863C2211yescharacteristic
40#2863C2211yescharacteristic
41#2863C2212yes—
42#2863C2212yes—
43#2862C2211yescharacteristic
44#2862C2211yescharacteristic
45#2859C2211yescharacteristic
46#2859C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2855C2212yes—
52#2855C2211yescharacteristic
53#2855C2211yescharacteristic
54#2855C2212yes—
55#2855C2212yes—
56#2855C2214yes—
57#2851C2212yes—
58#2851C2212yes—
59#2851C2214yes—
60#2841C2214yes—
61#2841C2214yes—
62#2806C2212yes—
63#2806C2212yes—
64#2805C2212yes—
65#2805C2212yes—
66#2804C2212yes—
67#2804C2212yes—
68#2792C2214yes—
69#2791C2214yes—
70#2790C2214yes—
71#2784C2214yes—
72#2784C2214yes—
73#2780C2214yes—
74#2780C2214yes—
75#2774C2214yes—
76#2768C2214yes—
77#2763C2214yes—
78#2755C2214yes—
79#2748C2214yes—
80#2748C2214yes—
81#2734C2212yes—
82#2734C2212yes—
83#2732C2212yes—
84#2732C2212yes—
85#2732C2214yes—
86#2732C2212yes—
87#2732C2212yes—
88#2729C2214yes—
89#2726C2212yes—
90#2726C2212yes—
91#2720C2214yes—
92#2720C2214yes—
93#2704C2214yes—
94#2692C2214yes—
95#2692C2214yes—
96#2692C2214yes—
97#2692C2214yes—
98#2683C2214yes—
99#2683C2212yes—
100#2683C2212yes—
101#2677C2214yes—
102#2667C2214yes—
103#2667C2214yes—
104#2666C2214yes—
105#2666C2214yes—
106#2665C2214yes—
107#2665C2214yes—
108#2660C2212yes—
109#2660C2212yes—
110#2647C2212yes—
111#2647C2212yes—
112#2608C2214yes—
113#2607C2214yes—
114#2606C2214yes—
115#2605C2214yes—
116#2590C2214yes—
117#2589C2214yes—
118#2588C2214yes—
119#2587C2214yes—
120#2587C2214yes—
121#2587C2214yes—
122#2586C2214yes—
123#2585C2214yes—
124#2583C2214yes—
125#2582C2212yes—
126#2581C2212yes—
127#2581C2212yes—
128#2580C2212yes—
129#2580C2214yes—
130#2580C2212yes—
131#2579C2214yes—
132#2579C2214yes—
133#2574C2214yes—
134#2574C2214yes—
135#2570C2212yes—
136#2570C2212yes—
137#2567C2212yes—
138#2566C2212yes—
139#2566C2214yes—
140#2566C2212yes—
141#2565C2212yes—
142#2565C2212yes—
143#2564C2214yes—
144#2564C2214yes—
145#2556C2214yes—
146#2556C2214yes—
147#2550C2212yes—
148#2550C2212yes—
149#2549C2214yes—
150#2549C2214yes—
151#2549C2214yes—
152#2542C2212yes—
153#2538C2212yes—
154#2522C2214yes—
155#2522C2214yes—
156#2522C2214yes—
157#2520C2214yes—
158#2520C2214yes—
159#2505C2214yes—
160#2492C2214yes—
161#2473C2214yes—
162#2465C2214yes—
163#2465C2214yes—
164#2465C2214yes—
165#2462C2214yes—
166#2462C2214yes—
167#2454C2214yes—
168#2454C2212yes—
169#2454C2212yes—
170#2453C2212yes—
171#2453C2212yes—
172#2452C2214yes—
173#2452C2212yes—
174#2452C2212yes—
175#2452C2212yes—
176#2452C2212yes—
177#2451C2212yes—
178#2451C2212yes—
179#2451C2212yes—
180#2451C2212yes—
181#2450C2214yes—
182#2450C2214yes—
183#2450C2214yes—
184#2450C2214yes—
185#2449C2214yes—
186#2449C2214yes—
187#2449C2214yes—
188#2449C2214yes—
189#2441C2214yes—
190#2441C2212yes—
191#2441C2212yes—
192#2439C2214yes—
193#2439C2212yes—
194#2439C2212yes—
195#2438C2214yes—
196#2438C2214yes—
197#2423C2214yes—
198#2377C2214yes—
199#2377C2214yes—
200#2368C2214yes—
201#2368C2214yes—
202#2367C2212yes—
203#2367C2212yes—
204#2367C2212yes—
205#2367C2212yes—
206#2360C2214yes—
207#2360C2214yes—
208#2353C2214yes—
209#2353C2214yes—
210#2351C2212yes—
211#2351C2212yes—
212Q8×C4⋊C4C2212yes—
213#2349C2212yes—
214#2349C2212yes—
215D4×C4⋊C4C2212yes—
216#2341C2212yes—
217#2341C2212yes—
218#2339C2212yes—
219#2339C2212yes—
220#2333C2214yes—
221#2333C2214yes—
222#2329C2214yes—
223#2329C2214yes—
224#2328C2212yes—
225#2328C2212yes—
226#2327C2212yes—
227#2327C2212yes—
228#2318C2214yes—
229#2318C2214yes—
230C4×C4⋊Q8C2211yescharacteristic
231C4×C4⋊Q8C2211yescharacteristic
232C4×C4⋊Q8C2211yescharacteristic
233C4×C4⋊Q8C2211yescharacteristic
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2211yescharacteristic
236C4×#127C2211yescharacteristic
237C4×#127C2211yescharacteristic
238C4×#125C2212yes—
239C4×#125C2212yes—
240C4×#124C2212yes—
241C4×#124C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2211yescharacteristic
246C4×C22⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2214yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250C4×#121C2212yes—
251C4×#121C2212yes—
252#2297C2212yes—
253#2295C2212yes—
254#2295C2212yes—
255#2295C2211yescharacteristic
256#2295C2211yescharacteristic
257#2295C2212yes—
258#2293C2212yes—
259#2293C2212yes—
260C2×#387C2214yes—
261#2285C2211yescharacteristic
262#2283C2212yes—
263#2283C2212yes—
264C42×D4C2212yes—
265C42×D4C2212yes—
266C2×C43C2211yescharacteristic
267C22×#41C2312yes—
268#557—48no—
269#554—48no—
270#532Q8116yescomplemented
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×#127C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#124C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C4×#41—48no—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×#117C2314yes—
332C2×#117C2312yes—
333C22×C4⋊C4C2314yes—
334C22×C4⋊C4C2314yes—
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2314yes—
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341C22×C42C2311yescharacteristic
342C22×C42C2311yescharacteristic
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
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#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
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#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2311yescharacteristic
445#391C2312yes—
446#391C2311yescharacteristic
447#391C2312yes—
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2311yescharacteristic
454#391C2311yescharacteristic
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2314yes—
467#390C2314yes—
468#390C2312yes—
469#390C2312yes—
470#390C2314yes—
471#390C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2311yescharacteristic
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2311yescharacteristic
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2311yescharacteristic
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
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#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#387C2314yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#385C2312yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#384C2311yescharacteristic
638#384C2311yescharacteristic
639#384C2311yescharacteristic
640#384C2311yescharacteristic
641#384C2311yescharacteristic
642#384C2311yescharacteristic
643#384C2312yes—
644#384C2312yes—
645#384C2314yes—
646#383C2314yes—
647#383C2312yes—
648#383C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2314yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2314yes—
658#382C2312yes—
659#382C2312yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#381C2312yes—
664#381C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2311yescharacteristic
681#380C2311yescharacteristic
682#380C2312yes—
683#380C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
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⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723#376C2312yes—
724#376C2312yes—
725#376C2314yes—
726C2×#95C2314yes—
727C2×#95C2314yes—
728C2×#95C2314yes—
729C2×#95C2314yes—
730C43C2311yescharacteristic
731C43C2311yescharacteristic
732C43C2311yescharacteristic
733C43C2311yescharacteristic
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C43C2311yescharacteristic
738C2×#41—44no—
739C2×#41—44no—
740C2×#41C2×Q8116yes—
741C22×Q8C2412yes—
742C22×Q8C2411yescharacteristic
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2414yes—
748C22×Q8C2414yes—
749C22×D4C2412yes—
750C22×D4C2412yes—
751C22×D4C2412yes—
752C22×D4C2414yes—
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2411yescharacteristic
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C4⋊Q8—42no—
768C4⋊Q8—42no—
769C4⋊Q8—42no—
770C4⋊Q8—44no—
771C4⋊Q8—44no—
772C4⋊Q8—42no—
773C4⋊Q8—48no—
774C4⋊Q8C2×Q818yes—
775#127C2×Q818yes—
776#125—28no—
777#125—44no—
778#125—44no—
779#125—48no—
780#125—44no—
781#125—48no—
782#124C2×Q8116yes—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790C22⋊Q8—48no—
791C22⋊Q8—42no—
792C22⋊Q8—48no—
793C22⋊Q8—44no—
794C22⋊Q8—44no—
795C22⋊Q8—42no—
796C22⋊Q8—48no—
797C22⋊Q8—44no—
798#121C2×Q8116yes—
799#121C2×Q8116yes—
800C4×Q8—28no—
801C4×Q8—24no—
802C4×Q8—24no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—48no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—44no—
811C4×Q8—44no—
812C4×D4—28no—
813C4×D4—44no—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4—44no—
819C4×D4—44no—
820C4×D4—44no—
821C4×D4—44no—
822C4×D4—48no—
823C4×D4—48no—
824C4×D4C2×Q8116yes—
825C4×D4C2×Q8116yes—
826#117—48no—
827#117—44no—
828C2×C4⋊C4—48no—
829C2×C4⋊C4—48no—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C42—24no—
931C2×C42—48no—
932C2×C42—42no—
933C2×C42—42no—
934C2×C42—42no—
935C2×C42—42no—
936C2×C42—42no—
937C2×C42C2×Q818yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2411yescharacteristic
977C2×C42C2411yescharacteristic
978C2×C42C2411yescharacteristic
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
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#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2412yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047C24C2514yes—
1048C24C2511yescharacteristic
1049#41—432no—
1050C2×Q8—24no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—24no—
1054C2×Q8—24no—
1055C2×Q8—24no—
1056C2×Q8—24no—
1057C2×Q8—44no—
1058C2×Q8—42no—
1059C2×Q8—42no—
1060C2×Q8—42no—
1061C2×Q8—41no—
1062C2×Q8—42no—
1063C2×Q8—41no—
1064C2×Q8—44no—
1065C2×Q8—44no—
1066C2×Q8—42no—
1067C2×Q8—42no—
1068C2×Q8—41no—
1069C2×Q8—41no—
1070C2×Q8—44no—
1071C2×Q8—44no—
1072C2×Q8—44no—
1073C2×Q8C22×Q818yes—
1074C2×D4—24no—
1075C2×D4—24no—
1076C2×D4—44no—
1077C2×D4—42no—
1078C2×D4—42no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4C22×Q818yes—
1083C2×D4C22×Q818yes—
1084C2×D4C22×Q818yes—
1085C2×D4C22×Q8116yes—
1086C22×C4—22no—
1087C22×C4—22no—
1088C22×C4—22no—
1089C22×C4—22no—
1090C22×C4—22no—
1091C22×C4—22no—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—28no—
1095C22×C4—28no—
1096C22×C4—44no—
1097C22×C4—41no—
1098C22×C4—41no—
1099C22×C4—41no—
1100C22×C4—41no—
1101C22×C4—41no—
1102C22×C4—41no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4C22×Q814yes—
1125C22×C4C22×Q814yes—
1126C22×C4C22×Q814yes—
1127C22×C4C22×Q8116yes—
1128C22×C4C2512yes—
1129C22×C4C2514yes—
1130C22×C4C2514yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2514yes—
1139C22×C4C2514yes—
1140C22×C4C2514yes—
1141C22×C4C2514yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2512yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2514yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—41no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—41no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—41no—
1227C4⋊C4—41no—
1228C4⋊C4C22×Q818yes—
1229C4⋊C4C22×Q818yes—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—28no—
1233C22⋊C4—28no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4C22×Q8116yes—
1256C22⋊C4C22×Q8116yes—
1257C42—22no—
1258C42—22no—
1259C42—22no—
1260C42—28no—
1261C42—24no—
1262C42—24no—
1263C42—22no—
1264C42—22no—
1265C42—22no—
1266C42—22no—
1267C42—22no—
1268C42—22no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—22no—
1273C42—24no—
1274C42—24no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42—41no—
1281C42—41no—
1282C42—41no—
1283C42—41no—
1284C42—41no—
1285C42—44no—
1286C42—44no—
1287C42—44no—
1288C42—44no—
1289C42—44no—
1290C42—44no—
1291C42—44no—
1292C42—44no—
1293C42C22×Q814yes—
1294C42C22×Q814yes—
1295C42C22×Q814yes—
1296C42C22×Q814yes—
1297C42H(5,𝔽2)14yes—
1298C23—24no—
1299C23—21no—
1300C23—24no—
1301C23—24no—
1302C23—24no—
1303C23—21no—
1304C23—21no—
1305C23—21no—
1306C23—21no—
1307C23—24no—
1308C23—24no—
1309C23—21no—
1310C23C23×Q818yes—
1311C23C23×Q812yes—
1312C23C2611yescharacteristic
1313Q8—216no—
1314Q8—84no—
1315Q8—82no—
1316Q8—82no—
1317Q8—84no—
1318Q8—84no—
1319Q8—88no—
1320Q8—164no—
1321D4—216no—
1322D4—48no—
1323D4—48no—
1324D4—416no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—24no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—24no—
1348C2×C4—21no—
1349C2×C4—28no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—21no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—44no—
1399C2×C4—44no—
1400C2×C4—416no—
1401C2×C4—44no—
1402C2×C4—44no—
1403C2×C4—44no—
1404C2×C4—44no—
1405C2×C4—88no—
1406C2×C4—88no—
1407C2×C4—88no—
1408C2×C4—88no—
1409C2×C4—164no—
1410C2×C4—164no—
1411C2×C4C23×Q812yes—
1412C2×C4C23×Q812yes—
1413C2×C4C23×Q812yes—
1414C2×C4C23×Q812yes—
1415C2×C4C23×Q812yes—
1416C2×C4C23×Q818yes—
1417C2×C4C23×Q812yes—
1418C2×C4C2×H(5,𝔽2)12yes—
1419C2×C4C2×H(5,𝔽2)12yes—
1420C2×C4C2×H(5,𝔽2)12yes—
1421C2×C4#58512yes—
1422C2×C4#58512yes—
1423C2×C4#58512yes—
1424C2×C4#58512yes—
1425C2×C4#58512yes—
1426C22—22no—
1427C22—28no—
1428C22—22no—
1429C22—22no—
1430C22—28no—
1431C22—28no—
1432C22—41no—
1433C22—44no—
1434C22—41no—
1435C22—44no—
1436C22—41no—
1437C22—44no—
1438C22—41no—
1439C22—44no—
1440C22C24×Q811yescharacteristic
1441C22C22×H(5,𝔽2)11yescharacteristic
1442C22C2×#58511yescharacteristic
1443C22C2×#58511yescharacteristic
1444C22C2×#58511yescharacteristic
1445C22C2×#58511yescharacteristic
1446C22C2×#58511yescharacteristic
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—28no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—22no—
1459C4—42no—
1460C4—41no—
1461C4—42no—
1462C4—44no—
1463C4—42no—
1464C4—44no—
1465C4—44no—
1466C4—42no—
1467C4—42no—
1468C4—44no—
1469C4—42no—
1470C4—42no—
1471C4—41no—
1472C4—44no—
1473C4—42no—
1474C4—44no—
1475C4#350114yes—
1476C2—42no—
1477C2—48no—
1478C2#6274311yescharacteristic
1479C2#6274811yescharacteristic
1480C2C2×#350111yescharacteristic
1481C2#6281311yescharacteristic
1482C2#6281311yescharacteristic
1483C2#6282811yescharacteristic
1484C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59909C2semidirect
2. #59833C2semidirect
3. #59461C2semidirect
4. #59460C2semidirect
5. #45796C2semidirect
6. #45793C2semidirect
7. #45792C2semidirect
8. #39981C2semidirect
9. #39980C2semidirect
10. #39710C2semidirect
11. #39708C2semidirect
12. #39696C2semidirect
13. #39673C2semidirect
14. #39672C2semidirect
15. #39629C2semidirect
16. #39628C2semidirect
17. #39612C2semidirect
18. #39611C2semidirect
19. #38453C2semidirect
20. #38452C2semidirect
21. #37567C2semidirect
22. #37137C2semidirect
23. #37136C2semidirect
24. #36635C2semidirect
25. #36635C2semidirect
26. #36431C2semidirect
27. #36281C2semidirect
28. #36219C2semidirect
29. #35018C2semidirect
270. #532Q8semidirect

Maximal subgroups

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

subgroupindex
#599092
#598332
#594612
#594602
#457962
#457932
#457922
#399812
#399802
#397102
#397082
#396962
#396732
#396722
#396292
#396282
#396122
#396112
#384532
#384522
#375672
#371372
#371362
#366352
#364312
#362812
#362192
#350182
#344022
C4×#5322