Finite Group Databasebeta

← #7898327

Subgroups — #7898327

Order 512.

4885 conjugacy classes of subgroups.

The subgroup lattice has 1453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59314C212yesmaximal, complemented
3#52267C211yesmaximal, characteristic, complemented
4#52039C214yesmaximal, complemented
5#51593C214yesmaximal, complemented
6#47974C214yesmaximal, complemented
7#46445C214yesmaximal, complemented
8#46282C212yesmaximal, complemented
9#44951C212yesmaximal, complemented
10#44942C212yesmaximal, complemented
11#44941C212yesmaximal, complemented
12#43529C214yesmaximal, complemented
13#42931C212yesmaximal, complemented
14#42823C212yesmaximal, complemented
15#40621C214yesmaximal, complemented
16#39985C212yesmaximal, complemented
17#39692C212yesmaximal, complemented
18#39611C211yesmaximal, characteristic, complemented
19#39611C212yesmaximal, complemented
20#39365C211yesmaximal, characteristic, complemented
21#38452C212yesmaximal, complemented
22#37874C212yesmaximal, complemented
23#37137C212yesmaximal, complemented
24#36285C211yesmaximal, characteristic, complemented
25#35806C212yesmaximal, complemented
26#35532C212yesmaximal, complemented
27#35208C211yesmaximal, characteristic, complemented
28#34477C212yesmaximal
29#34313C211yesmaximal, characteristic
30C2×#554C2212yes—
31C2×#554C2214yes—
32C2×#554C2212yes—
33C2×#550C2211yescharacteristic
34C2×#544C2212yes—
35C2×#520C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2859C2212yes—
39#2859C2211yescharacteristic
40#2851C2212yes—
41#2843C2214yes—
42#2841C2214yes—
43#2807C2212yes—
44#2806C2211yescharacteristic
45#2805C2211yescharacteristic
46#2804C2211yescharacteristic
47#2802C2212yes—
48#2792C2214yes—
49#2792C2214yes—
50#2791C2214yes—
51#2790C2214yes—
52#2790C2212yes—
53#2790C2214yes—
54#2790C2214yes—
55#2788C2212yes—
56#2780C2214yes—
57#2780C2214yes—
58#2780C2214yes—
59#2780C2212yes—
60#2780C2214yes—
61#2780C2214yes—
62#2780C2214yes—
63#2780C2214yes—
64#2780C2214yes—
65#2774C2214yes—
66#2768C2214yes—
67#2748C2214yes—
68#2748C2214yes—
69#2748C2214yes—
70#2734C2212yes—
71#2732C2214yes—
72#2732C2212yes—
73#2732C2211yescharacteristic
74#2732C2212yes—
75#2732C2212yes—
76#2732C2212yes—
77#2732C2214yes—
78#2732C2214yes—
79#2732C2212yes—
80#2729C2212yes—
81#2726C2214yes—
82#2726C2212yes—
83#2720C2214yes—
84#2720C2214yes—
85#2720C2214yes—
86#2720C2214yes—
87#2713C2214yes—
88#2704C2214yes—
89#2692C2214yes—
90#2692C2214yes—
91#2683C2212yes—
92#2683C2214yes—
93#2683C2214yes—
94#2683C2212yes—
95#2683C2212yes—
96#2677C2214yes—
97#2667C2214yes—
98#2667C2214yes—
99#2666C2214yes—
100#2666C2214yes—
101#2660C2214yes—
102#2660C2212yes—
103#2659C2214yes—
104#2629C2212yes—
105#2629C2212yes—
106#2627C2214yes—
107#2608C2214yes—
108#2606C2214yes—
109#2606C2214yes—
110#2590C2214yes—
111#2587C2214yes—
112#2583C2214yes—
113#2582C2211yescharacteristic
114#2582C2211yescharacteristic
115#2582C2211yescharacteristic
116#2579C2214yes—
117#2579C2214yes—
118#2579C2214yes—
119#2570C2212yes—
120#2569C2214yes—
121#2567C2212yes—
122#2567C2211yescharacteristic
123#2567C2211yescharacteristic
124#2566C2214yes—
125#2566C2212yes—
126#2566C2212yes—
127#2566C2214yes—
128#2566C2212yes—
129#2565C2212yes—
130#2565C2212yes—
131#2564C2214yes—
132#2556C2214yes—
133#2556C2214yes—
134#2552C2211yescharacteristic
135#2552C2212yes—
136#2552C2212yes—
137#2551C2212yes—
138#2550C2212yes—
139#2549C2214yes—
140#2542C2214yes—
141#2542C2212yes—
142#2542C2212yes—
143#2542C2212yes—
144#2538C2212yes—
145#2538C2212yes—
146#2538C2212yes—
147#2522C2214yes—
148#2511C2212yes—
149#2508C2212yes—
150#2507C2212yes—
151#2507C2212yes—
152#2506C2212yes—
153#2506C2212yes—
154#2505C2214yes—
155#2487C2214yes—
156#2487C2214yes—
157#2473C2214yes—
158#2473C2214yes—
159#2462C2214yes—
160#2454C2212yes—
161#2454C2212yes—
162#2454C2212yes—
163#2454C2214yes—
164#2453C2212yes—
165#2453C2212yes—
166#2452C2212yes—
167#2451C2212yes—
168#2450C2214yes—
169#2450C2214yes—
170#2450C2214yes—
171#2449C2214yes—
172#2449C2214yes—
173#2449C2214yes—
174#2449C2214yes—
175#2449C2214yes—
176#2449C2214yes—
177#2449C2214yes—
178#2449C2214yes—
179#2449C2214yes—
180#2449C2214yes—
181#2449C2214yes—
182#2449C2214yes—
183#2446C2212yes—
184#2442C2212yes—
185#2441C2214yes—
186#2441C2212yes—
187#2441C2212yes—
188#2441C2214yes—
189#2440C2214yes—
190#2440C2214yes—
191#2440C2214yes—
192#2440C2214yes—
193#2440C2212yes—
194#2440C2212yes—
195#2440C2212yes—
196#2438C2214yes—
197#2438C2214yes—
198#2429C2214yes—
199#2423C2214yes—
200#2417C2214yes—
201#2417C2214yes—
202#2402C2212yes—
203#2396C2212yes—
204#2396C2212yes—
205C2×#398C2214yes—
206#2380C2214yes—
207#2377C2214yes—
208#2370C2212yes—
209#2366C2212yes—
210#2366C2211yescharacteristic
211#2366C2212yes—
212#2364C2214yes—
213#2363C2212yes—
214#2361C2214yes—
215#2361C2212yes—
216#2361C2212yes—
217#2356C2212yes—
218#2355C2211yescharacteristic
219#2353C2214yes—
220#2352C2212yes—
221Q8×C4⋊C4C2211yescharacteristic
222Q8×C4⋊C4C2211yescharacteristic
223#2349C2212yes—
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2212yes—
227D4×C4⋊C4C2212yes—
228#2341C2212yes—
229#2339C2212yes—
230#2339C2212yes—
231#2333C2214yes—
232#2330C2212yes—
233#2329C2214yes—
234#2328C2214yes—
235#2328C2212yes—
236#2325C2214yes—
237#2324C2212yes—
238#2324C2214yes—
239#2324C2212yes—
240#2320C2212yes—
241#2318C2214yes—
242#2317C2212yes—
243#2311C2212yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×#127C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×#121C2212yes—
250#2297C2212yes—
251#2296C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2293C2212yes—
255#2293C2211yescharacteristic
256#2290C2212yes—
257C2×#384C2212yes—
258C42×Q8C2211yescharacteristic
259C22×#41C2312yes—
260#554—48no—
261#554—416no—
262#554—48no—
263#550Q8116yescomplemented
264#544—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
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×#121C2312yes—
300C2×#121C2314yes—
301#520—48no—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2314yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2312yes—
335C22×C4⋊C4C2314yes—
336C22×C4⋊C4C2314yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2314yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2314yes—
341C22×C42C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2312yes—
358#399C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
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#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#396C2314yes—
407#396C2312yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2312yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2312yes—
427#396C2312yes—
428#396C2314yes—
429#396C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2312yes—
441#395C2312yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#393C2314yes—
446#393C2312yes—
447#393C2312yes—
448#391C2311yescharacteristic
449#391C2312yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2311yescharacteristic
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2311yescharacteristic
465#390C2311yescharacteristic
466#390C2312yes—
467#390C2314yes—
468#390C2312yes—
469#390C2312yes—
470#390C2314yes—
471#390C2312yes—
472#390C2314yes—
473#390C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2312yes—
480#390C2311yescharacteristic
481#390C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2311yescharacteristic
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2311yescharacteristic
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
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#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2312yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2312yes—
635#385C2312yes—
636#385C2312yes—
637#385C2312yes—
638#385C2314yes—
639#384C2312yes—
640#384C2311yescharacteristic
641#384C2311yescharacteristic
642#384C2311yescharacteristic
643#384C2312yes—
644#384C2312yes—
645#384C2311yescharacteristic
646#384C2312yes—
647#384C2312yes—
648#384C2312yes—
649#384C2314yes—
650#384C2312yes—
651#384C2312yes—
652#384C2311yescharacteristic
653#384C2314yes—
654#384C2314yes—
655#383C2314yes—
656#383C2314yes—
657#382C2312yes—
658#382C2312yes—
659#382C2314yes—
660#382C2312yes—
661#382C2314yes—
662#381C2314yes—
663#381C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711#376C2312yes—
712#376C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C43C2312yes—
718C2×#41—44no—
719C2×#41—44no—
720C2×#41C2×Q8116yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2414yes—
726C22×Q8C2414yes—
727C22×Q8C2411yescharacteristic
728C22×D4C2412yes—
729C22×D4C2414yes—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2414yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C4⋊Q8—24no—
747C4⋊Q8—24no—
748C4⋊Q8—44no—
749C4⋊Q8—48no—
750C4⋊Q8—44no—
751C4⋊Q8—48no—
752#127C2×Q818yes—
753#127C2×Q8116yes—
754#125—28no—
755#125—44no—
756#125—44no—
757#125—48no—
758#125—44no—
759#125—48no—
760#125—48no—
761#125—48no—
762C22⋊Q8—28no—
763C22⋊Q8—216no—
764C22⋊Q8—48no—
765C22⋊Q8—48no—
766C22⋊Q8—48no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—48no—
772C22⋊Q8—48no—
773C22⋊Q8—48no—
774C22⋊Q8—48no—
775C22⋊Q8—84no—
776C22⋊Q8—84no—
777C22⋊Q8—84no—
778C22⋊Q8—84no—
779C22⋊Q8—84no—
780#121C2×Q8116yes—
781#121C2×Q8132yes—
782C4×Q8—28no—
783C4×Q8—24no—
784C4×Q8—24no—
785C4×Q8—42no—
786C4×Q8—42no—
787C4×Q8—44no—
788C4×Q8—42no—
789C4×Q8—44no—
790C4×Q8C2×Q818yes—
791C4×D4—28no—
792C4×D4—48no—
793C4×D4—48no—
794C4×D4—48no—
795C4×D4—44no—
796C4×D4—44no—
797C4×D4—44no—
798C4×D4—44no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—48no—
802C4×D4—48no—
803C4×D4—48no—
804C4×D4—82no—
805C4×D4—82no—
806C4×D4—82no—
807C4×D4C2×Q818yes—
808C4×D4C2×Q8116yes—
809#117—28no—
810#117—44no—
811#117—48no—
812#117—44no—
813C2×C4⋊C4—48no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4—48no—
817C2×C4⋊C4—48no—
818C2×C4⋊C4—48no—
819C2×C4⋊C4—48no—
820C2×C4⋊C4—84no—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2412yes—
939C2×C42—44no—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2411yescharacteristic
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2411yescharacteristic
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2411yescharacteristic
963C2×C42C2412yes—
964C2×C42C2411yescharacteristic
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026C24C2512yes—
1027C24C2514yes—
1028#41—432no—
1029C2×Q8—22no—
1030C2×Q8—22no—
1031C2×Q8—22no—
1032C2×Q8—24no—
1033C2×Q8—22no—
1034C2×Q8—41no—
1035C2×Q8—41no—
1036C2×Q8—42no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—41no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8C22×Q814yes—
1049C2×Q8H(5,𝔽2)14yes—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—41no—
1057C2×D4—44no—
1058C2×D4—42no—
1059C2×D4—41no—
1060C2×D4—42no—
1061C2×D4—44no—
1062C2×D4C22×Q818yes—
1063C2×D4C22×Q814yes—
1064C2×D4C22×Q818yes—
1065C2×D4C22×Q8116yes—
1066C2×D4C22×Q818yes—
1067C2×D4C22×Q8116yes—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—28no—
1072C22×C4—28no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4C22×Q818yes—
1103C22×C4C22×Q8116yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2514yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—22no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—28no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—22no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
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—44no—
1171C4⋊C4—41no—
1172C4⋊C4—41no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—41no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4—41no—
1192C4⋊C4—41no—
1193C4⋊C4—41no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—42no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4C22×Q814yes—
1213C4⋊C4C22×Q818yes—
1214C4⋊C4C22×Q814yes—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
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⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4C22×Q818yes—
1248C22⋊C4C22×Q8116yes—
1249C42—24no—
1250C42—24no—
1251C42—24no—
1252C42—28no—
1253C42—24no—
1254C42—22no—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—22no—
1259C42—42no—
1260C42—42no—
1261C42—42no—
1262C42—41no—
1263C42—44no—
1264C42—41no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—41no—
1269C42—42no—
1270C42—42no—
1271C42C22×Q818yes—
1272C42C22×Q814yes—
1273C42H(5,𝔽2)14yes—
1274C23—22no—
1275C23—24no—
1276C23—22no—
1277C23—24no—
1278C23—22no—
1279C23—24no—
1280C23—24no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—24no—
1285C23—24no—
1286C23C23×Q814yes—
1287C23C23×Q818yes—
1288C23C2611yescharacteristic
1289Q8—28no—
1290Q8—44no—
1291Q8—82no—
1292Q8—82no—
1293Q8—84no—
1294Q8—164no—
1295Q8—164no—
1296D4—216no—
1297D4—416no—
1298D4—48no—
1299D4—48no—
1300D4—44no—
1301D4—416no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—22no—
1320C2×C4—216no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—416no—
1373C2×C4—48no—
1374C2×C4—48no—
1375C2×C4—88no—
1376C2×C4—88no—
1377C2×C4—88no—
1378C2×C4—164no—
1379C2×C4—164no—
1380C2×C4—164no—
1381C2×C4—164no—
1382C2×C4—164no—
1383C2×C4C23×Q812yes—
1384C2×C4C23×Q814yes—
1385C2×C4C23×Q812yes—
1386C2×C4C23×Q814yes—
1387C2×C4C23×Q814yes—
1388C2×C4C23×Q812yes—
1389C2×C4C2×H(5,𝔽2)12yes—
1390C2×C4C2×H(5,𝔽2)12yes—
1391C2×C4C2×H(5,𝔽2)14yes—
1392C2×C4C2×H(5,𝔽2)12yes—
1393C2×C4C2×H(5,𝔽2)12yes—
1394C2×C4#58512yes—
1395C22—24no—
1396C22—28no—
1397C22—24no—
1398C22—28no—
1399C22—28no—
1400C22—24no—
1401C22—42no—
1402C22—44no—
1403C22—44no—
1404C22—42no—
1405C22—42no—
1406C22—44no—
1407C22—44no—
1408C22—42no—
1409C22C24×Q811yescharacteristic
1410C22C22×H(5,𝔽2)11yescharacteristic
1411C22C22×H(5,𝔽2)11yescharacteristic
1412C22C2×#58511yescharacteristic
1413C22H(7,𝔽2)11yescharacteristic
1414C222−1+611yescharacteristic
1415C222−1+611yescharacteristic
1416C4—24no—
1417C4—22no—
1418C4—24no—
1419C4—24no—
1420C4—22no—
1421C4—22no—
1422C4—24no—
1423C4—22no—
1424C4—22no—
1425C4—42no—
1426C4—41no—
1427C4—42no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—44no—
1432C4—42no—
1433C4—42no—
1434C4—44no—
1435C4—42no—
1436C4—44no—
1437C4—42no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—44no—
1442C4#350114yes—
1443C2—44no—
1444C2—48no—
1445C2C2×#350111yescharacteristic
1446C2#6285411yescharacteristic
1447C2#6288811yescharacteristic
1448C2#6290111yescharacteristic
1449C2#6291611yescharacteristic
1450C2Q8×H(5,𝔽2)11yescharacteristic
1451C2#6304711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59314C2semidirect
3. #52267C2semidirect
4. #52039C2semidirect
5. #51593C2semidirect
6. #47974C2semidirect
7. #46445C2semidirect
8. #46282C2semidirect
9. #44951C2semidirect
10. #44942C2semidirect
11. #44941C2semidirect
12. #43529C2semidirect
13. #42931C2semidirect
14. #42823C2semidirect
15. #40621C2semidirect
16. #39985C2semidirect
17. #39692C2semidirect
18. #39611C2semidirect
19. #39611C2semidirect
20. #39365C2semidirect
21. #38452C2semidirect
22. #37874C2semidirect
23. #37137C2semidirect
24. #36285C2semidirect
25. #35806C2semidirect
26. #35532C2semidirect
27. #35208C2semidirect
263. #550Q8semidirect

Maximal subgroups

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

subgroupindex
#598232
#593142
#522672
#520392
#515932
#479742
#464452
#462822
#449512
#449422
#449412
#435292
#429312
#428232
#406212
#399852
#396922
#396112
#393652
#384522
#378742
#371372
#362852
#358062
#355322
#352082
#344772
#343132