Finite Group Databasebeta

← #7901030

Subgroups — #7901030

Order 512.

4739 conjugacy classes of subgroups.

The subgroup lattice has 1425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic
2#59655C212yesmaximal, complemented
3#52287C211yesmaximal, characteristic, complemented
4#50705C214yesmaximal, complemented
5#48856C214yesmaximal, complemented
6#47982C214yesmaximal, complemented
7#46441C214yesmaximal, complemented
8#46005C212yesmaximal, complemented
9#45434C212yesmaximal, complemented
10#45424C212yesmaximal, complemented
11#44948C212yesmaximal
12#43909C214yesmaximal, complemented
13#42822C212yesmaximal, complemented
14#42494C212yesmaximal, complemented
15#40619C214yesmaximal, complemented
16#39702C212yesmaximal, complemented
17#39674C212yesmaximal, complemented
18#39628C211yesmaximal, characteristic
19#39621C211yesmaximal, characteristic, complemented
20#39370C212yesmaximal, complemented
21#39365C212yesmaximal, complemented
22#39180C212yesmaximal, complemented
23#37136C212yesmaximal, complemented
24#36474C211yesmaximal, characteristic, complemented
25#35950C212yesmaximal, complemented
26#35580C212yesmaximal, complemented
27#35208C211yesmaximal, characteristic, complemented
28#34500C212yesmaximal
29#34331C211yesmaximal, characteristic
30C2×#559C2211yescharacteristic
31C2×Q82C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#554C2212yes—
34C2×#554C2212yes—
35C2×#554C2212yes—
36C2×#544C2214yes—
37#2863C2212yes—
38#2862C2212yes—
39#2862C2211yescharacteristic
40#2859C2212yes—
41#2859C2212yes—
42#2845C2214yes—
43#2841C2214yes—
44#2811C2212yes—
45#2811C2211yescharacteristic
46#2806C2211yescharacteristic
47#2806C2212yes—
48#2806C2212yes—
49#2806C2212yes—
50#2806C2211yescharacteristic
51#2806C2214yes—
52#2806C2212yes—
53#2804C2212yes—
54#2804C2212yes—
55#2802C2214yes—
56#2792C2212yes—
57#2792C2212yes—
58#2792C2212yes—
59#2788C2214yes—
60#2788C2214yes—
61#2768C2214yes—
62#2768C2214yes—
63#2768C2214yes—
64#2768C2214yes—
65#2763C2214yes—
66#2755C2214yes—
67#2755C2214yes—
68#2734C2212yes—
69#2734C2212yes—
70#2734C2211yescharacteristic
71#2732C2212yes—
72#2732C2212yes—
73#2732C2212yes—
74#2732C2212yes—
75#2729C2214yes—
76#2729C2214yes—
77#2729C2214yes—
78#2729C2214yes—
79#2726C2214yes—
80#2726C2214yes—
81#2726C2214yes—
82#2720C2214yes—
83#2720C2214yes—
84#2713C2214yes—
85#2704C2214yes—
86#2704C2214yes—
87#2704C2214yes—
88#2704C2214yes—
89#2704C2214yes—
90#2704C2214yes—
91#2704C2214yes—
92#2704C2214yes—
93#2692C2214yes—
94#2692C2214yes—
95#2683C2214yes—
96#2683C2214yes—
97#2677C2214yes—
98#2666C2214yes—
99#2666C2214yes—
100#2666C2214yes—
101#2660C2212yes—
102#2659C2214yes—
103#2659C2214yes—
104#2647C2212yes—
105#2647C2212yes—
106#2629C2214yes—
107#2629C2214yes—
108#2607C2214yes—
109#2589C2214yes—
110#2589C2214yes—
111#2586C2214yes—
112#2584C2214yes—
113#2584C2212yes—
114#2583C2214yes—
115#2583C2214yes—
116#2582C2212yes—
117#2582C2214yes—
118#2582C2212yes—
119#2582C2211yescharacteristic
120#2580C2212yes—
121#2567C2212yes—
122#2567C2211yescharacteristic
123#2567C2211yescharacteristic
124#2567C2211yescharacteristic
125#2556C2214yes—
126#2556C2214yes—
127#2556C2214yes—
128#2556C2214yes—
129#2552C2212yes—
130#2552C2212yes—
131#2552C2212yes—
132#2552C2212yes—
133#2552C2211yescharacteristic
134#2551C2212yes—
135#2550C2212yes—
136#2550C2212yes—
137#2550C2212yes—
138#2550C2214yes—
139#2550C2214yes—
140#2550C2212yes—
141#2550C2214yes—
142#2550C2212yes—
143#2549C2214yes—
144#2549C2214yes—
145#2549C2214yes—
146#2549C2214yes—
147#2549C2214yes—
148#2546C2212yes—
149#2546C2212yes—
150#2546C2211yescharacteristic
151#2542C2212yes—
152#2538C2212yes—
153#2538C2212yes—
154#2538C2212yes—
155#2538C2212yes—
156#2538C2212yes—
157#2511C2212yes—
158#2507C2212yes—
159#2507C2212yes—
160#2506C2214yes—
161#2506C2212yes—
162#2506C2212yes—
163#2502C2214yes—
164#2492C2214yes—
165#2473C2214yes—
166#2473C2214yes—
167#2465C2214yes—
168#2465C2214yes—
169#2462C2214yes—
170#2454C2214yes—
171#2454C2212yes—
172#2454C2212yes—
173#2453C2212yes—
174#2453C2212yes—
175#2453C2214yes—
176#2452C2212yes—
177#2452C2212yes—
178#2452C2212yes—
179#2452C2212yes—
180#2451C2212yes—
181#2451C2214yes—
182#2450C2214yes—
183#2450C2214yes—
184#2449C2214yes—
185#2449C2214yes—
186#2442C2214yes—
187#2441C2214yes—
188#2440C2214yes—
189#2440C2214yes—
190#2440C2214yes—
191#2440C2214yes—
192#2439C2214yes—
193#2438C2214yes—
194#2438C2214yes—
195#2429C2214yes—
196#2429C2214yes—
197#2429C2214yes—
198#2429C2214yes—
199#2423C2214yes—
200#2417C2214yes—
201#2417C2214yes—
202#2417C2214yes—
203#2399C2212yes—
204#2399C2212yes—
205#2399C2212yes—
206C2×#398C2214yes—
207#2379C2214yes—
208#2376C2214yes—
209#2367C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2367C2212yes—
213#2366C2211yescharacteristic
214#2366C2212yes—
215#2360C2214yes—
216#2359C2214yes—
217#2359C2214yes—
218#2355C2212yes—
219#2355C2211yescharacteristic
220#2354C2212yes—
221#2352C2214yes—
222#2351C2212yes—
223#2351C2212yes—
224Q8×C4⋊C4C2211yescharacteristic
225#2349C2212yes—
226#2349C2212yes—
227#2349C2212yes—
228D4×C4⋊C4C2212yes—
229D4×C4⋊C4C2212yes—
230#2337C2214yes—
231#2335C2214yes—
232#2335C2214yes—
233#2331C2212yes—
234#2330C2212yes—
235#2330C2212yes—
236#2328C2212yes—
237#2326C2212yes—
238#2326C2212yes—
239#2322C2214yes—
240#2320C2212yes—
241#2319C2212yes—
242#2318C2214yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×C4⋊Q8C2211yescharacteristic
248C4×#127C2211yescharacteristic
249C4×#124C2212yes—
250C4×#124C2212yes—
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2211yescharacteristic
254#2295C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×Q8C2211yescharacteristic
259#559Q8116yescomplemented
260Q82—44no—
261#557—44no—
262#554—48no—
263#554—48no—
264#554—48no—
265#544—416no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2314yes—
279C2×#127C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×#117C2314yes—
338C2×#117C2314yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2314yes—
341C22×C4⋊C4C2314yes—
342C22×C4⋊C4C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#398C2312yes—
397#398C2312yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2312yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2312yes—
432#395C2312yes—
433#395C2312yes—
434#395C2312yes—
435#395C2312yes—
436#395C2312yes—
437#395C2312yes—
438#395C2312yes—
439#395C2312yes—
440#395C2312yes—
441#395C2312yes—
442#395C2314yes—
443#395C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#391C2311yescharacteristic
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2312yes—
480#391C2311yescharacteristic
481#391C2311yescharacteristic
482#391C2314yes—
483#391C2314yes—
484#391C2311yescharacteristic
485#391C2311yescharacteristic
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2314yes—
494#390C2312yes—
495#390C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2311yescharacteristic
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#389C2311yescharacteristic
556#389C2312yes—
557#389C2314yes—
558#389C2314yes—
559#389C2311yescharacteristic
560#389C2311yescharacteristic
561#389C2312yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
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#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#384C2311yescharacteristic
640#384C2312yes—
641#384C2311yescharacteristic
642#384C2311yescharacteristic
643#384C2312yes—
644#384C2312yes—
645#384C2312yes—
646#384C2312yes—
647#384C2312yes—
648#384C2312yes—
649#384C2312yes—
650#384C2314yes—
651#384C2312yes—
652#383C2314yes—
653#382C2314yes—
654#382C2314yes—
655#382C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2314yes—
659#382C2312yes—
660#382C2314yes—
661#381C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710#376C2312yes—
711#376C2312yes—
712#376C2312yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2314yes—
716C43C2311yescharacteristic
717C43C2312yes—
718C43C2312yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2412yes—
723C22×Q8C2414yes—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2414yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C4⋊Q8—28no—
742C4⋊Q8—28no—
743C4⋊Q8—24no—
744C4⋊Q8—28no—
745C4⋊Q8—24no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748C4⋊Q8—42no—
749C4⋊Q8—42no—
750C4⋊Q8—44no—
751C4⋊Q8—48no—
752C4⋊Q8—48no—
753C4⋊Q8—48no—
754#127C2×Q818yes—
755#125—28no—
756#125—28no—
757#125—48no—
758#125—48no—
759#125—44no—
760#125—48no—
761#125—48no—
762#125—48no—
763#125—48no—
764#125—84no—
765#124C2×Q8116yes—
766#124C2×Q8116yes—
767#123C2×Q8132yes—
768C22⋊Q8—216no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—48no—
772C22⋊Q8—48no—
773C22⋊Q8—48no—
774C22⋊Q8—48no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—84no—
781C22⋊Q8—84no—
782C22⋊Q8—84no—
783C22⋊Q8—84no—
784C4×Q8—24no—
785C4×Q8—24no—
786C4×Q8—24no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—42no—
790C4×Q8—42no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—82no—
797C4×Q8—84no—
798C4×Q8C2×Q818yes—
799C4×Q8C2×Q818yes—
800C4×D4—28no—
801C4×D4—28no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—48no—
808C4×D4—82no—
809C4×D4—82no—
810C4×D4C2×Q8116yes—
811C4×D4C2×Q8116yes—
812#117—48no—
813#117—48no—
814C2×C4⋊C4—48no—
815C2×C4⋊C4—48no—
816C2×C4⋊C4—48no—
817C2×C4⋊C4—48no—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
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⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
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⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
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×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2411yescharacteristic
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24C2514yes—
1026C2×Q8—22no—
1027C2×Q8—22no—
1028C2×Q8—28no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—22no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—41no—
1035C2×Q8—41no—
1036C2×Q8—41no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—41no—
1047C2×Q8—41no—
1048C2×Q8—44no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—41no—
1052C2×Q8—42no—
1053C2×Q8—44no—
1054C2×Q8—44no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—42no—
1058C2×Q8—44no—
1059C2×Q8C22×Q814yes—
1060C2×Q8C22×Q814yes—
1061C2×Q8H(5,𝔽2)14yes—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C2×D4C22×Q818yes—
1069C2×D4C22×Q818yes—
1070C2×D4C22×Q818yes—
1071C22×C4—28no—
1072C22×C4—28no—
1073C22×C4—28no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
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×C4C22×Q8116yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—28no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—22no—
1143C4⋊C4—22no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—41no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—41no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—41no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—41no—
1171C4⋊C4—42no—
1172C4⋊C4—41no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—41no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
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—42no—
1204C4⋊C4C22×Q814yes—
1205C4⋊C4C22×Q814yes—
1206C4⋊C4C22×Q818yes—
1207C4⋊C4C22×Q818yes—
1208C4⋊C4H(5,𝔽2)14yes—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4C22×Q8116yes—
1228C22⋊C4C22×Q8116yes—
1229C22⋊C4C22×Q8116yes—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—24no—
1234C42—22no—
1235C42—24no—
1236C42—24no—
1237C42—24no—
1238C42—22no—
1239C42—24no—
1240C42—24no—
1241C42—42no—
1242C42—41no—
1243C42—41no—
1244C42—42no—
1245C42—42no—
1246C42—44no—
1247C42—44no—
1248C42—44no—
1249C42—41no—
1250C42—42no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—42no—
1255C42—44no—
1256C42C22×Q818yes—
1257C42C22×Q818yes—
1258C42C22×Q814yes—
1259C422−1+414yes—
1260C23—24no—
1261C23—24no—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23C23×Q818yes—
1267C23C2611yescharacteristic
1268Q8—28no—
1269Q8—44no—
1270Q8—44no—
1271Q8—88no—
1272Q8—82no—
1273Q8—84no—
1274Q8—82no—
1275Q8—84no—
1276Q8—84no—
1277Q8—84no—
1278Q8—162no—
1279Q8—164no—
1280D4—216no—
1281D4—48no—
1282D4—48no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—21no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—24no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—416no—
1354C2×C4—88no—
1355C2×C4—88no—
1356C2×C4—88no—
1357C2×C4—164no—
1358C2×C4—164no—
1359C2×C4—164no—
1360C2×C4C23×Q812yes—
1361C2×C4C23×Q814yes—
1362C2×C4C23×Q814yes—
1363C2×C4C23×Q814yes—
1364C2×C4C23×Q814yes—
1365C2×C4C23×Q812yes—
1366C2×C4C23×Q812yes—
1367C2×C4C2×H(5,𝔽2)12yes—
1368C2×C4C2×H(5,𝔽2)14yes—
1369C2×C4C2×H(5,𝔽2)14yes—
1370C2×C4C2×H(5,𝔽2)12yes—
1371C2×C4C2×2−1+412yes—
1372C2×C4C2×2−1+412yes—
1373C2×C4C2×2−1+412yes—
1374C22—28no—
1375C22—28no—
1376C22—28no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22—44no—
1381C22C24×Q811yescharacteristic
1382C22C22×H(5,𝔽2)11yescharacteristic
1383C22C22×H(5,𝔽2)11yescharacteristic
1384C22C22×2−1+411yescharacteristic
1385C22H(7,𝔽2)11yescharacteristic
1386C222−1+611yescharacteristic
1387C222−1+611yescharacteristic
1388C4—24no—
1389C4—24no—
1390C4—22no—
1391C4—24no—
1392C4—24no—
1393C4—22no—
1394C4—24no—
1395C4—22no—
1396C4—24no—
1397C4—22no—
1398C4—22no—
1399C4—42no—
1400C4—42no—
1401C4—44no—
1402C4—42no—
1403C4—42no—
1404C4—41no—
1405C4—42no—
1406C4—44no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—44no—
1415C4#350314yes—
1416C2—48no—
1417C2C2×#350311yescharacteristic
1418C2#6285411yescharacteristic
1419C2#6288911yescharacteristic
1420C2#6289511yescharacteristic
1421C2#6291711yescharacteristic
1422C2Q8×H(5,𝔽2)11yescharacteristic
1423C2#6304911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59655C2semidirect
3. #52287C2semidirect
4. #50705C2semidirect
5. #48856C2semidirect
6. #47982C2semidirect
7. #46441C2semidirect
8. #46005C2semidirect
9. #45434C2semidirect
10. #45424C2semidirect
12. #43909C2semidirect
13. #42822C2semidirect
14. #42494C2semidirect
15. #40619C2semidirect
16. #39702C2semidirect
17. #39674C2semidirect
19. #39621C2semidirect
20. #39370C2semidirect
21. #39365C2semidirect
22. #39180C2semidirect
23. #37136C2semidirect
24. #36474C2semidirect
25. #35950C2semidirect
26. #35580C2semidirect
27. #35208C2semidirect
259. #559Q8semidirect

Maximal subgroups

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

subgroupindex
#598232
#596552
#522872
#507052
#488562
#479822
#464412
#460052
#454342
#454242
#449482
#439092
#428222
#424942
#406192
#397022
#396742
#396282
#396212
#393702
#393652
#391802
#371362
#364742
#359502
#355802
#352082
#345002
#343312