Finite Group Databasebeta

← #7732362

Subgroups — #7732362

Order 512.

4542 conjugacy classes of subgroups.

The subgroup lattice has 1426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51082C214yesmaximal, complemented
2#50707C214yesmaximal, complemented
3#47736C214yesmaximal, complemented
4#47735C214yesmaximal, complemented
5#44025C214yesmaximal, complemented
6#43981C214yesmaximal, complemented
7#39677C212yesmaximal, complemented
8#39668C212yesmaximal
9#39640C212yesmaximal, complemented
10#39631C212yesmaximal
11#39622C212yesmaximal, complemented
12#39182C212yesmaximal, complemented
13#38101C212yesmaximal, complemented
14#38101C212yesmaximal, complemented
15#37691C212yesmaximal, complemented
16#37686C212yesmaximal, complemented
17#37561C211yesmaximal, characteristic, complemented
18#37428C212yesmaximal, complemented
19#37313C212yesmaximal, complemented
20#36290C212yesmaximal, complemented
21#36131C212yesmaximal, complemented
22#35641C212yesmaximal, complemented
23#35566C212yesmaximal, complemented
24#35239C211yesmaximal, characteristic, complemented
25#35181C211yesmaximal, characteristic, complemented
26C2×#2550C211yesmaximal, characteristic, complemented
27#34382C211yesmaximal, characteristic
28#34243C211yesmaximal, characteristic
29#34083C211yesmaximal, characteristic
30C2×#544C2212yes—
31C2×#533C2212yes—
32C22×C4⋊Q8C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C22×#125C2211yescharacteristic
35#2859C2212yes—
36#2859C2212yes—
37#2857C2212yes—
38#2851C2212yes—
39#2851C2212yes—
40#2851C2212yes—
41#2851C2212yes—
42#2851C2212yes—
43#2845C2212yes—
44#2844C2212yes—
45#2807C2214yes—
46#2807C2214yes—
47#2807C2214yes—
48#2806C2214yes—
49#2806C2214yes—
50#2805C2214yes—
51#2805C2214yes—
52#2805C2214yes—
53#2805C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2802C2214yes—
57#2792C2214yes—
58#2792C2214yes—
59#2792C2214yes—
60#2774C2214yes—
61#2774C2214yes—
62#2774C2214yes—
63#2774C2214yes—
64#2774C2214yes—
65#2768C2214yes—
66#2768C2214yes—
67#2768C2214yes—
68#2763C2214yes—
69#2763C2214yes—
70#2755C2214yes—
71#2755C2214yes—
72#2742C2214yes—
73#2742C2214yes—
74#2734C2214yes—
75#2732C2214yes—
76#2729C2214yes—
77#2729C2214yes—
78#2726C2214yes—
79#2720C2214yes—
80#2720C2214yes—
81#2713C2214yes—
82#2704C2214yes—
83#2692C2214yes—
84#2677C2214yes—
85#2666C2214yes—
86#2666C2214yes—
87#2660C2212yes—
88#2660C2212yes—
89#2659C2212yes—
90#2647C2212yes—
91#2647C2212yes—
92#2646C2212yes—
93#2646C2212yes—
94#2646C2212yes—
95#2628C2212yes—
96#2628C2212yes—
97#2590C2214yes—
98#2589C2214yes—
99#2586C2214yes—
100#2586C2214yes—
101#2585C2214yes—
102#2584C2214yes—
103#2584C2214yes—
104#2583C2214yes—
105#2583C2214yes—
106#2574C2214yes—
107#2571C2212yes—
108#2571C2212yes—
109#2571C2212yes—
110#2571C2211yescharacteristic
111#2571C2212yes—
112#2570C2214yes—
113#2570C2212yes—
114#2570C2214yes—
115#2570C2212yes—
116#2568C2214yes—
117#2567C2214yes—
118#2556C2214yes—
119#2556C2214yes—
120#2552C2211yescharacteristic
121#2552C2212yes—
122#2552C2212yes—
123#2552C2211yescharacteristic
124#2552C2212yes—
125#2551C2212yes—
126#2551C2211yescharacteristic
127#2550C2212yes—
128#2550C2212yes—
129#2550C2214yes—
130#2550C2214yes—
131#2550C2212yes—
132#2550C2212yes—
133#2550C2212yes—
134#2550C2212yes—
135#2550C2212yes—
136#2550C2214yes—
137#2550C2212yes—
138#2550C2212yes—
139#2550C2212yes—
140#2549C2214yes—
141#2549C2214yes—
142#2546C2214yes—
143#2522C2214yes—
144#2520C2214yes—
145#2511C2214yes—
146#2509C2214yes—
147#2508C2214yes—
148#2507C2214yes—
149#2507C2214yes—
150#2507C2214yes—
151#2505C2214yes—
152#2505C2214yes—
153#2505C2214yes—
154#2505C2214yes—
155#2497C2214yes—
156#2487C2214yes—
157#2487C2214yes—
158#2473C2214yes—
159#2473C2214yes—
160#2473C2214yes—
161#2465C2214yes—
162#2462C2214yes—
163#2462C2214yes—
164#2462C2214yes—
165#2453C2214yes—
166#2450C2214yes—
167#2450C2214yes—
168#2449C2214yes—
169#2449C2214yes—
170#2449C2214yes—
171#2446C2214yes—
172#2442C2212yes—
173#2442C2212yes—
174#2442C2212yes—
175#2442C2212yes—
176#2442C2212yes—
177#2441C2212yes—
178#2441C2212yes—
179#2441C2212yes—
180#2440C2214yes—
181#2440C2212yes—
182#2440C2212yes—
183#2440C2212yes—
184#2440C2214yes—
185#2439C2212yes—
186#2438C2214yes—
187#2438C2214yes—
188#2434C2214yes—
189#2423C2214yes—
190#2409C2214yes—
191C2×#398C2212yes—
192C2×#395C2212yes—
193#2382C2212yes—
194#2379C2212yes—
195#2370C2212yes—
196#2367C2212yes—
197#2360C2214yes—
198#2360C2214yes—
199#2359C2214yes—
200#2359C2214yes—
201#2355C2212yes—
202#2355C2211yescharacteristic
203#2354C2211yescharacteristic
204#2352C2212yes—
205#2352C2212yes—
206#2352C2212yes—
207Q8×C4⋊C4C2211yescharacteristic
208#2349C2214yes—
209D4×C4⋊C4C2212yes—
210D4×C4⋊C4C2212yes—
211D4×C4⋊C4C2214yes—
212D4×C4⋊C4C2211yescharacteristic
213#2337C2212yes—
214#2336C2212yes—
215#2334C2212yes—
216#2334C2212yes—
217#2334C2214yes—
218#2334C2214yes—
219#2331C2212yes—
220#2331C2212yes—
221#2330C2212yes—
222#2330C2212yes—
223#2329C2211yescharacteristic
224#2329C2211yescharacteristic
225#2329C2212yes—
226#2325C2211yescharacteristic
227#2325C2211yescharacteristic
228#2325C2212yes—
229#2322C2212yes—
230#2322C2212yes—
231#2317C2212yes—
232#2317C2212yes—
233#2317C2212yes—
234#2316C2212yes—
235#2314C2212yes—
236#2314C2212yes—
237C4×#125C2212yes—
238C4×#125C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×#121C2212yes—
241#2298C2212yes—
242#2296C2212yes—
243#2295C2212yes—
244C2×#391C2212yes—
245C2×#389C2211yescharacteristic
246C2×#389C2212yes—
247C2×#389C2211yescharacteristic
248C2×#389C2212yes—
249#2290C2212yes—
250#2290C2212yes—
251#2285C2211yescharacteristic
252#2285C2211yescharacteristic
253#2283C2211yescharacteristic
254C2×#382C2211yescharacteristic
255#2274C2212yes—
256C42×D4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2312yes—
260#544—48no—
261#533—48no—
262C2×C4⋊Q8—44no—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2312yes—
271#529Q8116yescomplemented
272C2×#126C2312yes—
273C2×#125—44no—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#123C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×#121C2311yescharacteristic
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×#117C2312yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2311yescharacteristic
321C22×C4⋊C4C2311yescharacteristic
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2314yes—
326C22×C4⋊C4C2312yes—
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2312yes—
330C22×C42C2312yes—
331C22×C42C2311yescharacteristic
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
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#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#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
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#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#390C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2314yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#386C2312yes—
573#386C2312yes—
574#386C2312yes—
575#386C2312yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2312yes—
587#385C2312yes—
588#385C2312yes—
589#385C2312yes—
590#385C2312yes—
591#385C2312yes—
592#385C2312yes—
593#385C2312yes—
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#384C2314yes—
611#384C2314yes—
612#384C2311yescharacteristic
613#384C2312yes—
614#384C2314yes—
615#384C2312yes—
616#384C2312yes—
617#384C2311yescharacteristic
618#384C2311yescharacteristic
619#384C2312yes—
620#384C2312yes—
621#384C2311yescharacteristic
622#383C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2314yes—
626#382C2314yes—
627#382C2312yes—
628#382C2312yes—
629#382C2311yescharacteristic
630#382C2312yes—
631#382C2312yes—
632#382C2314yes—
633#382C2314yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2314yes—
638#382C2312yes—
639#382C2312yes—
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2312yes—
643#381C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2311yescharacteristic
652#380C2312yes—
653#380C2311yescharacteristic
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706#376C2312yes—
707#376C2312yes—
708C2×#95C2311yescharacteristic
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2314yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C2×#95C2312yes—
716C43C2312yes—
717C22×Q8—44no—
718C22×Q8—44no—
719C22×Q8—82no—
720C22×Q8C2414yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×Q8C2414yes—
724C22×Q8C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2414yes—
738C23×C4C2411yescharacteristic
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C4⋊Q8—28no—
744C4⋊Q8—28no—
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747C4⋊Q8—48no—
748C4⋊Q8—48no—
749C4⋊Q8—82no—
750C4⋊Q8—84no—
751#126C2×Q8116yescomplemented
752#125—28no—
753#125—28no—
754#125—44no—
755#125—44no—
756#125—44no—
757#125—44no—
758#125—48no—
759#125—48no—
760#125—82no—
761#125—84no—
762#125C2×Q818yescomplemented
763#124C2×Q818yescomplemented
764#123C2×Q8116yes—
765C22⋊Q8—48no—
766C22⋊Q8—48no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—84no—
772C22⋊Q8C2×Q818yes—
773#121C2×Q818yes—
774C4×Q8—48no—
775C4×Q8—48no—
776C4×Q8—82no—
777C4×Q8C2×Q818yescomplemented
778C4×D4—48no—
779C4×D4—48no—
780C4×D4—44no—
781C4×D4—44no—
782C4×D4—82no—
783C4×D4C2×Q8116yes—
784C4×D4C2×Q818yescomplemented
785#117—28no—
786#117—44no—
787#117—44no—
788#117—44no—
789#117—44no—
790#117C2×Q8116yescomplemented
791C2×C4⋊C4—24no—
792C2×C4⋊C4—24no—
793C2×C4⋊C4—28no—
794C2×C4⋊C4—42no—
795C2×C4⋊C4—44no—
796C2×C4⋊C4—44no—
797C2×C4⋊C4—42no—
798C2×C4⋊C4—44no—
799C2×C4⋊C4—44no—
800C2×C4⋊C4—42no—
801C2×C4⋊C4—42no—
802C2×C4⋊C4—44no—
803C2×C4⋊C4—82no—
804C2×C4⋊C4—84no—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2411yescharacteristic
888C2×C4⋊C4C2411yescharacteristic
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C42—42no—
911C2×C42—42no—
912C2×C42—44no—
913C2×C42—82no—
914C2×C42C2×Q818yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2411yescharacteristic
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2512yes—
1017C24C2511yescharacteristic
1018C2×Q8—28no—
1019C2×Q8—28no—
1020C2×Q8—41no—
1021C2×Q8—41no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—816no—
1033C2×Q8C22×Q814yes—
1034C2×D4—24no—
1035C2×D4—24no—
1036C2×D4—41no—
1037C2×D4—41no—
1038C2×D4C22×Q818yes—
1039C2×D4C22×Q814yes—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—24no—
1044C22×C4—22no—
1045C22×C4—24no—
1046C22×C4—22no—
1047C22×C4—24no—
1048C22×C4—22no—
1049C22×C4—24no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—41no—
1058C22×C4—41no—
1059C22×C4—41no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—41no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—41no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—41no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4C22×Q814yes—
1085C22×C4C22×Q814yes—
1086C22×C4C22×Q818yes—
1087C22×C4C22×Q814yes—
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C4⋊C4—24no—
1116C4⋊C4—22no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—41no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—41no—
1190C4⋊C4—42no—
1191C4⋊C4C22×Q818yes—
1192C4⋊C4C22×Q818yes—
1193C4⋊C4C22×Q818yes—
1194C4⋊C4C22×Q814yes—
1195C4⋊C4C22×Q814yes—
1196C4⋊C4C22×Q818yes—
1197C4⋊C4H(5,𝔽2)14yes—
1198C4⋊C42−1+414yes—
1199C22⋊C4—28no—
1200C22⋊C4—28no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—28no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4C22×Q818yes—
1216C22⋊C4C22×Q818yes—
1217C22⋊C4C22×Q818yes—
1218C22⋊C4C22×Q818yes—
1219C22⋊C4C22×Q818yes—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—28no—
1224C42—24no—
1225C42—42no—
1226C42—42no—
1227C42—42no—
1228C42—42no—
1229C42—42no—
1230C42—42no—
1231C42—42no—
1232C42—42no—
1233C42—44no—
1234C42—42no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—42no—
1241C42—42no—
1242C42—44no—
1243C42—42no—
1244C42C22×Q814yes—
1245C42C22×Q814yes—
1246C42C22×Q814yes—
1247C42C22×Q814yes—
1248C42C22×Q818yes—
1249C23—21no—
1250C23—21no—
1251C23—21no—
1252C23—21no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23C23×Q814yes—
1260C23C23×Q812yes—
1261C23#58512yes—
1262C23#58512yes—
1263C23C2611yescharacteristic
1264Q8—44no—
1265Q8—88no—
1266Q8—88no—
1267Q8—88no—
1268Q8—88no—
1269D4—216no—
1270D4—44no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—28no—
1292C2×C4—28no—
1293C2×C4—216no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—44no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—44no—
1346C2×C4—44no—
1347C2×C4—88no—
1348C2×C4—82no—
1349C2×C4—82no—
1350C2×C4—84no—
1351C2×C4—84no—
1352C2×C4—84no—
1353C2×C4—84no—
1354C2×C4—164no—
1355C2×C4C23×Q812yes—
1356C2×C4C23×Q812yes—
1357C2×C4C23×Q812yes—
1358C2×C4C23×Q812yes—
1359C2×C4C23×Q812yes—
1360C2×C4C23×Q814yes—
1361C2×C4C23×Q814yes—
1362C2×C4C23×Q814yes—
1363C2×C4C23×Q812yes—
1364C2×C4C2×H(5,𝔽2)14yes—
1365C2×C4C2×H(5,𝔽2)12yes—
1366C2×C4C2×2−1+414yes—
1367C2×C4C2×2−1+412yes—
1368C22—22no—
1369C22—22no—
1370C22—22no—
1371C22—22no—
1372C22—22no—
1373C22—22no—
1374C22—24no—
1375C22—24no—
1376C22—24no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22#350414yes—
1382C22C24×Q811yescharacteristic
1383C22C22×H(5,𝔽2)11yescharacteristic
1384C22C22×2−1+411yescharacteristic
1385C22C2×#58511yescharacteristic
1386C22C2×#58511yescharacteristic
1387C22H(7,𝔽2)11yescharacteristic
1388C222−1+611yescharacteristic
1389C4—24no—
1390C4—22no—
1391C4—22no—
1392C4—22no—
1393C4—24no—
1394C4—22no—
1395C4—22no—
1396C4—24no—
1397C4—24no—
1398C4—24no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—44no—
1403C4—42no—
1404C4—44no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—44no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4—42no—
1414C4—44no—
1415C4#350314yes—
1416C2—24no—
1417C2—44no—
1418C2C2×#350311yescharacteristic
1419C2C2×#350411yescharacteristic
1420C2#6285411yescharacteristic
1421C2#6289611yescharacteristic
1422C2#6289711yescharacteristic
1423C2#6294811yescharacteristic
1424C2#6294911yescharacteristic
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. #51082C2semidirect
2. #50707C2semidirect
3. #47736C2semidirect
4. #47735C2semidirect
5. #44025C2semidirect
6. #43981C2semidirect
7. #39677C2semidirect
9. #39640C2semidirect
11. #39622C2semidirect
12. #39182C2semidirect
13. #38101C2semidirect
14. #38101C2semidirect
15. #37691C2semidirect
16. #37686C2semidirect
17. #37561C2semidirect
18. #37428C2semidirect
19. #37313C2semidirect
20. #36290C2semidirect
21. #36131C2semidirect
22. #35641C2semidirect
23. #35566C2semidirect
24. #35239C2semidirect
25. #35181C2semidirect
26. C2×#2550C2semidirect
271. #529Q8semidirect
751. #126C2×Q8semidirect
762. #125C2×Q8semidirect
763. #124C2×Q8semidirect
777. C4×Q8C2×Q8semidirect
784. C4×D4C2×Q8semidirect
790. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#510822
#507072
#477362
#477352
#440252
#439812
#396772
#396682
#396402
#396312
#396222
#391822
#381012
#376912
#376862
#375612
#374282
#373132
#362902
#361312
#356412
#355662
#352392
#351812
C2×#25502
#343822
#342432
#340832