Finite Group Databasebeta

← #7657791

Subgroups — #7657791

Order 512.

4240 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42932C212yesmaximal, complemented
2#42932C212yesmaximal, complemented
3#42491C212yesmaximal, complemented
4#42489C212yesmaximal, complemented
5#42189C214yesmaximal, complemented
6#42007C214yesmaximal, complemented
7#40623C214yesmaximal
8#40622C214yesmaximal
9#39986C212yesmaximal, complemented
10#39983C212yesmaximal, complemented
11#38459C214yesmaximal, complemented
12#38457C214yesmaximal, complemented
13#37566C212yesmaximal, complemented
14#37565C212yesmaximal, complemented
15#37481C211yesmaximal, characteristic
16#37476C211yesmaximal, characteristic
17#36287C212yesmaximal, complemented
18#36284C212yesmaximal, complemented
19#36039C212yesmaximal, complemented
20#35783C212yesmaximal, complemented
21#35747C212yesmaximal, complemented
22#35708C212yesmaximal, complemented
23#35202C212yesmaximal, complemented
24#35079C211yesmaximal, characteristic
25#34644C212yesmaximal, complemented
26#34578C211yesmaximal, characteristic
27#34180C211yesmaximal, characteristic
28#34179C211yesmaximal, characteristic
29#34109C211yesmaximal, characteristic
30C22×#117C2211yescharacteristic
31#2864C2214yescomplemented
32#2859C2214yescomplemented
33#2857C2212yes—
34#2851C2212yes—
35#2843C2214yescomplemented
36#2843C2214yescomplemented
37#2842C2212yes—
38#2842C2212yes—
39#2841C2214yes—
40#2841C2214yes—
41#2841C2214yes—
42#2807C2214yes—
43#2805C2214yescomplemented
44#2802C2214yescomplemented
45#2792C2214yescomplemented
46#2792C2214yescomplemented
47#2791C2214yescomplemented
48#2790C2214yes—
49#2790C2214yes—
50#2790C2214yes—
51#2788C2214yes—
52#2788C2214yes—
53#2774C2214yescomplemented
54#2768C2214yes—
55#2742C2214yes—
56#2729C2214yes—
57#2726C2214yescomplemented
58#2720C2214yes—
59#2720C2214yes—
60#2720C2214yes—
61#2720C2214yes—
62#2713C2214yescomplemented
63#2704C2214yes—
64#2704C2214yes—
65#2704C2214yes—
66#2667C2212yes—
67#2667C2212yes—
68#2667C2211yescharacteristic
69#2667C2211yescharacteristic
70#2667C2214yes—
71#2667C2212yes—
72#2667C2214yes—
73#2667C2212yes—
74#2667C2212yes—
75#2667C2214yes—
76#2666C2214yescomplemented
77#2666C2214yescomplemented
78#2666C2214yescomplemented
79#2666C2214yescomplemented
80#2666C2214yescomplemented
81#2666C2214yescomplemented
82#2666C2214yescomplemented
83#2666C2214yescomplemented
84#2665C2212yes—
85#2665C2212yes—
86#2665C2211yescharacteristic
87#2665C2211yescharacteristic
88#2665C2212yes—
89#2665C2214yes—
90#2665C2214yes—
91#2659C2212yes—
92#2646C2212yes—
93#2629C2212yes—
94#2629C2212yes—
95#2629C2212yes—
96#2629C2214yes—
97#2628C2212yes—
98#2628C2214yes—
99#2626C2212yes—
100#2626C2212yes—
101#2626C2214yes—
102#2612C2214yescomplemented
103#2612C2214yescomplemented
104#2612C2214yescomplemented
105#2612C2214yescomplemented
106#2608C2214yes—
107#2608C2214yes—
108#2607C2214yes—
109#2606C2214yescomplemented
110#2606C2214yescomplemented
111#2606C2214yescomplemented
112#2605C2214yescomplemented
113#2590C2214yescomplemented
114#2589C2214yes—
115#2588C2214yescomplemented
116#2587C2214yes—
117#2587C2214yes—
118#2587C2214yes—
119#2586C2214yescomplemented
120#2585C2214yescomplemented
121#2584C2212yescomplemented
122#2584C2212yescomplemented
123#2584C2212yescomplemented
124#2584C2212yescomplemented
125#2574C2214yes—
126#2570C2214yescomplemented
127#2570C2214yescomplemented
128#2569C2212yes—
129#2569C2212yes—
130#2567C2212yescomplemented
131#2567C2212yescomplemented
132#2556C2214yes—
133#2556C2214yes—
134#2556C2214yes—
135#2552C2214yescomplemented
136#2552C2212yescomplemented
137#2552C2212yescomplemented
138#2552C2214yescomplemented
139#2552C2212yescomplemented
140#2551C2212yescomplemented
141#2550C2214yescomplemented
142#2550C2212yescomplemented
143#2550C2214yescomplemented
144#2550C2212yescomplemented
145#2549C2212yes—
146#2549C2212yes—
147#2522C2214yes—
148#2522C2214yes—
149#2511C2214yescomplemented
150#2509C2212yescomplemented
151#2509C2212yescomplemented
152#2509C2212yescomplemented
153#2508C2212yescomplemented
154#2507C2212yescomplemented
155#2507C2212yescomplemented
156#2507C2214yescomplemented
157#2507C2212yescomplemented
158#2506C2212yescomplemented
159#2506C2212yescomplemented
160#2506C2212yescomplemented
161#2506C2212yescomplemented
162#2506C2212yescomplemented
163#2497C2214yes—
164#2497C2214yes—
165#2465C2214yes—
166#2465C2214yes—
167#2462C2214yescomplemented
168#2462C2214yescomplemented
169#2442C2212yes—
170#2442C2212yes—
171#2441C2212yes—
172#2441C2212yes—
173#2441C2212yes—
174#2441C2212yes—
175#2441C2212yes—
176#2441C2212yes—
177#2441C2214yes—
178#2441C2214yes—
179#2441C2214yes—
180#2441C2214yes—
181#2440C2212yes—
182#2440C2212yes—
183#2439C2212yes—
184#2439C2212yes—
185#2437C2214yes—
186#2429C2214yes—
187#2423C2214yes—
188#2402C2214yescomplemented
189#2399C2214yescomplemented
190#2396C2212yes—
191#2396C2212yes—
192#2396C2212yes—
193#2396C2212yes—
194#2396C2214yes—
195#2396C2214yes—
196#2370C2212yescomplemented
197#2370C2212yescomplemented
198#2370C2212yescomplemented
199#2370C2212yescomplemented
200#2369C2212yescomplemented
201#2365C2212yescomplemented
202#2355C2212yescomplemented
203Q8×C4⋊C4C2212yescomplemented
204#2347C2214yes—
205#2347C2212yes—
206#2347C2211yescharacteristic
207#2347C2211yescharacteristic
208#2347C2212yes—
209#2347C2212yes—
210#2346C2211yescharacteristic
211#2346C2211yescharacteristic
212#2346C2212yes—
213#2346C2212yes—
214#2346C2211yescharacteristic
215#2346C2211yescharacteristic
216#2346C2211yescharacteristic
217#2346C2211yescharacteristic
218#2346C2212yes—
219#2345C2212yes—
220#2345C2211yescharacteristic
221#2345C2211yescharacteristic
222#2344C2212yes—
223#2344C2211yescharacteristic
224#2344C2211yescharacteristic
225#2343C2212yes—
226#2343C2214yes—
227#2343C2212yes—
228#2342C2214yes—
229#2342C2212yes—
230#2342C2212yes—
231#2330C2214yescomplemented
232#2330C2214yescomplemented
233#2329C2214yes—
234#2317C2212yes—
235#2316C2212yes—
236#2314C2214yes—
237#2312C2214yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240#2298C2214yes—
241#2296C2212yes—
242#2295C2214yescomplemented
243#2295C2214yescomplemented
244#2285C2212yes—
245#2283C2212yes—
246#2283C2212yes—
247#2283C2212yes—
248#2283C2212yes—
249#2280C2211yescharacteristic
250#2280C2211yescharacteristic
251#2280C2211yescharacteristic
252#2280C2211yescharacteristic
253C2×#380C2211yescharacteristic
254#2274C2212yes—
255#2274C2212yes—
256C4×#117C2212yes—
257C4×#117C2212yes—
258C2×C4×C22⋊C4C2211yescharacteristic
259C24×C4C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2314yes—
263C2×#125C2312yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2314yes—
281C2×#117Q8116yescomplemented
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2312yes—
290C2×#117C2311yescharacteristic
291C2×#117C2312yes—
292C2×#117C2311yescharacteristic
293C2×#117C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2312yes—
301C22×C42C2312yes—
302C22×C42C2312yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2312yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2312yes—
329#399C2312yes—
330#399C2312yes—
331#399C2312yes—
332#399C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#396C2314yes—
376#396C2312yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2312yes—
389#396C2312yes—
390#396C2312yes—
391#396C2314yes—
392#396C2312yes—
393#396C2312yes—
394#396C2312yes—
395#396C2312yes—
396#396C2314yes—
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#395C2312yes—
412#395C2312yes—
413#395C2312yes—
414#395C2312yes—
415#395C2314yes—
416#393C2312yes—
417#393C2312yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2312yes—
422#393C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
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#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2312yes—
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#387C2312yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2312yes—
568#385C2314yes—
569#385C2314yes—
570#385C2312yes—
571#385C2314yes—
572#385C2314yes—
573#385C2312yes—
574#385C2312yes—
575#384C2314yes—
576#384C2314yes—
577#384C2314yes—
578#384C2314yes—
579#384C2314yes—
580#384C2312yes—
581#384C2314yes—
582#384C2312yes—
583#384C2312yes—
584#384C2312yes—
585#383C2312yes—
586#383C2312yes—
587#383C2314yes—
588#383C2314yes—
589#383C2314yes—
590#382C2314yes—
591#382C2314yes—
592#382C2312yes—
593#382C2312yes—
594#382C2312yes—
595#382C2314yes—
596#382C2312yes—
597#382C2312yes—
598#382C2312yes—
599#382C2312yes—
600#382C2312yes—
601#381C2312yes—
602#381C2312yes—
603#381C2312yes—
604#381C2314yes—
605#381C2312yes—
606#381C2311yescharacteristic
607#381C2312yes—
608#381C2311yescharacteristic
609#380C2314yes—
610#380C2314yes—
611#380C2311yescharacteristic
612#380C2312yes—
613#380C2314yes—
614#380C2314yes—
615#380C2312yes—
616#380C2314yes—
617#380C2314yes—
618#380C2312yes—
619#380C2311yescharacteristic
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2311yescharacteristic
624#380C2312yes—
625#380C2311yescharacteristic
626#380C2311yescharacteristic
627#380C2311yescharacteristic
628#380C2311yescharacteristic
629#380C2311yescharacteristic
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2311yescharacteristic
635#380C2311yescharacteristic
636#379C2312yes—
637#379C2312yes—
638#379C2311yescharacteristic
639#379C2311yescharacteristic
640#379C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2312yes—
690C4×C22⋊C4C2311yescharacteristic
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2311yescharacteristic
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701#376C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2312yes—
705#376C2314yes—
706#376C2312yes—
707#376C2312yes—
708#376C2314yes—
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2311yescharacteristic
712C43C2314yes—
713C25C2411yescharacteristic
714C22×Q8C2412yes—
715C22×Q8C2414yes—
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C23×C4—44no—
719C23×C4C2×Q818yes—
720C23×C4C2411yescharacteristic
721C23×C4C2411yescharacteristic
722C23×C4C2411yescharacteristic
723C23×C4C2412yes—
724C23×C4C2414yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C4⋊Q8—44no—
732C4⋊Q8—44no—
733C4⋊Q8—84no—
734#125—44no—
735#125—44no—
736#125—44no—
737#125—44no—
738#125—48no—
739#125—48no—
740#125—84no—
741#125—84no—
742#125—84no—
743C22⋊Q8—48no—
744C22⋊Q8—44no—
745C22⋊Q8—44no—
746C22⋊Q8—84no—
747C22⋊Q8—84no—
748C4×Q8—44no—
749C4×Q8—44no—
750C4×Q8—48no—
751C4×Q8—48no—
752#117—44no—
753#117—44no—
754#117—48no—
755#117—44no—
756#117—44no—
757#117—82no—
758#117—82no—
759#117C2×Q818yes—
760#117C2×Q818yes—
761#117C2×Q818yes—
762#117C2×Q818yes—
763#117C2×Q8116yes—
764#117C2×Q8116yes—
765C2×C4⋊C4—44no—
766C2×C4⋊C4C2×Q818yes—
767C2×C4⋊C4C2×Q818yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C22⋊C4—44no—
846C2×C22⋊C4—82no—
847C2×C22⋊C4C2×Q8116yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C42—44no—
882C2×C42C2×Q8116yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909#95C2411yescharacteristic
910#95C2411yescharacteristic
911#95C2414yes—
912#95C2411yescharacteristic
913#95C2411yescharacteristic
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2411yescharacteristic
920#95C2411yescharacteristic
921#95C2411yescharacteristic
922#95C2412yes—
923#95C2411yescharacteristic
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986C24—42no—
987C24—41no—
988C24—42no—
989C24—41no—
990C24C22×Q814yes—
991C24C2511yescharacteristic
992C24C2511yescharacteristic
993C24C2511yescharacteristic
994C2×Q8—24no—
995C2×Q8—42no—
996C2×Q8—42no—
997C2×Q8—42no—
998C2×Q8—44no—
999C2×Q8—42no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—42no—
1003C2×Q8—44no—
1004C2×Q8—44no—
1005C2×Q8—44no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—416no—
1011C22×C4—44no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4C22×Q814yes—
1026C22×C4C22×Q814yes—
1027C22×C4C22×Q814yes—
1028C22×C4C22×Q814yes—
1029C22×C4C22×Q818yes—
1030C22×C4C22×Q818yes—
1031C22×C4C22×Q814yes—
1032C22×C4C22×Q814yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2514yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4C22×Q818yes—
1131C4⋊C4C22×Q818yes—
1132C4⋊C4C22×Q814yes—
1133C4⋊C4C22×Q814yes—
1134C4⋊C4C22×Q814yes—
1135C4⋊C4C22×Q814yes—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
1144C22⋊C4—42no—
1145C22⋊C4—42no—
1146C22⋊C4—41no—
1147C22⋊C4—41no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—41no—
1156C22⋊C4—41no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—42no—
1161C22⋊C4—42no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4C22×Q818yes—
1166C22⋊C4C22×Q818yes—
1167C22⋊C4C22×Q818yes—
1168C22⋊C4C22×Q818yes—
1169C42—24no—
1170C42—24no—
1171C42—28no—
1172C42—24no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—42no—
1177C42—42no—
1178C42—44no—
1179C42—44no—
1180C42—44no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42C22×Q818yes—
1192C42C22×Q818yes—
1193C42C22×Q818yes—
1194C42C22×Q818yes—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—21no—
1202C23—21no—
1203C23—21no—
1204C23—21no—
1205C23—21no—
1206C23—21no—
1207C23—44no—
1208C23—44no—
1209C23—44no—
1210C23—84no—
1211C23—84no—
1212C23C23×Q812yes—
1213C23C23×Q812yes—
1214C23C23×Q812yes—
1215C23C2611yescharacteristic
1216Q8—48no—
1217Q8—84no—
1218Q8—88no—
1219Q8—164no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—28no—
1232C2×C4—28no—
1233C2×C4—28no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—44no—
1286C2×C4—44no—
1287C2×C4—44no—
1288C2×C4—48no—
1289C2×C4—48no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—164no—
1293C2×C4C23×Q812yes—
1294C2×C4C23×Q812yes—
1295C2×C4C23×Q814yes—
1296C2×C4C23×Q814yes—
1297C2×C4C23×Q814yes—
1298C2×C4C23×Q814yes—
1299C2×C4C23×Q812yes—
1300C2×C4C23×Q812yes—
1301C2×C4#58514yes—
1302C2×C4#58514yes—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—22no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—88no—
1319C22C24×Q811yescharacteristic
1320C22C2×#58512yes—
1321C22C2×#58512yes—
1322C22H(7,𝔽2)11yescharacteristic
1323C222−1+611yescharacteristic
1324C4—24no—
1325C4—24no—
1326C4—24no—
1327C4—24no—
1328C4—24no—
1329C4—22no—
1330C4—22no—
1331C4—22no—
1332C4—44no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4—44no—
1347C4—42no—
1348C4—44no—
1349C4#345814yes—
1350C2—42no—
1351C2—42no—
1352C2—42no—
1353C2C2×#345811yescharacteristic
1354C2#6281311yescharacteristic
1355C2#6285411yescharacteristic
1356C2#6290712yes—
1357C2#6293712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42932C2semidirect
2. #42932C2semidirect
3. #42491C2semidirect
4. #42489C2semidirect
5. #42189C2semidirect
6. #42007C2semidirect
9. #39986C2semidirect
10. #39983C2semidirect
11. #38459C2semidirect
12. #38457C2semidirect
13. #37566C2semidirect
14. #37565C2semidirect
17. #36287C2semidirect
18. #36284C2semidirect
19. #36039C2semidirect
20. #35783C2semidirect
21. #35747C2semidirect
22. #35708C2semidirect
23. #35202C2semidirect
25. #34644C2semidirect
31. #2864C22semidirect
32. #2859C22semidirect
35. #2843C22semidirect
36. #2843C22semidirect
43. #2805C22semidirect
44. #2802C22semidirect
45. #2792C22semidirect
46. #2792C22semidirect
47. #2791C22semidirect
53. #2774C22semidirect
57. #2726C22semidirect
62. #2713C22semidirect
76. #2666C22semidirect
77. #2666C22semidirect
78. #2666C22semidirect
79. #2666C22semidirect
80. #2666C22semidirect
81. #2666C22semidirect
82. #2666C22semidirect
83. #2666C22semidirect
102. #2612C22semidirect
103. #2612C22semidirect
104. #2612C22semidirect
105. #2612C22semidirect
109. #2606C22semidirect
110. #2606C22semidirect
111. #2606C22semidirect
112. #2605C22semidirect
113. #2590C22semidirect
115. #2588C22semidirect
119. #2586C22semidirect
120. #2585C22semidirect
121. #2584C22semidirect
122. #2584C22semidirect
123. #2584C22semidirect
124. #2584C22semidirect
126. #2570C22semidirect
127. #2570C22semidirect
130. #2567C22semidirect
131. #2567C22semidirect
135. #2552C22semidirect
136. #2552C22semidirect
137. #2552C22semidirect
138. #2552C22semidirect
139. #2552C22semidirect
140. #2551C22semidirect
141. #2550C22semidirect
142. #2550C22semidirect
143. #2550C22semidirect
144. #2550C22semidirect
149. #2511C22semidirect
150. #2509C22semidirect
151. #2509C22semidirect
152. #2509C22semidirect
153. #2508C22semidirect
154. #2507C22semidirect
155. #2507C22semidirect
156. #2507C22semidirect
157. #2507C22semidirect
158. #2506C22semidirect
159. #2506C22semidirect
160. #2506C22semidirect
161. #2506C22semidirect
162. #2506C22semidirect
167. #2462C22semidirect
168. #2462C22semidirect
188. #2402C22semidirect
189. #2399C22semidirect
196. #2370C22semidirect
197. #2370C22semidirect
198. #2370C22semidirect
199. #2370C22semidirect
200. #2369C22semidirect
201. #2365C22semidirect
202. #2355C22semidirect
203. Q8×C4⋊C4C22semidirect
231. #2330C22semidirect
232. #2330C22semidirect
242. #2295C22semidirect
243. #2295C22semidirect
281. C2×#117Q8semidirect

Maximal subgroups

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

subgroupindex
#429322
#424912
#424892
#421892
#420072
#406232
#406222
#399862
#399832
#384592
#384572
#375662
#375652
#374812
#374762
#362872
#362842
#360392
#357832
#357472
#357082
#352022
#350792
#346442
#345782
#341802
#341792
#341092