Finite Group Databasebeta

← #7646777

Subgroups — #7646777

Order 512.

4112 conjugacy classes of subgroups.

The subgroup lattice has 1173 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42185C214yesmaximal, complemented
2#42183C214yesmaximal, complemented
3#42004C214yesmaximal, complemented
4#42002C214yesmaximal, complemented
5#38455C214yesmaximal, complemented
6#38454C214yesmaximal, complemented
7#38451C214yesmaximal, complemented
8#38451C214yesmaximal, complemented
9#37609C212yesmaximal
10#37562C211yesmaximal, characteristic
11#37562C211yesmaximal, characteristic
12#37194C214yesmaximal
13#36752C212yesmaximal
14#36751C212yesmaximal
15#35403C214yesmaximal
16#35304C211yesmaximal, characteristic
17#35304C211yesmaximal, characteristic
18#35235C212yesmaximal
19#35146C212yesmaximal
20#35015C212yesmaximal
21#35013C212yesmaximal
22#34878C212yesmaximal
23#34187C211yesmaximal, characteristic
24C2×#2356C211yesmaximal, characteristic
25#34059C211yesmaximal, characteristic
26C22×C4×Q8C2211yescharacteristic
27#2863C2214yes—
28#2863C2214yes—
29#2857C2212yes—
30#2857C2212yes—
31#2855C2214yes—
32#2855C2214yes—
33#2851C2212yes—
34#2851C2212yes—
35#2845C2214yes—
36#2844C2214yes—
37#2843C2214yes—
38#2843C2214yes—
39#2811C2214yes—
40#2809C2214yes—
41#2809C2214yes—
42#2809C2214yes—
43#2806C2214yes—
44#2806C2214yes—
45#2806C2214yes—
46#2806C2214yes—
47#2806C2214yes—
48#2806C2214yes—
49#2806C2214yes—
50#2805C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2799C2214yes—
54#2799C2214yes—
55#2799C2214yes—
56#2799C2214yes—
57#2799C2214yes—
58#2799C2214yes—
59#2792C2214yes—
60#2792C2214yes—
61#2791C2214yes—
62#2791C2214yes—
63#2774C2214yes—
64#2774C2214yes—
65#2755C2214yes—
66#2755C2214yes—
67#2734C2214yes—
68#2726C2214yes—
69#2713C2214yes—
70#2713C2214yes—
71#2666C2214yes—
72#2666C2214yes—
73#2666C2214yes—
74#2666C2214yes—
75#2666C2214yes—
76#2666C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2660C2212yes—
84#2660C2212yes—
85#2659C2212yes—
86#2659C2212yes—
87#2647C2212yes—
88#2647C2212yes—
89#2646C2212yes—
90#2646C2212yes—
91#2627C2214yes—
92#2627C2214yes—
93#2612C2214yes—
94#2612C2214yes—
95#2612C2214yes—
96#2612C2214yes—
97#2612C2214yes—
98#2612C2214yes—
99#2606C2212yes—
100#2606C2214yes—
101#2606C2212yes—
102#2606C2214yes—
103#2606C2214yes—
104#2606C2214yes—
105#2606C2212yes—
106#2606C2212yes—
107#2605C2212yes—
108#2605C2214yes—
109#2605C2212yes—
110#2605C2214yes—
111#2605C2214yes—
112#2605C2214yes—
113#2605C2212yes—
114#2605C2212yes—
115#2590C2214yes—
116#2590C2214yes—
117#2590C2214yes—
118#2590C2214yes—
119#2588C2214yes—
120#2588C2214yes—
121#2588C2214yes—
122#2588C2214yes—
123#2586C2214yes—
124#2586C2214yes—
125#2586C2214yes—
126#2586C2214yes—
127#2585C2214yes—
128#2585C2214yes—
129#2585C2214yes—
130#2585C2214yes—
131#2570C2214yes—
132#2569C2212yes—
133#2569C2212yes—
134#2569C2212yes—
135#2569C2212yes—
136#2569C2214yes—
137#2550C2214yes—
138#2549C2212yes—
139#2549C2212yes—
140#2549C2212yes—
141#2549C2212yes—
142#2549C2214yes—
143#2520C2214yes—
144#2520C2214yes—
145#2520C2214yes—
146#2520C2214yes—
147#2511C2214yes—
148#2511C2214yes—
149#2507C2214yes—
150#2507C2214yes—
151#2462C2214yes—
152#2462C2214yes—
153#2462C2214yes—
154#2462C2214yes—
155#2451C2214yes—
156#2451C2214yes—
157#2446C2214yes—
158#2446C2214yes—
159#2442C2214yes—
160#2440C2214yes—
161#2438C2214yes—
162#2438C2214yes—
163#2438C2214yes—
164#2438C2214yes—
165#2438C2214yes—
166#2438C2214yes—
167#2438C2214yes—
168#2438C2214yes—
169#2402C2214yes—
170#2399C2214yes—
171#2356C2212yes—
172#2356C2212yes—
173#2356C2214yes—
174#2356C2212yes—
175#2356C2212yes—
176#2356C2212yes—
177#2356C2214yes—
178#2356C2212yes—
179#2356C2212yes—
180#2356C2212yes—
181#2355C2214yes—
182#2355C2214yes—
183#2331C2212yes—
184#2331C2214yes—
185#2331C2212yes—
186#2330C2212yes—
187#2330C2214yes—
188#2330C2212yes—
189#2329C2214yes—
190#2329C2214yes—
191#2320C2214yes—
192#2320C2214yes—
193#2316C2211yescharacteristic
194#2316C2211yescharacteristic
195#2313C2212yes—
196#2313C2211yescharacteristic
197#2313C2211yescharacteristic
198#2313C2212yes—
199#2313C2212yes—
200#2310C2212yes—
201#2310C2212yes—
202C4×C22⋊Q8C2214yes—
203C4×C22⋊Q8C2214yes—
204#2295C2214yes—
205#2295C2214yes—
206#2295C2214yes—
207#2295C2214yes—
208C2×#391C2212yes—
209C2×#387C2212yes—
210C2×#387C2212yes—
211#2285C2211yescharacteristic
212#2285C2211yescharacteristic
213#2283C2212yes—
214#2283C2211yescharacteristic
215#2283C2211yescharacteristic
216#2283C2212yes—
217#2283C2212yes—
218C2×#383C2211yescharacteristic
219C2×#383C2211yescharacteristic
220C2×#382C2211yescharacteristic
221#2274C2212yes—
222C4×#117C2212yes—
223C2×C4×C4⋊C4C2211yescharacteristic
224C2×C4×C4⋊C4C2212yes—
225C2×#376C2211yescharacteristic
226C2×#376C2211yescharacteristic
227C23×Q8C2311yescharacteristic
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×#125C2312yes—
232C2×#125C2312yes—
233C2×#125C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C4×Q8Q8116yescomplemented
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#395C2314yes—
333#395C2314yes—
334#395C2314yes—
335#395C2314yes—
336#395C2314yes—
337#395C2314yes—
338#395C2314yes—
339#395C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2314yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#389C2314yes—
406#389C2314yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2314yes—
415#389C2312yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#384C2314yes—
521#384C2312yes—
522#384C2312yes—
523#384C2312yes—
524#384C2312yes—
525#383C2312yes—
526#383C2312yes—
527#383C2314yes—
528#383C2312yes—
529#383C2312yes—
530#383C2312yes—
531#383C2312yes—
532#383C2312yes—
533#383C2314yes—
534#383C2312yes—
535#383C2312yes—
536#383C2312yes—
537#383C2312yes—
538#383C2312yes—
539#382C2314yes—
540#382C2314yes—
541#382C2312yes—
542#382C2312yes—
543#382C2312yes—
544#382C2312yes—
545#382C2312yes—
546#382C2314yes—
547#382C2312yes—
548#382C2314yes—
549#382C2314yes—
550#382C2312yes—
551#382C2312yes—
552#381C2314yes—
553#381C2312yes—
554#381C2312yes—
555#381C2314yes—
556#381C2312yes—
557#381C2312yes—
558#380C2312yes—
559#380C2312yes—
560#380C2312yes—
561#380C2311yescharacteristic
562#380C2311yescharacteristic
563#380C2311yescharacteristic
564#380C2311yescharacteristic
565#380C2312yes—
566#380C2314yes—
567#380C2314yes—
568#380C2312yes—
569#380C2312yes—
570#380C2314yes—
571#380C2314yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2311yescharacteristic
583C4×C4⋊C4C2311yescharacteristic
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2311yescharacteristic
593C4×C4⋊C4C2311yescharacteristic
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2312yes—
608#376C2314yes—
609#376C2312yes—
610#376C2312yes—
611#376C2312yes—
612#376C2312yes—
613#376C2311yescharacteristic
614#376C2311yescharacteristic
615#376C2312yes—
616#376C2314yes—
617#376C2312yes—
618#376C2314yes—
619#376C2312yes—
620#376C2311yescharacteristic
621#376C2311yescharacteristic
622#376C2312yes—
623#376C2312yes—
624#376C2312yes—
625C2×#95C2311yescharacteristic
626C2×#95C2311yescharacteristic
627C2×#95C2311yescharacteristic
628C2×#95C2311yescharacteristic
629C2×#95C2312yes—
630C2×#95C2312yes—
631C2×#95C2312yes—
632C2×#95C2312yes—
633C2×#95C2312yes—
634C2×#95C2312yes—
635C2×#95C2312yes—
636C43C2314yes—
637C22×Q8—42no—
638C22×Q8—42no—
639C22×Q8C2×Q818yes—
640C22×Q8C2414yes—
641C22×Q8C2414yes—
642C22×Q8C2414yes—
643C22×Q8C2414yes—
644C22×Q8C2412yes—
645C22×Q8C2412yes—
646C23×C4C2412yes—
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2411yescharacteristic
654C23×C4C2411yescharacteristic
655C23×C4C2411yescharacteristic
656C23×C4C2411yescharacteristic
657C4⋊Q8—44no—
658C4⋊Q8—44no—
659C4⋊Q8—48no—
660#125—44no—
661#125—44no—
662#125—48no—
663C22⋊Q8—48no—
664C22⋊Q8—48no—
665C22⋊Q8—48no—
666C22⋊Q8—48no—
667C4×Q8—48no—
668C4×Q8—48no—
669C4×Q8C2×Q8116yes—
670C4×Q8C2×Q8116yes—
671C4×Q8C2×Q8116yes—
672C4×Q8C2×Q8116yes—
673#117—44no—
674#117—44no—
675#117—44no—
676#117—44no—
677C2×C4⋊C4—44no—
678C2×C4⋊C4—44no—
679C2×C4⋊C4C2×Q818yes—
680C2×C4⋊C4C2×Q818yes—
681C2×C4⋊C4C2×Q818yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2414yes—
750C2×C42—44no—
751C2×C42—44no—
752C2×C42—44no—
753C2×C42C2×Q818yes—
754C2×C42C2×Q818yes—
755C2×C42C2×Q818yes—
756C2×C42C2414yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2412yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782C2×C42C2412yes—
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2412yes—
786#95C2412yes—
787#95C2411yescharacteristic
788#95C2411yescharacteristic
789#95C2412yes—
790#95C2412yes—
791#95C2411yescharacteristic
792#95C2412yes—
793#95C2411yescharacteristic
794#95C2412yes—
795#95C2412yes—
796#95C2414yes—
797#95C2414yes—
798#95C2412yes—
799#95C2412yes—
800#95C2412yes—
801#95C2412yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2412yes—
813#95C2412yes—
814#95C2412yes—
815#95C2412yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2412yes—
822#95C2412yes—
823#95C2412yes—
824#95C2412yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872C24C2511yescharacteristic
873C2×Q8—28no—
874C2×Q8—416no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—44no—
880C2×Q8—44no—
881C2×Q8—44no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—44no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8C22×Q818yes—
891C2×Q8C22×Q818yes—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4C22×Q814yes—
915C22×C4C22×Q814yes—
916C22×C4C22×Q814yes—
917C22×C4C22×Q814yes—
918C22×C4C22×Q814yes—
919C22×C4C22×Q814yes—
920C22×C4C22×Q814yes—
921C22×C4C2512yes—
922C22×C4C2514yes—
923C22×C4C2514yes—
924C22×C4C2514yes—
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2514yes—
930C22×C4C2514yes—
931C22×C4C2514yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2512yes—
944C22×C4C2512yes—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—44no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—44no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4C22×Q818yes—
1002C4⋊C4C22×Q818yes—
1003C4⋊C4C22×Q818yes—
1004C4⋊C4C22×Q818yes—
1005C4⋊C4C22×Q818yes—
1006C4⋊C4C22×Q818yes—
1007C22⋊C4—28no—
1008C22⋊C4—24no—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—28no—
1012C22⋊C4—24no—
1013C42—28no—
1014C42—24no—
1015C42—24no—
1016C42—44no—
1017C42—42no—
1018C42—42no—
1019C42—44no—
1020C42—44no—
1021C42—44no—
1022C42—44no—
1023C42—42no—
1024C42—42no—
1025C42—42no—
1026C42—42no—
1027C42—44no—
1028C42—44no—
1029C42—44no—
1030C42—44no—
1031C42—44no—
1032C42—44no—
1033C42—44no—
1034C42—44no—
1035C42C22×Q818yes—
1036C42C22×Q814yes—
1037C42C22×Q814yes—
1038C42C22×Q818yes—
1039C42C22×Q818yes—
1040C42C22×Q814yes—
1041C42C22×Q814yes—
1042C42C22×Q818yes—
1043C23—22no—
1044C23—22no—
1045C23C23×Q812yes—
1046C23#58512yes—
1047C23#58512yes—
1048C23C2611yescharacteristic
1049Q8—48no—
1050Q8—48no—
1051Q8—88no—
1052Q8—88no—
1053Q8—164no—
1054Q8—164no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—28no—
1072C2×C4—28no—
1073C2×C4—28no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—48no—
1118C2×C4—84no—
1119C2×C4—84no—
1120C2×C4—84no—
1121C2×C4C23×Q812yes—
1122C2×C4C23×Q812yes—
1123C2×C4C23×Q814yes—
1124C2×C4C23×Q812yes—
1125C2×C4C23×Q812yes—
1126C2×C4C23×Q814yes—
1127C2×C4C23×Q812yes—
1128C2×C4C23×Q812yes—
1129C2×C4C23×Q814yes—
1130C2×C4C23×Q814yes—
1131C2×C4#58514yes—
1132C22—22no—
1133C22—22no—
1134C22—24no—
1135C22—24no—
1136C22#345814yes—
1137C22C24×Q811yescharacteristic
1138C22C2×#58512yes—
1139C22C2×#58511yescharacteristic
1140C22C2×#58511yescharacteristic
1141C222−1+612yes—
1142C4—24no—
1143C4—22no—
1144C4—22no—
1145C4—24no—
1146C4—22no—
1147C4—22no—
1148C4—24no—
1149C4—24no—
1150C4—22no—
1151C4—22no—
1152C4—24no—
1153C4—44no—
1154C4—42no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C4—42no—
1160C4—44no—
1161C4—42no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—44no—
1166C2—24no—
1167C2C2×#345811yescharacteristic
1168C2#6281311yescharacteristic
1169C2#6284911yescharacteristic
1170C2#6290912yes—
1171C2#6291112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42185C2semidirect
2. #42183C2semidirect
3. #42004C2semidirect
4. #42002C2semidirect
5. #38455C2semidirect
6. #38454C2semidirect
7. #38451C2semidirect
8. #38451C2semidirect
238. C2×C4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#421852
#421832
#420042
#420022
#384552
#384542
#384512
#376092
#375622
#371942
#367522
#367512
#354032
#353042
#352352
#351462
#350152
#350132
#348782
#341872
C2×#23562
#340592