Finite Group Databasebeta

← #7895486

Subgroups — #7895486

Order 512.

4299 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic
2#59832C212yesmaximal
3#52287C211yesmaximal, characteristic
4#51602C214yesmaximal
5#51080C214yesmaximal
6#50706C214yesmaximal
7#47727C214yesmaximal
8#46007C212yesmaximal
9#45389C212yesmaximal
10#45277C212yesmaximal
11#45276C212yesmaximal
12#44255C214yesmaximal
13#42822C212yesmaximal
14#42820C212yesmaximal
15#42002C214yesmaximal
16#39975C212yesmaximal
17#39703C212yesmaximal
18#39673C212yesmaximal
19#39629C211yesmaximal, characteristic
20#39621C212yesmaximal
21#39621C211yesmaximal, characteristic
22#39176C212yesmaximal
23#37195C212yesmaximal
24#36474C211yesmaximal, characteristic
25#35937C212yesmaximal
26#35583C212yesmaximal
27#35199C211yesmaximal, characteristic
28#34488C212yesmaximal
29#34328C211yesmaximal, characteristic
30C2×Q82C2212yes—
31C2×Q82C2211yescharacteristic
32C2×#557C2212yes—
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35#2864C2212yes—
36#2863C2212yes—
37#2862C2212yes—
38#2862C2211yescharacteristic
39#2862C2212yes—
40#2845C2214yes—
41#2843C2214yes—
42#2811C2211yescharacteristic
43#2811C2212yes—
44#2806C2214yes—
45#2806C2212yes—
46#2806C2212yes—
47#2806C2212yes—
48#2806C2212yes—
49#2806C2211yescharacteristic
50#2806C2212yes—
51#2806C2211yescharacteristic
52#2806C2214yes—
53#2806C2212yes—
54#2806C2212yes—
55#2806C2212yes—
56#2805C2212yes—
57#2805C2212yes—
58#2802C2214yes—
59#2802C2214yes—
60#2802C2214yes—
61#2799C2214yes—
62#2792C2212yes—
63#2792C2214yes—
64#2792C2212yes—
65#2792C2212yes—
66#2791C2214yes—
67#2791C2214yes—
68#2791C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2755C2214yes—
75#2755C2214yes—
76#2755C2214yes—
77#2734C2214yes—
78#2734C2212yes—
79#2734C2214yes—
80#2734C2214yes—
81#2734C2211yescharacteristic
82#2734C2214yes—
83#2734C2212yes—
84#2734C2214yes—
85#2734C2214yes—
86#2726C2214yes—
87#2726C2214yes—
88#2726C2214yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2713C2214yes—
93#2713C2214yes—
94#2713C2214yes—
95#2713C2214yes—
96#2666C2214yes—
97#2666C2214yes—
98#2666C2214yes—
99#2666C2214yes—
100#2666C2214yes—
101#2660C2214yes—
102#2660C2214yes—
103#2660C2212yes—
104#2647C2212yes—
105#2647C2212yes—
106#2612C2214yes—
107#2612C2214yes—
108#2606C2214yes—
109#2606C2214yes—
110#2605C2214yes—
111#2605C2214yes—
112#2590C2214yes—
113#2590C2214yes—
114#2590C2214yes—
115#2588C2214yes—
116#2588C2214yes—
117#2588C2214yes—
118#2586C2214yes—
119#2586C2214yes—
120#2586C2214yes—
121#2586C2214yes—
122#2585C2214yes—
123#2585C2214yes—
124#2585C2214yes—
125#2584C2214yes—
126#2584C2212yes—
127#2584C2214yes—
128#2582C2212yes—
129#2582C2212yes—
130#2582C2212yes—
131#2582C2212yes—
132#2582C2211yescharacteristic
133#2581C2212yes—
134#2581C2212yes—
135#2581C2212yes—
136#2570C2212yes—
137#2570C2212yes—
138#2568C2211yescharacteristic
139#2567C2211yescharacteristic
140#2567C2212yes—
141#2567C2212yes—
142#2552C2212yes—
143#2552C2212yes—
144#2551C2212yes—
145#2551C2214yes—
146#2551C2214yes—
147#2551C2212yes—
148#2551C2211yescharacteristic
149#2551C2214yes—
150#2550C2212yes—
151#2550C2212yes—
152#2550C2214yes—
153#2550C2214yes—
154#2550C2214yes—
155#2550C2212yes—
156#2550C2212yes—
157#2550C2214yes—
158#2550C2212yes—
159#2550C2214yes—
160#2550C2214yes—
161#2546C2214yes—
162#2546C2211yescharacteristic
163#2546C2212yes—
164#2546C2214yes—
165#2546C2212yes—
166#2546C2211yescharacteristic
167#2546C2214yes—
168#2520C2214yes—
169#2520C2214yes—
170#2520C2214yes—
171#2508C2212yes—
172#2507C2214yes—
173#2507C2212yes—
174#2506C2212yes—
175#2462C2214yes—
176#2462C2214yes—
177#2462C2214yes—
178#2462C2214yes—
179#2462C2214yes—
180#2462C2214yes—
181#2453C2212yes—
182#2453C2212yes—
183#2453C2212yes—
184#2451C2214yes—
185#2451C2212yes—
186#2451C2212yes—
187#2451C2212yes—
188#2451C2212yes—
189#2451C2212yes—
190#2451C2212yes—
191#2451C2214yes—
192#2451C2212yes—
193#2451C2214yes—
194#2451C2214yes—
195#2451C2214yes—
196#2451C2214yes—
197#2446C2214yes—
198#2446C2214yes—
199#2446C2214yes—
200#2446C2212yes—
201#2399C2214yes—
202#2399C2212yes—
203#2399C2212yes—
204#2399C2212yes—
205#2382C2214yes—
206#2382C2214yes—
207#2371C2214yes—
208#2370C2212yes—
209#2370C2214yes—
210#2369C2212yes—
211#2365C2214yes—
212#2365C2211yescharacteristic
213#2365C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2365C2212yes—
217#2356C2212yes—
218#2356C2212yes—
219#2355C2211yescharacteristic
220#2355C2212yes—
221#2355C2214yes—
222#2355C2211yescharacteristic
223#2351C2212yes—
224#2351C2212yes—
225#2351C2212yes—
226#2351C2212yes—
227Q8×C4⋊C4C2212yes—
228Q8×C4⋊C4C2212yes—
229#2336C2214yes—
230#2336C2214yes—
231#2336C2214yes—
232#2331C2212yes—
233#2331C2214yes—
234#2331C2212yes—
235#2330C2212yes—
236#2330C2214yes—
237#2327C2212yes—
238#2327C2212yes—
239#2327C2212yes—
240#2320C2214yes—
241#2320C2212yes—
242#2320C2212yes—
243C4×C4⋊Q8C2212yes—
244C4×C4⋊Q8C2212yes—
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2211yescharacteristic
248C4×C4⋊Q8C2211yescharacteristic
249C4×C4⋊Q8C2212yes—
250C4×#125C2212yes—
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2212yes—
254#2295C2212yes—
255#2295C2211yescharacteristic
256#2295C2212yes—
257#2276C2212yes—
258C42×Q8C2211yescharacteristic
259Q82—48no—
260Q82—44no—
261#557—44no—
262#557—48no—
263#557Q8116yescomplemented
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2311yescharacteristic
286C2×C4⋊Q8C2312yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2312yes—
295C2×#125C2314yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
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#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2312yes—
381#398C2314yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2314yes—
400#395C2312yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2312yes—
413#395C2312yes—
414#395C2314yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#395C2312yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#391C2311yescharacteristic
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2311yescharacteristic
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2311yescharacteristic
470#391C2314yes—
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2311yescharacteristic
477#391C2314yes—
478#391C2314yes—
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2311yescharacteristic
482#389C2311yescharacteristic
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2314yes—
536#389C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2311yescharacteristic
555#389C2312yes—
556#389C2311yescharacteristic
557#389C2312yes—
558#389C2311yescharacteristic
559#389C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2312yes—
610#387C2312yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2312yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2312yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#384C2312yes—
638#384C2311yescharacteristic
639#384C2312yes—
640#384C2311yescharacteristic
641#384C2312yes—
642#384C2311yescharacteristic
643#384C2312yes—
644#384C2312yes—
645#384C2314yes—
646#384C2314yes—
647#383C2314yes—
648#383C2314yes—
649#383C2314yes—
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2314yes—
654#382C2314yes—
655#382C2314yes—
656#382C2314yes—
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2314yes—
661#382C2314yes—
662#382C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2311yescharacteristic
708#376C2312yes—
709#376C2312yes—
710#376C2314yes—
711#376C2312yes—
712#376C2314yes—
713#376C2314yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2414yes—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2411yescharacteristic
731C4⋊Q8—28no—
732C4⋊Q8—28no—
733C4⋊Q8—24no—
734C4⋊Q8—28no—
735C4⋊Q8—28no—
736C4⋊Q8—24no—
737C4⋊Q8—42no—
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—42no—
741C4⋊Q8—48no—
742C4⋊Q8—44no—
743C4⋊Q8—48no—
744C4⋊Q8—48no—
745C4⋊Q8—48no—
746C4⋊Q8—48no—
747C4⋊Q8—84no—
748C4⋊Q8—84no—
749C4⋊Q8—84no—
750C4⋊Q8—82no—
751C4⋊Q8—82no—
752C4⋊Q8C2×Q818yes—
753C4⋊Q8C2×Q8116yes—
754#125—28no—
755#125—44no—
756#125—48no—
757#125—48no—
758#125—48no—
759#125—84no—
760#125—84no—
761#125C2×Q8116yes—
762#125C2×Q8132yes—
763C4×Q8—28no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—24no—
767C4×Q8—24no—
768C4×Q8—44no—
769C4×Q8—42no—
770C4×Q8—44no—
771C4×Q8—42no—
772C4×Q8—44no—
773C4×Q8—48no—
774C4×Q8—44no—
775C4×Q8—48no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×Q8—44no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—82no—
783C4×Q8—84no—
784C4×Q8C2×Q8116yes—
785C4×Q8C2×Q818yes—
786C4×Q8C2×Q8116yes—
787C4×Q8C2×Q818yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2414yes—
888C2×C42C2411yescharacteristic
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919C2×C42C2411yescharacteristic
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2412yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C2×Q8—24no—
1004C2×Q8—22no—
1005C2×Q8—28no—
1006C2×Q8—28no—
1007C2×Q8—24no—
1008C2×Q8—22no—
1009C2×Q8—24no—
1010C2×Q8—22no—
1011C2×Q8—24no—
1012C2×Q8—22no—
1013C2×Q8—24no—
1014C2×Q8—41no—
1015C2×Q8—42no—
1016C2×Q8—41no—
1017C2×Q8—41no—
1018C2×Q8—41no—
1019C2×Q8—42no—
1020C2×Q8—41no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8—44no—
1025C2×Q8—41no—
1026C2×Q8—44no—
1027C2×Q8—42no—
1028C2×Q8—41no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—44no—
1032C2×Q8—41no—
1033C2×Q8—44no—
1034C2×Q8—42no—
1035C2×Q8—42no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8C22×Q814yes—
1042C2×Q8C22×Q818yes—
1043C2×Q8C22×Q814yes—
1044C2×Q82−1+414yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2511yescharacteristic
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—42no—
1100C4⋊C4—41no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—41no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—41no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—41no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—41no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—41no—
1158C4⋊C4—44no—
1159C4⋊C4C22×Q814yes—
1160C4⋊C4C22×Q818yes—
1161C4⋊C4C22×Q8116yes—
1162C4⋊C4C22×Q814yes—
1163C4⋊C4C22×Q818yes—
1164C4⋊C4C22×Q818yes—
1165C4⋊C4C22×Q8116yes—
1166C4⋊C4C22×Q8116yes—
1167C4⋊C4C22×Q818yes—
1168C4⋊C4H(5,𝔽2)14yes—
1169C42—28no—
1170C42—24no—
1171C42—24no—
1172C42—22no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—28no—
1177C42—24no—
1178C42—24no—
1179C42—22no—
1180C42—24no—
1181C42—24no—
1182C42—41no—
1183C42—42no—
1184C42—42no—
1185C42—44no—
1186C42—41no—
1187C42—42no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—41no—
1195C42—42no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—42no—
1201C42C22×Q818yes—
1202C42C22×Q8116yes—
1203C42C22×Q814yes—
1204C42C22×Q818yes—
1205C422−1+414yes—
1206C23C2611yescharacteristic
1207Q8—216no—
1208Q8—28no—
1209Q8—44no—
1210Q8—44no—
1211Q8—48no—
1212Q8—88no—
1213Q8—88no—
1214Q8—82no—
1215Q8—84no—
1216Q8—82no—
1217Q8—84no—
1218Q8—84no—
1219Q8—164no—
1220Q8—162no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—21no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4C23×Q814yes—
1294C2×C4C23×Q812yes—
1295C2×C4C23×Q814yes—
1296C2×C4C23×Q814yes—
1297C2×C4C23×Q812yes—
1298C2×C4C23×Q814yes—
1299C2×C4C23×Q818yes—
1300C2×C4C23×Q812yes—
1301C2×C4C2×H(5,𝔽2)14yes—
1302C2×C4C2×H(5,𝔽2)12yes—
1303C2×C4C2×2−1+412yes—
1304C2×C4C2×2−1+412yes—
1305C2×C4C2×2−1+412yes—
1306C2×C4C2×2−1+414yes—
1307C2×C4C2×2−1+412yes—
1308C22C24×Q811yescharacteristic
1309C22C22×H(5,𝔽2)11yescharacteristic
1310C22C22×2−1+411yescharacteristic
1311C22C22×2−1+411yescharacteristic
1312C22H(7,𝔽2)11yescharacteristic
1313C222−1+611yescharacteristic
1314C222−1+611yescharacteristic
1315C4—22no—
1316C4—24no—
1317C4—24no—
1318C4—24no—
1319C4—28no—
1320C4—24no—
1321C4—22no—
1322C4—24no—
1323C4—22no—
1324C4—24no—
1325C4—22no—
1326C4—22no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—42no—
1332C4—44no—
1333C4—41no—
1334C4—44no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—42no—
1343C4#350314yes—
1344C2C2×#350311yescharacteristic
1345C2#6284911yescharacteristic
1346C2#6287911yescharacteristic
1347C2#6289311yescharacteristic
1348C2#6294711yescharacteristic
1349C2Q8×2−1+411yescharacteristic
1350C2#6304911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
263. #557Q8semidirect

Maximal subgroups

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

subgroupindex
#598712
#598322
#522872
#516022
#510802
#507062
#477272
#460072
#453892
#452772
#452762
#442552
#428222
#428202
#420022
#399752
#397032
#396732
#396292
#396212
#391762
#371952
#364742
#359372
#355832
#351992
#344882
#343282