Finite Group Databasebeta

← #7715666

Subgroups — #7715666

Order 512.

4052 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48846C214yesmaximal
2#48842C214yesmaximal
3#47971C214yesmaximal
4#47967C214yesmaximal
5#47819C214yesmaximal, complemented
6#47817C214yesmaximal, complemented
7#47774C214yesmaximal, complemented
8#47727C214yesmaximal, complemented
9#39754C212yesmaximal, complemented
10#39750C212yesmaximal, complemented
11#39625C212yesmaximal, complemented
12#39621C212yesmaximal, complemented
13#39182C212yesmaximal, complemented
14#39181C212yesmaximal, complemented
15#39177C212yesmaximal, complemented
16#39176C212yesmaximal, complemented
17#37642C211yesmaximal, characteristic
18#37565C211yesmaximal, characteristic
19#37428C211yesmaximal, characteristic
20#37311C212yesmaximal
21#37308C211yesmaximal, characteristic
22#35337C211yesmaximal, characteristic
23#35304C212yesmaximal
24#35283C211yesmaximal, characteristic
25#35282C212yesmaximal
26#34373C212yesmaximal
27#34074C211yesmaximal, characteristic
28C2×#533C2211yescharacteristic
29#2868C2211yescharacteristic
30#2864C2212yes—
31#2862C2211yescharacteristic
32#2862C2211yescharacteristic
33#2859C2211yescharacteristic
34#2859C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2844C2212yes—
40#2844C2212yes—
41#2843C2212yes—
42#2843C2212yes—
43#2811C2214yes—
44#2809C2214yes—
45#2807C2212yes—
46#2807C2212yes—
47#2806C2214yes—
48#2806C2214yes—
49#2806C2214yes—
50#2805C2214yes—
51#2805C2214yes—
52#2805C2214yes—
53#2802C2214yes—
54#2802C2214yes—
55#2802C2214yes—
56#2802C2214yes—
57#2799C2214yes—
58#2799C2214yes—
59#2799C2214yes—
60#2799C2214yes—
61#2792C2214yes—
62#2792C2214yes—
63#2792C2214yes—
64#2791C2214yes—
65#2788C2214yes—
66#2774C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2774C2214yes—
73#2768C2214yes—
74#2763C2212yes—
75#2763C2212yes—
76#2755C2214yes—
77#2755C2214yes—
78#2755C2214yes—
79#2755C2214yes—
80#2755C2214yes—
81#2742C2212yes—
82#2742C2212yes—
83#2734C2214yes—
84#2734C2214yes—
85#2734C2214yes—
86#2734C2214yes—
87#2729C2214yes—
88#2720C2214yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2713C2214yes—
93#2677C2212yes—
94#2677C2212yes—
95#2667C2214yes—
96#2665C2214yes—
97#2660C2212yes—
98#2660C2212yes—
99#2660C2212yes—
100#2660C2212yes—
101#2647C2212yes—
102#2647C2212yes—
103#2647C2212yes—
104#2647C2212yes—
105#2629C2212yes—
106#2628C2211yescharacteristic
107#2628C2211yescharacteristic
108#2628C2211yescharacteristic
109#2628C2214yes—
110#2628C2214yes—
111#2628C2212yes—
112#2628C2211yescharacteristic
113#2612C2212yes—
114#2612C2212yes—
115#2612C2214yes—
116#2612C2214yes—
117#2606C2214yes—
118#2605C2214yes—
119#2590C2214yes—
120#2589C2214yes—
121#2589C2214yes—
122#2588C2214yes—
123#2588C2214yes—
124#2588C2214yes—
125#2588C2214yes—
126#2588C2214yes—
127#2586C2214yes—
128#2586C2214yes—
129#2586C2214yes—
130#2585C2214yes—
131#2585C2214yes—
132#2585C2214yes—
133#2584C2214yes—
134#2581C2214yes—
135#2581C2214yes—
136#2574C2214yes—
137#2571C2212yes—
138#2571C2212yes—
139#2571C2212yes—
140#2571C2212yes—
141#2571C2212yes—
142#2571C2212yes—
143#2570C2212yes—
144#2570C2212yes—
145#2570C2212yes—
146#2570C2212yes—
147#2570C2212yes—
148#2570C2212yes—
149#2569C2214yes—
150#2568C2214yes—
151#2567C2214yes—
152#2556C2214yes—
153#2552C2212yes—
154#2552C2212yes—
155#2551C2212yes—
156#2551C2212yes—
157#2551C2212yes—
158#2551C2212yes—
159#2551C2212yes—
160#2551C2212yes—
161#2551C2214yes—
162#2550C2212yes—
163#2550C2212yes—
164#2550C2212yes—
165#2550C2212yes—
166#2550C2214yes—
167#2550C2212yes—
168#2550C2212yes—
169#2549C2214yes—
170#2546C2214yes—
171#2522C2214yes—
172#2520C2214yes—
173#2520C2214yes—
174#2520C2214yes—
175#2520C2214yes—
176#2511C2214yes—
177#2511C2214yes—
178#2509C2214yes—
179#2508C2214yes—
180#2508C2214yes—
181#2507C2214yes—
182#2492C2214yes—
183#2465C2214yes—
184#2462C2214yes—
185#2462C2214yes—
186#2453C2214yes—
187#2453C2214yes—
188#2451C2214yes—
189#2451C2214yes—
190#2451C2214yes—
191#2451C2214yes—
192#2451C2214yes—
193#2446C2214yes—
194#2438C2214yes—
195#2438C2214yes—
196#2423C2214yes—
197#2378C2214yes—
198#2378C2214yes—
199#2362C2214yes—
200#2362C2214yes—
201#2355C2212yes—
202#2355C2212yes—
203#2355C2212yes—
204#2355C2212yes—
205#2355C2212yes—
206#2355C2212yes—
207Q8×C4⋊C4C2212yes—
208Q8×C4⋊C4C2212yes—
209#2336C2214yes—
210#2336C2214yes—
211#2331C2211yescharacteristic
212#2331C2211yescharacteristic
213#2331C2211yescharacteristic
214#2331C2212yes—
215#2331C2211yescharacteristic
216#2331C2212yes—
217#2331C2212yes—
218#2331C2214yes—
219#2331C2212yes—
220#2331C2212yes—
221#2330C2212yes—
222#2330C2212yes—
223#2330C2212yes—
224#2330C2212yes—
225#2330C2212yes—
226#2329C2212yes—
227#2329C2212yes—
228#2329C2212yes—
229#2329C2212yes—
230#2327C2214yes—
231#2314C2212yes—
232#2314C2212yes—
233#2314C2212yes—
234#2314C2212yes—
235C4×C4⋊Q8C2212yes—
236C4×C4⋊Q8C2212yes—
237C4×#125C2212yes—
238C4×#125C2212yes—
239#2296C2211yescharacteristic
240#2296C2211yescharacteristic
241#2295C2212yes—
242#2295C2212yes—
243#2295C2212yes—
244#2295C2212yes—
245#2285C2211yescharacteristic
246#2285C2212yes—
247#2283C2212yes—
248C4×#117C2211yescharacteristic
249C4×#117C2211yescharacteristic
250C2×#376C2211yescharacteristic
251#533Q8116yescomplemented
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2314yes—
260C2×C4⋊Q8C2314yes—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2314yes—
263C2×C4⋊Q8C2314yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2314yes—
279C2×C4×Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C2×#117C2314yes—
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2311yescharacteristic
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2312yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2312yes—
318#400C2314yes—
319#399C2312yes—
320#399C2312yes—
321#399C2312yes—
322#399C2314yes—
323#399C2312yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
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#396C2314yes—
359#396C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2312yes—
377#395C2312yes—
378#395C2314yes—
379#395C2312yes—
380#395C2314yes—
381#395C2312yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#393C2314yes—
390#393C2312yes—
391#393C2312yes—
392#393C2312yes—
393#393C2312yes—
394#391C2314yes—
395#391C2314yes—
396#391C2312yes—
397#391C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
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#387C2314yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
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#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2311yescharacteristic
586#385C2311yescharacteristic
587#385C2312yes—
588#385C2311yescharacteristic
589#385C2311yescharacteristic
590#385C2312yes—
591#385C2314yes—
592#384C2312yes—
593#384C2312yes—
594#384C2314yes—
595#384C2314yes—
596#384C2312yes—
597#384C2312yes—
598#384C2312yes—
599#384C2312yes—
600#384C2312yes—
601#384C2311yescharacteristic
602#384C2312yes—
603#384C2311yescharacteristic
604#384C2312yes—
605#383C2314yes—
606#382C2312yes—
607#382C2312yes—
608#382C2314yes—
609#382C2314yes—
610#382C2312yes—
611#382C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2311yescharacteristic
615#382C2311yescharacteristic
616#382C2311yescharacteristic
617#382C2312yes—
618#382C2312yes—
619#382C2311yescharacteristic
620#382C2314yes—
621#382C2314yes—
622#382C2314yes—
623#382C2314yes—
624#382C2314yes—
625#382C2311yescharacteristic
626#382C2311yescharacteristic
627#382C2312yes—
628#381C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678#376C2314yes—
679#376C2312yes—
680#376C2312yes—
681#376C2312yes—
682#376C2312yes—
683#376C2312yes—
684#376C2311yescharacteristic
685#376C2311yescharacteristic
686C2×#95C2312yes—
687C2×#95C2312yes—
688C43C2311yescharacteristic
689C43C2312yes—
690C43C2311yescharacteristic
691C22×Q8C2414yes—
692C22×Q8C2414yes—
693C22×Q8C2414yes—
694C22×Q8C2412yes—
695C22×Q8C2412yes—
696C22×Q8C2412yes—
697C22×Q8C2412yes—
698C22×Q8C2412yes—
699C22×Q8C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2412yes—
705C4⋊Q8—28no—
706C4⋊Q8—44no—
707C4⋊Q8—44no—
708C4⋊Q8—42no—
709C4⋊Q8—42no—
710C4⋊Q8—42no—
711C4⋊Q8—42no—
712C4⋊Q8—84no—
713C4⋊Q8—84no—
714C4⋊Q8—84no—
715C4⋊Q8—84no—
716C4⋊Q8—84no—
717C4⋊Q8—84no—
718C4⋊Q8C2×Q8116yes—
719#125—28no—
720#125—44no—
721#125—44no—
722#125—84no—
723#125—84no—
724#125C2×Q8116yes—
725C22⋊Q8—84no—
726C22⋊Q8—84no—
727C22⋊Q8C2×Q8116yes—
728C22⋊Q8C2×Q8116yes—
729C4×Q8—84no—
730C4×Q8—84no—
731C4×Q8—84no—
732C4×Q8—84no—
733C4×Q8C2×Q8116yes—
734C4×Q8C2×Q8116yes—
735#117—42no—
736#117—42no—
737#117—84no—
738#117C2×Q818yes—
739#117C2×Q818yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2411yescharacteristic
829C2×C42—24no—
830C2×C42—42no—
831C2×C42C2×Q818yes—
832C2×C42C2412yes—
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835C2×C42C2412yes—
836C2×C42C2411yescharacteristic
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2411yescharacteristic
860C2×C42C2412yes—
861C2×C42C2411yescharacteristic
862C2×C42C2412yes—
863C2×C42C2411yescharacteristic
864C2×C42C2411yescharacteristic
865C2×C42C2411yescharacteristic
866#95C2412yes—
867#95C2412yes—
868#95C2412yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2412yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952C24C2511yescharacteristic
953C2×Q8—28no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—44no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q8—42no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—44no—
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8C22×Q818yes—
975C2×Q8C22×Q818yes—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—24no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4C22×Q814yes—
988C22×C4C22×Q818yes—
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2512yes—
995C22×C4C2514yes—
996C22×C4C2514yes—
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2514yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2511yescharacteristic
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—44no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—42no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4C22×Q818yes—
1087C4⋊C4C22×Q818yes—
1088C4⋊C4C22×Q818yes—
1089C4⋊C4C22×Q818yes—
1090C4⋊C4C22×Q818yes—
1091C4⋊C4C22×Q818yes—
1092C4⋊C4C22×Q818yes—
1093C4⋊C4C22×Q818yes—
1094C22⋊C4—44no—
1095C22⋊C4—42no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4C22×Q814yes—
1102C22⋊C4C22×Q818yes—
1103C22⋊C4C22×Q814yes—
1104C42—24no—
1105C42—22no—
1106C42—24no—
1107C42—24no—
1108C42—22no—
1109C42—22no—
1110C42—42no—
1111C42—42no—
1112C42—44no—
1113C42—44no—
1114C42—42no—
1115C42—42no—
1116C42—44no—
1117C42—42no—
1118C42—44no—
1119C42—44no—
1120C42—42no—
1121C42—44no—
1122C42—44no—
1123C42—42no—
1124C42—44no—
1125C42—44no—
1126C42—44no—
1127C42—44no—
1128C42—44no—
1129C42—42no—
1130C42—42no—
1131C42C22×Q818yes—
1132C42C22×Q814yes—
1133C42C22×Q814yes—
1134C42C22×Q814yes—
1135C42C22×Q818yes—
1136C42C22×Q814yes—
1137C422−1+414yes—
1138C23—21no—
1139C23—21no—
1140C23—22no—
1141C23—22no—
1142C23C23×Q812yes—
1143C23C2611yescharacteristic
1144Q8—48no—
1145Q8—48no—
1146Q8—88no—
1147Q8—88no—
1148Q8—164no—
1149Q8—162no—
1150Q8—162no—
1151Q8—162no—
1152Q8—162no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—28no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—48no—
1218C2×C4—84no—
1219C2×C4—82no—
1220C2×C4—82no—
1221C2×C4C23×Q812yes—
1222C2×C4C23×Q814yes—
1223C2×C4C23×Q814yes—
1224C2×C4C23×Q814yes—
1225C2×C4C23×Q814yes—
1226C2×C4C23×Q814yes—
1227C2×C4C23×Q814yes—
1228C2×C4C23×Q812yes—
1229C2×C4C2×2−1+414yes—
1230C2×C4C2×2−1+412yes—
1231C2×C4#58512yes—
1232C22—22no—
1233C22—24no—
1234C22—42no—
1235C22—41no—
1236C22—41no—
1237C22C24×Q811yescharacteristic
1238C22C22×2−1+411yescharacteristic
1239C22C2×#58511yescharacteristic
1240C22H(7,𝔽2)12yes—
1241C222−1+612yes—
1242C4—22no—
1243C4—24no—
1244C4—24no—
1245C4—24no—
1246C4—24no—
1247C4—24no—
1248C4—24no—
1249C4—24no—
1250C4—44no—
1251C4—44no—
1252C4—42no—
1253C4—44no—
1254C4—44no—
1255C4—42no—
1256C4—42no—
1257C4—44no—
1258C4—44no—
1259C4—41no—
1260C4—44no—
1261C4—41no—
1262C4—42no—
1263C4—41no—
1264C4—42no—
1265C4—44no—
1266C4—41no—
1267C4#350214yes—
1268C2—42no—
1269C2C2×#350211yescharacteristic
1270C2#6285412yes—
1271C2#6287912yes—
1272C2#6288511yescharacteristic
1273C2#6289111yescharacteristic
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
5. #47819C2semidirect
6. #47817C2semidirect
7. #47774C2semidirect
8. #47727C2semidirect
9. #39754C2semidirect
10. #39750C2semidirect
11. #39625C2semidirect
12. #39621C2semidirect
13. #39182C2semidirect
14. #39181C2semidirect
15. #39177C2semidirect
16. #39176C2semidirect
251. #533Q8semidirect

Maximal subgroups

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

subgroupindex
#488462
#488422
#479712
#479672
#478192
#478172
#477742
#477272
#397542
#397502
#396252
#396212
#391822
#391812
#391772
#391762
#376422
#375652
#374282
#373112
#373082
#353372
#353042
#352832
#352822
#343732
#340742