Finite Group Databasebeta

← #7652247

Subgroups — #7652247

Order 512.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42973C211yesmaximal, characteristic
2#42933C211yesmaximal, characteristic
3#42822C212yesmaximal, complemented
4#42820C212yesmaximal, complemented
5#42818C211yesmaximal, characteristic
6#42817C211yesmaximal, characteristic
7#42008C214yesmaximal
8#42006C214yesmaximal
9#42004C214yesmaximal, complemented
10#42002C214yesmaximal, complemented
11#39982C212yesmaximal
12#39978C212yesmaximal, complemented
13#39968C214yesmaximal
14#39625C212yesmaximal, complemented
15#39624C212yesmaximal
16#39621C214yesmaximal, complemented
17#38456C214yesmaximal
18#38451C214yesmaximal, complemented
19#35583C212yesmaximal, complemented
20#35582C212yesmaximal, complemented
21#35578C212yesmaximal
22#35283C211yesmaximal, characteristic
23#35199C212yesmaximal, complemented
24#34950C212yesmaximal, complemented
25#34882C211yesmaximal, characteristic
26#34262C212yesmaximal
27#34254C211yesmaximal, characteristic
28C2×#519C2211yescharacteristic
29#2868C2211yescharacteristic
30#2863C2214yes—
31#2862C2211yescharacteristic
32#2862C2214yes—
33#2857C2212yes—
34#2845C2214yes—
35#2844C2212yes—
36#2843C2212yes—
37#2843C2214yes—
38#2841C2212yes—
39#2841C2212yes—
40#2811C2214yes—
41#2811C2212yes—
42#2809C2212yes—
43#2807C2212yes—
44#2806C2214yes—
45#2806C2214yes—
46#2806C2214yes—
47#2806C2214yes—
48#2806C2214yes—
49#2806C2214yes—
50#2802C2214yes—
51#2799C2212yes—
52#2799C2214yes—
53#2799C2212yes—
54#2792C2214yes—
55#2792C2214yes—
56#2791C2214yes—
57#2788C2214yes—
58#2774C2214yes—
59#2768C2214yes—
60#2763C2212yes—
61#2755C2214yes—
62#2755C2214yes—
63#2734C2214yes—
64#2734C2214yes—
65#2734C2214yes—
66#2729C2214yes—
67#2726C2214yes—
68#2720C2214yes—
69#2713C2214yes—
70#2713C2214yes—
71#2713C2214yes—
72#2704C2214yes—
73#2677C2212yes—
74#2677C2212yes—
75#2677C2214yes—
76#2667C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2665C2214yes—
86#2660C2214yes—
87#2660C2214yes—
88#2660C2214yes—
89#2659C2214yes—
90#2647C2212yes—
91#2628C2211yescharacteristic
92#2628C2211yescharacteristic
93#2612C2214yes—
94#2612C2214yes—
95#2612C2214yes—
96#2612C2212yes—
97#2607C2212yes—
98#2607C2212yes—
99#2606C2214yes—
100#2606C2214yes—
101#2606C2214yes—
102#2605C2214yes—
103#2605C2214yes—
104#2605C2214yes—
105#2605C2214yes—
106#2590C2214yes—
107#2590C2214yes—
108#2589C2214yes—
109#2588C2214yes—
110#2586C2214yes—
111#2586C2214yes—
112#2586C2214yes—
113#2586C2214yes—
114#2586C2212yes—
115#2585C2212yes—
116#2585C2214yes—
117#2584C2212yes—
118#2582C2212yes—
119#2582C2212yes—
120#2582C2212yes—
121#2581C2212yes—
122#2574C2212yes—
123#2570C2212yes—
124#2568C2212yes—
125#2567C2212yes—
126#2567C2212yes—
127#2567C2212yes—
128#2565C2212yes—
129#2556C2214yes—
130#2556C2212yes—
131#2552C2212yes—
132#2551C2214yes—
133#2551C2212yes—
134#2551C2212yes—
135#2551C2212yes—
136#2551C2212yes—
137#2551C2212yes—
138#2550C2214yes—
139#2550C2214yes—
140#2550C2214yes—
141#2550C2214yes—
142#2550C2214yes—
143#2550C2212yes—
144#2550C2212yes—
145#2549C2214yes—
146#2549C2214yes—
147#2546C2212yes—
148#2546C2212yes—
149#2522C2212yes—
150#2520C2214yes—
151#2520C2212yes—
152#2520C2214yes—
153#2511C2214yes—
154#2509C2212yes—
155#2508C2212yes—
156#2508C2212yes—
157#2507C2214yes—
158#2507C2212yes—
159#2507C2212yes—
160#2507C2212yes—
161#2506C2212yes—
162#2506C2212yes—
163#2492C2214yes—
164#2465C2214yes—
165#2465C2212yes—
166#2462C2214yes—
167#2462C2214yes—
168#2462C2214yes—
169#2462C2212yes—
170#2453C2212yes—
171#2451C2214yes—
172#2451C2214yes—
173#2451C2214yes—
174#2451C2214yes—
175#2451C2212yes—
176#2451C2212yes—
177#2451C2214yes—
178#2451C2212yes—
179#2451C2212yes—
180#2451C2212yes—
181#2451C2212yes—
182#2451C2212yes—
183#2446C2214yes—
184#2446C2214yes—
185#2441C2212yes—
186#2440C2212yes—
187#2440C2212yes—
188#2439C2212yes—
189#2429C2214yes—
190#2423C2214yes—
191#2399C2214yes—
192#2399C2214yes—
193#2399C2211yescharacteristic
194#2399C2211yescharacteristic
195#2396C2211yescharacteristic
196#2396C2211yescharacteristic
197#2356C2214yes—
198#2356C2214yes—
199#2356C2212yes—
200#2355C2214yes—
201#2355C2214yes—
202#2355C2212yes—
203#2351C2212yes—
204Q8×C4⋊C4C2212yes—
205#2347C2214yes—
206#2347C2212yes—
207#2346C2214yes—
208#2346C2212yes—
209#2343C2214yes—
210#2343C2214yes—
211Q8×C22⋊C4C2212yes—
212Q8×C22⋊C4C2212yes—
213#2331C2214yes—
214#2331C2214yes—
215#2331C2211yescharacteristic
216#2331C2212yes—
217#2331C2211yescharacteristic
218#2330C2214yes—
219#2330C2212yes—
220#2329C2214yes—
221#2320C2214yes—
222#2320C2212yes—
223#2320C2212yes—
224#2320C2212yes—
225#2317C2211yescharacteristic
226#2314C2214yes—
227#2314C2212yes—
228#2310C2211yescharacteristic
229C4×C4⋊Q8C2214yes—
230C4×C4⋊Q8C2212yes—
231C4×C4⋊Q8C2212yes—
232C4×C4⋊Q8C2212yes—
233C4×#125C2212yes—
234C4×C22⋊Q8C2212yes—
235#2298C2214yes—
236#2298C2212yes—
237#2296C2211yescharacteristic
238#2295C2212yes—
239#2295C2214yes—
240#2295C2214yes—
241#2295C2212yes—
242#2295C2211yescharacteristic
243#2295C2212yes—
244#2295C2212yes—
245C2×#391C2211yescharacteristic
246#2276C2212yes—
247#2274C2211yescharacteristic
248C42×Q8C2211yescharacteristic
249C42×Q8C2212yes—
250C4×#117C2211yescharacteristic
251C23×Q8C2311yescharacteristic
252C2×C4⋊Q8C2314yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2312yes—
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×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274#519Q8116yescomplemented
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2314yes—
284C2×C4×Q8C2314yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2314yes—
289C2×#117C2311yescharacteristic
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2314yes—
293C2×#117C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C42C2311yescharacteristic
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2311yescharacteristic
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2311yescharacteristic
307#400C2314yes—
308#400C2312yes—
309#400C2314yes—
310#400C2312yes—
311#400C2314yes—
312#400C2314yes—
313#399C2311yescharacteristic
314#399C2312yes—
315#399C2314yes—
316#399C2311yescharacteristic
317#399C2312yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2312yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2312yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
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#398C2312yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#396C2312yes—
365#396C2314yes—
366#396C2314yes—
367#396C2312yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2312yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2311yescharacteristic
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2312yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2312yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2312yes—
394#395C2314yes—
395#395C2314yes—
396#395C2311yescharacteristic
397#395C2314yes—
398#395C2312yes—
399#395C2314yes—
400#395C2312yes—
401#395C2314yes—
402#395C2314yes—
403#393C2311yescharacteristic
404#393C2312yes—
405#393C2314yes—
406#393C2311yescharacteristic
407#393C2312yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2312yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#388C2312yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2312yes—
555#387C2314yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#385C2312yes—
588#385C2312yes—
589#385C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2312yes—
594#384C2312yes—
595#384C2312yes—
596#384C2312yes—
597#384C2314yes—
598#384C2312yes—
599#384C2314yes—
600#384C2312yes—
601#384C2312yes—
602#384C2314yes—
603#383C2314yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#383C2314yes—
608#382C2312yes—
609#382C2311yescharacteristic
610#382C2311yescharacteristic
611#382C2312yes—
612#382C2312yes—
613#382C2314yes—
614#382C2312yes—
615#382C2314yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2314yes—
620#382C2314yes—
621#382C2314yes—
622#381C2312yes—
623#381C2312yes—
624#380C2314yes—
625#380C2314yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2314yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677#376C2311yescharacteristic
678#376C2311yescharacteristic
679#376C2312yes—
680#376C2314yes—
681#376C2314yes—
682#376C2314yes—
683#376C2314yes—
684#376C2314yes—
685#376C2314yes—
686C2×#95C2314yes—
687C43C2311yescharacteristic
688C43C2311yescharacteristic
689C43C2312yes—
690C43C2314yes—
691C22×Q8—42no—
692C22×Q8—42no—
693C22×Q8C2×Q818yes—
694C22×Q8C2411yescharacteristic
695C22×Q8C2412yes—
696C22×Q8C2414yes—
697C22×Q8C2412yes—
698C22×Q8C2414yes—
699C22×Q8C2414yes—
700C22×Q8C2411yescharacteristic
701C22×Q8C2414yes—
702C22×Q8C2412yes—
703C22×Q8C2412yes—
704C22×Q8C2412yes—
705C23×C4C2411yescharacteristic
706C23×C4C2412yes—
707C23×C4C2412yes—
708C23×C4C2412yes—
709C4⋊Q8—216no—
710C4⋊Q8—44no—
711C4⋊Q8—42no—
712C4⋊Q8—42no—
713C4⋊Q8—44no—
714C4⋊Q8—44no—
715C4⋊Q8—44no—
716C4⋊Q8—84no—
717C4⋊Q8—84no—
718C4⋊Q8—84no—
719C4⋊Q8—84no—
720C4⋊Q8—84no—
721C4⋊Q8—84no—
722#125—28no—
723#125—44no—
724#125—84no—
725#125—84no—
726#125—84no—
727C22⋊Q8—28no—
728C22⋊Q8—84no—
729C22⋊Q8—84no—
730C22⋊Q8—84no—
731C4×Q8—28no—
732C4×Q8—44no—
733C4×Q8—42no—
734C4×Q8—42no—
735C4×Q8—44no—
736C4×Q8—44no—
737C4×Q8—44no—
738C4×Q8—44no—
739C4×Q8—84no—
740C4×Q8—84no—
741C4×Q8—84no—
742C4×Q8C2×Q8116yes—
743C4×Q8C2×Q8116yes—
744C4×Q8C2×Q8132yes—
745#117—42no—
746#117—42no—
747#117C2×Q818yes—
748#117C2×Q818yes—
749#117C2×Q8132yes—
750C2×C4⋊C4—42no—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C42—42no—
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2411yescharacteristic
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2411yescharacteristic
872C2×C42C2414yes—
873C2×C42C2411yescharacteristic
874C2×C42C2414yes—
875C2×C42C2412yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2414yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2414yes—
892#95C2412yes—
893#95C2414yes—
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#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2412yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2411yescharacteristic
921#95C2411yescharacteristic
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2412yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2414yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2411yescharacteristic
943#95C2411yescharacteristic
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960C24C2511yescharacteristic
961C2×Q8—24no—
962C2×Q8—24no—
963C2×Q8—28no—
964C2×Q8—28no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—41no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—41no—
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×Q8—44no—
977C2×Q8—44no—
978C2×Q8—44no—
979C2×Q8—42no—
980C2×Q8—42no—
981C2×Q8—44no—
982C2×Q8—42no—
983C2×Q8—42no—
984C2×Q8—44no—
985C2×Q8—44no—
986C2×Q8—44no—
987C2×Q8—44no—
988C2×Q8—416no—
989C2×Q8C22×Q818yes—
990C2×Q8C22×Q818yes—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—24no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4C22×Q814yes—
1001C22×C4C22×Q818yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C22×C4C2512yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2511yescharacteristic
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—42no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—41no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—41no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4C22×Q818yes—
1102C4⋊C4C22×Q8116yes—
1103C4⋊C4C22×Q8116yes—
1104C4⋊C4C22×Q818yes—
1105C4⋊C42−1+418yes—
1106C22⋊C4—24no—
1107C22⋊C4—24no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—44no—
1113C22⋊C4—42no—
1114C22⋊C4—44no—
1115C22⋊C4C22×Q818yes—
1116C22⋊C4C22×Q818yes—
1117C42—24no—
1118C42—24no—
1119C42—24no—
1120C42—24no—
1121C42—28no—
1122C42—22no—
1123C42—22no—
1124C42—22no—
1125C42—22no—
1126C42—24no—
1127C42—24no—
1128C42—24no—
1129C42—24no—
1130C42—42no—
1131C42—42no—
1132C42—44no—
1133C42—44no—
1134C42—44no—
1135C42—44no—
1136C42—42no—
1137C42—42no—
1138C42—44no—
1139C42—44no—
1140C42—42no—
1141C42—44no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C42—44no—
1146C42—42no—
1147C42C22×Q8116yes—
1148C42C22×Q818yes—
1149C42C22×Q8116yes—
1150C42C22×Q814yes—
1151C42C22×Q814yes—
1152C23—22no—
1153C23—21no—
1154C23—21no—
1155C23—22no—
1156C23C23×Q812yes—
1157C23C2611yescharacteristic
1158Q8—216no—
1159Q8—48no—
1160Q8—44no—
1161Q8—88no—
1162Q8—84no—
1163Q8—88no—
1164Q8—88no—
1165Q8—82no—
1166Q8—164no—
1167Q8—162no—
1168Q8—162no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—28no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—48no—
1234C2×C4—84no—
1235C2×C4—162no—
1236C2×C4C23×Q814yes—
1237C2×C4C23×Q818yes—
1238C2×C4C23×Q814yes—
1239C2×C4C23×Q812yes—
1240C2×C4C23×Q818yes—
1241C2×C4C23×Q812yes—
1242C2×C4C2×2−1+414yes—
1243C2×C4C2×2−1+414yes—
1244C2×C4C2×2−1+414yes—
1245C2×C4#58512yes—
1246C2×C4#58512yes—
1247C22—24no—
1248C22—22no—
1249C22—41no—
1250C22—41no—
1251C22—42no—
1252C22C24×Q811yescharacteristic
1253C22C22×2−1+412yes—
1254C22C2×#58511yescharacteristic
1255C22C2×#58511yescharacteristic
1256C22H(7,𝔽2)12yes—
1257C4—24no—
1258C4—24no—
1259C4—28no—
1260C4—24no—
1261C4—22no—
1262C4—28no—
1263C4—24no—
1264C4—24no—
1265C4—41no—
1266C4—42no—
1267C4—41no—
1268C4—44no—
1269C4—41no—
1270C4—42no—
1271C4—44no—
1272C4—42no—
1273C4—44no—
1274C4—41no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—44no—
1280C4—44no—
1281C4—44no—
1282C4#345814yes—
1283C2—42no—
1284C2C2×#345811yescharacteristic
1285C2#6283711yescharacteristic
1286C2#6288511yescharacteristic
1287C2#6295112yes—
1288C2Q8×2−1+412yes—
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
3. #42822C2semidirect
4. #42820C2semidirect
9. #42004C2semidirect
10. #42002C2semidirect
12. #39978C2semidirect
14. #39625C2semidirect
16. #39621C2semidirect
18. #38451C2semidirect
19. #35583C2semidirect
20. #35582C2semidirect
23. #35199C2semidirect
24. #34950C2semidirect
274. #519Q8semidirect

Maximal subgroups

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

subgroupindex
#429732
#429332
#428222
#428202
#428182
#428172
#420082
#420062
#420042
#420022
#399822
#399782
#399682
#396252
#396242
#396212
#384562
#384512
#355832
#355822
#355782
#352832
#351992
#349502
#348822
#342622
#342542