Finite Group Databasebeta

← #8096553

Subgroups — #8096553

Order 512.

3941 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53147C212yesmaximal, complemented
2#53118C212yesmaximal
3#53037C212yesmaximal
4#52828C214yesmaximal, complemented
5#52679C214yesmaximal, complemented
6#52580C214yesmaximal, complemented
7#52305C211yesmaximal, characteristic, complemented
8#52290C212yesmaximal, complemented
9#46295C212yesmaximal, complemented
10#46179C214yesmaximal, complemented
11#46105C212yesmaximal
12#46057C212yesmaximal
13#46022C211yesmaximal, characteristic, complemented
14#46007C211yesmaximal, characteristic, complemented
15#46006C212yesmaximal, complemented
16#46006C211yesmaximal, characteristic, complemented
17#45928C214yesmaximal, complemented
18#45854C214yesmaximal, complemented
19#45809C212yesmaximal, complemented
20#45794C212yesmaximal, complemented
21#36556C212yesmaximal, complemented
22#36497C212yesmaximal, complemented
23#36454C211yesmaximal, characteristic
24#36454C211yesmaximal, characteristic
25#36421C212yesmaximal
26#36407C211yesmaximal, characteristic
27#35870C212yesmaximal, complemented
28#35869C212yesmaximal
29#35867C212yesmaximal, complemented
30#2866C2214yes—
31#2864C2214yes—
32#2864C2214yes—
33#2862C2211yescharacteristic
34#2862C2211yescharacteristic
35#2862C2212yes—
36#2861C2212yes—
37#2859C2212yes—
38#2859C2211yescharacteristic
39#2857C2212yes—
40#2855C2212yes—
41#2855C2212yes—
42#2845C2212yes—
43#2844C2214yes—
44#2844C2212yes—
45#2841C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2838C2214yes—
51#2838C2214yes—
52#2836C2214yes—
53#2836C2214yes—
54#2836C2214yes—
55#2831C2214yes—
56#2831C2214yes—
57#2822C2212yes—
58#2821C2214yes—
59#2817C2214yes—
60#2810C2211yescharacteristic
61#2809C2212yes—
62#2806C2212yes—
63#2806C2212yes—
64#2805C2212yes—
65#2805C2214yes—
66#2805C2212yes—
67#2798C2214yes—
68#2794C2214yes—
69#2794C2214yes—
70#2791C2214yes—
71#2791C2214yes—
72#2788C2214yes—
73#2783C2214yes—
74#2777C2214yes—
75#2774C2214yes—
76#2774C2214yes—
77#2774C2214yes—
78#2773C2214yes—
79#2773C2214yes—
80#2772C2214yes—
81#2768C2214yes—
82#2767C2212yes—
83#2767C2212yes—
84#2767C2212yes—
85#2766C2214yes—
86#2762C2214yes—
87#2755C2214yes—
88#2755C2214yes—
89#2754C2214yes—
90#2747C2214yes—
91#2744C2214yes—
92#2739C2214yes—
93#2734C2212yes—
94#2734C2214yes—
95#2729C2214yes—
96#2726C2211yescharacteristic
97#2726C2211yescharacteristic
98#2726C2211yescharacteristic
99#2721C2214yes—
100#2720C2214yes—
101#2719C2212yes—
102#2719C2212yes—
103#2719C2212yes—
104#2713C2214yes—
105#2713C2214yes—
106#2713C2214yes—
107#2704C2214yes—
108#2698C2214yes—
109#2690C2214yes—
110#2689C2214yes—
111#2677C2214yes—
112#2666C2214yes—
113#2655C2214yes—
114#2650C2214yes—
115#2647C2212yes—
116#2642C2212yes—
117#2640C2212yes—
118#2612C2214yes—
119#2605C2214yes—
120#2596C2214yes—
121#2596C2214yes—
122#2590C2214yes—
123#2590C2214yes—
124#2588C2214yes—
125#2588C2214yes—
126#2588C2214yes—
127#2585C2214yes—
128#2577C2214yes—
129#2575C2214yes—
130#2575C2214yes—
131#2574C2214yes—
132#2574C2214yes—
133#2570C2214yes—
134#2567C2212yes—
135#2567C2212yes—
136#2565C2212yes—
137#2565C2212yes—
138#2556C2214yes—
139#2552C2212yes—
140#2552C2211yescharacteristic
141#2551C2212yes—
142#2551C2211yescharacteristic
143#2551C2212yes—
144#2550C2212yes—
145#2550C2214yes—
146#2547C2211yescharacteristic
147#2547C2211yescharacteristic
148#2546C2212yes—
149#2546C2212yes—
150#2545C2212yes—
151#2545C2212yes—
152#2542C2211yescharacteristic
153#2542C2211yescharacteristic
154#2533C2214yes—
155#2533C2214yes—
156#2530C2214yes—
157#2529C2214yes—
158#2529C2214yes—
159#2528C2214yes—
160#2525C2214yes—
161#2524C2214yes—
162#2522C2214yes—
163#2520C2214yes—
164#2520C2214yes—
165#2520C2214yes—
166#2520C2214yes—
167#2517C2214yes—
168#2517C2214yes—
169#2514C2212yes—
170#2513C2212yes—
171#2512C2212yes—
172#2511C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2511C2212yes—
176#2511C2212yes—
177#2511C2212yes—
178#2511C2212yes—
179#2509C2214yes—
180#2508C2214yes—
181#2489C2212yes—
182#2489C2212yes—
183#2478C2214yes—
184#2475C2214yes—
185#2469C2214yes—
186#2462C2214yes—
187#2462C2214yes—
188#2454C2212yes—
189#2453C2212yes—
190#2453C2212yes—
191#2453C2212yes—
192#2452C2212yes—
193#2451C2212yes—
194#2451C2212yes—
195#2451C2212yes—
196#2451C2214yes—
197#2451C2212yes—
198#2451C2212yes—
199#2448C2212yes—
200#2448C2212yes—
201#2447C2212yes—
202#2447C2212yes—
203#2446C2214yes—
204#2446C2212yes—
205#2446C2212yes—
206#2446C2212yes—
207#2446C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2441C2212yes—
211#2439C2212yes—
212#2421C2212yes—
213#2421C2212yes—
214#2402C2212yes—
215#2402C2212yes—
216#2402C2214yes—
217#2402C2212yes—
218#2399C2214yes—
219#2396C2214yes—
220#2382C2212yes—
221#2382C2214yes—
222#2382C2212yes—
223#2382C2212yes—
224#2378C2214yes—
225#2378C2214yes—
226#2370C2212yes—
227#2370C2212yes—
228#2369C2212yes—
229#2367C2212yes—
230#2367C2212yes—
231#2365C2211yescharacteristic
232#2365C2212yes—
233#2365C2212yes—
234#2365C2211yescharacteristic
235#2365C2212yes—
236#2365C2211yescharacteristic
237#2365C2211yescharacteristic
238#2356C2212yes—
239#2355C2212yes—
240#2355C2212yes—
241#2355C2212yes—
242#2354C2211yescharacteristic
243#2354C2211yescharacteristic
244C4×C4⋊Q8C2214yes—
245C4×#125C2212yes—
246C4×#125C2211yescharacteristic
247C4×#125C2214yes—
248C4×#125C2212yes—
249C4×#125C2211yescharacteristic
250C4×#125C2211yescharacteristic
251C4×#125C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254#2298C2214yes—
255#2296C2212yes—
256#2276C2212yes—
257C42×Q8C2212yes—
258C42×D4C2211yescharacteristic
259C2×C4⋊Q8C2314yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2311yescharacteristic
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#125C2311yescharacteristic
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2311yescharacteristic
300C2×#117C2312yes—
301C2×#117C2312yes—
302C22×C42C2312yes—
303#401C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2312yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2311yescharacteristic
469#389C2311yescharacteristic
470#389C2311yescharacteristic
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2311yescharacteristic
476#389C2311yescharacteristic
477#389C2312yes—
478#389C2311yescharacteristic
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2314yes—
544#387C2312yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
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#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#384C2314yes—
623#384C2311yescharacteristic
624#384C2312yes—
625#384C2311yescharacteristic
626#384C2312yes—
627#384C2312yes—
628#384C2312yes—
629#383C2314yes—
630#383C2314yes—
631#382C2312yes—
632#382C2311yescharacteristic
633#382C2312yes—
634#382C2311yescharacteristic
635#382C2314yes—
636#382C2312yes—
637#382C2311yescharacteristic
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#382C2312yes—
642#382C2314yes—
643#382C2312yes—
644#382C2314yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#381C2314yes—
650#381C2314yes—
651#380C2312yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706#376C2314yes—
707#376C2314yes—
708#376C2312yes—
709C43C2312yes—
710C43C2311yescharacteristic
711C43C2314yes—
712C22×Q8C2412yes—
713C22×Q8C2412yes—
714C22×Q8C2412yes—
715C22×Q8C2412yes—
716C22×Q8C2414yes—
717C22×Q8C2414yes—
718C22×D4C2411yescharacteristic
719C23×C4C2412yes—
720C23×C4C2412yes—
721C23×C4C2412yes—
722C4⋊Q8—42no—
723C4⋊Q8—42no—
724C4⋊Q8—44no—
725C4⋊Q8—44no—
726C4⋊Q8—42no—
727C4⋊Q8—42no—
728C4⋊Q8—44no—
729C4⋊Q8—44no—
730C4⋊Q8—48no—
731C4⋊Q8—82no—
732C4⋊Q8—84no—
733#126—84no—
734#125—24no—
735#125—28no—
736#125—28no—
737#125—24no—
738#125—44no—
739#125—44no—
740#125—42no—
741#125—44no—
742#125—44no—
743#125—84no—
744#124—44no—
745#124—44no—
746C22⋊Q8—28no—
747C22⋊Q8—48no—
748C22⋊Q8—44no—
749C22⋊Q8—82no—
750C22⋊Q8—82no—
751C4×Q8—28no—
752C4×Q8—28no—
753C4×Q8—44no—
754C4×Q8—44no—
755C4×Q8—44no—
756C4×Q8—44no—
757C4×Q8—82no—
758C4×Q8—82no—
759C4×Q8—84no—
760C4×D4—24no—
761C4×D4—42no—
762C4×D4—42no—
763#117—28no—
764#117—82no—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C42—82no—
866C2×C42C2414yes—
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2411yescharacteristic
879C2×C42C2412yes—
880C2×C42C2411yescharacteristic
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985C24C2512yes—
986C2×Q8—24no—
987C2×Q8—24no—
988C2×Q8—24no—
989C2×Q8—24no—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—42no—
995C2×Q8—42no—
996C2×Q8—44no—
997C2×Q8—42no—
998C2×Q8—42no—
999C2×Q8—44no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—44no—
1003C2×Q8—44no—
1004C2×D4—22no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—24no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4C2512yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C4⋊C4—24no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—22no—
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—22no—
1072C4⋊C4—28no—
1073C4⋊C4—22no—
1074C4⋊C4—24no—
1075C4⋊C4—41no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—41no—
1125C4⋊C4—42no—
1126C4⋊C42−1+414yes—
1127C4⋊C42−1+414yes—
1128C4⋊C42−1+414yes—
1129C22⋊C4—28no—
1130C22⋊C4—24no—
1131C22⋊C4—28no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C42—28no—
1145C42—22no—
1146C42—24no—
1147C42—28no—
1148C42—24no—
1149C42—28no—
1150C42—24no—
1151C42—24no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—22no—
1156C42—24no—
1157C42—24no—
1158C42—24no—
1159C42—24no—
1160C42—22no—
1161C42—41no—
1162C42—42no—
1163C42—42no—
1164C42—42no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—42no—
1173C42—42no—
1174C42—44no—
1175C42—44no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23C2611yescharacteristic
1184Q8—48no—
1185Q8—48no—
1186Q8—84no—
1187Q8—84no—
1188Q8—88no—
1189Q8—164no—
1190D4—44no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—24no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—48no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4C2×2−1+414yes—
1270C2×C4C2×2−1+414yes—
1271C2×C4C2×2−1+414yes—
1272C2×C4C2×2−1+412yes—
1273C2×C4C2×2−1+412yes—
1274C2×C4C2×2−1+412yes—
1275C2×C4#58512yes—
1276C2×C4#58512yes—
1277C2×C4#58512yes—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22C22×2−1+411yescharacteristic
1286C22C22×2−1+411yescharacteristic
1287C22C22×2−1+411yescharacteristic
1288C22C2×#58511yescharacteristic
1289C22C2×#58511yescharacteristic
1290C22C2×#58511yescharacteristic
1291C22H(7,𝔽2)11yescharacteristic
1292C4—24no—
1293C4—24no—
1294C4—22no—
1295C4—24no—
1296C4—22no—
1297C4—22no—
1298C4—42no—
1299C4—41no—
1300C4—41no—
1301C4—42no—
1302C4—44no—
1303C4—41no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—44no—
1309C4—44no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—44no—
1318C4—42no—
1319C4#353114yes—
1320C2—82no—
1321C2C2×#353111yescharacteristic
1322C2#6294511yescharacteristic
1323C2#6296211yescharacteristic
1324C2#6296511yescharacteristic
1325C2#6303211yescharacteristic
1326C2#6303211yescharacteristic
1327C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53147C2semidirect
4. #52828C2semidirect
5. #52679C2semidirect
6. #52580C2semidirect
7. #52305C2semidirect
8. #52290C2semidirect
9. #46295C2semidirect
10. #46179C2semidirect
13. #46022C2semidirect
14. #46007C2semidirect
15. #46006C2semidirect
16. #46006C2semidirect
17. #45928C2semidirect
18. #45854C2semidirect
19. #45809C2semidirect
20. #45794C2semidirect
21. #36556C2semidirect
22. #36497C2semidirect
27. #35870C2semidirect
29. #35867C2semidirect

Maximal subgroups

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

subgroupindex
#531472
#531182
#530372
#528282
#526792
#525802
#523052
#522902
#462952
#461792
#461052
#460572
#460222
#460072
#460062
#459282
#458542
#458092
#457942
#365562
#364972
#364542
#364212
#364072
#358702
#358692
#358672