Finite Group Databasebeta

← #8096550

Subgroups — #8096550

Order 512.

4233 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53126C212yesmaximal
2#53118C212yesmaximal, complemented
3#52998C212yesmaximal, complemented
4#52651C214yesmaximal, complemented
5#52575C214yesmaximal, complemented
6#52571C214yesmaximal, complemented
7#52305C211yesmaximal, characteristic, complemented
8#52162C212yesmaximal, complemented
9#46286C212yesmaximal, complemented
10#46173C214yesmaximal, complemented
11#46113C212yesmaximal, complemented
12#46057C212yesmaximal, complemented
13#46013C211yesmaximal, characteristic
14#46006C212yesmaximal, complemented
15#46006C211yesmaximal, characteristic, complemented
16#45998C211yesmaximal, characteristic
17#45964C212yesmaximal, complemented
18#45963C212yesmaximal, complemented
19#45927C214yesmaximal, complemented
20#45763C214yesmaximal, complemented
21#36497C211yesmaximal, characteristic, complemented
22#36454C212yesmaximal, complemented
23#36313C211yesmaximal, characteristic, complemented
24#36300C211yesmaximal, characteristic
25#36253C212yesmaximal
26#36132C212yesmaximal, complemented
27#35869C212yesmaximal, complemented
28#35869C212yesmaximal, complemented
29#35867C212yesmaximal, complemented
30C2×#563C2212yes—
31C2×#533C2214yes—
32#2864C2212yes—
33#2863C2212yes—
34#2862C2212yes—
35#2862C2211yescharacteristic
36#2861C2212yes—
37#2860C2212yes—
38#2859C2212yes—
39#2859C2211yescharacteristic
40#2858C2211yescharacteristic
41#2855C2214yes—
42#2853C2214yes—
43#2851C2214yes—
44#2844C2214yes—
45#2844C2212yes—
46#2838C2214yes—
47#2838C2214yes—
48#2838C2214yes—
49#2836C2214yes—
50#2835C2214yes—
51#2832C2214yes—
52#2831C2214yes—
53#2831C2214yes—
54#2831C2214yes—
55#2830C2214yes—
56#2827C2214yes—
57#2821C2214yes—
58#2820C2212yes—
59#2820C2212yes—
60#2817C2214yes—
61#2814C2214yes—
62#2810C2211yescharacteristic
63#2808C2212yes—
64#2805C2214yes—
65#2805C2212yes—
66#2786C2214yes—
67#2783C2214yes—
68#2777C2214yes—
69#2775C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2774C2214yes—
73#2772C2214yes—
74#2771C2214yes—
75#2768C2214yes—
76#2767C2212yes—
77#2767C2212yes—
78#2767C2212yes—
79#2765C2214yes—
80#2761C2214yes—
81#2754C2214yes—
82#2751C2214yes—
83#2744C2214yes—
84#2734C2214yes—
85#2734C2212yes—
86#2732C2212yes—
87#2729C2214yes—
88#2729C2214yes—
89#2727C2212yes—
90#2726C2211yescharacteristic
91#2726C2211yescharacteristic
92#2726C2211yescharacteristic
93#2725C2214yes—
94#2725C2214yes—
95#2723C2214yes—
96#2720C2214yes—
97#2719C2212yes—
98#2719C2212yes—
99#2719C2212yes—
100#2716C2214yes—
101#2713C2214yes—
102#2713C2214yes—
103#2713C2214yes—
104#2704C2214yes—
105#2700C2214yes—
106#2698C2214yes—
107#2692C2214yes—
108#2689C2214yes—
109#2689C2214yes—
110#2687C2214yes—
111#2683C2212yes—
112#2677C2214yes—
113#2674C2214yes—
114#2666C2214yes—
115#2650C2214yes—
116#2650C2214yes—
117#2647C2212yes—
118#2640C2212yes—
119#2640C2212yes—
120#2612C2214yes—
121#2605C2214yes—
122#2597C2214yes—
123#2596C2214yes—
124#2596C2214yes—
125#2590C2214yes—
126#2588C2214yes—
127#2578C2214yes—
128#2575C2214yes—
129#2575C2214yes—
130#2574C2214yes—
131#2574C2214yes—
132#2570C2212yes—
133#2568C2211yescharacteristic
134#2567C2212yes—
135#2567C2212yes—
136#2567C2211yescharacteristic
137#2566C2212yes—
138#2552C2211yescharacteristic
139#2551C2212yes—
140#2551C2212yes—
141#2551C2212yes—
142#2551C2211yescharacteristic
143#2550C2212yes—
144#2550C2212yes—
145#2548C2211yescharacteristic
146#2547C2212yes—
147#2546C2211yescharacteristic
148#2545C2212yes—
149#2545C2212yes—
150#2544C2212yes—
151#2542C2212yes—
152#2530C2214yes—
153#2530C2214yes—
154#2529C2214yes—
155#2529C2214yes—
156#2528C2214yes—
157#2526C2214yes—
158#2524C2214yes—
159#2521C2214yes—
160#2520C2214yes—
161#2518C2214yes—
162#2517C2214yes—
163#2517C2214yes—
164#2514C2212yes—
165#2514C2212yes—
166#2513C2212yes—
167#2513C2212yes—
168#2512C2212yes—
169#2512C2212yes—
170#2512C2212yes—
171#2511C2212yes—
172#2511C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2511C2212yes—
176#2489C2214yes—
177#2478C2214yes—
178#2478C2214yes—
179#2474C2214yes—
180#2470C2214yes—
181#2469C2214yes—
182#2469C2214yes—
183#2465C2214yes—
184#2465C2214yes—
185#2465C2214yes—
186#2465C2214yes—
187#2462C2214yes—
188#2460C2214yes—
189#2454C2212yes—
190#2453C2212yes—
191#2453C2212yes—
192#2453C2212yes—
193#2452C2212yes—
194#2452C2212yes—
195#2452C2212yes—
196#2452C2212yes—
197#2451C2214yes—
198#2451C2212yes—
199#2451C2212yes—
200#2451C2212yes—
201#2451C2212yes—
202#2448C2212yes—
203#2448C2212yes—
204#2448C2212yes—
205#2447C2212yes—
206#2447C2212yes—
207#2447C2212yes—
208#2446C2214yes—
209#2446C2212yes—
210#2446C2212yes—
211#2446C2212yes—
212#2445C2212yes—
213#2439C2214yes—
214#2439C2214yes—
215#2421C2214yes—
216#2402C2212yes—
217#2402C2212yes—
218#2402C2212yes—
219#2399C2214yes—
220#2396C2214yes—
221#2396C2214yes—
222#2383C2214yes—
223#2382C2212yes—
224#2382C2214yes—
225#2379C2212yes—
226#2378C2214yes—
227#2370C2212yes—
228#2369C2211yescharacteristic
229#2367C2212yes—
230#2367C2212yes—
231#2367C2212yes—
232#2366C2211yescharacteristic
233#2365C2212yes—
234#2365C2212yes—
235#2365C2211yescharacteristic
236#2365C2212yes—
237#2365C2212yes—
238#2365C2211yescharacteristic
239#2356C2212yes—
240#2355C2212yes—
241#2355C2211yescharacteristic
242#2355C2211yescharacteristic
243#2354C2212yes—
244#2354C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×#125C2211yescharacteristic
249C4×#125C2212yes—
250C4×#125C2211yescharacteristic
251C4×#125C2211yescharacteristic
252C4×C22⋊Q8C2214yes—
253#2295C2212yes—
254#2293C2212yes—
255#2290C2214yes—
256#2276C2212yes—
257C42×Q8C2211yescharacteristic
258C42×D4C2212yes—
259#563—48no—
260#533—416no—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×#127C2311yescharacteristic
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#125C2311yescharacteristic
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2311yescharacteristic
280C2×#125C2311yescharacteristic
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×#117C2314yes—
312C2×#117C2314yes—
313C22×C42C2314yes—
314#401C2314yes—
315#400C2312yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2312yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2312yes—
356#398C2312yes—
357#398C2312yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#395C2314yes—
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#395C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#389C2311yescharacteristic
482#389C2312yes—
483#389C2311yescharacteristic
484#389C2311yescharacteristic
485#389C2311yescharacteristic
486#389C2311yescharacteristic
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2311yescharacteristic
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
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#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#384C2312yes—
632#384C2312yes—
633#384C2312yes—
634#384C2311yescharacteristic
635#384C2312yes—
636#384C2311yescharacteristic
637#383C2314yes—
638#383C2314yes—
639#382C2311yescharacteristic
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2311yescharacteristic
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2314yes—
650#382C2314yes—
651#382C2312yes—
652#382C2312yes—
653#382C2314yes—
654#382C2312yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708#376C2314yes—
709#376C2314yes—
710#376C2312yes—
711C43C2311yescharacteristic
712C43C2312yes—
713C43C2312yes—
714C22×Q8C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2414yes—
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×D4C2412yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C23×C4C2414yes—
725C23×C4C2414yes—
726C23×C4C2414yes—
727C4⋊Q8—44no—
728C4⋊Q8—44no—
729C4⋊Q8—44no—
730C4⋊Q8—42no—
731C4⋊Q8—42no—
732C4⋊Q8—44no—
733C4⋊Q8—44no—
734C4⋊Q8—42no—
735C4⋊Q8—48no—
736C4⋊Q8—48no—
737C4⋊Q8—48no—
738#127—42no—
739#126—48no—
740#126—48no—
741#126—48no—
742#125—28no—
743#125—24no—
744#125—24no—
745#125—28no—
746#125—44no—
747#125—42no—
748#125—48no—
749#125—44no—
750#125—44no—
751#124—44no—
752#124—44no—
753#124—44no—
754#124—44no—
755#124—44no—
756#123—48no—
757C22⋊Q8—216no—
758C22⋊Q8—48no—
759C22⋊Q8—48no—
760C22⋊Q8—48no—
761C22⋊Q8—48no—
762C22⋊Q8—48no—
763C4×Q8—28no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—48no—
767C4×Q8—48no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—42no—
771C4×Q8—42no—
772C4×Q8—48no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—44no—
776C4×D4—44no—
777#117—48no—
778#117—48no—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C42—48no—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996C24C2514yes—
997C2×Q8—24no—
998C2×Q8—28no—
999C2×Q8—22no—
1000C2×Q8—24no—
1001C2×Q8—22no—
1002C2×Q8—24no—
1003C2×Q8—24no—
1004C2×Q8—22no—
1005C2×Q8—44no—
1006C2×Q8—44no—
1007C2×Q8—44no—
1008C2×Q8—42no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—42no—
1014C2×Q8—44no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8—42no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—24no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C2×D4—42no—
1025C2×D4—42no—
1026C2×D4—42no—
1027C22×C4—28no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2514yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—22no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—22no—
1088C4⋊C4—24no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—24no—
1095C4⋊C4—22no—
1096C4⋊C4—41no—
1097C4⋊C4—41no—
1098C4⋊C4—42no—
1099C4⋊C4—41no—
1100C4⋊C4—41no—
1101C4⋊C4—41no—
1102C4⋊C4—41no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4H(5,𝔽2)14yes—
1142C4⋊C42−1+414yes—
1143C4⋊C42−1+414yes—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C42—24no—
1170C42—28no—
1171C42—24no—
1172C42—22no—
1173C42—24no—
1174C42—24no—
1175C42—22no—
1176C42—24no—
1177C42—24no—
1178C42—28no—
1179C42—22no—
1180C42—24no—
1181C42—24no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—22no—
1186C42—22no—
1187C42—22no—
1188C42—24no—
1189C42—44no—
1190C42—44no—
1191C42—41no—
1192C42—42no—
1193C42—44no—
1194C42—44no—
1195C42—42no—
1196C42—42no—
1197C42—44no—
1198C42—44no—
1199C42—42no—
1200C42—44no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23C2611yescharacteristic
1209Q8—44no—
1210Q8—48no—
1211Q8—88no—
1212Q8—84no—
1213Q8—88no—
1214Q8—88no—
1215Q8—162no—
1216D4—48no—
1217D4—84no—
1218D4—162no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—416no—
1295C2×C4—88no—
1296C2×C4—88no—
1297C2×C4C2×H(5,𝔽2)12yes—
1298C2×C4C2×H(5,𝔽2)14yes—
1299C2×C4C2×2−1+414yes—
1300C2×C4C2×2−1+412yes—
1301C2×C4C2×2−1+414yes—
1302C2×C4C2×2−1+412yes—
1303C2×C4#58512yes—
1304C2×C4#58512yes—
1305C2×C4#58512yes—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22C22×H(5,𝔽2)11yescharacteristic
1314C22C22×2−1+411yescharacteristic
1315C22C22×2−1+411yescharacteristic
1316C22C2×#58511yescharacteristic
1317C22C2×#58511yescharacteristic
1318C22C2×#58511yescharacteristic
1319C222−1+611yescharacteristic
1320C4—24no—
1321C4—24no—
1322C4—24no—
1323C4—22no—
1324C4—22no—
1325C4—22no—
1326C4—41no—
1327C4—42no—
1328C4—44no—
1329C4—41no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—41no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4—42no—
1347C4#353114yes—
1348C2—84no—
1349C2C2×#353111yescharacteristic
1350C2#6294911yescharacteristic
1351C2#6295911yescharacteristic
1352C2#6296011yescharacteristic
1353C2#6301611yescharacteristic
1354C2#6302111yescharacteristic
1355C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #53118C2semidirect
3. #52998C2semidirect
4. #52651C2semidirect
5. #52575C2semidirect
6. #52571C2semidirect
7. #52305C2semidirect
8. #52162C2semidirect
9. #46286C2semidirect
10. #46173C2semidirect
11. #46113C2semidirect
12. #46057C2semidirect
14. #46006C2semidirect
15. #46006C2semidirect
17. #45964C2semidirect
18. #45963C2semidirect
19. #45927C2semidirect
20. #45763C2semidirect
21. #36497C2semidirect
22. #36454C2semidirect
23. #36313C2semidirect
26. #36132C2semidirect
27. #35869C2semidirect
28. #35869C2semidirect
29. #35867C2semidirect

Maximal subgroups

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

subgroupindex
#531262
#531182
#529982
#526512
#525752
#525712
#523052
#521622
#462862
#461732
#461132
#460572
#460132
#460062
#459982
#459642
#459632
#459272
#457632
#364972
#364542
#363132
#363002
#362532
#361322
#358692
#358672