Finite Group Databasebeta

← #8096278

Subgroups — #8096278

Order 512.

4239 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52952C212yesmaximal, complemented
2#52946C214yesmaximal, complemented
3#52703C214yesmaximal, complemented
4#52562C214yesmaximal, complemented
5#52554C214yesmaximal, complemented
6#52287C211yesmaximal, characteristic, complemented
7#52162C212yesmaximal, complemented
8#46312C211yesmaximal, characteristic
9#46283C212yesmaximal, complemented
10#46268C212yesmaximal, complemented
11#46029C214yesmaximal, complemented
12#45964C212yesmaximal, complemented
13#45956C212yesmaximal
14#45949C212yesmaximal, complemented
15#45827C214yesmaximal, complemented
16#45795C214yesmaximal, complemented
17#45763C214yesmaximal, complemented
18#36383C211yesmaximal, characteristic, complemented
19#36371C212yesmaximal, complemented
20#36333C214yesmaximal, complemented
21#36151C212yesmaximal, complemented
22#36002C212yesmaximal, complemented
23#35746C214yesmaximal, complemented
24C2×#563C2212yes—
25C2×#533C2214yes—
26#2865C2214yes—
27#2864C2211yescharacteristic
28#2863C2212yes—
29#2863C2212yes—
30#2862C2212yes—
31#2861C2212yes—
32#2860C2212yes—
33#2857C2214yes—
34#2855C2214yes—
35#2853C2214yes—
36#2843C2214yes—
37#2841C2214yes—
38#2841C2214yes—
39#2838C2214yes—
40#2837C2214yes—
41#2836C2214yes—
42#2833C2214yes—
43#2833C2212yes—
44#2833C2212yes—
45#2832C2214yes—
46#2832C2212yes—
47#2831C2214yes—
48#2831C2214yes—
49#2831C2214yes—
50#2830C2212yes—
51#2829C2214yes—
52#2823C2212yes—
53#2817C2214yes—
54#2814C2214yes—
55#2811C2211yescharacteristic
56#2811C2212yes—
57#2808C2212yes—
58#2806C2214yes—
59#2806C2214yes—
60#2806C2212yes—
61#2806C2214yes—
62#2805C2212yes—
63#2805C2214yes—
64#2802C2214yes—
65#2801C2214yes—
66#2799C2214yes—
67#2795C2212yes—
68#2792C2212yes—
69#2792C2214yes—
70#2792C2212yes—
71#2788C2214yes—
72#2786C2214yes—
73#2784C2212yes—
74#2762C2214yes—
75#2759C2214yes—
76#2756C2214yes—
77#2754C2214yes—
78#2742C2214yes—
79#2742C2214yes—
80#2739C2214yes—
81#2737C2214yes—
82#2734C2211yescharacteristic
83#2734C2212yes—
84#2734C2211yescharacteristic
85#2733C2211yescharacteristic
86#2732C2212yes—
87#2729C2214yes—
88#2726C2212yes—
89#2725C2214yes—
90#2720C2214yes—
91#2719C2214yes—
92#2716C2214yes—
93#2713C2214yes—
94#2713C2214yes—
95#2713C2214yes—
96#2705C2214yes—
97#2704C2214yes—
98#2704C2214yes—
99#2704C2214yes—
100#2700C2214yes—
101#2698C2214yes—
102#2692C2214yes—
103#2689C2214yes—
104#2687C2214yes—
105#2683C2212yes—
106#2677C2214yes—
107#2664C2214yes—
108#2655C2214yes—
109#2654C2214yes—
110#2637C2214yes—
111#2632C2212yes—
112#2612C2214yes—
113#2605C2212yes—
114#2604C2214yes—
115#2604C2214yes—
116#2594C2214yes—
117#2594C2214yes—
118#2592C2212yes—
119#2590C2214yes—
120#2588C2214yes—
121#2588C2214yes—
122#2586C2214yes—
123#2585C2214yes—
124#2584C2212yes—
125#2584C2214yes—
126#2581C2211yescharacteristic
127#2581C2211yescharacteristic
128#2560C2214yes—
129#2556C2214yes—
130#2556C2214yes—
131#2545C2212yes—
132#2536C2212yes—
133#2536C2212yes—
134#2533C2214yes—
135#2532C2214yes—
136#2532C2214yes—
137#2529C2214yes—
138#2529C2214yes—
139#2528C2214yes—
140#2527C2214yes—
141#2527C2214yes—
142#2526C2214yes—
143#2525C2214yes—
144#2524C2214yes—
145#2521C2214yes—
146#2521C2214yes—
147#2520C2214yes—
148#2519C2214yes—
149#2512C2212yes—
150#2511C2212yes—
151#2506C2212yes—
152#2489C2214yes—
153#2489C2214yes—
154#2478C2214yes—
155#2478C2214yes—
156#2474C2214yes—
157#2470C2214yes—
158#2469C2214yes—
159#2469C2214yes—
160#2469C2214yes—
161#2469C2214yes—
162#2468C2214yes—
163#2466C2214yes—
164#2465C2214yes—
165#2465C2214yes—
166#2465C2214yes—
167#2465C2214yes—
168#2465C2214yes—
169#2463C2214yes—
170#2462C2214yes—
171#2462C2214yes—
172#2462C2214yes—
173#2461C2214yes—
174#2460C2214yes—
175#2459C2214yes—
176#2453C2214yes—
177#2453C2214yes—
178#2453C2214yes—
179#2452C2212yes—
180#2451C2212yes—
181#2451C2214yes—
182#2446C2212yes—
183#2421C2214yes—
184#2421C2214yes—
185#2415C2214yes—
186#2415C2214yes—
187#2399C2214yes—
188#2399C2212yes—
189#2399C2214yes—
190#2396C2214yes—
191#2396C2214yes—
192#2381C2214yes—
193#2378C2214yes—
194#2378C2214yes—
195#2378C2214yes—
196#2373C2214yes—
197#2373C2214yes—
198#2372C2212yes—
199#2371C2214yes—
200#2370C2212yes—
201#2367C2212yes—
202#2362C2214yes—
203#2362C2214yes—
204#2356C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2212yes—
207C4×C4⋊Q8C2212yes—
208C4×C4⋊Q8C2211yescharacteristic
209C4×C4⋊Q8C2212yes—
210C4×C22⋊Q8C2214yes—
211#2295C2214yes—
212#2295C2212yes—
213#2295C2212yes—
214#2293C2212yes—
215#2290C2214yes—
216#2276C2212yes—
217C42×Q8C2211yescharacteristic
218C42×D4C2212yes—
219#563—48no—
220#533—416no—
221C2×C4⋊Q8C2312yes—
222C2×C4⋊Q8C2312yes—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2314yes—
225C2×C4⋊Q8C2312yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#125C2312yes—
231C2×#125C2314yes—
232C2×#125C2314yes—
233C2×#125C2314yes—
234C2×#125C2314yes—
235C2×#124C2312yes—
236C2×#124C2312yes—
237C2×#124C2312yes—
238C2×#123C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2312yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C22×C42C2314yes—
265#401C2314yes—
266#401C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2312yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2312yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#399C2314yes—
289#399C2314yes—
290#399C2314yes—
291#399C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2312yes—
295#398C2314yes—
296#398C2312yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2312yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2312yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#395C2314yes—
350#395C2312yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2312yes—
355#395C2314yes—
356#395C2314yes—
357#395C2312yes—
358#395C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2312yes—
367#394C2314yes—
368#394C2314yes—
369#394C2312yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2312yes—
375#394C2314yes—
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#392C2314yes—
385#391C2314yes—
386#391C2312yes—
387#391C2311yescharacteristic
388#391C2312yes—
389#391C2314yes—
390#391C2311yescharacteristic
391#391C2312yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2314yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#391C2314yes—
405#391C2312yes—
406#391C2312yes—
407#391C2314yes—
408#391C2312yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#390C2312yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2312yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2312yes—
435#389C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2312yes—
439#389C2312yes—
440#389C2314yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
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#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#384C2311yescharacteristic
558#384C2312yes—
559#384C2312yes—
560#383C2314yes—
561#383C2314yes—
562#383C2312yes—
563#382C2311yescharacteristic
564#382C2311yescharacteristic
565#382C2312yes—
566#382C2312yes—
567#382C2314yes—
568#382C2314yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#380C2314yes—
573#380C2314yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2311yescharacteristic
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2312yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608#376C2314yes—
609#376C2314yes—
610#376C2312yes—
611#376C2312yes—
612#376C2314yes—
613C43C2311yescharacteristic
614C43C2312yes—
615C43C2312yes—
616C22×Q8C2412yes—
617C22×Q8C2414yes—
618C22×Q8C2414yes—
619C22×Q8C2411yescharacteristic
620C22×Q8C2412yes—
621C22×Q8C2411yescharacteristic
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2411yescharacteristic
625C22×D4C2412yes—
626C22×D4C2412yes—
627C22×D4C2412yes—
628C23×C4C2414yes—
629C23×C4C2414yes—
630C23×C4C2414yes—
631C4⋊Q8—28no—
632C4⋊Q8—24no—
633C4⋊Q8—28no—
634C4⋊Q8—48no—
635C4⋊Q8—44no—
636#126—48no—
637#126—48no—
638#126—48no—
639#126—48no—
640#125—44no—
641#125—48no—
642#125—48no—
643#125—48no—
644#125—48no—
645#124—44no—
646#124—44no—
647#124—44no—
648#123—48no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—48no—
652C22⋊Q8—48no—
653C22⋊Q8—48no—
654C22⋊Q8—48no—
655C22⋊Q8—48no—
656C22⋊Q8—48no—
657C4×Q8—28no—
658C4×Q8—28no—
659C4×Q8—42no—
660C4×Q8—44no—
661C4×Q8—42no—
662C4×Q8—44no—
663C4×Q8—42no—
664C4×Q8—44no—
665C4×Q8—48no—
666C4×Q8—48no—
667C4×Q8—48no—
668C4×Q8—48no—
669C4×D4—28no—
670C4×D4—44no—
671C4×D4—48no—
672#117—48no—
673#117—48no—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2412yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C42—48no—
760C2×C42C2412yes—
761C2×C42C2414yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2411yescharacteristic
765C2×C42C2412yes—
766C2×C42C2414yes—
767C2×C42C2412yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2412yes—
771C2×C42C2411yescharacteristic
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2412yes—
784C2×C42C2414yes—
785C2×C42C2412yes—
786C2×C42C2411yescharacteristic
787C2×C42C2412yes—
788#95C2412yes—
789#95C2411yescharacteristic
790#95C2412yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2412yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2411yescharacteristic
813#95C2412yes—
814#95C2412yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2412yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
845#95C2412yes—
846#95C2414yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855C24C2514yes—
856C2×Q8—24no—
857C2×Q8—22no—
858C2×Q8—24no—
859C2×Q8—28no—
860C2×Q8—28no—
861C2×Q8—41no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—44no—
866C2×Q8—41no—
867C2×Q8—41no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—41no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—41no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8H(5,𝔽2)14yes—
881C2×D4—24no—
882C2×D4—42no—
883C2×D4—44no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C22×C4—28no—
890C22×C4—28no—
891C22×C4—28no—
892C22×C4—28no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4C2512yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2512yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2511yescharacteristic
910C22×C4C2512yes—
911C22×C4C2514yes—
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2512yes—
915C22×C4C2511yescharacteristic
916C22×C4C2512yes—
917C22×C4C2514yes—
918C22×C4C2511yescharacteristic
919C22×C4C2512yes—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—24no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—28no—
931C4⋊C4—28no—
932C4⋊C4—24no—
933C4⋊C4—28no—
934C4⋊C4—24no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—42no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—41no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C42−1+418yes—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C42—24no—
1006C42—28no—
1007C42—24no—
1008C42—22no—
1009C42—24no—
1010C42—24no—
1011C42—28no—
1012C42—24no—
1013C42—24no—
1014C42—22no—
1015C42—24no—
1016C42—28no—
1017C42—24no—
1018C42—28no—
1019C42—44no—
1020C42—44no—
1021C42—41no—
1022C42—42no—
1023C42—44no—
1024C42—44no—
1025C42—44no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—44no—
1030C42—44no—
1031C42—42no—
1032C42—42no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23C2611yescharacteristic
1041Q8—44no—
1042Q8—48no—
1043Q8—48no—
1044Q8—44no—
1045Q8—88no—
1046Q8—88no—
1047Q8—82no—
1048Q8—84no—
1049Q8—162no—
1050D4—48no—
1051D4—84no—
1052D4—162no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—416no—
1110C2×C4—88no—
1111C2×C4—88no—
1112C2×C4C2×H(5,𝔽2)12yes—
1113C2×C4C2×H(5,𝔽2)14yes—
1114C2×C4C2×2−1+414yes—
1115C2×C4C2×2−1+418yes—
1116C2×C4#58512yes—
1117C2×C4#58514yes—
1118C22—44no—
1119C22—44no—
1120C22—44no—
1121C22—44no—
1122C22—44no—
1123C22—44no—
1124C22—44no—
1125C22C22×H(5,𝔽2)11yescharacteristic
1126C22C22×2−1+412yes—
1127C22C2×#58512yes—
1128C22C2×#58511yescharacteristic
1129C222−1+611yescharacteristic
1130C4—24no—
1131C4—28no—
1132C4—22no—
1133C4—24no—
1134C4—22no—
1135C4—24no—
1136C4—42no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—42no—
1141C4—42no—
1142C4—44no—
1143C4—42no—
1144C4—44no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4—41no—
1150C4—44no—
1151C4—44no—
1152C2—84no—
1153C2#6269411yescharacteristic
1154C2#6290111yescharacteristic
1155C2#6295912yes—
1156C2#6301512yes—
1157C2#6303811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2733C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52952C2semidirect
2. #52946C2semidirect
3. #52703C2semidirect
4. #52562C2semidirect
5. #52554C2semidirect
6. #52287C2semidirect
7. #52162C2semidirect
9. #46283C2semidirect
10. #46268C2semidirect
11. #46029C2semidirect
12. #45964C2semidirect
14. #45949C2semidirect
15. #45827C2semidirect
16. #45795C2semidirect
17. #45763C2semidirect
18. #36383C2semidirect
19. #36371C2semidirect
20. #36333C2semidirect
21. #36151C2semidirect
22. #36002C2semidirect
23. #35746C2semidirect

Maximal subgroups

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

subgroupindex
#529522
#529462
#527032
#525622
#525542
#522872
#521622
#463122
#462832
#462682
#460292
#459642
#459562
#459492
#458272
#457952
#457632
#363832
#363712
#363332
#361512
#360022
#357462