Finite Group Databasebeta

← #7848989

Subgroups — #7848989

Order 512.

4490 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60001C214yesmaximal, complemented
2#59932C214yesmaximal, complemented
3#59923C211yesmaximal, characteristic, complemented
4#59832C211yesmaximal, characteristic, complemented
5#52306C211yesmaximal, characteristic, complemented
6#52072C212yesmaximal
7#51999C212yesmaximal, complemented
8#49988C214yesmaximal, complemented
9#49692C214yesmaximal, complemented
10#47791C212yesmaximal, complemented
11#47544C212yesmaximal, complemented
12#46313C211yesmaximal, characteristic, complemented
13#46205C211yesmaximal, characteristic, complemented
14#44829C214yesmaximal, complemented
15#44773C214yesmaximal, complemented
16#44341C214yesmaximal, complemented
17#43985C214yesmaximal, complemented
18#42211C212yesmaximal, complemented
19#39703C212yesmaximal, complemented
20#39574C212yesmaximal, complemented
21#38782C212yesmaximal
22#37208C211yesmaximal, characteristic, complemented
23#36512C212yesmaximal, complemented
24#35846C212yesmaximal
25#35670C212yesmaximal, complemented
26#34491C212yesmaximal, complemented
27#34276C211yesmaximal, characteristic
28C2×Q82C2212yes—
29C2×#556C2212yes—
30C2×#541C2212yes—
31C2×#536C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34#2863C2212yes—
35#2863C2212yes—
36#2851C2212yes—
37#2843C2212yes—
38#2833C2212yes—
39#2811C2211yescharacteristic
40#2809C2211yescharacteristic
41#2808C2212yes—
42#2806C2212yes—
43#2806C2212yes—
44#2805C2212yes—
45#2792C2214yes—
46#2791C2214yes—
47#2790C2214yes—
48#2789C2212yes—
49#2777C2214yes—
50#2776C2214yes—
51#2776C2214yes—
52#2775C2214yes—
53#2775C2214yes—
54#2773C2214yes—
55#2769C2212yes—
56#2766C2214yes—
57#2764C2214yes—
58#2764C2214yes—
59#2762C2214yes—
60#2762C2214yes—
61#2759C2214yes—
62#2759C2214yes—
63#2755C2214yes—
64#2755C2214yes—
65#2754C2214yes—
66#2734C2211yescharacteristic
67#2734C2214yes—
68#2734C2212yes—
69#2734C2211yescharacteristic
70#2731C2212yes—
71#2731C2212yes—
72#2727C2212yes—
73#2725C2214yes—
74#2723C2214yes—
75#2721C2214yes—
76#2721C2214yes—
77#2716C2214yes—
78#2716C2214yes—
79#2715C2214yes—
80#2713C2214yes—
81#2713C2214yes—
82#2698C2214yes—
83#2677C2214yes—
84#2677C2214yes—
85#2674C2214yes—
86#2674C2214yes—
87#2666C2214yes—
88#2651C2214yes—
89#2638C2212yes—
90#2638C2212yes—
91#2632C2214yes—
92#2621C2212yes—
93#2611C2214yes—
94#2607C2214yes—
95#2606C2214yes—
96#2605C2214yes—
97#2599C2214yes—
98#2596C2214yes—
99#2590C2214yes—
100#2590C2214yes—
101#2589C2214yes—
102#2589C2214yes—
103#2589C2214yes—
104#2588C2214yes—
105#2588C2214yes—
106#2586C2214yes—
107#2586C2212yes—
108#2586C2214yes—
109#2586C2214yes—
110#2585C2214yes—
111#2584C2214yes—
112#2583C2212yes—
113#2583C2212yes—
114#2582C2212yes—
115#2581C2212yes—
116#2565C2212yes—
117#2565C2212yes—
118#2565C2212yes—
119#2556C2214yes—
120#2556C2214yes—
121#2551C2214yes—
122#2550C2212yes—
123#2549C2214yes—
124#2546C2212yes—
125#2546C2212yes—
126#2546C2212yes—
127#2533C2214yes—
128#2532C2214yes—
129#2531C2214yes—
130#2528C2214yes—
131#2527C2214yes—
132#2527C2214yes—
133#2527C2214yes—
134#2525C2214yes—
135#2524C2214yes—
136#2523C2214yes—
137#2521C2214yes—
138#2520C2214yes—
139#2519C2214yes—
140#2517C2214yes—
141#2515C2214yes—
142#2515C2214yes—
143#2499C2212yes—
144#2499C2212yes—
145#2496C2212yes—
146#2495C2212yes—
147#2493C2214yes—
148#2492C2212yes—
149#2489C2212yes—
150#2484C2212yes—
151#2484C2212yes—
152#2478C2214yes—
153#2478C2214yes—
154#2478C2214yes—
155#2478C2214yes—
156#2478C2214yes—
157#2478C2214yes—
158#2466C2214yes—
159#2466C2214yes—
160#2465C2214yes—
161#2465C2214yes—
162#2465C2214yes—
163#2465C2214yes—
164#2462C2214yes—
165#2462C2214yes—
166#2462C2214yes—
167#2462C2214yes—
168#2462C2214yes—
169#2462C2214yes—
170#2458C2214yes—
171#2458C2214yes—
172#2453C2214yes—
173#2451C2214yes—
174#2451C2214yes—
175#2451C2214yes—
176#2447C2214yes—
177#2438C2214yes—
178#2434C2212yes—
179#2434C2212yes—
180#2432C2214yes—
181#2396C2212yes—
182#2396C2214yes—
183#2395C2212yes—
184#2395C2212yes—
185#2381C2214yes—
186#2381C2212yes—
187#2381C2212yes—
188#2373C2214yes—
189#2373C2214yes—
190#2373C2214yes—
191#2370C2212yes—
192#2369C2212yes—
193#2368C2214yes—
194#2365C2214yes—
195#2365C2214yes—
196#2365C2214yes—
197#2362C2214yes—
198#2360C2214yes—
199#2360C2214yes—
200#2359C2214yes—
201#2359C2214yes—
202#2357C2212yes—
203#2356C2212yes—
204#2356C2214yes—
205#2356C2214yes—
206#2355C2214yes—
207#2336C2214yes—
208#2331C2214yes—
209#2331C2214yes—
210#2327C2212yes—
211#2327C2214yes—
212#2327C2212yes—
213#2327C2211yescharacteristic
214#2327C2211yescharacteristic
215#2326C2211yescharacteristic
216#2326C2211yescharacteristic
217#2320C2214yes—
218#2320C2214yes—
219#2317C2211yescharacteristic
220C4×C4⋊Q8C2211yescharacteristic
221C4×C4⋊Q8C2212yes—
222C4×C4⋊Q8C2212yes—
223C4×C4⋊Q8C2212yes—
224C4×C4⋊Q8C2211yescharacteristic
225C4×#125C2212yes—
226C4×#126C2214yes—
227C4×#124C2211yescharacteristic
228C4×#124C2211yescharacteristic
229C4×C22⋊Q8C2212yes—
230#2298C2212yes—
231#2297C2211yescharacteristic
232#2295C2214yes—
233C2×#391C2211yescharacteristic
234C4×#117C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237Q82—216no—
238#556—48no—
239#541—48no—
240#536—28no—
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2314yes—
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2314yes—
247C2×C4⋊Q8C2314yes—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2311yescharacteristic
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#124C2311yescharacteristic
263C2×#124C2311yescharacteristic
264C2×#124C2314yes—
265C2×#123C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273#520—44no—
274#519—44no—
275C2×C4×Q8C2314yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2312yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×D4C2312yes—
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×#117C2311yescharacteristic
296C2×#117C2312yes—
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C42C2311yescharacteristic
306#401C2314yes—
307#401C2314yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2312yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2312yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2312yes—
337#398C2314yes—
338#398C2312yes—
339#398C2312yes—
340#398C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2312yes—
360#397C2312yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#395C2314yes—
375#395C2312yes—
376#395C2312yes—
377#395C2312yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2312yes—
401#393C2314yes—
402#391C2311yescharacteristic
403#391C2312yes—
404#391C2312yes—
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2311yescharacteristic
418#391C2314yes—
419#391C2311yescharacteristic
420#391C2314yes—
421#391C2314yes—
422#391C2311yescharacteristic
423#391C2314yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#390C2311yescharacteristic
441#390C2314yes—
442#390C2311yescharacteristic
443#389C2312yes—
444#389C2312yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
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#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
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#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#386C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#384C2312yes—
586#384C2312yes—
587#384C2312yes—
588#384C2311yescharacteristic
589#384C2311yescharacteristic
590#383C2314yes—
591#383C2314yes—
592#383C2314yes—
593#383C2314yes—
594#383C2314yes—
595#383C2314yes—
596#383C2314yes—
597#382C2312yes—
598#382C2312yes—
599#382C2312yes—
600#382C2311yescharacteristic
601#382C2311yescharacteristic
602#382C2314yes—
603#382C2312yes—
604#382C2314yes—
605#382C2314yes—
606#382C2312yes—
607#381C2314yes—
608#381C2312yes—
609#381C2312yes—
610#381C2314yes—
611#380C2312yes—
612#380C2312yes—
613#380C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2314yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2314yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C22⋊C4C2312yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2312yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654#376C2314yes—
655#376C2314yes—
656#376C2311yescharacteristic
657#376C2311yescharacteristic
658#376C2312yes—
659#376C2314yes—
660C2×#95C2314yes—
661C43C2312yes—
662C43C2311yescharacteristic
663C43C2311yescharacteristic
664C2×#41—24no—
665C2×#41—42no—
666C2×#41—42no—
667C22×Q8—24no—
668C22×Q8—42no—
669C22×Q8—42no—
670C22×Q8C2414yes—
671C22×Q8C2412yes—
672C22×Q8C2411yescharacteristic
673C22×Q8C2414yes—
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2412yes—
678C22×Q8C2411yescharacteristic
679C22×Q8C2411yescharacteristic
680C22×D4C2412yes—
681C22×D4C2411yescharacteristic
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2412yes—
689C4⋊Q8—24no—
690C4⋊Q8—28no—
691C4⋊Q8—28no—
692C4⋊Q8—216no—
693C4⋊Q8—216no—
694C4⋊Q8—216no—
695C4⋊Q8—28no—
696C4⋊Q8—44no—
697C4⋊Q8—44no—
698C4⋊Q8—44no—
699C4⋊Q8—44no—
700C4⋊Q8#4118yes—
701#126—216no—
702#126—216no—
703#126—48no—
704#126—48no—
705#125—28no—
706#125—44no—
707#125—44no—
708#125—48no—
709#125—48no—
710#124—24no—
711#124—24no—
712#124—48no—
713#123—216no—
714C22⋊Q8—216no—
715C22⋊Q8—28no—
716C22⋊Q8—44no—
717C22⋊Q8—44no—
718C22⋊Q8—44no—
719C22⋊Q8—48no—
720C22⋊Q8—44no—
721C4×Q8—216no—
722C4×Q8—216no—
723C4×Q8—216no—
724C4×Q8—42no—
725C4×Q8—42no—
726C4×Q8—42no—
727C4×Q8—44no—
728C4×Q8—44no—
729C4×Q8—42no—
730C4×Q8—42no—
731C4×Q8—44no—
732C4×Q8—44no—
733C4×Q8—42no—
734C4×Q8—44no—
735C4×Q8—44no—
736C4×Q8—48no—
737C4×D4—28no—
738C4×D4—42no—
739C4×D4—42no—
740C4×D4—44no—
741#117—24no—
742#117—28no—
743#117—24no—
744#117—44no—
745#117—44no—
746#117—44no—
747#117—42no—
748#117—44no—
749C2×C4⋊C4—44no—
750C2×C4⋊C4—42no—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2411yescharacteristic
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
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×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2411yescharacteristic
837C2×C42—42no—
838C2×C42C2411yescharacteristic
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2414yes—
843C2×C42C2412yes—
844C2×C42C2411yescharacteristic
845C2×C42C2412yes—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2411yescharacteristic
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2411yescharacteristic
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2411yescharacteristic
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2412yes—
882#95C2412yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2412yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2412yes—
898#95C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940C24C2512yes—
941C24C2511yescharacteristic
942#41—416no—
943C2×Q8—28no—
944C2×Q8—24no—
945C2×Q8—22no—
946C2×Q8—24no—
947C2×Q8—24no—
948C2×Q8—28no—
949C2×Q8—28no—
950C2×Q8—24no—
951C2×Q8—24no—
952C2×Q8—41no—
953C2×Q8—41no—
954C2×Q8—42no—
955C2×Q8—41no—
956C2×Q8—41no—
957C2×Q8—41no—
958C2×Q8—44no—
959C2×Q8—41no—
960C2×Q8—42no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—44no—
964C2×Q8—42no—
965C2×Q8—44no—
966C2×Q8—42no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—44no—
970C2×Q8—416no—
971C2×Q8C2×#4114yes—
972C2×Q8C2×#4114yes—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—22no—
976C2×D4—41no—
977C2×D4—41no—
978C2×D4—42no—
979C22×C4—22no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—44no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—42no—
996C22×C4—44no—
997C22×C4C2512yes—
998C22×C4C2514yes—
999C22×C4C2514yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2512yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2512yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2512yes—
1007C22×C4C2514yes—
1008C22×C4C2514yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2512yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2511yescharacteristic
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—22no—
1032C4⋊C4—24no—
1033C4⋊C4—22no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—24no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—24no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—42no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4C2×#41116yes—
1085C4⋊C42−1+418yes—
1086C22⋊C4—22no—
1087C22⋊C4—24no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—24no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—24no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—42no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4H(5,𝔽2)14yes—
1108C42—22no—
1109C42—24no—
1110C42—28no—
1111C42—28no—
1112C42—24no—
1113C42—28no—
1114C42—22no—
1115C42—22no—
1116C42—24no—
1117C42—24no—
1118C42—24no—
1119C42—28no—
1120C42—24no—
1121C42—28no—
1122C42—24no—
1123C42—24no—
1124C42—41no—
1125C42—41no—
1126C42—44no—
1127C42—44no—
1128C42—44no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—44no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—42no—
1140C42—42no—
1141C42C2×#4114yes—
1142C23—21no—
1143C23—22no—
1144C23—21no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—24no—
1149C23—22no—
1150C23—24no—
1151C23C2×H(5,𝔽2)12yes—
1152C23C2611yescharacteristic
1153Q8—44no—
1154Q8—44no—
1155Q8—416no—
1156Q8—48no—
1157Q8—44no—
1158Q8—88no—
1159Q8—84no—
1160Q8—84no—
1161Q8—84no—
1162Q8—84no—
1163D4—48no—
1164D4—44no—
1165C2×C4—28no—
1166C2×C4—24no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—48no—
1225C2×C4—48no—
1226C2×C4—84no—
1227C2×C4—84no—
1228C2×C4—84no—
1229C2×C4—162no—
1230C2×C4C22×#4114yes—
1231C2×C4C22×#4114yes—
1232C2×C4C22×#4114yes—
1233C2×C4C22×#4112yes—
1234C2×C4C2×H(5,𝔽2)12yes—
1235C2×C4C2×H(5,𝔽2)12yes—
1236C2×C4C2×2−1+414yes—
1237C2×C4C2×2−1+418yes—
1238C2×C4#58512yes—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22C23×#4111yescharacteristic
1250C22C22×H(5,𝔽2)11yescharacteristic
1251C22C22×2−1+412yes—
1252C22C2×#58511yescharacteristic
1253C222−1+612yes—
1254C4—24no—
1255C4—28no—
1256C4—22no—
1257C4—22no—
1258C4—24no—
1259C4—24no—
1260C4—22no—
1261C4—22no—
1262C4—24no—
1263C4—42no—
1264C4—44no—
1265C4—42no—
1266C4—44no—
1267C4—44no—
1268C4—41no—
1269C4—42no—
1270C4—44no—
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—41no—
1275C4—44no—
1276C4—44no—
1277C4—42no—
1278C4—44no—
1279C2—42no—
1280C2—82no—
1281C2#6277311yescharacteristic
1282C2#6293212yes—
1283C2#6299812yes—
1284C2#6303711yescharacteristic
1285C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60001C2semidirect
2. #59932C2semidirect
3. #59923C2semidirect
4. #59832C2semidirect
5. #52306C2semidirect
7. #51999C2semidirect
8. #49988C2semidirect
9. #49692C2semidirect
10. #47791C2semidirect
11. #47544C2semidirect
12. #46313C2semidirect
13. #46205C2semidirect
14. #44829C2semidirect
15. #44773C2semidirect
16. #44341C2semidirect
17. #43985C2semidirect
18. #42211C2semidirect
19. #39703C2semidirect
20. #39574C2semidirect
22. #37208C2semidirect
23. #36512C2semidirect
25. #35670C2semidirect
26. #34491C2semidirect

Maximal subgroups

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

subgroupindex
#600012
#599322
#599232
#598322
#523062
#520722
#519992
#499882
#496922
#477912
#475442
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