Finite Group Databasebeta

← #7697413

Subgroups — #7697413

Order 512.

4525 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59879C212yesmaximal, complemented
2#59827C211yesmaximal, characteristic
3#59491C214yesmaximal, complemented
4#59448C212yesmaximal, complemented
5#52304C212yesmaximal, complemented
6#52274C211yesmaximal, characteristic, complemented
7#45153C212yesmaximal, complemented
8#45137C212yesmaximal
9#45083C212yesmaximal, complemented
10#43868C214yesmaximal, complemented
11#43781C214yesmaximal, complemented
12#43435C214yesmaximal, complemented
13#39802C212yesmaximal, complemented
14#39757C211yesmaximal, characteristic, complemented
15#39611C211yesmaximal, characteristic
16#39173C212yesmaximal, complemented
17#38898C214yesmaximal, complemented
18#38808C212yesmaximal, complemented
19#38788C212yesmaximal, complemented
20#38600C214yesmaximal, complemented
21#36535C211yesmaximal, characteristic, complemented
22#36454C212yesmaximal, complemented
23#35973C212yesmaximal, complemented
24#35973C212yesmaximal, complemented
25#35936C212yesmaximal, complemented
26#34333C212yesmaximal, complemented
27#34331C211yesmaximal, characteristic
28#34329C212yesmaximal
29#34328C211yesmaximal, characteristic, complemented
30C2×#559C2212yes—
31C2×#559C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#554C2212yes—
34#2864C2212yes—
35#2862C2212yes—
36#2859C2211yescharacteristic
37#2855C2214yes—
38#2810C2212yes—
39#2810C2212yes—
40#2809C2211yescharacteristic
41#2806C2211yescharacteristic
42#2805C2211yescharacteristic
43#2805C2212yes—
44#2805C2212yes—
45#2802C2212yes—
46#2799C2212yes—
47#2791C2212yes—
48#2789C2214yes—
49#2787C2214yes—
50#2774C2212yes—
51#2770C2214yes—
52#2767C2214yes—
53#2765C2214yes—
54#2765C2214yes—
55#2762C2214yes—
56#2758C2214yes—
57#2755C2212yes—
58#2744C2214yes—
59#2739C2214yes—
60#2738C2214yes—
61#2738C2214yes—
62#2732C2212yes—
63#2732C2212yes—
64#2726C2211yescharacteristic
65#2724C2212yes—
66#2724C2212yes—
67#2717C2214yes—
68#2717C2214yes—
69#2717C2214yes—
70#2717C2214yes—
71#2713C2212yes—
72#2690C2214yes—
73#2690C2214yes—
74#2690C2214yes—
75#2690C2214yes—
76#2690C2214yes—
77#2690C2214yes—
78#2683C2212yes—
79#2683C2212yes—
80#2666C2214yes—
81#2660C2212yes—
82#2652C2214yes—
83#2652C2214yes—
84#2642C2212yes—
85#2642C2212yes—
86#2612C2214yes—
87#2611C2214yes—
88#2611C2214yes—
89#2606C2214yes—
90#2605C2214yes—
91#2590C2214yes—
92#2588C2214yes—
93#2588C2214yes—
94#2586C2214yes—
95#2585C2214yes—
96#2582C2212yes—
97#2581C2212yes—
98#2581C2212yes—
99#2577C2214yes—
100#2577C2214yes—
101#2577C2214yes—
102#2575C2214yes—
103#2575C2214yes—
104#2573C2214yes—
105#2573C2214yes—
106#2573C2214yes—
107#2571C2211yescharacteristic
108#2570C2212yes—
109#2570C2212yes—
110#2567C2212yes—
111#2566C2212yes—
112#2566C2212yes—
113#2565C2212yes—
114#2565C2212yes—
115#2552C2211yescharacteristic
116#2552C2212yes—
117#2550C2212yes—
118#2547C2212yes—
119#2547C2212yes—
120#2547C2212yes—
121#2547C2212yes—
122#2542C2212yes—
123#2533C2214yes—
124#2533C2214yes—
125#2530C2214yes—
126#2530C2214yes—
127#2530C2214yes—
128#2528C2214yes—
129#2524C2214yes—
130#2517C2214yes—
131#2517C2214yes—
132#2515C2214yes—
133#2515C2214yes—
134#2515C2214yes—
135#2514C2212yes—
136#2514C2212yes—
137#2511C2212yes—
138#2511C2212yes—
139#2511C2212yes—
140#2511C2212yes—
141#2505C2214yes—
142#2505C2214yes—
143#2493C2214yes—
144#2493C2214yes—
145#2493C2214yes—
146#2489C2214yes—
147#2486C2214yes—
148#2484C2214yes—
149#2475C2214yes—
150#2475C2214yes—
151#2473C2214yes—
152#2462C2214yes—
153#2462C2214yes—
154#2449C2214yes—
155#2449C2214yes—
156#2447C2214yes—
157#2447C2212yes—
158#2447C2212yes—
159#2447C2212yes—
160#2447C2212yes—
161#2447C2212yes—
162#2447C2212yes—
163#2442C2214yes—
164#2442C2214yes—
165#2438C2214yes—
166#2438C2214yes—
167#2421C2214yes—
168#2421C2214yes—
169#2421C2214yes—
170#2419C2214yes—
171#2419C2214yes—
172#2419C2214yes—
173#2419C2214yes—
174#2402C2212yes—
175#2402C2212yes—
176#2401C2214yes—
177#2401C2214yes—
178#2399C2212yes—
179#2399C2214yes—
180#2374C2214yes—
181#2372C2214yes—
182#2371C2214yes—
183#2370C2212yes—
184#2370C2212yes—
185#2370C2212yes—
186#2368C2214yes—
187#2368C2214yes—
188#2367C2212yes—
189#2367C2212yes—
190#2367C2212yes—
191#2367C2212yes—
192#2366C2211yescharacteristic
193#2365C2212yes—
194#2365C2211yescharacteristic
195#2365C2212yes—
196#2360C2214yes—
197#2359C2214yes—
198#2359C2214yes—
199#2357C2212yes—
200#2356C2212yes—
201#2356C2212yes—
202#2356C2212yes—
203#2356C2212yes—
204#2355C2211yescharacteristic
205#2355C2211yescharacteristic
206#2355C2212yes—
207#2355C2211yescharacteristic
208#2355C2212yes—
209#2355C2211yescharacteristic
210#2355C2211yescharacteristic
211#2354C2212yes—
212#2354C2212yes—
213#2353C2214yes—
214Q8×C4⋊C4C2211yescharacteristic
215#2349C2212yes—
216#2349C2212yes—
217#2349C2212yes—
218D4×C4⋊C4C2212yes—
219D4×C4⋊C4C2212yes—
220#2345C2214yes—
221#2343C2214yes—
222#2337C2214yes—
223#2336C2214yes—
224#2335C2214yes—
225#2335C2214yes—
226#2331C2212yes—
227#2330C2212yes—
228#2329C2214yes—
229#2329C2214yes—
230#2328C2212yes—
231#2327C2212yes—
232#2326C2212yes—
233#2326C2212yes—
234C4×C4⋊Q8C2211yescharacteristic
235C4×C4⋊Q8C2211yescharacteristic
236C4×#127C2211yescharacteristic
237C4×#125C2212yes—
238C4×#125C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×#124C2212yes—
242C4×#124C2212yes—
243C4×C22⋊Q8C2214yes—
244C4×C22⋊Q8C2214yes—
245C4×#123C2214yes—
246#2295C2212yes—
247#2295C2211yescharacteristic
248#2295C2212yes—
249#2295C2212yes—
250#2295C2211yescharacteristic
251#2293C2212yes—
252#2290C2214yes—
253C2×#387C2214yes—
254#2276C2212yes—
255#2275C2212yes—
256#2275C2212yes—
257C42×Q8C2211yescharacteristic
258C42×D4C2212yes—
259#559—216no—
260#559—28no—
261#557—28no—
262#554—216no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×#127C2311yescharacteristic
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2314yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#124C2314yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×#117C2314yes—
313C2×#117C2314yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2314yes—
316C22×C42C2314yes—
317#401C2314yes—
318#401C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#399C2314yes—
350#399C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2312yes—
357#398C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#397C2314yes—
376#397C2314yes—
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#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2312yes—
402#395C2314yes—
403#395C2314yes—
404#395C2312yes—
405#395C2312yes—
406#395C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2311yescharacteristic
430#391C2312yes—
431#391C2311yescharacteristic
432#391C2312yes—
433#391C2312yes—
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#389C2311yescharacteristic
444#389C2311yescharacteristic
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2311yescharacteristic
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2311yescharacteristic
478#389C2312yes—
479#389C2312yes—
480#389C2311yescharacteristic
481#389C2311yescharacteristic
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#387C2314yes—
501#387C2312yes—
502#387C2312yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2312yes—
508#387C2314yes—
509#387C2312yes—
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#387C2312yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2312yes—
562#387C2314yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#384C2311yescharacteristic
599#384C2311yescharacteristic
600#384C2311yescharacteristic
601#384C2312yes—
602#384C2312yes—
603#384C2311yescharacteristic
604#384C2312yes—
605#384C2311yescharacteristic
606#383C2314yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#382C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2314yes—
619#382C2312yes—
620#382C2312yes—
621#382C2314yes—
622#382C2312yes—
623#382C2314yes—
624#381C2314yes—
625#381C2314yes—
626#381C2314yes—
627#381C2314yes—
628#381C2314yes—
629#381C2314yes—
630#381C2314yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642C4×C4⋊C4C2311yescharacteristic
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702#376C2312yes—
703#376C2312yes—
704#376C2312yes—
705#376C2314yes—
706#376C2314yes—
707#376C2314yes—
708#376C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C43C2312yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2411yescharacteristic
718C22×Q8C2411yescharacteristic
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×Q8C2411yescharacteristic
722C22×D4C2412yes—
723C22×D4C2412yes—
724C22×D4C2412yes—
725C23×C4C2414yes—
726C23×C4C2414yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C4⋊Q8—28no—
733C4⋊Q8—24no—
734C4⋊Q8—28no—
735C4⋊Q8—42no—
736#127#4118yes—
737#125—216no—
738#125—28no—
739#125—28no—
740#125—28no—
741#125—44no—
742#125—44no—
743#125—84no—
744#124—28no—
745#124—28no—
746#124—28no—
747#124—216no—
748#124—28no—
749#123—216no—
750#123—216no—
751#123—216no—
752C22⋊Q8—216no—
753C22⋊Q8—216no—
754C22⋊Q8—216no—
755C22⋊Q8—48no—
756C22⋊Q8—84no—
757C4×Q8—28no—
758C4×Q8—24no—
759C4×Q8—28no—
760C4×Q8—24no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—84no—
767C4×Q8—82no—
768C4×Q8#4118yes—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—216no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—28no—
777C4×D4—28no—
778C4×D4—44no—
779C4×D4—82no—
780C4×D4—82no—
781#117—48no—
782#117—84no—
783C2×C4⋊C4—216no—
784C2×C4⋊C4—84no—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2411yescharacteristic
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×C42—84no—
882C2×C42C2412yes—
883C2×C42C2411yescharacteristic
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2411yescharacteristic
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2411yescharacteristic
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999C24C2514yes—
1000C2×Q8—22no—
1001C2×Q8—24no—
1002C2×Q8—22no—
1003C2×Q8—22no—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—28no—
1007C2×Q8—22no—
1008C2×Q8—24no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—44no—
1014C2×Q8—44no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8C2×#4114yes—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—42no—
1021C2×D4—42no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C2×D4C2×#4118yes—
1025C2×D4C2×#4118yes—
1026C2×D4C2×#4118yes—
1027C22×C4—28no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2512yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—28no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—22no—
1106C4⋊C4—22no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—41no—
1112C4⋊C4—42no—
1113C4⋊C4—41no—
1114C4⋊C4—41no—
1115C4⋊C4—42no—
1116C4⋊C4—41no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—41no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4C2×#4118yes—
1149C4⋊C4C2×#4114yes—
1150C4⋊C42−1+414yes—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C42—28no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—24no—
1177C42—24no—
1178C42—28no—
1179C42—24no—
1180C42—22no—
1181C42—24no—
1182C42—24no—
1183C42—28no—
1184C42—24no—
1185C42—22no—
1186C42—42no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—42no—
1191C42—41no—
1192C42—44no—
1193C42—41no—
1194C42—42no—
1195C42—42no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42—41no—
1200C42—42no—
1201C42—44no—
1202C42—42no—
1203C42C2×#4114yes—
1204C42C2×#4118yes—
1205C42C2×#4114yes—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23C22×#4118yes—
1213C23C2611yescharacteristic
1214Q8—44no—
1215Q8—44no—
1216Q8—48no—
1217Q8—44no—
1218Q8—84no—
1219Q8—88no—
1220D4—216no—
1221D4—48no—
1222D4—48no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—21no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—88no—
1297C2×C4—88no—
1298C2×C4—88no—
1299C2×C4—88no—
1300C2×C4—88no—
1301C2×C4—88no—
1302C2×C4—88no—
1303C2×C4C22×#4112yes—
1304C2×C4C22×#4112yes—
1305C2×C4C22×#4114yes—
1306C2×C4C22×#4112yes—
1307C2×C4C22×#4114yes—
1308C2×C4C22×#4112yes—
1309C2×C4C22×#4112yes—
1310C2×C4C22×#4112yes—
1311C2×C4C2×2−1+414yes—
1312C2×C4C2×2−1+412yes—
1313C2×C4#58512yes—
1314C22—28no—
1315C22—28no—
1316C22—28no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22C23×#4111yescharacteristic
1322C22C23×#4111yescharacteristic
1323C22C22×2−1+411yescharacteristic
1324C22C2×#58511yescharacteristic
1325C22H(7,𝔽2)11yescharacteristic
1326C222−1+611yescharacteristic
1327C222−1+611yescharacteristic
1328C4—22no—
1329C4—22no—
1330C4—24no—
1331C4—24no—
1332C4—22no—
1333C4—24no—
1334C4—22no—
1335C4—22no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—44no—
1343C4—42no—
1344C4—41no—
1345C4—42no—
1346C4—42no—
1347C4—44no—
1348C4—42no—
1349C4—42no—
1350C4—44no—
1351C4—42no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4#348214yes—
1356C2—48no—
1357C2C2×#348211yescharacteristic
1358C2#6284711yescharacteristic
1359C2#6286011yescharacteristic
1360C2#6294911yescharacteristic
1361C2#6299111yescharacteristic
1362C2#6301011yescharacteristic
1363C2#6305811yescharacteristic
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
1. #59879C2semidirect
3. #59491C2semidirect
4. #59448C2semidirect
5. #52304C2semidirect
6. #52274C2semidirect
7. #45153C2semidirect
9. #45083C2semidirect
10. #43868C2semidirect
11. #43781C2semidirect
12. #43435C2semidirect
13. #39802C2semidirect
14. #39757C2semidirect
16. #39173C2semidirect
17. #38898C2semidirect
18. #38808C2semidirect
19. #38788C2semidirect
20. #38600C2semidirect
21. #36535C2semidirect
22. #36454C2semidirect
23. #35973C2semidirect
24. #35973C2semidirect
25. #35936C2semidirect
26. #34333C2semidirect
29. #34328C2semidirect

Maximal subgroups

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

subgroupindex
#598792
#598272
#594912
#594482
#523042
#522742
#451532
#451372
#450832
#438682
#437812
#434352
#398022
#397572
#396112
#391732
#388982
#388082
#387882
#386002
#365352
#364542
#359732
#359362
#343332
#343312
#343292
#343282