Finite Group Databasebeta

← #7720490

Subgroups — #7720490

Order 512.

4249 conjugacy classes of subgroups.

The subgroup lattice has 1415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51619C214yesmaximal, complemented
2#51618C214yesmaximal, complemented
3#51228C212yesmaximal, complemented
4#51227C212yesmaximal, complemented
5#50920C212yesmaximal, complemented
6#50915C212yesmaximal, complemented
7#44512C214yesmaximal, complemented
8#44474C214yesmaximal
9#44463C212yesmaximal, complemented
10#44460C212yesmaximal, complemented
11#43516C212yesmaximal, complemented
12#43513C212yesmaximal, complemented
13#39274C212yesmaximal, complemented
14#39271C212yesmaximal, complemented
15#38243C212yesmaximal, complemented
16#38239C212yesmaximal, complemented
17#38113C212yesmaximal, complemented
18#38111C212yesmaximal, complemented
19#37385C212yesmaximal, complemented
20#37385C212yesmaximal, complemented
21#36304C212yesmaximal, complemented
22#36277C212yesmaximal, complemented
23#35323C212yesmaximal, complemented
24#35315C212yesmaximal, complemented
25#35304C211yesmaximal, characteristic, complemented
26#35279C211yesmaximal, characteristic
27#35138C211yesmaximal, characteristic
28C2×#2642C211yesmaximal, characteristic, complemented
29#34378C211yesmaximal, characteristic, complemented
30#34371C211yesmaximal, characteristic, complemented
31#34123C211yesmaximal, characteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2863C2212yes—
36#2863C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2855C2212yes—
41#2855C2212yes—
42#2851C2212yes—
43#2851C2212yes—
44#2851C2212yes—
45#2810C2214yes—
46#2807C2214yes—
47#2805C2214yes—
48#2799C2214yes—
49#2798C2214yes—
50#2798C2214yes—
51#2798C2214yes—
52#2796C2214yes—
53#2794C2214yes—
54#2794C2214yes—
55#2789C2214yes—
56#2789C2214yes—
57#2776C2214yes—
58#2776C2214yes—
59#2774C2214yes—
60#2774C2214yes—
61#2773C2214yes—
62#2771C2214yes—
63#2767C2214yes—
64#2767C2214yes—
65#2767C2214yes—
66#2766C2214yes—
67#2766C2214yes—
68#2762C2214yes—
69#2759C2214yes—
70#2758C2214yes—
71#2758C2214yes—
72#2758C2214yes—
73#2758C2214yes—
74#2755C2214yes—
75#2754C2214yes—
76#2751C2214yes—
77#2747C2214yes—
78#2747C2214yes—
79#2745C2214yes—
80#2745C2214yes—
81#2742C2214yes—
82#2742C2214yes—
83#2738C2214yes—
84#2738C2214yes—
85#2660C2212yes—
86#2647C2212yes—
87#2645C2212yes—
88#2645C2212yes—
89#2642C2212yes—
90#2642C2212yes—
91#2642C2212yes—
92#2642C2212yes—
93#2642C2214yes—
94#2642C2212yes—
95#2642C2212yes—
96#2634C2212yes—
97#2633C2212yes—
98#2628C2212yes—
99#2628C2212yes—
100#2625C2212yes—
101#2625C2212yes—
102#2612C2214yes—
103#2611C2212yes—
104#2611C2212yes—
105#2607C2214yes—
106#2606C2212yes—
107#2605C2212yes—
108#2605C2214yes—
109#2605C2214yes—
110#2596C2214yes—
111#2596C2214yes—
112#2595C2214yes—
113#2590C2214yes—
114#2590C2214yes—
115#2589C2214yes—
116#2589C2214yes—
117#2588C2214yes—
118#2588C2214yes—
119#2588C2214yes—
120#2584C2212yes—
121#2577C2214yes—
122#2577C2214yes—
123#2575C2214yes—
124#2570C2214yes—
125#2569C2214yes—
126#2569C2212yes—
127#2568C2211yescharacteristic
128#2568C2211yescharacteristic
129#2567C2212yes—
130#2564C2214yes—
131#2563C2212yes—
132#2562C2212yes—
133#2549C2212yes—
134#2542C2211yescharacteristic
135#2542C2211yescharacteristic
136#2533C2214yes—
137#2533C2214yes—
138#2533C2214yes—
139#2533C2214yes—
140#2533C2214yes—
141#2533C2214yes—
142#2530C2214yes—
143#2530C2214yes—
144#2528C2214yes—
145#2528C2214yes—
146#2528C2214yes—
147#2527C2214yes—
148#2524C2214yes—
149#2523C2214yes—
150#2520C2214yes—
151#2516C2214yes—
152#2514C2212yes—
153#2514C2212yes—
154#2514C2214yes—
155#2511C2212yes—
156#2511C2212yes—
157#2511C2214yes—
158#2510C2214yes—
159#2510C2214yes—
160#2509C2214yes—
161#2505C2214yes—
162#2505C2214yes—
163#2505C2214yes—
164#2505C2214yes—
165#2498C2214yes—
166#2493C2214yes—
167#2493C2214yes—
168#2493C2214yes—
169#2493C2214yes—
170#2492C2212yes—
171#2492C2212yes—
172#2489C2212yes—
173#2489C2212yes—
174#2488C2214yes—
175#2487C2211yescharacteristic
176#2487C2211yescharacteristic
177#2487C2212yes—
178#2487C2212yes—
179#2486C2211yescharacteristic
180#2486C2211yescharacteristic
181#2484C2212yes—
182#2453C2212yes—
183#2453C2212yes—
184#2451C2212yes—
185#2451C2212yes—
186#2438C2214yes—
187#2438C2214yes—
188#2423C2212yes—
189#2423C2212yes—
190#2421C2212yes—
191#2421C2212yes—
192#2419C2214yes—
193#2409C2212yes—
194#2409C2212yes—
195#2406C2212yes—
196C2×#400C2212yes—
197C2×#400C2212yes—
198C2×#400C2214yes—
199#2382C2214yes—
200#2381C2212yes—
201#2381C2212yes—
202#2370C2212yes—
203#2370C2212yes—
204#2368C2214yes—
205#2365C2212yes—
206#2365C2212yes—
207#2359C2214yes—
208#2356C2211yescharacteristic
209#2356C2211yescharacteristic
210#2353C2211yescharacteristic
211#2353C2211yescharacteristic
212#2353C2211yescharacteristic
213#2353C2211yescharacteristic
214#2353C2214yes—
215#2349C2211yescharacteristic
216#2349C2211yescharacteristic
217#2346C2212yes—
218#2345C2212yes—
219#2345C2212yes—
220#2345C2212yes—
221#2344C2214yes—
222#2344C2212yes—
223#2343C2212yes—
224#2343C2212yes—
225#2343C2214yes—
226Q8×C22⋊C4C2212yes—
227Q8×C22⋊C4C2212yes—
228#2339C2212yes—
229#2336C2212yes—
230#2336C2212yes—
231#2331C2214yes—
232#2331C2212yes—
233#2330C2212yes—
234#2330C2212yes—
235#2330C2212yes—
236#2327C2212yes—
237#2327C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2322C2212yes—
241#2322C2212yes—
242#2320C2212yes—
243#2320C2212yes—
244#2317C2212yes—
245#2316C2212yes—
246#2313C2214yes—
247#2313C2212yes—
248#2311C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×C22⋊Q8C2212yes—
251#2295C2212yes—
252#2295C2212yes—
253#2295C2212yes—
254C2×#391C2212yes—
255C2×#391C2212yes—
256#2290C2212yes—
257#2290C2212yes—
258#2285C2211yescharacteristic
259#2283C2211yescharacteristic
260#2283C2211yescharacteristic
261#2283C2211yescharacteristic
262#2283C2211yescharacteristic
263C42×D4C2212yes—
264C4×#117C2211yescharacteristic
265C2×#376C2211yescharacteristic
266C2×#376C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C23×Q8C2312yes—
269C2×C4⋊Q8—28no—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×#125—28no—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C4×#41—28no—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×D4C2311yescharacteristic
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2311yescharacteristic
299C2×C4×D4C2311yescharacteristic
300C2×C4×D4C2312yes—
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2312yes—
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2311yescharacteristic
307C2×#117C2312yes—
308C2×#117C2314yes—
309C2×#117C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#401C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2312yes—
329#400C2312yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#399C2314yes—
373#399C2312yes—
374#399C2312yes—
375#399C2312yes—
376#399C2312yes—
377#399C2312yes—
378#399C2312yes—
379#399C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2312yes—
401#397C2312yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#394C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2312yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#390C2312yes—
453#390C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2312yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2312yes—
505#388C2312yes—
506#388C2314yes—
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#387C2312yes—
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#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#386C2312yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2312yes—
591#386C2312yes—
592#386C2312yes—
593#385C2314yes—
594#385C2314yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2312yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2312yes—
604#385C2312yes—
605#385C2314yes—
606#385C2314yes—
607#385C2312yes—
608#385C2312yes—
609#385C2314yes—
610#385C2314yes—
611#384C2312yes—
612#384C2312yes—
613#384C2312yes—
614#384C2312yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#383C2314yes—
619#383C2311yescharacteristic
620#383C2311yescharacteristic
621#383C2312yes—
622#383C2314yes—
623#383C2312yes—
624#383C2314yes—
625#383C2311yescharacteristic
626#383C2311yescharacteristic
627#382C2312yes—
628#382C2312yes—
629#382C2314yes—
630#382C2314yes—
631#382C2314yes—
632#382C2314yes—
633#382C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2311yescharacteristic
638#382C2311yescharacteristic
639#382C2312yes—
640#381C2312yes—
641#381C2312yes—
642#381C2314yes—
643#381C2314yes—
644#381C2312yes—
645#381C2312yes—
646#381C2312yes—
647#381C2314yes—
648#381C2311yescharacteristic
649#381C2311yescharacteristic
650#380C2312yes—
651#380C2312yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2311yescharacteristic
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2311yescharacteristic
665#380C2312yes—
666#380C2311yescharacteristic
667#380C2312yes—
668#380C2311yescharacteristic
669#380C2311yescharacteristic
670#380C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2311yescharacteristic
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2312yes—
712#376C2311yescharacteristic
713#376C2311yescharacteristic
714#376C2312yes—
715#376C2312yes—
716#376C2312yes—
717#376C2312yes—
718#376C2314yes—
719#376C2311yescharacteristic
720#376C2314yes—
721#376C2311yescharacteristic
722#376C2311yescharacteristic
723#376C2311yescharacteristic
724#376C2311yescharacteristic
725#376C2311yescharacteristic
726C2×#95C2314yes—
727C2×#95C2311yescharacteristic
728C2×#95C2314yes—
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2314yes—
732C2×#95C2311yescharacteristic
733C2×#95C2311yescharacteristic
734C2×#95C2311yescharacteristic
735C2×#95C2314yes—
736C43C2312yes—
737C2×#41—24no—
738C2×#41—24no—
739C2×#41—42no—
740C22×Q8—28no—
741C22×Q8—44no—
742C22×Q8—44no—
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×Q8C2411yescharacteristic
746C22×Q8C2414yes—
747C22×Q8C2414yes—
748C22×D4C2411yescharacteristic
749C22×D4C2411yescharacteristic
750C22×D4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C23×C4C2412yes—
759C23×C4C2414yes—
760C23×C4C2411yescharacteristic
761C23×C4C2411yescharacteristic
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2412yes—
765C23×C4C2412yes—
766C23×C4C2411yescharacteristic
767C4⋊Q8—28no—
768C4⋊Q8—28no—
769C4⋊Q8—24no—
770C4⋊Q8—24no—
771C4⋊Q8—28no—
772C4⋊Q8—44no—
773#125—28no—
774#125—28no—
775#125—28no—
776#125—28no—
777#125—44no—
778#123—28no—
779#123—44no—
780C22⋊Q8—48no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C4×Q8—24no—
786C4×Q8—24no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×D4—28no—
792C4×D4—24no—
793C4×D4—24no—
794C4×D4—24no—
795C4×D4—24no—
796C4×D4—24no—
797C4×D4—24no—
798C4×D4—44no—
799#117—24no—
800#117—24no—
801#117—24no—
802#117—44no—
803#117—48no—
804#117—44no—
805C2×C4⋊C4—24no—
806C2×C4⋊C4—28no—
807C2×C4⋊C4—28no—
808C2×C4⋊C4—24no—
809C2×C4⋊C4—28no—
810C2×C4⋊C4—28no—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C42—24no—
896C2×C42—24no—
897C2×C42—44no—
898C2×C42—44no—
899C2×C42#4118yes—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933#95C2411yescharacteristic
934#95C2412yes—
935#95C2411yescharacteristic
936#95C2411yescharacteristic
937#95C2412yes—
938#95C2411yescharacteristic
939#95C2411yescharacteristic
940#95C2412yes—
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2411yescharacteristic
967#95C2411yescharacteristic
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027C24C2511yescharacteristic
1028C24C2511yescharacteristic
1029C24C2511yescharacteristic
1030#41—416no—
1031C2×Q8—22no—
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—28no—
1035C2×Q8—22no—
1036C2×Q8—24no—
1037C2×Q8—24no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—41no—
1041C2×Q8—44no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—816no—
1047C2×D4—22no—
1048C2×D4—22no—
1049C2×D4—22no—
1050C2×D4—22no—
1051C2×D4—22no—
1052C2×D4—22no—
1053C2×D4—22no—
1054C2×D4—41no—
1055C2×D42−1+414yes—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—22no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—28no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—22no—
1076C22×C4—22no—
1077C22×C4—42no—
1078C22×C4—41no—
1079C22×C4—41no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—44no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4C2×#4114yes—
1095C22×C4C2×#4114yes—
1096C22×C4C2×#4114yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2514yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2514yes—
1108C22×C4C2514yes—
1109C22×C4C2514yes—
1110C22×C4C2514yes—
1111C22×C4C2512yes—
1112C22×C4C2514yes—
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2514yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—22no—
1140C4⋊C4—22no—
1141C4⋊C4—22no—
1142C4⋊C4—22no—
1143C4⋊C4—22no—
1144C4⋊C4—22no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C22⋊C4—22no—
1185C22⋊C4—22no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—22no—
1194C22⋊C4—22no—
1195C22⋊C4—22no—
1196C22⋊C4—22no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—42no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—42no—
1221C42—42no—
1222C42—42no—
1223C42—42no—
1224C42—44no—
1225C42—42no—
1226C42—44no—
1227C42—44no—
1228C42—42no—
1229C42—42no—
1230C42—42no—
1231C42—44no—
1232C42—44no—
1233C42—42no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42C2×#4114yes—
1239C42C2×#4114yes—
1240C42C2×#4114yes—
1241C42C2×#4114yes—
1242C23—22no—
1243C23—22no—
1244C23—21no—
1245C23—22no—
1246C23—21no—
1247C23—22no—
1248C23—21no—
1249C23—21no—
1250C23—22no—
1251C23—21no—
1252C23—22no—
1253C23C22×#4112yes—
1254C23C2×2−1+412yes—
1255C23C2×2−1+412yes—
1256C23#58512yes—
1257C23C2611yescharacteristic
1258Q8—44no—
1259Q8—48no—
1260Q8—48no—
1261Q8—88no—
1262Q8—164no—
1263D4—28no—
1264D4—44no—
1265D4—44no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—28no—
1276C2×C4—28no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—44no—
1337C2×C4—44no—
1338C2×C4—44no—
1339C2×C4—48no—
1340C2×C4—44no—
1341C2×C4—44no—
1342C2×C4—82no—
1343C2×C4—82no—
1344C2×C4—84no—
1345C2×C4—84no—
1346C2×C4—84no—
1347C2×C4—84no—
1348C2×C4—88no—
1349C2×C4—84no—
1350C2×C4C22×#4112yes—
1351C2×C4C22×#4112yes—
1352C2×C4C22×#4112yes—
1353C2×C4C22×#4112yes—
1354C2×C4C22×#4112yes—
1355C2×C4C22×#4112yes—
1356C2×C4C2×2−1+412yes—
1357C2×C4#58514yes—
1358C22—22no—
1359C22—22no—
1360C22—24no—
1361C22—24no—
1362C22—22no—
1363C22—24no—
1364C22—41no—
1365C22—41no—
1366C22—42no—
1367C22—41no—
1368C22—41no—
1369C22—41no—
1370C22—42no—
1371C22—42no—
1372C22#349514yes—
1373C22C23×#4111yescharacteristic
1374C22C22×2−1+411yescharacteristic
1375C22C2×#58511yescharacteristic
1376C22C2×#58512yes—
1377C222−1+612yes—
1378C4—22no—
1379C4—22no—
1380C4—22no—
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—44no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—44no—
1389C4—44no—
1390C4—41no—
1391C4—41no—
1392C4—44no—
1393C4—42no—
1394C4—44no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—44no—
1405C4#351014yes—
1406C2—24no—
1407C2—42no—
1408C2—81no—
1409C2C2×#349511yescharacteristic
1410C2C2×#351011yescharacteristic
1411C2#6286011yescharacteristic
1412C2#6295012yes—
1413C2#6297112yes—
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. #51619C2semidirect
2. #51618C2semidirect
3. #51228C2semidirect
4. #51227C2semidirect
5. #50920C2semidirect
6. #50915C2semidirect
7. #44512C2semidirect
9. #44463C2semidirect
10. #44460C2semidirect
11. #43516C2semidirect
12. #43513C2semidirect
13. #39274C2semidirect
14. #39271C2semidirect
15. #38243C2semidirect
16. #38239C2semidirect
17. #38113C2semidirect
18. #38111C2semidirect
19. #37385C2semidirect
20. #37385C2semidirect
21. #36304C2semidirect
22. #36277C2semidirect
23. #35323C2semidirect
24. #35315C2semidirect
25. #35304C2semidirect
28. C2×#2642C2semidirect
29. #34378C2semidirect
30. #34371C2semidirect

Maximal subgroups

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

subgroupindex
#516192
#516182
#512282
#512272
#509202
#509152
#445122
#444742
#444632
#444602
#435162
#435132
#392742
#392712
#382432
#382392
#381132
#381112
#373852
#363042
#362772
#353232
#353152
#353042
#352792
#351382
C2×#26422
#343782
#343712
#341232