Finite Group Databasebeta

← #7658121

Subgroups — #7658121

Order 512.

4210 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42231C214yesmaximal, complemented
2#42230C214yesmaximal, complemented
3#42159C214yesmaximal, complemented
4#41685C214yesmaximal, complemented
5#41677C214yesmaximal, complemented
6#41394C212yesmaximal, complemented
7#41392C212yesmaximal
8#39274C212yesmaximal, complemented
9#39271C212yesmaximal, complemented
10#38243C212yesmaximal, complemented
11#38239C212yesmaximal, complemented
12#38113C212yesmaximal, complemented
13#38111C212yesmaximal, complemented
14#37615C211yesmaximal, characteristic
15#37598C212yesmaximal, complemented
16#37598C212yesmaximal, complemented
17#37549C211yesmaximal, characteristic
18#36304C212yesmaximal, complemented
19#36277C212yesmaximal, complemented
20#36068C214yesmaximal, complemented
21#36035C212yesmaximal, complemented
22#36034C212yesmaximal
23#35321C212yesmaximal, complemented
24#35304C211yesmaximal, characteristic, complemented
25#34629C212yesmaximal, complemented
26C2×#2642C211yesmaximal, characteristic, complemented
27#34239C211yesmaximal, characteristic, complemented
28#34216C211yesmaximal, characteristic, complemented
29#34149C211yesmaximal, characteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#529C2211yescharacteristic
32C22×#125C2211yescharacteristic
33#2863C2212yes—
34#2863C2212yes—
35#2857C2212yes—
36#2855C2212yes—
37#2855C2212yes—
38#2851C2212yes—
39#2839C2214yes—
40#2839C2214yes—
41#2838C2214yes—
42#2838C2214yes—
43#2822C2212yes—
44#2821C2214yes—
45#2820C2212yes—
46#2810C2214yes—
47#2807C2214yes—
48#2805C2214yes—
49#2799C2214yes—
50#2798C2214yes—
51#2798C2214yes—
52#2798C2214yes—
53#2796C2214yes—
54#2794C2214yes—
55#2794C2214yes—
56#2789C2214yes—
57#2789C2214yes—
58#2776C2214yes—
59#2776C2214yes—
60#2773C2214yes—
61#2771C2214yes—
62#2767C2214yes—
63#2762C2214yes—
64#2759C2214yes—
65#2758C2214yes—
66#2758C2214yes—
67#2755C2214yes—
68#2754C2214yes—
69#2751C2214yes—
70#2666C2214yes—
71#2666C2214yes—
72#2664C2214yes—
73#2660C2212yes—
74#2660C2212yes—
75#2655C2214yes—
76#2655C2214yes—
77#2655C2214yes—
78#2655C2214yes—
79#2654C2214yes—
80#2654C2214yes—
81#2652C2214yes—
82#2652C2214yes—
83#2650C2214yes—
84#2650C2214yes—
85#2647C2212yes—
86#2645C2212yes—
87#2645C2212yes—
88#2642C2211yescharacteristic
89#2642C2212yes—
90#2642C2212yes—
91#2642C2212yes—
92#2642C2212yes—
93#2642C2211yescharacteristic
94#2642C2211yescharacteristic
95#2642C2214yes—
96#2642C2211yescharacteristic
97#2640C2212yes—
98#2629C2212yes—
99#2629C2212yes—
100#2627C2212yes—
101#2625C2212yes—
102#2625C2212yes—
103#2623C2214yes—
104#2621C2212yes—
105#2621C2212yes—
106#2618C2212yes—
107#2612C2214yes—
108#2607C2214yes—
109#2606C2212yes—
110#2605C2214yes—
111#2605C2214yes—
112#2605C2212yes—
113#2596C2214yes—
114#2596C2214yes—
115#2595C2214yes—
116#2589C2214yes—
117#2589C2214yes—
118#2588C2214yes—
119#2588C2214yes—
120#2588C2214yes—
121#2585C2214yes—
122#2585C2214yes—
123#2584C2211yescharacteristic
124#2584C2211yescharacteristic
125#2575C2214yes—
126#2573C2214yes—
127#2573C2214yes—
128#2570C2214yes—
129#2569C2214yes—
130#2569C2212yes—
131#2568C2212yes—
132#2564C2214yes—
133#2562C2211yescharacteristic
134#2562C2211yescharacteristic
135#2549C2212yes—
136#2542C2212yes—
137#2533C2214yes—
138#2533C2214yes—
139#2528C2214yes—
140#2527C2214yes—
141#2525C2214yes—
142#2525C2214yes—
143#2524C2214yes—
144#2524C2214yes—
145#2524C2214yes—
146#2523C2214yes—
147#2520C2214yes—
148#2520C2214yes—
149#2520C2214yes—
150#2516C2214yes—
151#2515C2214yes—
152#2515C2214yes—
153#2514C2214yes—
154#2514C2212yes—
155#2514C2212yes—
156#2511C2212yes—
157#2511C2212yes—
158#2511C2214yes—
159#2510C2214yes—
160#2510C2214yes—
161#2509C2214yes—
162#2505C2214yes—
163#2505C2214yes—
164#2504C2212yes—
165#2502C2212yes—
166#2498C2214yes—
167#2493C2214yes—
168#2493C2214yes—
169#2492C2212yes—
170#2492C2212yes—
171#2489C2212yes—
172#2489C2212yes—
173#2488C2214yes—
174#2487C2212yes—
175#2486C2212yes—
176#2453C2212yes—
177#2453C2212yes—
178#2451C2212yes—
179#2451C2212yes—
180#2438C2214yes—
181#2438C2214yes—
182#2423C2212yes—
183#2423C2212yes—
184#2421C2212yes—
185#2421C2212yes—
186#2419C2214yes—
187#2413C2214yes—
188#2409C2212yes—
189#2409C2212yes—
190#2402C2214yes—
191#2402C2214yes—
192#2401C2214yes—
193#2401C2214yes—
194C2×#400C2214yes—
195C2×#400C2212yes—
196C2×#400C2212yes—
197#2373C2212yes—
198#2373C2212yes—
199#2372C2212yes—
200#2371C2212yes—
201#2371C2214yes—
202#2370C2212yes—
203#2370C2212yes—
204#2369C2214yes—
205#2368C2211yescharacteristic
206#2368C2211yescharacteristic
207#2368C2214yes—
208#2365C2212yes—
209#2365C2212yes—
210#2364C2211yescharacteristic
211#2364C2211yescharacteristic
212#2359C2212yes—
213#2359C2212yes—
214#2359C2214yes—
215#2353C2214yes—
216#2345C2212yes—
217#2345C2212yes—
218#2345C2211yescharacteristic
219#2345C2211yescharacteristic
220#2344C2212yes—
221#2344C2211yescharacteristic
222#2344C2211yescharacteristic
223#2344C2212yes—
224#2343C2214yes—
225Q8×C22⋊C4C2212yes—
226Q8×C22⋊C4C2212yes—
227#2336C2214yes—
228#2331C2212yes—
229#2331C2214yes—
230#2330C2212yes—
231#2323C2212yes—
232#2323C2212yes—
233#2320C2212yes—
234#2320C2212yes—
235#2316C2212yes—
236#2313C2212yes—
237C4×C4⋊Q8C2212yes—
238C4×C4⋊Q8C2212yes—
239C4×#125C2212yes—
240C4×#125C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243#2298C2212yes—
244#2295C2212yes—
245#2295C2212yes—
246#2295C2212yes—
247C2×#391C2212yes—
248C2×#391C2212yes—
249#2290C2212yes—
250#2290C2212yes—
251#2285C2211yescharacteristic
252#2283C2211yescharacteristic
253#2274C2212yes—
254#2274C2212yes—
255C42×D4C2212yes—
256C4×#117C2212yes—
257C4×#117C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C23×Q8C2312yes—
260C2×C4⋊Q8—28no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267#529—28no—
268C2×#126C2312yes—
269C2×#125—28no—
270C2×#125C2311yescharacteristic
271C2×#125C2311yescharacteristic
272C2×#125C2311yescharacteristic
273C2×#125C2311yescharacteristic
274C2×#125C2312yes—
275C2×#125C2311yescharacteristic
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#124C2311yescharacteristic
279C2×#123C2312yes—
280C2×#123C2314yes—
281C2×C22⋊Q8C2311yescharacteristic
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×#121C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C2×#117C2312yes—
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C42C2312yes—
311C22×C42C2312yes—
312C22×C42C2311yescharacteristic
313#401C2314yes—
314#401C2314yes—
315#401C2314yes—
316#401C2314yes—
317#400C2312yes—
318#400C2312yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2312yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2312yes—
413#395C2312yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#394C2312yes—
420#394C2312yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#390C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2312yes—
499#388C2312yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2314yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2314yes—
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#387C2312yes—
541#387C2312yes—
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#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2312yes—
586#386C2312yes—
587#386C2312yes—
588#386C2314yes—
589#386C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2312yes—
597#385C2314yes—
598#385C2314yes—
599#385C2312yes—
600#385C2312yes—
601#385C2312yes—
602#385C2314yes—
603#384C2312yes—
604#384C2314yes—
605#384C2312yes—
606#383C2312yes—
607#383C2314yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#382C2312yes—
614#382C2312yes—
615#382C2314yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2314yes—
620#382C2312yes—
621#381C2312yes—
622#381C2312yes—
623#381C2314yes—
624#381C2314yes—
625#381C2314yes—
626#381C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2314yes—
633#380C2312yes—
634#380C2314yes—
635#380C2312yes—
636#380C2314yes—
637#380C2311yescharacteristic
638#380C2312yes—
639#380C2311yescharacteristic
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2311yescharacteristic
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C22⋊C4C2311yescharacteristic
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2311yescharacteristic
683C4×C22⋊C4C2311yescharacteristic
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695#376C2312yes—
696#376C2312yes—
697#376C2312yes—
698#376C2314yes—
699#376C2311yescharacteristic
700#376C2314yes—
701#376C2311yescharacteristic
702#376C2312yes—
703#376C2312yes—
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706C2×#95C2314yes—
707C2×#95C2311yescharacteristic
708C2×#95C2314yes—
709C2×#95C2314yes—
710C2×#95C2312yes—
711C2×#95C2314yes—
712C2×#95C2311yescharacteristic
713C43C2312yes—
714C43C2312yes—
715C22×Q8—28no—
716C22×Q8—44no—
717C22×Q8—44no—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×D4C2412yes—
724C22×D4C2411yescharacteristic
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2414yes—
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2411yescharacteristic
736C4⋊Q8—24no—
737C4⋊Q8—24no—
738C4⋊Q8—28no—
739C4⋊Q8—28no—
740C4⋊Q8—28no—
741C4⋊Q8—44no—
742#126—28no—
743#125—24no—
744#125—24no—
745#125—24no—
746#125—24no—
747#125—28no—
748#125—28no—
749#125—24no—
750#125—44no—
751#124—24no—
752#123—28no—
753#123—48no—
754C22⋊Q8—24no—
755C22⋊Q8—48no—
756C22⋊Q8—44no—
757C22⋊Q8—44no—
758C22⋊Q8—44no—
759C22⋊Q8—44no—
760#121—24no—
761C4×Q8—24no—
762C4×Q8—44no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×Q8—44no—
766C4×D4—28no—
767C4×D4—28no—
768C4×D4—24no—
769C4×D4—44no—
770#117—24no—
771#117—28no—
772#117—28no—
773#117—44no—
774#117—42no—
775#117—44no—
776#117—44no—
777C2×C4⋊C4—24no—
778C2×C4⋊C4—28no—
779C2×C4⋊C4—28no—
780C2×C4⋊C4—24no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C22⋊C4C2411yescharacteristic
849C2×C22⋊C4C2411yescharacteristic
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2411yescharacteristic
874C2×C42—44no—
875C2×C42—44no—
876C2×C42#4118yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909#95C2411yescharacteristic
910#95C2412yes—
911#95C2411yescharacteristic
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2411yescharacteristic
917#95C2412yes—
918#95C2411yescharacteristic
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#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997C24C2512yes—
998C24C2511yescharacteristic
999C2×Q8—24no—
1000C2×Q8—24no—
1001C2×Q8—22no—
1002C2×Q8—28no—
1003C2×Q8—24no—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—24no—
1007C2×Q8—44no—
1008C2×Q8—44no—
1009C2×Q8—42no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—816no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—22no—
1018C2×D4—42no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—28no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4C2×#4114yes—
1047C22×C4C2×#4114yes—
1048C22×C4C2×#4114yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2514yes—
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2511yescharacteristic
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2511yescharacteristic
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—22no—
1099C4⋊C4—24no—
1100C4⋊C4—22no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C22⋊C4—24no—
1142C22⋊C4—22no—
1143C22⋊C4—24no—
1144C22⋊C4—22no—
1145C22⋊C4—22no—
1146C22⋊C4—24no—
1147C22⋊C4—28no—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C42−1+414yes—
1167C42—24no—
1168C42—24no—
1169C42—28no—
1170C42—24no—
1171C42—24no—
1172C42—24no—
1173C42—24no—
1174C42—24no—
1175C42—42no—
1176C42—42no—
1177C42—42no—
1178C42—42no—
1179C42—42no—
1180C42—44no—
1181C42—42no—
1182C42—42no—
1183C42—44no—
1184C42—44no—
1185C42—42no—
1186C42—42no—
1187C42—42no—
1188C42—42no—
1189C42—44no—
1190C42—42no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42C2×#4114yes—
1196C42C2×#4114yes—
1197C42C2×#4114yes—
1198C42C2×#4114yes—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23C22×#4112yes—
1209C23C2×2−1+412yes—
1210C23#58512yes—
1211C23C2611yescharacteristic
1212Q8—48no—
1213Q8—48no—
1214Q8—82no—
1215Q8—88no—
1216Q8—164no—
1217D4—48no—
1218D4—82no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—28no—
1229C2×C4—28no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
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—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—44no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—84no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—84no—
1295C2×C4—88no—
1296C2×C4—84no—
1297C2×C4C22×#4112yes—
1298C2×C4C22×#4112yes—
1299C2×C4C22×#4112yes—
1300C2×C4C22×#4112yes—
1301C2×C4C22×#4112yes—
1302C2×C4C22×#4112yes—
1303C2×C4C2×2−1+414yes—
1304C2×C4#58514yes—
1305C22—22no—
1306C22—22no—
1307C22—24no—
1308C22—24no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22#346114yes—
1317C22C23×#4111yescharacteristic
1318C22C22×2−1+411yescharacteristic
1319C22C2×#58512yes—
1320C22C2×#58511yescharacteristic
1321C222−1+612yes—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—22no—
1326C4—22no—
1327C4—24no—
1328C4—42no—
1329C4—44no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—44no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—44no—
1348C4#351014yes—
1349C2—24no—
1350C2—82no—
1351C2C2×#346111yescharacteristic
1352C2C2×#351011yescharacteristic
1353C2#6286011yescharacteristic
1354C2#6295012yes—
1355C2#6297112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42231C2semidirect
2. #42230C2semidirect
3. #42159C2semidirect
4. #41685C2semidirect
5. #41677C2semidirect
6. #41394C2semidirect
8. #39274C2semidirect
9. #39271C2semidirect
10. #38243C2semidirect
11. #38239C2semidirect
12. #38113C2semidirect
13. #38111C2semidirect
15. #37598C2semidirect
16. #37598C2semidirect
18. #36304C2semidirect
19. #36277C2semidirect
20. #36068C2semidirect
21. #36035C2semidirect
23. #35321C2semidirect
24. #35304C2semidirect
25. #34629C2semidirect
26. C2×#2642C2semidirect
27. #34239C2semidirect
28. #34216C2semidirect

Maximal subgroups

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

subgroupindex
#422312
#422302
#421592
#416852
#416772
#413942
#413922
#392742
#392712
#382432
#382392
#381132
#381112
#376152
#375982
#375492
#363042
#362772
#360682
#360352
#360342
#353212
#353042
#346292
C2×#26422
#342392
#342162
#341492