Finite Group Databasebeta

← #7656033

Subgroups — #7656033

Order 512.

4362 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42703C212yesmaximal, complemented
2#42698C212yesmaximal, complemented
3#42530C212yesmaximal, complemented
4#42525C212yesmaximal, complemented
5#41751C214yesmaximal, complemented
6#41746C214yesmaximal, complemented
7#41098C214yesmaximal, complemented
8#41095C214yesmaximal, complemented
9#39199C212yesmaximal, complemented
10#39039C214yesmaximal, complemented
11#38982C212yesmaximal, complemented
12#38197C214yesmaximal, complemented
13#37540C211yesmaximal, characteristic, complemented
14#37539C211yesmaximal, characteristic
15#37464C212yesmaximal, complemented
16#37463C212yesmaximal, complemented
17#36487C212yesmaximal, complemented
18#36255C212yesmaximal, complemented
19#35973C212yesmaximal, complemented
20#35968C212yesmaximal, complemented
21#35958C212yesmaximal, complemented
22#35952C212yesmaximal, complemented
23#35180C211yesmaximal, characteristic
24#35021C212yesmaximal, complemented
25#34595C211yesmaximal, characteristic, complemented
26#34584C212yesmaximal, complemented
27#34236C211yesmaximal, characteristic
28#34235C211yesmaximal, characteristic, complemented
29C2×#2370C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C22×#125C2211yescharacteristic
33#2853C2214yes—
34#2852C2214yes—
35#2850C2212yes—
36#2850C2212yes—
37#2839C2214yes—
38#2838C2214yes—
39#2831C2214yes—
40#2830C2214yes—
41#2822C2212yes—
42#2822C2212yes—
43#2820C2212yes—
44#2820C2212yes—
45#2807C2214yes—
46#2798C2214yes—
47#2787C2214yes—
48#2783C2214yes—
49#2777C2214yes—
50#2773C2214yes—
51#2771C2214yes—
52#2762C2214yes—
53#2762C2214yes—
54#2761C2214yes—
55#2758C2214yes—
56#2757C2214yes—
57#2755C2214yes—
58#2747C2214yes—
59#2747C2214yes—
60#2745C2214yes—
61#2744C2214yes—
62#2742C2214yes—
63#2739C2214yes—
64#2738C2214yes—
65#2737C2214yes—
66#2723C2214yes—
67#2722C2214yes—
68#2689C2214yes—
69#2666C2212yes—
70#2666C2212yes—
71#2666C2212yes—
72#2666C2212yes—
73#2666C2214yes—
74#2665C2214yes—
75#2660C2212yes—
76#2660C2212yes—
77#2659C2211yescharacteristic
78#2659C2211yescharacteristic
79#2655C2214yes—
80#2655C2214yes—
81#2654C2214yes—
82#2652C2214yes—
83#2651C2214yes—
84#2651C2214yes—
85#2650C2214yes—
86#2650C2214yes—
87#2646C2211yescharacteristic
88#2646C2211yescharacteristic
89#2643C2214yes—
90#2642C2212yes—
91#2641C2212yes—
92#2639C2212yes—
93#2639C2212yes—
94#2638C2214yes—
95#2637C2214yes—
96#2634C2214yes—
97#2633C2214yes—
98#2627C2212yes—
99#2627C2212yes—
100#2627C2212yes—
101#2627C2212yes—
102#2623C2214yes—
103#2618C2212yes—
104#2618C2212yes—
105#2612C2214yes—
106#2605C2214yes—
107#2597C2214yes—
108#2596C2214yes—
109#2596C2214yes—
110#2594C2214yes—
111#2593C2214yes—
112#2592C2214yes—
113#2592C2212yes—
114#2592C2212yes—
115#2589C2214yes—
116#2586C2214yes—
117#2585C2214yes—
118#2582C2212yes—
119#2581C2212yes—
120#2580C2212yes—
121#2577C2214yes—
122#2577C2214yes—
123#2575C2214yes—
124#2574C2214yes—
125#2574C2214yes—
126#2573C2214yes—
127#2571C2212yes—
128#2571C2212yes—
129#2570C2212yes—
130#2570C2212yes—
131#2570C2212yes—
132#2570C2212yes—
133#2569C2214yes—
134#2568C2212yes—
135#2566C2212yes—
136#2566C2212yes—
137#2565C2212yes—
138#2565C2212yes—
139#2563C2212yes—
140#2562C2214yes—
141#2548C2212yes—
142#2547C2212yes—
143#2538C2212yes—
144#2532C2214yes—
145#2531C2214yes—
146#2530C2214yes—
147#2526C2214yes—
148#2525C2214yes—
149#2524C2214yes—
150#2522C2214yes—
151#2520C2214yes—
152#2520C2214yes—
153#2515C2214yes—
154#2514C2212yes—
155#2514C2212yes—
156#2513C2212yes—
157#2513C2212yes—
158#2512C2212yes—
159#2512C2212yes—
160#2511C2212yes—
161#2511C2212yes—
162#2510C2214yes—
163#2505C2214yes—
164#2504C2212yes—
165#2503C2212yes—
166#2502C2212yes—
167#2501C2212yes—
168#2493C2214yes—
169#2488C2214yes—
170#2488C2214yes—
171#2484C2214yes—
172#2481C2214yes—
173#2479C2214yes—
174#2478C2214yes—
175#2469C2214yes—
176#2468C2214yes—
177#2468C2214yes—
178#2465C2214yes—
179#2450C2214yes—
180#2449C2214yes—
181#2448C2212yes—
182#2448C2212yes—
183#2447C2212yes—
184#2447C2212yes—
185#2438C2214yes—
186#2419C2214yes—
187#2419C2214yes—
188#2406C2214yes—
189#2402C2214yes—
190#2402C2212yes—
191#2402C2212yes—
192#2401C2214yes—
193#2399C2212yes—
194#2399C2212yes—
195#2396C2214yes—
196#2395C2214yes—
197#2370C2214yes—
198#2370C2214yes—
199#2370C2212yes—
200#2370C2212yes—
201#2370C2212yes—
202#2370C2212yes—
203#2369C2211yescharacteristic
204#2369C2211yescharacteristic
205#2367C2212yes—
206#2367C2212yes—
207#2366C2211yescharacteristic
208#2366C2211yescharacteristic
209#2365C2211yescharacteristic
210#2365C2211yescharacteristic
211#2365C2211yescharacteristic
212#2365C2211yescharacteristic
213#2361C2212yes—
214#2361C2212yes—
215#2360C2212yes—
216#2360C2212yes—
217#2357C2212yes—
218#2357C2212yes—
219#2356C2212yes—
220#2356C2212yes—
221#2355C2212yes—
222#2355C2212yes—
223#2355C2212yes—
224#2354C2212yes—
225#2351C2212yes—
226#2349C2212yes—
227#2343C2214yes—
228#2339C2214yes—
229#2337C2214yes—
230#2336C2214yes—
231#2322C2214yes—
232#2320C2212yes—
233#2319C2212yes—
234#2318C2214yes—
235#2311C2212yes—
236#2311C2212yes—
237C4×C22⋊Q8C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×C22⋊Q8C2212yes—
240C4×C22⋊Q8C2212yes—
241C4×#123C2214yes—
242C4×#121C2212yes—
243C4×#121C2212yes—
244C2×#389C2211yescharacteristic
245C2×#389C2212yes—
246C2×#389C2211yescharacteristic
247#2290C2214yes—
248C2×#387C2212yes—
249C2×#387C2212yes—
250#2283C2211yescharacteristic
251#2283C2211yescharacteristic
252#2276C2212yes—
253#2275C2212yes—
254C2×C4×C4⋊C4C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C22×#41C2312yes—
260#533—28no—
261#532—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×#127C2311yescharacteristic
266C2×#126C2314yes—
267C2×#126C2314yes—
268C2×#125—28no—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×#121C2312yes—
285C2×#121C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×#117C2312yes—
303C2×#117C2314yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2312yes—
317C22×C42C2312yes—
318C22×C42C2312yes—
319C22×C42C2311yescharacteristic
320#401C2314yes—
321#401C2314yes—
322#400C2314yes—
323#400C2314yes—
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#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2312yes—
379#398C2312yes—
380#398C2314yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
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#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2312yes—
419#395C2314yes—
420#395C2312yes—
421#395C2314yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2312yes—
457#391C2314yes—
458#391C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2314yes—
466#390C2314yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
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#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2312yes—
564#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2312yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2312yes—
601#385C2312yes—
602#385C2314yes—
603#385C2314yes—
604#384C2312yes—
605#384C2312yes—
606#384C2312yes—
607#384C2312yes—
608#383C2314yes—
609#383C2314yes—
610#383C2314yes—
611#383C2312yes—
612#383C2312yes—
613#383C2314yes—
614#382C2312yes—
615#382C2312yes—
616#382C2311yescharacteristic
617#382C2311yescharacteristic
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2311yescharacteristic
623#382C2311yescharacteristic
624#382C2314yes—
625#382C2314yes—
626#382C2314yes—
627#382C2314yes—
628#381C2314yes—
629#381C2314yes—
630#381C2314yes—
631#381C2314yes—
632#381C2312yes—
633#381C2312yes—
634#381C2314yes—
635#381C2314yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2311yescharacteristic
644#380C2311yescharacteristic
645#380C2311yescharacteristic
646#380C2311yescharacteristic
647#380C2312yes—
648#380C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2314yes—
692C4×C4⋊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⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703#376C2312yes—
704#376C2312yes—
705#376C2314yes—
706#376C2314yes—
707C2×#95C2314yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2311yescharacteristic
711C2×#95C2311yescharacteristic
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C2×#41—28no—
716C2×#41—44no—
717C2×#41—44no—
718C22×Q8C2412yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×D4C2412yes—
724C22×D4C2414yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2411yescharacteristic
741C4⋊Q8—24no—
742C4⋊Q8—24no—
743C4⋊Q8—24no—
744#127—24no—
745#126—84no—
746#126—84no—
747#125—28no—
748#125—28no—
749#125—28no—
750#125—28no—
751#125—28no—
752#124—28no—
753#124—44no—
754#124—44no—
755#123—48no—
756#123—48no—
757C22⋊Q8—28no—
758C22⋊Q8—28no—
759C22⋊Q8—44no—
760C22⋊Q8—44no—
761C22⋊Q8—84no—
762#121—28no—
763#121—28no—
764C4×Q8—28no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—44no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—82no—
771C4×Q8—82no—
772C4×D4—28no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—44no—
776C4×D4—48no—
777C4×D4—48no—
778C4×D4—82no—
779C4×D4—82no—
780#117—28no—
781#117—84no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—24no—
785C2×C4⋊C4—28no—
786C2×C4⋊C4—24no—
787C2×C4⋊C4—42no—
788C2×C4⋊C4—42no—
789C2×C4⋊C4—42no—
790C2×C4⋊C4—44no—
791C2×C4⋊C4—82no—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C42—42no—
892C2×C42—42no—
893C2×C42—44no—
894C2×C42—82no—
895C2×C42—82no—
896C2×C42#4118yes—
897C2×C42C2414yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004C24C2514yes—
1005C24C2511yescharacteristic
1006#41—816no—
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—24no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—42no—
1013C2×Q8—42no—
1014C2×Q8—42no—
1015C2×Q8—42no—
1016C2×Q8—42no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8—42no—
1020C2×Q8—42no—
1021C2×Q8—42no—
1022C2×D4—28no—
1023C2×D4—28no—
1024C2×D4—28no—
1025C2×D4—24no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—24no—
1029C2×D4—24no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C2×D4—42no—
1033C2×D4—42no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—22no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—22no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—28no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—42no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—41no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—41no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4C2×#4114yes—
1074C22×C4C2×#4114yes—
1075C22×C4C2×#4114yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—22no—
1121C4⋊C4—28no—
1122C4⋊C4—22no—
1123C4⋊C4—22no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—41no—
1134C4⋊C4—41no—
1135C4⋊C4—41no—
1136C4⋊C4—41no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—44no—
1155C4⋊C4—41no—
1156C4⋊C4—41no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C42−1+414yes—
1173C22⋊C4—28no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C42—28no—
1203C42—24no—
1204C42—24no—
1205C42—28no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—42no—
1211C42—42no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C42—42no—
1216C42—42no—
1217C42—42no—
1218C42—42no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42C2×#4114yes—
1226C42C2×#4114yes—
1227C42C2×#4114yes—
1228C42C2×#4114yes—
1229C23—21no—
1230C23—21no—
1231C23—21no—
1232C23—21no—
1233C23—24no—
1234C23—24no—
1235C23—24no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23C22×#4112yes—
1241C23#58512yes—
1242C23#58512yes—
1243C23C2611yescharacteristic
1244Q8—48no—
1245Q8—48no—
1246Q8—84no—
1247Q8—84no—
1248Q8—84no—
1249D4—48no—
1250D4—416no—
1251D4—48no—
1252D4—84no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—28no—
1266C2×C4—28no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—44no—
1328C2×C4—48no—
1329C2×C4—48no—
1330C2×C4—44no—
1331C2×C4—44no—
1332C2×C4—48no—
1333C2×C4—88no—
1334C2×C4—88no—
1335C2×C4—82no—
1336C2×C4—84no—
1337C2×C4—82no—
1338C2×C4—164no—
1339C2×C4C22×#4112yes—
1340C2×C4C22×#4112yes—
1341C2×C4C22×#4112yes—
1342C2×C4C22×#4112yes—
1343C2×C4C22×#4112yes—
1344C2×C4C22×#4112yes—
1345C2×C4C2×2−1+414yes—
1346C2×C4C2×2−1+412yes—
1347C2×C4#58512yes—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—22no—
1354C22—44no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22#351014yes—
1362C22C23×#4111yescharacteristic
1363C22C22×2−1+411yescharacteristic
1364C22C2×#58511yescharacteristic
1365C22C2×#58511yescharacteristic
1366C22C2×#58511yescharacteristic
1367C22H(7,𝔽2)11yescharacteristic
1368C222−1+611yescharacteristic
1369C4—22no—
1370C4—22no—
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—24no—
1375C4—44no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—44no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—42no—
1395C4#346114yes—
1396C2—24no—
1397C2—84no—
1398C2C2×#346111yescharacteristic
1399C2C2×#351011yescharacteristic
1400C2#6284511yescharacteristic
1401C2#6290711yescharacteristic
1402C2#6290811yescharacteristic
1403C2#6294811yescharacteristic
1404C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42703C2semidirect
2. #42698C2semidirect
3. #42530C2semidirect
4. #42525C2semidirect
5. #41751C2semidirect
6. #41746C2semidirect
7. #41098C2semidirect
8. #41095C2semidirect
9. #39199C2semidirect
10. #39039C2semidirect
11. #38982C2semidirect
12. #38197C2semidirect
13. #37540C2semidirect
15. #37464C2semidirect
16. #37463C2semidirect
17. #36487C2semidirect
18. #36255C2semidirect
19. #35973C2semidirect
20. #35968C2semidirect
21. #35958C2semidirect
22. #35952C2semidirect
24. #35021C2semidirect
25. #34595C2semidirect
26. #34584C2semidirect
28. #34235C2semidirect
29. C2×#2370C2semidirect

Maximal subgroups

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

subgroupindex
#427032
#426982
#425302
#425252
#417512
#417462
#410982
#410952
#391992
#390392
#389822
#381972
#375402
#375392
#374642
#374632
#364872
#362552
#359732
#359682
#359582
#359522
#351802
#350212
#345952
#345842
#342362
#342352
C2×#23702