Finite Group Databasebeta

← #7697079

Subgroups — #7697079

Order 512.

5423 conjugacy classes of subgroups.

The subgroup lattice has 1465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59941C212yesmaximal, complemented
2#59933C211yesmaximal, characteristic, complemented
3#59882C214yesmaximal, complemented
4#59867C212yesmaximal, complemented
5#52257C211yesmaximal, characteristic, complemented
6C2×#2799C212yesmaximal, complemented
7#45351C211yesmaximal, characteristic, complemented
8#45305C212yesmaximal, complemented
9#45116C212yesmaximal, complemented
10#45115C211yesmaximal, characteristic, complemented
11#44795C212yesmaximal, complemented
12#44043C214yesmaximal, complemented
13#43727C212yesmaximal, complemented
14#43647C214yesmaximal, complemented
15#39563C212yesmaximal, complemented
16#39559C214yesmaximal, complemented
17#38251C212yesmaximal, complemented
18#38247C214yesmaximal, complemented
19#38115C214yesmaximal, complemented
20#38111C212yesmaximal, complemented
21#36303C211yesmaximal, characteristic, complemented
22#36274C212yesmaximal, complemented
23#36085C211yesmaximal, characteristic
24#36067C211yesmaximal, characteristic, complemented
25#35998C212yesmaximal, complemented
26#35888C212yesmaximal, complemented
27#34289C212yesmaximal, complemented
28#34260C212yesmaximal, complemented
29#34259C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic
31C2×D4×Q8C2211yescharacteristic
32C2×#547C2212yes—
33C2×#547C2211yescharacteristic
34C2×#520C2212yes—
35C2×#520C2211yescharacteristic
36C2×C4×#41C2212yes—
37#2862C2211yescharacteristic
38#2857C2212yes—
39#2855C2214yes—
40#2850C2212yes—
41#2799C2214yes—
42#2799C2212yes—
43#2799C2211yescharacteristic
44#2799C2212yes—
45#2799C2212yes—
46#2799C2214yes—
47#2799C2214yes—
48#2799C2214yes—
49#2799C2214yes—
50#2799C2214yes—
51#2798C2212yes—
52#2798C2214yes—
53#2797C2212yes—
54#2796C2212yes—
55#2789C2211yescharacteristic
56#2789C2214yes—
57#2786C2212yes—
58#2786C2214yes—
59#2782C2211yescharacteristic
60#2778C2212yes—
61#2762C2214yes—
62#2759C2214yes—
63#2758C2214yes—
64#2758C2214yes—
65#2755C2214yes—
66#2755C2214yes—
67#2754C2214yes—
68#2751C2214yes—
69#2750C2214yes—
70#2748C2212yes—
71#2747C2214yes—
72#2745C2214yes—
73#2744C2214yes—
74#2743C2214yes—
75#2740C2214yes—
76#2739C2214yes—
77#2730C2212yes—
78#2728C2211yescharacteristic
79#2722C2212yes—
80#2693C2212yes—
81#2645C2212yes—
82#2643C2214yes—
83#2625C2212yes—
84#2625C2211yescharacteristic
85#2623C2214yes—
86#2623C2212yes—
87#2616C2211yescharacteristic
88#2614C2212yes—
89#2612C2212yes—
90#2607C2214yes—
91#2605C2214yes—
92#2605C2214yes—
93#2601C2214yes—
94#2589C2214yes—
95#2588C2214yes—
96#2588C2214yes—
97#2586C2212yes—
98#2582C2212yes—
99#2574C2214yes—
100#2572C2212yes—
101#2572C2214yes—
102#2569C2214yes—
103#2568C2212yes—
104#2568C2211yescharacteristic
105#2560C2214yes—
106#2557C2214yes—
107#2547C2211yescharacteristic
108#2530C2214yes—
109#2527C2214yes—
110#2527C2214yes—
111#2527C2214yes—
112#2523C2212yes—
113#2523C2214yes—
114#2522C2214yes—
115#2521C2214yes—
116#2520C2214yes—
117#2520C2214yes—
118#2517C2212yes—
119#2515C2214yes—
120#2514C2212yes—
121#2511C2212yes—
122#2511C2212yes—
123#2510C2214yes—
124#2505C2214yes—
125#2505C2214yes—
126#2503C2211yescharacteristic
127#2503C2212yes—
128#2502C2212yes—
129#2498C2212yes—
130#2498C2214yes—
131#2498C2214yes—
132#2497C2212yes—
133#2496C2212yes—
134#2495C2212yes—
135#2493C2214yes—
136#2493C2214yes—
137#2493C2214yes—
138#2493C2214yes—
139#2492C2212yes—
140#2492C2212yes—
141#2488C2214yes—
142#2488C2214yes—
143#2488C2214yes—
144#2487C2211yescharacteristic
145#2486C2212yes—
146#2484C2212yes—
147#2484C2214yes—
148#2481C2214yes—
149#2481C2214yes—
150#2477C2214yes—
151#2451C2212yes—
152#2451C2212yes—
153#2450C2214yes—
154#2450C2214yes—
155#2446C2212yes—
156#2446C2212yes—
157#2446C2212yes—
158#2444C2214yes—
159#2443C2214yes—
160#2443C2214yes—
161#2439C2212yes—
162#2439C2212yes—
163#2438C2214yes—
164#2438C2214yes—
165#2438C2214yes—
166#2436C2212yes—
167#2434C2212yes—
168#2434C2211yescharacteristic
169#2430C2214yes—
170#2430C2212yes—
171#2423C2212yes—
172#2423C2212yes—
173#2421C2212yes—
174#2419C2214yes—
175#2419C2214yes—
176#2419C2214yes—
177#2417C2214yes—
178#2409C2211yescharacteristic
179#2409C2214yes—
180#2409C2212yes—
181#2406C2214yes—
182#2406C2212yes—
183#2401C2212yes—
184#2395C2211yescharacteristic
185#2395C2212yes—
186C2×#400C2214yes—
187C2×#400C2212yes—
188C2×#398C2214yes—
189#2388C2211yescharacteristic
190C2×#395C2212yes—
191#2372C2212yes—
192#2368C2214yes—
193#2365C2212yes—
194#2364C2214yes—
195#2362C2212yes—
196#2360C2212yes—
197#2359C2214yes—
198#2359C2214yes—
199#2356C2212yes—
200#2355C2212yes—
201#2353C2214yes—
202#2352C2214yes—
203#2352C2212yes—
204#2349C2212yes—
205#2349C2212yes—
206D4×C4⋊C4C2212yes—
207D4×C4⋊C4C2212yes—
208#2345C2212yes—
209#2344C2214yes—
210#2344C2212yes—
211#2343C2214yes—
212#2343C2214yes—
213Q8×C22⋊C4C2212yes—
214Q8×C22⋊C4C2212yes—
215Q8×C22⋊C4C2212yes—
216Q8×C22⋊C4C2212yes—
217#2339C2214yes—
218#2339C2214yes—
219#2339C2211yescharacteristic
220#2339C2212yes—
221#2339C2212yes—
222#2339C2214yes—
223#2339C2214yes—
224#2339C2211yescharacteristic
225#2339C2212yes—
226#2339C2212yes—
227#2339C2212yes—
228#2339C2212yes—
229#2327C2212yes—
230#2325C2214yes—
231#2323C2212yes—
232#2322C2214yes—
233#2320C2212yes—
234#2318C2214yes—
235#2314C2212yes—
236#2313C2214yes—
237#2311C2214yes—
238#2311C2212yes—
239#2310C2212yes—
240#2310C2214yes—
241C4×#124C2211yescharacteristic
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×#123C2214yes—
245#2298C2212yes—
246#2297C2212yes—
247#2297C2214yes—
248#2295C2212yes—
249C2×#391C2212yes—
250C2×#391C2214yes—
251C2×#391C2214yes—
252C2×#391C2212yes—
253#2290C2212yes—
254#2290C2214yes—
255C2×#387C2214yes—
256C2×#387C2214yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C2×2−1+4—216no—
260C2×2−1+4—44no—
261C22×#41C2311yescharacteristic
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2314yes—
265C22×#41C2312yes—
266C22×#41C2312yes—
267C23×Q8C2312yes—
268C23×Q8C2312yes—
269C23×Q8C2311yescharacteristic
270C23×Q8C2312yes—
271D4×Q8—44no—
272#547—216no—
273#547—44no—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×#126C2314yes—
279C2×#124C2311yescharacteristic
280C2×#124C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2312yes—
284C2×#123C2312yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2311yescharacteristic
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2314yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296#520—216no—
297#520—44no—
298C4×#41—48no—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2311yescharacteristic
318C2×#117C2312yes—
319C2×#117C2314yes—
320C2×#117C2314yes—
321C2×#117C2312yes—
322C2×#117C2311yescharacteristic
323C2×#117C2312yes—
324C2×#117C2314yes—
325C22×C4⋊C4C2314yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2314yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2311yescharacteristic
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2314yes—
332C22×C4⋊C4C2314yes—
333C22×C42C2314yes—
334C22×C42C2312yes—
335C22×C42C2312yes—
336#401C2314yes—
337#401C2314yes—
338#401C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2311yescharacteristic
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2312yes—
367#400C2312yes—
368#400C2314yes—
369#399C2314yes—
370#399C2312yes—
371#399C2314yes—
372#399C2311yescharacteristic
373#399C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2311yescharacteristic
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2311yescharacteristic
403#397C2312yes—
404#397C2312yes—
405#397C2312yes—
406#397C2312yes—
407#396C2312yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2312yes—
414#395C2312yes—
415#395C2314yes—
416#395C2312yes—
417#395C2314yes—
418#395C2311yescharacteristic
419#395C2314yes—
420#395C2312yes—
421#394C2314yes—
422#394C2311yescharacteristic
423#394C2312yes—
424#394C2312yes—
425#394C2312yes—
426#394C2312yes—
427#394C2312yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2312yes—
433#393C2314yes—
434#393C2311yescharacteristic
435#392C2311yescharacteristic
436#392C2312yes—
437#391C2314yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2312yes—
473#391C2314yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#391C2311yescharacteristic
479#391C2312yes—
480#391C2314yes—
481#391C2312yes—
482#390C2314yes—
483#390C2312yes—
484#390C2311yescharacteristic
485#390C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2312yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2312yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2312yes—
521#388C2312yes—
522#387C2314yes—
523#387C2312yes—
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#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
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#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2312yes—
575#386C2312yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2312yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2312yes—
592#386C2312yes—
593#386C2312yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2312yes—
599#386C2312yes—
600#386C2312yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2312yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#385C2312yes—
623#384C2312yes—
624#384C2312yes—
625#383C2314yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2314yes—
633#382C2314yes—
634#382C2314yes—
635#382C2311yescharacteristic
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2312yes—
648#381C2312yes—
649#380C2314yes—
650#380C2312yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2312yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2314yes—
661#380C2312yes—
662#380C2312yes—
663#380C2314yes—
664#380C2311yescharacteristic
665#380C2311yescharacteristic
666#380C2314yes—
667#380C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703#376C2312yes—
704#376C2314yes—
705#376C2314yes—
706C2×#95C2314yes—
707C2×#95C2314yes—
708C2×#95C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
7202−1+4—464no—
721C2×#41—28no—
722C2×#41—28no—
723C2×#41—216no—
724C2×#41—216no—
725C2×#41—28no—
726C2×#41—28no—
727C2×#41—24no—
728C2×#41—24no—
729C2×#41—28no—
730C2×#41—216no—
731C2×#41—42no—
732C2×#41—48no—
733C2×#41—44no—
734C2×#41#41116yes—
735C22×Q8—28no—
736C22×Q8—28no—
737C22×Q8—28no—
738C22×Q8—216no—
739C22×Q8—28no—
740C22×Q8—44no—
741C22×Q8—44no—
742C22×Q8—44no—
743C22×Q8—42no—
744C22×Q8—82no—
745C22×Q8C2411yescharacteristic
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2414yes—
749C22×Q8C2412yes—
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×Q8C2412yes—
753C22×Q8C2411yescharacteristic
754C22×D4C2412yes—
755C22×D4C2412yes—
756C22×D4C2411yescharacteristic
757C22×D4C2412yes—
758C22×D4C2414yes—
759C22×D4C2412yes—
760C22×D4C2411yescharacteristic
761C22×D4C2411yescharacteristic
762C23×C4C2412yes—
763C23×C4C2411yescharacteristic
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2414yes—
767C23×C4C2412yes—
768C23×C4C2414yes—
769C23×C4C2412yes—
770C23×C4C2414yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2414yes—
774C23×C4C2414yes—
775C23×C4C2414yes—
776C23×C4C2414yes—
777C23×C4C2412yes—
778C23×C4C2412yes—
779C23×C4C2412yes—
780C4⋊Q8—28no—
781C4⋊Q8—44no—
782C4⋊Q8—42no—
783C4⋊Q8—42no—
784#126—84no—
785#124—24no—
786#124—82no—
787#123—216no—
788#123—216no—
789#123—44no—
790#123—44no—
791#123—84no—
792C22⋊Q8—28no—
793C22⋊Q8—28no—
794C22⋊Q8—28no—
795C22⋊Q8—44no—
796C22⋊Q8—48no—
797C22⋊Q8—42no—
798C22⋊Q8—42no—
799C22⋊Q8—84no—
800#121—216no—
801#121—44no—
802C4×Q8—28no—
803C4×Q8—28no—
804C4×Q8—42no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×D4—216no—
809C4×D4—216no—
810C4×D4—28no—
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—28no—
815C4×D4—24no—
816C4×D4—28no—
817C4×D4—42no—
818C4×D4—48no—
819C4×D4—48no—
820C4×D4—48no—
821#117—216no—
822#117—28no—
823#117—42no—
824#117—48no—
825#117—44no—
826#117—44no—
827#117—84no—
828C2×C4⋊C4—216no—
829C2×C4⋊C4—28no—
830C2×C4⋊C4—216no—
831C2×C4⋊C4—42no—
832C2×C4⋊C4—44no—
833C2×C4⋊C4—44no—
834C2×C4⋊C4—84no—
835C2×C4⋊C4—84no—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C42—44no—
928C2×C42—48no—
929C2×C42—82no—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2411yescharacteristic
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2411yescharacteristic
964#95C2411yescharacteristic
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2411yescharacteristic
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2412yes—
1019#95C2411yescharacteristic
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033C24C2511yescharacteristic
1034C24C2511yescharacteristic
1035C24C2512yes—
1036C24C2512yes—
1037#41—264no—
1038#41—416no—
1039#41—464no—
1040#41—432no—
1041#41—416no—
1042#41—416no—
1043C2×Q8—24no—
1044C2×Q8—24no—
1045C2×Q8—28no—
1046C2×Q8—28no—
1047C2×Q8—24no—
1048C2×Q8—28no—
1049C2×Q8—24no—
1050C2×Q8—24no—
1051C2×Q8—22no—
1052C2×Q8—22no—
1053C2×Q8—24no—
1054C2×Q8—28no—
1055C2×Q8—41no—
1056C2×Q8—41no—
1057C2×Q8—44no—
1058C2×Q8—42no—
1059C2×Q8—41no—
1060C2×Q8—44no—
1061C2×Q8—42no—
1062C2×Q8—44no—
1063C2×Q8—42no—
1064C2×Q8—432no—
1065C2×Q8—432no—
1066C2×Q8—416no—
1067C2×Q8—816no—
1068C2×Q8C2×#4118yes—
1069C2×Q82−1+414yescomplemented
1070C2×D4—28no—
1071C2×D4—28no—
1072C2×D4—28no—
1073C2×D4—24no—
1074C2×D4—24no—
1075C2×D4—28no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—22no—
1081C2×D4—42no—
1082C2×D4—41no—
1083C2×D4—41no—
1084C2×D4—42no—
1085C2×D4—41no—
1086C2×D4—42no—
1087C2×D4C2×#41116yes—
1088C2×D4C2×#4118yes—
1089C2×D4H(5,𝔽2)14yes—
1090C22×C4—28no—
1091C22×C4—28no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—28no—
1095C22×C4—28no—
1096C22×C4—28no—
1097C22×C4—28no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—28no—
1102C22×C4—28no—
1103C22×C4—28no—
1104C22×C4—28no—
1105C22×C4—28no—
1106C22×C4—24no—
1107C22×C4—28no—
1108C22×C4—28no—
1109C22×C4—24no—
1110C22×C4—22no—
1111C22×C4—22no—
1112C22×C4—24no—
1113C22×C4—28no—
1114C22×C4—24no—
1115C22×C4—42no—
1116C22×C4—44no—
1117C22×C4—42no—
1118C22×C4—44no—
1119C22×C4—42no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—42no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—42no—
1132C22×C4—44no—
1133C22×C4—42no—
1134C22×C4—42no—
1135C22×C4—44no—
1136C22×C4C2×#41116yes—
1137C22×C4C2×#4118yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2514yes—
1148C22×C4C2514yes—
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2512yes—
1152C22×C4C2514yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2512yes—
1159C22×C4C2514yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2512yes—
1162C22×C4C2511yescharacteristic
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—28no—
1171C4⋊C4—28no—
1172C4⋊C4—28no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—28no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—22no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—41no—
1183C4⋊C4—42no—
1184C4⋊C4—41no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—41no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—41no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—44no—
1213C4⋊C4—42no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—41no—
1245C22⋊C4—41no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C42—28no—
1255C42—28no—
1256C42—24no—
1257C42—24no—
1258C42—24no—
1259C42—24no—
1260C42—24no—
1261C42—22no—
1262C42—22no—
1263C42—42no—
1264C42—42no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—41no—
1269C42—44no—
1270C42—42no—
1271C42—42no—
1272C42—44no—
1273C42—44no—
1274C42—44no—
1275C42—44no—
1276C23—22no—
1277C23—22no—
1278C23—24no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—22no—
1294C23—22no—
1295C23C22×#4114yes—
1296C23C22×#4118yes—
1297C23C2×H(5,𝔽2)14yes—
1298C23C2611yescharacteristic
1299Q8—216no—
1300Q8—44no—
1301Q8—44no—
1302Q8—416no—
1303Q8—48no—
1304Q8—44no—
1305Q8—44no—
1306Q8—88no—
1307Q8—84no—
1308D4—232no—
1309D4—48no—
1310D4—44no—
1311D4—48no—
1312D4—48no—
1313D4—82no—
1314D4—84no—
1315D4#551116yes—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—232no—
1325C2×C4—216no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—48no—
1382C2×C4—416no—
1383C2×C4—416no—
1384C2×C4—48no—
1385C2×C4—48no—
1386C2×C4—48no—
1387C2×C4—44no—
1388C2×C4—44no—
1389C2×C4—84no—
1390C2×C4—88no—
1391C2×C4—88no—
1392C2×C4—88no—
1393C2×C4—88no—
1394C2×C4—88no—
1395C2×C4—84no—
1396C2×C4—162no—
1397C2×C4C22×#4118yes—
1398C2×C4C22×#4114yes—
1399C2×C4C22×#4114yes—
1400C2×C4C2×H(5,𝔽2)12yes—
1401C2×C4C2×2−1+412yes—
1402C2×C4C2×2−1+414yes—
1403C22—28no—
1404C22—24no—
1405C22—28no—
1406C22—24no—
1407C22—24no—
1408C22—24no—
1409C22—24no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—41no—
1417C22—41no—
1418C22—42no—
1419C22—42no—
1420C22—41no—
1421C22—41no—
1422C22—41no—
1423C22—41no—
1424C22C2×#55118yes—
1425C22C23×#4112yes—
1426C22C22×H(5,𝔽2)11yescharacteristic
1427C22C22×2−1+411yescharacteristic
1428C22H(7,𝔽2)11yescharacteristic
1429C222−1+612yes—
1430C4—24no—
1431C4—22no—
1432C4—24no—
1433C4—28no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—41no—
1438C4—42no—
1439C4—42no—
1440C4—44no—
1441C4—44no—
1442C4—44no—
1443C4—42no—
1444C4—44no—
1445C4—42no—
1446C4—42no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—41no—
1451C4—41no—
1452C4—42no—
1453C4—42no—
1454C4C2×#55114yes—
1455C2—28no—
1456C2—44no—
1457C2—81no—
1458C2—81no—
1459C2C22×#55111yescharacteristic
1460C2#6285712yes—
1461C2#6289411yescharacteristic
1462C2#6300112yes—
1463C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36085C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59941C2semidirect
2. #59933C2semidirect
3. #59882C2semidirect
4. #59867C2semidirect
5. #52257C2semidirect
6. C2×#2799C2semidirect
7. #45351C2semidirect
8. #45305C2semidirect
9. #45116C2semidirect
10. #45115C2semidirect
11. #44795C2semidirect
12. #44043C2semidirect
13. #43727C2semidirect
14. #43647C2semidirect
15. #39563C2semidirect
16. #39559C2semidirect
17. #38251C2semidirect
18. #38247C2semidirect
19. #38115C2semidirect
20. #38111C2semidirect
21. #36303C2semidirect
22. #36274C2semidirect
24. #36067C2semidirect
25. #35998C2semidirect
26. #35888C2semidirect
27. #34289C2semidirect
28. #34260C2semidirect
29. #34259C2semidirect
1069. C2×Q82−1+4semidirect

Maximal subgroups

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

subgroupindex
#599412
#599332
#598822
#598672
#522572
C2×#27992
#453512
#453052
#451162
#451152
#447952
#440432
#437272
#436472
#395632
#395592
#382512
#382472
#381152
#381112
#363032
#362742
#360852
#360672
#359982
#358882
#342892
#342602
#342592