Finite Group Databasebeta

← #7652263

Subgroups — #7652263

Order 512.

4318 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42980C211yesmaximal, characteristic
2#42933C211yesmaximal, characteristic, complemented
3#42710C212yesmaximal, complemented
4#42697C211yesmaximal, characteristic, complemented
5#42637C212yesmaximal, complemented
6#42502C211yesmaximal, characteristic
7#41777C214yesmaximal, complemented
8#41757C214yesmaximal, complemented
9#41354C214yesmaximal, complemented
10#40987C214yesmaximal, complemented
11#40408C214yesmaximal, complemented
12#40178C212yesmaximal, complemented
13#39890C212yesmaximal, complemented
14#39689C214yesmaximal, complemented
15#39660C212yesmaximal, complemented
16#39604C212yesmaximal, complemented
17#38772C214yesmaximal
18#38647C214yesmaximal, complemented
19#35645C212yesmaximal, complemented
20#35608C212yesmaximal, complemented
21#35583C212yesmaximal, complemented
22#35324C211yesmaximal, characteristic, complemented
23#35239C212yesmaximal, complemented
24#34879C211yesmaximal, characteristic
25#34772C212yesmaximal, complemented
26#34304C212yesmaximal, complemented
27#34214C211yesmaximal, characteristic, complemented
28C2×#552C2212yes—
29C2×#533C2211yescharacteristic
30#2864C2211yescharacteristic
31#2862C2211yescharacteristic
32#2857C2214yes—
33#2855C2212yes—
34#2851C2214yes—
35#2843C2212yes—
36#2839C2214yes—
37#2839C2214yes—
38#2835C2212yes—
39#2835C2212yes—
40#2822C2212yes—
41#2807C2212yes—
42#2802C2214yes—
43#2802C2214yes—
44#2794C2212yes—
45#2794C2214yes—
46#2792C2212yes—
47#2792C2214yes—
48#2791C2214yes—
49#2790C2214yes—
50#2782C2212yes—
51#2774C2214yes—
52#2769C2212yes—
53#2767C2214yes—
54#2763C2214yes—
55#2762C2214yes—
56#2758C2214yes—
57#2755C2214yes—
58#2746C2214yes—
59#2739C2214yes—
60#2738C2214yes—
61#2729C2214yes—
62#2729C2214yes—
63#2729C2214yes—
64#2722C2212yes—
65#2720C2214yes—
66#2720C2214yes—
67#2719C2214yes—
68#2719C2214yes—
69#2698C2214yes—
70#2698C2214yes—
71#2695C2214yes—
72#2693C2212yes—
73#2689C2214yes—
74#2687C2214yes—
75#2680C2214yes—
76#2677C2212yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2655C2214yes—
82#2655C2214yes—
83#2652C2214yes—
84#2652C2214yes—
85#2645C2212yes—
86#2634C2214yes—
87#2634C2214yes—
88#2633C2214yes—
89#2629C2214yes—
90#2628C2211yescharacteristic
91#2628C2214yes—
92#2627C2214yes—
93#2621C2211yescharacteristic
94#2612C2214yes—
95#2609C2212yes—
96#2606C2214yes—
97#2605C2214yes—
98#2599C2214yes—
99#2588C2214yes—
100#2588C2214yes—
101#2588C2214yes—
102#2585C2214yes—
103#2581C2212yes—
104#2578C2214yes—
105#2577C2214yes—
106#2575C2214yes—
107#2575C2214yes—
108#2574C2212yes—
109#2574C2214yes—
110#2573C2212yes—
111#2573C2214yes—
112#2572C2212yes—
113#2571C2212yes—
114#2570C2214yes—
115#2567C2212yes—
116#2565C2214yes—
117#2553C2212yes—
118#2552C2212yes—
119#2552C2212yes—
120#2551C2212yes—
121#2551C2212yes—
122#2550C2214yes—
123#2550C2214yes—
124#2550C2212yes—
125#2546C2212yes—
126#2533C2214yes—
127#2530C2214yes—
128#2528C2214yes—
129#2527C2214yes—
130#2524C2214yes—
131#2524C2212yes—
132#2524C2214yes—
133#2524C2214yes—
134#2524C2214yes—
135#2522C2214yes—
136#2522C2214yes—
137#2520C2214yes—
138#2517C2212yes—
139#2515C2212yes—
140#2511C2212yes—
141#2511C2212yes—
142#2511C2212yes—
143#2509C2212yes—
144#2508C2214yes—
145#2507C2212yes—
146#2507C2212yes—
147#2506C2212yes—
148#2506C2214yes—
149#2506C2212yes—
150#2505C2214yes—
151#2502C2212yes—
152#2499C2212yes—
153#2497C2212yes—
154#2495C2212yes—
155#2495C2212yes—
156#2492C2212yes—
157#2492C2212yes—
158#2489C2214yes—
159#2489C2212yes—
160#2487C2212yes—
161#2485C2212yes—
162#2477C2214yes—
163#2477C2214yes—
164#2475C2214yes—
165#2475C2214yes—
166#2473C2214yes—
167#2468C2212yes—
168#2465C2214yes—
169#2463C2212yes—
170#2462C2214yes—
171#2457C2212yes—
172#2453C2212yes—
173#2453C2212yes—
174#2451C2214yes—
175#2451C2214yes—
176#2451C2212yes—
177#2450C2214yes—
178#2449C2214yes—
179#2446C2212yes—
180#2442C2212yes—
181#2442C2212yes—
182#2440C2212yes—
183#2440C2212yes—
184#2440C2212yes—
185#2440C2212yes—
186#2438C2214yes—
187#2438C2214yes—
188#2429C2212yes—
189#2423C2212yes—
190#2417C2212yes—
191#2417C2212yes—
192#2402C2214yes—
193#2402C2211yescharacteristic
194#2398C2211yescharacteristic
195#2396C2214yes—
196#2396C2211yescharacteristic
197#2392C2211yescharacteristic
198#2373C2214yes—
199#2370C2214yes—
200#2370C2212yes—
201#2360C2212yes—
202#2360C2212yes—
203#2360C2214yes—
204#2360C2214yes—
205#2359C2214yes—
206#2355C2212yes—
207#2355C2214yes—
208Q8×C4⋊C4C2214yes—
209D4×C4⋊C4C2212yes—
210#2347C2212yes—
211#2344C2212yes—
212#2343C2214yes—
213#2336C2214yes—
214#2334C2214yes—
215#2334C2214yes—
216#2331C2212yes—
217#2331C2211yescharacteristic
218#2330C2212yes—
219#2330C2212yes—
220#2330C2212yes—
221#2327C2211yescharacteristic
222#2323C2212yes—
223#2323C2214yes—
224#2323C2214yes—
225#2322C2214yes—
226#2320C2212yes—
227#2317C2211yescharacteristic
228#2317C2211yescharacteristic
229C4×C4⋊Q8C2212yes—
230C4×C4⋊Q8C2212yes—
231C4×#126C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2214yes—
234C4×C22⋊Q8C2212yes—
235C4×#123C2214yes—
236C4×#123C2212yes—
237#2296C2214yes—
238#2295C2211yescharacteristic
239#2295C2212yes—
240#2290C2212yes—
241#2290C2214yes—
242#2285C2212yes—
243C2×#384C2211yescharacteristic
244#2283C2212yes—
245#2276C2212yes—
246#2274C2211yescharacteristic
247#2274C2211yescharacteristic
248C42×D4C2211yescharacteristic
249C4×#117C2211yescharacteristic
250C2×C4×C4⋊C4C2212yes—
251#552—216no—
252#533—28no—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2314yes—
258C2×C4⋊Q8C2314yes—
259C2×#126C2312yes—
260C2×#126C2314yes—
261C2×#125C2314yes—
262C2×#125C2312yes—
263C2×#125C2312yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2314yes—
267C2×#123C2312yes—
268C2×#123C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2314yes—
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C2×#117C2314yes—
291C2×#117C2311yescharacteristic
292C2×#117C2314yes—
293C2×#117C2314yes—
294C2×#117C2311yescharacteristic
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2314yes—
300C22×C42C2311yescharacteristic
301C22×C42C2312yes—
302C22×C42C2314yes—
303#401C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2311yescharacteristic
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#399C2312yes—
338#399C2314yes—
339#399C2314yes—
340#399C2311yescharacteristic
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2311yescharacteristic
346#398C2314yes—
347#398C2314yes—
348#398C2312yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#397C2314yes—
377#397C2312yes—
378#397C2312yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2311yescharacteristic
384#397C2314yes—
385#397C2312yes—
386#396C2312yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2312yes—
391#396C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2311yescharacteristic
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#394C2312yes—
406#394C2314yes—
407#394C2311yescharacteristic
408#394C2312yes—
409#393C2311yescharacteristic
410#393C2312yes—
411#393C2314yes—
412#393C2312yes—
413#393C2314yes—
414#392C2311yescharacteristic
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2314yes—
478#388C2312yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2312yes—
485#388C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2312yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#387C2312yes—
499#387C2312yes—
500#387C2312yes—
501#387C2312yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2312yes—
511#387C2312yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2312yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2312yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2312yes—
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#386C2312yes—
561#386C2312yes—
562#386C2314yes—
563#386C2312yes—
564#386C2314yes—
565#386C2314yes—
566#385C2312yes—
567#385C2312yes—
568#385C2312yes—
569#385C2312yes—
570#385C2314yes—
571#385C2312yes—
572#385C2312yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2312yes—
587#385C2314yes—
588#385C2314yes—
589#384C2312yes—
590#384C2314yes—
591#384C2312yes—
592#384C2312yes—
593#384C2312yes—
594#384C2312yes—
595#384C2312yes—
596#384C2314yes—
597#384C2312yes—
598#383C2312yes—
599#383C2312yes—
600#383C2314yes—
601#383C2312yes—
602#383C2314yes—
603#383C2314yes—
604#383C2314yes—
605#382C2314yes—
606#382C2312yes—
607#382C2312yes—
608#382C2314yes—
609#382C2311yescharacteristic
610#382C2312yes—
611#382C2312yes—
612#382C2314yes—
613#382C2312yes—
614#382C2314yes—
615#382C2311yescharacteristic
616#382C2314yes—
617#382C2314yes—
618#381C2312yes—
619#381C2312yes—
620#381C2312yes—
621#381C2314yes—
622#381C2314yes—
623#380C2314yes—
624#380C2312yes—
625#380C2314yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684#376C2312yes—
685#376C2311yescharacteristic
686#376C2311yescharacteristic
687#376C2314yes—
688#376C2314yes—
689C2×#95C2314yes—
690C43C2311yescharacteristic
691C43C2311yescharacteristic
692C22×Q8C2412yes—
693C22×Q8C2414yes—
694C22×Q8C2411yescharacteristic
695C22×Q8C2414yes—
696C22×Q8C2412yes—
697C22×D4C2412yes—
698C22×D4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2414yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2411yescharacteristic
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2414yes—
708C4⋊Q8—28no—
709C4⋊Q8—42no—
710C4⋊Q8—44no—
711C4⋊Q8—42no—
712C4⋊Q8—84no—
713C4⋊Q8—84no—
714#126—216no—
715#126—28no—
716#125—28no—
717#125—28no—
718#125—216no—
719#125—84no—
720#125—84no—
721#125—84no—
722#123—216no—
723#123—28no—
724C22⋊Q8—28no—
725C22⋊Q8—28no—
726C22⋊Q8—216no—
727C22⋊Q8—216no—
728C22⋊Q8—44no—
729C22⋊Q8—84no—
730C22⋊Q8—84no—
731C22⋊Q8—84no—
732C4×Q8—28no—
733C4×Q8—216no—
734C4×Q8—28no—
735C4×Q8—42no—
736C4×Q8—44no—
737C4×Q8—84no—
738C4×Q8—84no—
739C4×D4—28no—
740C4×D4—28no—
741C4×D4—42no—
742C4×D4—84no—
743#117—24no—
744#117—216no—
745#117—24no—
746#117—42no—
747#117—84no—
748#117—84no—
749#117#4118yes—
750C2×C4⋊C4—28no—
751C2×C4⋊C4—42no—
752C2×C4⋊C4—44no—
753C2×C4⋊C4—42no—
754C2×C4⋊C4—84no—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2411yescharacteristic
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C42—24no—
851C2×C42—28no—
852C2×C42—84no—
853C2×C42C2411yescharacteristic
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2411yescharacteristic
864C2×C42C2412yes—
865C2×C42C2411yescharacteristic
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2411yescharacteristic
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2412yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965C24C2511yescharacteristic
966C24C2512yes—
967C2×Q8—24no—
968C2×Q8—28no—
969C2×Q8—24no—
970C2×Q8—28no—
971C2×Q8—24no—
972C2×Q8—44no—
973C2×Q8—41no—
974C2×Q8—42no—
975C2×Q8—44no—
976C2×Q8—44no—
977C2×Q8—44no—
978C2×Q8—42no—
979C2×Q8—44no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—41no—
984C2×D4—42no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—28no—
990C22×C4—28no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4C2×#4114yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2514yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2514yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2514yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2511yescharacteristic
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—41no—
1076C4⋊C4—44no—
1077C4⋊C4—41no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4C2×#4118yes—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—24no—
1109C22⋊C4—24no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—28no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—42no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—42no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4C2×#4118yes—
1129C22⋊C42−1+418yes—
1130C42—24no—
1131C42—22no—
1132C42—22no—
1133C42—24no—
1134C42—28no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—22no—
1140C42—24no—
1141C42—28no—
1142C42—24no—
1143C42—22no—
1144C42—22no—
1145C42—24no—
1146C42—44no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—42no—
1156C42—42no—
1157C42—44no—
1158C42C2×#4118yes—
1159C422−1+414yes—
1160C23—22no—
1161C23—21no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—21no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23C22×#4112yes—
1171C23C2×2−1+414yes—
1172C23C2611yescharacteristic
1173Q8—416no—
1174Q8—48no—
1175Q8—82no—
1176Q8—162no—
1177Q8—164no—
1178D4—48no—
1179D4—44no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—21no—
1184C2×C4—24no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—22no—
1190C2×C4—28no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—48no—
1245C2×C4—416no—
1246C2×C4—48no—
1247C2×C4—48no—
1248C2×C4—48no—
1249C2×C4—88no—
1250C2×C4—162no—
1251C2×C4—162no—
1252C2×C4C22×#4112yes—
1253C2×C4C22×#4118yes—
1254C2×C4C22×#4112yes—
1255C2×C4C2×2−1+414yes—
1256C2×C4C2×2−1+414yes—
1257C2×C4C2×2−1+414yes—
1258C2×C4C2×2−1+412yes—
1259C2×C4#58512yes—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—22no—
1264C22—24no—
1265C22—42no—
1266C22—41no—
1267C22—42no—
1268C22—41no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22C23×#4111yescharacteristic
1273C22C22×2−1+412yes—
1274C22C22×2−1+411yescharacteristic
1275C22C2×#58511yescharacteristic
1276C22H(7,𝔽2)12yes—
1277C4—28no—
1278C4—24no—
1279C4—22no—
1280C4—24no—
1281C4—24no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—42no—
1286C4—44no—
1287C4—41no—
1288C4—42no—
1289C4—41no—
1290C4—44no—
1291C4—44no—
1292C4—44no—
1293C4—41no—
1294C4—42no—
1295C4—41no—
1296C4—42no—
1297C4—44no—
1298C4—42no—
1299C4—44no—
1300C4—42no—
1301C4#346114yes—
1302C2—44no—
1303C2—42no—
1304C2C2×#346111yescharacteristic
1305C2#6283711yescharacteristic
1306C2#6288511yescharacteristic
1307C2#6294512yes—
1308C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#392C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42933C2semidirect
3. #42710C2semidirect
4. #42697C2semidirect
5. #42637C2semidirect
7. #41777C2semidirect
8. #41757C2semidirect
9. #41354C2semidirect
10. #40987C2semidirect
11. #40408C2semidirect
12. #40178C2semidirect
13. #39890C2semidirect
14. #39689C2semidirect
15. #39660C2semidirect
16. #39604C2semidirect
18. #38647C2semidirect
19. #35645C2semidirect
20. #35608C2semidirect
21. #35583C2semidirect
22. #35324C2semidirect
23. #35239C2semidirect
25. #34772C2semidirect
26. #34304C2semidirect
27. #34214C2semidirect

Maximal subgroups

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

subgroupindex
#429802
#429332
#427102
#426972
#426372
#425022
#417772
#417572
#413542
#409872
#404082
#401782
#398902
#396892
#396602
#396042
#387722
#386472
#356452
#356082
#355832
#353242
#352392
#348792
#347722
#343042
#342142