Finite Group Databasebeta

← #7658953

Subgroups — #7658953

Order 512.

4286 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42230C214yesmaximal, complemented
2#42062C214yesmaximal, complemented
3#42010C214yesmaximal, complemented
4#41766C214yesmaximal, complemented
5#41752C214yesmaximal, complemented
6#41391C212yesmaximal, complemented
7#41388C212yesmaximal, complemented
8#41134C214yesmaximal, complemented
9#41124C214yesmaximal, complemented
10#40547C212yesmaximal, complemented
11#40544C212yesmaximal
12#37612C212yesmaximal, complemented
13#37609C211yesmaximal, characteristic, complemented
14#37600C212yesmaximal, complemented
15#37600C212yesmaximal, complemented
16#37540C211yesmaximal, characteristic, complemented
17#37537C211yesmaximal, characteristic
18#36698C212yesmaximal, complemented
19C2×#2820C211yesmaximal, characteristic
20#36013C212yesmaximal, complemented
21#35839C212yesmaximal, complemented
22#35824C214yesmaximal, complemented
23#35743C212yesmaximal, complemented
24#35731C212yesmaximal
25#34240C211yesmaximal, characteristic
26#34239C211yesmaximal, characteristic, complemented
27#34215C211yesmaximal, characteristic, complemented
28C2×#533C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C22×#124C2211yescharacteristic
31#2845C2212yescomplemented
32#2844C2212yescomplemented
33#2838C2214yescomplemented
34#2838C2214yescomplemented
35#2836C2214yescomplemented
36#2836C2214yescomplemented
37#2833C2214yescomplemented
38#2830C2214yes—
39#2822C2212yescomplemented
40#2822C2212yescomplemented
41#2820C2212yes—
42#2820C2212yes—
43#2820C2214yes—
44#2820C2211yescharacteristic
45#2820C2212yes—
46#2820C2212yes—
47#2820C2211yescharacteristic
48#2820C2211yescharacteristic
49#2820C2211yescharacteristic
50#2820C2212yes—
51#2820C2212yes—
52#2798C2214yescomplemented
53#2798C2214yescomplemented
54#2796C2214yes—
55#2793C2214yescomplemented
56#2790C2214yescomplemented
57#2789C2214yescomplemented
58#2783C2214yescomplemented
59#2775C2214yescomplemented
60#2773C2214yescomplemented
61#2765C2214yescomplemented
62#2759C2214yescomplemented
63#2758C2214yescomplemented
64#2754C2214yescomplemented
65#2754C2214yescomplemented
66#2751C2214yes—
67#2744C2214yescomplemented
68#2721C2214yescomplemented
69#2721C2214yescomplemented
70#2721C2214yescomplemented
71#2720C2214yescomplemented
72#2715C2214yes—
73#2713C2214yescomplemented
74#2713C2214yescomplemented
75#2700C2214yes—
76#2667C2214yescomplemented
77#2667C2214yescomplemented
78#2666C2214yescomplemented
79#2666C2214yescomplemented
80#2666C2214yescomplemented
81#2666C2214yescomplemented
82#2664C2214yescomplemented
83#2664C2214yescomplemented
84#2660C2212yescomplemented
85#2658C2212yes—
86#2654C2214yescomplemented
87#2654C2214yescomplemented
88#2654C2214yescomplemented
89#2654C2214yescomplemented
90#2652C2214yescomplemented
91#2652C2214yescomplemented
92#2651C2214yes—
93#2651C2214yes—
94#2650C2214yescomplemented
95#2650C2214yescomplemented
96#2642C2212yescomplemented
97#2640C2212yes—
98#2638C2214yes—
99#2634C2212yescomplemented
100#2634C2212yescomplemented
101#2634C2214yescomplemented
102#2632C2212yes—
103#2632C2212yes—
104#2627C2214yes—
105#2627C2212yes—
106#2627C2212yes—
107#2626C2212yes—
108#2626C2212yes—
109#2612C2214yescomplemented
110#2607C2214yescomplemented
111#2605C2214yescomplemented
112#2595C2214yes—
113#2594C2214yescomplemented
114#2593C2214yes—
115#2589C2214yescomplemented
116#2588C2214yescomplemented
117#2587C2214yescomplemented
118#2586C2214yescomplemented
119#2575C2214yescomplemented
120#2574C2214yescomplemented
121#2573C2214yescomplemented
122#2573C2214yescomplemented
123#2573C2214yescomplemented
124#2569C2212yes—
125#2569C2212yes—
126#2565C2214yescomplemented
127#2561C2214yes—
128#2556C2214yescomplemented
129#2556C2214yescomplemented
130#2550C2214yescomplemented
131#2549C2212yes—
132#2549C2212yes—
133#2545C2214yes—
134#2529C2214yescomplemented
135#2527C2214yescomplemented
136#2525C2214yescomplemented
137#2525C2214yescomplemented
138#2525C2214yescomplemented
139#2523C2214yescomplemented
140#2522C2214yescomplemented
141#2522C2214yescomplemented
142#2521C2214yes—
143#2519C2214yescomplemented
144#2519C2214yescomplemented
145#2517C2214yescomplemented
146#2516C2214yes—
147#2515C2214yescomplemented
148#2515C2214yescomplemented
149#2503C2212yes—
150#2502C2212yes—
151#2493C2214yes—
152#2493C2214yes—
153#2484C2214yes—
154#2483C2214yes—
155#2482C2214yes—
156#2482C2214yes—
157#2480C2214yes—
158#2480C2214yes—
159#2475C2214yescomplemented
160#2474C2214yes—
161#2473C2214yes—
162#2473C2214yes—
163#2469C2214yescomplemented
164#2468C2214yes—
165#2468C2214yes—
166#2462C2214yescomplemented
167#2462C2214yescomplemented
168#2451C2214yescomplemented
169#2442C2214yes—
170#2441C2214yescomplemented
171#2438C2214yes—
172#2437C2214yes—
173#2435C2212yes—
174#2434C2212yes—
175#2423C2214yescomplemented
176#2401C2214yescomplemented
177#2401C2214yescomplemented
178#2399C2214yescomplemented
179#2396C2214yescomplemented
180#2396C2214yescomplemented
181#2395C2214yes—
182C2×#399C2212yes—
183C2×#397C2212yes—
184C2×#396C2214yes—
185C2×#395C2212yes—
186C2×#394C2212yes—
187#2372C2214yes—
188#2371C2214yescomplemented
189#2370C2212yescomplemented
190#2370C2212yescomplemented
191#2368C2212yes—
192#2368C2212yes—
193#2368C2212yes—
194#2368C2212yes—
195#2367C2212yes—
196#2367C2212yes—
197#2360C2214yes—
198#2355C2214yescomplemented
199#2355C2214yescomplemented
200#2345C2211yescharacteristic
201#2345C2211yescharacteristic
202#2344C2212yes—
203#2344C2211yescharacteristic
204#2344C2211yescharacteristic
205#2344C2212yes—
206#2343C2214yes—
207#2342C2212yes—
208#2342C2214yes—
209#2342C2214yes—
210#2342C2212yes—
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213D4×C22⋊C4C2211yescharacteristic
214D4×C22⋊C4C2211yescharacteristic
215#2337C2214yes—
216#2336C2214yescomplemented
217#2331C2212yescomplemented
218#2331C2212yescomplemented
219#2317C2212yes—
220#2313C2212yes—
221#2312C2212yes—
222C4×#125C2212yescomplemented
223C4×#125C2212yescomplemented
224C4×#125C2212yescomplemented
225C4×#125C2212yescomplemented
226C4×#124C2212yes—
227C4×#124C2212yes—
228#2283C2211yescharacteristic
229#2283C2211yescharacteristic
230C2×#382C2211yescharacteristic
231#2274C2212yes—
232#2274C2212yes—
233#2273C2212yes—
234C4×#117C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×D4C2311yescharacteristic
237#533—28no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#125—28no—
244C2×#125C2311yescharacteristic
245C2×#125C2311yescharacteristic
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#125C2311yescharacteristic
249C2×#125C2311yescharacteristic
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#125C2314yes—
253C2×#125C2314yes—
254C2×#124—28no—
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2312yes—
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×#117C2312yes—
274C2×#117C2312yes—
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2312yes—
278C2×#117C2314yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2314yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2314yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2314yes—
291C22×C42C2311yescharacteristic
292#401C2314yes—
293#401C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2312yes—
312#400C2312yes—
313#400C2314yes—
314#400C2312yes—
315#400C2314yes—
316#400C2314yes—
317#399C2312yes—
318#399C2314yes—
319#399C2314yes—
320#399C2312yes—
321#399C2312yes—
322#399C2312yes—
323#399C2314yes—
324#399C2314yes—
325#399C2312yes—
326#399C2314yes—
327#399C2314yes—
328#399C2312yes—
329#399C2312yes—
330#399C2312yes—
331#399C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2312yes—
361#397C2314yes—
362#397C2312yes—
363#397C2312yes—
364#397C2312yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#395C2312yes—
397#395C2312yes—
398#395C2314yes—
399#395C2314yes—
400#395C2312yes—
401#395C2312yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2312yes—
411#395C2312yes—
412#395C2312yes—
413#394C2312yes—
414#394C2312yes—
415#394C2314yes—
416#394C2312yes—
417#394C2312yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2312yes—
425#393C2312yes—
426#393C2312yes—
427#393C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#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#386C2314yes—
547#386C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#384C2314yes—
565#384C2314yes—
566#383C2314yes—
567#383C2314yes—
568#383C2312yes—
569#383C2312yes—
570#383C2314yes—
571#382C2311yescharacteristic
572#382C2312yes—
573#382C2311yescharacteristic
574#382C2312yes—
575#382C2312yes—
576#382C2312yes—
577#382C2314yes—
578#382C2312yes—
579#382C2314yes—
580#382C2314yes—
581#382C2314yes—
582#381C2312yes—
583#381C2314yes—
584#381C2312yes—
585#381C2314yes—
586#381C2314yes—
587#381C2314yes—
588#381C2312yes—
589#381C2314yes—
590#381C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594#380C2312yes—
595#380C2311yescharacteristic
596#380C2314yes—
597#380C2311yescharacteristic
598#380C2314yes—
599#380C2311yescharacteristic
600#380C2311yescharacteristic
601#380C2314yes—
602#379C2312yes—
603#379C2314yes—
604#379C2312yes—
605#379C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2311yescharacteristic
634C4×C22⋊C4C2312yes—
635C4×C22⋊C4C2311yescharacteristic
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2311yescharacteristic
645C4×C22⋊C4C2312yes—
646C4×C22⋊C4C2312yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2312yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2311yescharacteristic
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653#376C2312yes—
654#376C2314yes—
655#376C2312yes—
656#376C2312yes—
657C2×#95C2312yes—
658C2×#95C2312yes—
659C2×#95C2314yes—
660C43C2312yes—
661C25C2412yes—
662C22×Q8—24no—
663C22×Q8—82no—
664C22×Q8C2411yescharacteristic
665C22×Q8C2411yescharacteristic
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×Q8C2412yes—
669C22×Q8C2414yes—
670C22×D4—24no—
671C22×D4—82no—
672C22×D4C2411yescharacteristic
673C22×D4C2411yescharacteristic
674C22×D4C2412yes—
675C23×C4C2412yes—
676C23×C4C2411yescharacteristic
677C23×C4C2412yes—
678C23×C4C2414yes—
679C23×C4C2412yes—
680C23×C4C2414yes—
681C23×C4C2414yes—
682C23×C4C2411yescharacteristic
683C23×C4C2411yescharacteristic
684C4⋊Q8—24no—
685C4⋊Q8—24no—
686C4⋊Q8—84no—
687#126—84no—
688#126—84no—
689#125—28no—
690#125—24no—
691#125—24no—
692#125—24no—
693#125—24no—
694#125—28no—
695#125—28no—
696#125—84no—
697#125—84no—
698#125—84no—
699#124—24no—
700#124—24no—
701#124—28no—
702#124—24no—
703#124—24no—
704#124—28no—
705#124—84no—
706C22⋊Q8—28no—
707C22⋊Q8—28no—
708C22⋊Q8—48no—
709C22⋊Q8—84no—
710C4×Q8—28no—
711C4×Q8—28no—
712C4×Q8—84no—
713C4×Q8—82no—
714C4×Q8—82no—
715C4×D4—82no—
716C4×D4—82no—
717#117—28no—
718#117—24no—
719#117—28no—
720#117—42no—
721#117—44no—
722#117—84no—
723C2×C4⋊C4—24no—
724C2×C4⋊C4—28no—
725C2×C4⋊C4—28no—
726C2×C4⋊C4—24no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4—84no—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C22⋊C4—28no—
790C2×C22⋊C4—28no—
791C2×C22⋊C4—28no—
792C2×C22⋊C4—44no—
793C2×C22⋊C4—48no—
794C2×C22⋊C4—84no—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2411yescharacteristic
834C2×C42#4118yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2412yes—
841C2×C42C2414yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2411yescharacteristic
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858#95C2414yes—
859#95C2412yes—
860#95C2412yes—
861#95C2412yes—
862#95C2412yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2412yes—
869#95C2414yes—
870#95C2412yes—
871#95C2412yes—
872#95C2412yes—
873#95C2414yes—
874#95C2412yes—
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924C24—24no—
925C24—24no—
926C24—24no—
927C24—44no—
928C24—44no—
929C24C2512yes—
930C24C2512yes—
931C24C2511yescharacteristic
932C2×Q8—22no—
933C2×Q8—22no—
934C2×Q8—24no—
935C2×Q8—24no—
936C2×Q8—24no—
937C2×Q8—42no—
938C2×Q8—42no—
939C2×Q8—44no—
940C2×Q8—44no—
941C2×Q8—44no—
942C2×Q8—44no—
943C2×Q8—44no—
944C2×Q8—44no—
945C2×Q8—88no—
946C2×D4—22no—
947C2×D4—22no—
948C2×D4—24no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—44no—
952C2×D4—88no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—28no—
961C22×C4—28no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4C2×#4114yes—
974C22×C4C2×#4114yes—
975C22×C4C2×#4114yes—
976C22×C4C2514yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2512yes—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—24no—
1021C4⋊C4—28no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—42no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C22⋊C4—28no—
1061C22⋊C4—24no—
1062C22⋊C4—22no—
1063C22⋊C4—24no—
1064C22⋊C4—22no—
1065C22⋊C4—24no—
1066C22⋊C4—22no—
1067C22⋊C4—24no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—24no—
1074C22⋊C4—24no—
1075C22⋊C4—24no—
1076C22⋊C4—28no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C42−1+414yes—
1099C42—28no—
1100C42—24no—
1101C42—28no—
1102C42—42no—
1103C42—44no—
1104C42—42no—
1105C42—44no—
1106C42—44no—
1107C42—42no—
1108C42—44no—
1109C42—44no—
1110C42—44no—
1111C42—42no—
1112C42—42no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—44no—
1117C42—44no—
1118C42C2×#4114yes—
1119C42C2×#4114yes—
1120C42C2×#4114yes—
1121C42C2×#4114yes—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—24no—
1133C23—24no—
1134C23—48no—
1135C23—84no—
1136C23—88no—
1137C23—88no—
1138C23—84no—
1139C23C22×#4112yes—
1140C23C2×2−1+412yes—
1141C23#58512yes—
1142C23C2611yescharacteristic
1143Q8—44no—
1144Q8—44no—
1145Q8—84no—
1146Q8—84no—
1147Q8—84no—
1148Q8—88no—
1149D4—44no—
1150D4—44no—
1151D4—84no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—28no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—48no—
1213C2×C4—88no—
1214C2×C4—88no—
1215C2×C4—84no—
1216C2×C4—84no—
1217C2×C4—164no—
1218C2×C4C22×#4112yes—
1219C2×C4C22×#4112yes—
1220C2×C4C22×#4112yes—
1221C2×C4C22×#4112yes—
1222C2×C4C22×#4112yes—
1223C2×C4C22×#4112yes—
1224C2×C4C2×2−1+414yes—
1225C22—24no—
1226C22—24no—
1227C22—22no—
1228C22—22no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—168no—
1240C22#346114yes—
1241C22C23×#4111yescharacteristic
1242C22C22×2−1+411yescharacteristic
1243C22C2×#58511yescharacteristic
1244C22H(7,𝔽2)12yes—
1245C222−1+612yes—
1246C4—24no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—22no—
1253C4—42no—
1254C4—44no—
1255C4—44no—
1256C4—42no—
1257C4—44no—
1258C4—44no—
1259C4—42no—
1260C4—44no—
1261C4—44no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—44no—
1267C4—44no—
1268C4—42no—
1269C4—42no—
1270C2—24no—
1271C2—82no—
1272C2—82no—
1273C2C2×#346111yescharacteristic
1274C2#6285511yescharacteristic
1275C2#6286011yescharacteristic
1276C2#6305012yes—
1277C2#6305812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42230C2semidirect
2. #42062C2semidirect
3. #42010C2semidirect
4. #41766C2semidirect
5. #41752C2semidirect
6. #41391C2semidirect
7. #41388C2semidirect
8. #41134C2semidirect
9. #41124C2semidirect
10. #40547C2semidirect
12. #37612C2semidirect
13. #37609C2semidirect
14. #37600C2semidirect
15. #37600C2semidirect
16. #37540C2semidirect
18. #36698C2semidirect
20. #36013C2semidirect
21. #35839C2semidirect
22. #35824C2semidirect
23. #35743C2semidirect
26. #34239C2semidirect
27. #34215C2semidirect
31. #2845C22semidirect
32. #2844C22semidirect
33. #2838C22semidirect
34. #2838C22semidirect
35. #2836C22semidirect
36. #2836C22semidirect
37. #2833C22semidirect
39. #2822C22semidirect
40. #2822C22semidirect
52. #2798C22semidirect
53. #2798C22semidirect
55. #2793C22semidirect
56. #2790C22semidirect
57. #2789C22semidirect
58. #2783C22semidirect
59. #2775C22semidirect
60. #2773C22semidirect
61. #2765C22semidirect
62. #2759C22semidirect
63. #2758C22semidirect
64. #2754C22semidirect
65. #2754C22semidirect
67. #2744C22semidirect
68. #2721C22semidirect
69. #2721C22semidirect
70. #2721C22semidirect
71. #2720C22semidirect
73. #2713C22semidirect
74. #2713C22semidirect
76. #2667C22semidirect
77. #2667C22semidirect
78. #2666C22semidirect
79. #2666C22semidirect
80. #2666C22semidirect
81. #2666C22semidirect
82. #2664C22semidirect
83. #2664C22semidirect
84. #2660C22semidirect
86. #2654C22semidirect
87. #2654C22semidirect
88. #2654C22semidirect
89. #2654C22semidirect
90. #2652C22semidirect
91. #2652C22semidirect
94. #2650C22semidirect
95. #2650C22semidirect
96. #2642C22semidirect
99. #2634C22semidirect
100. #2634C22semidirect
101. #2634C22semidirect
109. #2612C22semidirect
110. #2607C22semidirect
111. #2605C22semidirect
113. #2594C22semidirect
115. #2589C22semidirect
116. #2588C22semidirect
117. #2587C22semidirect
118. #2586C22semidirect
119. #2575C22semidirect
120. #2574C22semidirect
121. #2573C22semidirect
122. #2573C22semidirect
123. #2573C22semidirect
126. #2565C22semidirect
128. #2556C22semidirect
129. #2556C22semidirect
130. #2550C22semidirect
134. #2529C22semidirect
135. #2527C22semidirect
136. #2525C22semidirect
137. #2525C22semidirect
138. #2525C22semidirect
139. #2523C22semidirect
140. #2522C22semidirect
141. #2522C22semidirect
143. #2519C22semidirect
144. #2519C22semidirect
145. #2517C22semidirect
147. #2515C22semidirect
148. #2515C22semidirect
159. #2475C22semidirect
163. #2469C22semidirect
166. #2462C22semidirect
167. #2462C22semidirect
168. #2451C22semidirect
170. #2441C22semidirect
175. #2423C22semidirect
176. #2401C22semidirect
177. #2401C22semidirect
178. #2399C22semidirect
179. #2396C22semidirect
180. #2396C22semidirect
188. #2371C22semidirect
189. #2370C22semidirect
190. #2370C22semidirect
198. #2355C22semidirect
199. #2355C22semidirect
216. #2336C22semidirect
217. #2331C22semidirect
218. #2331C22semidirect
222. C4×#125C22semidirect
223. C4×#125C22semidirect
224. C4×#125C22semidirect
225. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#422302
#420622
#420102
#417662
#417522
#413912
#413882
#411342
#411242
#405472
#405442
#376122
#376092
#376002
#375402
#375372
#366982
C2×#28202
#360132
#358392
#358242
#357432
#357312
#342402
#342392
#342152