Finite Group Databasebeta

← #7658725

Subgroups — #7658725

Order 512.

5272 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42239C214yesmaximal, complemented
2#42078C214yesmaximal, complemented
3#42074C214yesmaximal, complemented
4#42071C214yesmaximal, complemented
5#41964C214yesmaximal, complemented
6#41962C214yesmaximal, complemented
7#41016C212yesmaximal, complemented
8#41005C214yesmaximal, complemented
9#41001C212yesmaximal, complemented
10#40640C212yesmaximal, complemented
11#40638C212yesmaximal, complemented
12#37533C212yesmaximal, complemented
13#37529C214yesmaximal, complemented
14#37479C211yesmaximal, characteristic, complemented
15#37440C212yesmaximal, complemented
16#36677C212yesmaximal, complemented
17C2×#2815C211yesmaximal, characteristic, complemented
18#35977C214yesmaximal, complemented
19#35695C212yesmaximal, complemented
20#35692C212yesmaximal, complemented
21#35681C214yesmaximal, complemented
22#34204C212yesmaximal, complemented
23#34199C211yesmaximal, characteristic, complemented
24C2×#546C2212yes—
25C22×#123C2211yescharacteristic
26C22×#121C2212yes—
27C2×#518C2211yescharacteristic
28C2×#518C2212yescomplemented
29C22×#117C2211yescharacteristic
30#2841C2212yescomplemented
31#2841C2212yescomplemented
32#2838C2214yescomplemented
33#2837C2214yescomplemented
34#2829C2214yescomplemented
35#2828C2214yescomplemented
36#2826C2212yescomplemented
37#2825C2214yescomplemented
38#2824C2212yescomplemented
39#2815C2214yes—
40#2815C2214yes—
41#2815C2212yescomplemented
42#2815C2212yescomplemented
43#2815C2211yescharacteristic, complemented
44#2815C2212yescomplemented
45#2815C2211yescharacteristic, complemented
46#2813C2214yescomplemented
47#2813C2214yescomplemented
48#2808C2214yescomplemented
49#2803C2214yescomplemented
50#2803C2214yescomplemented
51#2797C2214yescomplemented
52#2796C2214yescomplemented
53#2796C2214yescomplemented
54#2787C2214yescomplemented
55#2783C2214yescomplemented
56#2777C2214yescomplemented
57#2760C2212yescomplemented
58#2752C2212yescomplemented
59#2749C2214yescomplemented
60#2733C2214yescomplemented
61#2724C2214yescomplemented
62#2714C2214yescomplemented
63#2714C2214yescomplemented
64#2710C2214yescomplemented
65#2706C2214yescomplemented
66#2705C2214yescomplemented
67#2696C2214yescomplemented
68#2693C2214yescomplemented
69#2689C2214yescomplemented
70#2682C2214yescomplemented
71#2678C2214yescomplemented
72#2670C2212yescomplemented
73#2668C2212yescomplemented
74#2667C2214yescomplemented
75#2665C2214yescomplemented
76#2663C2214yescomplemented
77#2662C2214yescomplemented
78#2661C2214yescomplemented
79#2661C2214yescomplemented
80#2661C2214yescomplemented
81#2661C2214yescomplemented
82#2654C2214yescomplemented
83#2652C2214yescomplemented
84#2651C2214yescomplemented
85#2650C2214yescomplemented
86#2649C2214yescomplemented
87#2648C2214yescomplemented
88#2648C2214yescomplemented
89#2636C2214yescomplemented
90#2635C2214yescomplemented
91#2635C2212yescomplemented
92#2635C2214yescomplemented
93#2631C2212yescomplemented
94#2631C2214yescomplemented
95#2630C2214yescomplemented
96#2630C2214yescomplemented
97#2626C2212yes—
98#2626C2212yes—
99#2623C2214yes—
100#2618C2214yescomplemented
101#2617C2214yescomplemented
102#2613C2214yes—
103#2610C2212yescomplemented
104#2608C2212yescomplemented
105#2607C2211yescharacteristic, complemented
106#2607C2211yescharacteristic, complemented
107#2602C2214yescomplemented
108#2600C2214yescomplemented
109#2598C2212yescomplemented
110#2597C2214yescomplemented
111#2597C2214yescomplemented
112#2594C2214yescomplemented
113#2591C2212yescomplemented
114#2591C2212yescomplemented
115#2577C2214yescomplemented
116#2573C2214yescomplemented
117#2569C2212yescomplemented
118#2564C2212yes—
119#2557C2214yescomplemented
120#2555C2214yescomplemented
121#2554C2214yescomplemented
122#2554C2214yescomplemented
123#2553C2214yescomplemented
124#2539C2212yescomplemented
125#2539C2212yescomplemented
126#2539C2212yescomplemented
127#2532C2214yescomplemented
128#2525C2214yescomplemented
129#2521C2214yescomplemented
130#2516C2214yescomplemented
131#2515C2214yescomplemented
132#2513C2214yescomplemented
133#2510C2214yes—
134#2505C2214yescomplemented
135#2480C2214yescomplemented
136#2480C2214yescomplemented
137#2478C2214yescomplemented
138#2472C2214yes—
139#2471C2214yescomplemented
140#2471C2214yescomplemented
141#2467C2214yescomplemented
142#2464C2214yescomplemented
143#2464C2214yescomplemented
144#2463C2212yescomplemented
145#2461C2214yescomplemented
146#2459C2214yescomplemented
147#2459C2214yescomplemented
148#2457C2214yescomplemented
149#2457C2214yescomplemented
150#2456C2214yescomplemented
151#2456C2214yescomplemented
152#2456C2214yescomplemented
153#2456C2214yescomplemented
154#2456C2214yescomplemented
155#2455C2214yescomplemented
156#2455C2212yescomplemented
157#2447C2214yescomplemented
158#2438C2214yescomplemented
159#2438C2214yescomplemented
160#2437C2214yescomplemented
161#2435C2212yescomplemented
162#2424C2214yescomplemented
163#2418C2214yes—
164#2414C2214yescomplemented
165#2412C2214yes—
166#2411C2214yes—
167#2411C2214yes—
168#2410C2214yes—
169#2408C2212yes—
170#2407C2214yescomplemented
171#2405C2214yes—
172#2405C2214yescomplemented
173#2404C2212yescomplemented
174#2403C2214yes—
175#2401C2214yescomplemented
176#2397C2212yescomplemented
177#2395C2214yescomplemented
178#2392C2214yescomplemented
179#2392C2214yescomplemented
180C2×#397C2214yescomplemented
181#2388C2212yescomplemented
182#2388C2214yescomplemented
183C2×#392C2212yes—
184C2×#392C2212yes—
185C2×#392C2214yescomplemented
186#2368C2212yescomplemented
187#2363C2214yescomplemented
188#2363C2214yescomplemented
189#2361C2214yescomplemented
190#2361C2214yescomplemented
191#2359C2214yes—
192#2359C2214yes—
193#2358C2214yes—
194#2353C2212yes—
195#2344C2214yescomplemented
196#2342C2214yescomplemented
197#2342C2214yescomplemented
198#2342C2214yescomplemented
199#2342C2214yescomplemented
200D4×C22⋊C4C2214yes—
201D4×C22⋊C4C2214yes—
202D4×C22⋊C4C2212yescomplemented
203#2324C2214yescomplemented
204#2324C2214yescomplemented
205#2322C2212yescomplemented
206#2322C2212yescomplemented
207#2316C2212yescomplemented
208#2315C2211yescharacteristic
209#2309C2212yescomplemented
210#2308C2211yescharacteristic
211C4×#123C2212yescomplemented
212C4×#123C2212yescomplemented
213C4×#121C2214yescomplemented
214C4×#121C2214yescomplemented
215#2280C2212yes—
216C2×#381C2211yescharacteristic
217#2274C2212yescomplemented
218#2273C2211yescharacteristic
219C22×#41C2312yes—
220C23×D4C2311yescharacteristic
221C23×D4C2312yes—
222C23×D4C2314yes—
223C23×D4C2312yes—
224C23×D4C2312yes—
225C24×C4C2311yescharacteristic
226#546—48no—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#124C2312yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#123—28no—
233C2×#123C2312yes—
234C2×#123C2314yes—
235C2×#123C2312yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×#121—216no—
247C2×#121C2312yes—
248C2×#121C2312yes—
249C2×#121C2314yes—
250C2×#121C2314yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258C2×#120C2314yes—
259C2×#120C2314yes—
260C2×#120C2314yes—
261C2×#120C2314yes—
262#518—48no—
263#518—44no—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×#117—44no—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2314yes—
285C2×#117C2312yes—
286C2×#117C2314yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2312yes—
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2314yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2314yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2314yes—
302C22×C42C2312yes—
303#401C2314yes—
304#400C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#399C2312yes—
315#399C2312yes—
316#399C2314yes—
317#399C2314yes—
318#399C2312yes—
319#399C2312yes—
320#399C2314yes—
321#399C2312yes—
322#399C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#395C2312yes—
366#395C2314yes—
367#395C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2312yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2312yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2312yes—
397#393C2314yes—
398#393C2312yes—
399#393C2312yes—
400#393C2312yes—
401#393C2312yes—
402#393C2314yes—
403#392C2312yes—
404#392C2312yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2312yes—
409#392C2314yes—
410#392C2314yes—
411#392C2312yes—
412#392C2314yes—
413#392C2314yes—
414#392C2312yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2312yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#392C2312yes—
426#392C2312yes—
427#392C2312yes—
428#392C2312yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#388C2314yes—
465#388C2314yes—
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#387C2314yes—
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#386C2312yes—
517#386C2312yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#385C2314yes—
544#385C2312yes—
545#385C2314yes—
546#385C2312yes—
547#385C2314yes—
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#383C2314yes—
562#383C2312yes—
563#382C2314yes—
564#381C2312yes—
565#381C2314yes—
566#381C2311yescharacteristic
567#381C2311yescharacteristic
568#381C2311yescharacteristic
569#381C2311yescharacteristic
570#381C2314yes—
571#381C2314yes—
572#381C2314yes—
573#381C2312yes—
574#380C2314yes—
575#380C2312yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2312yes—
582#380C2314yes—
583#379C2312yes—
584#379C2314yes—
585#379C2314yes—
586#379C2314yes—
587#379C2314yes—
588#379C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2312yes—
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2312yes—
616#376C2312yes—
617C2×#95C2312yes—
618C2×#95C2312yes—
619C2×#95C2314yes—
620C25C2414yes—
621C25C2411yescharacteristic
622C25C2411yescharacteristic
623C2×#41—44no—
624C2×#41—84no—
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×D4—24no—
628C22×D4—216no—
629C22×D4—28no—
630C22×D4—44no—
631C22×D4—44no—
632C22×D4—44no—
633C22×D4—44no—
634C22×D4—42no—
635C22×D4—42no—
636C22×D4—84no—
637C22×D4—84no—
638C22×D4—84no—
639C22×D4—84no—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C22×D4C2414yes—
651C22×D4C2412yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2414yes—
656C22×D4C2412yes—
657C22×D4C2412yes—
658C22×D4C2414yes—
659C23×C4—42no—
660C23×C4—42no—
661C23×C4#4118yescomplemented
662C23×C4C2412yes—
663C23×C4C2414yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2414yes—
669C23×C4C2412yes—
670C23×C4C2414yes—
671C23×C4C2411yescharacteristic
672C23×C4C2412yes—
673C23×C4C2414yes—
674C23×C4C2414yes—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679#126—84no—
680#126—84no—
681#124—44no—
682#124—84no—
683#124—84no—
684#123—216no—
685#123—28no—
686#123—28no—
687#123—48no—
688#123—84no—
689#123—84no—
690#123—84no—
691#123—84no—
692#123—84no—
693#123—84no—
694C22⋊Q8—44no—
695C22⋊Q8—44no—
696C22⋊Q8—84no—
697#121—28no—
698#121—28no—
699#121—216no—
700#121—216no—
701#121—28no—
702#121—28no—
703#121—44no—
704#121—48no—
705#121—84no—
706#121—84no—
707#121—84no—
708#120—48no—
709#120—48no—
710#120—84no—
711#120—84no—
712C4×D4—28no—
713C4×D4—48no—
714C4×D4—48no—
715C4×D4—44no—
716C4×D4—44no—
717C4×D4—48no—
718C4×D4—48no—
719C4×D4—44no—
720C4×D4—44no—
721C4×D4—84no—
722C4×D4—84no—
723C4×D4—84no—
724C4×D4—84no—
725C4×D4—84no—
726C4×D4—84no—
727#117—28no—
728#117—48no—
729#117—44no—
730#117—44no—
731#117—44no—
732#117—44no—
733#117—84no—
734C2×C4⋊C4—28no—
735C2×C4⋊C4—28no—
736C2×C4⋊C4—44no—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C22⋊C4—24no—
769C2×C22⋊C4—216no—
770C2×C22⋊C4—28no—
771C2×C22⋊C4—24no—
772C2×C22⋊C4—216no—
773C2×C22⋊C4—44no—
774C2×C22⋊C4—42no—
775C2×C22⋊C4—48no—
776C2×C22⋊C4—42no—
777C2×C22⋊C4—42no—
778C2×C22⋊C4—84no—
779C2×C22⋊C4—84no—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2411yescharacteristic
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⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2411yescharacteristic
845C2×C42—44no—
846C2×C42C2414yes—
847C2×C42C2412yes—
848C2×C42C2414yes—
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2412yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2412yes—
867#95C2414yes—
868#95C2414yes—
869#95C2412yes—
870#95C2412yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2412yes—
897#95C2412yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904C24—22no—
905C24—22no—
906C24—22no—
907C24—28no—
908C24—28no—
909C24—28no—
910C24—44no—
911C24—41no—
912C24—41no—
913C24—44no—
914C24—44no—
915C24—44no—
916C24—44no—
917C24—44no—
918C24C2×#4114yes—
919C24C2512yes—
920C24C2514yes—
921C24C2514yes—
922C24C2511yescharacteristic
923C24C2511yescharacteristic
924C24C2511yescharacteristic
925#41—816no—
926C2×Q8—42no—
927C2×Q8—44no—
928C2×Q8—42no—
929C2×Q8—44no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—24no—
933C2×D4—24no—
934C2×D4—24no—
935C2×D4—24no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—24no—
939C2×D4—24no—
940C2×D4—28no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—44no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—44no—
957C2×D4—432no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—42no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—416no—
985C2×D4—832no—
986C2×D4—816no—
987C2×D4—816no—
988C22×C4—24no—
989C22×C4—24no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—28no—
993C22×C4—24no—
994C22×C4—24no—
995C22×C4—24no—
996C22×C4—28no—
997C22×C4—28no—
998C22×C4—24no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—42no—
1002C22×C4—41no—
1003C22×C4—416no—
1004C22×C4—41no—
1005C22×C4—42no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—42no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4C2×#4118yes—
1030C22×C4C2×#4118yes—
1031C22×C4C2×#4114yes—
1032C22×C4C2×#4114yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C4⋊C4—28no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—24no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C22⋊C4—24no—
1082C22⋊C4—24no—
1083C22⋊C4—28no—
1084C22⋊C4—22no—
1085C22⋊C4—24no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—24no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—24no—
1097C22⋊C4—42no—
1098C22⋊C4—41no—
1099C22⋊C4—42no—
1100C22⋊C4—41no—
1101C22⋊C4—42no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—41no—
1105C22⋊C4—42no—
1106C22⋊C4—41no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4H(5,𝔽2)14yes—
1146C42—28no—
1147C42—24no—
1148C42—44no—
1149C42—42no—
1150C42—42no—
1151C42—42no—
1152C42—42no—
1153C42—42no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C23—24no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—24no—
1166C23—24no—
1167C23—28no—
1168C23—22no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—22no—
1173C23—24no—
1174C23—24no—
1175C23—24no—
1176C23—22no—
1177C23—24no—
1178C23—24no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—24no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—48no—
1188C23—44no—
1189C23—416no—
1190C23—84no—
1191C23—84no—
1192C23—88no—
1193C23—88no—
1194C23—88no—
1195C23—88no—
1196C23—88no—
1197C23—88no—
1198C23—84no—
1199C23—162no—
1200C23—162no—
1201C23C22×#4112yes—
1202C23C22×#4112yes—
1203C23C22×#4112yes—
1204C23C2×H(5,𝔽2)12yes—
1205C23#58512yes—
1206C23C2611yescharacteristic
1207Q8—84no—
1208Q8—162no—
1209D4—48no—
1210D4—48no—
1211D4—416no—
1212D4—48no—
1213D4—416no—
1214D4—416no—
1215D4—48no—
1216D4—48no—
1217D4—48no—
1218D4—88no—
1219D4—88no—
1220D4—88no—
1221D4—84no—
1222D4—88no—
1223D4—84no—
1224D4—88no—
1225D4—88no—
1226D4—164no—
1227D4—164no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—216no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—48no—
1272C2×C4—44no—
1273C2×C4—44no—
1274C2×C4—44no—
1275C2×C4—84no—
1276C2×C4—88no—
1277C2×C4—84no—
1278C2×C4—88no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—88no—
1283C2×C4—84no—
1284C2×C4—162no—
1285C2×C4—164no—
1286C2×C4—164no—
1287C2×C4C22×#4114yes—
1288C2×C4C22×#4114yes—
1289C2×C4C2×H(5,𝔽2)14yes—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—22no—
1296C22—22no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—44no—
1302C22—42no—
1303C22—44no—
1304C22—44no—
1305C22—42no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—42no—
1320C22—88no—
1321C22—1616no—
1322C22—164no—
1323C22#345914yes—
1324C22C23×#4111yescharacteristic
1325C22C22×H(5,𝔽2)11yescharacteristic
1326C22C2×#58511yescharacteristic
1327C22H(7,𝔽2)14yes—
1328C4—24no—
1329C4—24no—
1330C4—24no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—42no—
1335C4—44no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—44no—
1341C4—44no—
1342C4—44no—
1343C4—44no—
1344C4—42no—
1345C2—24no—
1346C2—42no—
1347C2—42no—
1348C2—84no—
1349C2—82no—
1350C2—84no—
1351C2C2×#345911yescharacteristic
1352C2#6285512yes—
1353C2#6304112yes—
1354C2#6304212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42239C2semidirect
2. #42078C2semidirect
3. #42074C2semidirect
4. #42071C2semidirect
5. #41964C2semidirect
6. #41962C2semidirect
7. #41016C2semidirect
8. #41005C2semidirect
9. #41001C2semidirect
10. #40640C2semidirect
11. #40638C2semidirect
12. #37533C2semidirect
13. #37529C2semidirect
14. #37479C2semidirect
15. #37440C2semidirect
16. #36677C2semidirect
17. C2×#2815C2semidirect
18. #35977C2semidirect
19. #35695C2semidirect
20. #35692C2semidirect
21. #35681C2semidirect
22. #34204C2semidirect
23. #34199C2semidirect
28. C2×#518C22semidirect
30. #2841C22semidirect
31. #2841C22semidirect
32. #2838C22semidirect
33. #2837C22semidirect
34. #2829C22semidirect
35. #2828C22semidirect
36. #2826C22semidirect
37. #2825C22semidirect
38. #2824C22semidirect
41. #2815C22semidirect
42. #2815C22semidirect
43. #2815C22semidirect
44. #2815C22semidirect
45. #2815C22semidirect
46. #2813C22semidirect
47. #2813C22semidirect
48. #2808C22semidirect
49. #2803C22semidirect
50. #2803C22semidirect
51. #2797C22semidirect
52. #2796C22semidirect
53. #2796C22semidirect
54. #2787C22semidirect
55. #2783C22semidirect
56. #2777C22semidirect
57. #2760C22semidirect
58. #2752C22semidirect
59. #2749C22semidirect
60. #2733C22semidirect
61. #2724C22semidirect
62. #2714C22semidirect
63. #2714C22semidirect
64. #2710C22semidirect
65. #2706C22semidirect
66. #2705C22semidirect
67. #2696C22semidirect
68. #2693C22semidirect
69. #2689C22semidirect
70. #2682C22semidirect
71. #2678C22semidirect
72. #2670C22semidirect
73. #2668C22semidirect
74. #2667C22semidirect
75. #2665C22semidirect
76. #2663C22semidirect
77. #2662C22semidirect
78. #2661C22semidirect
79. #2661C22semidirect
80. #2661C22semidirect
81. #2661C22semidirect
82. #2654C22semidirect
83. #2652C22semidirect
84. #2651C22semidirect
85. #2650C22semidirect
86. #2649C22semidirect
87. #2648C22semidirect
88. #2648C22semidirect
89. #2636C22semidirect
90. #2635C22semidirect
91. #2635C22semidirect
92. #2635C22semidirect
93. #2631C22semidirect
94. #2631C22semidirect
95. #2630C22semidirect
96. #2630C22semidirect
100. #2618C22semidirect
101. #2617C22semidirect
103. #2610C22semidirect
104. #2608C22semidirect
105. #2607C22semidirect
106. #2607C22semidirect
107. #2602C22semidirect
108. #2600C22semidirect
109. #2598C22semidirect
110. #2597C22semidirect
111. #2597C22semidirect
112. #2594C22semidirect
113. #2591C22semidirect
114. #2591C22semidirect
115. #2577C22semidirect
116. #2573C22semidirect
117. #2569C22semidirect
119. #2557C22semidirect
120. #2555C22semidirect
121. #2554C22semidirect
122. #2554C22semidirect
123. #2553C22semidirect
124. #2539C22semidirect
125. #2539C22semidirect
126. #2539C22semidirect
127. #2532C22semidirect
128. #2525C22semidirect
129. #2521C22semidirect
130. #2516C22semidirect
131. #2515C22semidirect
132. #2513C22semidirect
134. #2505C22semidirect
135. #2480C22semidirect
136. #2480C22semidirect
137. #2478C22semidirect
139. #2471C22semidirect
140. #2471C22semidirect
141. #2467C22semidirect
142. #2464C22semidirect
143. #2464C22semidirect
144. #2463C22semidirect
145. #2461C22semidirect
146. #2459C22semidirect
147. #2459C22semidirect
148. #2457C22semidirect
149. #2457C22semidirect
150. #2456C22semidirect
151. #2456C22semidirect
152. #2456C22semidirect
153. #2456C22semidirect
154. #2456C22semidirect
155. #2455C22semidirect
156. #2455C22semidirect
157. #2447C22semidirect
158. #2438C22semidirect
159. #2438C22semidirect
160. #2437C22semidirect
161. #2435C22semidirect
162. #2424C22semidirect
164. #2414C22semidirect
170. #2407C22semidirect
172. #2405C22semidirect
173. #2404C22semidirect
175. #2401C22semidirect
176. #2397C22semidirect
177. #2395C22semidirect
178. #2392C22semidirect
179. #2392C22semidirect
180. C2×#397C22semidirect
181. #2388C22semidirect
182. #2388C22semidirect
185. C2×#392C22semidirect
186. #2368C22semidirect
187. #2363C22semidirect
188. #2363C22semidirect
189. #2361C22semidirect
190. #2361C22semidirect
195. #2344C22semidirect
196. #2342C22semidirect
197. #2342C22semidirect
198. #2342C22semidirect
199. #2342C22semidirect
202. D4×C22⋊C4C22semidirect
203. #2324C22semidirect
204. #2324C22semidirect
205. #2322C22semidirect
206. #2322C22semidirect
207. #2316C22semidirect
209. #2309C22semidirect
211. C4×#123C22semidirect
212. C4×#123C22semidirect
213. C4×#121C22semidirect
214. C4×#121C22semidirect
217. #2274C22semidirect
661. C23×C4#41semidirect

Maximal subgroups

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

subgroupindex
#422392
#420782
#420742
#420712
#419642
#419622
#410162
#410052
#410012
#406402
#406382
#375332
#375292
#374792
#374402
#366772
C2×#28152
#359772
#356952
#356922
#356812
#342042
#341992