Finite Group Databasebeta

← #27124664

Subgroups — #27124664

Order 12032.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257468C212yesmaximal, complemented
2#20257411C216yesmaximal, complemented
3#20257389C212yesmaximal, complemented
4#20257340C216yesmaximal, complemented
5#20257295C213yesmaximal, complemented
6#20257262C213yesmaximal, complemented
7#20257207C211yesmaximal, characteristic, complemented
8#20257120C216yesmaximal, complemented
9#20257050C212yesmaximal, complemented
10#20257011C212yesmaximal, complemented
11#20256989C216yesmaximal, complemented
12#20256987C212yesmaximal, complemented
13D4×#10625352C216yesmaximal, complemented
14#20256801C216yesmaximal, complemented
15#20256683C213yesmaximal, complemented
16C2×#15689671C213yesmaximal, complemented
17H(5,𝔽2)×Dic47C212yesmaximal, complemented
18C4×#41×D47C211yesmaximal, characteristic, complemented
19C47×#3498C211yesmaximal, characteristic, complemented
20C22×#10625352C2216yescomplemented
21C2×#41×D47C2211yescharacteristic
22#15689859C2216yescomplemented
23#15689859C2216yescomplemented
24Q8×Dic94C2212yescomplemented
25#15689852C2212yescomplemented
26#15689843C2216yescomplemented
27#15689838C2216yescomplemented
28#15689837C22112yescomplemented
29#15689830C2216yescomplemented
30#15689830C2216yescomplemented
31#15689825C22112yescomplemented
32#15689825C22112yescomplemented
33#15689820C22112yescomplemented
34#15689804C22124yescomplemented
35#15689793C2216yescomplemented
36#15689793C2216yescomplemented
37#15689792C2214yescomplemented
38D4×Dic94C2216yescomplemented
39#15689780C2214yescomplemented
40#15689779C22112yescomplemented
41#15689777C2216yescomplemented
42#15689773C22112yescomplemented
43#15689767C22112yescomplemented
44#15689767C22112yescomplemented
45#15689767C22112yescomplemented
46#15689760C22124yescomplemented
47D4×C22⋊D47C22112yescomplemented
48#15689751C2216yescomplemented
49#15689742C22112yescomplemented
50#15689740C22112yescomplemented
51#15689727C22112yescomplemented
52#15689726C22112yescomplemented
53#15689708C22124yescomplemented
54#15689701C2216yescomplemented
55#15689690C2216yescomplemented
56#15689680C2213yescomplemented
57#15689678C2213yescomplemented
58#15689678C2211yescharacteristic, complemented
59#15689671C2216yescomplemented
60#15689671C2216yescomplemented
61#15689671C2216yescomplemented
62#15689671C2216yescomplemented
63#15689671C2216yescomplemented
64#15689671C2216yescomplemented
65#15689671C2213yescomplemented
66#15689671C2216yescomplemented
67#15689671C2213yescomplemented
68#15689668C22112yescomplemented
69C2×#13094024C2213yescomplemented
70#15689655C2216yescomplemented
71#15689655C2216yescomplemented
72#15689654C22112yescomplemented
73#15689654C2216yescomplemented
74#15689654C2216yescomplemented
75#15689652C2216yescomplemented
76#15689652C2216yescomplemented
77C2×#13094011C2216yescomplemented
78#15689633C2216yescomplemented
79#15689633C2216yescomplemented
80#15689630C2216yescomplemented
81#15689629C22124yescomplemented
82C2×#13093995C2216yescomplemented
83C2×#13093995C2216yescomplemented
84#15689606C2212yes—
85#15689606C2216yescomplemented
86#15689606C2214yescomplemented
87#15689598C22112yescomplemented
88#15689598C2216yescomplemented
89#41×Dic47C2211yescharacteristic
90#41×Dic47C2216yescomplemented
91#41×Dic47C2214yescomplemented
92C4×#10625354C2211yescharacteristic, complemented
93C4×#10625354C2211yescharacteristic, complemented
94C4×#10625350C2213yescomplemented
95#15689591C2213yescomplemented
96C4×#10625352C2213yescomplemented
97C4×#10625352C2213yescomplemented
98C4×#10625352C2216yescomplemented
99C4×#10625352C2216yescomplemented
100C4×Q8×D47C2211yescharacteristic, complemented
101C4×Q8×D47C2211yescharacteristic, complemented
102C2×D4×Dic47C2216yescomplemented
103C2×D4×Dic47C22112yescomplemented
104C2×D4×Dic47C2216yescomplemented
105C4×D4×D47C2213yescomplemented
106C4×D4×D47C2213yescomplemented
107#117×D47C2213yescomplemented
108C2×C42×D47C2213yescomplemented
109C2×H(5,𝔽2)×C47C2212yes—
110C47×#550C2212yescomplemented
111C47×#550C2212yescomplemented
112D42×C47C2216yescomplemented
113D42×C47C2216yescomplemented
114C47×#535C2216yescomplemented
115C47×#532C2213yescomplemented
116C2×#127×C47C2213yescomplemented
117C4×#41×C47C2211yescharacteristic
118C2×#10625354C2311yescharacteristic
119C2×#10625350C2313yes—
120C2×#10625352—424no—
121C2×#10625352C2313yes—
122C2×#10625352C2316yes—
123C2×#10625352C23112yes—
124C2×#10625352C2316yes—
125C2×#10625352C23112yes—
126C2×#10625352C23112yes—
127#41×D47—28no—
128C22×Dic94C2316yes—
129C2×Q8×D47C2311yescharacteristic
130C22×C22⋊D47C23112yes—
131C2×D4×D47C2313yes—
132C23×Dic47C23112yes—
133C22×C4×D47C2313yes—
134C22×C4×D47C2313yes—
135C22×C4×D47C2313yes—
136#13094024C2316yes—
137#13094024C2316yes—
138#13094024C2316yes—
139#13094024C2313yes—
140#13094024C2311yescharacteristic
141#13094023C23112yes—
142#13094020C23112yes—
143#13094017C23112yes—
144#13094017C23124yes—
145#13094017C23112yes—
146#13094016C2316yes—
147#13094015C23112yes—
148#13094015C2316yes—
149#13094015C2312yes—
150#13094011C23112yes—
151#13094011C23112yes—
152#13094011C2316yes—
153#13094011C23112yes—
154#13094011C23112yes—
155#13094011C2316yes—
156#13094010C23124yes—
157#13094008C23124yes—
158#13094006C23112yes—
159#13094006C23112yes—
160#13094005C23124yes—
161#13094005C23112yes—
162#13094005C23124yes—
163#13094004C2316yes—
164#13094004C2312yes—
165#13094003C23112yes—
166#13094003C2316yes—
167#13094003C2316yes—
168#13094001C23124yes—
169#13094001C23124yes—
170#13094000C2316yes—
171#13094000C2312yes—
172#13093998C23112yes—
173#13093996C23124yes—
174#13093996C23124yes—
175#13093996C23124yes—
176#13093995C23112yes—
177#13093995C23112yes—
178#13093995C23112yes—
179#13093995C2316yes—
180#13093995C23112yes—
181#13093995C23112yes—
182#13093995C2316yes—
183#13093995C2316yes—
184#13093995C23112yes—
185#13093995C2316yes—
186#13093993C23124yes—
187#13093992C23112yes—
188Q8×Dic47C2316yes—
189Q8×Dic47C2314yes—
190Q8×Dic47C2311yescharacteristic
191Q8×Dic47C2311yescharacteristic
192Q8×Dic47C2312yes—
193C4×Dic94C2316yes—
194C4×Dic94C2316yes—
195C4×Dic94C2313yes—
196C4×Dic94C2313yes—
197#13093989C2313yes—
198#13093989C2316yes—
199#13093989C2313yes—
200#13093989C2312yes—
201C4×D188C2313yes—
202C4×D188C2313yes—
203D4×Dic47C23112yes—
204D4×Dic47C23112yes—
205D4×Dic47C23112yes—
206D4×Dic47C23124yes—
207D4×Dic47C2316yes—
208D4×Dic47C23112yes—
209D4×Dic47C23112yes—
210D4×Dic47C23112yes—
211D4×Dic47C23112yes—
212D4×Dic47C2313yes—
213D4×Dic47C2313yes—
214D4×Dic47C2316yes—
215D4×Dic47C23112yes—
216D4×Dic47C2316yes—
217D4×Dic47C23112yes—
218D4×Dic47C23112yes—
219D4×Dic47C23112yes—
220D4×Dic47C2316yes—
221#13093986C2313yes—
222#13093986C2313yes—
223C4×C22⋊D47C23112yes—
224C4×C22⋊D47C2316yes—
225C4×C22⋊D47C2316yes—
226C4×C22⋊D47C23112yes—
227(C22⋊D47)⋊C4C23112yes—
228(C22⋊D47)⋊C4C2316yes—
229(C22⋊D47)⋊C4C2316yes—
230(C22⋊D47)⋊C4C23112yes—
231#13093983C23112yes—
232#13093983C2316yes—
233#13093983C23112yes—
234#13093983C2313yes—
235#13093982C2313yes—
236#13093982C2316yes—
237#13093982C2313yes—
238#13093982C2312yes—
239#13093981C2316yes—
240#13093980C2316yes—
241#13093980C23112yes—
242#13093980C23112yes—
243C2×C4⋊Dic47C2316yes—
244C2×C4⋊Dic47C23112yes—
245C2×C4⋊Dic47C2316yes—
246C4⋊C4×D47C2313yes—
247C4⋊C4×D47C2313yes—
248C2×C22⋊Dic47C23124yes—
249C2×C22⋊Dic47C23112yes—
250C2×C22⋊Dic47C23112yes—
251C22⋊C4×D47C2316yes—
252C2×C4×Dic47C2313yes—
253C2×C4×Dic47C2313yes—
254C2×C4×Dic47C2313yes—
255C2×C4×Dic47C23112yes—
256C42×D47C2311yescharacteristic
257C42×D47C2313yes—
258C42×D47C2313yes—
259C42×D47C2313yes—
260C42×D47C2313yes—
261C42×D47C2313yes—
262C42×D47C2313yes—
263C42×D47C2313yes—
264H(5,𝔽2)×C47—216no—
265C2×#41×C47C2314yes—
266C2×#41×C47C2316yes—
267C2×#41×C47C2311yescharacteristic
268C22×D4×C47C23112yes—
269C22×D4×C47C2316yes—
270C22×D4×C47C2316yes—
271C22×D4×C47C2316yes—
272C4⋊Q8×C47C2311yescharacteristic
273#127×C47C2316yes—
274#127×C47C2316yes—
275#127×C47C2313yes—
276#127×C47C2316yes—
277#124×C47C2316yes—
278#121×C47C23112yes—
279#121×C47C2316yes—
280#121×C47C2316yes—
281#121×C47C23112yes—
282#120×C47C23124yes—
283C4×Q8×C47C2311yescharacteristic
284C4×Q8×C47C2311yescharacteristic
285C4×D4×C47C2316yes—
286C4×D4×C47C2313yes—
287C4×D4×C47C2313yes—
288C4×D4×C47C2316yes—
289#117×C47C2313yes—
290C2×C42×C47C2313yes—
291C24×C47C24112yes—
292C23×D47C2413yes—
293#41×C47—216no—
294#41×C47—224no—
295#41×C47#4118yescomplemented
296C2×Q8×C47C2412yes—
297C2×Q8×C47C2411yescharacteristic
298C2×D4×C47—248no—
299C2×D4×C47—224no—
300C2×D4×C47—412no—
301C2×D4×C47—412no—
302C2×D4×C47C2416yes—
303C2×D4×C47C2416yes—
304C2×D4×C47C24112yes—
305C2×D4×C47C24112yes—
306C2×D4×C47C2416yes—
307C2×D4×C47C24112yes—
308C2×D4×C47C24112yes—
309C2×D4×C47C2413yes—
310C22×C4×C47C2413yes—
311C22×C4×C47C2413yes—
312C22×C4×C47C24112yes—
313C22×C4×C47C2413yes—
314C2×C22⋊D47—424no—
315C2×C22⋊D47C2416yes—
316C2×C22⋊D47C24112yes—
317C2×C22⋊D47C24112yes—
318C2×C22⋊D47C24124yes—
319C22×Dic47—424no—
320C22×Dic47C2413yes—
321C22×Dic47C2413yes—
322C22×Dic47C24112yes—
323C22×Dic47C2413yes—
324C22×Dic47C24112yes—
325C22×Dic47C24112yes—
326C22×Dic47C24124yes—
327#10625354—24no—
328Q8×D47—24no—
329#10625352—212no—
330#10625352—224no—
331#10625352—424no—
332#10625352—412no—
333#10625352—424no—
334#10625352—424no—
335D4×D47—212no—
336#10625350—212no—
337C2×D188C2413yes—
338C2×C4×D47—212no—
339C2×C4×D47—212no—
340C2×C4×D47—46no—
341C2×C4×D47C2411yescharacteristic
342C2×C4×D47C2411yescharacteristic
343C2×C4×D47C2413yes—
344C2×C4×D47C2413yes—
345C2×C4×D47C2413yes—
346C2×C4×D47C2413yes—
347C2×C4×D47C2413yes—
348C2×C4×D47C2413yes—
349C2×C4×D47C2413yes—
350C2×C4×D47C2413yes—
351C2×C4×D47C2413yes—
352C2×C4×D47C2411yescharacteristic
353C2×Dic94—412no—
354C2×Dic94C2413yes—
355C2×Dic94C2412yes—
356C2×Dic94C2416yes—
357C2×Dic94C24112yes—
358C4⋊C4×C47C2413yes—
359C4⋊C4×C47C2413yes—
360C4⋊C4×C47C2412yes—
361C4⋊C4×C47C2412yes—
362C22⋊C4×C47C2416yes—
363C22⋊C4×C47C24112yes—
364C22⋊C4×C47C24112yes—
365C42×C47C2411yescharacteristic
366C42×C47C2413yes—
367C42×C47C2413yes—
368C42×C47C2413yes—
369C22⋊Dic47C2416yes—
370C22⋊Dic47C24112yes—
371C22⋊Dic47C24112yes—
372C22⋊Dic47C24112yes—
373C22⋊Dic47C24124yes—
374C22⋊Dic47C24112yes—
375C22⋊Dic47C24124yes—
376C22⋊Dic47C24112yes—
377(C2×D47)⋊C4C2416yes—
378(C2×D47)⋊C4C2416yes—
379(C2×D47)⋊C4C2414yes—
380(C2×D47)⋊C4C24112yes—
381C4⋊Dic47C2413yes—
382C4⋊Dic47C2413yes—
383C4⋊Dic47C2416yes—
384C4⋊Dic47C2416yes—
385C4⋊Dic47C24112yes—
386C4⋊Dic47C24112yes—
387C4⋊Dic47C24112yes—
388C4⋊Dic47C2412yes—
389C4⋊Dic47C2412yes—
390C4⋊Dic47C2414yes—
391Dic47⋊C4C2416yes—
392Dic47⋊C4C2416yes—
393Dic47⋊C4C2414yes—
394Dic47⋊C4C24112yes—
395Dic47⋊C4C24112yes—
396Dic47⋊C4C24112yes—
397C4×Dic47C2411yescharacteristic
398C4×Dic47C2411yescharacteristic
399C4×Dic47C2411yescharacteristic
400C4×Dic47C2413yes—
401C4×Dic47C2413yes—
402C4×Dic47C2413yes—
403C4×Dic47C2413yes—
404C4×Dic47C2413yes—
405C4×Dic47C2413yes—
406C4×Dic47C2413yes—
407C4×Dic47C2413yes—
408C4×Dic47C2413yes—
409C4×Dic47C2414yes—
410C4×Dic47C24112yes—
411C4×Dic47C24112yes—
412C23×C47—224no—
413C23×C47—412no—
414C23×C47—412no—
415C23×C47C25112yes—
416C23×C47C2513yes—
417C22×D47—26no—
418C22×D47—26no—
419C22×D47—43no—
420C22×D47C2513yes—
421C22×D47C2511yescharacteristic
422Q8×C47—24no—
423Q8×C47C2×#4114yescomplemented
424D4×C47—224no—
425D4×C47—224no—
426D4×C47—212no—
427D4×C47—212no—
428D4×C47—212no—
429D4×C47—412no—
430D4×C47—412no—
431D4×C47C2×#41112yescomplemented
432C2×C4×C47—224no—
433C2×C4×C47—26no—
434C2×C4×C47—26no—
435C2×C4×C47C2×#41112yescomplemented
436C2×C4×C47C2514yes—
437C2×C4×C47C2513yes—
438C2×C4×C47C2513yes—
439C2×C4×C47C2513yes—
440C2×C4×C47C2511yescharacteristic
441C2×C4×C47C2511yescharacteristic
442C2×C4×C47C2511yescharacteristic
443C22⋊D47—212no—
444C22⋊D47—224no—
445C22⋊D47—424no—
446C22⋊D47—412no—
447C2×Dic47—26no—
448C2×Dic47—26no—
449C2×Dic47—224no—
450C2×Dic47—412no—
451C2×Dic47—43no—
452C2×Dic47—424no—
453C2×Dic47—412no—
454C2×Dic47C2511yescharacteristic
455C2×Dic47C2513yes—
456C2×Dic47C2511yescharacteristic
457C2×Dic47C2513yes—
458C2×Dic47C2514yes—
459C2×Dic47C2513yes—
460C2×Dic47C25112yes—
461C2×Dic47C2511yescharacteristic
462D188—26no—
463C4×D47—26no—
464C4×D47—22no—
465C4×D47—26no—
466C4×D47—26no—
467C4×D47—26no—
468C4×D47—26no—
469C4×D47—22no—
470C4×D47—26no—
471C4×D47—26no—
472C4×D47—43no—
473C4×D47—43no—
474C4×D47H(5,𝔽2)14yescomplemented
475Dic94—26no—
476Dic94—212no—
477Dic94—24no—
478Dic94—412no—
479#62800—471nomaximal, Sylow
480C22×C47—23no—
481C22×C47—23no—
482C22×C47—212no—
483C22×C47—212no—
484C22×C47—212no—
485C22×C47—824no—
486C22×C47C22×#4116yes—
487C22×C47C2611yescharacteristic
488C2×D47—21no—
489C2×D47—21no—
490C2×D47—23no—
491C2×D47—23no—
492C2×D47—23no—
493C2×D47—412no—
494C2×D47C2×H(5,𝔽2)12yes—
495C4×C47—24no—
496C4×C47—23no—
497C4×C47—23no—
498C4×C47C22×#4116yes—
499C4×C47C22×#4112yes—
500C4×C47C2×H(5,𝔽2)12yes—
501C4×C47#58512yes—
502Dic47—23no—
503Dic47—21no—
504Dic47—212no—
505Dic47—23no—
506Dic47—24no—
507Dic47—21no—
508Dic47—23no—
509Dic47C2×H(5,𝔽2)12yes—
510#3522—472no—
511#3519—476no—
512#3517—472no—
513#3514—476no—
514#3511—473no—
515#3508—473no—
516#3503—471no—
517#3498D4711yescharacteristic, complemented
518#3494—476no—
519#3488—472no—
520#3483—472no—
521#3481—476no—
522#3480—472no—
523D4×#41—476no—
524#3460—476no—
525#3444—473no—
526C2×#532—473no—
527C4×H(5,𝔽2)—472no—
528C2×C4×#41—471no—
529C2×C47—26no—
530C2×C47—412no—
531C2×C47C23×#4111yescharacteristic
532C2×C47C22×H(5,𝔽2)11yescharacteristic
533C2×C47C2×#58511yescharacteristic
534D47—22no—
535D47—43no—
536C2×H(5,𝔽2)C2×D4712yes—
537C22×#41—471no—
538C22×#41—476no—
539#559—476no—
540#559—476no—
541Q82—472no—
542#557—472no—
543#556—476no—
544#555—4712no—
545#555—476no—
546#554—476no—
547#554—476no—
548#553—4712no—
549#553—4712no—
550#553—4712no—
551#551—4724no—
552#550—474no—
553#550—476no—
554#550—476no—
555#550C2×D4712yescomplemented
556#550C2×D4712yescomplemented
557D4×Q8—476no—
558#548—474no—
559#548—4712no—
560#547—4712no—
561#547—476no—
562#546—4712no—
563#546—4712no—
564#546—4712no—
565#546—4724no—
566D42—4712no—
567D42C2×D4716yescomplemented
568D42C2×D4716yescomplemented
569#544—476no—
570#542—4712no—
571#542—4712no—
572#540—4712no—
573#540—4712no—
574#538—4724no—
575#537—476no—
576#535—476no—
577#535C2×D4716yescomplemented
578#533—471no—
579#533—473no—
580#533—473no—
581#532—473no—
582#532—476no—
583#532—476no—
584#532—476no—
585#532—476no—
586#532—476no—
587#532—476no—
588#532—476no—
589#532—473no—
590#532—4712no—
591#532C2×D4713yescomplemented
592C2×C4⋊Q8—473no—
593C2×#127C2×D4713yescomplemented
594#529—476no—
595#529—476no—
596#529—476no—
597#529—476no—
598#529—4712no—
599#529—476no—
600#529—476no—
601C2×#124—476no—
602#525—476no—
603#525—476no—
604#525—476no—
605#525—4724no—
606C2×#121—476no—
607C2×#121—476no—
608#520—472no—
609#520—476no—
610#520—474no—
611#518—476no—
612#518—4712no—
613C4×#41—471no—
614C4×#41—476no—
615C4×#41—474no—
616C4×#41—471no—
617C4×#41—471no—
618C4×#41—473no—
619C4×#41—473no—
620C4×#41—476no—
621C4×#41—476no—
622C4×#41—473no—
623C4×#41—473no—
624C4×#41C2×D4711yescharacteristic
625C2×C4×Q8—471no—
626C2×C4×Q8—471no—
627C2×C4×D4—476no—
628C2×C4×D4—4712no—
629C2×C4×D4—476no—
630C2×C4×D4—473no—
631C2×C4×D4—473no—
632C2×#117—473no—
633C22×C42—473no—
634C47#6280011yescharacteristic, complemented, Sylow
635H(5,𝔽2)—216no—
636C2×#41—471no—
637C2×#41—473no—
638C2×#41—476no—
639C2×#41—476no—
640C2×#41—4712no—
641C2×#41—4712no—
642C2×#41—4712no—
643C2×#41—473no—
644C2×#41—948no—
645C2×#41—18824no—
646C2×#41C22×D4716yes—
647C2×#41C22×D4714yes—
648C2×#41C22×D4711yescharacteristic
649C22×Q8—471no—
650C22×Q8—476no—
651C22×D4—4712no—
652C22×D4—473no—
653C22×D4C22×D4716yes—
654C22×D4C22×D47112yes—
655C22×D4C22×D4716yes—
656C22×D4C22×D4716yes—
657C23×C4—4712no—
658C23×C4—473no—
659C23×C4—473no—
660C23×C4—473no—
661C4⋊Q8—4712no—
662C4⋊Q8—473no—
663C4⋊Q8—476no—
664C4⋊Q8—476no—
665C4⋊Q8—476no—
666C4⋊Q8—471no—
667C4⋊Q8C22×D4711yescharacteristic
668#127—4712no—
669#127C22×D4713yes—
670#127C22×D4716yes—
671#127C22×D4716yes—
672#127C22×D4716yes—
673#126—4712no—
674#126—4712no—
675#126—4724no—
676#125—472no—
677#125—476no—
678#125—4712no—
679#125—476no—
680#124—476no—
681#124—4712no—
682#124—4712no—
683#124—4712no—
684#124—476no—
685#124—4712no—
686#124—4724no—
687#124C22×D4716yes—
688#123—4712no—
689#123—4724no—
690#123—4724no—
691#123—4712no—
692#123—4712no—
693#123—4724no—
694C22⋊Q8—472no—
695C22⋊Q8—476no—
696C22⋊Q8—476no—
697C22⋊Q8—476no—
698C22⋊Q8—4712no—
699C22⋊Q8—472no—
700C22⋊Q8—476no—
701C22⋊Q8—4724no—
702C22⋊Q8—4724no—
703#121—476no—
704#121—476no—
705#121—4712no—
706#121—4712no—
707#121—4712no—
708#121—4712no—
709#121—4712no—
710#121—4712no—
711#121—476no—
712#121—476no—
713#121—4724no—
714#121—4724no—
715#121—4724no—
716#121—4712no—
717#121C22×D4716yes—
718#121C22×D4716yes—
719#121C22×D47112yes—
720#121C22×D47112yes—
721#120—4724no—
722#120—4712no—
723#120C22×D47124yes—
724C4×Q8—471no—
725C4×Q8—471no—
726C4×Q8—472no—
727C4×Q8—476no—
728C4×Q8—474no—
729C4×Q8—473no—
730C4×Q8—473no—
731C4×Q8—472no—
732C4×Q8—476no—
733C4×Q8—473no—
734C4×Q8—473no—
735C4×Q8—476no—
736C4×Q8—476no—
737C4×Q8C22×D4711yescharacteristic
738C4×Q8C22×D4711yescharacteristic
739C4×D4—473no—
740C4×D4—4712no—
741C4×D4—476no—
742C4×D4—4712no—
743C4×D4—476no—
744C4×D4—473no—
745C4×D4—4712no—
746C4×D4—4712no—
747C4×D4—4712no—
748C4×D4—4724no—
749C4×D4—4712no—
750C4×D4—4712no—
751C4×D4—4712no—
752C4×D4—4712no—
753C4×D4—4712no—
754C4×D4—476no—
755C4×D4—4712no—
756C4×D4—476no—
757C4×D4—476no—
758C4×D4—476no—
759C4×D4—4712no—
760C4×D4—4712no—
761C4×D4—473no—
762C4×D4—473no—
763C4×D4—476no—
764C4×D4—476no—
765C4×D4—4712no—
766C4×D4—4712no—
767C4×D4—473no—
768C4×D4—473no—
769C4×D4C22×D4713yes—
770C4×D4C22×D4713yes—
771C4×D4C22×D4716yes—
772C4×D4C22×D4716yes—
773#117—473no—
774#117—476no—
775#117—4712no—
776#117—4712no—
777#117—473no—
778#117—473no—
779#117—472no—
780#117—476no—
781#117—476no—
782#117—4712no—
783#117—4712no—
784#117—476no—
785#117C22×D4713yes—
786C2×C4⋊C4—476no—
787C2×C4⋊C4—4712no—
788C2×C4⋊C4—476no—
789C2×C4⋊C4—473no—
790C2×C4⋊C4—473no—
791C2×C22⋊C4—4712no—
792C2×C22⋊C4—4724no—
793C2×C22⋊C4—4712no—
794C2×C22⋊C4—476no—
795C2×C42—473no—
796C2×C42—473no—
797C2×C42—4712no—
798C2×C42—473no—
799C2×C42—473no—
800C2×C42—473no—
801C2×C42—473no—
802C2×C42—473no—
803C2×C42—473no—
804C2×C42—473no—
805C2×C42—473no—
806C2×C42—471no—
807C2×C42C22×D4713yes—
808C24—473no—
809C24C23×D47112yes—
810#41—216no—
811#41—224no—
812#41—9424no—
813#41—944no—
814#41—9412no—
815#41—9412no—
816#41—18824no—
817#41—18812no—
818#41—18824no—
819#41—18824no—
820#41#1062535218yescomplemented
821C2×Q8—473no—
822C2×Q8—472no—
823C2×Q8—476no—
824C2×Q8—4712no—
825C2×Q8—944no—
826C2×Q8—18812no—
827C2×Q8C23×D4712yes—
828C2×Q8C23×D4711yescharacteristic
829C2×D4—248no—
830C2×D4—224no—
831C2×D4—412no—
832C2×D4—412no—
833C2×D4—476no—
834C2×D4—4712no—
835C2×D4—4712no—
836C2×D4—4724no—
837C2×D4—473no—
838C2×D4—9412no—
839C2×D4—18824no—
840C2×D4C23×D47112yes—
841C2×D4C23×D4716yes—
842C2×D4C23×D47112yes—
843C2×D4C23×D4716yes—
844C2×D4C23×D4716yes—
845C2×D4C23×D47112yes—
846C2×D4C23×D47112yes—
847C2×D4C23×D4713yes—
848C22×C4—471no—
849C22×C4—473no—
850C22×C4—473no—
851C22×C4—4712no—
852C22×C4—473no—
853C22×C4—4712no—
854C22×C4—4712no—
855C22×C4—4724no—
856C22×C4—471no—
857C22×C4—471no—
858C22×C4—473no—
859C22×C4—473no—
860C22×C4—473no—
861C22×C4—473no—
862C22×C4—473no—
863C22×C4—473no—
864C22×C4—473no—
865C22×C4—473no—
866C22×C4—473no—
867C22×C4—9412no—
868C22×C4—9412no—
869C22×C4—1886no—
870C22×C4—18824no—
871C22×C4C23×D4713yes—
872C22×C4C23×D4713yes—
873C22×C4C23×D47112yes—
874C22×C4C23×D4713yes—
875C4⋊C4—476no—
876C4⋊C4—476no—
877C4⋊C4—474no—
878C4⋊C4—4712no—
879C4⋊C4—4712no—
880C4⋊C4—4712no—
881C4⋊C4—473no—
882C4⋊C4—4712no—
883C4⋊C4—476no—
884C4⋊C4—476no—
885C4⋊C4—4712no—
886C4⋊C4—473no—
887C4⋊C4—4712no—
888C4⋊C4—472no—
889C4⋊C4—474no—
890C4⋊C4—472no—
891C4⋊C4C23×D4713yes—
892C4⋊C4C23×D4713yes—
893C4⋊C4C23×D4712yes—
894C4⋊C4C23×D4712yes—
895C22⋊C4—476no—
896C22⋊C4—4712no—
897C22⋊C4—4712no—
898C22⋊C4—4712no—
899C22⋊C4—4712no—
900C22⋊C4—4724no—
901C22⋊C4—4724no—
902C22⋊C4—4712no—
903C22⋊C4—476no—
904C22⋊C4—476no—
905C22⋊C4—474no—
906C22⋊C4—4712no—
907C22⋊C4C23×D4716yes—
908C22⋊C4C23×D47112yes—
909C22⋊C4C23×D47112yes—
910C42—473no—
911C42—471no—
912C42—471no—
913C42—471no—
914C42—473no—
915C42—473no—
916C42—474no—
917C42—473no—
918C42—473no—
919C42—473no—
920C42—473no—
921C42—473no—
922C42—473no—
923C42—4712no—
924C42—4712no—
925C42C23×D4711yescharacteristic
926C42C23×D4713yes—
927C42C23×D4713yes—
928C42C23×D4713yes—
929C23—224no—
930C23—412no—
931C23—412no—
932C23—471no—
933C23—473no—
934C23—946no—
935C23—946no—
936C23—1883no—
937C23C24×D47112yes—
938C23C24×D4713yes—
939Q8—24no—
940Q8—946no—
941Q8—9412no—
942Q8—944no—
943Q8—18812no—
944Q8C2×#1062535214yescomplemented
945D4—224no—
946D4—224no—
947D4—212no—
948D4—212no—
949D4—212no—
950D4—412no—
951D4—412no—
952D4—9424no—
953D4—9412no—
954D4—946no—
955D4—18824no—
956D4—18812no—
957D4C2×#10625352112yescomplemented
958C2×C4—224no—
959C2×C4—26no—
960C2×C4—26no—
961C2×C4—471no—
962C2×C4—474no—
963C2×C4—471no—
964C2×C4—473no—
965C2×C4—471no—
966C2×C4—473no—
967C2×C4—474no—
968C2×C4—473no—
969C2×C4—4712no—
970C2×C4—946no—
971C2×C4—946no—
972C2×C4—946no—
973C2×C4—9424no—
974C2×C4—946no—
975C2×C4—942no—
976C2×C4—946no—
977C2×C4—946no—
978C2×C4—946no—
979C2×C4—946no—
980C2×C4—942no—
981C2×C4—946no—
982C2×C4—1883no—
983C2×C4—1883no—
984C2×C4—1883no—
985C2×C4—18812no—
986C2×C4—18824no—
987C2×C4—18812no—
988C2×C4C2×#10625352112yescomplemented
989C2×C4C24×D4714yes—
990C2×C4C24×D4713yes—
991C2×C4C24×D4713yes—
992C2×C4C24×D4713yes—
993C2×C4C24×D4711yescharacteristic
994C2×C4C24×D4711yescharacteristic
995C2×C4C24×D4711yescharacteristic
996C22—23no—
997C22—23no—
998C22—212no—
999C22—212no—
1000C22—212no—
1001C22—824no—
1002C22—472no—
1003C22—941no—
1004C22—941no—
1005C22—943no—
1006C22—943no—
1007C22—943no—
1008C22—18812no—
1009C22C22×#1062535216yes—
1010C22C25×D4711yescharacteristic
1011C4—24no—
1012C4—23no—
1013C4—23no—
1014C4—472no—
1015C4—941no—
1016C4—943no—
1017C4—943no—
1018C4—9412no—
1019C4—941no—
1020C4—943no—
1021C4—944no—
1022C4C22×#1062535216yes—
1023C4C22×#1062535212yes—
1024C4H(5,𝔽2)×D4712yes—
1025C4#1568995812yes—
1026C2—26no—
1027C2—412no—
1028C2—942no—
1029C2—1883no—
1030C2C23×#1062535211yescharacteristic
1031C2C2×H(5,𝔽2)×D4711yescharacteristic
1032C2C2×#1568995811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3498C2
hypercenter#3498D47
hypocenterC47#62800
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #20257468C2semidirect
2. #20257411C2semidirect
3. #20257389C2semidirect
4. #20257340C2semidirect
5. #20257295C2semidirect
6. #20257262C2semidirect
7. #20257207C2semidirect
8. #20257120C2semidirect
9. #20257050C2semidirect
10. #20257011C2semidirect
11. #20256989C2semidirect
12. #20256987C2semidirect
13. D4×#10625352C2semidirect
14. #20256801C2semidirect
15. #20256683C2semidirect
16. C2×#15689671C2semidirect
17. H(5,𝔽2)×Dic47C2semidirect
18. C4×#41×D47C2semidirect
19. C47×#3498C2semidirect
20. C22×#10625352C22semidirect
22. #15689859C22semidirect
23. #15689859C22semidirect
24. Q8×Dic94C22semidirect
25. #15689852C22semidirect
26. #15689843C22semidirect
27. #15689838C22semidirect
28. #15689837C22semidirect
29. #15689830C22semidirect
30. #15689830C22semidirect
31. #15689825C22semidirect
32. #15689825C22semidirect
33. #15689820C22semidirect
34. #15689804C22semidirect
35. #15689793C22semidirect
36. #15689793C22semidirect
37. #15689792C22semidirect
38. D4×Dic94C22semidirect
39. #15689780C22semidirect
40. #15689779C22semidirect
41. #15689777C22semidirect
42. #15689773C22semidirect
43. #15689767C22semidirect
44. #15689767C22semidirect
45. #15689767C22semidirect
46. #15689760C22semidirect
47. D4×C22⋊D47C22semidirect
48. #15689751C22semidirect
49. #15689742C22semidirect
50. #15689740C22semidirect
51. #15689727C22semidirect
52. #15689726C22semidirect
53. #15689708C22semidirect
54. #15689701C22semidirect
55. #15689690C22semidirect
56. #15689680C22semidirect
57. #15689678C22semidirect
58. #15689678C22semidirect
59. #15689671C22semidirect
60. #15689671C22semidirect
61. #15689671C22semidirect
62. #15689671C22semidirect
63. #15689671C22semidirect
64. #15689671C22semidirect
65. #15689671C22semidirect
66. #15689671C22semidirect
67. #15689671C22semidirect
68. #15689668C22semidirect
69. C2×#13094024C22semidirect
70. #15689655C22semidirect
71. #15689655C22semidirect
72. #15689654C22semidirect
73. #15689654C22semidirect
74. #15689654C22semidirect
75. #15689652C22semidirect
76. #15689652C22semidirect
77. C2×#13094011C22semidirect
78. #15689633C22semidirect
79. #15689633C22semidirect
80. #15689630C22semidirect
81. #15689629C22semidirect
82. C2×#13093995C22semidirect
83. C2×#13093995C22semidirect
85. #15689606C22semidirect
86. #15689606C22semidirect
87. #15689598C22semidirect
88. #15689598C22semidirect
90. #41×Dic47C22semidirect
91. #41×Dic47C22semidirect
92. C4×#10625354C22semidirect
93. C4×#10625354C22semidirect
94. C4×#10625350C22semidirect
95. #15689591C22semidirect
96. C4×#10625352C22semidirect
97. C4×#10625352C22semidirect
98. C4×#10625352C22semidirect
99. C4×#10625352C22semidirect
100. C4×Q8×D47C22semidirect
101. C4×Q8×D47C22semidirect
102. C2×D4×Dic47C22semidirect
103. C2×D4×Dic47C22semidirect
104. C2×D4×Dic47C22semidirect
105. C4×D4×D47C22semidirect
106. C4×D4×D47C22semidirect
107. #117×D47C22semidirect
108. C2×C42×D47C22semidirect
110. C47×#550C22semidirect
111. C47×#550C22semidirect
112. D42×C47C22semidirect
113. D42×C47C22semidirect
114. C47×#535C22semidirect
115. C47×#532C22semidirect
116. C2×#127×C47C22semidirect
295. #41×C47#41semidirect
423. Q8×C47C2×#41semidirect
431. D4×C47C2×#41semidirect
435. C2×C4×C47C2×#41semidirect
474. C4×D47H(5,𝔽2)semidirect
517. #3498D47semidirect
555. #550C2×D47semidirect
556. #550C2×D47semidirect
567. D42C2×D47semidirect
568. D42C2×D47semidirect
577. #535C2×D47semidirect
591. #532C2×D47semidirect
593. C2×#127C2×D47semidirect
634. C47#62800semidirect
820. #41#10625352semidirect
944. Q8C2×#10625352semidirect
957. D4C2×#10625352semidirect
988. C2×C4C2×#10625352semidirect

Maximal subgroups

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

subgroupindex
#202574682
#202574112
#202573892
#202573402
#202572952
#202572622
#202572072
#202571202
#202570502
#202570112
#202569892
#202569872
D4×#106253522
#202568012
#202566832
C2×#156896712
H(5,𝔽2)×Dic472
C4×#41×D472
C47×#34982
#6280047