Finite Group Databasebeta

← C47×#26400 #26066098

Subgroups — C47×#26400 #26066098

Order 12032.

740 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3083C211yesmaximal, characteristic, complemented
2C47×#3081C211yesmaximal, characteristic, complemented
3C47×#2946C211yesmaximal, characteristic
4C47×#2913C211yesmaximal, characteristic, complemented
5C47×#2093C211yesmaximal, characteristic, complemented
6C47×#2089C211yesmaximal, characteristic, complemented
7C47×#2063C211yesmaximal, characteristic, complemented
8C47×#2060C211yesmaximal, characteristic, complemented
9C47×#1952C211yesmaximal, characteristic, complemented
10C47×#1922C211yesmaximal, characteristic, complemented
11C47×#1907C211yesmaximal, characteristic
12C47×#1883C211yesmaximal, characteristic
13C47×#1866C211yesmaximal, characteristic, complemented
14C47×#1859C211yesmaximal, characteristic, complemented
15C47×#1856C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
17C2×#131×C47C2211yescharacteristic
18C47×#544C2211yescharacteristic
19C47×#520C2211yescharacteristic
20C47×#520C2211yescharacteristic
21C47×#518C2211yescharacteristic
22C47×#479—21no—
23C47×#478—21no—
24C47×#478—21no—
25C47×#478—21no—
26C47×#477—21no—
27C47×#476—21no—
28C47×#474—21no—
29C47×#474—21no—
30C47×#442—21no—
31C47×#440—21no—
32C4×SD16×C47—21no—
33C4×D8×C47—21no—
34C2×#108×C47C2211yescharacteristic
35C47×#428—21no—
36C47×#428—21no—
37C47×#428C2211yescharacteristic
38C47×#428C2211yescharacteristic
39C47×#428C2211yescharacteristic
40C47×#428C2211yescharacteristic
41C47×#428C2211yescharacteristic
42C47×#427—21no—
43C47×#427C2211yescharacteristic
44C2×#107×C47—21no—
45C2×#107×C47C2211yescharacteristic
46C2×#107×C47C2211yescharacteristic
47C47×#424C2211yescharacteristic
48C47×#424C2211yescharacteristic
49C2×#104×C47C2211yescharacteristic
50C47×#418C2211yescharacteristic
51C47×#417C2211yescharacteristic
52C47×#416C2211yescharacteristic
53C2×#102×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×#100×C47C2211yescharacteristic
56C47×#405C2211yescharacteristic
57C47×#390C2211yescharacteristic
58C47×#384C2211yescharacteristic
59C47×#343C2211yescharacteristic
60C47×#343C2211yescharacteristic
61C47×#343C2211yescharacteristic
62C47×#341C2211yescharacteristic
63C47×#339C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#41×C47C2311yescharacteristic
68C22×D4×C47C2311yescharacteristic
69AGL(1,ℤ/8)×C47—22no—
70AGL(1,ℤ/8)×C47Q814yescomplemented
71C2×SD16×C47—21no—
72C2×D8×C47—21no—
73#131×C47—22no—
74#131×C47—22no—
75C2×M16×C47—21no—
76C2×M16×C47C2311yescharacteristic
77C2×M16×C47C2311yescharacteristic
78C2×M16×C47C2311yescharacteristic
79C2×M16×C47C2311yescharacteristic
80C22×C8×C47—21no—
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C4⋊Q8×C47—21no—
84C4⋊Q8×C47—21no—
85#125×C47—21no—
86#125×C47—21no—
87C22⋊Q8×C47—41no—
88C4×Q8×C47—21no—
89C4×Q8×C47—21no—
90C4×D4×C47—21no—
91C4×D4×C47—21no—
92C4×D4×C47—21no—
93C4×D4×C47—21no—
94C4×D4×C47—21no—
95C4×D4×C47—21no—
96C4×D4×C47—41no—
97C4×D4×C47—41no—
98#117×C47—21no—
99#117×C47—21no—
100#117×C47C2311yescharacteristic
101#117×C47C2311yescharacteristic
102#117×C47C2311yescharacteristic
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—41no—
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47—41no—
110C2×C22⋊C4×C47—41no—
111C2×C42×C47C2311yescharacteristic
112#108×C47—22no—
113#107×C47—21no—
114#107×C47—21no—
115#107×C47—21no—
116#107×C47—21no—
117#107×C47—21no—
118#107×C47—21no—
119#107×C47—21no—
120#107×C47—21no—
121#107×C47—21no—
122#107×C47D411yescharacteristic
123#107×C47D411yescharacteristic
124#106×C47—21no—
125#106×C47—21no—
126#106×C47—21no—
127#106×C47—21no—
128#106×C47—21no—
129#106×C47D411yescharacteristic
130#106×C47D411yescharacteristic
131C4⋊C8×C47—21no—
132C4⋊C8×C47—21no—
133C4⋊C8×C47—21no—
134C4⋊C8×C47—21no—
135#104×C47—22no—
136#103×C47—21no—
137#103×C47D411yescharacteristic
138#103×C47D411yescharacteristic
139#102×C47—21no—
140#102×C47—21no—
141#102×C47—21no—
142#102×C47—21no—
143#102×C47—21no—
144#102×C47—21no—
145#102×C47—21no—
146#102×C47D411yescharacteristic
147#102×C47D411yescharacteristic
148#100×C47—22no—
149#97×C47—21no—
150C4×C8×C47—21no—
151C24×C47—21no—
152#41×C47—21no—
153#41×C47—21no—
154#41×C47C2×Q812yes—
155#41×C47#4112yes—
156C2×Q8×C47—41no—
157C2×Q8×C47C2×D411yescharacteristic
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47C2×D411yescharacteristic
165C2×D4×C47C2×Q812yes—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—41no—
172C22×C4×C47—41no—
173C22×C4×C47—41no—
174C22×C4×C47—41no—
175C22×C4×C47C2411yescharacteristic
176SD16×C47—24no—
177D8×C47—24no—
178M16×C47—24no—
179M16×C47—21no—
180M16×C47—21no—
181M16×C47—21no—
182M16×C47—21no—
183M16×C47—21no—
184M16×C47—21no—
185M16×C47C2×Q812yes—
186M16×C47#4112yes—
187C2×C8×C47—24no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47C2×D411yescharacteristic
197C2×C8×C47C2×D411yescharacteristic
198C2×C8×C47C2×D411yescharacteristic
199C2×C8×C47C2×D411yescharacteristic
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—41no—
207C4⋊C4×C47—41no—
208C4⋊C4×C47—41no—
209C4⋊C4×C47—41no—
210C4⋊C4×C47—41no—
211C4⋊C4×C47—82no—
212C4⋊C4×C47C2×D411yescharacteristic
213C4⋊C4×C47C2×D411yescharacteristic
214C4⋊C4×C47C2×D411yescharacteristic
215C4⋊C4×C47C2×D411yescharacteristic
216C4⋊C4×C47C2×D411yescharacteristic
217C4⋊C4×C47C2×D411yescharacteristic
218C22⋊C4×C47—21no—
219C22⋊C4×C47—21no—
220C22⋊C4×C47—21no—
221C22⋊C4×C47—41no—
222C22⋊C4×C47—41no—
223C22⋊C4×C47—41no—
224C22⋊C4×C47—41no—
225C22⋊C4×C47—82no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47—21no—
231C42×C47—41no—
232C42×C47—41no—
233C23×C47—21no—
234C23×C47—22no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—81no—
238C23×C47—81no—
239C23×C47H(5,𝔽2)11yescharacteristic
240Q8×C47—21no—
241Q8×C47—161no—
242Q8×C47C22⋊Q812yes—
243D4×C47—22no—
244D4×C47—22no—
245D4×C47—22no—
246D4×C47—21no—
247D4×C47—22no—
248D4×C47—41no—
249D4×C47—41no—
250D4×C47C22⋊Q812yes—
251C2×C4×C47—21no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—81no—
267C2×C4×C47—81no—
268C2×C4×C47—81no—
269C2×C4×C47—161no—
270C2×C4×C47—161no—
271C2×C4×C47—161no—
272C2×C4×C47—161no—
273C2×C4×C47C22×D411yescharacteristic
274C2×C4×C47C22×D411yescharacteristic
275C2×C4×C47C22×Q811yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C2×C4×C472−1+411yescharacteristic
279C8×C47—22no—
280C8×C47—21no—
281C8×C47—22no—
282C8×C47—21no—
283C8×C47—21no—
284C8×C47—21no—
285C8×C47—41no—
286C8×C47—41no—
287#26400C4711yesmaximal, characteristic, direct product factor, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—22no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47—42no—
294C22×C47—82no—
295C22×C47—81no—
296C22×C47—81no—
297C22×C47—161no—
298C22×C47#53911yescharacteristic
299C22×C47D4211yescharacteristic
300C22×C47#55411yescharacteristic
301C4×C47—22no—
302C4×C47—42no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—41no—
308C4×C47—41no—
309C4×C47—81no—
310C4×C47—81no—
311C4×C47—81no—
312C4×C47C2×C22⋊Q811yescharacteristic
313C4×C47#52511yescharacteristic
314C4×C47#54711yescharacteristic
315C4×C47D4×Q811yescharacteristic
316#3083C2×C4711yescharacteristic, complemented
317#3081C2×C4711yescharacteristic, complemented
318#2946C2×C4711yescharacteristic
319#2913C2×C4711yescharacteristic, complemented
320#2093C2×C4711yescharacteristic, complemented
321#2089C2×C4711yescharacteristic, complemented
322#2063C2×C4711yescharacteristic, complemented
323#2060C2×C4711yescharacteristic, complemented
324#1952C2×C4711yescharacteristic, complemented
325#1922C2×C4711yescharacteristic, complemented
326#1907C2×C4711yescharacteristic
327#1883C2×C4711yescharacteristic
328#1866C2×C4711yescharacteristic, complemented
329#1859C2×C4711yescharacteristic, complemented
330#1856C2×C4711yescharacteristic, complemented
331C2×C47—21no—
332C2×C47—21no—
333C2×C47—42no—
334C2×C47—82no—
335C2×C47#244911yescharacteristic
336C2×C47#328911yescharacteristic
337C2×C47#329211yescharacteristic
338C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
339C2×#131C22×C4711yescharacteristic
340#544C22×C4711yescharacteristic
341#520C22×C4711yescharacteristic
342#520C22×C4711yescharacteristic
343#518C22×C4711yescharacteristic
344#479—21no—
345#478—21no—
346#478—21no—
347#478—21no—
348#477—21no—
349#476—21no—
350#474—21no—
351#474—21no—
352#442—21no—
353#440—21no—
354C4×SD16—21no—
355C4×D8—21no—
356C2×#108C22×C4711yescharacteristic
357#428—21no—
358#428—21no—
359#428C22×C4711yescharacteristic
360#428C22×C4711yescharacteristic
361#428C22×C4711yescharacteristic
362#428C22×C4711yescharacteristic
363#428C22×C4711yescharacteristic
364#427—21no—
365#427C22×C4711yescharacteristic
366C2×#107—21no—
367C2×#107C22×C4711yescharacteristic
368C2×#107C22×C4711yescharacteristic
369#424C22×C4711yescharacteristic
370#424C22×C4711yescharacteristic
371C2×#104C22×C4711yescharacteristic
372#418C22×C4711yescharacteristic
373#417C22×C4711yescharacteristic
374#416C22×C4711yescharacteristic
375C2×#102C22×C4711yescharacteristic
376C2×#102C22×C4711yescharacteristic
377C2×#100C22×C4711yescharacteristic
378#405C22×C4711yescharacteristic
379#390C22×C4711yescharacteristic
380#384C22×C4711yescharacteristic
381#343C22×C4711yescharacteristic
382#343C22×C4711yescharacteristic
383#343C22×C4711yescharacteristic
384#341C22×C4711yescharacteristic
385#339C22×C4711yescharacteristic
386#339C22×C4711yescharacteristic
387#339C22×C4711yescharacteristic
388#336C22×C4711yescharacteristic
389C47#2640011yescharacteristic, direct product factor, Sylow
390C2×#41C23×C4711yescharacteristic
391C22×D4C23×C4711yescharacteristic
392AGL(1,ℤ/8)—22no—
393AGL(1,ℤ/8)Q8×C4714yescomplemented
394C2×SD16—21no—
395C2×D8—21no—
396#131—22no—
397#131—22no—
398C2×M16—21no—
399C2×M16C23×C4711yescharacteristic
400C2×M16C23×C4711yescharacteristic
401C2×M16C23×C4711yescharacteristic
402C2×M16C23×C4711yescharacteristic
403C22×C8—21no—
404C22×C8C23×C4711yescharacteristic
405C22×C8C23×C4711yescharacteristic
406C4⋊Q8—21no—
407C4⋊Q8—21no—
408#125—21no—
409#125—21no—
410C22⋊Q8—41no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—41no—
420C4×D4—41no—
421#117—21no—
422#117—21no—
423#117C23×C4711yescharacteristic
424#117C23×C4711yescharacteristic
425#117C23×C4711yescharacteristic
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4C23×C4711yescharacteristic
430C2×C4⋊C4C23×C4711yescharacteristic
431C2×C4⋊C4C23×C4711yescharacteristic
432C2×C22⋊C4—41no—
433C2×C22⋊C4—41no—
434C2×C42C23×C4711yescharacteristic
435#108—22no—
436#107—21no—
437#107—21no—
438#107—21no—
439#107—21no—
440#107—21no—
441#107—21no—
442#107—21no—
443#107—21no—
444#107—21no—
445#107D4×C4711yescharacteristic
446#107D4×C4711yescharacteristic
447#106—21no—
448#106—21no—
449#106—21no—
450#106—21no—
451#106—21no—
452#106D4×C4711yescharacteristic
453#106D4×C4711yescharacteristic
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—21no—
457C4⋊C8—21no—
458#104—22no—
459#103—21no—
460#103D4×C4711yescharacteristic
461#103D4×C4711yescharacteristic
462#102—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—21no—
467#102—21no—
468#102—21no—
469#102D4×C4711yescharacteristic
470#102D4×C4711yescharacteristic
471#100—22no—
472#97—21no—
473C4×C8—21no—
474C24—21no—
475#41—21no—
476#41—21no—
477#41C2×Q8×C4712yes—
478#41#41×C4712yes—
479C2×Q8—41no—
480C2×Q8C2×D4×C4711yescharacteristic
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×D4×C4711yescharacteristic
488C2×D4C2×Q8×C4712yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4C24×C4711yescharacteristic
499SD16—24no—
500D8—24no—
501M16—24no—
502M16—21no—
503M16—21no—
504M16—21no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16C2×Q8×C4712yes—
509M16#41×C4712yes—
510C2×C8—24no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8C2×D4×C4711yescharacteristic
520C2×C8C2×D4×C4711yescharacteristic
521C2×C8C2×D4×C4711yescharacteristic
522C2×C8C2×D4×C4711yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—82no—
535C4⋊C4C2×D4×C4711yescharacteristic
536C4⋊C4C2×D4×C4711yescharacteristic
537C4⋊C4C2×D4×C4711yescharacteristic
538C4⋊C4C2×D4×C4711yescharacteristic
539C4⋊C4C2×D4×C4711yescharacteristic
540C4⋊C4C2×D4×C4711yescharacteristic
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—82no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—41no—
555C42—41no—
556C23—21no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—81no—
561C23—81no—
562C23H(5,𝔽2)×C4711yescharacteristic
563Q8—21no—
564Q8—161no—
565Q8C22⋊Q8×C4712yes—
566D4—22no—
567D4—22no—
568D4—22no—
569D4—21no—
570D4—22no—
571D4—41no—
572D4—41no—
573D4C22⋊Q8×C4712yes—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—161no—
593C2×C4—161no—
594C2×C4—161no—
595C2×C4—161no—
596C2×C4C22×D4×C4711yescharacteristic
597C2×C4C22×D4×C4711yescharacteristic
598C2×C4C22×Q8×C4711yescharacteristic
599C2×C4C2×#41×C4711yescharacteristic
600C2×C4C2×#41×C4711yescharacteristic
601C2×C42−1+4×C4711yescharacteristic
602C8—22no—
603C8—21no—
604C8—22no—
605C8—21no—
606C8—21no—
607C8—21no—
608C8—41no—
609C8—41no—
610C22—21no—
611C22—21no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—42no—
616C22—82no—
617C22—81no—
618C22—81no—
619C22—161no—
620C22C47×#53911yescharacteristic
621C22D42×C4711yescharacteristic
622C22C47×#55411yescharacteristic
623C4—22no—
624C4—42no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4C2×C22⋊Q8×C4711yescharacteristic
635C4C47×#52511yescharacteristic
636C4C47×#54711yescharacteristic
637C4D4×Q8×C4711yescharacteristic
638C2—21no—
639C2—21no—
640C2—42no—
641C2—82no—
642C2C47×#244911yescharacteristic
643C2C47×#328911yescharacteristic
644C2C47×#329211yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×AGL(1,ℤ/8)×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3083C2semidirect
2. C47×#3081C2semidirect
4. C47×#2913C2semidirect
5. C47×#2093C2semidirect
6. C47×#2089C2semidirect
7. C47×#2063C2semidirect
8. C47×#2060C2semidirect
9. C47×#1952C2semidirect
10. C47×#1922C2semidirect
13. C47×#1866C2semidirect
14. C47×#1859C2semidirect
15. C47×#1856C2semidirect
70. AGL(1,ℤ/8)×C47Q8semidirect
287. #26400C47direct (N × H)
316. #3083C2×C47semidirect
317. #3081C2×C47semidirect
319. #2913C2×C47semidirect
320. #2093C2×C47semidirect
321. #2089C2×C47semidirect
322. #2063C2×C47semidirect
323. #2060C2×C47semidirect
324. #1952C2×C47semidirect
325. #1922C2×C47semidirect
328. #1866C2×C47semidirect
329. #1859C2×C47semidirect
330. #1856C2×C47semidirect
389. C47#26400direct (N × H)
393. AGL(1,ℤ/8)Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30832
C47×#30812
C47×#29462
C47×#29132
C47×#20932
C47×#20892
C47×#20632
C47×#20602
C47×#19522
C47×#19222
C47×#19072
C47×#18832
C47×#18662
C47×#18592
C47×#18562
#2640047