Finite Group Databasebeta

← C47×#24987 #26064685

Subgroups — C47×#24987 #26064685

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#471C211yesmaximal, characteristic
2C47×#2949C211yesmaximal, characteristic, complemented
3C47×#2082C211yesmaximal, characteristic, complemented
4C47×#2081C211yesmaximal, characteristic, complemented
5C47×#2049C211yesmaximal, characteristic, complemented
6C47×#2048C211yesmaximal, characteristic
7C47×#1977C211yesmaximal, characteristic, complemented
8C47×#1953C211yesmaximal, characteristic, complemented
9C47×#1905C211yesmaximal, characteristic, complemented
10C47×#1904C211yesmaximal, characteristic
11C47×#1833C211yesmaximal, characteristic, complemented
12C47×#1830C211yesmaximal, characteristic, complemented
13C47×#1829C211yesmaximal, characteristic, complemented
14C47×#1814C211yesmaximal, characteristic, complemented
15C47×#1757C211yesmaximal, characteristic, complemented
16C2×#137×C47C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C2×#131×C47C2211yescharacteristic
20C47×#519C2211yescharacteristic
21C47×#518C2211yescharacteristic
22C47×#471—22no—
23C47×#471—22no—
24C47×#440—22no—
25C4×SD16×C47—22no—
26C47×#430C2211yescharacteristic
27C47×#430C2211yescharacteristic
28C2×#108×C47C2211yescharacteristic
29C2×#108×C47C2211yescharacteristic
30C47×#427C2211yescharacteristic
31C47×#421C2211yescharacteristic
32C47×#421C2211yescharacteristic
33C47×#419C2211yescharacteristic
34C47×#419C2211yescharacteristic
35C47×#418C2211yescharacteristic
36C47×#418C2211yescharacteristic
37C47×#413C2211yescharacteristic
38C2×#101×C47C2211yescharacteristic
39C2×#101×C47C2211yescharacteristic
40C2×#100×C47C2211yescharacteristic
41C2×#100×C47C2211yescharacteristic
42C47×#410C2211yescharacteristic
43C47×#405C2211yescharacteristic
44C47×#405C2211yescharacteristic
45C47×#344C2211yescharacteristic
46C47×#344C2211yescharacteristic
47C47×#344C2211yescharacteristic
48C47×#344C2211yescharacteristic
49C47×#344C2211yescharacteristic
50C47×#344C2211yescharacteristic
51C47×#344C2211yescharacteristic
52C47×#344C2211yescharacteristic
53C47×H(3,ℤ/4)C2211yescharacteristic
54C47×H(3,ℤ/4)C2211yescharacteristic
55C2×#41×C47C2311yescharacteristic
56C22×Q8×C47C2311yescharacteristic
57C22×D4×C47C2311yescharacteristic
58#137×C47—22no—
59#137×C47—41no—
60AGL(1,ℤ/8)×C47—22no—
61AGL(1,ℤ/8)×C47—41no—
62C2×Q16×C47—21no—
63C2×SD16×C47—21no—
64C2×SD16×C47—21no—
65C2×SD16×C47—21no—
66C2×SD16×C47—21no—
67C2×SD16×C47—21no—
68C2×SD16×C47—21no—
69C2×SD16×C47D412yes—
70C2×SD16×C47D412yes—
71C2×D8×C47—21no—
72#131×C47—21no—
73#131×C47—21no—
74#131×C47—21no—
75#131×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47C2311yescharacteristic
78C2×M16×C47C2311yescharacteristic
79C2×M16×C47C2311yescharacteristic
80C2×M16×C47C2311yescharacteristic
81C2×M16×C47C2311yescharacteristic
82C2×M16×C47C2311yescharacteristic
83C2×M16×C47C2311yescharacteristic
84C22×C8×C47—21no—
85C22×C8×C47C2311yescharacteristic
86C4×Q8×C47—22no—
87C4×Q8×C47—41no—
88C4×D4×C47—22no—
89C4×D4×C47—41no—
90#117×C47—22no—
91#117×C47C2311yescharacteristic
92#117×C47C2311yescharacteristic
93#117×C47C2311yescharacteristic
94#117×C47C2311yescharacteristic
95C2×C22⋊C4×C47—22no—
96#108×C47—21no—
97#108×C47—21no—
98#108×C47—21no—
99#108×C47—21no—
100#108×C47—41no—
101#108×C47—41no—
102#107×C47—21no—
103#106×C47—21no—
104#104×C47—41no—
105#104×C47—41no—
106#103×C47—22no—
107#103×C47—41no—
108#102×C47—22no—
109#102×C47—41no—
110#101×C47—22no—
111#101×C47—21no—
112#101×C47—41no—
113#100×C47—22no—
114#100×C47—21no—
115#100×C47—41no—
116#99×C47—22no—
117#97×C47—21no—
118#97×C47—21no—
119C4×C8×C47—21no—
120C4×C8×C47—21no—
121C24×C47—21no—
122#41×C47—21no—
123#41×C47—21no—
124#41×C47—21no—
125#41×C47—21no—
126C2×Q8×C47—21no—
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47C2×D412yes—
132C2×Q8×C47#4111yescharacteristic
133C2×D4×C47—21no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47—21no—
137C2×D4×C47—21no—
138C2×D4×C47—21no—
139C2×D4×C47C2×D412yes—
140C2×D4×C47#4111yescharacteristic
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—42no—
144C22×C4×C47C2411yescharacteristic
145Q16×C47—42no—
146SD16×C47—22no—
147SD16×C47—22no—
148SD16×C47—22no—
149SD16×C47—22no—
150SD16×C47—42no—
151SD16×C47—42no—
152D8×C47—42no—
153M16×C47—21no—
154M16×C47—21no—
155M16×C47—21no—
156M16×C47—21no—
157M16×C47—21no—
158M16×C47—21no—
159M16×C47—21no—
160M16×C47—21no—
161M16×C47—21no—
162M16×C47—21no—
163M16×C47—21no—
164M16×C47—21no—
165M16×C47—21no—
166M16×C47—21no—
167M16×C47—41no—
168M16×C47—41no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—41no—
177C2×C8×C47—41no—
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47#4111yescharacteristic
181C2×C8×C47#4111yescharacteristic
182C2×C8×C47#4111yescharacteristic
183C2×C8×C47#4111yescharacteristic
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—42no—
189C22⋊C4×C47—21no—
190C22⋊C4×C47—21no—
191C22⋊C4×C47—21no—
192C22⋊C4×C47—42no—
193C22⋊C4×C47#4112yes—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—42no—
199C23×C47—21no—
200C23×C47—22no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—161no—
204C23×C47C2×#4111yescharacteristic
205Q8×C47—22no—
206Q8×C47—21no—
207Q8×C47—22no—
208Q8×C47—21no—
209Q8×C47—41no—
210Q8×C47—41no—
211D4×C47—22no—
212D4×C47—21no—
213D4×C47—22no—
214D4×C47—21no—
215D4×C47—41no—
216D4×C47—41no—
217D4×C47—41no—
218D4×C47—41no—
219C2×C4×C47—21no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—162no—
230C2×C4×C47C22×D411yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47H(5,𝔽2)11yescharacteristic
235C2×C4×C47H(5,𝔽2)11yescharacteristic
236C8×C47—41no—
237C8×C47—41no—
238C8×C47—41no—
239C8×C47—41no—
240C8×C47—41no—
241C8×C47—41no—
242C8×C47—41no—
243C8×C47#12311yescharacteristic
244C8×C47#12311yescharacteristic
245C8×C47#12311yescharacteristic
246C8×C47#12311yescharacteristic
247#24987C4711yesmaximal, characteristic, direct product factor, Sylow
248C22×C47—41no—
249C22×C47—41no—
250C22×C47—42no—
251C22×C47—82no—
252C22×C47—81no—
253C22×C47—161no—
254C22×C47—161no—
255C22×C47#52911yescharacteristic
256C22×C47#54611yescharacteristic
257C22×C47#55511yescharacteristic
258C4×C47—42no—
259C4×C47—41no—
260C4×C47—42no—
261C4×C47—81no—
262C4×C47—81no—
263C4×C47—81no—
264C4×C47C2×#12311yescharacteristic
265C4×C47#54011yescharacteristic
266C4×C47#54611yescharacteristic
267C4×C47#55311yescharacteristic
268C2×#471C2×C4711yescharacteristic
269#2949C2×C4711yescharacteristic, complemented
270#2082C2×C4711yescharacteristic, complemented
271#2081C2×C4711yescharacteristic, complemented
272#2049C2×C4711yescharacteristic, complemented
273#2048C2×C4711yescharacteristic
274#1977C2×C4711yescharacteristic, complemented
275#1953C2×C4711yescharacteristic, complemented
276#1905C2×C4711yescharacteristic, complemented
277#1904C2×C4711yescharacteristic
278#1833C2×C4711yescharacteristic, complemented
279#1830C2×C4711yescharacteristic, complemented
280#1829C2×C4711yescharacteristic, complemented
281#1814C2×C4711yescharacteristic, complemented
282#1757C2×C4711yescharacteristic, complemented
283C2×C47—21no—
284C2×C47—21no—
285C2×C47—21no—
286C2×C47—81no—
287C2×C47—82no—
288C2×C47#242011yescharacteristic
289C2×#137C22×C4711yescharacteristic
290C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
291C22×SD16C22×C4711yescharacteristic
292C2×#131C22×C4711yescharacteristic
293#519C22×C4711yescharacteristic
294#518C22×C4711yescharacteristic
295#471—22no—
296#471—22no—
297#440—22no—
298C4×SD16—22no—
299#430C22×C4711yescharacteristic
300#430C22×C4711yescharacteristic
301C2×#108C22×C4711yescharacteristic
302C2×#108C22×C4711yescharacteristic
303#427C22×C4711yescharacteristic
304#421C22×C4711yescharacteristic
305#421C22×C4711yescharacteristic
306#419C22×C4711yescharacteristic
307#419C22×C4711yescharacteristic
308#418C22×C4711yescharacteristic
309#418C22×C4711yescharacteristic
310#413C22×C4711yescharacteristic
311C2×#101C22×C4711yescharacteristic
312C2×#101C22×C4711yescharacteristic
313C2×#100C22×C4711yescharacteristic
314C2×#100C22×C4711yescharacteristic
315#410C22×C4711yescharacteristic
316#405C22×C4711yescharacteristic
317#405C22×C4711yescharacteristic
318#344C22×C4711yescharacteristic
319#344C22×C4711yescharacteristic
320#344C22×C4711yescharacteristic
321#344C22×C4711yescharacteristic
322#344C22×C4711yescharacteristic
323#344C22×C4711yescharacteristic
324#344C22×C4711yescharacteristic
325#344C22×C4711yescharacteristic
326H(3,ℤ/4)C22×C4711yescharacteristic
327H(3,ℤ/4)C22×C4711yescharacteristic
328C47#2498711yescharacteristic, direct product factor, Sylow
329C2×#41C23×C4711yescharacteristic
330C22×Q8C23×C4711yescharacteristic
331C22×D4C23×C4711yescharacteristic
332#137—22no—
333#137—41no—
334AGL(1,ℤ/8)—22no—
335AGL(1,ℤ/8)—41no—
336C2×Q16—21no—
337C2×SD16—21no—
338C2×SD16—21no—
339C2×SD16—21no—
340C2×SD16—21no—
341C2×SD16—21no—
342C2×SD16—21no—
343C2×SD16D4×C4712yes—
344C2×SD16D4×C4712yes—
345C2×D8—21no—
346#131—21no—
347#131—21no—
348#131—21no—
349#131—21no—
350C2×M16—21no—
351C2×M16C23×C4711yescharacteristic
352C2×M16C23×C4711yescharacteristic
353C2×M16C23×C4711yescharacteristic
354C2×M16C23×C4711yescharacteristic
355C2×M16C23×C4711yescharacteristic
356C2×M16C23×C4711yescharacteristic
357C2×M16C23×C4711yescharacteristic
358C22×C8—21no—
359C22×C8C23×C4711yescharacteristic
360C4×Q8—22no—
361C4×Q8—41no—
362C4×D4—22no—
363C4×D4—41no—
364#117—22no—
365#117C23×C4711yescharacteristic
366#117C23×C4711yescharacteristic
367#117C23×C4711yescharacteristic
368#117C23×C4711yescharacteristic
369C2×C22⋊C4—22no—
370#108—21no—
371#108—21no—
372#108—21no—
373#108—21no—
374#108—41no—
375#108—41no—
376#107—21no—
377#106—21no—
378#104—41no—
379#104—41no—
380#103—22no—
381#103—41no—
382#102—22no—
383#102—41no—
384#101—22no—
385#101—21no—
386#101—41no—
387#100—22no—
388#100—21no—
389#100—41no—
390#99—22no—
391#97—21no—
392#97—21no—
393C4×C8—21no—
394C4×C8—21no—
395C24—21no—
396#41—21no—
397#41—21no—
398#41—21no—
399#41—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8C2×D4×C4712yes—
406C2×Q8#41×C4711yescharacteristic
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4C2×D4×C4712yes—
414C2×D4#41×C4711yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4C24×C4711yescharacteristic
419Q16—42no—
420SD16—22no—
421SD16—22no—
422SD16—22no—
423SD16—22no—
424SD16—42no—
425SD16—42no—
426D8—42no—
427M16—21no—
428M16—21no—
429M16—21no—
430M16—21no—
431M16—21no—
432M16—21no—
433M16—21no—
434M16—21no—
435M16—21no—
436M16—21no—
437M16—21no—
438M16—21no—
439M16—21no—
440M16—21no—
441M16—41no—
442M16—41no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—41no—
451C2×C8—41no—
452C2×C8C2×D4×C4711yescharacteristic
453C2×C8C2×D4×C4711yescharacteristic
454C2×C8#41×C4711yescharacteristic
455C2×C8#41×C4711yescharacteristic
456C2×C8#41×C4711yescharacteristic
457C2×C8#41×C4711yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—42no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—42no—
467C22⋊C4#41×C4712yes—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—42no—
473C23—21no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—161no—
478C23C2×#41×C4711yescharacteristic
479Q8—22no—
480Q8—21no—
481Q8—22no—
482Q8—21no—
483Q8—41no—
484Q8—41no—
485D4—22no—
486D4—21no—
487D4—22no—
488D4—21no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—162no—
504C2×C4C22×D4×C4711yescharacteristic
505C2×C4C2×#41×C4711yescharacteristic
506C2×C4C2×#41×C4711yescharacteristic
507C2×C4C2×#41×C4711yescharacteristic
508C2×C4H(5,𝔽2)×C4711yescharacteristic
509C2×C4H(5,𝔽2)×C4711yescharacteristic
510C8—41no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8#123×C4711yescharacteristic
518C8#123×C4711yescharacteristic
519C8#123×C4711yescharacteristic
520C8#123×C4711yescharacteristic
521C22—41no—
522C22—41no—
523C22—42no—
524C22—82no—
525C22—81no—
526C22—161no—
527C22—161no—
528C22C47×#52911yescharacteristic
529C22C47×#54611yescharacteristic
530C22C47×#55511yescharacteristic
531C4—42no—
532C4—41no—
533C4—42no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×#123×C4711yescharacteristic
538C4C47×#54011yescharacteristic
539C4C47×#54611yescharacteristic
540C4C47×#55311yescharacteristic
541C2—21no—
542C2—21no—
543C2—21no—
544C2—82no—
545C2—81no—
546C2C47×#242011yescharacteristic
subgroupG/H
center, socleC2×C47#2420
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×AGL(1,ℤ/8)×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2949C2semidirect
3. C47×#2082C2semidirect
4. C47×#2081C2semidirect
5. C47×#2049C2semidirect
7. C47×#1977C2semidirect
8. C47×#1953C2semidirect
9. C47×#1905C2semidirect
11. C47×#1833C2semidirect
12. C47×#1830C2semidirect
13. C47×#1829C2semidirect
14. C47×#1814C2semidirect
15. C47×#1757C2semidirect
247. #24987C47direct (N × H)
269. #2949C2×C47semidirect
270. #2082C2×C47semidirect
271. #2081C2×C47semidirect
272. #2049C2×C47semidirect
274. #1977C2×C47semidirect
275. #1953C2×C47semidirect
276. #1905C2×C47semidirect
278. #1833C2×C47semidirect
279. #1830C2×C47semidirect
280. #1829C2×C47semidirect
281. #1814C2×C47semidirect
282. #1757C2×C47semidirect
328. C47#24987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4712
C47×#29492
C47×#20822
C47×#20812
C47×#20492
C47×#20482
C47×#19772
C47×#19532
C47×#19052
C47×#19042
C47×#18332
C47×#18302
C47×#18292
C47×#18142
C47×#17572
#2498747