Finite Group Databasebeta

← C47×#12752 #26052450

Subgroups — C47×#12752 #26052450

Order 12032.

888 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3584C211yesmaximal, characteristic
2C47×#2148C211yesmaximal, characteristic, complemented
3C2×C47×#360C211yesmaximal, characteristic, complemented
4C2×C47×#360C211yesmaximal, characteristic, complemented
5C47×#2143C211yesmaximal, characteristic, complemented
6C47×#2117C211yesmaximal, characteristic, complemented
7C47×#1815C211yesmaximal, characteristic, complemented
8C47×#585—21no—
9C47×#578—21no—
10C47×#578C412yescomplemented
11C47×#577—22no—
12C47×#577—22no—
13C47×#576—21no—
14C47×#576C412yescomplemented
15C47×#575—22no—
16C47×#575—21no—
17C2×#135×C47—22no—
18C2×#135×C47C2211yescharacteristic
19C2×#135×C47C2211yescharacteristic
20C2×#131×C47C2211yescharacteristic
21C2×M32×C47C2211yescharacteristic, complemented
22C2×M32×C47C2211yescharacteristic, complemented
23C2×#108×C47C2211yescharacteristic, complemented
24C2×#106×C47C2211yescharacteristic, complemented
25C47×#417—21no—
26C47×#362—21no—
27C47×#361—21no—
28C47×#360—22no—
29C47×#360—22no—
30C47×#359—22no—
31C47×#350—22no—
32C47×#343—21no—
332−1+4×C47—22no—
342−1+4×C47—22no—
352−1+4×C47—41no—
36H(5,𝔽2)×C47—22no—
37H(5,𝔽2)×C47—22no—
38H(5,𝔽2)×C47—42no—
39H(5,𝔽2)×C47—41no—
40C2×#41×C47—24no—
41C2×#41×C47—21no—
42C2×#41×C47—21no—
43C2×#41×C47—42no—
44C2×#41×C47—42no—
45C2×#41×C47D411yescharacteristic
46#137×C47—22no—
47#137×C47—24no—
48#137×C47—24no—
49#137×C47—22no—
50AGL(1,ℤ/8)×C47—22no—
51AGL(1,ℤ/8)×C47—24no—
52AGL(1,ℤ/8)×C47—24no—
53AGL(1,ℤ/8)×C47—22no—
54#135×C47—24no—
55#135×C47—24no—
56#135×C47—22no—
57#135×C47—22no—
58#135×C47—21no—
59#135×C47—21no—
60#135×C47—21no—
61#135×C47—21no—
62#135×C47C2×C412yes—
63#135×C47D412yes—
64#135×C47D412yes—
65#135×C47D412yes—
66C2×Q16×C47—22no—
67C2×Q16×C47C2×C411yescharacteristic
68C2×Q16×C47D411yescharacteristic
69C2×SD16×C47—24no—
70C2×SD16×C47—21no—
71C2×SD16×C47—21no—
72C2×D8×C47—22no—
73C2×D8×C47C2×C411yescharacteristic
74C2×D8×C47D411yescharacteristic
75#131×C47—21no—
76#131×C47—21no—
77#131×C47C2×C412yes—
78#131×C47D412yes—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47D411yescharacteristic
82C22×C8×C47—21no—
83C22×C8×C47C2311yescharacteristic
84C2×C4⋊C4×C47—21no—
85M32×C47—21no—
86M32×C47—21no—
87M32×C47—21no—
88M32×C47—21no—
89C2×C16×C47—21no—
90C2×C16×C47—21no—
91#108×C47—21no—
92#108×C47—21no—
93#106×C47—21no—
94#106×C47—21no—
95#103×C47—41no—
96#102×C47—41no—
97#41×C47—21no—
98#41×C47—21no—
99#41×C47—24no—
100#41×C47—24no—
101#41×C47—22no—
102#41×C47—22no—
103#41×C47—22no—
104#41×C47—22no—
105#41×C47—44no—
106#41×C47—44no—
107#41×C47—44no—
108#41×C47—44no—
109#41×C47—42no—
110#41×C47—42no—
111#41×C47—42no—
112#41×C47—42no—
113#41×C47—41no—
114#41×C47—41no—
115#41×C47—41no—
116#41×C47—41no—
117#41×C47C22⋊C412yes—
118#41×C47SD1612yes—
119C2×Q8×C47—24no—
120C2×Q8×C47—21no—
121C2×Q8×C47—21no—
122C2×Q8×C47—42no—
123C2×Q8×C47—42no—
124C2×Q8×C47D811yescharacteristic
125C2×D4×C47—21no—
126C2×D4×C47—24no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—44no—
130C2×D4×C47—44no—
131C2×D4×C47—42no—
132C2×D4×C47—44no—
133C2×D4×C47—41no—
134C2×D4×C47—41no—
135C2×D4×C47—42no—
136C2×D4×C47D811yescharacteristic
137C22×C4×C47—21no—
138C22×C4×C47—44no—
139C22×C4×C47—41no—
140C22×C4×C47—41no—
141C22×C4×C47—41no—
142C22×C4×C47C2×D411yescharacteristic
143Q16×C47—24no—
144Q16×C47—21no—
145Q16×C47—21no—
146Q16×C47C22⋊C412yes—
147Q16×C47C22⋊C412yes—
148SD16×C47—24no—
149SD16×C47—24no—
150SD16×C47—22no—
151SD16×C47—22no—
152SD16×C47—22no—
153SD16×C47—22no—
154D8×C47—24no—
155D8×C47—21no—
156D8×C47—21no—
157D8×C47C22⋊C412yes—
158D8×C47C22⋊C412yes—
159M16×C47—21no—
160M16×C47—22no—
161M16×C47—22no—
162M16×C47—41no—
163M16×C47—41no—
164M16×C47C22⋊C412yes—
165C2×C8×C47—21no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47—41no—
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C4⋊C4×C47—41no—
176C4⋊C4×C47—41no—
177C16×C47—41no—
178C16×C47—41no—
179C23×C47—21no—
180C23×C47—44no—
181C23×C47—41no—
182C23×C47—41no—
183C23×C47AGL(1,ℤ/8)11yescharacteristic
184Q8×C47—21no—
185Q8×C47—22no—
186Q8×C47—22no—
187Q8×C47—44no—
188Q8×C47—41no—
189Q8×C47—41no—
190Q8×C47#10212yes—
191D4×C47—22no—
192D4×C47—22no—
193D4×C47—22no—
194D4×C47—22no—
195D4×C47—21no—
196D4×C47—44no—
197D4×C47—44no—
198D4×C47—44no—
199D4×C47—42no—
200D4×C47—42no—
201D4×C47—42no—
202D4×C47—42no—
203D4×C47—41no—
204D4×C47—41no—
205D4×C47#10212yes—
206C2×C4×C47—21no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—44no—
210C2×C4×C47—44no—
211C2×C4×C47—44no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—81no—
219C2×C4×C47—161no—
220C2×C4×C47C2×C22⋊C411yescharacteristic
221C2×C4×C47#12011yescharacteristic
222C2×C4×C47#12011yescharacteristic
223C2×C4×C47C2×D811yescharacteristic
224C2×C4×C47C2×SD1611yescharacteristic
225C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
226C8×C47—22no—
227C8×C47—81no—
228C8×C47C2×C22⋊C411yescharacteristic
229C8×C47C2×C22⋊C411yescharacteristic
230C8×C47#12011yescharacteristic
231C8×C47#12011yescharacteristic
232#12752C4711yesmaximal, characteristic, direct product factor, Sylow
233C22×C47—22no—
234C22×C47—41no—
235C22×C47—42no—
236C22×C47—42no—
237C22×C47—81no—
238C22×C47—161no—
239C22×C47—161no—
240C22×C47—164no—
241C22×C47#41811yescharacteristic
242C22×C47#44711yescharacteristic
243C22×C47#45011yescharacteristic
244C4×C47—22no—
245C4×C47—42no—
246C4×C47—42no—
247C4×C47—161no—
248C4×C47#37911yescharacteristic
249C4×C47C2×#10211yescharacteristic
250C4×C47#44711yescharacteristic
251C4×C47#45011yescharacteristic
252#3584C2×C4711yescharacteristic
253#2148C2×C4711yescharacteristic, complemented
254C2×#360C2×C4711yescharacteristic, complemented
255C2×#360C2×C4711yescharacteristic, complemented
256#2143C2×C4711yescharacteristic, complemented
257#2117C2×C4711yescharacteristic, complemented
258#1815C2×C4711yescharacteristic, complemented
259C2×C47—21no—
260C2×C47—21no—
261C2×C47—21no—
262C2×C47—42no—
263C2×C47—82no—
264C2×C47—82no—
265C2×C47#178611yescharacteristic
266#585—21no—
267#578—21no—
268#578C4×C4712yescomplemented
269#577—22no—
270#577—22no—
271#576—21no—
272#576C4×C4712yescomplemented
273#575—22no—
274#575—21no—
275C2×#135—22no—
276C2×#135C22×C4711yescharacteristic
277C2×#135C22×C4711yescharacteristic
278C2×#131C22×C4711yescharacteristic
279C2×M32C22×C4711yescharacteristic, complemented
280C2×M32C22×C4711yescharacteristic, complemented
281C2×#108C22×C4711yescharacteristic, complemented
282C2×#106C22×C4711yescharacteristic, complemented
283#417—21no—
284#362—21no—
285#361—21no—
286#360—22no—
287#360—22no—
288#359—22no—
289#350—22no—
290#343—21no—
291C47#1275211yescharacteristic, direct product factor, Sylow
2922−1+4—22no—
2932−1+4—22no—
2942−1+4—41no—
295H(5,𝔽2)—22no—
296H(5,𝔽2)—22no—
297H(5,𝔽2)—42no—
298H(5,𝔽2)—41no—
299C2×#41—24no—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41—42no—
303C2×#41—42no—
304C2×#41D4×C4711yescharacteristic
305#137—22no—
306#137—24no—
307#137—24no—
308#137—22no—
309AGL(1,ℤ/8)—22no—
310AGL(1,ℤ/8)—24no—
311AGL(1,ℤ/8)—24no—
312AGL(1,ℤ/8)—22no—
313#135—24no—
314#135—24no—
315#135—22no—
316#135—22no—
317#135—21no—
318#135—21no—
319#135—21no—
320#135—21no—
321#135C2×C4×C4712yes—
322#135D4×C4712yes—
323#135D4×C4712yes—
324#135D4×C4712yes—
325C2×Q16—22no—
326C2×Q16C2×C4×C4711yescharacteristic
327C2×Q16D4×C4711yescharacteristic
328C2×SD16—24no—
329C2×SD16—21no—
330C2×SD16—21no—
331C2×D8—22no—
332C2×D8C2×C4×C4711yescharacteristic
333C2×D8D4×C4711yescharacteristic
334#131—21no—
335#131—21no—
336#131C2×C4×C4712yes—
337#131D4×C4712yes—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16D4×C4711yescharacteristic
341C22×C8—21no—
342C22×C8C23×C4711yescharacteristic
343C2×C4⋊C4—21no—
344M32—21no—
345M32—21no—
346M32—21no—
347M32—21no—
348C2×C16—21no—
349C2×C16—21no—
350#108—21no—
351#108—21no—
352#106—21no—
353#106—21no—
354#103—41no—
355#102—41no—
356#41—21no—
357#41—21no—
358#41—24no—
359#41—24no—
360#41—22no—
361#41—22no—
362#41—22no—
363#41—22no—
364#41—44no—
365#41—44no—
366#41—44no—
367#41—44no—
368#41—42no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—41no—
373#41—41no—
374#41—41no—
375#41—41no—
376#41C22⋊C4×C4712yes—
377#41SD16×C4712yes—
378C2×Q8—24no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—42no—
382C2×Q8—42no—
383C2×Q8D8×C4711yescharacteristic
384C2×D4—21no—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—42no—
391C2×D4—44no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—42no—
395C2×D4D8×C4711yescharacteristic
396C22×C4—21no—
397C22×C4—44no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C2×D4×C4711yescharacteristic
402Q16—24no—
403Q16—21no—
404Q16—21no—
405Q16C22⋊C4×C4712yes—
406Q16C22⋊C4×C4712yes—
407SD16—24no—
408SD16—24no—
409SD16—22no—
410SD16—22no—
411SD16—22no—
412SD16—22no—
413D8—24no—
414D8—21no—
415D8—21no—
416D8C22⋊C4×C4712yes—
417D8C22⋊C4×C4712yes—
418M16—21no—
419M16—22no—
420M16—22no—
421M16—41no—
422M16—41no—
423M16C22⋊C4×C4712yes—
424C2×C8—21no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—41no—
428C2×C8C22×C4×C4711yescharacteristic
429C2×C8C2×D4×C4711yescharacteristic
430C2×C8C2×D4×C4711yescharacteristic
431C2×C8C2×D4×C4711yescharacteristic
432C2×C8C2×D4×C4711yescharacteristic
433C2×C8C2×D4×C4711yescharacteristic
434C4⋊C4—41no—
435C4⋊C4—41no—
436C16—41no—
437C16—41no—
438C23—21no—
439C23—44no—
440C23—41no—
441C23—41no—
442C23AGL(1,ℤ/8)×C4711yescharacteristic
443Q8—21no—
444Q8—22no—
445Q8—22no—
446Q8—44no—
447Q8—41no—
448Q8—41no—
449Q8#102×C4712yes—
450D4—22no—
451D4—22no—
452D4—22no—
453D4—22no—
454D4—21no—
455D4—44no—
456D4—44no—
457D4—44no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—41no—
463D4—41no—
464D4#102×C4712yes—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—81no—
478C2×C4—161no—
479C2×C4C2×C22⋊C4×C4711yescharacteristic
480C2×C4#120×C4711yescharacteristic
481C2×C4#120×C4711yescharacteristic
482C2×C4C2×D8×C4711yescharacteristic
483C2×C4C2×SD16×C4711yescharacteristic
484C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
485C8—22no—
486C8—81no—
487C8C2×C22⋊C4×C4711yescharacteristic
488C8C2×C22⋊C4×C4711yescharacteristic
489C8#120×C4711yescharacteristic
490C8#120×C4711yescharacteristic
491C22—22no—
492C22—41no—
493C22—42no—
494C22—42no—
495C22—81no—
496C22—161no—
497C22—161no—
498C22—164no—
499C22C47×#41811yescharacteristic
500C22C47×#44711yescharacteristic
501C22C47×#45011yescharacteristic
502C4—22no—
503C4—42no—
504C4—42no—
505C4—161no—
506C4C47×#37911yescharacteristic
507C4C2×#102×C4711yescharacteristic
508C4C47×#44711yescharacteristic
509C4C47×#45011yescharacteristic
510C2—21no—
511C2—21no—
512C2—21no—
513C2—42no—
514C2—82no—
515C2—82no—
516C2C47×#178611yescharacteristic
subgroupG/H
center, socleC2×C47#1786
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
prime radicalC47×#3584C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ C2×#131×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2148C2semidirect
3. C2×C47×#360C2semidirect
4. C2×C47×#360C2semidirect
5. C47×#2143C2semidirect
6. C47×#2117C2semidirect
7. C47×#1815C2semidirect
10. C47×#578C4semidirect
14. C47×#576C4semidirect
21. C2×M32×C47C22semidirect
22. C2×M32×C47C22semidirect
23. C2×#108×C47C22semidirect
24. C2×#106×C47C22semidirect
232. #12752C47direct (N × H)
253. #2148C2×C47semidirect
254. C2×#360C2×C47semidirect
255. C2×#360C2×C47semidirect
256. #2143C2×C47semidirect
257. #2117C2×C47semidirect
258. #1815C2×C47semidirect
268. #578C4×C47semidirect
272. #576C4×C47semidirect
279. C2×M32C22×C47semidirect
280. C2×M32C22×C47semidirect
281. C2×#108C22×C47semidirect
282. C2×#106C22×C47semidirect
291. C47#12752direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35842
C47×#21482
C2×C47×#3602
C47×#21432
C47×#21172
C47×#18152
#1275247