Finite Group Databasebeta

← C47×#60317 #26100015

Subgroups — C47×#60317 #26100015

Order 12032.

1892 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3481C211yesmaximal, characteristic
2C47×#2993C214yesmaximal, complemented
3C47×#2991C212yesmaximal, complemented
4C47×#2979C211yesmaximal, characteristic, complemented
5C47×#2978C214yesmaximal, complemented
6C47×#2975C214yesmaximal, complemented
7C47×#2969C214yesmaximal, complemented
8C47×#2965C212yesmaximal, complemented
9D4×M16×C47C214yesmaximal, complemented
10C47×#2931C211yesmaximal, characteristic, complemented
11C47×#2930C214yesmaximal, complemented
12C2×#131×C47C2212yescomplemented
13C22×M16×C47C2214yescomplemented
14C47×#559C411yescharacteristic
15C47×#554C412yes—
16C47×#553C414yes—
17C47×#551C414yes—
18C47×#546C414yes—
19D42×C47C411yescharacteristic
20C47×#532C2211yescharacteristic
21C47×#529C2214yes—
22C47×#525C2214yes—
23C4×#41×C47C2212yes—
24C2×C4×D4×C47C2214yes—
25C47×#446C2212yescomplemented
26C47×#446C2212yescomplemented
27C8×Q8×C47C2214yescomplemented
28C47×#436C2212yes—
29C47×#436C2214yes—
30C47×#436C2212yes—
31C47×#436C2218yescomplemented
32C47×#436C2218yescomplemented
33C47×#436C2214yescomplemented
34C47×#436C2218yescomplemented
35C47×#436C2214yescomplemented
36C47×#435C2214yescomplemented
37C47×#435C2218yescomplemented
38C47×#435C2218yescomplemented
39C47×#435C2214yescomplemented
40C8×D4×C47C2214yescomplemented
41C8×D4×C47C2214yescomplemented
42C47×#433C2218yescomplemented
43C47×#431C2214yescomplemented
44C47×#431C2212yescomplemented
45C47×#431C2214yescomplemented
46C47×#424C2214yescomplemented
47C47×#423C2211yescharacteristic, complemented
48C47×#423C2214yescomplemented
49C47×#408C2214yescomplemented
50C47×#408C2212yescomplemented
51C47×#407C2214yescomplemented
52C47×#407C2218yescomplemented
53C47×#405C2214yescomplemented
54C4×M16×C47C2214yescomplemented
55C2×C4×C8×C47C2211yescharacteristic, complemented
56C2×#41×C47C2×C412yes—
57C2×#41×C47C2312yes—
58C22×D4×C47C2×C414yes—
59C23×C4×C47C2314yes—
60#131×C47—44no—
61C2×M16×C47—48no—
62C2×M16×C47C2314yes—
63C2×M16×C47C2318yes—
64C2×M16×C47C2314yes—
65C2×M16×C47C2312yes—
66C2×M16×C47C2314yes—
67C2×M16×C47C2314yes—
68C22×C8×C47C2314yes—
69C22×C8×C47C2311yescharacteristic
70C22×C8×C47C2314yes—
71C22×C8×C47C2311yescharacteristic
72C4⋊Q8×C47C2×C411yescharacteristic
73#127×C47C2×C411yescharacteristic
74#126×C47C2×C418yes—
75#125×C47C2×C414yes—
76#124×C47C2×C414yes—
77#124×C47C2×C412yes—
78#123×C47C2×C414yes—
79#123×C47C2×C414yes—
80#123×C47C2×C418yes—
81C22⋊Q8×C47C2×C418yes—
82C22⋊Q8×C47C2×C414yes—
83#121×C47C2×C418yes—
84#121×C47C2×C414yes—
85#121×C47C2×C414yes—
86#120×C47C2×C414yes—
87#120×C47C2×C414yes—
88C4×Q8×C47C2×C412yes—
89C4×Q8×C47C2312yes—
90C4×D4×C47C2×C414yes—
91C4×D4×C47C2×C418yes—
92C4×D4×C47C2×C414yes—
93C4×D4×C47C2×C412yes—
94C4×D4×C47C2×C414yes—
95C4×D4×C47C2312yes—
96C4×D4×C47C2318yes—
97C4×D4×C47C2314yes—
98C4×D4×C47C2314yes—
99#117×C47C2×C414yes—
100#117×C47C2×C412yes—
101#117×C47C2314yes—
102C2×C4⋊C4×C47C2×C414yes—
103C2×C22⋊C4×C47C2×C418yes—
104C2×C42×C47C2314yes—
105C2×C42×C47C2311yescharacteristic
106C4⋊C8×C47C2312yes—
107C4⋊C8×C47C2314yes—
108C4⋊C8×C47C2318yes—
109C4⋊C8×C47C2314yes—
110C4⋊C8×C47C2312yes—
111C4⋊C8×C47C2314yes—
112C22⋊C8×C47C2314yes—
113C22⋊C8×C47C2314yes—
114C22⋊C8×C47C2318yes—
115C22⋊C8×C47C2318yes—
116C22⋊C8×C47C2318yes—
117C22⋊C8×C47C2314yes—
118#97×C47C2314yes—
119#97×C47C2314yes—
120C4×C8×C47C2312yes—
121C4×C8×C47C2312yes—
122C4×C8×C47C2314yes—
123C4×C8×C47C2318yes—
124C24×C47C22×C414yes—
125#41×C47—42no—
126#41×C47—42no—
127#41×C47—44no—
128C2×Q8×C47C22×C412yes—
129C2×Q8×C47C22×C412yes—
130C2×D4×C47—48no—
131C2×D4×C47C22×C412yes—
132C2×D4×C47C22×C414yes—
133C2×D4×C47C22×C414yes—
134C2×D4×C47C22×C418yes—
135C2×D4×C47C22×C412yes—
136C2×D4×C47C22×C414yes—
137C22×C4×C47—44no—
138C22×C4×C47—44no—
139C22×C4×C47C22×C414yes—
140C22×C4×C47C22×C412yes—
141C22×C4×C47C22×C414yes—
142C22×C4×C47C22×C418yes—
143C22×C4×C47C22×C414yes—
144C22×C4×C47C2411yescharacteristic
145C22×C4×C47C2414yes—
146C22×C4×C47C2414yes—
147M16×C47—28no—
148M16×C47—48no—
149M16×C47—44no—
150M16×C47—44no—
151M16×C47—44no—
152M16×C47—42no—
153C2×C8×C47—28no—
154C2×C8×C47—22no—
155C2×C8×C47—41no—
156C2×C8×C47—44no—
157C2×C8×C47C2414yes—
158C2×C8×C47C2414yes—
159C2×C8×C47C2411yescharacteristic
160C2×C8×C47C2412yes—
161C2×C8×C47C2414yes—
162C2×C8×C47C2411yescharacteristic
163C4⋊C4×C47C22×C412yes—
164C4⋊C4×C47C22×C414yes—
165C4⋊C4×C47C22×C418yes—
166C4⋊C4×C47C22×C412yes—
167C4⋊C4×C47C22×C414yes—
168C4⋊C4×C47C22×C414yes—
169C4⋊C4×C47C22×C418yes—
170C22⋊C4×C47C22×C414yes—
171C22⋊C4×C47C22×C418yes—
172C22⋊C4×C47C22×C418yes—
173C22⋊C4×C47C22×C418yes—
174C22⋊C4×C47C22×C414yes—
175C22⋊C4×C47C22×C414yes—
176C22⋊C4×C47C22×C414yes—
177C22⋊C4×C47C22×C414yes—
178C42×C47C22×C411yescharacteristic
179C42×C47C22×C414yes—
180C42×C47C22×C414yes—
181C42×C47C22×C411yescharacteristic
182C42×C47C2412yes—
183C42×C47C2414yes—
184C23×C47—44no—
185C23×C47—48no—
186C23×C47C23×C414yes—
187C23×C47C23×C414yes—
188C23×C47C23×C411yescharacteristic
189Q8×C47—24no—
190Q8×C47—42no—
191D4×C47—24no—
192D4×C47—28no—
193D4×C47—48no—
194D4×C47—44no—
195D4×C47—42no—
196D4×C47—44no—
197C2×C4×C47—28no—
198C2×C4×C47—24no—
199C2×C4×C47—24no—
200C2×C4×C47—21no—
201C2×C4×C47—24no—
202C2×C4×C47—21no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—44no—
206C2×C4×C47—48no—
207C2×C4×C47—44no—
208C2×C4×C47C23×C412yes—
209C2×C4×C47C23×C414yes—
210C2×C4×C47C23×C411yescharacteristic
211C2×C4×C47C23×C414yes—
212C2×C4×C47C23×C414yes—
213C2×C4×C47C23×C414yes—
214C2×C4×C47C23×C412yes—
215C2×C4×C47C2511yescharacteristic
216C8×C47—24no—
217C8×C47—21no—
218C8×C47—24no—
219C8×C47—22no—
220C8×C47—24no—
221C8×C47H(5,𝔽2)12yes—
222#60317C4711yesmaximal, characteristic, direct product factor, Sylow
223C22×C47—24no—
224C22×C47—24no—
225C22×C47—21no—
226C22×C47—22no—
227C22×C47—24no—
228C22×C47—24no—
229C22×C47—28no—
230C22×C47—88no—
231C22×C47C24×C411yescharacteristic
232C4×C47—24no—
233C4×C47—24no—
234C4×C47—21no—
235C4×C47—22no—
236C4×C47—24no—
237C4×C47—24no—
238C4×C47#56814yes—
239C4×C47C2×H(5,𝔽2)11yescharacteristic
240C4×C47#58511yescharacteristic
241#3481C2×C4711yescharacteristic
242#2993C2×C4714yescomplemented
243#2991C2×C4712yescomplemented
244#2979C2×C4711yescharacteristic, complemented
245#2978C2×C4714yescomplemented
246#2975C2×C4714yescomplemented
247#2969C2×C4714yescomplemented
248#2965C2×C4712yescomplemented
249D4×M16C2×C4714yescomplemented
250#2931C2×C4711yescharacteristic, complemented
251#2930C2×C4714yescomplemented
252C2×C47—41no—
253C2×C47—44no—
254C2×C47—44no—
255C2×C47C4×H(5,𝔽2)11yescharacteristic
256C2×C47C2×#56812yes—
257C2×#131C22×C4712yescomplemented
258C22×M16C22×C4714yescomplemented
259#559C4×C4711yescharacteristic
260#554C4×C4712yes—
261#553C4×C4714yes—
262#551C4×C4714yes—
263#546C4×C4714yes—
264D42C4×C4711yescharacteristic
265#532C22×C4711yescharacteristic
266#529C22×C4714yes—
267#525C22×C4714yes—
268C4×#41C22×C4712yes—
269C2×C4×D4C22×C4714yes—
270#446C22×C4712yescomplemented
271#446C22×C4712yescomplemented
272C8×Q8C22×C4714yescomplemented
273#436C22×C4712yes—
274#436C22×C4714yes—
275#436C22×C4712yes—
276#436C22×C4718yescomplemented
277#436C22×C4718yescomplemented
278#436C22×C4714yescomplemented
279#436C22×C4718yescomplemented
280#436C22×C4714yescomplemented
281#435C22×C4714yescomplemented
282#435C22×C4718yescomplemented
283#435C22×C4718yescomplemented
284#435C22×C4714yescomplemented
285C8×D4C22×C4714yescomplemented
286C8×D4C22×C4714yescomplemented
287#433C22×C4718yescomplemented
288#431C22×C4714yescomplemented
289#431C22×C4712yescomplemented
290#431C22×C4714yescomplemented
291#424C22×C4714yescomplemented
292#423C22×C4711yescharacteristic, complemented
293#423C22×C4714yescomplemented
294#408C22×C4714yescomplemented
295#408C22×C4712yescomplemented
296#407C22×C4714yescomplemented
297#407C22×C4718yescomplemented
298#405C22×C4714yescomplemented
299C4×M16C22×C4714yescomplemented
300C2×C4×C8C22×C4711yescharacteristic, complemented
301C47#6031711yescharacteristic, direct product factor, Sylow
302C2×#41C2×C4×C4712yes—
303C2×#41C23×C4712yes—
304C22×D4C2×C4×C4714yes—
305C23×C4C23×C4714yes—
306#131—44no—
307C2×M16—48no—
308C2×M16C23×C4714yes—
309C2×M16C23×C4718yes—
310C2×M16C23×C4714yes—
311C2×M16C23×C4712yes—
312C2×M16C23×C4714yes—
313C2×M16C23×C4714yes—
314C22×C8C23×C4714yes—
315C22×C8C23×C4711yescharacteristic
316C22×C8C23×C4714yes—
317C22×C8C23×C4711yescharacteristic
318C4⋊Q8C2×C4×C4711yescharacteristic
319#127C2×C4×C4711yescharacteristic
320#126C2×C4×C4718yes—
321#125C2×C4×C4714yes—
322#124C2×C4×C4714yes—
323#124C2×C4×C4712yes—
324#123C2×C4×C4714yes—
325#123C2×C4×C4714yes—
326#123C2×C4×C4718yes—
327C22⋊Q8C2×C4×C4718yes—
328C22⋊Q8C2×C4×C4714yes—
329#121C2×C4×C4718yes—
330#121C2×C4×C4714yes—
331#121C2×C4×C4714yes—
332#120C2×C4×C4714yes—
333#120C2×C4×C4714yes—
334C4×Q8C2×C4×C4712yes—
335C4×Q8C23×C4712yes—
336C4×D4C2×C4×C4714yes—
337C4×D4C2×C4×C4718yes—
338C4×D4C2×C4×C4714yes—
339C4×D4C2×C4×C4712yes—
340C4×D4C2×C4×C4714yes—
341C4×D4C23×C4712yes—
342C4×D4C23×C4718yes—
343C4×D4C23×C4714yes—
344C4×D4C23×C4714yes—
345#117C2×C4×C4714yes—
346#117C2×C4×C4712yes—
347#117C23×C4714yes—
348C2×C4⋊C4C2×C4×C4714yes—
349C2×C22⋊C4C2×C4×C4718yes—
350C2×C42C23×C4714yes—
351C2×C42C23×C4711yescharacteristic
352C4⋊C8C23×C4712yes—
353C4⋊C8C23×C4714yes—
354C4⋊C8C23×C4718yes—
355C4⋊C8C23×C4714yes—
356C4⋊C8C23×C4712yes—
357C4⋊C8C23×C4714yes—
358C22⋊C8C23×C4714yes—
359C22⋊C8C23×C4714yes—
360C22⋊C8C23×C4718yes—
361C22⋊C8C23×C4718yes—
362C22⋊C8C23×C4718yes—
363C22⋊C8C23×C4714yes—
364#97C23×C4714yes—
365#97C23×C4714yes—
366C4×C8C23×C4712yes—
367C4×C8C23×C4712yes—
368C4×C8C23×C4714yes—
369C4×C8C23×C4718yes—
370C24C22×C4×C4714yes—
371#41—42no—
372#41—42no—
373#41—44no—
374C2×Q8C22×C4×C4712yes—
375C2×Q8C22×C4×C4712yes—
376C2×D4—48no—
377C2×D4C22×C4×C4712yes—
378C2×D4C22×C4×C4714yes—
379C2×D4C22×C4×C4714yes—
380C2×D4C22×C4×C4718yes—
381C2×D4C22×C4×C4712yes—
382C2×D4C22×C4×C4714yes—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4C22×C4×C4714yes—
386C22×C4C22×C4×C4712yes—
387C22×C4C22×C4×C4714yes—
388C22×C4C22×C4×C4718yes—
389C22×C4C22×C4×C4714yes—
390C22×C4C24×C4711yescharacteristic
391C22×C4C24×C4714yes—
392C22×C4C24×C4714yes—
393M16—28no—
394M16—48no—
395M16—44no—
396M16—44no—
397M16—44no—
398M16—42no—
399C2×C8—28no—
400C2×C8—22no—
401C2×C8—41no—
402C2×C8—44no—
403C2×C8C24×C4714yes—
404C2×C8C24×C4712yes—
405C2×C8C24×C4711yescharacteristic
406C2×C8C24×C4714yes—
407C2×C8C24×C4714yes—
408C2×C8C24×C4711yescharacteristic
409C4⋊C4C22×C4×C4712yes—
410C4⋊C4C22×C4×C4714yes—
411C4⋊C4C22×C4×C4718yes—
412C4⋊C4C22×C4×C4712yes—
413C4⋊C4C22×C4×C4714yes—
414C4⋊C4C22×C4×C4714yes—
415C4⋊C4C22×C4×C4718yes—
416C22⋊C4C22×C4×C4714yes—
417C22⋊C4C22×C4×C4718yes—
418C22⋊C4C22×C4×C4718yes—
419C22⋊C4C22×C4×C4718yes—
420C22⋊C4C22×C4×C4714yes—
421C22⋊C4C22×C4×C4714yes—
422C22⋊C4C22×C4×C4714yes—
423C22⋊C4C22×C4×C4714yes—
424C42C22×C4×C4711yescharacteristic
425C42C22×C4×C4714yes—
426C42C22×C4×C4714yes—
427C42C22×C4×C4711yescharacteristic
428C42C24×C4712yes—
429C42C24×C4714yes—
430C23—44no—
431C23—48no—
432C23C23×C4×C4714yes—
433C23C23×C4×C4714yes—
434C23C23×C4×C4711yescharacteristic
435Q8—24no—
436Q8—42no—
437D4—24no—
438D4—28no—
439D4—48no—
440D4—44no—
441D4—44no—
442D4—42no—
443C2×C4—28no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—44no—
452C2×C4—48no—
453C2×C4—44no—
454C2×C4C23×C4×C4712yes—
455C2×C4C23×C4×C4714yes—
456C2×C4C23×C4×C4711yescharacteristic
457C2×C4C23×C4×C4714yes—
458C2×C4C23×C4×C4714yes—
459C2×C4C23×C4×C4714yes—
460C2×C4C23×C4×C4712yes—
461C2×C4C25×C4711yescharacteristic
462C8—24no—
463C8—21no—
464C8—24no—
465C8—22no—
466C8—24no—
467C8H(5,𝔽2)×C4712yes—
468C22—22no—
469C22—24no—
470C22—24no—
471C22—28no—
472C22—24no—
473C22—24no—
474C22—21no—
475C22—88no—
476C22C24×C4×C4711yescharacteristic
477C4—22no—
478C4—24no—
479C4—24no—
480C4—24no—
481C4—24no—
482C4—21no—
483C4C47×#56814yes—
484C4C2×H(5,𝔽2)×C4711yescharacteristic
485C4C47×#58511yescharacteristic
486C2—44no—
487C2—44no—
488C2—41no—
489C2C4×H(5,𝔽2)×C4711yescharacteristic
490C2C2×C47×#56812yes—
subgroupG/H
centerC2×C4×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC22×C47C24×C4
prime radicalC47×#3481C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2993C2semidirect
3. C47×#2991C2semidirect
4. C47×#2979C2semidirect
5. C47×#2978C2semidirect
6. C47×#2975C2semidirect
7. C47×#2969C2semidirect
8. C47×#2965C2semidirect
9. D4×M16×C47C2semidirect
10. C47×#2931C2semidirect
11. C47×#2930C2semidirect
12. C2×#131×C47C22semidirect
13. C22×M16×C47C22semidirect
25. C47×#446C22semidirect
26. C47×#446C22semidirect
27. C8×Q8×C47C22semidirect
31. C47×#436C22semidirect
32. C47×#436C22semidirect
33. C47×#436C22semidirect
34. C47×#436C22semidirect
35. C47×#436C22semidirect
36. C47×#435C22semidirect
37. C47×#435C22semidirect
38. C47×#435C22semidirect
39. C47×#435C22semidirect
40. C8×D4×C47C22semidirect
41. C8×D4×C47C22semidirect
42. C47×#433C22semidirect
43. C47×#431C22semidirect
44. C47×#431C22semidirect
45. C47×#431C22semidirect
46. C47×#424C22semidirect
47. C47×#423C22semidirect
48. C47×#423C22semidirect
49. C47×#408C22semidirect
50. C47×#408C22semidirect
51. C47×#407C22semidirect
52. C47×#407C22semidirect
53. C47×#405C22semidirect
54. C4×M16×C47C22semidirect
55. C2×C4×C8×C47C22semidirect
222. #60317C47direct (N × H)
242. #2993C2×C47semidirect
243. #2991C2×C47semidirect
244. #2979C2×C47semidirect
245. #2978C2×C47semidirect
246. #2975C2×C47semidirect
247. #2969C2×C47semidirect
248. #2965C2×C47semidirect
249. D4×M16C2×C47semidirect
250. #2931C2×C47semidirect
251. #2930C2×C47semidirect
257. C2×#131C22×C47semidirect
258. C22×M16C22×C47semidirect
270. #446C22×C47semidirect
271. #446C22×C47semidirect
272. C8×Q8C22×C47semidirect
276. #436C22×C47semidirect
277. #436C22×C47semidirect
278. #436C22×C47semidirect
279. #436C22×C47semidirect
280. #436C22×C47semidirect
281. #435C22×C47semidirect
282. #435C22×C47semidirect
283. #435C22×C47semidirect
284. #435C22×C47semidirect
285. C8×D4C22×C47semidirect
286. C8×D4C22×C47semidirect
287. #433C22×C47semidirect
288. #431C22×C47semidirect
289. #431C22×C47semidirect
290. #431C22×C47semidirect
291. #424C22×C47semidirect
292. #423C22×C47semidirect
293. #423C22×C47semidirect
294. #408C22×C47semidirect
295. #408C22×C47semidirect
296. #407C22×C47semidirect
297. #407C22×C47semidirect
298. #405C22×C47semidirect
299. C4×M16C22×C47semidirect
300. C2×C4×C8C22×C47semidirect
301. C47#60317direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34812
C47×#29932
C47×#29912
C47×#29792
C47×#29782
C47×#29752
C47×#29692
C47×#29652
D4×M16×C472
C47×#29312
C47×#29302
#6031747