Finite Group Databasebeta

← C47×#60325 #26100023

Subgroups — C47×#60325 #26100023

Order 12032.

2130 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×H(5,𝔽2)×C47C211yesmaximal, characteristic
2C47×#2991C212yesmaximal, complemented
3C47×#2989C213yesmaximal, complemented
4C47×#2988C211yesmaximal, characteristic, complemented
5C47×#2975C213yesmaximal, complemented
6C47×#2974C216yesmaximal, complemented
7C47×#2971C212yesmaximal, complemented
8C47×#2965C213yesmaximal, complemented
9C8×#41×C47C211yesmaximal, characteristic, complemented
10D4×M16×C47C216yesmaximal, complemented
11C2×C47×#436C213yesmaximal, complemented
12C2×H(5,𝔽2)×C47C411yescharacteristic
13C22×M16×C47C2216yescomplemented
14C47×#520C412yes—
15C47×#520C413yes—
16C47×#520C411yescharacteristic
17C47×#518C416yes—
18C47×#518C413yes—
19C4×#41×C47C2211yescharacteristic
20C4×#41×C47C2213yes—
21C4×#41×C47C2212yes—
22C2×C4×D4×C47C2213yes—
23C2×C4×D4×C47C2216yes—
24C47×#446C2211yescharacteristic, complemented
25C47×#446C2213yescomplemented
26C8×Q8×C47C2211yescharacteristic, complemented
27C8×Q8×C47C2211yescharacteristic, complemented
28C8×Q8×C47C2212yescomplemented
29C47×#436C2213yescomplemented
30C47×#436C2216yescomplemented
31C47×#436C2216yescomplemented
32C47×#436C2216yescomplemented
33C47×#436C2216yescomplemented
34C47×#436C2213yescomplemented
35C47×#436C2216yescomplemented
36C47×#435C2216yescomplemented
37C47×#435C22112yescomplemented
38C47×#435C2216yescomplemented
39C8×D4×C47C2213yescomplemented
40C8×D4×C47C2216yescomplemented
41C8×D4×C47C2213yescomplemented
42C47×#432C2216yescomplemented
43C47×#431C2213yescomplemented
44C47×#431C2216yescomplemented
45C47×#431C2213yescomplemented
46C47×#423C2216yescomplemented
47C2×C4⋊C8×C47C2213yescomplemented
48C47×#407C22112yescomplemented
49C2×C22⋊C8×C47C2216yescomplemented
50C4×M16×C47C2216yescomplemented
51C2×C4×C8×C47C2213yescomplemented
52H(5,𝔽2)×C47—28no—
53C2×#41×C47C2×C412yes—
54C2×#41×C47C2×C413yes—
55C2×#41×C47C2×C411yescharacteristic
56C22×D4×C47C2×C416yes—
57C22×D4×C47C2×C413yes—
58C23×C4×C47C2316yes—
59C2×M16×C47—412no—
60C2×M16×C47C2316yes—
61C2×M16×C47C23112yes—
62C2×M16×C47C2316yes—
63C22×C8×C47C2313yes—
64C22×C8×C47C2316yes—
65C22×C8×C47C2313yes—
66C4×Q8×C47C2×C413yes—
67C4×Q8×C47C2×C411yescharacteristic
68C4×Q8×C47C2×C412yes—
69C4×Q8×C47C2311yescharacteristic
70C4×Q8×C47C2311yescharacteristic
71C4×D4×C47C2×C416yes—
72C4×D4×C47C2×C416yes—
73C4×D4×C47C2×C4112yes—
74C4×D4×C47C2×C416yes—
75C4×D4×C47C2×C416yes—
76C4×D4×C47C2×C416yes—
77C4×D4×C47C2×C413yes—
78C4×D4×C47C2×C416yes—
79C4×D4×C47C2×C413yes—
80C4×D4×C47C2313yes—
81C4×D4×C47C2316yes—
82C4×D4×C47C2313yes—
83C4×D4×C47C2316yes—
84#117×C47C2×C416yes—
85#117×C47C2×C416yes—
86#117×C47C2×C413yes—
87#117×C47C2×C413yes—
88C2×C4⋊C4×C47C2×C416yes—
89C2×C4⋊C4×C47C2×C413yes—
90C2×C22⋊C4×C47C2×C416yes—
91C2×C22⋊C4×C47C2×C4112yes—
92C2×C42×C47C2313yes—
93C2×C42×C47C2316yes—
94C4⋊C8×C47C2313yes—
95C4⋊C8×C47C2316yes—
96C4⋊C8×C47C2313yes—
97C4⋊C8×C47C2316yes—
98C4⋊C8×C47C2312yes—
99C4⋊C8×C47C2311yescharacteristic
100C4⋊C8×C47C2313yes—
101C22⋊C8×C47C2316yes—
102C22⋊C8×C47C23112yes—
103C22⋊C8×C47C2316yes—
104C22⋊C8×C47C2316yes—
105C22⋊C8×C47C2316yes—
106#97×C47C2312yes—
107#97×C47C2316yes—
108C4×C8×C47C2311yescharacteristic
109C4×C8×C47C2313yes—
110C4×C8×C47C2313yes—
111C4×C8×C47C2313yes—
112C4×C8×C47C2316yes—
113C24×C47C22×C416yes—
114#41×C47—28no—
115#41×C47—212no—
116#41×C47M1618yescomplemented
117C2×Q8×C47C22×C411yescharacteristic
118C2×Q8×C47C22×C411yescharacteristic
119C2×D4×C47—224no—
120C2×D4×C47—212no—
121C2×D4×C47C22×C416yes—
122C2×D4×C47C22×C416yes—
123C2×D4×C47C22×C413yes—
124C2×D4×C47C22×C413yes—
125C22×C4×C47—46no—
126C22×C4×C47—46no—
127C22×C4×C47C22×C416yes—
128C22×C4×C47C22×C416yes—
129C22×C4×C47C22×C413yes—
130C22×C4×C47C22×C4112yes—
131C22×C4×C47C22×C416yes—
132C22×C4×C47C22×C413yes—
133C22×C4×C47C2413yes—
134C22×C4×C47C2416yes—
135M16×C47—212no—
136M16×C47—412no—
137M16×C47—46no—
138C2×C8×C47—26no—
139C2×C8×C47—43no—
140C2×C8×C47—46no—
141C2×C8×C47C2416yes—
142C2×C8×C47C2413yes—
143C2×C8×C47C2411yescharacteristic
144C2×C8×C47C2413yes—
145C2×C8×C47C2412yes—
146C2×C8×C47C2411yescharacteristic
147C4⋊C4×C47C22×C416yes—
148C4⋊C4×C47C22×C413yes—
149C4⋊C4×C47C22×C416yes—
150C4⋊C4×C47C22×C413yes—
151C4⋊C4×C47C22×C412yes—
152C4⋊C4×C47C22×C413yes—
153C4⋊C4×C47C22×C411yescharacteristic
154C22⋊C4×C47C22×C416yes—
155C22⋊C4×C47C22×C416yes—
156C22⋊C4×C47C22×C4112yes—
157C22⋊C4×C47C22×C416yes—
158C22⋊C4×C47C22×C416yes—
159C42×C47C22×C416yes—
160C42×C47C22×C413yes—
161C42×C47C22×C413yes—
162C42×C47C22×C416yes—
163C42×C47C2411yescharacteristic
164C42×C47C2413yes—
165C42×C47C2412yes—
166C23×C47—212no—
167C23×C47—46no—
168C23×C47—46no—
169C23×C47C23×C416yes—
170C23×C47C23×C413yes—
171Q8×C47—22no—
172Q8×C47C2×M1614yescomplemented
173D4×C47—212no—
174D4×C47—212no—
175D4×C47—26no—
176D4×C47C2×M16112yescomplemented
177C2×C4×C47—212no—
178C2×C4×C47—23no—
179C2×C4×C47—26no—
180C2×C4×C47—23no—
181C2×C4×C47—26no—
182C2×C4×C47—46no—
183C2×C4×C47—412no—
184C2×C4×C47—43no—
185C2×C4×C47—46no—
186C2×C4×C47C2×M16112yescomplemented
187C2×C4×C47C23×C413yes—
188C2×C4×C47C23×C411yescharacteristic
189C2×C4×C47C23×C412yes—
190C2×C4×C47C23×C412yes—
191C2×C4×C47C23×C413yes—
192C2×C4×C47C23×C416yes—
193C2×C4×C47C23×C413yes—
194C2×C4×C47C23×C411yescharacteristic
195C2×C4×C47C2511yescharacteristic
196C8×C47—23no—
197C8×C47—26no—
198C8×C47—21no—
199C8×C47—23no—
200C8×C47—22no—
201C8×C47H(5,𝔽2)12yescomplemented
202#60325C4711yesmaximal, characteristic, direct product factor, Sylow
203C22×C47—23no—
204C22×C47—23no—
205C22×C47—26no—
206C22×C47—26no—
207C22×C47—26no—
208C22×C47—812no—
209C22×C47C22×M1616yes—
210C22×C47C24×C411yescharacteristic
211C4×C47—23no—
212C4×C47—26no—
213C4×C47—22no—
214C4×C47—21no—
215C4×C47—23no—
216C4×C47—22no—
217C4×C47C22×M1616yes—
218C4×C47C22×M1612yes—
219C4×C47C2×H(5,𝔽2)11yescharacteristic
220C4×C47#58511yescharacteristic
221C4×H(5,𝔽2)C2×C4711yescharacteristic
222#2991C2×C4712yescomplemented
223#2989C2×C4713yescomplemented
224#2988C2×C4711yescharacteristic, complemented
225#2975C2×C4713yescomplemented
226#2974C2×C4716yescomplemented
227#2971C2×C4712yescomplemented
228#2965C2×C4713yescomplemented
229C8×#41C2×C4711yescharacteristic, complemented
230D4×M16C2×C4716yescomplemented
231C2×#436C2×C4713yescomplemented
232C2×C47—26no—
233C2×C47—46no—
234C2×C47C4×H(5,𝔽2)11yescharacteristic
235C2×C47C23×M1611yescharacteristic
236C2×C47#357311yescharacteristic
237C2×H(5,𝔽2)C4×C4711yescharacteristic
238C22×M16C22×C4716yescomplemented
239#520C4×C4712yes—
240#520C4×C4713yes—
241#520C4×C4711yescharacteristic
242#518C4×C4716yes—
243#518C4×C4713yes—
244C4×#41C22×C4711yescharacteristic
245C4×#41C22×C4713yes—
246C4×#41C22×C4712yes—
247C2×C4×D4C22×C4713yes—
248C2×C4×D4C22×C4716yes—
249#446C22×C4711yescharacteristic, complemented
250#446C22×C4713yescomplemented
251C8×Q8C22×C4711yescharacteristic, complemented
252C8×Q8C22×C4711yescharacteristic, complemented
253C8×Q8C22×C4712yescomplemented
254#436C22×C4713yescomplemented
255#436C22×C4716yescomplemented
256#436C22×C4716yescomplemented
257#436C22×C4716yescomplemented
258#436C22×C4716yescomplemented
259#436C22×C4713yescomplemented
260#436C22×C4716yescomplemented
261#435C22×C4716yescomplemented
262#435C22×C47112yescomplemented
263#435C22×C4716yescomplemented
264C8×D4C22×C4713yescomplemented
265C8×D4C22×C4716yescomplemented
266C8×D4C22×C4713yescomplemented
267#432C22×C4716yescomplemented
268#431C22×C4713yescomplemented
269#431C22×C4716yescomplemented
270#431C22×C4713yescomplemented
271#423C22×C4716yescomplemented
272C2×C4⋊C8C22×C4713yescomplemented
273#407C22×C47112yescomplemented
274C2×C22⋊C8C22×C4716yescomplemented
275C4×M16C22×C4716yescomplemented
276C2×C4×C8C22×C4713yescomplemented
277C47#6032511yescharacteristic, direct product factor, Sylow
278H(5,𝔽2)—28no—
279C2×#41C2×C4×C4712yes—
280C2×#41C2×C4×C4713yes—
281C2×#41C2×C4×C4711yescharacteristic
282C22×D4C2×C4×C4716yes—
283C22×D4C2×C4×C4713yes—
284C23×C4C23×C4716yes—
285C2×M16—412no—
286C2×M16C23×C4716yes—
287C2×M16C23×C47112yes—
288C2×M16C23×C4716yes—
289C22×C8C23×C4713yes—
290C22×C8C23×C4716yes—
291C22×C8C23×C4713yes—
292C4×Q8C2×C4×C4713yes—
293C4×Q8C2×C4×C4711yescharacteristic
294C4×Q8C2×C4×C4712yes—
295C4×Q8C23×C4711yescharacteristic
296C4×Q8C23×C4711yescharacteristic
297C4×D4C2×C4×C4716yes—
298C4×D4C2×C4×C4716yes—
299C4×D4C2×C4×C47112yes—
300C4×D4C2×C4×C4716yes—
301C4×D4C2×C4×C4716yes—
302C4×D4C2×C4×C4716yes—
303C4×D4C2×C4×C4713yes—
304C4×D4C2×C4×C4716yes—
305C4×D4C2×C4×C4713yes—
306C4×D4C23×C4713yes—
307C4×D4C23×C4716yes—
308C4×D4C23×C4713yes—
309C4×D4C23×C4716yes—
310#117C2×C4×C4716yes—
311#117C2×C4×C4716yes—
312#117C2×C4×C4713yes—
313#117C2×C4×C4713yes—
314C2×C4⋊C4C2×C4×C4716yes—
315C2×C4⋊C4C2×C4×C4713yes—
316C2×C22⋊C4C2×C4×C4716yes—
317C2×C22⋊C4C2×C4×C47112yes—
318C2×C42C23×C4713yes—
319C2×C42C23×C4716yes—
320C4⋊C8C23×C4713yes—
321C4⋊C8C23×C4716yes—
322C4⋊C8C23×C4713yes—
323C4⋊C8C23×C4716yes—
324C4⋊C8C23×C4712yes—
325C4⋊C8C23×C4711yescharacteristic
326C4⋊C8C23×C4713yes—
327C22⋊C8C23×C4716yes—
328C22⋊C8C23×C47112yes—
329C22⋊C8C23×C4716yes—
330C22⋊C8C23×C4716yes—
331C22⋊C8C23×C4716yes—
332#97C23×C4712yes—
333#97C23×C4716yes—
334C4×C8C23×C4711yescharacteristic
335C4×C8C23×C4713yes—
336C4×C8C23×C4713yes—
337C4×C8C23×C4713yes—
338C4×C8C23×C4716yes—
339C24C22×C4×C4716yes—
340#41—28no—
341#41—212no—
342#41M16×C4718yescomplemented
343C2×Q8C22×C4×C4711yescharacteristic
344C2×Q8C22×C4×C4711yescharacteristic
345C2×D4—224no—
346C2×D4—212no—
347C2×D4C22×C4×C4716yes—
348C2×D4C22×C4×C4716yes—
349C2×D4C22×C4×C4713yes—
350C2×D4C22×C4×C4713yes—
351C22×C4—46no—
352C22×C4—46no—
353C22×C4C22×C4×C4716yes—
354C22×C4C22×C4×C4716yes—
355C22×C4C22×C4×C4713yes—
356C22×C4C22×C4×C47112yes—
357C22×C4C22×C4×C4716yes—
358C22×C4C22×C4×C4713yes—
359C22×C4C24×C4713yes—
360C22×C4C24×C4716yes—
361M16—212no—
362M16—412no—
363M16—46no—
364C2×C8—26no—
365C2×C8—43no—
366C2×C8—46no—
367C2×C8C24×C4711yescharacteristic
368C2×C8C24×C4712yes—
369C2×C8C24×C4713yes—
370C2×C8C24×C4713yes—
371C2×C8C24×C4716yes—
372C2×C8C24×C4711yescharacteristic
373C4⋊C4C22×C4×C4716yes—
374C4⋊C4C22×C4×C4713yes—
375C4⋊C4C22×C4×C4716yes—
376C4⋊C4C22×C4×C4713yes—
377C4⋊C4C22×C4×C4712yes—
378C4⋊C4C22×C4×C4713yes—
379C4⋊C4C22×C4×C4711yescharacteristic
380C22⋊C4C22×C4×C4716yes—
381C22⋊C4C22×C4×C4716yes—
382C22⋊C4C22×C4×C47112yes—
383C22⋊C4C22×C4×C4716yes—
384C22⋊C4C22×C4×C4716yes—
385C42C22×C4×C4716yes—
386C42C22×C4×C4713yes—
387C42C22×C4×C4713yes—
388C42C22×C4×C4716yes—
389C42C24×C4711yescharacteristic
390C42C24×C4713yes—
391C42C24×C4712yes—
392C23—212no—
393C23—46no—
394C23—46no—
395C23C23×C4×C4716yes—
396C23C23×C4×C4713yes—
397Q8—22no—
398Q8C2×M16×C4714yescomplemented
399D4—212no—
400D4—212no—
401D4—26no—
402D4C2×M16×C47112yescomplemented
403C2×C4—212no—
404C2×C4—23no—
405C2×C4—26no—
406C2×C4—23no—
407C2×C4—26no—
408C2×C4—46no—
409C2×C4—412no—
410C2×C4—43no—
411C2×C4—46no—
412C2×C4C2×M16×C47112yescomplemented
413C2×C4C23×C4×C4713yes—
414C2×C4C23×C4×C4711yescharacteristic
415C2×C4C23×C4×C4712yes—
416C2×C4C23×C4×C4712yes—
417C2×C4C23×C4×C4713yes—
418C2×C4C23×C4×C4716yes—
419C2×C4C23×C4×C4713yes—
420C2×C4C23×C4×C4711yescharacteristic
421C2×C4C25×C4711yescharacteristic
422C8—23no—
423C8—26no—
424C8—21no—
425C8—23no—
426C8—22no—
427C8H(5,𝔽2)×C4712yescomplemented
428C22—23no—
429C22—23no—
430C22—26no—
431C22—26no—
432C22—26no—
433C22—812no—
434C22C22×M16×C4716yes—
435C22C24×C4×C4711yescharacteristic
436C4—22no—
437C4—21no—
438C4—23no—
439C4—22no—
440C4—23no—
441C4—26no—
442C4C22×M16×C4716yes—
443C4C22×M16×C4712yes—
444C4C2×H(5,𝔽2)×C4711yescharacteristic
445C4C47×#58511yescharacteristic
446C2—26no—
447C2—46no—
448C2C4×H(5,𝔽2)×C4711yescharacteristic
449C2C23×M16×C4711yescharacteristic
450C2C47×#357311yescharacteristic
subgroupG/H
centerC2×C4×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC22×C47C24×C4
prime radicalC2×H(5,𝔽2)×C47C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2991C2semidirect
3. C47×#2989C2semidirect
4. C47×#2988C2semidirect
5. C47×#2975C2semidirect
6. C47×#2974C2semidirect
7. C47×#2971C2semidirect
8. C47×#2965C2semidirect
9. C8×#41×C47C2semidirect
10. D4×M16×C47C2semidirect
11. C2×C47×#436C2semidirect
13. C22×M16×C47C22semidirect
24. C47×#446C22semidirect
25. C47×#446C22semidirect
26. C8×Q8×C47C22semidirect
27. C8×Q8×C47C22semidirect
28. C8×Q8×C47C22semidirect
29. C47×#436C22semidirect
30. C47×#436C22semidirect
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. C8×D4×C47C22semidirect
40. C8×D4×C47C22semidirect
41. C8×D4×C47C22semidirect
42. C47×#432C22semidirect
43. C47×#431C22semidirect
44. C47×#431C22semidirect
45. C47×#431C22semidirect
46. C47×#423C22semidirect
47. C2×C4⋊C8×C47C22semidirect
48. C47×#407C22semidirect
49. C2×C22⋊C8×C47C22semidirect
50. C4×M16×C47C22semidirect
51. C2×C4×C8×C47C22semidirect
116. #41×C47M16semidirect
172. Q8×C47C2×M16semidirect
176. D4×C47C2×M16semidirect
186. C2×C4×C47C2×M16semidirect
201. C8×C47H(5,𝔽2)semidirect
202. #60325C47direct (N × H)
222. #2991C2×C47semidirect
223. #2989C2×C47semidirect
224. #2988C2×C47semidirect
225. #2975C2×C47semidirect
226. #2974C2×C47semidirect
227. #2971C2×C47semidirect
228. #2965C2×C47semidirect
229. C8×#41C2×C47semidirect
230. D4×M16C2×C47semidirect
231. C2×#436C2×C47semidirect
238. C22×M16C22×C47semidirect
249. #446C22×C47semidirect
250. #446C22×C47semidirect
251. C8×Q8C22×C47semidirect
252. C8×Q8C22×C47semidirect
253. C8×Q8C22×C47semidirect
254. #436C22×C47semidirect
255. #436C22×C47semidirect
256. #436C22×C47semidirect
257. #436C22×C47semidirect
258. #436C22×C47semidirect
259. #436C22×C47semidirect
260. #436C22×C47semidirect
261. #435C22×C47semidirect
262. #435C22×C47semidirect
263. #435C22×C47semidirect
264. C8×D4C22×C47semidirect
265. C8×D4C22×C47semidirect
266. C8×D4C22×C47semidirect
267. #432C22×C47semidirect
268. #431C22×C47semidirect
269. #431C22×C47semidirect
270. #431C22×C47semidirect
271. #423C22×C47semidirect
272. C2×C4⋊C8C22×C47semidirect
273. #407C22×C47semidirect
274. C2×C22⋊C8C22×C47semidirect
275. C4×M16C22×C47semidirect
276. C2×C4×C8C22×C47semidirect
277. C47#60325direct (N × H)
342. #41M16×C47semidirect
398. Q8C2×M16×C47semidirect
402. D4C2×M16×C47semidirect
412. C2×C4C2×M16×C47semidirect
427. C8H(5,𝔽2)×C47semidirect

Maximal subgroups

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

subgroupindex
C4×H(5,𝔽2)×C472
C47×#29912
C47×#29892
C47×#29882
C47×#29752
C47×#29742
C47×#29712
C47×#29652
C8×#41×C472
D4×M16×C472
C2×C47×#4362
#6032547