Finite Group Databasebeta

← C47×#3282 #20240892

Subgroups — C47×#3282 #20240892

Order 6016.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#135×C47C211yesmaximal, characteristic, complemented
2C22×SD16×C47C211yesmaximal, characteristic, complemented
3C47×#548C211yesmaximal, characteristic, complemented
4C47×#546C211yesmaximal, characteristic, complemented
5C47×#495C211yesmaximal, characteristic, complemented
6C47×#465C211yesmaximal, characteristic, complemented
7C47×#465C211yesmaximal, characteristic, complemented
8C47×#464C211yesmaximal, characteristic, complemented
9C47×#463C211yesmaximal, characteristic, complemented
10C47×#452C211yesmaximal, characteristic, complemented
11C47×#451C211yesmaximal, characteristic, complemented
12C47×#449C211yesmaximal, characteristic, complemented
13C47×#447C211yesmaximal, characteristic, complemented
14C4×SD16×C47C211yesmaximal, characteristic, complemented
15C8×D4×C47C211yesmaximal, characteristic, complemented
16C2×#41×C47C2211yescharacteristic
17C2×#41×C47C2211yescharacteristic, complemented
18C22×Q8×C47C2211yescharacteristic
19C22×D4×C47C2211yescharacteristic
20#135×C47—24no—
21C2×Q16×C47C2211yescharacteristic, complemented
22C2×Q16×C47C2211yescharacteristic, complemented
23C2×SD16×C47—24no—
24C2×SD16×C47C2211yescharacteristic
25C2×SD16×C47C2211yescharacteristic
26C2×SD16×C47C2211yescharacteristic
27C2×SD16×C47C2211yescharacteristic
28C2×SD16×C47C2211yescharacteristic, complemented
29C2×D8×C47C2211yescharacteristic
30C2×D8×C47C2211yescharacteristic
31C22×C8×C47C2211yescharacteristic
32C22×C8×C47C2211yescharacteristic, complemented
33#124×C47—21no—
34#124×C47C2211yescharacteristic
35#124×C47C2211yescharacteristic, complemented
36#123×C47—21no—
37C22⋊Q8×C47—21no—
38C22⋊Q8×C47C2211yescharacteristic
39C22⋊Q8×C47C2211yescharacteristic, complemented
40#121×C47—21no—
41#121×C47—21no—
42#121×C47C2211yescharacteristic
43#121×C47C2211yescharacteristic
44#120×C47—21no—
45C4×Q8×C47C2211yescharacteristic, complemented
46C4×D4×C47—21no—
47C4×D4×C47C2211yescharacteristic
48C4×D4×C47C2211yescharacteristic
49C2×C22⋊C4×C47—21no—
50#106×C47C2211yescharacteristic, complemented
51C4⋊C8×C47C2211yescharacteristic, complemented
52#103×C47C2211yescharacteristic, complemented
53#103×C47C2211yescharacteristic, complemented
54#103×C47C2211yescharacteristic, complemented
55#102×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C22⋊C8×C47C2211yescharacteristic, complemented
60C4×C8×C47C2211yescharacteristic, complemented
61C24×C47—21no—
62#41×C47—22no—
63#41×C47—22no—
64#41×C47—41no—
65#41×C47—41no—
66C2×Q8×C47—21no—
67C2×Q8×C47—22no—
68C2×Q8×C47—41no—
69C2×Q8×C47C2311yescharacteristic
70C2×Q8×C47C2311yescharacteristic
71C2×Q8×C47C2311yescharacteristic
72C2×D4×C47—22no—
73C2×D4×C47—21no—
74C2×D4×C47—21no—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—41no—
79C2×D4×C47D411yescharacteristic
80C2×D4×C47C2311yescharacteristic
81C2×D4×C47C2311yescharacteristic
82C2×D4×C47C2311yescharacteristic
83C22×C4×C47—21no—
84C22×C4×C47—21no—
85C22×C4×C47—21no—
86C22×C4×C47—21no—
87C22×C4×C47C2311yescharacteristic
88C22×C4×C47C2311yescharacteristic
89Q16×C47—22no—
90Q16×C47—41no—
91SD16×C47—22no—
92SD16×C47—22no—
93SD16×C47—22no—
94SD16×C47—22no—
95SD16×C47D414yescomplemented
96D8×C47—22no—
97D8×C47—41no—
98C2×C8×C47—22no—
99C2×C8×C47—22no—
100C2×C8×C47C2311yescharacteristic
101C2×C8×C47C2311yescharacteristic
102C2×C8×C47C2311yescharacteristic
103C2×C8×C47C2311yescharacteristic
104C4⋊C4×C47—21no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47D411yescharacteristic
108C4⋊C4×C47C2311yescharacteristic
109C4⋊C4×C47C2311yescharacteristic
110C22⋊C4×C47—21no—
111C22⋊C4×C47—21no—
112C22⋊C4×C47—21no—
113C22⋊C4×C47—21no—
114C22⋊C4×C47—21no—
115C22⋊C4×C47—21no—
116C22⋊C4×C47—21no—
117C22⋊C4×C47—21no—
118C22⋊C4×C47—21no—
119C22⋊C4×C47D411yescharacteristic
120C22⋊C4×C47D411yescharacteristic
121C42×C47—21no—
122C42×C47C2311yescharacteristic
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—42no—
127C23×C47—42no—
128C23×C47—81no—
129C23×C47C2×D411yescharacteristic
130C23×C47C2×D411yescharacteristic
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135Q8×C47—21no—
136Q8×C47—42no—
137Q8×C47C2×D412yes—
138D4×C47—22no—
139D4×C47—21no—
140D4×C47—21no—
141D4×C47—21no—
142D4×C47—21no—
143D4×C47—21no—
144D4×C47—42no—
145D4×C47—42no—
146D4×C47—42no—
147D4×C47—42no—
148D4×C47—81no—
149D4×C47C2×D412yes—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—42no—
160C2×C4×C47—42no—
161C2×C4×C47—42no—
162C2×C4×C47—81no—
163C2×C4×C47C2×D411yescharacteristic
164C2×C4×C47C2×D411yescharacteristic
165C2×C4×C47C2×D411yescharacteristic
166C2×C4×C47C2×D411yescharacteristic
167C2×C4×C47C2411yescharacteristic
168C8×C47—21no—
169C8×C47—21no—
170C8×C47—21no—
171C8×C47C2×D412yes—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—22no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—84no—
187C22×C47#13512yescomplemented
188C22×C47C22×D411yescharacteristic
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—22no—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—41no—
195C4×C47—41no—
196C4×C47—41no—
197C4×C47—41no—
198C4×C47C22×D411yescharacteristic
199C4×C47H(5,𝔽2)11yescharacteristic
200#3282C4711yesmaximal, characteristic, direct product factor, Sylow
201C2×C47—22no—
202C2×C47—41no—
203C2×C47—42no—
204C2×C47—81no—
205C2×C47—81no—
206C2×C47D4211yescharacteristic
207C2×C47C2×#13511yescharacteristic
208C2×C47#57711yescharacteristic
209C2×#135C2×C4711yescharacteristic, complemented
210C22×SD16C2×C4711yescharacteristic, complemented
211#548C2×C4711yescharacteristic, complemented
212#546C2×C4711yescharacteristic, complemented
213#495C2×C4711yescharacteristic, complemented
214#465C2×C4711yescharacteristic, complemented
215#465C2×C4711yescharacteristic, complemented
216#464C2×C4711yescharacteristic, complemented
217#463C2×C4711yescharacteristic, complemented
218#452C2×C4711yescharacteristic, complemented
219#451C2×C4711yescharacteristic, complemented
220#449C2×C4711yescharacteristic, complemented
221#447C2×C4711yescharacteristic, complemented
222C4×SD16C2×C4711yescharacteristic, complemented
223C8×D4C2×C4711yescharacteristic, complemented
224C47#328211yescharacteristic, direct product factor, Sylow
225C2×#41C22×C4711yescharacteristic
226C2×#41C22×C4711yescharacteristic, complemented
227C22×Q8C22×C4711yescharacteristic
228C22×D4C22×C4711yescharacteristic
229#135—24no—
230C2×Q16C22×C4711yescharacteristic, complemented
231C2×Q16C22×C4711yescharacteristic, complemented
232C2×SD16—24no—
233C2×SD16C22×C4711yescharacteristic
234C2×SD16C22×C4711yescharacteristic
235C2×SD16C22×C4711yescharacteristic
236C2×SD16C22×C4711yescharacteristic
237C2×SD16C22×C4711yescharacteristic, complemented
238C2×D8C22×C4711yescharacteristic
239C2×D8C22×C4711yescharacteristic
240C22×C8C22×C4711yescharacteristic
241C22×C8C22×C4711yescharacteristic, complemented
242#124—21no—
243#124C22×C4711yescharacteristic
244#124C22×C4711yescharacteristic, complemented
245#123—21no—
246C22⋊Q8—21no—
247C22⋊Q8C22×C4711yescharacteristic
248C22⋊Q8C22×C4711yescharacteristic, complemented
249#121—21no—
250#121—21no—
251#121C22×C4711yescharacteristic
252#121C22×C4711yescharacteristic
253#120—21no—
254C4×Q8C22×C4711yescharacteristic, complemented
255C4×D4—21no—
256C4×D4C22×C4711yescharacteristic
257C4×D4C22×C4711yescharacteristic
258C2×C22⋊C4—21no—
259#106C22×C4711yescharacteristic, complemented
260C4⋊C8C22×C4711yescharacteristic, complemented
261#103C22×C4711yescharacteristic, complemented
262#103C22×C4711yescharacteristic, complemented
263#103C22×C4711yescharacteristic, complemented
264#102C22×C4711yescharacteristic
265#102C22×C4711yescharacteristic
266#102C22×C4711yescharacteristic, complemented
267C22⋊C8C22×C4711yescharacteristic
268C22⋊C8C22×C4711yescharacteristic, complemented
269C4×C8C22×C4711yescharacteristic, complemented
270C24—21no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C23×C4711yescharacteristic
279C2×Q8C23×C4711yescharacteristic
280C2×Q8C23×C4711yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—41no—
288C2×D4D4×C4711yescharacteristic
289C2×D4C23×C4711yescharacteristic
290C2×D4C23×C4711yescharacteristic
291C2×D4C23×C4711yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4C23×C4711yescharacteristic
297C22×C4C23×C4711yescharacteristic
298Q16—22no—
299Q16—41no—
300SD16—22no—
301SD16—22no—
302SD16—22no—
303SD16—22no—
304SD16D4×C4714yescomplemented
305D8—22no—
306D8—41no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C23×C4711yescharacteristic
310C2×C8C23×C4711yescharacteristic
311C2×C8C23×C4711yescharacteristic
312C2×C8C23×C4711yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4D4×C4711yescharacteristic
317C4⋊C4C23×C4711yescharacteristic
318C4⋊C4C23×C4711yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4D4×C4711yescharacteristic
329C22⋊C4D4×C4711yescharacteristic
330C42—21no—
331C42C23×C4711yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23C2×D4×C4711yescharacteristic
339C23C2×D4×C4711yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—21no—
345Q8—42no—
346Q8C2×D4×C4712yes—
347D4—22no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—81no—
358D4C2×D4×C4712yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4C2×D4×C4711yescharacteristic
373C2×C4C2×D4×C4711yescharacteristic
374C2×C4C2×D4×C4711yescharacteristic
375C2×C4C2×D4×C4711yescharacteristic
376C2×C4C24×C4711yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8C2×D4×C4712yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—84no—
396C22#135×C4712yescomplemented
397C22C22×D4×C4711yescharacteristic
398C4—21no—
399C4—21no—
400C4—22no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4C22×D4×C4711yescharacteristic
408C4H(5,𝔽2)×C4711yescharacteristic
409C2—22no—
410C2—41no—
411C2—42no—
412C2—81no—
413C2—81no—
414C2D42×C4711yescharacteristic
415C2C2×#135×C4711yescharacteristic
416C2C47×#57711yescharacteristic
subgroupG/H
center, socleC22×C47C22×D4
commutator, Frattini, cosocleC2×C4C24×C47
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#135×C47C2semidirect
2. C22×SD16×C47C2semidirect
3. C47×#548C2semidirect
4. C47×#546C2semidirect
5. C47×#495C2semidirect
6. C47×#465C2semidirect
7. C47×#465C2semidirect
8. C47×#464C2semidirect
9. C47×#463C2semidirect
10. C47×#452C2semidirect
11. C47×#451C2semidirect
12. C47×#449C2semidirect
13. C47×#447C2semidirect
14. C4×SD16×C47C2semidirect
15. C8×D4×C47C2semidirect
17. C2×#41×C47C22semidirect
21. C2×Q16×C47C22semidirect
22. C2×Q16×C47C22semidirect
28. C2×SD16×C47C22semidirect
32. C22×C8×C47C22semidirect
35. #124×C47C22semidirect
39. C22⋊Q8×C47C22semidirect
45. C4×Q8×C47C22semidirect
50. #106×C47C22semidirect
51. C4⋊C8×C47C22semidirect
52. #103×C47C22semidirect
53. #103×C47C22semidirect
54. #103×C47C22semidirect
57. #102×C47C22semidirect
59. C22⋊C8×C47C22semidirect
60. C4×C8×C47C22semidirect
95. SD16×C47D4semidirect
187. C22×C47#135semidirect
200. #3282C47direct (N × H)
209. C2×#135C2×C47semidirect
210. C22×SD16C2×C47semidirect
211. #548C2×C47semidirect
212. #546C2×C47semidirect
213. #495C2×C47semidirect
214. #465C2×C47semidirect
215. #465C2×C47semidirect
216. #464C2×C47semidirect
217. #463C2×C47semidirect
218. #452C2×C47semidirect
219. #451C2×C47semidirect
220. #449C2×C47semidirect
221. #447C2×C47semidirect
222. C4×SD16C2×C47semidirect
223. C8×D4C2×C47semidirect
224. C47#3282direct (N × H)
226. C2×#41C22×C47semidirect
230. C2×Q16C22×C47semidirect
231. C2×Q16C22×C47semidirect
237. C2×SD16C22×C47semidirect
241. C22×C8C22×C47semidirect
244. #124C22×C47semidirect
248. C22⋊Q8C22×C47semidirect
254. C4×Q8C22×C47semidirect
259. #106C22×C47semidirect
260. C4⋊C8C22×C47semidirect
261. #103C22×C47semidirect
262. #103C22×C47semidirect
263. #103C22×C47semidirect
266. #102C22×C47semidirect
268. C22⋊C8C22×C47semidirect
269. C4×C8C22×C47semidirect
304. SD16D4×C47semidirect
396. C22#135×C47semidirect

Maximal subgroups

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

subgroupindex
C2×#135×C472
C22×SD16×C472
C47×#5482
C47×#5462
C47×#4952
C47×#4652
C47×#4642
C47×#4632
C47×#4522
C47×#4512
C47×#4492
C47×#4472
C4×SD16×C472
C8×D4×C472
#328247