Finite Group Databasebeta

← C47×#3244 #20240854

Subgroups — C47×#3244 #20240854

Order 6016.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#544C211yesmaximal, characteristic, complemented
2C47×#542C211yesmaximal, characteristic
3C47×#501C211yesmaximal, characteristic, complemented
4C47×#498C211yesmaximal, characteristic, complemented
5C47×#489C211yesmaximal, characteristic, complemented
6C47×#488C211yesmaximal, characteristic, complemented
7C47×#485C211yesmaximal, characteristic, complemented
8C47×#483C211yesmaximal, characteristic, complemented
9C47×#482C211yesmaximal, characteristic
10C47×#481C211yesmaximal, characteristic
11C47×#479C211yesmaximal, characteristic, complemented
12C47×#478C211yesmaximal, characteristic, complemented
13C47×#476C211yesmaximal, characteristic, complemented
14C47×#475C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16C4⋊Q8×C47—21no—
17C4⋊Q8×C47C2211yescharacteristic
18C4⋊Q8×C47C2211yescharacteristic
19C4⋊Q8×C47C2211yescharacteristic
20#126×C47—21no—
21#125×C47—21no—
22#125×C47C2211yescharacteristic
23#125×C47C2211yescharacteristic
24#124×C47—21no—
25#124×C47C2211yescharacteristic
26#123×C47—21no—
27C22⋊Q8×C47—21no—
28C22⋊Q8×C47—21no—
29C22⋊Q8×C47—21no—
30C22⋊Q8×C47C2211yescharacteristic
31#121×C47C2211yescharacteristic
32C4×Q8×C47C2211yescharacteristic
33C4×D4×C47C2211yescharacteristic
34#117×C47C2211yescharacteristic
35#117×C47C2211yescharacteristic
36C2×C4⋊C4×C47C2211yescharacteristic
37#107×C47C2211yescharacteristic
38#107×C47C2211yescharacteristic
39#106×C47C2211yescharacteristic
40#106×C47C2211yescharacteristic
41#106×C47C2211yescharacteristic
42#106×C47C2211yescharacteristic
43#106×C47C2211yescharacteristic
44#106×C47C2211yescharacteristic
45C4⋊C8×C47C2211yescharacteristic
46C4⋊C8×C47C2211yescharacteristic
47#103×C47C2211yescharacteristic
48#103×C47C2211yescharacteristic
49#103×C47C2211yescharacteristic
50#103×C47C2211yescharacteristic
51#102×C47C2211yescharacteristic
52#102×C47C2211yescharacteristic
53#102×C47C2211yescharacteristic
54#102×C47C2211yescharacteristic
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47—21no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47D411yescharacteristic
83C4⋊C4×C47D411yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C22⋊C4×C47—21no—
93C22⋊C4×C47—21no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊C4×C47D411yescharacteristic
97C22⋊C4×C47D411yescharacteristic
98C42×C47—21no—
99C42×C47—21no—
100C42×C47C2311yescharacteristic
101C42×C47C2311yescharacteristic
102C23×C47—21no—
103C23×C47C2×D411yescharacteristic
104Q8×C47—21no—
105Q8×C47—21no—
106Q8×C47—81no—
107Q8×C47—81no—
108Q8×C47—81no—
109D4×C47—21no—
110D4×C47—21no—
111D4×C47—81no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—81no—
122C2×C4×C47—81no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C8×C47—21no—
130C8×C47—21no—
131C8×C47—21no—
132C8×C47—21no—
133C22×C47—21no—
134C22×C47—21no—
135C22×C47—21no—
136C22×C47—41no—
137C22×C47—41no—
138C22×C47—41no—
139C22×C47C22×D411yescharacteristic
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—41no—
146C4×C47—41no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152C4×C472−1+411yescharacteristic
153C4×C472−1+411yescharacteristic
154#3244C4711yesmaximal, characteristic, direct product factor, Sylow
155C2×C47—41no—
156C2×C47—81no—
157C2×C47#53611yescharacteristic
158C2×C47#57711yescharacteristic
159C2×C47#57711yescharacteristic
160#544C2×C4711yescharacteristic, complemented
161#542C2×C4711yescharacteristic
162#501C2×C4711yescharacteristic, complemented
163#498C2×C4711yescharacteristic, complemented
164#489C2×C4711yescharacteristic, complemented
165#488C2×C4711yescharacteristic, complemented
166#485C2×C4711yescharacteristic, complemented
167#483C2×C4711yescharacteristic, complemented
168#482C2×C4711yescharacteristic
169#481C2×C4711yescharacteristic
170#479C2×C4711yescharacteristic, complemented
171#478C2×C4711yescharacteristic, complemented
172#476C2×C4711yescharacteristic, complemented
173#475C2×C4711yescharacteristic, complemented
174#433C2×C4711yescharacteristic, complemented
175C47#324411yescharacteristic, direct product factor, Sylow
176C4⋊Q8—21no—
177C4⋊Q8C22×C4711yescharacteristic
178C4⋊Q8C22×C4711yescharacteristic
179C4⋊Q8C22×C4711yescharacteristic
180#126—21no—
181#125—21no—
182#125C22×C4711yescharacteristic
183#125C22×C4711yescharacteristic
184#124—21no—
185#124C22×C4711yescharacteristic
186#123—21no—
187C22⋊Q8—21no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190C22⋊Q8C22×C4711yescharacteristic
191#121C22×C4711yescharacteristic
192C4×Q8C22×C4711yescharacteristic
193C4×D4C22×C4711yescharacteristic
194#117C22×C4711yescharacteristic
195#117C22×C4711yescharacteristic
196C2×C4⋊C4C22×C4711yescharacteristic
197#107C22×C4711yescharacteristic
198#107C22×C4711yescharacteristic
199#106C22×C4711yescharacteristic
200#106C22×C4711yescharacteristic
201#106C22×C4711yescharacteristic
202#106C22×C4711yescharacteristic
203#106C22×C4711yescharacteristic
204#106C22×C4711yescharacteristic
205C4⋊C8C22×C4711yescharacteristic
206C4⋊C8C22×C4711yescharacteristic
207#103C22×C4711yescharacteristic
208#103C22×C4711yescharacteristic
209#103C22×C4711yescharacteristic
210#103C22×C4711yescharacteristic
211#102C22×C4711yescharacteristic
212#102C22×C4711yescharacteristic
213#102C22×C4711yescharacteristic
214#102C22×C4711yescharacteristic
215C22⋊C8C22×C4711yescharacteristic
216C22⋊C8C22×C4711yescharacteristic
217#97C22×C4711yescharacteristic
218C4×C8C22×C4711yescharacteristic
219C2×Q8—21no—
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8C23×C4711yescharacteristic
223C2×D4—21no—
224C2×D4C23×C4711yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4C23×C4711yescharacteristic
228C2×C8C23×C4711yescharacteristic
229C2×C8C23×C4711yescharacteristic
230C2×C8C23×C4711yescharacteristic
231C2×C8C23×C4711yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4D4×C4711yescharacteristic
243C4⋊C4D4×C4711yescharacteristic
244C4⋊C4C23×C4711yescharacteristic
245C4⋊C4C23×C4711yescharacteristic
246C4⋊C4C23×C4711yescharacteristic
247C4⋊C4C23×C4711yescharacteristic
248C4⋊C4C23×C4711yescharacteristic
249C4⋊C4C23×C4711yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4D4×C4711yescharacteristic
257C22⋊C4D4×C4711yescharacteristic
258C42—21no—
259C42—21no—
260C42C23×C4711yescharacteristic
261C42C23×C4711yescharacteristic
262C23—21no—
263C23C2×D4×C4711yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—81no—
267Q8—81no—
268Q8—81no—
269D4—21no—
270D4—21no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4C2×D4×C4711yescharacteristic
284C2×C4C2×D4×C4711yescharacteristic
285C2×C4C2×D4×C4711yescharacteristic
286C2×C4C2×D4×C4711yescharacteristic
287C2×C4C2×D4×C4711yescharacteristic
288C2×C4C24×C4711yescharacteristic
289C8—21no—
290C8—21no—
291C8—21no—
292C8—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22C22×D4×C4711yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C42−1+4×C4711yescharacteristic
313C42−1+4×C4711yescharacteristic
314C2—41no—
315C2—81no—
316C2C47×#53611yescharacteristic
317C2C47×#57711yescharacteristic
318C2C47×#57711yescharacteristic
subgroupG/H
center, socleC22×C47C22×D4
commutator, Frattini, cosocleC2×C4C24×C47
prime radical#121×C47C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ #117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#544C2semidirect
3. C47×#501C2semidirect
4. C47×#498C2semidirect
5. C47×#489C2semidirect
6. C47×#488C2semidirect
7. C47×#485C2semidirect
8. C47×#483C2semidirect
11. C47×#479C2semidirect
12. C47×#478C2semidirect
13. C47×#476C2semidirect
14. C47×#475C2semidirect
15. C47×#433C2semidirect
154. #3244C47direct (N × H)
160. #544C2×C47semidirect
162. #501C2×C47semidirect
163. #498C2×C47semidirect
164. #489C2×C47semidirect
165. #488C2×C47semidirect
166. #485C2×C47semidirect
167. #483C2×C47semidirect
170. #479C2×C47semidirect
171. #478C2×C47semidirect
172. #476C2×C47semidirect
173. #475C2×C47semidirect
174. #433C2×C47semidirect
175. C47#3244direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#5442
C47×#5422
C47×#5012
C47×#4982
C47×#4892
C47×#4882
C47×#4852
C47×#4832
C47×#4822
C47×#4812
C47×#4792
C47×#4782
C47×#4762
C47×#4752
C47×#4332
#324447