Finite Group Databasebeta

← C47×#3480 #20241090

Subgroups — C47×#3480 #20241090

Order 6016.

1112 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#559C213yesmaximal, complemented
2C47×#557C211yesmaximal, characteristic, complemented
3C47×#556C213yesmaximal, complemented
4C47×#553C216yesmaximal, complemented
5C47×#550C211yesmaximal, characteristic, complemented
6C47×#548C212yesmaximal, complemented
7C47×#532C213yesmaximal, complemented
8C47×#529C216yesmaximal, complemented
9C4×#41×C47C213yesmaximal, complemented
10C4×#41×C47C212yesmaximal, complemented
11C2×C4×Q8×C47C211yesmaximal, characteristic, complemented
12C2×#41×C47C2213yes—
13C2×#41×C47C2212yes—
14C22×Q8×C47C2211yescharacteristic
15C4⋊Q8×C47C2213yes—
16#127×C47C2213yes—
17#126×C47C22112yes—
18#125×C47C2216yes—
19#124×C47C2216yes—
20#124×C47C2216yes—
21#123×C47C22112yes—
22C22⋊Q8×C47C2216yes—
23#121×C47C2216yes—
24#121×C47C2216yes—
25#121×C47C2216yes—
26C4×Q8×C47C2211yescharacteristic
27C4×Q8×C47C2213yes—
28C4×Q8×C47C2211yescharacteristic
29C4×Q8×C47C2213yes—
30C4×Q8×C47C2212yes—
31C4×Q8×C47C2213yes—
32C4×Q8×C47C2213yes—
33C4×D4×C47C2216yes—
34C4×D4×C47C2216yes—
35C4×D4×C47C2213yes—
36C4×D4×C47C2216yes—
37C4×D4×C47C2216yes—
38C4×D4×C47C2213yes—
39C4×D4×C47C2216yes—
40#117×C47C2211yescharacteristic
41#117×C47C2216yes—
42#117×C47C2216yes—
43C2×C4⋊C4×C47C2213yes—
44C2×C42×C47C2213yes—
45C2×C42×C47C2216yes—
46#41×C47—28no—
47#41×C47—212no—
48C2×Q8×C47—24no—
49C2×Q8×C47C2313yes—
50C2×Q8×C47C2313yes—
51C2×Q8×C47C2311yescharacteristic
52C2×D4×C47C2316yes—
53C2×D4×C47C2316yes—
54C2×D4×C47C2313yes—
55C2×D4×C47C2316yes—
56C22×C4×C47C2313yes—
57C22×C4×C47C2316yes—
58C22×C4×C47C2316yes—
59C22×C4×C47C2313yes—
60C22×C4×C47C2316yes—
61C22×C4×C47C2311yescharacteristic
62C4⋊C4×C47C2313yes—
63C4⋊C4×C47C2313yes—
64C4⋊C4×C47C2316yes—
65C4⋊C4×C47C2311yescharacteristic
66C4⋊C4×C47C2311yescharacteristic
67C4⋊C4×C47C2316yes—
68C4⋊C4×C47C2316yes—
69C4⋊C4×C47C2316yes—
70C4⋊C4×C47C2316yes—
71C22⋊C4×C47C2312yes—
72C22⋊C4×C47C2316yes—
73C22⋊C4×C47C23112yes—
74C22⋊C4×C47C2316yes—
75C22⋊C4×C47C23112yes—
76C42×C47C2316yes—
77C42×C47C2316yes—
78C42×C47C2313yes—
79C42×C47C2313yes—
80C42×C47C2312yes—
81C42×C47C2313yes—
82C42×C47C2313yes—
83C23×C47C2416yes—
84C23×C47C2411yescharacteristic
85Q8×C47—26no—
86Q8×C47—26no—
87Q8×C47#4114yescomplemented
88D4×C47—212no—
89D4×C47—212no—
90D4×C47—26no—
91D4×C47—46no—
92C2×C4×C47—26no—
93C2×C4×C47—212no—
94C2×C4×C47—212no—
95C2×C4×C47—46no—
96C2×C4×C47—43no—
97C2×C4×C47#4114yescomplemented
98C2×C4×C47C2412yes—
99C2×C4×C47C2413yes—
100C2×C4×C47C2412yes—
101C2×C4×C47C2413yes—
102C2×C4×C47C2416yes—
103C2×C4×C47C2413yes—
104C2×C4×C47C2411yescharacteristic
105C2×C4×C47C2413yes—
106C2×C4×C47C2411yescharacteristic
107C22×C47—21no—
108C22×C47—21no—
109C22×C47—26no—
110C22×C47—26no—
111C22×C47—26no—
112C22×C47C2×#4112yes—
113C22×C47C2511yescharacteristic
114C4×C47—22no—
115C4×C47—26no—
116C4×C47—23no—
117C4×C47—22no—
118C4×C47—23no—
119C4×C47—23no—
120C4×C47C2×#4112yes—
121C4×C47C2×#4116yes—
122C4×C47C2×#4112yes—
123#3480C4711yesmaximal, characteristic, direct product factor, Sylow
124C2×C47—22no—
125C2×C47—46no—
126C2×C47C22×#4111yescharacteristic
127C2×C47C22×#4111yescharacteristic
128C2×C47#58511yescharacteristic
129#559C2×C4713yescomplemented
130#557C2×C4711yescharacteristic, complemented
131#556C2×C4713yescomplemented
132#553C2×C4716yescomplemented
133#550C2×C4711yescharacteristic, complemented
134#548C2×C4712yescomplemented
135#532C2×C4713yescomplemented
136#529C2×C4716yescomplemented
137C4×#41C2×C4713yescomplemented
138C4×#41C2×C4712yescomplemented
139C2×C4×Q8C2×C4711yescharacteristic, complemented
140C47#348011yescharacteristic, direct product factor, Sylow
141C2×#41C22×C4713yes—
142C2×#41C22×C4712yes—
143C22×Q8C22×C4711yescharacteristic
144C4⋊Q8C22×C4713yes—
145#127C22×C4713yes—
146#126C22×C47112yes—
147#125C22×C4716yes—
148#124C22×C4716yes—
149#124C22×C4716yes—
150#123C22×C47112yes—
151C22⋊Q8C22×C4716yes—
152#121C22×C4716yes—
153#121C22×C4716yes—
154#121C22×C4716yes—
155C4×Q8C22×C4711yescharacteristic
156C4×Q8C22×C4713yes—
157C4×Q8C22×C4711yescharacteristic
158C4×Q8C22×C4713yes—
159C4×Q8C22×C4712yes—
160C4×Q8C22×C4713yes—
161C4×Q8C22×C4713yes—
162C4×D4C22×C4716yes—
163C4×D4C22×C4716yes—
164C4×D4C22×C4713yes—
165C4×D4C22×C4716yes—
166C4×D4C22×C4716yes—
167C4×D4C22×C4713yes—
168C4×D4C22×C4716yes—
169#117C22×C4711yescharacteristic
170#117C22×C4716yes—
171#117C22×C4716yes—
172C2×C4⋊C4C22×C4713yes—
173C2×C42C22×C4713yes—
174C2×C42C22×C4716yes—
175#41—28no—
176#41—212no—
177C2×Q8—24no—
178C2×Q8C23×C4713yes—
179C2×Q8C23×C4713yes—
180C2×Q8C23×C4711yescharacteristic
181C2×D4C23×C4716yes—
182C2×D4C23×C4716yes—
183C2×D4C23×C4713yes—
184C2×D4C23×C4716yes—
185C22×C4C23×C4713yes—
186C22×C4C23×C4716yes—
187C22×C4C23×C4716yes—
188C22×C4C23×C4713yes—
189C22×C4C23×C4716yes—
190C22×C4C23×C4711yescharacteristic
191C4⋊C4C23×C4713yes—
192C4⋊C4C23×C4713yes—
193C4⋊C4C23×C4716yes—
194C4⋊C4C23×C4711yescharacteristic
195C4⋊C4C23×C4711yescharacteristic
196C4⋊C4C23×C4716yes—
197C4⋊C4C23×C4716yes—
198C4⋊C4C23×C4716yes—
199C4⋊C4C23×C4716yes—
200C22⋊C4C23×C4712yes—
201C22⋊C4C23×C4716yes—
202C22⋊C4C23×C47112yes—
203C22⋊C4C23×C4716yes—
204C22⋊C4C23×C47112yes—
205C42C23×C4712yes—
206C42C23×C4713yes—
207C42C23×C4713yes—
208C42C23×C4716yes—
209C42C23×C4716yes—
210C42C23×C4713yes—
211C42C23×C4713yes—
212C23C24×C4716yes—
213C23C24×C4711yescharacteristic
214Q8—26no—
215Q8—26no—
216Q8#41×C4714yescomplemented
217D4—212no—
218D4—212no—
219D4—26no—
220D4—46no—
221C2×C4—26no—
222C2×C4—212no—
223C2×C4—212no—
224C2×C4—46no—
225C2×C4—43no—
226C2×C4#41×C4714yescomplemented
227C2×C4C24×C4712yes—
228C2×C4C24×C4712yes—
229C2×C4C24×C4713yes—
230C2×C4C24×C4713yes—
231C2×C4C24×C4716yes—
232C2×C4C24×C4713yes—
233C2×C4C24×C4711yescharacteristic
234C2×C4C24×C4713yes—
235C2×C4C24×C4711yescharacteristic
236C22—21no—
237C22—21no—
238C22—26no—
239C22—26no—
240C22—26no—
241C22C2×#41×C4712yes—
242C22C25×C4711yescharacteristic
243C4—22no—
244C4—26no—
245C4—23no—
246C4—22no—
247C4—23no—
248C4—23no—
249C4C2×#41×C4712yes—
250C4C2×#41×C4716yes—
251C4C2×#41×C4712yes—
252C2—22no—
253C2—46no—
254C2C22×#41×C4711yescharacteristic
255C2C22×#41×C4711yescharacteristic
256C2C47×#58511yescharacteristic
subgroupG/H
centerC2×C4×C47C24
commutator, Frattini, cosocleC22C25×C47
socleC22×C47C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#559C2semidirect
2. C47×#557C2semidirect
3. C47×#556C2semidirect
4. C47×#553C2semidirect
5. C47×#550C2semidirect
6. C47×#548C2semidirect
7. C47×#532C2semidirect
8. C47×#529C2semidirect
9. C4×#41×C47C2semidirect
10. C4×#41×C47C2semidirect
11. C2×C4×Q8×C47C2semidirect
87. Q8×C47#41semidirect
97. C2×C4×C47#41semidirect
123. #3480C47direct (N × H)
129. #559C2×C47semidirect
130. #557C2×C47semidirect
131. #556C2×C47semidirect
132. #553C2×C47semidirect
133. #550C2×C47semidirect
134. #548C2×C47semidirect
135. #532C2×C47semidirect
136. #529C2×C47semidirect
137. C4×#41C2×C47semidirect
138. C4×#41C2×C47semidirect
139. C2×C4×Q8C2×C47semidirect
140. C47#3480direct (N × H)
216. Q8#41×C47semidirect
226. C2×C4#41×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#5592
C47×#5572
C47×#5562
C47×#5532
C47×#5502
C47×#5482
C47×#5322
C47×#5292
C4×#41×C472
C2×C4×Q8×C472
#348047