Finite Group Databasebeta

← C47×#33381 #26073079

Subgroups — C47×#33381 #26073079

Order 12032.

1176 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#576C211yesmaximal, characteristic
2C2×C47×#504C211yesmaximal, characteristic, complemented
3C47×#2913C211yesmaximal, characteristic, complemented
4C47×#2140C213yesmaximal, complemented
5C47×#2139C213yesmaximal, complemented
6C47×#2138C213yesmaximal, complemented
7C2×C47×#357C213yesmaximal, complemented
8C2×H(5,𝔽2)×C47—21no—
9C47×#576—24no—
10C47×#576C418yescomplemented
11C2×AGL(1,ℤ/8)×C47—23no—
12C2×#135×C47C2213yes—
13C22×D8×C47C2213yes—
14C2×#131×C47C2211yescharacteristic
15C47×#520—21no—
16C47×#504—24no—
17C2×M32×C47C2213yescomplemented
18C22×C16×C47C2213yescomplemented
19C47×#428—23no—
20C47×#427C2213yescomplemented
21C2×#107×C47C2213yescomplemented
22C47×#358C2211yescharacteristic, complemented
23C47×#358C2213yescomplemented
24C47×#357C2213yescomplemented
25C47×#357C2216yescomplemented
26C47×#357C2213yescomplemented
27H(5,𝔽2)×C47—28no—
28H(5,𝔽2)×C47—44no—
29C2×#41×C47—23no—
30C2×#41×C47—41no—
31C2×#41×C47D411yescharacteristic
32C22×D4×C47—23no—
33C22×D4×C47—43no—
34AGL(1,ℤ/8)×C47—224no—
35#135×C47—26no—
36#135×C47C2×C4112yescomplemented
37C2×Q16×C47C2311yescharacteristic
38C2×SD16×C47—23no—
39C2×D8×C47—23no—
40C2×D8×C47—26no—
41C2×D8×C47C2×C4112yescomplemented
42C2×D8×C47C2313yes—
43#131×C47C2×C414yes—
44#131×C47D414yes—
45C2×M16×C47D413yes—
46C22×C8×C47C2313yes—
47C4×Q8×C47—41no—
48C4×D4×C47—43no—
49#117×C47—23no—
50C2×C4⋊C4×C47—23no—
51M32×C47—26no—
52C2×C16×C47—26no—
53C2×C16×C47C2311yescharacteristic
54C2×C16×C47C2313yes—
55#107×C47—23no—
56#107×C47C2313yes—
57#107×C47C2311yescharacteristic
58#106×C47—23no—
59C24×C47—43no—
60#41×C47—212no—
61#41×C47—48no—
62#41×C47—46no—
63#41×C47C22⋊C414yes—
64#41×C47SD1614yes—
65C2×Q8×C47—21no—
66C2×Q8×C47D811yescharacteristic
67C2×D4×C47—212no—
68C2×D4×C47—23no—
69C2×D4×C47—43no—
70C2×D4×C47—424no—
71C2×D4×C47—43no—
72C2×D4×C47—46no—
73C2×D4×C47D813yes—
74C22×C4×C47—43no—
75C22×C4×C47—43no—
76C22×C4×C47C2×D413yes—
77Q16×C47—21no—
78Q16×C47C22×C412yes—
79SD16×C47—212no—
80D8×C47—212no—
81D8×C47—23no—
82D8×C47C22×C416yes—
83M16×C47C22⋊C4112yes—
84C2×C8×C47C22×C416yes—
85C2×C8×C47C2×D413yes—
86C2×C8×C47C2×D416yes—
87C2×C8×C47C2411yescharacteristic
88C4⋊C4×C47—21no—
89C4⋊C4×C47—23no—
90C4⋊C4×C47—43no—
91C22⋊C4×C47—43no—
92C42×C47—43no—
93C16×C47—21no—
94C16×C47—23no—
95C23×C47—43no—
96C23×C47—412no—
97C23×C47—163no—
98C23×C47—163no—
99C23×C47C2×D813yes—
100Q8×C47—22no—
101Q8×C47—41no—
102Q8×C47#10214yes—
103D4×C47—26no—
104D4×C47—412no—
105D4×C47—43no—
106D4×C47—412no—
107D4×C47#102112yes—
108C2×C4×C47—41no—
109C2×C4×C47—412no—
110C2×C4×C47—41no—
111C2×C4×C47—43no—
112C2×C4×C47—163no—
113C2×C4×C47C2×C22⋊C416yes—
114C2×C4×C47C2×D813yes—
115C2×C4×C47C2×SD1616yes—
116C2×C4×C47C22×D411yescharacteristic
117C8×C47C2×C22⋊C416yes—
118C8×C47C23×C411yescharacteristic
119C8×C47C22×D411yescharacteristic
120#33381C4711yesmaximal, characteristic, direct product factor, Sylow
121C22×C47—23no—
122C22×C47—23no—
123C22×C47—46no—
124C22×C47—83no—
125C22×C47—83no—
126C22×C47—1612no—
127C22×C47C2×#10216yes—
128C22×C47C22×D811yescharacteristic
129C4×C47—42no—
130C4×C47—83no—
131C4×C47—81no—
132C4×C47C2×#10216yes—
133C4×C47C22×C22⋊C411yescharacteristic
134C4×C47C22×SD1611yescharacteristic
135C2×#576C2×C4711yescharacteristic
136C2×#504C2×C4711yescharacteristic, complemented
137#2913C2×C4711yescharacteristic, complemented
138#2140C2×C4713yescomplemented
139#2139C2×C4713yescomplemented
140#2138C2×C4713yescomplemented
141C2×#357C2×C4713yescomplemented
142C2×C47—26no—
143C2×C47—86no—
144C2×C47C22×#10211yescharacteristic
145C2×C47#341511yescharacteristic
146C2×C47#341611yescharacteristic
147C2×H(5,𝔽2)—21no—
148#576—24no—
149#576C4×C4718yescomplemented
150C2×AGL(1,ℤ/8)—23no—
151C2×#135C22×C4713yes—
152C22×D8C22×C4713yes—
153C2×#131C22×C4711yescharacteristic
154#520—21no—
155#504—24no—
156C2×M32C22×C4713yescomplemented
157C22×C16C22×C4713yescomplemented
158#428—23no—
159#427C22×C4713yescomplemented
160C2×#107C22×C4713yescomplemented
161#358C22×C4711yescharacteristic, complemented
162#358C22×C4713yescomplemented
163#357C22×C4713yescomplemented
164#357C22×C4716yescomplemented
165#357C22×C4713yescomplemented
166C47#3338111yescharacteristic, direct product factor, Sylow
167H(5,𝔽2)—28no—
168H(5,𝔽2)—44no—
169C2×#41—23no—
170C2×#41—41no—
171C2×#41D4×C4711yescharacteristic
172C22×D4—23no—
173C22×D4—43no—
174AGL(1,ℤ/8)—224no—
175#135—26no—
176#135C2×C4×C47112yescomplemented
177C2×Q16C23×C4711yescharacteristic
178C2×SD16—23no—
179C2×D8—23no—
180C2×D8—26no—
181C2×D8C2×C4×C47112yescomplemented
182C2×D8C23×C4713yes—
183#131C2×C4×C4714yes—
184#131D4×C4714yes—
185C2×M16D4×C4713yes—
186C22×C8C23×C4713yes—
187C4×Q8—41no—
188C4×D4—43no—
189#117—23no—
190C2×C4⋊C4—23no—
191M32—26no—
192C2×C16—26no—
193C2×C16C23×C4711yescharacteristic
194C2×C16C23×C4713yes—
195#107—23no—
196#107C23×C4713yes—
197#107C23×C4711yescharacteristic
198#106—23no—
199C24—43no—
200#41—212no—
201#41—48no—
202#41—46no—
203#41C22⋊C4×C4714yes—
204#41SD16×C4714yes—
205C2×Q8—21no—
206C2×Q8D8×C4711yescharacteristic
207C2×D4—212no—
208C2×D4—23no—
209C2×D4—43no—
210C2×D4—424no—
211C2×D4—43no—
212C2×D4—46no—
213C2×D4D8×C4713yes—
214C22×C4—43no—
215C22×C4—43no—
216C22×C4C2×D4×C4713yes—
217Q16—21no—
218Q16C22×C4×C4712yes—
219SD16—212no—
220D8—212no—
221D8—23no—
222D8C22×C4×C4716yes—
223M16C22⋊C4×C47112yes—
224C2×C8C22×C4×C4716yes—
225C2×C8C2×D4×C4713yes—
226C2×C8C2×D4×C4716yes—
227C2×C8C24×C4711yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—23no—
230C4⋊C4—43no—
231C22⋊C4—43no—
232C42—43no—
233C16—21no—
234C16—23no—
235C23—43no—
236C23—412no—
237C23—163no—
238C23—163no—
239C23C2×D8×C4713yes—
240Q8—22no—
241Q8—41no—
242Q8#102×C4714yes—
243D4—26no—
244D4—412no—
245D4—43no—
246D4—412no—
247D4#102×C47112yes—
248C2×C4—41no—
249C2×C4—412no—
250C2×C4—41no—
251C2×C4—43no—
252C2×C4—163no—
253C2×C4C2×C22⋊C4×C4716yes—
254C2×C4C2×D8×C4713yes—
255C2×C4C2×SD16×C4716yes—
256C2×C4C22×D4×C4711yescharacteristic
257C8C2×C22⋊C4×C4716yes—
258C8C23×C4×C4711yescharacteristic
259C8C22×D4×C4711yescharacteristic
260C22—23no—
261C22—23no—
262C22—46no—
263C22—83no—
264C22—83no—
265C22—1612no—
266C22C2×#102×C4716yes—
267C22C22×D8×C4711yescharacteristic
268C4—42no—
269C4—83no—
270C4—81no—
271C4C2×#102×C4716yes—
272C4C22×C22⋊C4×C4711yescharacteristic
273C4C22×SD16×C4711yescharacteristic
274C2—26no—
275C2—86no—
276C2C22×#102×C4711yescharacteristic
277C2C47×#341511yescharacteristic
278C2C47×#341611yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutatorC8C23×C4×C47
Frattini, cosocleC2×C8C24×C47
prime radicalC2×C47×#576C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×#41×C47 ◁ C2×#131×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#504C2semidirect
3. C47×#2913C2semidirect
4. C47×#2140C2semidirect
5. C47×#2139C2semidirect
6. C47×#2138C2semidirect
7. C2×C47×#357C2semidirect
10. C47×#576C4semidirect
17. C2×M32×C47C22semidirect
18. C22×C16×C47C22semidirect
20. C47×#427C22semidirect
21. C2×#107×C47C22semidirect
22. C47×#358C22semidirect
23. C47×#358C22semidirect
24. C47×#357C22semidirect
25. C47×#357C22semidirect
26. C47×#357C22semidirect
36. #135×C47C2×C4semidirect
41. C2×D8×C47C2×C4semidirect
120. #33381C47direct (N × H)
136. C2×#504C2×C47semidirect
137. #2913C2×C47semidirect
138. #2140C2×C47semidirect
139. #2139C2×C47semidirect
140. #2138C2×C47semidirect
141. C2×#357C2×C47semidirect
149. #576C4×C47semidirect
156. C2×M32C22×C47semidirect
157. C22×C16C22×C47semidirect
159. #427C22×C47semidirect
160. C2×#107C22×C47semidirect
161. #358C22×C47semidirect
162. #358C22×C47semidirect
163. #357C22×C47semidirect
164. #357C22×C47semidirect
165. #357C22×C47semidirect
166. C47#33381direct (N × H)
176. #135C2×C4×C47semidirect
181. C2×D8C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5762
C2×C47×#5042
C47×#29132
C47×#21402
C47×#21392
C47×#21382
C2×C47×#3572
#3338147