Finite Group Databasebeta

← C47×#11980 #26051678

Subgroups — C47×#11980 #26051678

Order 12032.

314 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3168C211yesmaximal, characteristic
2C47×#2150C211yesmaximal, characteristic, complemented
3C47×#1566C211yesmaximal, characteristic, complemented
4C47×#1363C212yesmaximal, complemented
5C47×#1360C212yesmaximal, complemented
6C47×#529—21no—
7C2×M32×C47—21no—
8C47×#499C2211yescharacteristic
9C47×#495C2211yescharacteristic
10C47×#488—21no—
11C47×#467C411yescharacteristic
12C47×#466C411yescharacteristic
13C47×#465—21no—
14C4×Q16×C47C411yescharacteristic
15C4×SD16×C47—21no—
16C4×D8×C47C411yescharacteristic
17C47×#423—21no—
18C2×C4×C8×C47C2211yescharacteristic
19C47×C4⋊C16—21no—
20C47×C4⋊C16C2212yes—
21C47×#334—21no—
22C47×#334C2212yes—
23C2×Q16×C47C2×C411yescharacteristic
24C2×SD16×C47—21no—
25C2×D8×C47C2×C411yescharacteristic
26C2×M16×C47—41no—
27C22×C8×C47C2×C411yescharacteristic
28C22×C8×C47D411yescharacteristic
29#126×C47—41no—
30#125×C47—21no—
31#124×C47—21no—
32#123×C47—41no—
33C22⋊Q8×C47—21no—
34#121×C47—21no—
35C4×Q8×C47—21no—
36C4×D4×C47—21no—
37C4×D4×C47—41no—
38#117×C47—41no—
39C2×C42×C47D411yescharacteristic
40M32×C47—42no—
41C2×C16×C47—22no—
42#107×C47C2×C411yescharacteristic
43#107×C47C2×C411yescharacteristic
44#106×C47—21no—
45C4⋊C8×C47—22no—
46C4⋊C8×C47—41no—
47#103×C47—21no—
48#103×C47—21no—
49#102×C47—21no—
50#102×C47—21no—
51C4×C8×C47C2×C411yescharacteristic
52C4×C8×C47D411yescharacteristic
53C4×C8×C47D411yescharacteristic
54C4×C8×C47C2311yescharacteristic
55C2×Q8×C47—21no—
56C2×D4×C47—21no—
57C2×D4×C47—41no—
58C22×C4×C47—41no—
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47D811yescharacteristic
61C22×C4×C47SD1611yescharacteristic
62Q16×C47—41no—
63SD16×C47—41no—
64SD16×C47—41no—
65D8×C47—41no—
66M16×C47—82no—
67C2×C8×C47—21no—
68C2×C8×C47—21no—
69C2×C8×C47—41no—
70C2×C8×C47—42no—
71C2×C8×C47C22⋊C411yescharacteristic
72C2×C8×C47C22⋊C411yescharacteristic
73C2×C8×C47C22×C411yescharacteristic
74C2×C8×C47C2×D411yescharacteristic
75C4⋊C4×C47—21no—
76C4⋊C4×C47—21no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C22⋊C4×C47—41no—
82C22⋊C4×C47—41no—
83C22⋊C4×C47—41no—
84C22⋊C4×C47—41no—
85C22⋊C4×C47—41no—
86C42×C47—41no—
87C42×C47C22⋊C411yescharacteristic
88C42×C47D811yescharacteristic
89C42×C47SD1611yescharacteristic
90C42×C47C2×D411yescharacteristic
91C16×C47—42no—
92C23×C47—41no—
93C23×C47#10211yescharacteristic
94Q8×C47—41no—
95Q8×C47—41no—
96D4×C47—41no—
97D4×C47—41no—
98D4×C47—82no—
99C2×C4×C47—22no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—41no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—82no—
107C2×C4×C47#10211yescharacteristic
108C2×C4×C47#10211yescharacteristic
109C2×C4×C47#10211yescharacteristic
110C2×C4×C47C2×C22⋊C411yescharacteristic
111C2×C4×C47C2×D811yescharacteristic
112C2×C4×C47C2×SD1611yescharacteristic
113C8×C47—21no—
114C8×C47—21no—
115C8×C47—21no—
116C8×C47—82no—
117C8×C47AGL(1,ℤ/8)11yescharacteristic
118C8×C47#13711yescharacteristic
119#11980C4711yesmaximal, characteristic, direct product factor, Sylow
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—81no—
124C22×C47—81no—
125C22×C47—81no—
126C22×C47C2×#10211yescharacteristic
127C4×C47—21no—
128C4×C47—21no—
129C4×C47—21no—
130C4×C47—21no—
131C4×C47—81no—
132C4×C47—81no—
133C4×C47—81no—
134C4×C47#36012yes—
135C4×C47#41311yescharacteristic
136C4×C47#41711yescharacteristic
137#3168C2×C4711yescharacteristic
138#2150C2×C4711yescharacteristic, complemented
139#1566C2×C4711yescharacteristic, complemented
140#1363C2×C4712yescomplemented
141#1360C2×C4712yescomplemented
142C2×C47—41no—
143C2×C47—161no—
144C2×C47#154711yescharacteristic
145C2×C47#214311yescharacteristic
146C2×C47C2×#36011yescharacteristic
147#529—21no—
148C2×M32—21no—
149#499C22×C4711yescharacteristic
150#495C22×C4711yescharacteristic
151#488—21no—
152#467C4×C4711yescharacteristic
153#466C4×C4711yescharacteristic
154#465—21no—
155C4×Q16C4×C4711yescharacteristic
156C4×SD16—21no—
157C4×D8C4×C4711yescharacteristic
158#423—21no—
159C2×C4×C8C22×C4711yescharacteristic
160C4⋊C16—21no—
161C4⋊C16C22×C4712yes—
162#334—21no—
163#334C22×C4712yes—
164C47#1198011yescharacteristic, direct product factor, Sylow
165C2×Q16C2×C4×C4711yescharacteristic
166C2×SD16—21no—
167C2×D8C2×C4×C4711yescharacteristic
168C2×M16—41no—
169C22×C8C2×C4×C4711yescharacteristic
170C22×C8D4×C4711yescharacteristic
171#126—41no—
172#125—21no—
173#124—21no—
174#123—41no—
175C22⋊Q8—21no—
176#121—21no—
177C4×Q8—21no—
178C4×D4—21no—
179C4×D4—41no—
180#117—41no—
181C2×C42D4×C4711yescharacteristic
182M32—42no—
183C2×C16—22no—
184#107C2×C4×C4711yescharacteristic
185#107C2×C4×C4711yescharacteristic
186#106—21no—
187C4⋊C8—22no—
188C4⋊C8—41no—
189#103—21no—
190#103—21no—
191#102—21no—
192#102—21no—
193C4×C8C2×C4×C4711yescharacteristic
194C4×C8D4×C4711yescharacteristic
195C4×C8D4×C4711yescharacteristic
196C4×C8C23×C4711yescharacteristic
197C2×Q8—21no—
198C2×D4—21no—
199C2×D4—41no—
200C22×C4—41no—
201C22×C4C22⋊C4×C4711yescharacteristic
202C22×C4D8×C4711yescharacteristic
203C22×C4SD16×C4711yescharacteristic
204Q16—41no—
205SD16—41no—
206SD16—41no—
207D8—41no—
208M16—82no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—41no—
212C2×C8—42no—
213C2×C8C22⋊C4×C4711yescharacteristic
214C2×C8C22⋊C4×C4711yescharacteristic
215C2×C8C22×C4×C4711yescharacteristic
216C2×C8C2×D4×C4711yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C42—41no—
229C42C22⋊C4×C4711yescharacteristic
230C42D8×C4711yescharacteristic
231C42SD16×C4711yescharacteristic
232C42C2×D4×C4711yescharacteristic
233C16—42no—
234C23—41no—
235C23#102×C4711yescharacteristic
236Q8—41no—
237Q8—41no—
238D4—41no—
239D4—41no—
240D4—82no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—82no—
249C2×C4#102×C4711yescharacteristic
250C2×C4#102×C4711yescharacteristic
251C2×C4#102×C4711yescharacteristic
252C2×C4C2×C22⋊C4×C4711yescharacteristic
253C2×C4C2×D8×C4711yescharacteristic
254C2×C4C2×SD16×C4711yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—82no—
259C8AGL(1,ℤ/8)×C4711yescharacteristic
260C8#137×C4711yescharacteristic
261C22—21no—
262C22—21no—
263C22—21no—
264C22—81no—
265C22—81no—
266C22—81no—
267C22C2×#102×C4711yescharacteristic
268C4—21no—
269C4—21no—
270C4—21no—
271C4—21no—
272C4—81no—
273C4—81no—
274C4—81no—
275C4C47×#36012yes—
276C4C47×#41311yescharacteristic
277C4C47×#41711yescharacteristic
278C2—41no—
279C2—161no—
280C2C47×#154711yescharacteristic
281C2C47×#214311yescharacteristic
282C2C2×C47×#36011yescharacteristic
subgroupG/H
center, socleC22×C47C2×#102
commutatorC2×C8C22×C4×C47
Frattini, cosocleC4×C8C23×C47
prime radicalC47×#466C4
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ C2×C4×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2150C2semidirect
3. C47×#1566C2semidirect
4. C47×#1363C2semidirect
5. C47×#1360C2semidirect
119. #11980C47direct (N × H)
138. #2150C2×C47semidirect
139. #1566C2×C47semidirect
140. #1363C2×C47semidirect
141. #1360C2×C47semidirect
164. C47#11980direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31682
C47×#21502
C47×#15662
C47×#13632
C47×#13602
#1198047