Finite Group Databasebeta

← C2×C47×#1776 #26060148

Subgroups — C2×C47×#1776 #26060148

Order 12032.

1318 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#107×C47C211yesmaximal, characteristic
2C22×#106×C47C211yesmaximal, characteristic
3C22×#97×C47C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C47C212yesmaximal
5C47×#1776C218yesmaximal, direct product factor
6C2×C47×#340C212yesmaximal
7C23×C8×C47C2211yescharacteristic
8C23×C8×C47C2211yescharacteristic
9C22×C4⋊C4×C47C2212yes—
10C22×C4⋊C4×C47C2212yes—
11C22×C42×C47—22no—
12C22×C42×C47C2211yescharacteristic
13C2×#107×C47C418yescomplemented
14C2×#107×C47C2214yes—
15C2×#106×C47C418yescomplemented
16C2×#106×C47C2214yes—
17C2×#97×C47C418yescomplemented
18C2×#97×C47C2214yes—
19C4×C4⋊C4×C47—24no—
20C4×C4⋊C4×C47C2218yes—
21C2×#95×C47—22no—
22C47×#340C2218yes—
23C23×C4×C47—22no—
24C23×C4×C47—22no—
25C23×C4×C47D412yes—
26C23×C4×C47C2311yescharacteristic
27C22×C8×C47—22no—
28C22×C8×C47—22no—
29C22×C8×C47C2×C414yes—
30C22×C8×C47C2×C414yes—
31C22×C8×C47C2×C414yes—
32C22×C8×C47C2×C414yes—
33C22×C8×C47C2312yes—
34C22×C8×C47C2312yes—
35C2×C4⋊C4×C47—22no—
36C2×C4⋊C4×C47—22no—
37C2×C4⋊C4×C47—24no—
38C2×C4⋊C4×C47—24no—
39C2×C4⋊C4×C47C2×C418yes—
40C2×C4⋊C4×C47C2×C418yes—
41C2×C4⋊C4×C47C2314yes—
42C2×C4⋊C4×C47C2314yes—
43C2×C42×C47—28no—
44C2×C42×C47—48no—
45C2×C42×C47C2×C414yes—
46C2×C42×C47D412yes—
47C2×C42×C47Q814yes—
48C2×C42×C47C2312yes—
49#107×C47C2×C4116yescomplemented
50#106×C47C2×C4116yescomplemented
51#97×C47C2×C4116yescomplemented
52#95×C47—28no—
53C24×C47C2×D411yescharacteristic
54C22×C4×C47—24no—
55C22×C4×C47—24no—
56C22×C4×C47—28no—
57C22×C4×C47—28no—
58C22×C4×C47—24no—
59C22×C4×C47—24no—
60C22×C4×C47—44no—
61C22×C4×C47—44no—
62C22×C4×C47—44no—
63C22×C4×C47—44no—
64C22×C4×C47C4⋊C418yes—
65C22×C4×C47C22×C412yes—
66C22×C4×C47C22×C412yes—
67C22×C4×C47C22×C412yes—
68C22×C4×C47C2×D414yes—
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×Q812yes—
71C22×C4×C47#4112yes—
72C22×C4×C47#4112yes—
73C22×C4×C47C2411yescharacteristic
74C2×C8×C47—28no—
75C2×C8×C47—22no—
76C2×C8×C47—22no—
77C2×C8×C47C42116yescomplemented
78C2×C8×C47C22×C414yes—
79C2×C8×C47C22×C414yes—
80C2×C8×C47C22×C414yes—
81C2×C8×C47C22×C414yes—
82C4⋊C4×C47—28no—
83C4⋊C4×C47—28no—
84C4⋊C4×C47—24no—
85C4⋊C4×C47—24no—
86C4⋊C4×C47C22×C418yes—
87C4⋊C4×C47C22×C418yes—
88C42×C47—416no—
89C42×C47C4⋊C418yes—
90C42×C47C22×C414yes—
91C42×C47C2×Q814yes—
92C23×C47C2×C4⋊C412yes—
93C23×C47C4×D412yes—
94C23×C47C4×D412yes—
95C23×C47AGL(1,ℤ/8)14yes—
96C23×C47#13714yes—
97C23×C47C22×D411yescharacteristic
98C2×C4×C47—24no—
99C2×C4×C47—24no—
100C2×C4×C47—216no—
101C2×C4×C47—28no—
102C2×C4×C47—28no—
103C2×C4×C47—44no—
104C2×C4×C47—44no—
105C2×C4×C47—44no—
106C2×C4×C47—44no—
107C2×C4×C47—416no—
108C2×C4×C47—416no—
109C2×C4×C47C2×C4214yes—
110C2×C4×C47C2×C4⋊C418yes—
111C2×C4×C47C2×C4⋊C412yes—
112C2×C4×C47#11714yes—
113C2×C4×C47C4×D412yes—
114C2×C4×C47C4×D412yes—
115C2×C4×C47C4×Q814yes—
116C2×C4×C47C4×Q814yes—
117C2×C4×C47C23×C411yescharacteristic
118C2×C4×C47C23×C411yescharacteristic
119C2×C4×C47C23×C411yescharacteristic
120C2×C4×C47C22×Q811yescharacteristic
121C2×C4×C47C2×#4111yescharacteristic
122C2×C4×C47C2×#4111yescharacteristic
123C8×C47—24no—
124C8×C47C2×C4218yescomplemented
125C2×#1776C4711yesmaximal, characteristic, direct product factor, Sylow
126C22×C47C4×C4⋊C414yes—
127C22×C47#42818yes—
128C22×C47#44018yes—
129C22×C47#44114yes—
130C22×C47#44214yes—
131C22×C47C22×C4⋊C411yescharacteristic
132C22×C47C2×C4×D411yescharacteristic
133C22×C47C2×C4×D411yescharacteristic
134C22×C47C2×AGL(1,ℤ/8)12yes—
135C22×C47C2×#13712yes—
136C4×C47—28no—
137C4×C47—48no—
138C4×C47—48no—
139C4×C47C4×C4⋊C414yes—
140C4×C47C22×C4211yescharacteristic
141C4×C47C2×#11711yescharacteristic
142C4×C47C2×C4×Q811yescharacteristic
143C4×C47C2×C4×Q811yescharacteristic
144C22×#107C2×C4711yescharacteristic
145C22×#106C2×C4711yescharacteristic
146C22×#97C2×C4711yescharacteristic
147C2×C4×C4⋊C4C2×C4712yes—
148#1776C2×C4718yesdirect product factor
149C2×#340C2×C4712yes—
150C2×C47#177618yesdirect product factor
151C2×C47C2×C4×C4⋊C411yescharacteristic
152C2×C47C2×#42812yes—
153C2×C47C2×#44012yes—
154C2×C47C2×#44111yescharacteristic
155C2×C47C2×#44211yescharacteristic
156C23×C8C22×C4711yescharacteristic
157C23×C8C22×C4711yescharacteristic
158C22×C4⋊C4C22×C4712yes—
159C22×C4⋊C4C22×C4712yes—
160C22×C42—22no—
161C22×C42C22×C4711yescharacteristic
162C2×#107C4×C4718yescomplemented
163C2×#107C22×C4714yes—
164C2×#106C4×C4718yescomplemented
165C2×#106C22×C4714yes—
166C2×#97C4×C4718yescomplemented
167C2×#97C22×C4714yes—
168C4×C4⋊C4—24no—
169C4×C4⋊C4C22×C4718yes—
170C2×#95—22no—
171#340C22×C4718yes—
172C47C2×#177611yescharacteristic, direct product factor, Sylow
173C23×C4—22no—
174C23×C4—22no—
175C23×C4D4×C4712yes—
176C23×C4C23×C4711yescharacteristic
177C22×C8—22no—
178C22×C8—22no—
179C22×C8C2×C4×C4714yes—
180C22×C8C2×C4×C4714yes—
181C22×C8C2×C4×C4714yes—
182C22×C8C2×C4×C4714yes—
183C22×C8C23×C4712yes—
184C22×C8C23×C4712yes—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4C2×C4×C4718yes—
190C2×C4⋊C4C2×C4×C4718yes—
191C2×C4⋊C4C23×C4714yes—
192C2×C4⋊C4C23×C4714yes—
193C2×C42—28no—
194C2×C42—48no—
195C2×C42C2×C4×C4714yes—
196C2×C42D4×C4712yes—
197C2×C42Q8×C4714yes—
198C2×C42C23×C4712yes—
199#107C2×C4×C47116yescomplemented
200#106C2×C4×C47116yescomplemented
201#97C2×C4×C47116yescomplemented
202#95—28no—
203C24C2×D4×C4711yescharacteristic
204C22×C4—24no—
205C22×C4—24no—
206C22×C4—28no—
207C22×C4—28no—
208C22×C4—24no—
209C22×C4—24no—
210C22×C4—44no—
211C22×C4—44no—
212C22×C4—44no—
213C22×C4—44no—
214C22×C4C4⋊C4×C4718yes—
215C22×C4C22×C4×C4712yes—
216C22×C4C22×C4×C4712yes—
217C22×C4C22×C4×C4712yes—
218C22×C4C2×D4×C4714yes—
219C22×C4C2×D4×C4711yescharacteristic
220C22×C4C2×Q8×C4712yes—
221C22×C4#41×C4712yes—
222C22×C4#41×C4712yes—
223C22×C4C24×C4711yescharacteristic
224C2×C8—28no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8C42×C47116yescomplemented
228C2×C8C22×C4×C4714yes—
229C2×C8C22×C4×C4714yes—
230C2×C8C22×C4×C4714yes—
231C2×C8C22×C4×C4714yes—
232C4⋊C4—28no—
233C4⋊C4—28no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4C22×C4×C4718yes—
237C4⋊C4C22×C4×C4718yes—
238C42—416no—
239C42C4⋊C4×C4718yes—
240C42C22×C4×C4714yes—
241C42C2×Q8×C4714yes—
242C23C2×C4⋊C4×C4712yes—
243C23C4×D4×C4712yes—
244C23C4×D4×C4712yes—
245C23AGL(1,ℤ/8)×C4714yes—
246C23#137×C4714yes—
247C23C22×D4×C4711yescharacteristic
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—216no—
251C2×C4—28no—
252C2×C4—28no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—416no—
258C2×C4—416no—
259C2×C4C2×C42×C4714yes—
260C2×C4C2×C4⋊C4×C4718yes—
261C2×C4C2×C4⋊C4×C4712yes—
262C2×C4#117×C4714yes—
263C2×C4C4×D4×C4712yes—
264C2×C4C4×D4×C4712yes—
265C2×C4C4×Q8×C4714yes—
266C2×C4C4×Q8×C4714yes—
267C2×C4C23×C4×C4711yescharacteristic
268C2×C4C23×C4×C4711yescharacteristic
269C2×C4C23×C4×C4711yescharacteristic
270C2×C4C22×Q8×C4711yescharacteristic
271C2×C4C2×#41×C4711yescharacteristic
272C2×C4C2×#41×C4711yescharacteristic
273C8—24no—
274C8C2×C42×C4718yescomplemented
275C22C4×C4⋊C4×C4714yes—
276C22C47×#42818yes—
277C22C47×#44018yes—
278C22C47×#44114yes—
279C22C47×#44214yes—
280C22C22×C4⋊C4×C4711yescharacteristic
281C22C2×C4×D4×C4711yescharacteristic
282C22C2×C4×D4×C4711yescharacteristic
283C22C2×AGL(1,ℤ/8)×C4712yes—
284C22C2×#137×C4712yes—
285C4—28no—
286C4—48no—
287C4—48no—
288C4C4×C4⋊C4×C4714yes—
289C4C22×C42×C4711yescharacteristic
290C4C2×#117×C4711yescharacteristic
291C4C2×C4×Q8×C4711yescharacteristic
292C4C2×C4×Q8×C4711yescharacteristic
293C2C47×#177618yesdirect product factor
294C2C2×C4×C4⋊C4×C4711yescharacteristic
295C2C2×C47×#42812yes—
296C2C2×C47×#44012yes—
297C2C2×C47×#44111yescharacteristic
298C2C2×C47×#44211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C47C2×D4
commutatorC4C22×C42×C47
Frattini, cosocleC22×C4C24×C47
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
5. C47×#1776C2direct (N × H)
13. C2×#107×C47C4semidirect
15. C2×#106×C47C4semidirect
17. C2×#97×C47C4semidirect
49. #107×C47C2×C4semidirect
50. #106×C47C2×C4semidirect
51. #97×C47C2×C4semidirect
77. C2×C8×C47C42semidirect
124. C8×C47C2×C42semidirect
125. C2×#1776C47direct (N × H)
148. #1776C2×C47direct (N × H)
150. C2×C47#1776direct (N × H)
162. C2×#107C4×C47semidirect
164. C2×#106C4×C47semidirect
166. C2×#97C4×C47semidirect
172. C47C2×#1776direct (N × H)
199. #107C2×C4×C47semidirect
200. #106C2×C4×C47semidirect
201. #97C2×C4×C47semidirect
227. C2×C8C42×C47semidirect
274. C8C2×C42×C47semidirect
293. C2C47×#1776direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#107×C472
C22×#106×C472
C22×#97×C472
C2×C4×C4⋊C4×C472
C47×#17762
C2×C47×#3402
C2×#177647