Finite Group Databasebeta

← C2×C47×#2401 #26074247

Subgroups — C2×C47×#2401 #26074247

Order 12032.

2294 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×#2401C2116yesmaximal, direct product factor
2C2×C47×#401C211yesmaximal, characteristic, complemented
3C2×C47×#400C213yesmaximal, complemented
4C2×C47×#397C213yesmaximal
5C2×C47×#396C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C47C213yesmaximal, complemented
7C2×C4×C22⋊C4×C47C213yesmaximal
8C2×C47×#376C211yesmaximal, characteristic, complemented
9C24×C4×C47C2211yescharacteristic
10C22×C4⋊C4×C47C2213yes—
11C22×C4⋊C4×C47C2213yes—
12C22×C22⋊C4×C47C2213yes—
13C22×C22⋊C4×C47C2213yes—
14C22×C42×C47C2213yes—
15C22×C42×C47C2213yes—
16C47×#401C2218yescomplemented
17C47×#400C22124yescomplemented
18C47×#397C22124yes—
19C47×#396C2218yes—
20C4×C4⋊C4×C47C22124yescomplemented
21C4×C22⋊C4×C47C22124yes—
22C47×#376C2218yescomplemented
23C2×#95×C47C2211yescharacteristic
24C2×#95×C47C2213yes—
25C2×#95×C47C2213yes—
26C2×#95×C47C2213yes—
27C2×#95×C47C2213yes—
28C2×#95×C47C2213yes—
29C25×C47C2311yescharacteristic
30C23×C4×C47—212no—
31C23×C4×C47C2313yes—
32C23×C4×C47C2313yes—
33C23×C4×C47C2313yes—
34C23×C4×C47C2311yescharacteristic
35C23×C4×C47C2314yes—
36C23×C4×C47C2313yes—
37C23×C4×C47C2311yescharacteristic
38C2×C4⋊C4×C47—212no—
39C2×C4⋊C4×C47—212no—
40C2×C4⋊C4×C47C23112yes—
41C2×C4⋊C4×C47C23112yes—
42C2×C22⋊C4×C47—212no—
43C2×C22⋊C4×C47—212no—
44C2×C22⋊C4×C47C23112yes—
45C2×C22⋊C4×C47C23112yes—
46C2×C42×C47—212no—
47C2×C42×C47—212no—
48C2×C42×C47C23112yes—
49C2×C42×C47C23112yes—
50#95×C47C2314yes—
51#95×C47C23112yes—
52#95×C47C23112yes—
53#95×C47C23112yes—
54#95×C47C23112yes—
55#95×C47C23112yes—
56C24×C47—26no—
57C24×C47—26no—
58C24×C47#4114yes—
59C24×C47C2412yes—
60C24×C47C2411yescharacteristic
61C22×C4×C47—26no—
62C22×C4×C47—26no—
63C22×C4×C47—26no—
64C22×C4×C47—26no—
65C22×C4×C47—26no—
66C22×C4×C47—26no—
67C22×C4×C47—26no—
68C22×C4×C47—26no—
69C22×C4×C47—26no—
70C22×C4×C47—26no—
71C22×C4×C47—26no—
72C22×C4×C47—26no—
73C22×C4×C47—224no—
74C22×C4×C47—416no—
75C22×C4×C47#41112yes—
76C22×C4×C47#41112yes—
77C22×C4×C47C2416yes—
78C22×C4×C47C2416yes—
79C22×C4×C47C2416yes—
80C22×C4×C47C2412yes—
81C22×C4×C47C2416yes—
82C22×C4×C47C2412yes—
83C4⋊C4×C47—224no—
84C4⋊C4×C47—224no—
85C22⋊C4×C47—224no—
86C22⋊C4×C47—224no—
87C42×C47—224no—
88C42×C47—224no—
89C23×C47—224no—
90C23×C47—26no—
91C23×C47—26no—
92C23×C47—44no—
93C23×C47—412no—
94C23×C47C2×#4114yes—
95C23×C47C2×#4116yes—
96C23×C47C2×#4112yes—
97C23×C47C2×#4116yes—
98C23×C47C2511yescharacteristic
99C2×C4×C47—224no—
100C2×C4×C47—26no—
101C2×C4×C47—26no—
102C2×C4×C47—26no—
103C2×C4×C47—26no—
104C2×C4×C47—26no—
105C2×C4×C47—26no—
106C2×C4×C47—26no—
107C2×C4×C47—26no—
108C2×C4×C47—26no—
109C2×C4×C47—26no—
110C2×C4×C47—26no—
111C2×C4×C47—26no—
112C2×C4×C47—44no—
113C2×C4×C47—412no—
114C2×C4×C47—412no—
115C2×C4×C47—412no—
116C2×C4×C47—416no—
117C2×C4×C47#126116yes—
118C2×C4×C47C2×#41112yes—
119C2×C4×C47C2×#41112yes—
120C2×#2401C4711yesmaximal, characteristic, direct product factor, Sylow
121C22×C47—212no—
122C22×C47—416no—
123C22×C47—42no—
124C22×C47—46no—
125C22×C47C2×#12614yes—
126C22×C47#529112yes—
127C22×C47#529112yes—
128C22×C47C22×#4113yes—
129C22×C47C22×#4111yescharacteristic
130C22×C47C22×#4113yes—
131C4×C47—212no—
132C4×C47—42no—
133C4×C47—46no—
134C4×C47—46no—
135C4×C47—46no—
136C4×C47C2×#12618yes—
137#2401C2×C47116yesdirect product factor
138C2×#401C2×C4711yescharacteristic, complemented
139C2×#400C2×C4713yescomplemented
140C2×#397C2×C4713yes—
141C2×#396C2×C4711yescharacteristic
142C2×C4×C4⋊C4C2×C4713yescomplemented
143C2×C4×C22⋊C4C2×C4713yes—
144C2×#376C2×C4711yescharacteristic, complemented
145C2×C47—44no—
146C2×C47#240118yesdirect product factor
147C2×C47C22×#12611yescharacteristic
148C2×C47C2×#52913yes—
149C2×C47C2×#52913yes—
150C24×C4C22×C4711yescharacteristic
151C22×C4⋊C4C22×C4713yes—
152C22×C4⋊C4C22×C4713yes—
153C22×C22⋊C4C22×C4713yes—
154C22×C22⋊C4C22×C4713yes—
155C22×C42C22×C4713yes—
156C22×C42C22×C4713yes—
157#401C22×C4718yescomplemented
158#400C22×C47124yescomplemented
159#397C22×C47124yes—
160#396C22×C4718yes—
161C4×C4⋊C4C22×C47124yescomplemented
162C4×C22⋊C4C22×C47124yes—
163#376C22×C4718yescomplemented
164C2×#95C22×C4711yescharacteristic
165C2×#95C22×C4713yes—
166C2×#95C22×C4713yes—
167C2×#95C22×C4713yes—
168C2×#95C22×C4713yes—
169C2×#95C22×C4713yes—
170C47C2×#240111yescharacteristic, direct product factor, Sylow
171C25C23×C4711yescharacteristic
172C23×C4—212no—
173C23×C4C23×C4713yes—
174C23×C4C23×C4713yes—
175C23×C4C23×C4713yes—
176C23×C4C23×C4711yescharacteristic
177C23×C4C23×C4714yes—
178C23×C4C23×C4713yes—
179C23×C4C23×C4711yescharacteristic
180C2×C4⋊C4—212no—
181C2×C4⋊C4—212no—
182C2×C4⋊C4C23×C47112yes—
183C2×C4⋊C4C23×C47112yes—
184C2×C22⋊C4—212no—
185C2×C22⋊C4—212no—
186C2×C22⋊C4C23×C47112yes—
187C2×C22⋊C4C23×C47112yes—
188C2×C42—212no—
189C2×C42—212no—
190C2×C42C23×C47112yes—
191C2×C42C23×C47112yes—
192#95C23×C4714yes—
193#95C23×C47112yes—
194#95C23×C47112yes—
195#95C23×C47112yes—
196#95C23×C47112yes—
197#95C23×C47112yes—
198C24—26no—
199C24—26no—
200C24#41×C4714yes—
201C24C24×C4712yes—
202C24C24×C4711yescharacteristic
203C22×C4—26no—
204C22×C4—26no—
205C22×C4—26no—
206C22×C4—26no—
207C22×C4—26no—
208C22×C4—26no—
209C22×C4—26no—
210C22×C4—26no—
211C22×C4—26no—
212C22×C4—26no—
213C22×C4—26no—
214C22×C4—26no—
215C22×C4—224no—
216C22×C4—416no—
217C22×C4#41×C47112yes—
218C22×C4#41×C47112yes—
219C22×C4C24×C4712yes—
220C22×C4C24×C4716yes—
221C22×C4C24×C4716yes—
222C22×C4C24×C4716yes—
223C22×C4C24×C4716yes—
224C22×C4C24×C4712yes—
225C4⋊C4—224no—
226C4⋊C4—224no—
227C22⋊C4—224no—
228C22⋊C4—224no—
229C42—224no—
230C42—224no—
231C23—224no—
232C23—26no—
233C23—26no—
234C23—44no—
235C23—412no—
236C23C2×#41×C4714yes—
237C23C2×#41×C4716yes—
238C23C2×#41×C4712yes—
239C23C2×#41×C4716yes—
240C23C25×C4711yescharacteristic
241C2×C4—224no—
242C2×C4—26no—
243C2×C4—26no—
244C2×C4—26no—
245C2×C4—26no—
246C2×C4—26no—
247C2×C4—26no—
248C2×C4—26no—
249C2×C4—26no—
250C2×C4—26no—
251C2×C4—26no—
252C2×C4—26no—
253C2×C4—26no—
254C2×C4—44no—
255C2×C4—412no—
256C2×C4—412no—
257C2×C4—412no—
258C2×C4—416no—
259C2×C4#126×C47116yes—
260C2×C4C2×#41×C47112yes—
261C2×C4C2×#41×C47112yes—
262C22—212no—
263C22—416no—
264C22—42no—
265C22—46no—
266C22C2×#126×C4714yes—
267C22C47×#529112yes—
268C22C47×#529112yes—
269C22C22×#41×C4713yes—
270C22C22×#41×C4711yescharacteristic
271C22C22×#41×C4713yes—
272C4—212no—
273C4—42no—
274C4—46no—
275C4—46no—
276C4—46no—
277C4C2×#126×C4718yes—
278C2—44no—
279C2C47×#240118yesdirect product factor
280C2C22×#126×C4711yescharacteristic
281C2C2×C47×#52913yes—
282C2C2×C47×#52913yes—
subgroupG/H
centerC23×C4×C47C23
commutator, Frattini, cosocleC23C25×C47
socleC24×C47C24
prime radicalC25×C47C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2401C2direct (N × H)
2. C2×C47×#401C2semidirect
3. C2×C47×#400C2semidirect
6. C2×C4×C4⋊C4×C47C2semidirect
8. C2×C47×#376C2semidirect
16. C47×#401C22semidirect
17. C47×#400C22semidirect
20. C4×C4⋊C4×C47C22semidirect
22. C47×#376C22semidirect
120. C2×#2401C47direct (N × H)
137. #2401C2×C47direct (N × H)
138. C2×#401C2×C47semidirect
139. C2×#400C2×C47semidirect
142. C2×C4×C4⋊C4C2×C47semidirect
144. C2×#376C2×C47semidirect
146. C2×C47#2401direct (N × H)
157. #401C22×C47semidirect
158. #400C22×C47semidirect
161. C4×C4⋊C4C22×C47semidirect
163. #376C22×C47semidirect
170. C47C2×#2401direct (N × H)
279. C2C47×#2401direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#24012
C2×C47×#4012
C2×C47×#4002
C2×C47×#3972
C2×C47×#3962
C2×C4×C4⋊C4×C472
C2×C4×C22⋊C4×C472
C2×C47×#3762
C2×#240147