Finite Group Databasebeta

← C22×C47×#380 #26073702

Subgroups — C22×C47×#380 #26073702

Order 12032.

8670 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4×C47C211yesmaximal, characteristic
2C23×C4⋊C4×C47C212yesmaximal, complemented
3C23×C22⋊C4×C47C212yesmaximal
4C2×C47×#380C2124yesmaximal, direct product factor
5C22×#95×C47C212yesmaximal, complemented
6C26×C47C2211yescharacteristic
7C24×C4×C47—216no—
8C24×C4×C47C4116yescomplemented
9C24×C4×C47C2214yes—
10C24×C4×C47C2211yescharacteristic
11C24×C4×C47C22112yes—
12C24×C4×C47C2211yescharacteristic
13C22×C4⋊C4×C47—216no—
14C22×C4⋊C4×C47C22124yescomplemented
15C22×C22⋊C4×C47—216no—
16C22×C22⋊C4×C47C22124yes—
17C47×#380C22164yesdirect product factor
18C2×#95×C47C22124yescomplemented
19C25×C47—28no—
20C25×C47—28no—
21C25×C47C2×C418yes—
22C25×C47D418yes—
23C25×C47Q818yes—
24C25×C47C2316yes—
25C25×C47C2311yescharacteristic
26C23×C4×C47—28no—
27C23×C4×C47—2128no—
28C23×C4×C47—296no—
29C23×C4×C47—216no—
30C23×C4×C47—216no—
31C23×C4×C47—216no—
32C23×C4×C47C2×C418yes—
33C23×C4×C47C2×C418yes—
34C23×C4×C47C2×C4196yescomplemented
35C23×C4×C47D4116yes—
36C23×C4×C47C23124yes—
37C23×C4×C47C2316yes—
38C23×C4×C47C23116yes—
39C23×C4×C47C2316yes—
40C2×C4⋊C4×C47—296no—
41C2×C4⋊C4×C47C23132yescomplemented
42C2×C22⋊C4×C47—296no—
43C2×C22⋊C4×C47C23132yes—
44#95×C47C23132yescomplemented
45C24×C47—232no—
46C24×C47—232no—
47C24×C47—264no—
48C24×C47—264no—
49C24×C47—224no—
50C24×C47—224no—
51C24×C47C4⋊C4164yescomplemented
52C24×C47C22×C4124yes—
53C24×C47C22×C414yes—
54C24×C47C2×D4124yes—
55C24×C47C2×D418yes—
56C24×C47C2×D414yes—
57C24×C47C2×Q8124yes—
58C24×C47C2×Q814yes—
59C24×C47#4118yes—
60C24×C47C2414yes—
61C24×C47C2413yes—
62C22×C4×C47—232no—
63C22×C4×C47—224no—
64C22×C4×C47—2384no—
65C22×C4×C47—264no—
66C22×C4×C47—248no—
67C22×C4×C47—248no—
68C22×C4×C47—248no—
69C22×C4×C47—464no—
70C22×C4×C47C22⋊C4164yescomplemented
71C22×C4×C47C22×C4124yes—
72C22×C4×C47C22×C4124yes—
73C22×C4×C47C22×C4164yescomplemented
74C22×C4×C47C2×D4148yes—
75C22×C4×C47C24116yes—
76C22×C4×C47C2414yes—
77C22×C4×C47C2414yes—
78C4⋊C4×C47—264no—
79C22⋊C4×C47—264no—
80C23×C47—248no—
81C23×C47—248no—
82C23×C47—296no—
83C23×C47—296no—
84C23×C47—28no—
85C23×C47—28no—
86C23×C47—2256no—
87C23×C47C2×C22⋊C4116yes—
88C23×C47C2×C4⋊C4116yes—
89C23×C47C2×C4⋊C4196yescomplemented
90C23×C47#117116yes—
91C23×C47#121132yes—
92C23×C47C22⋊Q8132yes—
93C23×C47C23×C418yes—
94C23×C47C23×C416yes—
95C23×C47C22×D418yes—
96C23×C47C22×D4112yes—
97C23×C47C22×D416yes—
98C23×C47C22×Q818yes—
99C23×C47C22×Q816yes—
100C23×C47C2×#41112yes—
101C23×C47C2511yescharacteristic
102C2×C4×C47—248no—
103C2×C4×C47—28no—
104C2×C4×C47—2128no—
105C2×C4×C47—216no—
106C2×C4×C47—216no—
107C2×C4×C47—216no—
108C2×C4×C47—496no—
109C2×C4×C47C2×C22⋊C4196yescomplemented
110C2×C4×C47C23×C418yes—
111C2×C4×C47C23×C418yes—
112C2×C4×C47C22×D4116yes—
113C22×#380C4711yesmaximal, characteristic, direct product factor, Sylow
114C22×C47—28no—
115C22×C47—28no—
116C22×C47—216no—
117C22×C47—216no—
118C22×C47—2192no—
119C22×C47#380164yesdirect product factor
120C22×C47C22×C22⋊C4112yes—
121C22×C47C22×C4⋊C4112yes—
122C22×C47C22×C4⋊C4116yescomplemented
123C22×C47C2×#117112yes—
124C22×C47C2×#121124yes—
125C22×C47C2×C22⋊Q8124yes—
126C22×C47C24×C411yescharacteristic
127C22×C47C23×D412yes—
128C22×C47C23×D411yescharacteristic
129C22×C47C23×Q811yescharacteristic
130C22×C47C22×#4112yes—
131C4×C47—28no—
132C4×C47—416no—
133C4×C47C22×C22⋊C4116yescomplemented
134C25×C4C2×C4711yescharacteristic
135C23×C4⋊C4C2×C4712yescomplemented
136C23×C22⋊C4C2×C4712yes—
137C2×#380C2×C47124yesdirect product factor
138C22×#95C2×C4712yescomplemented
139C2×C47—216no—
140C2×C47C2×#380124yesdirect product factor
141C2×C47C23×C22⋊C411yescharacteristic
142C2×C47C23×C4⋊C411yescharacteristic
143C2×C47C22×#11711yescharacteristic
144C2×C47C22×#12112yes—
145C2×C47C22×C22⋊Q812yes—
146C26C22×C4711yescharacteristic
147C24×C4—216no—
148C24×C4C4×C47116yescomplemented
149C24×C4C22×C4714yes—
150C24×C4C22×C4711yescharacteristic
151C24×C4C22×C47112yes—
152C24×C4C22×C4711yescharacteristic
153C22×C4⋊C4—216no—
154C22×C4⋊C4C22×C47124yescomplemented
155C22×C22⋊C4—216no—
156C22×C22⋊C4C22×C47124yes—
157#380C22×C47164yesdirect product factor
158C2×#95C22×C47124yescomplemented
159C47C22×#38011yescharacteristic, direct product factor, Sylow
160C25—28no—
161C25—28no—
162C25C2×C4×C4718yes—
163C25D4×C4718yes—
164C25Q8×C4718yes—
165C25C23×C4716yes—
166C25C23×C4711yescharacteristic
167C23×C4—28no—
168C23×C4—2128no—
169C23×C4—296no—
170C23×C4—216no—
171C23×C4—216no—
172C23×C4—216no—
173C23×C4C2×C4×C4718yes—
174C23×C4C2×C4×C4718yes—
175C23×C4C2×C4×C47196yescomplemented
176C23×C4D4×C47116yes—
177C23×C4C23×C47124yes—
178C23×C4C23×C4716yes—
179C23×C4C23×C47116yes—
180C23×C4C23×C4716yes—
181C2×C4⋊C4—296no—
182C2×C4⋊C4C23×C47132yescomplemented
183C2×C22⋊C4—296no—
184C2×C22⋊C4C23×C47132yes—
185#95C23×C47132yescomplemented
186C24—232no—
187C24—232no—
188C24—264no—
189C24—264no—
190C24—224no—
191C24—224no—
192C24C4⋊C4×C47164yescomplemented
193C24C22×C4×C47124yes—
194C24C22×C4×C4714yes—
195C24C2×D4×C47124yes—
196C24C2×D4×C4718yes—
197C24C2×D4×C4714yes—
198C24C2×Q8×C47124yes—
199C24C2×Q8×C4714yes—
200C24#41×C4718yes—
201C24C24×C4714yes—
202C24C24×C4713yes—
203C22×C4—232no—
204C22×C4—224no—
205C22×C4—2384no—
206C22×C4—264no—
207C22×C4—248no—
208C22×C4—248no—
209C22×C4—248no—
210C22×C4—464no—
211C22×C4C22⋊C4×C47164yescomplemented
212C22×C4C22×C4×C47124yes—
213C22×C4C22×C4×C47124yes—
214C22×C4C22×C4×C47164yescomplemented
215C22×C4C2×D4×C47148yes—
216C22×C4C24×C47116yes—
217C22×C4C24×C4714yes—
218C22×C4C24×C4714yes—
219C4⋊C4—264no—
220C22⋊C4—264no—
221C23—248no—
222C23—248no—
223C23—296no—
224C23—296no—
225C23—28no—
226C23—28no—
227C23—2256no—
228C23C2×C22⋊C4×C47116yes—
229C23C2×C4⋊C4×C47116yes—
230C23C2×C4⋊C4×C47196yescomplemented
231C23#117×C47116yes—
232C23#121×C47132yes—
233C23C22⋊Q8×C47132yes—
234C23C23×C4×C4718yes—
235C23C23×C4×C4716yes—
236C23C22×D4×C4718yes—
237C23C22×D4×C47112yes—
238C23C22×D4×C4716yes—
239C23C22×Q8×C4718yes—
240C23C22×Q8×C4716yes—
241C23C2×#41×C47112yes—
242C23C25×C4711yescharacteristic
243C2×C4—248no—
244C2×C4—28no—
245C2×C4—2128no—
246C2×C4—216no—
247C2×C4—216no—
248C2×C4—216no—
249C2×C4—496no—
250C2×C4C2×C22⋊C4×C47196yescomplemented
251C2×C4C23×C4×C4718yes—
252C2×C4C23×C4×C4718yes—
253C2×C4C22×D4×C47116yes—
254C22—2192no—
255C22—28no—
256C22—28no—
257C22—216no—
258C22—216no—
259C22C47×#380164yesdirect product factor
260C22C22×C22⋊C4×C47112yes—
261C22C22×C4⋊C4×C47112yes—
262C22C22×C4⋊C4×C47116yescomplemented
263C22C2×#117×C47112yes—
264C22C2×#121×C47124yes—
265C22C2×C22⋊Q8×C47124yes—
266C22C24×C4×C4711yescharacteristic
267C22C23×D4×C4712yes—
268C22C23×D4×C4711yescharacteristic
269C22C23×Q8×C4711yescharacteristic
270C22C22×#41×C4712yes—
271C4—28no—
272C4—416no—
273C4C22×C22⋊C4×C47116yescomplemented
274C2—216no—
275C2C2×C47×#380124yesdirect product factor
276C2C23×C22⋊C4×C4711yescharacteristic
277C2C23×C4⋊C4×C4711yescharacteristic
278C2C22×#117×C4711yescharacteristic
279C2C22×#121×C4712yes—
280C2C22×C22⋊Q8×C4712yes—
subgroupG/H
center, socleC25×C47C23
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
prime radicalC26×C47C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊C4×C47C2semidirect
4. C2×C47×#380C2direct (N × H)
5. C22×#95×C47C2semidirect
8. C24×C4×C47C4semidirect
14. C22×C4⋊C4×C47C22semidirect
17. C47×#380C22direct (N × H)
18. C2×#95×C47C22semidirect
34. C23×C4×C47C2×C4semidirect
41. C2×C4⋊C4×C47C23semidirect
44. #95×C47C23semidirect
51. C24×C47C4⋊C4semidirect
70. C22×C4×C47C22⋊C4semidirect
73. C22×C4×C47C22×C4semidirect
89. C23×C47C2×C4⋊C4semidirect
109. C2×C4×C47C2×C22⋊C4semidirect
113. C22×#380C47direct (N × H)
119. C22×C47#380direct (N × H)
122. C22×C47C22×C4⋊C4semidirect
133. C4×C47C22×C22⋊C4semidirect
135. C23×C4⋊C4C2×C47semidirect
137. C2×#380C2×C47direct (N × H)
138. C22×#95C2×C47semidirect
140. C2×C47C2×#380direct (N × H)
148. C24×C4C4×C47semidirect
154. C22×C4⋊C4C22×C47semidirect
157. #380C22×C47direct (N × H)
158. C2×#95C22×C47semidirect
159. C47C22×#380direct (N × H)
175. C23×C4C2×C4×C47semidirect
182. C2×C4⋊C4C23×C47semidirect
185. #95C23×C47semidirect
192. C24C4⋊C4×C47semidirect
211. C22×C4C22⋊C4×C47semidirect
214. C22×C4C22×C4×C47semidirect
230. C23C2×C4⋊C4×C47semidirect
250. C2×C4C2×C22⋊C4×C47semidirect
259. C22C47×#380direct (N × H)
262. C22C22×C4⋊C4×C47semidirect
273. C4C22×C22⋊C4×C47semidirect
275. C2C2×C47×#380direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C4×C472
C23×C4⋊C4×C472
C23×C22⋊C4×C472
C2×C47×#3802
C22×#95×C472
C22×#38047