Finite Group Databasebeta

← C2×Q8×C22⋊C4×C47 #26073798

Subgroups — C2×Q8×C22⋊C4×C47 #26073798

Order 12032.

5414 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×Q8×C47C211yesmaximal, characteristic
2C22×C4×Q8×C47C212yesmaximal, complemented
3Q8×C22⋊C4×C47C2116yesmaximal, direct product factor
4C2×C47×#391C216yesmaximal, complemented
5C2×C47×#380C213yesmaximal
6C2×C4×C22⋊C4×C47C213yesmaximal
7C23×Q8×C47—216no—
8C23×Q8×C47C4116yescomplemented
9C23×Q8×C47C2213yes—
10C23×Q8×C47C2218yes—
11C23×Q8×C47C2211yescharacteristic
12C24×C4×C47C2213yes—
13C2×C4×Q8×C47—216no—
14C2×C4×Q8×C47C22116yescomplemented
15C22×C4⋊C4×C47C2216yes—
16C22×C22⋊C4×C47C2213yes—
17C22×C22⋊C4×C47C2211yescharacteristic
18C22×C42×C47C2216yes—
19C47×#391C22148yescomplemented
20C47×#380C22124yes—
21C4×C22⋊C4×C47C22124yes—
22C2×#95×C47C2216yes—
23C2×#95×C47C2216yes—
24C25×C47C2311yescharacteristic
25C22×Q8×C47—2128no—
26C22×Q8×C47—264no—
27C22×Q8×C47—224no—
28C22×Q8×C47C2×C4124yes—
29C22×Q8×C47C2×C418yes—
30C22×Q8×C47C2×C4164yescomplemented
31C22×Q8×C47D4116yes—
32C22×Q8×C47C23112yes—
33C22×Q8×C47C2314yes—
34C23×C4×C47—224no—
35C23×C4×C47C2×C4124yes—
36C23×C4×C47C2316yes—
37C23×C4×C47C23112yes—
38C23×C4×C47C2313yes—
39C23×C4×C47C2312yes—
40C23×C4×C47C2313yes—
41C4×Q8×C47—264no—
42C2×C4⋊C4×C47—224no—
43C2×C4⋊C4×C47C23124yes—
44C2×C22⋊C4×C47—212no—
45C2×C22⋊C4×C47Q818yesdirect product factor
46C2×C22⋊C4×C47C23112yes—
47C2×C22⋊C4×C47C2314yes—
48C2×C42×C47—224no—
49C2×C42×C47C23124yes—
50#95×C47C23124yes—
51#95×C47C23124yes—
52C24×C47—24no—
53C24×C47—24no—
54C24×C47C22×C414yes—
55C24×C47C2×Q814yes—
56C24×C47#4114yes—
57C24×C47C2412yes—
58C24×C47C2411yescharacteristic
59C2×Q8×C47—2256no—
60C2×Q8×C47—296no—
61C2×Q8×C47—248no—
62C2×Q8×C47C22⋊C4164yesdirect product factor
63C2×Q8×C47C22×C4148yes—
64C2×Q8×C47C22×C4116yes—
65C2×Q8×C47C2×D4132yes—
66C22×C4×C47—24no—
67C22×C4×C47—212no—
68C22×C4×C47—24no—
69C22×C4×C47—296no—
70C22×C4×C47—248no—
71C22×C4×C47—212no—
72C22×C4×C47—212no—
73C22×C4×C47—212no—
74C22×C4×C47C22×C4112yes—
75C22×C4×C47C22×C4148yes—
76C22×C4×C47C22×C4112yes—
77C22×C4×C47C2×D4124yes—
78C22×C4×C47C2×Q818yescomplemented
79C22×C4×C47C24112yes—
80C22×C4×C47C2416yes—
81C22×C4×C47C2414yes—
82C22×C4×C47C2416yes—
83C4⋊C4×C47—248no—
84C22⋊C4×C47—224no—
85C22⋊C4×C47C2×Q8116yesdirect product factor
86C42×C47—248no—
87C23×C47—28no—
88C23×C47—28no—
89C23×C47—216no—
90C23×C47—216no—
91C23×C47—24no—
92C23×C47—24no—
93C23×C47C4×Q8116yescomplemented
94C23×C47C23×C414yes—
95C23×C47C23×C412yes—
96C23×C47C22×D414yes—
97C23×C47C22×Q814yes—
98C23×C47C22×Q812yes—
99C23×C47C2×#4114yes—
100C23×C47C2×#4112yes—
101C23×C472−1+414yes—
102C23×C47C2511yescharacteristic
103Q8×C47—296no—
104Q8×C47C2×C22⋊C4164yesdirect product factor
105C2×C4×C47—224no—
106C2×C4×C47—216no—
107C2×C4×C47—24no—
108C2×C4×C47—212no—
109C2×C4×C47—24no—
110C2×C4×C47—296no—
111C2×C4×C47—212no—
112C2×C4×C47—212no—
113C2×C4×C47—212no—
114C2×C4×C47—424no—
115C2×C4×C47C2×C22⋊C4148yes—
116C2×C4×C47C23×C4112yes—
117C2×C4×C47C23×C4112yes—
118C2×C4×C47C22×D4124yes—
119C2×C4×C47C22×Q818yescomplemented
120C2×Q8×C22⋊C4C4711yesmaximal, characteristic, direct product factor, Sylow
121C22×C47—232no—
122C22×C47—24no—
123C22×C47—24no—
124C22×C47—28no—
125C22×C47—28no—
126C22×C47C22×C22⋊C414yes—
127C22×C47C2×C4×Q814yes—
128C22×C47C2×C4×Q818yescomplemented
129C22×C47#51914yes—
130C22×C47#54818yes—
131C22×C47D4×Q818yes—
132C22×C47C24×C411yescharacteristic
133C22×C47C23×D412yes—
134C22×C47C23×Q811yescharacteristic
135C22×C47C22×#4111yescharacteristic
136C22×C47C2×2−1+412yes—
137C4×C47—212no—
138C4×C47—28no—
139C4×C47—412no—
140C4×C47C22×C22⋊C4124yes—
141C24×Q8C2×C4711yescharacteristic
142C22×C4×Q8C2×C4712yescomplemented
143Q8×C22⋊C4C2×C47116yesdirect product factor
144C2×#391C2×C4716yescomplemented
145C2×#380C2×C4713yes—
146C2×C4×C22⋊C4C2×C4713yes—
147C2×C47—28no—
148C2×C47Q8×C22⋊C418yesdirect product factor
149C2×C47C23×C22⋊C411yescharacteristic
150C2×C47C22×C4×Q811yescharacteristic
151C2×C47C2×#51911yescharacteristic
152C2×C47C2×#54812yes—
153C2×C47C2×D4×Q812yes—
154C23×Q8—216no—
155C23×Q8C4×C47116yescomplemented
156C23×Q8C22×C4713yes—
157C23×Q8C22×C4718yes—
158C23×Q8C22×C4711yescharacteristic
159C24×C4C22×C4713yes—
160C2×C4×Q8—216no—
161C2×C4×Q8C22×C47116yescomplemented
162C22×C4⋊C4C22×C4716yes—
163C22×C22⋊C4C22×C4713yes—
164C22×C22⋊C4C22×C4711yescharacteristic
165C22×C42C22×C4716yes—
166#391C22×C47148yescomplemented
167#380C22×C47124yes—
168C4×C22⋊C4C22×C47124yes—
169C2×#95C22×C4716yes—
170C2×#95C22×C4716yes—
171C47C2×Q8×C22⋊C411yescharacteristic, direct product factor, Sylow
172C25C23×C4711yescharacteristic
173C22×Q8—2128no—
174C22×Q8—264no—
175C22×Q8—224no—
176C22×Q8C2×C4×C47124yes—
177C22×Q8C2×C4×C4718yes—
178C22×Q8C2×C4×C47164yescomplemented
179C22×Q8D4×C47116yes—
180C22×Q8C23×C47112yes—
181C22×Q8C23×C4714yes—
182C23×C4—224no—
183C23×C4C2×C4×C47124yes—
184C23×C4C23×C4716yes—
185C23×C4C23×C4713yes—
186C23×C4C23×C47112yes—
187C23×C4C23×C4712yes—
188C23×C4C23×C4713yes—
189C4×Q8—264no—
190C2×C4⋊C4—224no—
191C2×C4⋊C4C23×C47124yes—
192C2×C22⋊C4—212no—
193C2×C22⋊C4Q8×C4718yesdirect product factor
194C2×C22⋊C4C23×C47112yes—
195C2×C22⋊C4C23×C4714yes—
196C2×C42—224no—
197C2×C42C23×C47124yes—
198#95C23×C47124yes—
199#95C23×C47124yes—
200C24—24no—
201C24—24no—
202C24C22×C4×C4714yes—
203C24C2×Q8×C4714yes—
204C24#41×C4714yes—
205C24C24×C4712yes—
206C24C24×C4711yescharacteristic
207C2×Q8—2256no—
208C2×Q8—296no—
209C2×Q8—248no—
210C2×Q8C22⋊C4×C47164yesdirect product factor
211C2×Q8C22×C4×C47148yes—
212C2×Q8C22×C4×C47116yes—
213C2×Q8C2×D4×C47132yes—
214C22×C4—24no—
215C22×C4—212no—
216C22×C4—24no—
217C22×C4—296no—
218C22×C4—248no—
219C22×C4—212no—
220C22×C4—212no—
221C22×C4—212no—
222C22×C4C22×C4×C47112yes—
223C22×C4C22×C4×C47148yes—
224C22×C4C22×C4×C47112yes—
225C22×C4C2×D4×C47124yes—
226C22×C4C2×Q8×C4718yescomplemented
227C22×C4C24×C47112yes—
228C22×C4C24×C4716yes—
229C22×C4C24×C4714yes—
230C22×C4C24×C4716yes—
231C4⋊C4—248no—
232C22⋊C4—224no—
233C22⋊C4C2×Q8×C47116yesdirect product factor
234C42—248no—
235C23—28no—
236C23—28no—
237C23—216no—
238C23—216no—
239C23—24no—
240C23—24no—
241C23C4×Q8×C47116yescomplemented
242C23C23×C4×C4714yes—
243C23C23×C4×C4712yes—
244C23C22×D4×C4714yes—
245C23C22×Q8×C4714yes—
246C23C22×Q8×C4712yes—
247C23C2×#41×C4714yes—
248C23C2×#41×C4712yes—
249C232−1+4×C4714yes—
250C23C25×C4711yescharacteristic
251Q8—296no—
252Q8C2×C22⋊C4×C47164yesdirect product factor
253C2×C4—224no—
254C2×C4—216no—
255C2×C4—24no—
256C2×C4—212no—
257C2×C4—24no—
258C2×C4—296no—
259C2×C4—212no—
260C2×C4—212no—
261C2×C4—212no—
262C2×C4—424no—
263C2×C4C2×C22⋊C4×C47148yes—
264C2×C4C23×C4×C47112yes—
265C2×C4C23×C4×C47112yes—
266C2×C4C22×D4×C47124yes—
267C2×C4C22×Q8×C4718yescomplemented
268C22—232no—
269C22—24no—
270C22—24no—
271C22—28no—
272C22—28no—
273C22C22×C22⋊C4×C4714yes—
274C22C2×C4×Q8×C4714yes—
275C22C2×C4×Q8×C4718yescomplemented
276C22C47×#51914yes—
277C22C47×#54818yes—
278C22D4×Q8×C4718yes—
279C22C24×C4×C4711yescharacteristic
280C22C23×D4×C4712yes—
281C22C23×Q8×C4711yescharacteristic
282C22C22×#41×C4711yescharacteristic
283C22C2×2−1+4×C4712yes—
284C4—212no—
285C4—28no—
286C4—412no—
287C4C22×C22⋊C4×C47124yes—
288C2—28no—
289C2Q8×C22⋊C4×C4718yesdirect product factor
290C2C23×C22⋊C4×C4711yescharacteristic
291C2C22×C4×Q8×C4711yescharacteristic
292C2C2×C47×#51911yescharacteristic
293C2C2×C47×#54812yes—
294C2C2×D4×Q8×C4712yes—
subgroupG/H
center, socleC24×C47C24
commutatorC22C24×C4×C47
Frattini, cosocleC23C25×C47
prime radicalC25×C47C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4×Q8×C47C2semidirect
3. Q8×C22⋊C4×C47C2direct (N × H)
4. C2×C47×#391C2semidirect
8. C23×Q8×C47C4semidirect
14. C2×C4×Q8×C47C22semidirect
19. C47×#391C22semidirect
30. C22×Q8×C47C2×C4semidirect
45. C2×C22⋊C4×C47Q8direct (N × H)
62. C2×Q8×C47C22⋊C4direct (N × H)
78. C22×C4×C47C2×Q8semidirect
85. C22⋊C4×C47C2×Q8direct (N × H)
93. C23×C47C4×Q8semidirect
104. Q8×C47C2×C22⋊C4direct (N × H)
119. C2×C4×C47C22×Q8semidirect
120. C2×Q8×C22⋊C4C47direct (N × H)
128. C22×C47C2×C4×Q8semidirect
142. C22×C4×Q8C2×C47semidirect
143. Q8×C22⋊C4C2×C47direct (N × H)
144. C2×#391C2×C47semidirect
148. C2×C47Q8×C22⋊C4direct (N × H)
155. C23×Q8C4×C47semidirect
161. C2×C4×Q8C22×C47semidirect
166. #391C22×C47semidirect
171. C47C2×Q8×C22⋊C4direct (N × H)
178. C22×Q8C2×C4×C47semidirect
193. C2×C22⋊C4Q8×C47direct (N × H)
210. C2×Q8C22⋊C4×C47direct (N × H)
226. C22×C4C2×Q8×C47semidirect
233. C22⋊C4C2×Q8×C47direct (N × H)
241. C23C4×Q8×C47semidirect
252. Q8C2×C22⋊C4×C47direct (N × H)
267. C2×C4C22×Q8×C47semidirect
275. C22C2×C4×Q8×C47semidirect
289. C2Q8×C22⋊C4×C47direct (N × H)

Maximal subgroups

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

subgroupindex
C24×Q8×C472
C22×C4×Q8×C472
Q8×C22⋊C4×C472
C2×C47×#3912
C2×C47×#3802
C2×C4×C22⋊C4×C472
C2×Q8×C22⋊C447