Finite Group Databasebeta

← C151×#12624 #50317549

Subgroups — C151×#12624 #50317549

Order 38656.

456 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2930×C151C211yesmaximal, characteristic
2#2120×C151C212yesmaximal
3#1757×C151C212yesmaximal, complemented
4#1392×C151C211yesmaximal, characteristic, complemented
5#1391×C151C211yesmaximal, characteristic, complemented
6C2×#131×C151C2211yescharacteristic
7C22×M16×C151C411yescharacteristic, complemented
8#525×C151C2211yescharacteristic
9#436×C151—22no—
10#435×C151—22no—
11#424×C151C411yescharacteristic, complemented
12#413×C151C2212yes—
13#410×C151C2212yes—
14#408×C151C2211yescharacteristic
15#407×C151C411yescharacteristic, complemented
16#405×C151—22no—
17#405×C151C411yescharacteristic, complemented
18#352×C151C414yescomplemented
19AΣL(1,𝔽16)×C151C414yescomplemented
20#344×C151—22no—
21C2×#41×C151C2311yescharacteristic
22C23×C4×C151C2×C411yescharacteristic
23#131×C151—42no—
24C2×M16×C151—21no—
25C2×M16×C151—21no—
26C2×M16×C151—22no—
27C2×M16×C151—42no—
28C2×M16×C151C2×C411yescharacteristic
29C2×M16×C151C2×C411yescharacteristic
30C2×M16×C151D412yes—
31C22×C8×C151C2×C411yescharacteristic
32C22×C8×C151C2×C411yescharacteristic
33C22×C8×C151D412yes—
34#123×C151C2×C412yes—
35C22⋊Q8×C151—21no—
36#121×C151—21no—
37#120×C151C2×C412yes—
38C4×D4×C151—22no—
39#117×C151—22no—
40#117×C151C2×C411yescharacteristic
41C4⋊C8×C151—22no—
42#101×C151—22no—
43#100×C151C2×C414yes—
44#99×C151—22no—
45#99×C151C2×C414yes—
46C22⋊C8×C151—22no—
47C22⋊C8×C151—22no—
48#97×C151—21no—
49#97×C151—42no—
50C4×C8×C151—21no—
51C4×C8×C151—42no—
52C24×C151C4211yescharacteristic
53#41×C151—41no—
54#41×C151—41no—
55C2×Q8×C151#4111yescharacteristic
56C2×D4×C151—22no—
57C2×D4×C151C22×C412yes—
58C2×D4×C151#4111yescharacteristic
59C22×C4×C151—21no—
60C22×C4×C151—21no—
61C22×C4×C151—41no—
62C22×C4×C151—41no—
63C22×C4×C151C4211yescharacteristic
64C22×C4×C151C22×C411yescharacteristic
65C22×C4×C151C2×D412yes—
66M16×C151—24no—
67M16×C151—41no—
68M16×C151—42no—
69M16×C151—42no—
70M16×C151—42no—
71M16×C151—42no—
72M16×C151—41no—
73C2×C8×C151—22no—
74C2×C8×C151—22no—
75C2×C8×C151—22no—
76C2×C8×C151—21no—
77C2×C8×C151—21no—
78C2×C8×C151—42no—
79C2×C8×C151—41no—
80C2×C8×C151C22⋊C411yescharacteristic
81C2×C8×C151C22⋊C412yes—
82C2×C8×C151C22⋊C411yescharacteristic
83C4⋊C4×C151—21no—
84C4⋊C4×C151—22no—
85C4⋊C4×C151—42no—
86C22⋊C4×C151—22no—
87C22⋊C4×C151—22no—
88C22⋊C4×C151—24no—
89C22⋊C4×C151C4212yes—
90C42×C151—21no—
91C42×C151—42no—
92C23×C151—21no—
93C23×C151—41no—
94C23×C151—81no—
95C23×C151C2×C4211yescharacteristic
96C23×C151C4×D412yes—
97Q8×C151—41no—
98D4×C151—42no—
99D4×C151—41no—
100D4×C151—82no—
101C2×C4×C151—22no—
102C2×C4×C151—21no—
103C2×C4×C151—22no—
104C2×C4×C151—21no—
105C2×C4×C151—22no—
106C2×C4×C151—21no—
107C2×C4×C151—42no—
108C2×C4×C151—41no—
109C2×C4×C151—41no—
110C2×C4×C151—41no—
111C2×C4×C151—44no—
112C2×C4×C151C2×C22⋊C411yescharacteristic
113C2×C4×C151#11711yescharacteristic
114C2×C4×C151C4×D412yes—
115C8×C151—22no—
116C8×C151—21no—
117C8×C151—44no—
118C8×C151—41no—
119C8×C151—41no—
120C8×C151#9912yes—
121C22×C151—22no—
122C22×C151—21no—
123C22×C151—42no—
124C22×C151—41no—
125C22×C151—41no—
126C22×C151—41no—
127C22×C151—41no—
128C22×C151—82no—
129C22×C151C4×C22⋊C411yescharacteristic
130C4×C151—22no—
131C4×C151—21no—
132C4×C151—42no—
133C4×C151—41no—
134C4×C151—84no—
135C4×C151C2×#9911yescharacteristic
136C4×C151#41011yescharacteristic
137C2×C151—21no—
138C2×C151—42no—
139C2×C151—41no—
140C2×C151—81no—
141C2×C151C4×#9911yescharacteristic
142#12624C15111yesmaximal, characteristic, direct product factor, Sylow
143C151#1262411yescharacteristic, direct product factor, Sylow
144#2930C2×C15111yescharacteristic
145#2120C2×C15112yes—
146#1757C2×C15112yescomplemented
147#1392C2×C15111yescharacteristic, complemented
148#1391C2×C15111yescharacteristic, complemented
149C2×#131C22×C15111yescharacteristic
150C22×M16C4×C15111yescharacteristic, complemented
151#525C22×C15111yescharacteristic
152#436—22no—
153#435—22no—
154#424C4×C15111yescharacteristic, complemented
155#413C22×C15112yes—
156#410C22×C15112yes—
157#408C22×C15111yescharacteristic
158#407C4×C15111yescharacteristic, complemented
159#405—22no—
160#405C4×C15111yescharacteristic, complemented
161#352C4×C15114yescomplemented
162AΣL(1,𝔽16)C4×C15114yescomplemented
163#344—22no—
164C2×#41C23×C15111yescharacteristic
165C23×C4C2×C4×C15111yescharacteristic
166#131—42no—
167C2×M16—21no—
168C2×M16—21no—
169C2×M16—22no—
170C2×M16—42no—
171C2×M16C2×C4×C15111yescharacteristic
172C2×M16C2×C4×C15111yescharacteristic
173C2×M16D4×C15112yes—
174C22×C8C2×C4×C15111yescharacteristic
175C22×C8C2×C4×C15111yescharacteristic
176C22×C8D4×C15112yes—
177#123C2×C4×C15112yes—
178C22⋊Q8—21no—
179#121—21no—
180#120C2×C4×C15112yes—
181C4×D4—22no—
182#117—22no—
183#117C2×C4×C15111yescharacteristic
184C4⋊C8—22no—
185#101—22no—
186#100C2×C4×C15114yes—
187#99—22no—
188#99C2×C4×C15114yes—
189C22⋊C8—22no—
190C22⋊C8—22no—
191#97—21no—
192#97—42no—
193C4×C8—21no—
194C4×C8—42no—
195C24C42×C15111yescharacteristic
196#41—41no—
197#41—41no—
198C2×Q8#41×C15111yescharacteristic
199C2×D4—22no—
200C2×D4C22×C4×C15112yes—
201C2×D4#41×C15111yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C42×C15111yescharacteristic
207C22×C4C22×C4×C15111yescharacteristic
208C22×C4C2×D4×C15112yes—
209M16—24no—
210M16—41no—
211M16—42no—
212M16—42no—
213M16—42no—
214M16—42no—
215M16—41no—
216C2×C8—22no—
217C2×C8—22no—
218C2×C8—22no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—42no—
222C2×C8—41no—
223C2×C8C22⋊C4×C15111yescharacteristic
224C2×C8C22⋊C4×C15112yes—
225C2×C8C22⋊C4×C15111yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—22no—
228C4⋊C4—42no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—24no—
232C22⋊C4C42×C15112yes—
233C42—21no—
234C42—42no—
235C23—21no—
236C23—41no—
237C23—81no—
238C23C2×C42×C15111yescharacteristic
239C23C4×D4×C15112yes—
240Q8—41no—
241D4—41no—
242D4—42no—
243D4—82no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—44no—
255C2×C4C2×C22⋊C4×C15111yescharacteristic
256C2×C4#117×C15111yescharacteristic
257C2×C4C4×D4×C15112yes—
258C8—21no—
259C8—22no—
260C8—44no—
261C8—41no—
262C8—41no—
263C8#99×C15112yes—
264C22—22no—
265C22—21no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—82no—
272C22C4×C22⋊C4×C15111yescharacteristic
273C4—22no—
274C4—21no—
275C4—42no—
276C4—41no—
277C4—84no—
278C4C2×#99×C15111yescharacteristic
279C4#410×C15111yescharacteristic
280C2—21no—
281C2—42no—
282C2—41no—
283C2—81no—
284C2C4×#99×C15111yescharacteristic
subgroupG/H
centerC4×C151C2×#99
commutatorC23C2×C42×C151
Frattini, cosocleC2×#41C23×C151
socleC2×C151C4×#99
prime radical#525×C151C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C2×C8×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1757×C151C2semidirect
4. #1392×C151C2semidirect
5. #1391×C151C2semidirect
7. C22×M16×C151C4semidirect
11. #424×C151C4semidirect
15. #407×C151C4semidirect
17. #405×C151C4semidirect
18. #352×C151C4semidirect
19. AΣL(1,𝔽16)×C151C4semidirect
142. #12624C151direct (N × H)
143. C151#12624direct (N × H)
146. #1757C2×C151semidirect
147. #1392C2×C151semidirect
148. #1391C2×C151semidirect
150. C22×M16C4×C151semidirect
154. #424C4×C151semidirect
158. #407C4×C151semidirect
160. #405C4×C151semidirect
161. #352C4×C151semidirect
162. AΣL(1,𝔽16)C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2930×C1512
#2120×C1512
#1757×C1512
#1392×C1512
#1391×C1512
#12624151