Finite Group Databasebeta

← C151×#9106 #50314031

Subgroups — C151×#9106 #50314031

Order 38656.

522 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
1#2983×C151C211yesmaximal, characteristic, complemented
2#2326×C151C211yesmaximal, characteristic
3#1478×C151C212yesmaximal
4#1461×C151C211yesmaximal, characteristic, complemented
5#1274×C151C212yesmaximal, complemented
6C2×#124×C151C411yescharacteristic
7C2×C4×Q8×C151C2211yescharacteristic
8C2×C4×D4×C151C2211yescharacteristic
9#446×C151—24no—
10#432×C151—22no—
11#431×C151C2212yes—
12#431×C151C2212yes—
13#391×C151C411yescharacteristic
14#390×C151C411yescharacteristic
15#388×C151—22no—
16#385×C151—22no—
17#384×C151C411yescharacteristic
18#376×C151C2211yescharacteristic
19D4⋊C8×C151—24no—
20#324×C151—22no—
21C22×Q8×C151C2×C411yescharacteristic
22C22×D4×C151C2×C411yescharacteristic
23C23×C4×C151—21no—
24#124×C151—22no—
25#124×C151—22no—
26C4×Q8×C151—22no—
27C4×Q8×C151—22no—
28C4×D4×C151—22no—
29C4×D4×C151—22no—
30C2×C4⋊C4×C151—22no—
31C2×C4⋊C4×C151C2×C411yescharacteristic
32C2×C4⋊C4×C151C2×C411yescharacteristic
33C2×C4⋊C4×C151D412yes—
34C2×C22⋊C4×C151—22no—
35C2×C22⋊C4×C151—21no—
36C2×C22⋊C4×C151—22no—
37C2×C42×C151C2×C411yescharacteristic
38C2×C42×C151C2×C411yescharacteristic
39C2×C42×C151D412yes—
40C2×C42×C151C2311yescharacteristic
41C4⋊C8×C151—24no—
42C4⋊C8×C151—22no—
43C4⋊C8×C151—22no—
44C22⋊C8×C151—22no—
45C22⋊C8×C151—22no—
46#97×C151—24no—
47C4×C8×C151—22no—
48C4×C8×C151D414yes—
49#95×C151—22no—
50#95×C151—21no—
51#95×C151—21no—
52C24×C151—21no—
53C2×Q8×C151—22no—
54C2×Q8×C151—21no—
55C2×Q8×C151—21no—
56C2×Q8×C151—22no—
57C2×D4×C151—22no—
58C2×D4×C151—21no—
59C2×D4×C151—22no—
60C2×D4×C151M1612yes—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—42no—
65C22×C4×C151—82no—
66C22×C4×C151C22⋊C412yes—
67C22×C4×C151C22⋊C412yes—
68C22×C4×C151C22×C411yescharacteristic
69C22×C4×C151C2×D411yescharacteristic
70C22×C4×C151C2×D411yescharacteristic
71C2×C8×C151—24no—
72C2×C8×C151—42no—
73C4⋊C4×C151—22no—
74C4⋊C4×C151—24no—
75C4⋊C4×C151—22no—
76C4⋊C4×C151—82no—
77C22⋊C4×C151—28no—
78C22⋊C4×C151—41no—
79C22⋊C4×C151—41no—
80C22⋊C4×C151—82no—
81C42×C151—22no—
82C42×C151—22no—
83C42×C151—21no—
84C42×C151—22no—
85C42×C151M1612yes—
86C42×C151C2×D412yes—
87C42×C151#4112yes—
88C23×C151—22no—
89C23×C151—42no—
90C23×C151—42no—
91C23×C151—41no—
92C23×C151—41no—
93C23×C151C2×C22⋊C411yescharacteristic
94Q8×C151—42no—
95Q8×C151—42no—
96D4×C151—24no—
97D4×C151—42no—
98C2×C4×C151—22no—
99C2×C4×C151—22no—
100C2×C4×C151—22no—
101C2×C4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151—41no—
104C2×C4×C151—41no—
105C2×C4×C151—41no—
106C2×C4×C151—41no—
107C2×C4×C151—42no—
108C2×C4×C151—41no—
109C2×C4×C151—42no—
110C2×C4×C151—41no—
111C2×C4×C151—41no—
112C2×C4×C151—41no—
113C2×C4×C151—84no—
114C2×C4×C151C4×D412yes—
115C2×C4×C151#12011yescharacteristic
116C2×C4×C151#12112yes—
117C2×C4×C151#12311yescharacteristic
118C2×C4×C151C2×M1611yescharacteristic
119C2×C4×C151C2×M1611yescharacteristic
120C2×C4×C151#13112yes—
121C8×C151—44no—
122C8×C151—82no—
123C22×C151—21no—
124C22×C151—21no—
125C22×C151—44no—
126C22×C151—42no—
127C22×C151—82no—
128C22×C151—81no—
129C22×C151—81no—
130C22×C151#38611yescharacteristic
131C22×C151#40711yescharacteristic
132C22×C151#40811yescharacteristic
133C4×C151—22no—
134C4×C151—21no—
135C4×C151—21no—
136C4×C151—42no—
137C4×C151—42no—
138C4×C151—42no—
139C4×C151—81no—
140C4×C151—81no—
141C4×C151#43512yes—
142C4×C151#43612yes—
143C2×C151—21no—
144C2×C151—21no—
145C2×C151—82no—
146C2×C151#187011yescharacteristic
147C2×C151#191011yescharacteristic
148C2×C151#191211yescharacteristic
149#9106C15111yesmaximal, characteristic, direct product factor, Sylow
150C151#910611yescharacteristic, direct product factor, Sylow
151#2983C2×C15111yescharacteristic, complemented
152#2326C2×C15111yescharacteristic
153#1478C2×C15112yes—
154#1461C2×C15111yescharacteristic, complemented
155#1274C2×C15112yescomplemented
156C2×#124C4×C15111yescharacteristic
157C2×C4×Q8C22×C15111yescharacteristic
158C2×C4×D4C22×C15111yescharacteristic
159#446—24no—
160#432—22no—
161#431C22×C15112yes—
162#431C22×C15112yes—
163#391C4×C15111yescharacteristic
164#390C4×C15111yescharacteristic
165#388—22no—
166#385—22no—
167#384C4×C15111yescharacteristic
168#376C22×C15111yescharacteristic
169D4⋊C8—24no—
170#324—22no—
171C22×Q8C2×C4×C15111yescharacteristic
172C22×D4C2×C4×C15111yescharacteristic
173C23×C4—21no—
174#124—22no—
175#124—22no—
176C4×Q8—22no—
177C4×Q8—22no—
178C4×D4—22no—
179C4×D4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4C2×C4×C15111yescharacteristic
182C2×C4⋊C4C2×C4×C15111yescharacteristic
183C2×C4⋊C4D4×C15112yes—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—22no—
187C2×C42C2×C4×C15111yescharacteristic
188C2×C42C2×C4×C15111yescharacteristic
189C2×C42D4×C15112yes—
190C2×C42C23×C15111yescharacteristic
191C4⋊C8—24no—
192C4⋊C8—22no—
193C4⋊C8—22no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#97—24no—
197C4×C8—22no—
198C4×C8D4×C15114yes—
199#95—22no—
200#95—21no—
201#95—21no—
202C24—21no—
203C2×Q8—22no—
204C2×Q8—21no—
205C2×Q8—21no—
206C2×Q8—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—22no—
210C2×D4M16×C15112yes—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—42no—
215C22×C4—82no—
216C22×C4C22⋊C4×C15112yes—
217C22×C4C22⋊C4×C15112yes—
218C22×C4C22×C4×C15111yescharacteristic
219C22×C4C2×D4×C15111yescharacteristic
220C22×C4C2×D4×C15111yescharacteristic
221C2×C8—24no—
222C2×C8—42no—
223C4⋊C4—22no—
224C4⋊C4—24no—
225C4⋊C4—22no—
226C4⋊C4—82no—
227C22⋊C4—28no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—82no—
231C42—22no—
232C42—22no—
233C42—21no—
234C42—22no—
235C42M16×C15112yes—
236C42C2×D4×C15112yes—
237C42#41×C15112yes—
238C23—22no—
239C23—42no—
240C23—42no—
241C23—41no—
242C23—41no—
243C23C2×C22⋊C4×C15111yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—24no—
247D4—42no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—84no—
264C2×C4C4×D4×C15112yes—
265C2×C4#120×C15111yescharacteristic
266C2×C4#121×C15112yes—
267C2×C4#123×C15111yescharacteristic
268C2×C4C2×M16×C15111yescharacteristic
269C2×C4C2×M16×C15111yescharacteristic
270C2×C4#131×C15112yes—
271C8—44no—
272C8—82no—
273C22—21no—
274C22—21no—
275C22—44no—
276C22—42no—
277C22—82no—
278C22—81no—
279C22—81no—
280C22#386×C15111yescharacteristic
281C22#407×C15111yescharacteristic
282C22#408×C15111yescharacteristic
283C4—22no—
284C4—21no—
285C4—21no—
286C4—42no—
287C4—42no—
288C4—42no—
289C4—81no—
290C4—81no—
291C4#435×C15112yes—
292C4#436×C15112yes—
293C2—21no—
294C2—21no—
295C2—82no—
296C2#1870×C15111yescharacteristic
297C2#1910×C15111yescharacteristic
298C2#1912×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2983×C151C2semidirect
4. #1461×C151C2semidirect
5. #1274×C151C2semidirect
149. #9106C151direct (N × H)
150. C151#9106direct (N × H)
151. #2983C2×C151semidirect
154. #1461C2×C151semidirect
155. #1274C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2983×C1512
#2326×C1512
#1478×C1512
#1461×C1512
#1274×C1512
#9106151