Finite Group Databasebeta

← C151×#8701 #50313626

Subgroups — C151×#8701 #50313626

Order 38656.

642 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
2#1817×C151C212yesmaximal
3#1280×C151C214yesmaximal
4C22×C4⋊C4×C151C411yescharacteristic
5C22×C4⋊C4×C151C411yescharacteristic
6C22×C42×C151C412yes—
7C22×C42×C151C2211yescharacteristic
8C2×C22⋊C8×C151C2214yes—
9C4×C4⋊C4×C151—22no—
10C4×C4⋊C4×C151—22no—
11C2×#95×C151C2212yes—
12#336×C151—22no—
13#336×C151—22no—
14C23×C4×C151C2×C411yescharacteristic
15C23×C4×C151C2×C411yescharacteristic
16C23×C4×C151C2×C412yes—
17C23×C4×C151C2×C412yes—
18C23×C4×C151C2311yescharacteristic
19C22×C8×C151—24no—
20C2×C4⋊C4×C151—22no—
21C2×C4⋊C4×C151—22no—
22C2×C4⋊C4×C151—24no—
23C2×C4⋊C4×C151—22no—
24C2×C4⋊C4×C151C814yescomplemented
25C2×C42×C151—24no—
26C2×C42×C151—22no—
27C2×C42×C151—22no—
28C2×C42×C151—44no—
29C2×C42×C151D412yes—
30C2×C42×C151D412yes—
31C22⋊C8×C151—28no—
32#95×C151—24no—
33C24×C151C22×C411yescharacteristic
34C22×C4×C151—22no—
35C22×C4×C151—22no—
36C22×C4×C151—22no—
37C22×C4×C151—22no—
38C22×C4×C151—22no—
39C22×C4×C151—22no—
40C22×C4×C151—22no—
41C22×C4×C151—22no—
42C22×C4×C151—22no—
43C22×C4×C151—41no—
44C22×C4×C151—41no—
45C22×C4×C151—42no—
46C22×C4×C151—42no—
47C22×C4×C151—42no—
48C22×C4×C151—42no—
49C22×C4×C151C22⋊C412yes—
50C22×C4×C151C22⋊C411yescharacteristic
51C22×C4×C151C22⋊C411yescharacteristic
52C22×C4×C151C2×C812yes—
53C22×C4×C151C2×C814yes—
54C22×C4×C151M1612yes—
55C22×C4×C151M1614yes—
56C22×C4×C151C2×D412yes—
57C22×C4×C151#4114yes—
58C2×C8×C151—44no—
59C2×C8×C151—44no—
60C2×C8×C151—44no—
61C4⋊C4×C151—28no—
62C4⋊C4×C151—28no—
63C42×C151—24no—
64C42×C151—24no—
65C42×C151—44no—
66C42×C151—44no—
67C23×C151—21no—
68C23×C151—21no—
69C23×C151—21no—
70C23×C151—21no—
71C23×C151C2×C22⋊C411yescharacteristic
72C23×C151#11712yes—
73C23×C151C22×C811yescharacteristic
74C23×C151C2×M1611yescharacteristic
75C23×C151C2×M1612yes—
76C2×C4×C151—28no—
77C2×C4×C151—22no—
78C2×C4×C151—21no—
79C2×C4×C151—21no—
80C2×C4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151—22no—
83C2×C4×C151—21no—
84C2×C4×C151—21no—
85C2×C4×C151—24no—
86C2×C4×C151—24no—
87C2×C4×C151—24no—
88C2×C4×C151—24no—
89C2×C4×C151—44no—
90C2×C4×C151—44no—
91C2×C4×C151—44no—
92C2×C4×C151—42no—
93C2×C4×C151—42no—
94C2×C4×C151—42no—
95C2×C4×C151—42no—
96C2×C4×C151—44no—
97C2×C4×C151—44no—
98C2×C4×C151C22⋊C814yes—
99C2×C4×C151#10012yes—
100C2×C4×C151#10112yes—
101C2×C4×C151#12314yes—
102C8×C151—84no—
103C22×C151—22no—
104C22×C151—22no—
105C22×C151—21no—
106C22×C151—21no—
107C22×C151—21no—
108C22×C151—21no—
109C22×C151—22no—
110C22×C151—22no—
111C22×C151#38111yescharacteristic
112C22×C151C2×C22⋊C811yescharacteristic
113C22×C151#40711yescharacteristic
114C22×C151#41011yescharacteristic
115C22×C151#41011yescharacteristic
116C22×C151C2×#10011yescharacteristic
117C22×C151C2×#10111yescharacteristic
118C22×C151#43112yes—
119C22×C151#43212yes—
120C4×C151—24no—
121C4×C151—24no—
122C4×C151—22no—
123C4×C151—22no—
124C4×C151—44no—
125C4×C151—44no—
126C2×C151—22no—
127C2×C151—22no—
128C2×C151#146011yescharacteristic
129C2×C151#146111yescharacteristic
130C2×C151#146611yescharacteristic
131C2×C151#146711yescharacteristic
132C2×C151#181711yescharacteristic
133C2×C151#182011yescharacteristic
134C2×C151#182111yescharacteristic
135#8701C15111yesmaximal, characteristic, direct product factor, Sylow
136C151#870111yescharacteristic, direct product factor, Sylow
137C2×C4×C4⋊C4C2×C15111yescharacteristic
138#1817C2×C15112yes—
139#1280C2×C15114yes—
140C22×C4⋊C4C4×C15111yescharacteristic
141C22×C4⋊C4C4×C15111yescharacteristic
142C22×C42C4×C15112yes—
143C22×C42C22×C15111yescharacteristic
144C2×C22⋊C8C22×C15114yes—
145C4×C4⋊C4—22no—
146C4×C4⋊C4—22no—
147C2×#95C22×C15112yes—
148#336—22no—
149#336—22no—
150C23×C4C2×C4×C15111yescharacteristic
151C23×C4C2×C4×C15111yescharacteristic
152C23×C4C2×C4×C15112yes—
153C23×C4C2×C4×C15112yes—
154C23×C4C23×C15111yescharacteristic
155C22×C8—24no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4C8×C15114yescomplemented
161C2×C42—24no—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—44no—
165C2×C42D4×C15112yes—
166C2×C42D4×C15112yes—
167C22⋊C8—28no—
168#95—24no—
169C24C22×C4×C15111yescharacteristic
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4C22⋊C4×C15112yes—
186C22×C4C22⋊C4×C15111yescharacteristic
187C22×C4C22⋊C4×C15111yescharacteristic
188C22×C4C2×C8×C15112yes—
189C22×C4C2×C8×C15114yes—
190C22×C4M16×C15112yes—
191C22×C4M16×C15114yes—
192C22×C4C2×D4×C15112yes—
193C22×C4#41×C15114yes—
194C2×C8—44no—
195C2×C8—44no—
196C2×C8—44no—
197C4⋊C4—28no—
198C4⋊C4—28no—
199C42—24no—
200C42—24no—
201C42—44no—
202C42—44no—
203C23—21no—
204C23—21no—
205C23—21no—
206C23—21no—
207C23C2×C22⋊C4×C15111yescharacteristic
208C23#117×C15112yes—
209C23C22×C8×C15111yescharacteristic
210C23C2×M16×C15111yescharacteristic
211C23C2×M16×C15112yes—
212C2×C4—28no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—24no—
222C2×C4—24no—
223C2×C4—24no—
224C2×C4—24no—
225C2×C4—44no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—44no—
234C2×C4C22⋊C8×C15114yes—
235C2×C4#100×C15112yes—
236C2×C4#101×C15112yes—
237C2×C4#123×C15114yes—
238C8—84no—
239C22—22no—
240C22—22no—
241C22—21no—
242C22—21no—
243C22—21no—
244C22—21no—
245C22—22no—
246C22—22no—
247C22#381×C15111yescharacteristic
248C22C2×C22⋊C8×C15111yescharacteristic
249C22#407×C15111yescharacteristic
250C22#410×C15111yescharacteristic
251C22#410×C15111yescharacteristic
252C22C2×#100×C15111yescharacteristic
253C22C2×#101×C15111yescharacteristic
254C22#431×C15112yes—
255C22#432×C15112yes—
256C4—24no—
257C4—22no—
258C4—22no—
259C4—24no—
260C4—44no—
261C4—44no—
262C2—22no—
263C2—22no—
264C2#1460×C15111yescharacteristic
265C2#1461×C15111yescharacteristic
266C2#1466×C15111yescharacteristic
267C2#1467×C15111yescharacteristic
268C2#1817×C15111yescharacteristic
269C2#1820×C15111yescharacteristic
270C2#1821×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC23C22×C8×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC24×C151C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
24. C2×C4⋊C4×C151C8semidirect
135. #8701C151direct (N × H)
136. C151#8701direct (N × H)
160. C2×C4⋊C4C8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊C4×C1512
#1817×C1512
#1280×C1512
#8701151