Finite Group Databasebeta

← C151×#11441 #50316366

Subgroups — C151×#11441 #50316366

Order 38656.

392 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×#424×C151C211yesmaximal, characteristic
2#2112×C151C211yesmaximal, characteristic
3C2×C22⋊C16×C151C211yesmaximal, characteristic
4#1322×C151C214yesmaximal, complemented
5C22×M16×C151C411yescharacteristic
6C23×C8×C151C2211yescharacteristic
7C2×#117×C151C411yescharacteristic
8C2×M32×C151—21no—
9C22×C16×C151—21no—
10#424×C151—21no—
11#424×C151—21no—
12#424×C151—21no—
13#424×C151—21no—
14C2×C4⋊C8×C151C412yes—
15C2×C4⋊C8×C151C2212yes—
16C22⋊C16×C151—21no—
17C22⋊C16×C151—21no—
18C22⋊C16×C151C2212yes—
19C22⋊C16×C151C2212yes—
20C23×C4×C151C2×C411yescharacteristic
21C2×M16×C151—21no—
22C2×M16×C151—21no—
23C2×M16×C151—42no—
24C22×C8×C151—42no—
25C22×C8×C151C2×C412yes—
26C22×C8×C151C2×C411yescharacteristic
27C22×C8×C151D411yescharacteristic
28C22×C8×C151D411yescharacteristic
29C22×C8×C151D411yescharacteristic
30C22×C8×C151D411yescharacteristic
31C22×C8×C151C2311yescharacteristic
32#117×C151—21no—
33#117×C151—21no—
34#117×C151—21no—
35#117×C151—21no—
36C2×C4⋊C4×C151C811yescharacteristic
37C2×C4⋊C4×C151C811yescharacteristic
38C2×C22⋊C4×C151C812yes—
39C2×C42×C151C2×C412yes—
40M32×C151—42no—
41C2×C16×C151—22no—
42C2×C16×C151—22no—
43C2×C16×C151—42no—
44C4⋊C8×C151—22no—
45C4⋊C8×C151—22no—
46C4⋊C8×C151—22no—
47C4⋊C8×C151—22no—
48C24×C151C2×C811yescharacteristic
49C22×C4×C151—22no—
50C22×C4×C151—22no—
51C22×C4×C151C22⋊C411yescharacteristic
52C22×C4×C151C22⋊C411yescharacteristic
53C22×C4×C151C2×C812yes—
54C22×C4×C151C2×C811yescharacteristic
55C22×C4×C151C2×C812yes—
56C22×C4×C151M1611yescharacteristic
57C22×C4×C151M1611yescharacteristic
58C22×C4×C151C22×C411yescharacteristic
59M16×C151—42no—
60M16×C151—42no—
61C2×C8×C151—22no—
62C2×C8×C151—22no—
63C2×C8×C151—22no—
64C2×C8×C151—41no—
65C2×C8×C151—41no—
66C2×C8×C151—41no—
67C2×C8×C151—41no—
68C2×C8×C151—42no—
69C2×C8×C151C22⋊C411yescharacteristic
70C2×C8×C151C22⋊C411yescharacteristic
71C2×C8×C151C2×D411yescharacteristic
72C2×C8×C151C2×D411yescharacteristic
73C4⋊C4×C151—21no—
74C4⋊C4×C151—21no—
75C4⋊C4×C151—21no—
76C4⋊C4×C151—21no—
77C22⋊C4×C151—22no—
78C22⋊C4×C151—22no—
79C42×C151—22no—
80C42×C151—22no—
81C16×C151—42no—
82C16×C151—42no—
83C23×C151—22no—
84C23×C151—22no—
85C23×C151—41no—
86C23×C151C22⋊C811yescharacteristic
87C23×C151C22⋊C811yescharacteristic
88C23×C151C22×C811yescharacteristic
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—24no—
99C2×C4×C151—42no—
100C2×C4×C151C22⋊C811yescharacteristic
101C2×C4×C151C22⋊C811yescharacteristic
102C2×C4×C151#9912yes—
103C2×C4×C151#10112yes—
104C2×C4×C151C2×C22⋊C411yescharacteristic
105C2×C4×C151C2×M1611yescharacteristic
106C8×C151—21no—
107C8×C151—21no—
108C8×C151—21no—
109C8×C151—21no—
110C8×C151—42no—
111C22×C151—21no—
112C22×C151—21no—
113C22×C151—21no—
114C22×C151—21no—
115C22×C151—21no—
116C22×C151—21no—
117C22×C151—21no—
118C22×C151—44no—
119C22×C151#32412yes—
120C22×C151C2×C22⋊C811yescharacteristic
121C22×C151#50412yes—
122C4×C151—21no—
123C4×C151—21no—
124C4×C151—42no—
125C4×C151—42no—
126C4×C151#32412yes—
127C4×C151C2×#9911yescharacteristic
128C4×C151C2×#10111yescharacteristic
129C2×C151—22no—
130C2×C151—22no—
131C2×C151—41no—
132C2×C151C2×#32411yescharacteristic
133C2×C151#211311yescharacteristic
134C2×C151#211511yescharacteristic
135#11441C15111yesmaximal, characteristic, direct product factor, Sylow
136C151#1144111yescharacteristic, direct product factor, Sylow
137C2×#424C2×C15111yescharacteristic
138#2112C2×C15111yescharacteristic
139C2×C22⋊C16C2×C15111yescharacteristic
140#1322C2×C15114yescomplemented
141C22×M16C4×C15111yescharacteristic
142C23×C8C22×C15111yescharacteristic
143C2×#117C4×C15111yescharacteristic
144C2×M32—21no—
145C22×C16—21no—
146#424—21no—
147#424—21no—
148#424—21no—
149#424—21no—
150C2×C4⋊C8C4×C15112yes—
151C2×C4⋊C8C22×C15112yes—
152C22⋊C16—21no—
153C22⋊C16—21no—
154C22⋊C16C22×C15112yes—
155C22⋊C16C22×C15112yes—
156C23×C4C2×C4×C15111yescharacteristic
157C2×M16—21no—
158C2×M16—21no—
159C2×M16—42no—
160C22×C8—42no—
161C22×C8C2×C4×C15112yes—
162C22×C8C2×C4×C15111yescharacteristic
163C22×C8D4×C15111yescharacteristic
164C22×C8D4×C15111yescharacteristic
165C22×C8D4×C15111yescharacteristic
166C22×C8D4×C15111yescharacteristic
167C22×C8C23×C15111yescharacteristic
168#117—21no—
169#117—21no—
170#117—21no—
171#117—21no—
172C2×C4⋊C4C8×C15111yescharacteristic
173C2×C4⋊C4C8×C15111yescharacteristic
174C2×C22⋊C4C8×C15112yes—
175C2×C42C2×C4×C15112yes—
176M32—42no—
177C2×C16—22no—
178C2×C16—22no—
179C2×C16—42no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—22no—
184C24C2×C8×C15111yescharacteristic
185C22×C4—22no—
186C22×C4—22no—
187C22×C4C22⋊C4×C15111yescharacteristic
188C22×C4C22⋊C4×C15111yescharacteristic
189C22×C4C2×C8×C15112yes—
190C22×C4C2×C8×C15111yescharacteristic
191C22×C4C2×C8×C15112yes—
192C22×C4M16×C15111yescharacteristic
193C22×C4M16×C15111yescharacteristic
194C22×C4C22×C4×C15111yescharacteristic
195M16—42no—
196M16—42no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—42no—
205C2×C8C22⋊C4×C15111yescharacteristic
206C2×C8C22⋊C4×C15111yescharacteristic
207C2×C8C2×D4×C15111yescharacteristic
208C2×C8C2×D4×C15111yescharacteristic
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C22⋊C4—22no—
214C22⋊C4—22no—
215C42—22no—
216C42—22no—
217C16—42no—
218C16—42no—
219C23—22no—
220C23—22no—
221C23—41no—
222C23C22⋊C8×C15111yescharacteristic
223C23C22⋊C8×C15111yescharacteristic
224C23C22×C8×C15111yescharacteristic
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—42no—
236C2×C4C22⋊C8×C15111yescharacteristic
237C2×C4C22⋊C8×C15111yescharacteristic
238C2×C4#99×C15112yes—
239C2×C4#101×C15112yes—
240C2×C4C2×C22⋊C4×C15111yescharacteristic
241C2×C4C2×M16×C15111yescharacteristic
242C8—21no—
243C8—21no—
244C8—21no—
245C8—21no—
246C8—42no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—44no—
255C22#324×C15112yes—
256C22C2×C22⋊C8×C15111yescharacteristic
257C22#504×C15112yes—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—42no—
262C4#324×C15112yes—
263C4C2×#99×C15111yescharacteristic
264C4C2×#101×C15111yescharacteristic
265C2—22no—
266C2—22no—
267C2—41no—
268C2C2×#324×C15111yescharacteristic
269C2#2113×C15111yescharacteristic
270C2#2115×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151C2×C22⋊C4
commutatorC23C22×C8×C151
Frattini, cosocleC22×C8C23×C151
socleC22×C151C2×C22⋊C8
prime radicalC24×C151C2×C8
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C23×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1322×C151C2semidirect
135. #11441C151direct (N × H)
136. C151#11441direct (N × H)
140. #1322C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#424×C1512
#2112×C1512
C2×C22⋊C16×C1512
#1322×C1512
#11441151