Finite Group Databasebeta

← C151×#11514 #50316439

Subgroups — C151×#11514 #50316439

Order 38656.

434 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2317×C151C211yesmaximal, characteristic
2#1463×C151C212yesmaximal
3#1325×C151C212yesmaximal, complemented
4#1324×C151C212yesmaximal, complemented
5C2×#117×C151C411yescharacteristic
6C2×#117×C151C411yescharacteristic
7C22×C4⋊C4×C151C2211yescharacteristic
8#407×C151—22no—
9#389×C151—22no—
10#385×C151—22no—
11#384×C151C411yescharacteristic
12#384×C151C2211yescharacteristic
13#382×C151C411yescharacteristic
14#382×C151C2211yescharacteristic
15#324×C151—22no—
16#324×C151C2214yes—
17C23×C4×C151C2×C411yescharacteristic
18C23×C4×C151D412yes—
19C2×M16×C151—42no—
20#117×C151—22no—
21#117×C151—22no—
22#117×C151—42no—
23C2×C4⋊C4×C151—21no—
24C2×C4⋊C4×C151—22no—
25C2×C4⋊C4×C151—22no—
26C2×C4⋊C4×C151—42no—
27C2×C4⋊C4×C151C2×C411yescharacteristic
28C2×C4⋊C4×C151C2×C411yescharacteristic
29C2×C4⋊C4×C151C2×C411yescharacteristic
30C2×C4⋊C4×C151D412yes—
31C2×C4⋊C4×C151C2311yescharacteristic
32C2×C22⋊C4×C151—21no—
33C2×C22⋊C4×C151—21no—
34C2×C42×C151—21no—
35C2×C42×C151C2×C411yescharacteristic
36C2×C42×C151C2×C411yescharacteristic
37C22⋊C8×C151—24no—
38C22⋊C8×C151—42no—
39#95×C151—22no—
40#95×C151—22no—
41C24×C151C22⋊C411yescharacteristic
42C22×C4×C151—22no—
43C22×C4×C151—22no—
44C22×C4×C151—21no—
45C22×C4×C151—21no—
46C22×C4×C151—22no—
47C22×C4×C151—21no—
48C22×C4×C151—21no—
49C22×C4×C151—22no—
50C22×C4×C151—21no—
51C22×C4×C151—21no—
52C22×C4×C151—82no—
53C22×C4×C151C22⋊C411yescharacteristic
54C22×C4×C151C22⋊C412yes—
55C22×C4×C151C22×C411yescharacteristic
56C22×C4×C151C2×D412yes—
57M16×C151—84no—
58C2×C8×C151—44no—
59C4⋊C4×C151—24no—
60C4⋊C4×C151—41no—
61C4⋊C4×C151—42no—
62C4⋊C4×C151—41no—
63C4⋊C4×C151—41no—
64C4⋊C4×C151—41no—
65C4⋊C4×C151—82no—
66C4⋊C4×C151—82no—
67C22⋊C4×C151—24no—
68C22⋊C4×C151—42no—
69C42×C151—21no—
70C42×C151—21no—
71C42×C151—42no—
72C42×C151M1612yescomplemented
73C42×C151M1612yescomplemented
74C23×C151—21no—
75C23×C151—21no—
76C23×C151—41no—
77C23×C151—41no—
78C23×C151#9912yes—
79C23×C151C2×C22⋊C411yescharacteristic
80C2×C4×C151—24no—
81C2×C4×C151—24no—
82C2×C4×C151—21no—
83C2×C4×C151—21no—
84C2×C4×C151—21no—
85C2×C4×C151—21no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—41no—
91C2×C4×C151—41no—
92C2×C4×C151—44no—
93C2×C4×C151—41no—
94C2×C4×C151—41no—
95C2×C4×C151—42no—
96C2×C4×C151—42no—
97C2×C4×C151—42no—
98C2×C4×C151—42no—
99C2×C4×C151—41no—
100C2×C4×C151—41no—
101C2×C4×C151—82no—
102C2×C4×C151#10112yes—
103C2×C4×C151C2×M1611yescharacteristic
104C2×C4×C151C2×M1611yescharacteristic
105C8×C151—84no—
106C22×C151—21no—
107C22×C151—21no—
108C22×C151—22no—
109C22×C151—22no—
110C22×C151—22no—
111C22×C151—42no—
112C22×C151—42no—
113C22×C151#40711yescharacteristic
114C22×C151C2×#9911yescharacteristic
115C22×C151C2×#10111yescharacteristic
116C4×C151—22no—
117C4×C151—21no—
118C4×C151—21no—
119C4×C151—42no—
120C4×C151—42no—
121C4×C151—42no—
122C4×C151—42no—
123C4×C151—81no—
124C4×C151—81no—
125C2×C151—21no—
126C2×C151—21no—
127C2×C151—42no—
128C2×C151#146311yescharacteristic
129C2×C151#212711yescharacteristic
130C2×C151#213311yescharacteristic
131#11514C15111yesmaximal, characteristic, direct product factor, Sylow
132C151#1151411yescharacteristic, direct product factor, Sylow
133#2317C2×C15111yescharacteristic
134#1463C2×C15112yes—
135#1325C2×C15112yescomplemented
136#1324C2×C15112yescomplemented
137C2×#117C4×C15111yescharacteristic
138C2×#117C4×C15111yescharacteristic
139C22×C4⋊C4C22×C15111yescharacteristic
140#407—22no—
141#389—22no—
142#385—22no—
143#384C4×C15111yescharacteristic
144#384C22×C15111yescharacteristic
145#382C4×C15111yescharacteristic
146#382C22×C15111yescharacteristic
147#324—22no—
148#324C22×C15114yes—
149C23×C4C2×C4×C15111yescharacteristic
150C23×C4D4×C15112yes—
151C2×M16—42no—
152#117—22no—
153#117—22no—
154#117—42no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4C2×C4×C15111yescharacteristic
160C2×C4⋊C4C2×C4×C15111yescharacteristic
161C2×C4⋊C4C2×C4×C15111yescharacteristic
162C2×C4⋊C4D4×C15112yes—
163C2×C4⋊C4C23×C15111yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—21no—
166C2×C42—21no—
167C2×C42C2×C4×C15111yescharacteristic
168C2×C42C2×C4×C15111yescharacteristic
169C22⋊C8—24no—
170C22⋊C8—42no—
171#95—22no—
172#95—22no—
173C24C22⋊C4×C15111yescharacteristic
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—82no—
185C22×C4C22⋊C4×C15111yescharacteristic
186C22×C4C22⋊C4×C15112yes—
187C22×C4C22×C4×C15111yescharacteristic
188C22×C4C2×D4×C15112yes—
189M16—84no—
190C2×C8—44no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C22⋊C4—24no—
200C22⋊C4—42no—
201C42—21no—
202C42—21no—
203C42—42no—
204C42M16×C15112yescomplemented
205C42M16×C15112yescomplemented
206C23—21no—
207C23—21no—
208C23—41no—
209C23—41no—
210C23#99×C15112yes—
211C23C2×C22⋊C4×C15111yescharacteristic
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—44no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—82no—
234C2×C4#101×C15112yes—
235C2×C4C2×M16×C15111yescharacteristic
236C2×C4C2×M16×C15111yescharacteristic
237C8—84no—
238C22—21no—
239C22—21no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—42no—
244C22—42no—
245C22#407×C15111yescharacteristic
246C22C2×#99×C15111yescharacteristic
247C22C2×#101×C15111yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—42no—
260C2#1463×C15111yescharacteristic
261C2#2127×C15111yescharacteristic
262C2#2133×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radicalC24×C151C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C24×C151 ◁ C22×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1325×C151C2semidirect
4. #1324×C151C2semidirect
72. C42×C151M16semidirect
73. C42×C151M16semidirect
131. #11514C151direct (N × H)
132. C151#11514direct (N × H)
135. #1325C2×C151semidirect
136. #1324C2×C151semidirect
204. C42M16×C151semidirect
205. C42M16×C151semidirect

Maximal subgroups

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

subgroupindex
#2317×C1512
#1463×C1512
#1325×C1512
#1324×C1512
#11514151