Finite Group Databasebeta

← C151×#9067 #50313992

Subgroups — C151×#9067 #50313992

Order 38656.

444 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 126 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#3131×C151C211yesmaximal, characteristic
2#2979×C151C211yesmaximal, characteristic
3#1525×C151C211yesmaximal, characteristic
4#1485×C151C212yesmaximal, complemented
5#1278×C151C212yesmaximal, complemented
6#533×C151C2211yescharacteristic
7#532×C151C2211yescharacteristic
8#488×C151—22no—
9#487×C151C412yes—
10#486×C151C412yes—
11#436×C151—22no—
12C8×D4×C151—22no—
13#431×C151C2212yes—
14#416×C151—22no—
15#408×C151—22no—
16C4×M16×C151C2212yes—
17C2×C4×C8×C151C2211yescharacteristic
18#329×C151—22no—
19Q8⋊C8×C151—22no—
20Q8⋊C8×C151—22no—
21C2×#41×C151D412yes—
22C2×M16×C151—22no—
23C2×M16×C151—22no—
24C22×C8×C151—21no—
25C22×C8×C151—22no—
26C4⋊Q8×C151C2×C412yes—
27C4⋊Q8×C151C2×C411yescharacteristic
28#127×C151C2×C411yescharacteristic
29#125×C151—21no—
30#124×C151D412yes—
31C22⋊Q8×C151—22no—
32#121×C151—22no—
33C4×Q8×C151—22no—
34C4×D4×C151—22no—
35#117×C151—21no—
36C2×C42×C151C2311yescharacteristic
37C4⋊C8×C151D412yes—
38C4⋊C8×C151D412yes—
39#103×C151—24no—
40#102×C151—24no—
41C22⋊C8×C151—24no—
42C22⋊C8×C151—22no—
43#97×C151—22no—
44C4×C8×C151—21no—
45C4×C8×C151—22no—
46C4×C8×C151—22no—
47C4×C8×C151C2×C412yes—
48#41×C151—42no—
49#41×C151—42no—
50C2×Q8×C151—22no—
51C2×Q8×C151C22⋊C412yes—
52C2×D4×C151—22no—
53C2×D4×C151—22no—
54C2×D4×C151C22⋊C412yes—
55C22×C4×C151—22no—
56C22×C4×C151C2×D411yescharacteristic
57C22×C4×C151#4112yes—
58M16×C151—24no—
59M16×C151—42no—
60M16×C151—82no—
61C2×C8×C151—22no—
62C2×C8×C151—22no—
63C2×C8×C151—22no—
64C2×C8×C151—41no—
65C2×C8×C151—41no—
66C2×C8×C151—42no—
67C2×C8×C151—82no—
68C4⋊C4×C151—22no—
69C4⋊C4×C151—22no—
70C4⋊C4×C151—22no—
71C4⋊C4×C151—42no—
72C22⋊C4×C151—24no—
73C22⋊C4×C151—41no—
74C42×C151—41no—
75C42×C151C22×C411yescharacteristic
76C42×C151C2×D411yescharacteristic
77C42×C151C2×D412yes—
78C23×C151—22no—
79C23×C151#12311yescharacteristic
80Q8×C151—42no—
81Q8×C151—42no—
82Q8×C151—42no—
83D4×C151—42no—
84D4×C151—42no—
85D4×C151—42no—
86D4×C151—82no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—21no—
90C2×C4×C151—21no—
91C2×C4×C151—22no—
92C2×C4×C151—42no—
93C2×C4×C151—42no—
94C2×C4×C151—42no—
95C2×C4×C151C2×C22⋊C411yescharacteristic
96C2×C4×C151C4×D412yes—
97C2×C4×C151#12011yescharacteristic
98C2×C4×C151#12112yes—
99C8×C151—42no—
100C8×C151—44no—
101C8×C151—42no—
102C8×C151—42no—
103C22×C151—22no—
104C22×C151—21no—
105C22×C151—44no—
106C22×C151—42no—
107C22×C151#38611yescharacteristic
108C4×C151—22no—
109C4×C151—21no—
110C4×C151—42no—
111C4×C151—82no—
112C4×C151#44312yes—
113C4×C151#44412yes—
114C4×C151#45511yescharacteristic
115C4×C151#45511yescharacteristic
116C2×C151—41no—
117C2×C151—82no—
118C2×C151#187612yes—
119C2×C151#188511yescharacteristic
120#9067C15111yesmaximal, characteristic, direct product factor, Sylow
121C151#906711yescharacteristic, direct product factor, Sylow
122#3131C2×C15111yescharacteristic
123#2979C2×C15111yescharacteristic
124#1525C2×C15111yescharacteristic
125#1485C2×C15112yescomplemented
126#1278C2×C15112yescomplemented
127#533C22×C15111yescharacteristic
128#532C22×C15111yescharacteristic
129#488—22no—
130#487C4×C15112yes—
131#486C4×C15112yes—
132#436—22no—
133C8×D4—22no—
134#431C22×C15112yes—
135#416—22no—
136#408—22no—
137C4×M16C22×C15112yes—
138C2×C4×C8C22×C15111yescharacteristic
139#329—22no—
140Q8⋊C8—22no—
141Q8⋊C8—22no—
142C2×#41D4×C15112yes—
143C2×M16—22no—
144C2×M16—22no—
145C22×C8—21no—
146C22×C8—22no—
147C4⋊Q8C2×C4×C15112yes—
148C4⋊Q8C2×C4×C15111yescharacteristic
149#127C2×C4×C15111yescharacteristic
150#125—21no—
151#124D4×C15112yes—
152C22⋊Q8—22no—
153#121—22no—
154C4×Q8—22no—
155C4×D4—22no—
156#117—21no—
157C2×C42C23×C15111yescharacteristic
158C4⋊C8D4×C15112yes—
159C4⋊C8D4×C15112yes—
160#103—24no—
161#102—24no—
162C22⋊C8—24no—
163C22⋊C8—22no—
164#97—22no—
165C4×C8—21no—
166C4×C8—22no—
167C4×C8—22no—
168C4×C8C2×C4×C15112yes—
169#41—42no—
170#41—42no—
171C2×Q8—22no—
172C2×Q8C22⋊C4×C15112yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4C22⋊C4×C15112yes—
176C22×C4—22no—
177C22×C4C2×D4×C15111yescharacteristic
178C22×C4#41×C15112yes—
179M16—24no—
180M16—42no—
181M16—82no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—42no—
188C2×C8—82no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C22⋊C4—24no—
194C22⋊C4—41no—
195C42—41no—
196C42C22×C4×C15111yescharacteristic
197C42C2×D4×C15111yescharacteristic
198C42C2×D4×C15112yes—
199C23—22no—
200C23#123×C15111yescharacteristic
201Q8—42no—
202Q8—42no—
203Q8—42no—
204D4—42no—
205D4—42no—
206D4—42no—
207D4—82no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4C2×C22⋊C4×C15111yescharacteristic
217C2×C4C4×D4×C15112yes—
218C2×C4#120×C15111yescharacteristic
219C2×C4#121×C15112yes—
220C8—42no—
221C8—44no—
222C8—42no—
223C8—42no—
224C22—22no—
225C22—21no—
226C22—44no—
227C22—42no—
228C22#386×C15111yescharacteristic
229C4—22no—
230C4—21no—
231C4—42no—
232C4—82no—
233C4#443×C15112yes—
234C4#444×C15112yes—
235C4#455×C15111yescharacteristic
236C4#455×C15111yescharacteristic
237C2—41no—
238C2—82no—
239C2#1876×C15112yes—
240C2#1885×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#120
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#386
prime radical#532×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1485×C151C2semidirect
5. #1278×C151C2semidirect
120. #9067C151direct (N × H)
121. C151#9067direct (N × H)
125. #1485C2×C151semidirect
126. #1278C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3131×C1512
#2979×C1512
#1525×C1512
#1485×C1512
#1278×C1512
#9067151