Finite Group Databasebeta

← C151×#10014 #50314939

Subgroups — C151×#10014 #50314939

Order 38656.

566 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 122 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#3103×C151C212yesmaximal
2#2399×C151C211yesmaximal, characteristic, complemented
3#1963×C151C211yesmaximal, characteristic
4#1487×C151C212yesmaximal, complemented
5#1274×C151C211yesmaximal, characteristic, complemented
6#532×C151C2211yescharacteristic
7C2×C4×Q8×C151C2212yes—
8#481×C151—22no—
9#475×C151—22no—
10#460×C151—22no—
11#448×C151—22no—
12C4×SD16×C151—24no—
13#431×C151C2212yes—
14#423×C151C2211yescharacteristic
15C2×#104×C151—22no—
16#398×C151—22no—
17#395×C151—22no—
18C4×C4⋊C4×C151—22no—
19#376×C151C2211yescharacteristic
20Q8⋊C8×C151—24no—
21C2×#41×C151—21no—
22C22×Q8×C151D412yes—
23C2×SD16×C151—24no—
24C2×M16×C151—21no—
25C4⋊Q8×C151D411yescharacteristic
26#127×C151D411yescharacteristic
27#124×C151—21no—
28#121×C151—22no—
29C4×Q8×C151—22no—
30C4×Q8×C151—22no—
31C4×Q8×C151—22no—
32C4×Q8×C151—22no—
33C4×D4×C151—22no—
34C2×C4⋊C4×C151—24no—
35C2×C4⋊C4×C151—22no—
36C2×C4⋊C4×C151D412yes—
37C2×C42×C151—22no—
38C2×C42×C151D412yes—
39C2×C42×C151C2311yescharacteristic
40#106×C151—24no—
41C4⋊C8×C151—22no—
42C4⋊C8×C151—22no—
43#104×C151—44no—
44#103×C151—24no—
45#102×C151—24no—
46C22⋊C8×C151—22no—
47C4×C8×C151D414yes—
48#95×C151—22no—
49#95×C151—22no—
50#95×C151—22no—
51#41×C151—42no—
52#41×C151—42no—
53C2×Q8×C151—22no—
54C2×Q8×C151—22no—
55C2×Q8×C151—21no—
56C2×Q8×C151—44no—
57C2×D4×C151—22no—
58C2×D4×C151—21no—
59C2×D4×C151—41no—
60C22×C4×C151—22no—
61C22×C4×C151—22no—
62C22×C4×C151—22no—
63C22×C4×C151—41no—
64C22×C4×C151C2×D412yes—
65C22×C4×C151C2×D411yescharacteristic
66SD16×C151—48no—
67M16×C151—42no—
68C2×C8×C151—24no—
69C2×C8×C151—41no—
70C4⋊C4×C151—22no—
71C4⋊C4×C151—22no—
72C4⋊C4×C151—22no—
73C4⋊C4×C151—48no—
74C4⋊C4×C151—42no—
75C4⋊C4×C151—42no—
76C22⋊C4×C151—42no—
77C42×C151—22no—
78C42×C151—42no—
79C42×C151—42no—
80C42×C151SD1614yescomplemented
81C42×C151C2×D411yescharacteristic
82C42×C151C2×D412yes—
83C42×C151#4111yescharacteristic
84C23×C151—41no—
85C23×C151#12011yescharacteristic
86Q8×C151—24no—
87Q8×C151—24no—
88Q8×C151—42no—
89Q8×C151—42no—
90Q8×C151—42no—
91D4×C151—44no—
92D4×C151—42no—
93D4×C151—82no—
94C2×C4×C151—24no—
95C2×C4×C151—24no—
96C2×C4×C151—42no—
97C2×C4×C151—42no—
98C2×C4×C151—44no—
99C2×C4×C151—42no—
100C2×C4×C151—44no—
101C2×C4×C151—41no—
102C2×C4×C151—42no—
103C2×C4×C151—81no—
104C2×C4×C151—81no—
105C2×C4×C151#12012yes—
106C2×C4×C151#12112yes—
107C2×C4×C151#12111yescharacteristic
108C2×C4×C151#12711yescharacteristic
109C2×C4×C151C2×SD1612yes—
110C2×C4×C151#13712yes—
111C8×C151—44no—
112C8×C151—81no—
113C22×C151—22no—
114C22×C151—82no—
115C22×C151—81no—
116C22×C151#39211yescharacteristic
117C22×C151#44812yes—
118C4×C151—22no—
119C4×C151—22no—
120C4×C151—44no—
121C4×C151—44no—
122C4×C151—82no—
123C4×C151—81no—
124C4×C151#46112yes—
125C4×C151#49211yescharacteristic
126C4×C151#49711yescharacteristic
127C2×C151—22no—
128C2×C151—161no—
129C2×C151#201012yes—
130C2×C151#201311yescharacteristic
131#10014C15111yesmaximal, characteristic, direct product factor, Sylow
132C151#1001411yescharacteristic, direct product factor, Sylow
133#3103C2×C15112yes—
134#2399C2×C15111yescharacteristic, complemented
135#1963C2×C15111yescharacteristic
136#1487C2×C15112yescomplemented
137#1274C2×C15111yescharacteristic, complemented
138#532C22×C15111yescharacteristic
139C2×C4×Q8C22×C15112yes—
140#481—22no—
141#475—22no—
142#460—22no—
143#448—22no—
144C4×SD16—24no—
145#431C22×C15112yes—
146#423C22×C15111yescharacteristic
147C2×#104—22no—
148#398—22no—
149#395—22no—
150C4×C4⋊C4—22no—
151#376C22×C15111yescharacteristic
152Q8⋊C8—24no—
153C2×#41—21no—
154C22×Q8D4×C15112yes—
155C2×SD16—24no—
156C2×M16—21no—
157C4⋊Q8D4×C15111yescharacteristic
158#127D4×C15111yescharacteristic
159#124—21no—
160#121—22no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×D4—22no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4D4×C15112yes—
169C2×C42—22no—
170C2×C42D4×C15112yes—
171C2×C42C23×C15111yescharacteristic
172#106—24no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175#104—44no—
176#103—24no—
177#102—24no—
178C22⋊C8—22no—
179C4×C8D4×C15114yes—
180#95—22no—
181#95—22no—
182#95—22no—
183#41—42no—
184#41—42no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—44no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—41no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—41no—
196C22×C4C2×D4×C15112yes—
197C22×C4C2×D4×C15111yescharacteristic
198SD16—48no—
199M16—42no—
200C2×C8—24no—
201C2×C8—41no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—48no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C22⋊C4—42no—
209C42—22no—
210C42—42no—
211C42—42no—
212C42SD16×C15114yescomplemented
213C42C2×D4×C15111yescharacteristic
214C42C2×D4×C15112yes—
215C42#41×C15111yescharacteristic
216C23—41no—
217C23#120×C15111yescharacteristic
218Q8—24no—
219Q8—24no—
220Q8—42no—
221Q8—42no—
222Q8—42no—
223D4—44no—
224D4—42no—
225D4—82no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4#120×C15112yes—
238C2×C4#121×C15112yes—
239C2×C4#121×C15111yescharacteristic
240C2×C4#127×C15111yescharacteristic
241C2×C4C2×SD16×C15112yes—
242C2×C4#137×C15112yes—
243C8—44no—
244C8—81no—
245C22—22no—
246C22—82no—
247C22—81no—
248C22#392×C15111yescharacteristic
249C22#448×C15112yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—44no—
254C4—82no—
255C4—81no—
256C4#461×C15112yes—
257C4#492×C15111yescharacteristic
258C4#497×C15111yescharacteristic
259C2—22no—
260C2—161no—
261C2#2010×C15112yes—
262C2#2013×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#127
commutator, Frattini, cosocleC2×C42C23×C151
socleC22×C151#392
prime radical#532×C151C22
LCSG ▷ C2×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
2. #2399×C151C2semidirect
4. #1487×C151C2semidirect
5. #1274×C151C2semidirect
80. C42×C151SD16semidirect
131. #10014C151direct (N × H)
132. C151#10014direct (N × H)
134. #2399C2×C151semidirect
136. #1487C2×C151semidirect
137. #1274C2×C151semidirect
212. C42SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3103×C1512
#2399×C1512
#1963×C1512
#1487×C1512
#1274×C1512
#10014151