Finite Group Databasebeta

← C151×#10015 #50314940

Subgroups — C151×#10015 #50314940

Order 38656.

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

normal subgroups only

This group has 696 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#3101×C151C212yesmaximal, complemented
2#2397×C151C211yesmaximal, characteristic
3#1995×C151C211yesmaximal, characteristic, complemented
4#1486×C151C212yesmaximal, complemented
5#1274×C151C211yesmaximal, characteristic, complemented
6#533×C151C2211yescharacteristic
7C2×C4×D4×C151—22no—
8C2×C4×D4×C151C2212yes—
9#483×C151—22no—
10#476×C151—22no—
11#461×C151—22no—
12#450×C151—22no—
13C4×SD16×C151—24no—
14#431×C151C2212yes—
15#423×C151C2211yescharacteristic
16#399×C151—22no—
17#392×C151—22no—
18#376×C151C2211yescharacteristic
19#339×C151—22no—
20D4⋊C8×C151—24no—
21C22×D4×C151—22no—
22C22×D4×C151D412yes—
23C23×C4×C151—22no—
24C2×SD16×C151—24no—
25C2×M16×C151—21no—
26C4⋊Q8×C151D412yescomplemented
27#125×C151—21no—
28C22⋊Q8×C151—22no—
29C4×Q8×C151—22no—
30C4×D4×C151—22no—
31C4×D4×C151—22no—
32C4×D4×C151—22no—
33C4×D4×C151—22no—
34C4×D4×C151—44no—
35C4×D4×C151—44no—
36#117×C151—21no—
37C2×C4⋊C4×C151—22no—
38C2×C4⋊C4×C151D412yes—
39C2×C22⋊C4×C151—24no—
40C2×C22⋊C4×C151—22no—
41C2×C42×C151D412yes—
42C2×C42×C151C2311yescharacteristic
43#106×C151—24no—
44C4⋊C8×C151—22no—
45C4⋊C8×C151—22no—
46#103×C151—24no—
47#102×C151—24no—
48C22⋊C8×C151—22no—
49C4×C8×C151D414yescomplemented
50#95×C151—22no—
51C24×C151—22no—
52C2×Q8×C151—22no—
53C2×D4×C151—22no—
54C2×D4×C151—22no—
55C2×D4×C151—44no—
56C2×D4×C151—44no—
57C2×D4×C151—48no—
58C22×C4×C151—22no—
59C22×C4×C151—22no—
60C22×C4×C151—42no—
61C22×C4×C151—42no—
62C22×C4×C151—44no—
63C22×C4×C151—44no—
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—22no—
74C4⋊C4×C151—44no—
75C4⋊C4×C151—42no—
76C22⋊C4×C151—48no—
77C22⋊C4×C151—41no—
78C22⋊C4×C151—42no—
79C22⋊C4×C151—42no—
80C42×C151—22no—
81C42×C151—41no—
82C42×C151SD1614yescomplemented
83C42×C151C2×D411yescharacteristic
84C42×C151C2×D412yes—
85C42×C151#4111yescharacteristic
86C23×C151—24no—
87C23×C151—44no—
88C23×C151—42no—
89C23×C151—42no—
90C23×C151—44no—
91C23×C151#12011yescharacteristic
92Q8×C151—44no—
93D4×C151—24no—
94D4×C151—24no—
95D4×C151—42no—
96D4×C151—42no—
97D4×C151—416no—
98C2×C4×C151—24no—
99C2×C4×C151—42no—
100C2×C4×C151—44no—
101C2×C4×C151—42no—
102C2×C4×C151—42no—
103C2×C4×C151—44no—
104C2×C4×C151—84no—
105C2×C4×C151—82no—
106C2×C4×C151—82no—
107C2×C4×C151#12012yes—
108C2×C4×C151#12112yes—
109C2×C4×C151#12111yescharacteristic
110C2×C4×C151#12711yescharacteristic
111C2×C4×C151C2×SD1612yes—
112C2×C4×C151AGL(1,ℤ/8)12yes—
113C8×C151—44no—
114C8×C151—81no—
115C22×C151—22no—
116C22×C151—48no—
117C22×C151—44no—
118C22×C151—84no—
119C22×C151—82no—
120C22×C151—82no—
121C22×C151#39211yescharacteristic
122C22×C151#45012yes—
123C4×C151—22no—
124C4×C151—22no—
125C4×C151—44no—
126C4×C151—82no—
127C4×C151—82no—
128C4×C151#46012yes—
129C4×C151#49211yescharacteristic
130C4×C151#49611yescharacteristic
131C2×C151—22no—
132C2×C151—84no—
133C2×C151#201012yes—
134C2×C151#201411yescharacteristic
135#10015C15111yesmaximal, characteristic, direct product factor, Sylow
136C151#1001511yescharacteristic, direct product factor, Sylow
137#3101C2×C15112yescomplemented
138#2397C2×C15111yescharacteristic
139#1995C2×C15111yescharacteristic, complemented
140#1486C2×C15112yescomplemented
141#1274C2×C15111yescharacteristic, complemented
142#533C22×C15111yescharacteristic
143C2×C4×D4—22no—
144C2×C4×D4C22×C15112yes—
145#483—22no—
146#476—22no—
147#461—22no—
148#450—22no—
149C4×SD16—24no—
150#431C22×C15112yes—
151#423C22×C15111yescharacteristic
152#399—22no—
153#392—22no—
154#376C22×C15111yescharacteristic
155#339—22no—
156D4⋊C8—24no—
157C22×D4—22no—
158C22×D4D4×C15112yes—
159C23×C4—22no—
160C2×SD16—24no—
161C2×M16—21no—
162C4⋊Q8D4×C15112yescomplemented
163#125—21no—
164C22⋊Q8—22no—
165C4×Q8—22no—
166C4×D4—22no—
167C4×D4—22no—
168C4×D4—22no—
169C4×D4—22no—
170C4×D4—44no—
171C4×D4—44no—
172#117—21no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4D4×C15112yes—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—22no—
177C2×C42D4×C15112yes—
178C2×C42C23×C15111yescharacteristic
179#106—24no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182#103—24no—
183#102—24no—
184C22⋊C8—22no—
185C4×C8D4×C15114yescomplemented
186#95—22no—
187C24—22no—
188C2×Q8—22no—
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—44no—
192C2×D4—44no—
193C2×D4—48no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—44no—
199C22×C4—44no—
200C22×C4C2×D4×C15112yes—
201C22×C4C2×D4×C15111yescharacteristic
202SD16—48no—
203M16—42no—
204C2×C8—24no—
205C2×C8—41no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—44no—
211C4⋊C4—42no—
212C22⋊C4—48no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C42—22no—
217C42—41no—
218C42SD16×C15114yescomplemented
219C42C2×D4×C15111yescharacteristic
220C42C2×D4×C15112yes—
221C42#41×C15111yescharacteristic
222C23—24no—
223C23—44no—
224C23—42no—
225C23—42no—
226C23—44no—
227C23#120×C15111yescharacteristic
228Q8—44no—
229D4—24no—
230D4—24no—
231D4—42no—
232D4—42no—
233D4—416no—
234C2×C4—24no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—44no—
240C2×C4—84no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4#120×C15112yes—
244C2×C4#121×C15112yes—
245C2×C4#121×C15111yescharacteristic
246C2×C4#127×C15111yescharacteristic
247C2×C4C2×SD16×C15112yes—
248C2×C4AGL(1,ℤ/8)×C15112yes—
249C8—44no—
250C8—81no—
251C22—22no—
252C22—48no—
253C22—44no—
254C22—84no—
255C22—82no—
256C22—82no—
257C22#392×C15111yescharacteristic
258C22#450×C15112yes—
259C4—22no—
260C4—22no—
261C4—44no—
262C4—82no—
263C4—82no—
264C4#460×C15112yes—
265C4#492×C15111yescharacteristic
266C4#496×C15111yescharacteristic
267C2—22no—
268C2—84no—
269C2#2010×C15112yes—
270C2#2014×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#127
commutator, Frattini, cosocleC2×C42C23×C151
socleC22×C151#392
prime radical#2397×C151C2
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
1. #3101×C151C2semidirect
3. #1995×C151C2semidirect
4. #1486×C151C2semidirect
5. #1274×C151C2semidirect
26. C4⋊Q8×C151D4semidirect
49. C4×C8×C151D4semidirect
82. C42×C151SD16semidirect
135. #10015C151direct (N × H)
136. C151#10015direct (N × H)
137. #3101C2×C151semidirect
139. #1995C2×C151semidirect
140. #1486C2×C151semidirect
141. #1274C2×C151semidirect
162. C4⋊Q8D4×C151semidirect
185. C4×C8D4×C151semidirect
218. C42SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3101×C1512
#2397×C1512
#1995×C1512
#1486×C1512
#1274×C1512
#10015151