Finite Group Databasebeta

← C151×#10034 #50314959

Subgroups — C151×#10034 #50314959

Order 38656.

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

normal subgroups only

This group has 584 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#3150×C151C211yesmaximal, characteristic
2#3103×C151C212yesmaximal, complemented
3#1985×C151C211yesmaximal, characteristic, complemented
4#1480×C151C212yesmaximal, complemented
5#1275×C151C211yesmaximal, characteristic, complemented
6C2×#135×C151—22no—
7#532×C151C2212yes—
8C2×C4×Q8×C151C2211yescharacteristic
9#497×C151—22no—
10#496×C151—22no—
11#481×C151—22no—
12#475×C151—22no—
13#460×C151—22no—
14#448×C151—22no—
15C4×SD16×C151—24no—
16#431×C151C2212yes—
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×#97×C151C2211yescharacteristic
19#336×C151—22no—
20D4⋊C8×C151—24no—
21C2×#41×C151—22no—
22C22×Q8×C151D411yescharacteristic
23#135×C151—44no—
24#135×C151—44no—
25C2×Q16×C151—22no—
26C2×SD16×C151—24no—
27C2×SD16×C151—24no—
28C2×D8×C151—22no—
29C22×C8×C151—21no—
30C22×C8×C151D412yes—
31C4⋊Q8×C151D412yes—
32#127×C151D412yes—
33#124×C151—22no—
34#121×C151—22no—
35#121×C151—22no—
36C4×Q8×C151—22no—
37C4×Q8×C151—22no—
38C4×D4×C151—22no—
39C4×D4×C151—22no—
40C2×C4⋊C4×C151—21no—
41C2×C4⋊C4×C151D411yescharacteristic
42C2×C42×C151—21no—
43C2×C42×C151C2311yescharacteristic
44#106×C151—24no—
45C4⋊C8×C151—22no—
46C4⋊C8×C151—22no—
47#103×C151—24no—
48#102×C151—24no—
49C22⋊C8×C151—22no—
50#97×C151—22no—
51C4×C8×C151D414yes—
52#41×C151—44no—
53#41×C151—44no—
54C2×Q8×C151—22no—
55C2×Q8×C151—22no—
56C2×Q8×C151—42no—
57C2×D4×C151—22no—
58C2×D4×C151—22no—
59C2×D4×C151—22no—
60C2×D4×C151—42no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—42no—
64C22×C4×C151C2×D411yescharacteristic
65C22×C4×C151C2×D411yescharacteristic
66C22×C4×C151#4111yescharacteristic
67Q16×C151—44no—
68SD16×C151—48no—
69SD16×C151—48no—
70D8×C151—44no—
71C2×C8×C151—22no—
72C2×C8×C151—22no—
73C2×C8×C151—24no—
74C2×C8×C151—41no—
75C2×C8×C151—42no—
76C2×C8×C151SD1614yescomplemented
77C4⋊C4×C151—22no—
78C4⋊C4×C151—22no—
79C4⋊C4×C151—22no—
80C4⋊C4×C151—42no—
81C22⋊C4×C151—42no—
82C22⋊C4×C151—42no—
83C42×C151—41no—
84C42×C151—41no—
85C42×C151C2×D412yes—
86C42×C151C2×D412yes—
87C23×C151—42no—
88C23×C151#12111yescharacteristic
89Q8×C151—24no—
90Q8×C151—42no—
91Q8×C151—44no—
92D4×C151—44no—
93D4×C151—44no—
94D4×C151—44no—
95D4×C151—84no—
96C2×C4×C151—22no—
97C2×C4×C151—41no—
98C2×C4×C151—41no—
99C2×C4×C151—41no—
100C2×C4×C151—41no—
101C2×C4×C151—42no—
102C2×C4×C151—42no—
103C2×C4×C151—41no—
104C2×C4×C151—82no—
105C2×C4×C151—82no—
106C2×C4×C151#12012yes—
107C2×C4×C151#12011yescharacteristic
108C2×C4×C151#12112yes—
109C2×C4×C151#12711yescharacteristic
110C2×C4×C151C2×SD1612yes—
111C2×C4×C151AGL(1,ℤ/8)12yes—
112C8×C151—24no—
113C8×C151—44no—
114C8×C151—81no—
115C22×C151—21no—
116C22×C151—21no—
117C22×C151—82no—
118C22×C151—82no—
119C22×C151—82no—
120C22×C151#39211yescharacteristic
121C22×C151#46012yes—
122C4×C151—22no—
123C4×C151—22no—
124C4×C151—42no—
125C4×C151—82no—
126C4×C151—81no—
127C4×C151#45012yes—
128C4×C151#49211yescharacteristic
129C4×C151#49611yescharacteristic
130C2×C151—22no—
131C2×C151—162no—
132C2×C151#201011yescharacteristic
133C2×C151#201411yescharacteristic
134C2×C151#201711yescharacteristic
135#10034C15111yesmaximal, characteristic, direct product factor, Sylow
136C151#1003411yescharacteristic, direct product factor, Sylow
137#3150C2×C15111yescharacteristic
138#3103C2×C15112yescomplemented
139#1985C2×C15111yescharacteristic, complemented
140#1480C2×C15112yescomplemented
141#1275C2×C15111yescharacteristic, complemented
142C2×#135—22no—
143#532C22×C15112yes—
144C2×C4×Q8C22×C15111yescharacteristic
145#497—22no—
146#496—22no—
147#481—22no—
148#475—22no—
149#460—22no—
150#448—22no—
151C4×SD16—24no—
152#431C22×C15112yes—
153C2×C4⋊C8C22×C15111yescharacteristic
154C2×#97C22×C15111yescharacteristic
155#336—22no—
156D4⋊C8—24no—
157C2×#41—22no—
158C22×Q8D4×C15111yescharacteristic
159#135—44no—
160#135—44no—
161C2×Q16—22no—
162C2×SD16—24no—
163C2×SD16—24no—
164C2×D8—22no—
165C22×C8—21no—
166C22×C8D4×C15112yes—
167C4⋊Q8D4×C15112yes—
168#127D4×C15112yes—
169#124—22no—
170#121—22no—
171#121—22no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×D4—22no—
175C4×D4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4D4×C15111yescharacteristic
178C2×C42—21no—
179C2×C42C23×C15111yescharacteristic
180#106—24no—
181C4⋊C8—22no—
182C4⋊C8—22no—
183#103—24no—
184#102—24no—
185C22⋊C8—22no—
186#97—22no—
187C4×C8D4×C15114yes—
188#41—44no—
189#41—44no—
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—42no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—42no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4C2×D4×C15111yescharacteristic
201C22×C4C2×D4×C15111yescharacteristic
202C22×C4#41×C15111yescharacteristic
203Q16—44no—
204SD16—48no—
205SD16—48no—
206D8—44no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—24no—
210C2×C8—41no—
211C2×C8—42no—
212C2×C8SD16×C15114yescomplemented
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C42—41no—
220C42—41no—
221C42C2×D4×C15112yes—
222C42C2×D4×C15112yes—
223C23—42no—
224C23#121×C15111yescharacteristic
225Q8—24no—
226Q8—42no—
227Q8—44no—
228D4—44no—
229D4—44no—
230D4—44no—
231D4—84no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4#120×C15112yes—
243C2×C4#120×C15111yescharacteristic
244C2×C4#121×C15112yes—
245C2×C4#127×C15111yescharacteristic
246C2×C4C2×SD16×C15112yes—
247C2×C4AGL(1,ℤ/8)×C15112yes—
248C8—24no—
249C8—44no—
250C8—81no—
251C22—21no—
252C22—21no—
253C22—82no—
254C22—82no—
255C22—82no—
256C22#392×C15111yescharacteristic
257C22#460×C15112yes—
258C4—22no—
259C4—22no—
260C4—42no—
261C4—82no—
262C4—81no—
263C4#450×C15112yes—
264C4#492×C15111yescharacteristic
265C4#496×C15111yescharacteristic
266C2—22no—
267C2—162no—
268C2#2010×C15111yescharacteristic
269C2#2014×C15111yescharacteristic
270C2#2017×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#127
commutator, Frattini, cosocleC2×C42C23×C151
socleC22×C151#392
prime radical#3150×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
2. #3103×C151C2semidirect
3. #1985×C151C2semidirect
4. #1480×C151C2semidirect
5. #1275×C151C2semidirect
76. C2×C8×C151SD16semidirect
135. #10034C151direct (N × H)
136. C151#10034direct (N × H)
138. #3103C2×C151semidirect
139. #1985C2×C151semidirect
140. #1480C2×C151semidirect
141. #1275C2×C151semidirect
212. C2×C8SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3150×C1512
#3103×C1512
#1985×C1512
#1480×C1512
#1275×C1512
#10034151