Finite Group Databasebeta

← C151×#19067 #50323992

Subgroups — C151×#19067 #50323992

Order 38656.

784 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 222 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#3556×C151C211yesmaximal, characteristic
2#3237×C151C212yesmaximal
3#3162×C151C211yesmaximal, characteristic
4#1663×C151C218yesmaximal, complemented
5#1537×C151C211yesmaximal, characteristic
6#1531×C151C212yesmaximal
7#564×C151C2214yes—
8#557×C151—22no—
9#557×C151—22no—
10#557×C151—22no—
11#541×C151—22no—
12#541×C151—24no—
13#533×C151C2211yescharacteristic
14#533×C151C2211yescharacteristic
15#533×C151C2212yes—
16#501×C151—22no—
17#501×C151C2214yes—
18#501×C151C2214yes—
19#491×C151C2214yes—
20#485×C151—24no—
21#477×C151—22no—
22#475×C151—22no—
23#432×C151C2212yes—
24#427×C151—22no—
25C2×#97×C151C2211yescharacteristic
26#330×C151C2218yes—
27#330×C151C2214yes—
28C22×C8×C151—21no—
29C4⋊Q8×C151—24no—
30C4⋊Q8×C151—22no—
31C4⋊Q8×C151D412yes—
32C4⋊Q8×C151D412yes—
33C4⋊Q8×C151D412yes—
34C4⋊Q8×C151C2312yes—
35#126×C151—28no—
36#125×C151—24no—
37#125×C151—22no—
38#125×C151—28no—
39#125×C151—28no—
40#125×C151—28no—
41#125×C151—21no—
42#125×C151C2314yes—
43#125×C151C2312yes—
44C22⋊Q8×C151—22no—
45C22⋊Q8×C151—22no—
46C22⋊Q8×C151—22no—
47C22⋊Q8×C151—22no—
48C4×Q8×C151—24no—
49C4×Q8×C151—24no—
50C4×Q8×C151—24no—
51C4×Q8×C151—22no—
52C4×Q8×C151—22no—
53C4×Q8×C151—22no—
54C4×Q8×C151—22no—
55#117×C151—21no—
56#117×C151D412yes—
57#117×C151D414yes—
58C2×C42×C151C2311yescharacteristic
59#107×C151—24no—
60#107×C151—24no—
61#106×C151—24no—
62#106×C151—24no—
63C4⋊C8×C151—22no—
64#103×C151—24no—
65#103×C151—24no—
66C22⋊C8×C151—22no—
67#97×C151—21no—
68#97×C151C2312yes—
69#97×C151C2314yes—
70C2×Q8×C151—22no—
71C2×Q8×C151—22no—
72C2×Q8×C151—22no—
73C2×Q8×C151—22no—
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151C2×D412yes—
76C2×C8×C151—24no—
77C2×C8×C151—22no—
78C2×C8×C151—24no—
79C4⋊C4×C151—28no—
80C4⋊C4×C151—28no—
81C4⋊C4×C151—28no—
82C4⋊C4×C151—22no—
83C4⋊C4×C151—22no—
84C4⋊C4×C151—22no—
85C4⋊C4×C151—24no—
86C4⋊C4×C151—24no—
87C4⋊C4×C151—24no—
88C4⋊C4×C151—22no—
89C4⋊C4×C151—22no—
90C4⋊C4×C151—42no—
91C4⋊C4×C151C2×D414yes—
92C4⋊C4×C151C2×D414yes—
93C4⋊C4×C151C2×D414yes—
94C22⋊C4×C151—22no—
95C22⋊C4×C151—24no—
96C22⋊C4×C151—41no—
97C42×C151—28no—
98C42×C151—24no—
99C42×C151—22no—
100C42×C151—41no—
101C42×C151C2×D411yescharacteristic
102C42×C151C2×D412yes—
103C42×C151C2411yescharacteristic
104C23×C151#12011yescharacteristic
105Q8×C151—44no—
106Q8×C151—44no—
107Q8×C151—44no—
108Q8×C151—44no—
109C2×C4×C151—22no—
110C2×C4×C151—24no—
111C2×C4×C151—24no—
112C2×C4×C151—24no—
113C2×C4×C151—42no—
114C2×C4×C151—42no—
115C2×C4×C151#12012yes—
116C2×C4×C151#12011yescharacteristic
117C2×C4×C151C22×D412yes—
118C2×C4×C151C22×D411yescharacteristic
119C8×C151—24no—
120C8×C151—44no—
121C22×C151—21no—
122C22×C151—22no—
123C22×C151C2×#12011yescharacteristic
124C4×C151—21no—
125C4×C151—22no—
126C4×C151—22no—
127C4×C151—44no—
128C4×C151—44no—
129C4×C151—44no—
130C4×C151—82no—
131C4×C151#45612yes—
132C2×C151—41no—
133C2×C151C2×#45611yescharacteristic
134C2×C151#302012yes—
135#19067C15111yesmaximal, characteristic, direct product factor, Sylow
136C151#1906711yescharacteristic, direct product factor, Sylow
137#3556C2×C15111yescharacteristic
138#3237C2×C15112yes—
139#3162C2×C15111yescharacteristic
140#1663C2×C15118yescomplemented
141#1537C2×C15111yescharacteristic
142#1531C2×C15112yes—
143#564C22×C15114yes—
144#557—22no—
145#557—22no—
146#557—22no—
147#541—22no—
148#541—24no—
149#533C22×C15111yescharacteristic
150#533C22×C15111yescharacteristic
151#533C22×C15112yes—
152#501—22no—
153#501C22×C15114yes—
154#501C22×C15114yes—
155#491C22×C15114yes—
156#485—24no—
157#477—22no—
158#475—22no—
159#432C22×C15112yes—
160#427—22no—
161C2×#97C22×C15111yescharacteristic
162#330C22×C15114yes—
163#330C22×C15118yes—
164C22×C8—21no—
165C4⋊Q8—24no—
166C4⋊Q8—22no—
167C4⋊Q8D4×C15112yes—
168C4⋊Q8D4×C15112yes—
169C4⋊Q8D4×C15112yes—
170C4⋊Q8C23×C15112yes—
171#126—28no—
172#125—24no—
173#125—22no—
174#125—28no—
175#125—28no—
176#125—28no—
177#125—21no—
178#125C23×C15114yes—
179#125C23×C15112yes—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C4×Q8—24no—
185C4×Q8—24no—
186C4×Q8—24no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191#117—21no—
192#117D4×C15112yes—
193#117D4×C15114yes—
194C2×C42C23×C15111yescharacteristic
195#107—24no—
196#107—24no—
197#106—24no—
198#106—24no—
199C4⋊C8—22no—
200#103—24no—
201#103—24no—
202C22⋊C8—22no—
203#97—21no—
204#97C23×C15112yes—
205#97C23×C15114yes—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—22no—
210C22×C4C2×D4×C15111yescharacteristic
211C22×C4C2×D4×C15112yes—
212C2×C8—24no—
213C2×C8—22no—
214C2×C8—24no—
215C4⋊C4—28no—
216C4⋊C4—28no—
217C4⋊C4—28no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—42no—
227C4⋊C4C2×D4×C15114yes—
228C4⋊C4C2×D4×C15114yes—
229C4⋊C4C2×D4×C15114yes—
230C22⋊C4—22no—
231C22⋊C4—24no—
232C22⋊C4—41no—
233C42—28no—
234C42—24no—
235C42—22no—
236C42—41no—
237C42C2×D4×C15111yescharacteristic
238C42C2×D4×C15112yes—
239C42C24×C15111yescharacteristic
240C23#120×C15111yescharacteristic
241Q8—44no—
242Q8—44no—
243Q8—44no—
244Q8—44no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—24no—
248C2×C4—24no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4#120×C15112yes—
252C2×C4#120×C15111yescharacteristic
253C2×C4C22×D4×C15111yescharacteristic
254C2×C4C22×D4×C15112yes—
255C8—24no—
256C8—44no—
257C22—21no—
258C22—22no—
259C22C2×#120×C15111yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—44no—
264C4—44no—
265C4—44no—
266C4—82no—
267C4#456×C15112yes—
268C2—41no—
269C2C2×#456×C15111yescharacteristic
270C2#3020×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC23×C151#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1663×C151C2semidirect
135. #19067C151direct (N × H)
136. C151#19067direct (N × H)
140. #1663C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3556×C1512
#3237×C1512
#3162×C1512
#1663×C1512
#1537×C1512
#1531×C1512
#19067151