Finite Group Databasebeta

← C151×#12932 #50317857

Subgroups — C151×#12932 #50317857

Order 38656.

402 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 146 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#2911×C151C211yesmaximal, characteristic
2#2155×C151C212yesmaximal, complemented
3C2×#349×C151C211yesmaximal, characteristic
4#1811×C151C211yesmaximal, characteristic
5#1389×C151C212yesmaximal, complemented
6C22×M16×C151C2211yescharacteristic
7C2×#117×C151—21no—
8C2×M32×C151C2212yes—
9C2×#108×C151C2211yescharacteristic
10C2×#108×C151C2211yescharacteristic
11#428×C151—24no—
12#427×C151—21no—
13#427×C151C2212yes—
14#407×C151—21no—
15#365×C151—24no—
16#349×C151C414yescomplemented
17#341×C151—21no—
18C23×C4×C151D411yescharacteristic
19C2×M16×C151—22no—
20C2×M16×C151—22no—
21C2×M16×C151—21no—
22C2×M16×C151—21no—
23C2×M16×C151C2×C412yes—
24C2×M16×C151Q812yes—
25C22×C8×C151D411yescharacteristic
26C22×C8×C151C2311yescharacteristic
27#117×C151—22no—
28#117×C151—22no—
29#117×C151—41no—
30#117×C151—41no—
31C2×C4⋊C4×C151—22no—
32C2×C22⋊C4×C151—41no—
33C2×C42×C151—41no—
34M32×C151—22no—
35M32×C151C2×C414yescomplemented
36C2×C16×C151—22no—
37#108×C151—22no—
38#108×C151—22no—
39#107×C151—22no—
40#107×C151—22no—
41#106×C151—22no—
42#106×C151D414yes—
43C22⋊C8×C151—42no—
44C24×C151SD1611yescharacteristic
45C22×C4×C151—21no—
46C22×C4×C151—21no—
47C22×C4×C151—21no—
48C22×C4×C151—21no—
49C22×C4×C151—42no—
50C22×C4×C151C4⋊C412yes—
51C22×C4×C151SD1611yescharacteristic
52C22×C4×C151SD1612yes—
53C22×C4×C151C2×D411yescharacteristic
54M16×C151—24no—
55M16×C151—24no—
56M16×C151—41no—
57M16×C151—41no—
58M16×C151—41no—
59M16×C151—41no—
60C2×C8×C151—21no—
61C2×C8×C151—21no—
62C2×C8×C151—41no—
63C2×C8×C151—41no—
64C2×C8×C151C4⋊C412yes—
65C2×C8×C151C22×C411yescharacteristic
66C2×C8×C151C2×D412yes—
67C2×C8×C151C2×Q811yescharacteristic
68C2×C8×C151#4112yes—
69C4⋊C4×C151—24no—
70C4⋊C4×C151—42no—
71C22⋊C4×C151—42no—
72C22⋊C4×C151—42no—
73C42×C151—42no—
74C42×C151—42no—
75C16×C151—24no—
76C23×C151—21no—
77C23×C151—21no—
78C23×C151—81no—
79C23×C151#10612yes—
80C23×C151C2×SD1611yescharacteristic
81C2×C4×C151—21no—
82C2×C4×C151—21no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151—44no—
88C2×C4×C151—84no—
89C2×C4×C151#10612yes—
90C2×C4×C151C2×C4⋊C411yescharacteristic
91C2×C4×C151#12011yescharacteristic
92C2×C4×C151#12311yescharacteristic
93C2×C4×C151C2×SD1611yescharacteristic
94C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C151#13711yescharacteristic
96C8×C151—22no—
97C8×C151—81no—
98C8×C151—81no—
99C8×C151C4×D412yes—
100C8×C151C22⋊Q812yes—
101C22×C151—22no—
102C22×C151—41no—
103C22×C151—42no—
104C22×C151—42no—
105C22×C151—81no—
106C22×C151C2×#10611yescharacteristic
107C22×C151#45011yescharacteristic
108C22×C151#48311yescharacteristic
109C4×C151—22no—
110C4×C151—84no—
111C4×C151#38511yescharacteristic
112C4×C151#42811yescharacteristic
113C4×C151#44811yescharacteristic
114C4×C151#48111yescharacteristic
115C2×C151—21no—
116C2×C151—21no—
117C2×C151—21no—
118C2×C151—42no—
119C2×C151#185311yescharacteristic
120#12932C15111yesmaximal, characteristic, direct product factor, Sylow
121C151#1293211yescharacteristic, direct product factor, Sylow
122#2911C2×C15111yescharacteristic
123#2155C2×C15112yescomplemented
124C2×#349C2×C15111yescharacteristic
125#1811C2×C15111yescharacteristic
126#1389C2×C15112yescomplemented
127C22×M16C22×C15111yescharacteristic
128C2×#117—21no—
129C2×M32C22×C15112yes—
130C2×#108C22×C15111yescharacteristic
131C2×#108C22×C15111yescharacteristic
132#428—24no—
133#427—21no—
134#427C22×C15112yes—
135#407—21no—
136#365—24no—
137#349C4×C15114yescomplemented
138#341—21no—
139C23×C4D4×C15111yescharacteristic
140C2×M16—22no—
141C2×M16—22no—
142C2×M16—21no—
143C2×M16—21no—
144C2×M16C2×C4×C15112yes—
145C2×M16Q8×C15112yes—
146C22×C8D4×C15111yescharacteristic
147C22×C8C23×C15111yescharacteristic
148#117—22no—
149#117—22no—
150#117—41no—
151#117—41no—
152C2×C4⋊C4—22no—
153C2×C22⋊C4—41no—
154C2×C42—41no—
155M32—22no—
156M32C2×C4×C15114yescomplemented
157C2×C16—22no—
158#108—22no—
159#108—22no—
160#107—22no—
161#107—22no—
162#106—22no—
163#106D4×C15114yes—
164C22⋊C8—42no—
165C24SD16×C15111yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—42no—
171C22×C4C4⋊C4×C15112yes—
172C22×C4SD16×C15111yescharacteristic
173C22×C4SD16×C15112yes—
174C22×C4C2×D4×C15111yescharacteristic
175M16—24no—
176M16—24no—
177M16—41no—
178M16—41no—
179M16—41no—
180M16—41no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8C4⋊C4×C15112yes—
186C2×C8C22×C4×C15111yescharacteristic
187C2×C8C2×D4×C15112yes—
188C2×C8C2×Q8×C15111yescharacteristic
189C2×C8#41×C15112yes—
190C4⋊C4—24no—
191C4⋊C4—42no—
192C22⋊C4—42no—
193C22⋊C4—42no—
194C42—42no—
195C42—42no—
196C16—24no—
197C23—21no—
198C23—21no—
199C23—81no—
200C23#106×C15112yes—
201C23C2×SD16×C15111yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—44no—
209C2×C4—84no—
210C2×C4#106×C15112yes—
211C2×C4C2×C4⋊C4×C15111yescharacteristic
212C2×C4#120×C15111yescharacteristic
213C2×C4#123×C15111yescharacteristic
214C2×C4C2×SD16×C15111yescharacteristic
215C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
216C2×C4#137×C15111yescharacteristic
217C8—22no—
218C8—81no—
219C8—81no—
220C8C4×D4×C15112yes—
221C8C22⋊Q8×C15112yes—
222C22—22no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22—81no—
227C22C2×#106×C15111yescharacteristic
228C22#450×C15111yescharacteristic
229C22#483×C15111yescharacteristic
230C4—22no—
231C4—84no—
232C4#385×C15111yescharacteristic
233C4#428×C15111yescharacteristic
234C4#448×C15111yescharacteristic
235C4#481×C15111yescharacteristic
236C2—21no—
237C2—21no—
238C2—21no—
239C2—42no—
240C2#1853×C15111yescharacteristic
subgroupG/H
centerC4×C151#481
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
socleC2×C151#1853
prime radicalC24×C151SD16
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C22×C4×C151 ◁ C22×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2155×C151C2semidirect
5. #1389×C151C2semidirect
16. #349×C151C4semidirect
35. M32×C151C2×C4semidirect
120. #12932C151direct (N × H)
121. C151#12932direct (N × H)
123. #2155C2×C151semidirect
126. #1389C2×C151semidirect
137. #349C4×C151semidirect
156. M32C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2911×C1512
#2155×C1512
C2×#349×C1512
#1811×C1512
#1389×C1512
#12932151