Finite Group Databasebeta

← C151×#8755 #50313680

Subgroups — C151×#8755 #50313680

Order 38656.

398 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 110 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#2313×C151C211yesmaximal, characteristic
2#1821×C151C212yesmaximal
3#1306×C151C214yesmaximal
4C22×C4⋊C4×C151C2211yescharacteristic
5#407×C151C2214yes—
6#387×C151—24no—
7#381×C151C2212yes—
8#380×C151C412yes—
9C4×C22⋊C4×C151C412yes—
10#343×C151—24no—
11C23×C4×C151C2×C411yescharacteristic
12C23×C4×C151C2×C411yescharacteristic
13C23×C4×C151C2311yescharacteristic
14C2×M16×C151—24no—
15C2×C4⋊C4×C151—24no—
16C2×C4⋊C4×C151—22no—
17C2×C4⋊C4×C151D414yes—
18C2×C22⋊C4×C151C2×C414yes—
19C2×C42×C151—22no—
20C22⋊C8×C151—28no—
21#95×C151—22no—
22#95×C151—22no—
23#95×C151—24no—
24C24×C151C22×C411yescharacteristic
25C22×C4×C151—22no—
26C22×C4×C151—22no—
27C22×C4×C151—24no—
28C22×C4×C151—42no—
29C22×C4×C151—81no—
30C22×C4×C151—81no—
31C22×C4×C151C22⋊C412yes—
32C22×C4×C151C22⋊C412yes—
33C22×C4×C151C2×D412yes—
34C22×C4×C151#4114yes—
35M16×C151—48no—
36C2×C8×C151—44no—
37C4⋊C4×C151—28no—
38C4⋊C4×C151—82no—
39C22⋊C4×C151—44no—
40C42×C151—82no—
41C23×C151—22no—
42C23×C151—41no—
43C23×C151—41no—
44C23×C151C2×C22⋊C411yescharacteristic
45C23×C151#11712yes—
46C2×C4×C151—24no—
47C2×C4×C151—22no—
48C2×C4×C151—22no—
49C2×C4×C151—44no—
50C2×C4×C151—42no—
51C2×C4×C151—42no—
52C2×C4×C151—44no—
53C2×C4×C151—44no—
54C2×C4×C151—44no—
55C2×C4×C151—82no—
56C2×C4×C151—82no—
57C2×C4×C151#12314yes—
58C8×C151—84no—
59C22×C151—21no—
60C22×C151—21no—
61C22×C151—22no—
62C22×C151—22no—
63C22×C151—22no—
64C22×C151—44no—
65C22×C151#38111yescharacteristic
66C22×C151#41012yes—
67C4×C151—24no—
68C4×C151—42no—
69C4×C151—42no—
70C4×C151—84no—
71C2×C151—22no—
72C2×C151—42no—
73C2×C151#182011yescharacteristic
74C2×C151#182911yescharacteristic
75C2×C151#183011yescharacteristic
76#8755C15111yesmaximal, characteristic, direct product factor, Sylow
77C151#875511yescharacteristic, direct product factor, Sylow
78#2313C2×C15111yescharacteristic
79#1821C2×C15112yes—
80#1306C2×C15114yes—
81C22×C4⋊C4C22×C15111yescharacteristic
82#407C22×C15114yes—
83#387—24no—
84#381C22×C15112yes—
85#380C4×C15112yes—
86C4×C22⋊C4C4×C15112yes—
87#343—24no—
88C23×C4C2×C4×C15111yescharacteristic
89C23×C4C2×C4×C15111yescharacteristic
90C23×C4C23×C15111yescharacteristic
91C2×M16—24no—
92C2×C4⋊C4—24no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4D4×C15114yes—
95C2×C22⋊C4C2×C4×C15114yes—
96C2×C42—22no—
97C22⋊C8—28no—
98#95—22no—
99#95—22no—
100#95—24no—
101C24C22×C4×C15111yescharacteristic
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—24no—
105C22×C4—42no—
106C22×C4—81no—
107C22×C4—81no—
108C22×C4C22⋊C4×C15112yes—
109C22×C4C22⋊C4×C15112yes—
110C22×C4C2×D4×C15112yes—
111C22×C4#41×C15114yes—
112M16—48no—
113C2×C8—44no—
114C4⋊C4—28no—
115C4⋊C4—82no—
116C22⋊C4—44no—
117C42—82no—
118C23—22no—
119C23—41no—
120C23—41no—
121C23C2×C22⋊C4×C15111yescharacteristic
122C23#117×C15112yes—
123C2×C4—24no—
124C2×C4—22no—
125C2×C4—22no—
126C2×C4—44no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—44no—
130C2×C4—44no—
131C2×C4—44no—
132C2×C4—82no—
133C2×C4—82no—
134C2×C4#123×C15114yes—
135C8—84no—
136C22—21no—
137C22—21no—
138C22—22no—
139C22—22no—
140C22—22no—
141C22—44no—
142C22#381×C15111yescharacteristic
143C22#410×C15112yes—
144C4—24no—
145C4—42no—
146C4—42no—
147C4—84no—
148C2—22no—
149C2—42no—
150C2#1820×C15111yescharacteristic
151C2#1829×C15111yescharacteristic
152C2#1830×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#381
commutatorC24C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC24×C151C22×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
76. #8755C151direct (N × H)
77. C151#8755direct (N × H)

Maximal subgroups

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

subgroupindex
#2313×C1512
#1821×C1512
#1306×C1512
#8755151