Finite Group Databasebeta

← C151×#7388 #50312313

Subgroups — C151×#7388 #50312313

Order 38656.

118 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 54 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#2178×C151C211yesmaximal, characteristic
2#1397×C151C211yesmaximal, characteristic, complemented
3#1373×C151C211yesmaximal, characteristic, complemented
4#508×C151C411yescharacteristic
5#443×C151—21no—
6C2×C32×C151—21no—
7#368×C151C411yescharacteristic
8#364×C151—21no—
9#359×C151—21no—
10C4×C16×C151C2211yescharacteristic
11#135×C151—21no—
12#131×C151—41no—
13Q32×C151C811yescharacteristic
14SD32×C151—21no—
15D16×C151C811yescharacteristic
16M32×C151—41no—
17C2×C16×C151C2×C411yescharacteristic
18C2×C16×C151D411yescharacteristic
19#108×C151—21no—
20#104×C151—41no—
21C4×C8×C151D411yescharacteristic
22C32×C151—22no—
23#41×C151—41no—
24Q16×C151—21no—
25SD16×C151—41no—
26D8×C151—21no—
27M16×C151—41no—
28M16×C151—81no—
29C2×C8×C151—81no—
30C2×C8×C151C22⋊C411yescharacteristic
31C2×C8×C151D811yescharacteristic
32C42×C151SD1611yescharacteristic
33C16×C151—21no—
34C16×C151—81no—
35C16×C151C2×C811yescharacteristic
36C16×C151M1611yescharacteristic
37Q8×C151—41no—
38D4×C151—41no—
39D4×C151—81no—
40C2×C4×C151—21no—
41C2×C4×C151—81no—
42C2×C4×C151#10211yescharacteristic
43C8×C151—81no—
44C8×C151C22⋊C811yescharacteristic
45C8×C151#10411yescharacteristic
46C8×C151D1611yescharacteristic
47C8×C151SD3211yescharacteristic
48C22×C151—81no—
49C22×C151#35911yescharacteristic
50C4×C151—41no—
51C4×C151—81no—
52C4×C151D4⋊C811yescharacteristic
53C4×C151#35711yescharacteristic
54C2×C151—21no—
55C2×C151—161no—
56C2×C151#133111yescharacteristic
57#7388C15111yesmaximal, characteristic, direct product factor, Sylow
58C151#738811yescharacteristic, direct product factor, Sylow
59#2178C2×C15111yescharacteristic
60#1397C2×C15111yescharacteristic, complemented
61#1373C2×C15111yescharacteristic, complemented
62#508C4×C15111yescharacteristic
63#443—21no—
64C2×C32—21no—
65#368C4×C15111yescharacteristic
66#364—21no—
67#359—21no—
68C4×C16C22×C15111yescharacteristic
69#135—21no—
70#131—41no—
71Q32C8×C15111yescharacteristic
72SD32—21no—
73D16C8×C15111yescharacteristic
74M32—41no—
75C2×C16C2×C4×C15111yescharacteristic
76C2×C16D4×C15111yescharacteristic
77#108—21no—
78#104—41no—
79C4×C8D4×C15111yescharacteristic
80C32—22no—
81#41—41no—
82Q16—21no—
83SD16—41no—
84D8—21no—
85M16—41no—
86M16—81no—
87C2×C8—81no—
88C2×C8C22⋊C4×C15111yescharacteristic
89C2×C8D8×C15111yescharacteristic
90C42SD16×C15111yescharacteristic
91C16—21no—
92C16—81no—
93C16C2×C8×C15111yescharacteristic
94C16M16×C15111yescharacteristic
95Q8—41no—
96D4—41no—
97D4—81no—
98C2×C4—21no—
99C2×C4—81no—
100C2×C4#102×C15111yescharacteristic
101C8—81no—
102C8C22⋊C8×C15111yescharacteristic
103C8#104×C15111yescharacteristic
104C8D16×C15111yescharacteristic
105C8SD32×C15111yescharacteristic
106C22—81no—
107C22#359×C15111yescharacteristic
108C4—41no—
109C4—81no—
110C4D4⋊C8×C15111yescharacteristic
111C4#357×C15111yescharacteristic
112C2—21no—
113C2—161no—
114C2#1331×C15111yescharacteristic
subgroupG/H
centerC4×C151#357
commutatorC16C2×C8×C151
Frattini, cosocleC4×C16C22×C151
socleC2×C151#1331
prime radical#508×C151C4
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C2×C8×C151 ◁ C4×C8×C151 ◁ C4×C16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1397×C151C2semidirect
3. #1373×C151C2semidirect
57. #7388C151direct (N × H)
58. C151#7388direct (N × H)
60. #1397C2×C151semidirect
61. #1373C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2178×C1512
#1397×C1512
#1373×C1512
#7388151