Finite Group Databasebeta

← #1341×C151 #34064673

Subgroups — #1341×C151 #34064673

Order 19328.

110 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 36 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#469×C151C211yesmaximal, characteristic
2#349×C151C211yesmaximal, characteristic, complemented
3#338×C151C211yesmaximal, characteristic, complemented
4C2×D8×C151C411yescharacteristic
5C2×M16×C151—21no—
6C2×M16×C151C2211yescharacteristic
7#121×C151—21no—
8M32×C151—21no—
9#106×C151C411yescharacteristic
10#102×C151—21no—
11C2×D4×C151—21no—
12C2×D4×C151—41no—
13C22×C4×C151D411yescharacteristic
14D8×C151—41no—
15M16×C151—41no—
16M16×C151—41no—
17M16×C151—41no—
18C2×C8×C151—22no—
19C2×C8×C151C2×C411yescharacteristic
20C2×C8×C151D411yescharacteristic
21C4⋊C4×C151—21no—
22C22⋊C4×C151—41no—
23C16×C151—41no—
24C23×C151—41no—
25C23×C151SD1611yescharacteristic
26D4×C151—41no—
27D4×C151—41no—
28D4×C151—82no—
29C2×C4×C151—21no—
30C2×C4×C151—21no—
31C2×C4×C151—41no—
32C2×C4×C151C22⋊C411yescharacteristic
33C2×C4×C151D811yescharacteristic
34C8×C151—21no—
35C8×C151—21no—
36C8×C151—42no—
37C22×C151—21no—
38C22×C151—41no—
39C22×C151—81no—
40C22×C151—81no—
41C22×C151—81no—
42C22×C151#10211yescharacteristic
43C4×C151—21no—
44C4×C151—81no—
45C4×C151#9911yescharacteristic
46C4×C151#10411yescharacteristic
47C2×C151—21no—
48C2×C151—41no—
49C2×C151—161no—
50C2×C151#32711yescharacteristic
51C151#134111yescharacteristic, direct product factor, Sylow
52#1341C15111yesmaximal, characteristic, direct product factor, Sylow
53#469C2×C15111yescharacteristic
54#349C2×C15111yescharacteristic, complemented
55#338C2×C15111yescharacteristic, complemented
56C2×D8C4×C15111yescharacteristic
57C2×M16—21no—
58C2×M16C22×C15111yescharacteristic
59#121—21no—
60M32—21no—
61#106C4×C15111yescharacteristic
62#102—21no—
63C2×D4—21no—
64C2×D4—41no—
65C22×C4D4×C15111yescharacteristic
66D8—41no—
67M16—41no—
68M16—41no—
69M16—41no—
70C2×C8—22no—
71C2×C8C2×C4×C15111yescharacteristic
72C2×C8D4×C15111yescharacteristic
73C4⋊C4—21no—
74C22⋊C4—41no—
75C16—41no—
76C23—41no—
77C23SD16×C15111yescharacteristic
78D4—41no—
79D4—41no—
80D4—82no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—41no—
84C2×C4C22⋊C4×C15111yescharacteristic
85C2×C4D8×C15111yescharacteristic
86C8—21no—
87C8—21no—
88C8—42no—
89C22—21no—
90C22—41no—
91C22—81no—
92C22—81no—
93C22—81no—
94C22#102×C15111yescharacteristic
95C4—21no—
96C4—81no—
97C4#99×C15111yescharacteristic
98C4#104×C15111yescharacteristic
99C2—21no—
100C2—41no—
101C2—161no—
102C2#327×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#327
commutatorC2×C8C2×C4×C151
Frattini, cosocleC2×M16C22×C151
prime radical#469×C151C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C2×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #349×C151C2semidirect
3. #338×C151C2semidirect
51. C151#1341direct (N × H)
52. #1341C151direct (N × H)
54. #349C2×C151semidirect
55. #338C2×C151semidirect

Maximal subgroups

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

subgroupindex
#469×C1512
#349×C1512
#338×C1512
#1341151