Finite Group Databasebeta

← #16955384

Subgroups — #16955384

Order 4352.

134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 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#14531093C211yesmaximal, characteristic, complemented
2C2×D544C211yesmaximal, characteristic, complemented
3#14527000C212yesmaximal, complemented
4D1088C212yesmaximal, complemented
5C17×M128C211yesmaximal, characteristic, complemented
6#11763241—21no—
7C2×D272—21no—
8Dic272C2211yescharacteristic, complemented
9#11762648—21no—
10D544—21no—
11D544C2212yes—
12D544C2211yescharacteristic, complemented
13C2×C17×C32C2211yescharacteristic
14C17×C64C2212yescomplemented
15#10587590—41no—
16C2×D136—41no—
17C2×C16×C17D411yescharacteristic
18Dic136—21no—
19#10587471—41no—
20D272—22no—
21D272—21no—
22D272—41no—
23C17×C32D411yescharacteristic
24C17×C32C2311yescharacteristic
25#63252—81no—
26C2×D68—81no—
27C2×C8×C17D811yescharacteristic
28Dic68—41no—
29D136—42no—
30D136—41no—
31D136—81no—
32#63219—81no—
33C16×C17D811yescharacteristic
34C16×C17C2×D411yescharacteristic
35#13742—171nomaximal, Sylow
36C22×D17—161no—
37C2×C4×C17D1611yescharacteristic
38C22⋊D17—161no—
39D68—82no—
40D68—81no—
41D68—161no—
42C4×D17—161no—
43Dic34—81no—
44C8×C17D1611yescharacteristic
45C8×C17C2×D811yescharacteristic
46#2262—171no—
47C2×D32—171no—
48SD128—172no—
49D64—172no—
50M128D1711yescharacteristic, complemented
51C22×C17D3211yescharacteristic
52C2×D17—161no—
53C2×D17—162no—
54C2×D17—322no—
55C4×C17D3211yescharacteristic
56C4×C17C2×D1611yescharacteristic
57Dic17—161no—
58#508—341no—
59C2×D16—341no—
60Q64—171no—
61SD64—341no—
62D32—171no—
63D32—172no—
64D32—341no—
65C2×C32C2×D1711yescharacteristic
66C64C2×D1712yescomplemented
67C2×C17—21no—
68C2×C17C2×D3211yescharacteristic
69D17—321no—
70D17—322no—
71#135—681no—
72C2×D8—681no—
73Q32—341no—
74SD32—681no—
75D16—342no—
76D16—341no—
77D16—681no—
78C2×C16D6811yescharacteristic
79C32D6811yescharacteristic
80C32C22×D1711yescharacteristic
81C17#1374211yescharacteristic, complemented, Sylow
82#41—1361no—
83C2×D4—1361no—
84Q16—681no—
85SD16—1361no—
86D8—682no—
87D8—681no—
88D8—1361no—
89C2×C8D13611yescharacteristic
90C16D13611yescharacteristic
91C16C2×D6811yescharacteristic
92C23—2721no—
93Q8—1361no—
94D4—2721no—
95D4—2721no—
96D4—1362no—
97D4—1361no—
98C2×C4—2721no—
99C2×C4D27211yescharacteristic
100C8D27211yescharacteristic
101C8C2×D13611yescharacteristic
102C22—2721no—
103C22—2722no—
104C22—5442no—
105C22D54411yescharacteristic
106C4—2721no—
107C4D54411yescharacteristic
108C4C2×D27211yescharacteristic
109C2—21no—
110C2—5442no—
111C2—5441no—
112C2C2×D54411yescharacteristic
subgroupG/H
centerC2C2×D544
commutator, cosocleC17×C32C23
FrattiniC32C22×D17
FittingC17×M128C2
socleC2×C17C2×D32
hypercenterM128D17
hypocenterC17#13742
LCSG ▷ C17×C32 ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ M128

Complements

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

NH ≅ G/Ntype
1. #14531093C2semidirect
2. C2×D544C2semidirect
3. #14527000C2semidirect
4. D1088C2semidirect
5. C17×M128C2semidirect
8. Dic272C22semidirect
12. D544C22semidirect
14. C17×C64C22semidirect
50. M128D17semidirect
66. C64C2×D17semidirect
81. C17#13742semidirect

Maximal subgroups

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

subgroupindex
#145310932
C2×D5442
#145270002
D10882
C17×M1282
#1374217