Finite Group Databasebeta

← #11772689

Subgroups — #11772689

Order 1152.

246 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×C32×C16C211yesmaximal, characteristic
2C2×C3⋊(C3⋊C32)C212yesmaximal, complemented
3#67803—34nomaximal
4C22×C32×C8C411yescharacteristic
5C2×C32×C16—22no—
6C2×C32×C16C411yescharacteristic
7C2×C32×C16C2211yescharacteristic
8C3⋊(C3⋊C32)—22no—
9C22×C3×C16D314yes—
10C2×C3⋊C32—38no—
11C22×C32×C4C811yescharacteristic
12C2×C32×C8—21no—
13C2×C32×C8—21no—
14C2×C32×C8C811yescharacteristic
15C2×C32×C8C2×C411yescharacteristic
16C32×C16—21no—
17C32×C16D412yes—
18C22⋊C32—91noSylow
19C22×C3×C8Dic314yes—
20C2×C3×C16—28no—
21C2×C3×C16Dic314yes—
22C2×C3×C16C2×D314yes—
23C3⋊C32—68no—
24C23×C32C1611yescharacteristic
25C2×C32×C4—21no—
26C2×C32×C4—21no—
27C2×C32×C4C1611yescharacteristic
28C2×C32×C4C2×C811yescharacteristic
29C32×C8—21no—
30C32×C8C22⋊C411yescharacteristic
31C32×C8M1611yescharacteristic
32C22×C16C3⋊D311yescharacteristic
33C2×C32—92no—
34C22×C3×C4C3⋊C814yes—
35C2×C3×C8—24no—
36C2×C3×C8—24no—
37C2×C3×C8C3⋊C814yes—
38C2×C3×C8C2×Dic314yes—
39C3×C16—24no—
40C3×C16#6718yes—
41C22×C32—21no—
42C22×C32—21no—
43C22×C32C3212yescomplemented
44C22×C32C2×C1611yescharacteristic
45C32×C4—21no—
46C32×C4C22⋊C811yescharacteristic
47C32×C4M3211yescharacteristic
48C22×C8C3⋊Dic311yescharacteristic
49C2×C16—22no—
50C2×C16C3⋊Dic311yescharacteristic
51C2×C16C2×C3⋊D311yescharacteristic
52C32—182no—
53C23×C3C3⋊C1614yes—
54C2×C3×C4—24no—
55C2×C3×C4—24no—
56C2×C3×C4C3⋊C1614yes—
57C2×C3×C4C2×C3⋊C814yes—
58C3×C8—24no—
59C3×C8#20814yes—
60C3×C8#21714yes—
61C2×C32—22no—
62C2×C32C22⋊C1611yescharacteristic
63C2×C32C2×C3211yescharacteristic
64C2×C32M6411yescharacteristic
65C22×C4C3⋊(C3⋊C8)11yescharacteristic
66C2×C8—21no—
67C2×C8—21no—
68C2×C8C3⋊(C3⋊C8)11yescharacteristic
69C2×C8C2×C3⋊Dic311yescharacteristic
70C16—21no—
71C16#63812yes—
72C22×C3—24no—
73C22×C3—24no—
74C22×C3C3⋊C3218yescomplemented
75C22×C3C2×C3⋊C1614yes—
76C3×C4—24no—
77C3×C4#81214yes—
78C3×C4#83014yes—
79C32C22⋊C3211yescharacteristic, complemented, Sylow
80C23C3⋊(C3⋊C16)11yescharacteristic
81C2×C4—21no—
82C2×C4—21no—
83C2×C4C3⋊(C3⋊C16)11yescharacteristic
84C2×C4C2×C3⋊(C3⋊C8)11yescharacteristic
85C8—21no—
86C8#374811yescharacteristic
87C8#375711yescharacteristic
88C2×C3—28no—
89C2×C3C2×C3⋊C3214yes—
90C2×C3#449914yes—
91C2×C3#454914yes—
92C22—21no—
93C22—21no—
94C22C3⋊(C3⋊C32)12yescomplemented
95C22C2×C3⋊(C3⋊C16)11yescharacteristic
96C4—21no—
97C4#6363911yescharacteristic
98C4#6365711yescharacteristic
99C3#6780314yescomplemented
100C2—22no—
101C2C2×C3⋊(C3⋊C32)11yescharacteristic
102C2#1058936511yescharacteristic
103C2#1058941511yescharacteristic
subgroupG/H
center, FrattiniC2×C16C2×C3⋊D3
commutatorC2×C32C2×C32
FittingC22×C32×C16C2
socleC22×C32C2×C16
prime radicalC23×C32C16
cosocleC2×C32×C16C22
hypercenterC22×C16C3⋊D3
hypocenterC32C22⋊C32
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C16 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊(C3⋊C32)C2semidirect
43. C22×C32C32semidirect
74. C22×C3C3⋊C32semidirect
79. C32C22⋊C32semidirect
94. C22C3⋊(C3⋊C32)semidirect
99. C3#67803semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C162
C2×C3⋊(C3⋊C32)2
#678033