Finite Group Databasebeta

← #64148

Subgroups — #64148

Order 288.

282 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×C32×D4C211yesmaximal, characteristic, complemented
2C2×#638C211yesmaximal, characteristic, complemented
3C2×#638C211yesmaximal, characteristic, complemented
4C22×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#3757C211yesmaximal, characteristic, complemented
6#3752C211yesmaximal, characteristic, complemented
7#3750C211yesmaximal, characteristic, complemented
8#939—34nomaximal
9C23×C32C2211yescharacteristic
10C23×C32C2211yescharacteristic
11C22×C3⋊D3C2211yescharacteristic
12C32×D4—22no—
13C2×C32×C4C2211yescharacteristic
14#638—22no—
15#638—22no—
16C2×C3⋊Dic3—22no—
17C2×C3⋊Dic3C2211yescharacteristic
18C2×C3⋊Dic3C2211yescharacteristic
19C2×C3⋊Dic3C2211yescharacteristic
20C2×C3×D4D314yescomplemented
21C2×#67—34no—
22C2×#67—34no—
23C22×Dic3—34no—
24#217—34no—
25(C2×D3)⋊C4—34no—
26Dic3⋊C4—34no—
27C22×C32—21no—
28C22×C32—21no—
29C22×C32—21no—
30C22×C32—21no—
31C22×C32—21no—
32C22×C32D412yescomplemented
33C22×C32C2311yescharacteristic
34C2×C3⋊D3—21no—
35C2×C3⋊D3—21no—
36C2×C3⋊D3—21no—
37C32×C4—21no—
38C3⋊Dic3—21no—
39C3⋊Dic3—21no—
40C3⋊Dic3D412yescomplemented
41#121—91noSylow
42C23×C3C2×D314yes—
43C23×C3C2×D314yes—
44C22×D3—34no—
45C3×D4—28no—
46C2×C3×C4C2×D314yes—
47#67—68no—
48#67—68no—
49C2×Dic3—34no—
50C2×Dic3—34no—
51C2×Dic3—34no—
52C2×Dic3—68no—
53C2×C32—22no—
54C2×C32—41no—
55C2×C32C2×D411yescharacteristic
56C2×C32C2×D411yescharacteristic
57C2×C32#4111yescharacteristic
58C3⋊D3—41no—
59C2×D4—91no—
60C2×D4—91no—
61C2×D4C3⋊D311yescharacteristic, complemented
62C22×C4—91no—
63C4⋊C4—91no—
64C22⋊C4—91no—
65C22⋊C4—91no—
66C22×C3—24no—
67C22×C3—24no—
68C22×C3—24no—
69C22×C3—24no—
70C22×C3—24no—
71C22×C3#6718yescomplemented
72C22×C3C22×D314yes—
73C2×D3—64no—
74C2×D3—64no—
75C2×D3—64no—
76C3×C4—24no—
77Dic3—38no—
78Dic3—64no—
79Dic3—64no—
80C32#12111yescharacteristic, complemented, Sylow
81C23—91no—
82C23C2×C3⋊D311yescharacteristic
83C23C2×C3⋊D311yescharacteristic
84D4—22no—
85D4—182no—
86D4—182no—
87C2×C4—91no—
88C2×C4—91no—
89C2×C4—91no—
90C2×C4—182no—
91C2×C4C2×C3⋊D311yescharacteristic
92C2×C3—28no—
93C2×C3—44no—
94C2×C3D3×D414yes—
95C2×C3#23714yes—
96C2×C3C2×#6714yes—
97D3—124no—
98C22—21no—
99C22—21no—
100C22—21no—
101C22—21no—
102C22—21no—
103C22—181no—
104C22—181no—
105C22—181no—
106C22#63812yescomplemented
107C22C22×C3⋊D311yescharacteristic
108C4—21no—
109C4—92no—
110C4—181no—
111C4—181no—
112C3#93914yescomplemented
113C2—22no—
114C2—41no—
115C2—361no—
116C2D4×C3⋊D311yescharacteristic
117C2#383011yescharacteristic
118C2C2×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊D3
commutator, socle, cosocleC22×C32C23
FittingC2×C32×D4C2
hypercenterC2×D4C3⋊D3
hypocenterC32#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D4C2semidirect
2. C2×#638C2semidirect
3. C2×#638C2semidirect
4. C22×C3⋊Dic3C2semidirect
5. #3757C2semidirect
6. #3752C2semidirect
7. #3750C2semidirect
20. C2×C3×D4D3semidirect
32. C22×C32D4semidirect
40. C3⋊Dic3D4semidirect
61. C2×D4C3⋊D3semidirect
71. C22×C3#67semidirect
80. C32#121semidirect
106. C22#638semidirect
112. C3#939semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D42
C2×#6382
C22×C3⋊Dic32
#37572
#37522
#37502
#9393