Finite Group Databasebeta

← C3×D27⋊A4 #14518144

Subgroups — C3×D27⋊A4 #14518144

Order 1944.

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

normal subgroups only

This group has 167 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
1C3×C27⋊A4C211yesmaximal, characteristic, complemented
2C3×A4×D9—31nomaximal
3C22×C3×D27C311yesmaximal, characteristic, complemented
4D27⋊A4C313yesmaximal, direct product factor
5C3×D27⋊C3—41nomaximal
6C3×C9×A4D311yescharacteristic
7C22×C3×C27C2×C311yescharacteristic, complemented
8C2×C3×D27—31no—
9C2×C3×D27—31no—
10C3×C22⋊C27—21no—
11C27⋊A4—23no—
12C27⋊A4C2×C313yescomplemented
13C3×C27⋊C3—41noSylow
14C3×D3×A4—91no—
15C22×C3×D9—31no—
16A4×D9—33no—
17C22×D27C3211yescharacteristic, complemented
18C32×D9—121no—
19C2×C3×C27—31no—
20D27⋊C3—43no—
21C3×D27—31no—
22C3×D27A411yescharacteristic, complemented
23C32×A4D911yescharacteristic
24C22×C3×C9C3×D311yescharacteristic
25C2×C3×D9—91no—
26C2×C3×D9—91no—
27C3×C22⋊C9—21no—
28C9×A4—23no—
29C9×A4C3×D313yes—
30C22×C27—21no—
31C22×C27C2×C3211yescharacteristic, complemented
32C2×D27—31no—
33C2×D27—31no—
34C22⋊C27—23no—
35C32×C9—41no—
36C27⋊C3—43no—
37C27⋊C3—83no—
38C3×C27—81no—
39C3×C27C2×A411yescharacteristic, complemented
40C22×C3×D3—91no—
41C2×C3×A4—271no—
42D3×A4—93no—
43C22×D9—31no—
44C32×D3—361no—
45C2×C3×C9—31no—
46C3×D9—31no—
47C3×D9—91no—
48C3×D9—123no—
49C2×C27—31no—
50C2×C27—61no—
51D27—31no—
52D27C3×A411yescharacteristic, complemented
53C22×C32C3×D911yescharacteristic
54C2×C3×D3—271no—
55C2×C3×D3—271no—
56C3×A4—31no—
57C3×A4—61no—
58C3×A4C3×D913yes—
59C22×C9—21no—
60C22×C9C32×D311yescharacteristic
61C2×D9—91no—
62C2×D9—91no—
63C22⋊C9—23no—
64C33—41no—
65C3×C9—43no—
66C3×C9—83no—
67C3×C9—81no—
68C3×C9D3×A411yescharacteristic
69C27—21no—
70C27—83no—
71C27C2×C3×A411yescharacteristic, complemented
72C23×C3—271no—
73C22×D3—91no—
74C2×A4—273no—
75C2×C32—31no—
76C2×C32—1081no—
77C3×D3—91no—
78C3×D3—271no—
79C3×D3—363no—
80C2×C9—31no—
81C2×C9—61no—
82D9—31no—
83D9—91no—
84C22×C3—21no—
85C22×C3—811no—
86C22×C3—811no—
87C22×C3D27⋊C311yescharacteristic, complemented
88C22×C3C32×D911yescharacteristic
89C2×D3—271no—
90C2×D3—271no—
91A4—33no—
92C32—43no—
93C32—121no—
94C32—241no—
95C32A4×D911yescharacteristic
96C9—21no—
97C9—83no—
98C9C3×D3×A411yescharacteristic
99C23—271noSylow
100C2×C3—31no—
101C2×C3—31no—
102C2×C3—61no—
103C2×C3—271no—
104C2×C3—811no—
105C2×C3—1083no—
106D3—91no—
107D3—271no—
108C22—811no—
109C22—811no—
110C22C3×D27⋊C311yescharacteristic, complemented
111C3—21no—
112C3—123no—
113C3D27⋊A411yescharacteristic, direct product factor
114C3C3×A4×D911yescharacteristic
115C2—31no—
116C2—271no—
117C2—811no—
subgroupG/H
center, hypercenterC3D27⋊A4
commutator, cosocle, hypocenterC22×C27C2×C32
FrattiniC9C3×D3×A4
FittingC22×C3×C27C2×C3
socleC22×C32C3×D9
LCSG ▷ C22×C27
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C27⋊A4C2semidirect
3. C22×C3×D27C3semidirect
4. D27⋊A4C3direct (N × H)
7. C22×C3×C27C2×C3semidirect
12. C27⋊A4C2×C3semidirect
17. C22×D27C32semidirect
22. C3×D27A4semidirect
31. C22×C27C2×C32semidirect
39. C3×C27C2×A4semidirect
52. D27C3×A4semidirect
71. C27C2×C3×A4semidirect
87. C22×C3D27⋊C3semidirect
110. C22C3×D27⋊C3semidirect
113. C3D27⋊A4direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C27⋊A42
C3×A4×D93
C22×C3×D273
D27⋊A43
C3×D27⋊C34