Finite Group Databasebeta

← A4⋊(D27⋊C3) #14518024

Subgroups — A4⋊(D27⋊C3) #14518024

Order 1944.

170 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 33 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
1A4×C27⋊C3C211yesmaximal, characteristic, complemented
2C3×C9⋊S4—31nomaximal
3A4⋊D27C311yesmaximal, characteristic, complemented
4((C22⋊C27)⋊C2)⋊C3—32nomaximal
5#6171⋊C3—31nomaximal
6C3⋊(D27⋊C3)—41nomaximal
7C3×C9×A4D311yescharacteristic
8C22×C27⋊C3D311yescharacteristic, complemented
9C2×D27⋊C3—31no—
10#66353D312yescomplemented
11C27⋊A4—21no—
12C27⋊A4—22no—
13A4×C27—21no—
14A4×C27C2×C311yescharacteristic, complemented
15(C27⋊C3)⋊C4—31no—
16C3×C27⋊C3—41noSylow
17C3×C3⋊S4—91no—
18C9⋊S4—31no—
19C3×(C22⋊C9)⋊C2—92no—
20C3×#611—91no—
21(C22⋊C27)⋊C2—32no—
22#6171—31no—
23C3×C3⋊D9—121no—
24C2×C27⋊C3—31no—
25C3⋊D27—41no—
26D27⋊C3—61no—
27D27⋊C3—122no—
28C32×A4D911yescharacteristic
29C22×C3×C9C3⋊D311yescharacteristic
30C2×C3×D9—91no—
31C3×C22⋊C9D912yes—
32C9×A4—21no—
33C9×A4—21no—
34C9×A4—22no—
35C9×A4C3×D311yescharacteristic
36C3×Dic9—91no—
37C22×C27—21no—
38C22×C27C3×D311yescharacteristic, complemented
39C2×D27—31no—
40C22⋊C27—22no—
41C22⋊C27C3×D312yescomplemented
42Dic27—31no—
43C32×C9—41no—
44C27⋊C3—42no—
45C27⋊C3—82no—
46C27⋊C3—81no—
47C27⋊C3S411yescharacteristic, complemented
48C3×C27—41no—
49C3×C27—81no—
50C3⋊S4—91no—
51C3×S4—273no—
52C3×#67—271no—
53(C22⋊C9)⋊C2—92no—
54#611—91no—
55C3×C3⋊D3—361no—
56C2×C3×C9—31no—
57C3⋊D9—121no—
58C3×D9—181no—
59C3×D9—362no—
60C2×C27—31no—
61C2×C27—61no—
62D27—61no—
63D27—122no—
64C22×C32C3⋊D911yescharacteristic
65C2×C3×D3—271no—
66C3×A4—21no—
67C3×A4—33no—
68C3×A4C3×D911yescharacteristic
69C3×Dic3—271no—
70C22×C9—21no—
71C22×C9C3×C3⋊D311yescharacteristic
72C2×D9—91no—
73C22⋊C9—22no—
74C22⋊C9C3×D912yes—
75Dic9—91no—
76C33—41no—
77C3×C9—41no—
78C3×C9—42no—
79C3×C9—82no—
80C3×C9—81no—
81C3×C9—81no—
82C3×C9C3⋊S411yescharacteristic
83C27—21no—
84C27—42no—
85C27—82no—
86C27C3×S411yescharacteristic, complemented
87S4—273no—
88C3×D4—811no—
89#67—271no—
90C2×C32—31no—
91C3⋊D3—361no—
92C3×D3—541no—
93C3×D3—1083no—
94C2×C9—31no—
95C2×C9—61no—
96D9—181no—
97D9—362no—
98C22×C3—31no—
99C22×C3—811no—
100C22×C3C3×C3⋊D911yescharacteristic
101C2×D3—271no—
102A4—61no—
103A4D27⋊C313yescomplemented
104C3×C4—811no—
105Dic3—271no—
106C32—41no—
107C32—81no—
108C32—123no—
109C32C9⋊S411yescharacteristic
110C9—21no—
111C9—42no—
112C9—82no—
113C9C3×C3⋊S411yescharacteristic
114D4—811noSylow
115C2×C3—31no—
116C2×C3—91no—
117C2×C3—1621no—
118D3—541no—
119D3—1083no—
120C22—811no—
121C22C3⋊(D27⋊C3)11yescharacteristic, complemented
122C4—811no—
123C3—31no—
124C3—43no—
125C3—241no—
126C3C3×C9⋊S411yescharacteristic
127C2—31no—
128C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterA4×C27C2×C3
FrattiniC9C3×C3⋊S4
FittingC22×C27⋊C3D3
socleC22×C3C3×C3⋊D9
LCSG ▷ A4×C27
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×C27⋊C3C2semidirect
3. A4⋊D27C3semidirect
8. C22×C27⋊C3D3semidirect
10. #66353D3semidirect
14. A4×C27C2×C3semidirect
38. C22×C27C3×D3semidirect
41. C22⋊C27C3×D3semidirect
47. C27⋊C3S4semidirect
86. C27C3×S4semidirect
103. A4D27⋊C3semidirect
121. C22C3⋊(D27⋊C3)semidirect

Maximal subgroups

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

subgroupindex
A4×C27⋊C32
C3×C9⋊S43
A4⋊D273
((C22⋊C27)⋊C2)⋊C33
#6171⋊C33
C3⋊(D27⋊C3)4