Finite Group Databasebeta

← A4⋊(#733⋊C2) #14518106

Subgroups — A4⋊(#733⋊C2) #14518106

Order 1944.

267 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 267 conjugacy classes of subgroups — too many to draw. Only its 43 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×#733C211yesmaximal, characteristic, complemented
2A4⋊AGL(1,ℤ/9)—33nomaximal
3C3×C9⋊S4—31nomaximal
4#66364⋊C2—36nomaximal
5#66359⋊C2—32nomaximal
6#10619685—31nomaximal
7C3⋊(#733⋊C2)—41nomaximal
8A4×3−1+2D313yes—
9C3×C9×A4D311yescharacteristic
10C22×#733D311yescharacteristic, complemented
11C2×#733⋊C2—31no—
12#66364D316yescomplemented
13#66359D312yescomplemented
14#733⋊C4—31no—
15C3×#733—41noSylow
16C3×C3⋊S4—91no—
17C9⋊S4—31no—
18C9⋊S4—33no—
19C3×(C22⋊C9)⋊C2—92no—
20((C22⋊C9)⋊C2)⋊C3—96no—
21#611⋊C3—93no—
22C3×#611—91no—
23C3⋊AGL(1,ℤ/9)—123no—
24C3×C3⋊D9—121no—
25C2×#733—31no—
26#733⋊C2—61no—
27#733⋊C2—122no—
28#733⋊C2—126no—
29C32×A4C3⋊D311yescharacteristic
30C22×3−1+2C3⋊D313yes—
31C22×C3×C9C3⋊D311yescharacteristic
32C2×AGL(1,ℤ/9)—93no—
33C2×C3×D9—91no—
34#1094C3⋊D316yes—
35C3×C22⋊C9C3⋊D312yes—
36C9⋊A4—63no—
37C9×A4—31no—
38C9×A4—33no—
39C9×A4—61no—
403−1+2⋊C4—93no—
41C3×Dic9—91no—
42C3×3−1+2—43no—
43C32×C9—41no—
44#733—46no—
45#733—42no—
46#733S411yescharacteristic, complemented
47C3⋊S4—91no—
48C3×S4—273no—
49C3×#67—271no—
50(C22⋊C9)⋊C2—96no—
51(C22⋊C9)⋊C2—92no—
52#611—91no—
53#611—93no—
54C3×C3⋊D3—361no—
55C2×3−1+2—33no—
56C2×C3×C9—31no—
57C3⋊D9—121no—
58C3⋊D9—123no—
59AGL(1,ℤ/9)—183no—
60AGL(1,ℤ/9)—366no—
61C3×D9—181no—
62C3×D9—362no—
63C22×C32C3⋊(C3⋊D3)11yescharacteristic
64C2×C3×D3—271no—
65C3×A4—21no—
66C3×A4—33no—
67C3×A4#27211yescharacteristic
68C3×Dic3—271no—
69C22×C9—31no—
70C22×C9—33no—
71C2×D9—91no—
72C2×D9—93no—
73C22⋊C9—32no—
74C22⋊C9—36no—
75Dic9—91no—
76Dic9—93no—
77C33—41no—
783−1+2—46no—
793−1+2—243no—
803−1+2C3⋊S413yes—
81C3×C9—42no—
82C3×C9—121no—
83C3×C9—123no—
84C3×C9—241no—
85C3×C9C3⋊S411yescharacteristic
86S4—273no—
87C3×D4—811no—
88#67—271no—
89C2×C32—31no—
90C3⋊D3—361no—
91C3×D3—541no—
92C3×D3—1083no—
93C2×C9—91no—
94C2×C9—93no—
95D9—181no—
96D9—183no—
97D9—362no—
98D9—366no—
99C22×C3—31no—
100C22×C3—811no—
101C22×C3C3⋊#27211yescharacteristic
102C2×D3—271no—
103A4—61no—
104A4#733⋊C213yescomplemented
105C3×C4—811no—
106Dic3—271no—
107C32—41no—
108C32—81no—
109C32—123no—
110C32C3⋊(C3⋊S4)11yescharacteristic
111C9—31no—
112C9—33no—
113C9—122no—
114C9—126no—
115D4—811noSylow
116C2×C3—31no—
117C2×C3—91no—
118C2×C3—1621no—
119D3—541no—
120D3—1083no—
121C22—811no—
122C22C3⋊(#733⋊C2)11yescharacteristic, complemented
123C4—811no—
124C3—31no—
125C3—43no—
126C3—241no—
127C3A4⋊#27211yescharacteristic
128C2—31no—
129C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterA4×#733C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×#733D3
socleC22×C3C3⋊#272
LCSG ▷ A4×#733
UCSC1

Complements

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

NH ≅ G/Ntype
1. A4×#733C2semidirect
10. C22×#733D3semidirect
12. #66364D3semidirect
13. #66359D3semidirect
46. #733S4semidirect
104. A4#733⋊C2semidirect
122. C22C3⋊(#733⋊C2)semidirect

Maximal subgroups

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

subgroupindex
A4×#7332
A4⋊AGL(1,ℤ/9)3
C3×C9⋊S43
#66364⋊C23
#66359⋊C23
#106196853
C3⋊(#733⋊C2)4