Finite Group Databasebeta

← C22×C3⋊(#733⋊C2) #14518550

Subgroups — C22×C3⋊(#733⋊C2) #14518550

Order 1944.

894 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 181 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×C3×#733C211yesmaximal, characteristic, complemented
2C2×C3⋊(#733⋊C2)C216yesmaximal, direct product factor
3C22×C3⋊AGL(1,ℤ/9)—33nomaximal
4C22×C3×C3⋊D9—31nomaximal
5C22×#733⋊C2—39nomaximal
6C2×C3×#733C2213yescomplemented
7C3⋊(#733⋊C2)C2214yesdirect product factor
8C22×C3×3−1+2D313yes—
9C22×C32×C9D311yescharacteristic
10C2×C3⋊AGL(1,ℤ/9)—318no—
11C2×C3×C3⋊D9—36no—
12C22×#733D319yescomplemented
13C2×#733⋊C2—354no—
14C3×#733C2311yescharacteristic, complemented, Sylow
15C22×C3×C3⋊D3—91no—
16C22×C3⋊D9—31no—
17C22×C3⋊D9—33no—
18C22×AGL(1,ℤ/9)—99no—
19C22×C3×D9—93no—
20C2×C3×3−1+2C2×D319yes—
21C2×C32×C9C2×D313yes—
22C3⋊AGL(1,ℤ/9)—312no—
23C3×C3⋊D9—34no—
24C2×#733C2×D3127yescomplemented
25#733⋊C2—336no—
26C22×C33C3⋊D311yescharacteristic
27C2×C3×C3⋊D3—96no—
28C22×3−1+2—63no—
29C22×3−1+2C3⋊D319yes—
30C22×C3×C9—31no—
31C22×C3×C9—33no—
32C22×C3×C9—61no—
33C22×C3×C9C3⋊D313yes—
34C2×C3⋊D9—36no—
35C2×C3⋊D9—318no—
36C2×AGL(1,ℤ/9)—954no—
37C2×C3×D9—918no—
38C3×3−1+2C22×D313yes—
39C32×C9C22×D311yescharacteristic
40#733C22×D319yescomplemented
41C22×C3⋊D3—91no—
42C22×C3×D3—273no—
43C22×C3×D3—271no—
44C22×D9—93no—
45C22×D9—99no—
46C2×C33C2×C3⋊D313yes—
47C3×C3⋊D3—94no—
48C2×3−1+2—69no—
49C2×3−1+2C2×C3⋊D3127yes—
50C2×C3×C9—33no—
51C2×C3×C9—39no—
52C2×C3×C9—63no—
53C2×C3×C9C2×C3⋊D319yes—
54C3⋊D9—34no—
55C3⋊D9—312no—
56AGL(1,ℤ/9)—936no—
57C3×D9—912no—
58C22×C32—21no—
59C22×C32—33no—
60C22×C32#27211yescharacteristic
61C22×C32C3⋊(C3⋊D3)11yescharacteristic
62C2×C3⋊D3—96no—
63C2×C3×D3—2718no—
64C2×C3×D3—276no—
65C22×C9—33no—
66C22×C9—39no—
67C2×D9—918no—
68C2×D9—954no—
69C33C22×C3⋊D311yescharacteristic
703−1+2—63no—
713−1+2C22×C3⋊D319yes—
72C3×C9—31no—
73C3×C9—33no—
74C3×C9—61no—
75C3×C9C22×C3⋊D313yes—
76C23×C3—811no—
77C22×D3—273no—
78C22×D3—271no—
79C2×C32—23no—
80C2×C32—39no—
81C2×C32C2×#27213yes—
82C2×C32C2×C3⋊(C3⋊D3)13yes—
83C3⋊D3—94no—
84C3×D3—2712no—
85C3×D3—274no—
86C2×C9—39no—
87C2×C9—327no—
88D9—912no—
89D9—936no—
90C22×C3—31no—
91C22×C3—61no—
92C22×C3—816no—
93C22×C3#733⋊C213yescomplemented
94C22×C3C3⋊#27211yescharacteristic
95C2×D3—2718no—
96C2×D3—276no—
97C32—21no—
98C32—33no—
99C32C22×#27211yescharacteristic
100C32C22×C3⋊(C3⋊D3)11yescharacteristic
101C9—33no—
102C9—39no—
103C23—811noSylow
104C2×C3—33no—
105C2×C3—63no—
106C2×C3—814no—
107C2×C3C2×#733⋊C219yescomplemented
108C2×C3C2×C3⋊#27213yes—
109D3—2712no—
110D3—274no—
111C22—816no—
112C22C3⋊(#733⋊C2)11yescharacteristic, direct product factor
113C3—31no—
114C3—61no—
115C3C22×#733⋊C213yescomplemented
116C3C22×C3⋊#27211yescharacteristic
117C2—814no—
118C2C2×C3⋊(#733⋊C2)13yesdirect product factor
subgroupG/H
center, hypercenterC22C3⋊(#733⋊C2)
commutator, cosocle, hypocenterC3×#733C23
FrattiniC32C22×C3⋊(C3⋊D3)
FittingC22×C3×#733C2
socleC22×C32#272
LCSG ▷ C3×#733
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×#733C2semidirect
2. C2×C3⋊(#733⋊C2)C2direct (N × H)
6. C2×C3×#733C22semidirect
7. C3⋊(#733⋊C2)C22direct (N × H)
12. C22×#733D3semidirect
14. C3×#733C23semidirect
24. C2×#733C2×D3semidirect
40. #733C22×D3semidirect
93. C22×C3#733⋊C2semidirect
107. C2×C3C2×#733⋊C2semidirect
112. C22C3⋊(#733⋊C2)direct (N × H)
115. C3C22×#733⋊C2semidirect
118. C2C2×C3⋊(#733⋊C2)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7332
C2×C3⋊(#733⋊C2)2
C22×C3⋊AGL(1,ℤ/9)3
C22×C3×C3⋊D93
C22×#733⋊C23