Finite Group Databasebeta

← C3×A4×D27 #14518143

Subgroups — C3×A4×D27 #14518143

Order 1944.

179 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 179 conjugacy classes of subgroups — too many to draw. Only its 40 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×A4×C27C211yesmaximal, characteristic, complemented
2C3×A4×D9—31nomaximal
3C22×C3×D27C311yesmaximal, characteristic, complemented
4A4×D27C313yesmaximal, direct product factor
5C32×D27—41nomaximal
6C3×C9×A4D311yescharacteristic
7C22×C3×C27C2×C311yescharacteristic, complemented
8C2×C3×D27—31no—
9C2×C3×D27—31no—
10C3×C22⋊C27—21no—
11A4×C27—23no—
12A4×C27C2×C313yescomplemented
13C32×C27—41noSylow
14C3×D3×A4—91no—
15C22×C3×D9—31no—
16A4×D9—33no—
17C22×D27C3211yescharacteristic, complemented
18C32×D9—121no—
19C2×C3×C27—31no—
20C3×D27—31no—
21C3×D27—43no—
22C3×D27A411yescharacteristic, direct product factor
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—
36C3×C27—43no—
37C3×C27—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, direct product factor
53C22×C32C3×D911yescharacteristic
54C2×C3×D3—271no—
55C2×C3×D3—271no—
56C3×A4—21no—
57C3×A4—23no—
58C3×A4D2711yescharacteristic, direct product factor
59C3×A4C3×D913yes—
60C22×C9—21no—
61C22×C9C32×D311yescharacteristic
62C2×D9—91no—
63C2×D9—91no—
64C22⋊C9—23no—
65C33—41no—
66C3×C9—43no—
67C3×C9—83no—
68C3×C9—81no—
69C3×C9D3×A411yescharacteristic
70C27—21no—
71C27—83no—
72C27C2×C3×A411yescharacteristic, complemented
73C23×C3—271no—
74C22×D3—91no—
75C2×A4—273no—
76C2×C32—31no—
77C2×C32—1081no—
78C3×D3—91no—
79C3×D3—271no—
80C3×D3—363no—
81C2×C9—31no—
82C2×C9—61no—
83D9—31no—
84D9—91no—
85C22×C3—21no—
86C22×C3—811no—
87C22×C3—811no—
88C22×C3C3×D2711yescharacteristic, complemented
89C22×C3C32×D911yescharacteristic
90C2×D3—271no—
91C2×D3—271no—
92A4—23no—
93A4C3×D2713yesdirect product factor
94C32—41no—
95C32—43no—
96C32—83no—
97C32—81no—
98C32A4×D911yescharacteristic
99C9—21no—
100C9—83no—
101C9C3×D3×A411yescharacteristic
102C23—271noSylow
103C2×C3—31no—
104C2×C3—31no—
105C2×C3—61no—
106C2×C3—271no—
107C2×C3—811no—
108C2×C3—1083no—
109D3—91no—
110D3—271no—
111C22—811no—
112C22—811no—
113C22C32×D2711yescharacteristic, complemented
114C3—21no—
115C3—43no—
116C3—83no—
117C3A4×D2711yescharacteristic, direct product factor
118C3C3×A4×D911yescharacteristic
119C2—31no—
120C2—271no—
121C2—811no—
subgroupG/H
center, hypercenterC3A4×D27
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×A4×C27C2semidirect
3. C22×C3×D27C3semidirect
4. A4×D27C3direct (N × H)
7. C22×C3×C27C2×C3semidirect
12. A4×C27C2×C3semidirect
17. C22×D27C32semidirect
22. C3×D27A4direct (N × H)
31. C22×C27C2×C32semidirect
39. C3×C27C2×A4semidirect
52. D27C3×A4direct (N × H)
58. C3×A4D27direct (N × H)
72. C27C2×C3×A4semidirect
88. C22×C3C3×D27semidirect
93. A4C3×D27direct (N × H)
113. C22C32×D27semidirect
117. C3A4×D27direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×C272
C3×A4×D93
C22×C3×D273
A4×D273
C32×D274