Finite Group Databasebeta

← A4×C3⋊D27 #14518233

Subgroups — A4×C3⋊D27 #14518233

Order 1944.

212 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 45 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
2A4×C3⋊D9—31nomaximal
3C22×C3⋊D27C311yesmaximal, characteristic, complemented
4A4×D27—33nomaximal
5C3×C3⋊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×C27D313yescomplemented
13C32×C27—41noSylow
14A4×C3⋊D3—91no—
15C22×C3⋊D9—31no—
16A4×D9—92no—
17A4×D9—91no—
18C22×D27—33no—
19C3×C3⋊D9—121no—
20C2×C3×C27—31no—
21C3⋊D27—31no—
22C3⋊D27A411yescharacteristic, direct product factor
23C3×D27—123no—
24C32×A4D911yescharacteristic
25C22×C3×C9C3×D311yescharacteristic
26C2×C3⋊D9—91no—
27C2×C3⋊D9—91no—
28C3×C22⋊C9—21no—
29C9×A4—22no—
30C9×A4—21no—
31C9×A4D912yes—
32C9×A4C3⋊D311yescharacteristic
33C22×C27C3×D313yescomplemented
34C2×D27—93no—
35C2×D27—93no—
36C22⋊C27—23no—
37C32×C9—41no—
38C3×C27—43no—
39C3×C27—81no—
40C3×C27—83no—
41C3×C27C2×A411yescharacteristic, complemented
42C22×C3⋊D3—91no—
43D3×A4—273no—
44D3×A4—271no—
45C22×D9—92no—
46C22×D9—91no—
47C3×C3⋊D3—361no—
48C2×C3×C9—31no—
49C3⋊D9—31no—
50C3⋊D9—91no—
51C3×D9—361no—
52C3×D9—362no—
53C2×C27—33no—
54D27—33no—
55D27—93no—
56C22×C32C3×D911yescharacteristic
57C2×C3⋊D3—271no—
58C2×C3⋊D3—271no—
59C3×A4—23no—
60C3×A4—21no—
61C3×A4D2713yescomplemented
62C3×A4C3⋊D911yescharacteristic
63C22×C9C3×D912yes—
64C22×C9C3×C3⋊D311yescharacteristic
65C2×D9—271no—
66C2×D9—272no—
67C2×D9—271no—
68C2×D9—272no—
69C22⋊C9—22no—
70C22⋊C9—21no—
71C33—41no—
72C3×C9—42no—
73C3×C9—41no—
74C3×C9—81no—
75C3×C9—82no—
76C3×C9—81no—
77C3×C9D3×A411yescharacteristic
78C27—83no—
79C27D3×A413yescomplemented
80C22×D3—273no—
81C22×D3—271no—
82C2×A4—811no—
83C2×C32—31no—
84C3⋊D3—91no—
85C3⋊D3—271no—
86C3×D3—1081no—
87C3×D3—1083no—
88C2×C9—32no—
89C2×C9—31no—
90D9—92no—
91D9—91no—
92D9—272no—
93D9—271no—
94C22×C3C3×D2713yescomplemented
95C22×C3C3×C3⋊D911yescharacteristic
96C2×D3—811no—
97C2×D3—813no—
98C2×D3—811no—
99C2×D3—813no—
100A4—23no—
101A4—21no—
102A4C3⋊D2711yescharacteristic, direct product factor
103C32—43no—
104C32—41no—
105C32—83no—
106C32—81no—
107C32A4×D911yescharacteristic
108C9—82no—
109C9—81no—
110C9A4×D912yes—
111C9A4×C3⋊D311yescharacteristic
112C23—811noSylow
113C2×C3—33no—
114C2×C3—31no—
115C2×C3—3241no—
116D3—273no—
117D3—271no—
118D3—813no—
119D3—811no—
120C22—2431no—
121C22—2431no—
122C22C3×C3⋊D2711yescharacteristic, complemented
123C3—41no—
124C3—83no—
125C3—81no—
126C3A4×D2713yescomplemented
127C3A4×C3⋊D911yescharacteristic
128C2—31no—
129C2—811no—
130C2—2431no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC22×C3×C27C2×C3
FrattiniC9A4×C3⋊D3
socleC22×C32C3×D9
LCSG ▷ C22×C3×C27
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×A4×C27C2semidirect
3. C22×C3⋊D27C3semidirect
7. C22×C3×C27C2×C3semidirect
12. A4×C27D3semidirect
22. C3⋊D27A4direct (N × H)
33. C22×C27C3×D3semidirect
41. C3×C27C2×A4semidirect
61. C3×A4D27semidirect
79. C27D3×A4semidirect
94. C22×C3C3×D27semidirect
102. A4C3⋊D27direct (N × H)
122. C22C3×C3⋊D27semidirect
126. C3A4×D27semidirect

Maximal subgroups

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

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