Finite Group Databasebeta

← #11757797⋊C2 #14518025

Subgroups — #11757797⋊C2 #14518025

Order 1944.

150 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 30 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
1#11757797C211yesmaximal, characteristic, complemented
2#10620045—31nomaximal
3A4⋊D27C311yesmaximal, characteristic, complemented
4C3×(C22⋊C27)⋊C2—31nomaximal
5((C22⋊C27)⋊C2)⋊C3—31nomaximal
6#6171⋊C3—31nomaximal
7#92318—41nomaximal
8#66436D311yescharacteristic
9C22×C27⋊C3D311yescharacteristic, complemented
10C2×D27⋊C3—31no—
11#66353D311yescharacteristic, complemented
12C3×C22⋊C27D311yescharacteristic, complemented
13C27⋊A4—21no—
14C27⋊A4—21no—
15C27⋊A4—21no—
16A4×C27—21no—
17A4×C27C2×C311yescharacteristic, complemented
18(C27⋊C3)⋊C4—31no—
19#6903—41noSylow
20C9⋊S4—31no—
21(C3⋊S4)⋊C3—91no—
22((C22⋊C9)⋊C2)⋊C3—92no—
23C3×#611—91no—
24(C22⋊C27)⋊C2—31no—
25(C22⋊C27)⋊C2—31no—
26#6171—31no—
27#4207—121no—
28C2×C27⋊C3—31no—
29C3⋊D27—41no—
30D27⋊C3—61no—
31D27⋊C3—121no—
32C3×D27—121no—
33C22×C3×C9C3⋊D311yescharacteristic
34C2×C3×D9—91no—
35C22⋊H(3,𝔽3)D911yescharacteristic
36#1094D912yes—
37C9⋊A4—21no—
38C9⋊A4—22no—
39C9×A4—21no—
40C9×A4C3×D311yescharacteristic
41C3×Dic9—91no—
42C22×C27—21no—
43C22×C27C3×D311yescharacteristic
44C2×D27—31no—
45C22⋊C27—21no—
46C22⋊C27—21no—
47C22⋊C27C3×D311yescharacteristic
48C22⋊C27C3×D311yescharacteristic
49Dic27—31no—
50#737—41no—
51C27⋊C3—41no—
52C27⋊C3—81no—
53C27⋊C3—81no—
54C27⋊C3—81no—
55C27⋊C3S411yescharacteristic, complemented
56C3×C27—41no—
57C3×C27—41no—
58C3×C27—81no—
59C3⋊S4—91no—
60C3×#67—271no—
61(C22⋊C9)⋊C2—92no—
62#611—91no—
63C2×C3×C9—31no—
64C3⋊D9—121no—
65AGL(1,ℤ/9)—362no—
66(C3⋊D3)⋊C3—361no—
67C3×D9—181no—
68C2×C27—31no—
69C2×C27—61no—
70D27—61no—
71D27—121no—
72D27—121no—
73C22×C32C3⋊D911yescharacteristic
74C2×C3×D3—271no—
75C3×A4—21no—
76C3×A4C3×D911yescharacteristic
77C3×Dic3—271no—
78C22×C9—21no—
79C22×C9C3×C3⋊D311yescharacteristic
80C2×D9—91no—
81C22⋊C9—22no—
82C22⋊C9C3×D912yes—
83Dic9—91no—
843−1+2—42no—
853−1+2—82no—
863−1+2—81no—
87H(3,𝔽3)—41no—
88C3×C9—41no—
89C3×C9—81no—
90C3×C9C3⋊S411yescharacteristic
91C27—21no—
92C27—41no—
93C27—41no—
94C27—81no—
95C27—81no—
96C27C3×S411yescharacteristic
97S4—811no—
98C3×D4—811no—
99#67—271no—
100C2×C32—31no—
101C3⋊D3—361no—
102C3×D3—541no—
103C2×C9—31no—
104C2×C9—61no—
105D9—181no—
106D9—362no—
107C22×C3—31no—
108C22×C3—811no—
109C22×C3C3×C3⋊D911yescharacteristic
110C2×D3—271no—
111A4—31no—
112A4—61no—
113C3×C4—811no—
114Dic3—271no—
115C32—41no—
116C32—81no—
117C32C9⋊S411yescharacteristic
118C9—21no—
119C9—42no—
120C9—82no—
121C9C3×C3⋊S411yescharacteristic
122D4—811noSylow
123C2×C3—31no—
124C2×C3—91no—
125C2×C3—1621no—
126D3—541no—
127D3—3241no—
128C22—811no—
129C22#9231811yescharacteristic, complemented
130C4—811no—
131C3—31no—
132C3—121no—
133C3—241no—
134C3C3×C9⋊S411yescharacteristic
135C2—31no—
136C2—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. #11757797C2semidirect
3. A4⋊D27C3semidirect
9. C22×C27⋊C3D3semidirect
11. #66353D3semidirect
12. C3×C22⋊C27D3semidirect
17. A4×C27C2×C3semidirect
55. C27⋊C3S4semidirect
129. C22#92318semidirect

Maximal subgroups

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

subgroupindex
#117577972
#106200453
A4⋊D273
C3×(C22⋊C27)⋊C23
((C22⋊C27)⋊C2)⋊C33
#6171⋊C33
#923184