Finite Group Databasebeta

← #11757455⋊C2 #14516495

Subgroups — #11757455⋊C2 #14516495

Order 1944.

209 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 209 conjugacy classes of subgroups — too many to draw. Only its 21 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#11757455C211yesmaximal, characteristic, complemented
2C3⋊(((C22⋊C9)⋊C2)⋊C3)—31nomaximal
3#10619980—31nomaximal
4#10619746—31nomaximal
5#10619746—31nomaximal
6#6860⋊C2—41nomaximal
7C22×C3×3−1+2D311yescharacteristic
8C2×C3⋊AGL(1,ℤ/9)—31no—
9C3×#1094D311yescharacteristic
10C3⋊(3−1+2⋊C4)—31no—
11C32⋊(C22⋊C9)D311yescharacteristic
12C32⋊(C22⋊C9)D311yescharacteristic
13#6860—41noSylow
14C3×#638—91no—
15C3⋊((C22⋊C9)⋊C2)—31no—
16C3⋊((C22⋊C9)⋊C2)—31no—
17C3⋊((C22⋊C9)⋊C2)—31no—
18((C22⋊C9)⋊C2)⋊C3—93no—
19#6233—31no—
20#611⋊C3—93no—
21C2×C3×3−1+2—31no—
22C3⋊AGL(1,ℤ/9)—61no—
23C3⋊AGL(1,ℤ/9)—121no—
24#4169—121no—
25#4169—121no—
26C22×C33C3⋊D311yescharacteristic
27C2×C3×C3⋊D3—91no—
28C3×C3⋊Dic3—91no—
29C22×3−1+2—33no—
30C22×C3×C9—31no—
31C2×C3⋊D9—31no—
32C2×AGL(1,ℤ/9)—93no—
33#1094—33no—
34C3×C22⋊C9—31no—
35C3×C22⋊C9—31no—
36C3×C22⋊C9—31no—
37C3⋊Dic9—31no—
383−1+2⋊C4—93no—
39C3×3−1+2—41no—
40C3×3−1+2S411yescharacteristic
41C32⋊C9—41no—
42C32⋊C9—41no—
43#638—91no—
44C3×#67—271no—
45C3×#67—271no—
46C3×#67—272no—
47(C22⋊C9)⋊C2—93no—
48(C22⋊C9)⋊C2—271no—
49(C22⋊C9)⋊C2—271no—
50#611—93no—
51C2×C33—31no—
52C3×C3⋊D3—181no—
53C2×3−1+2—33no—
54C2×3−1+2—63no—
55C2×C3×C9—31no—
56C2×C3×C9—61no—
57C3⋊D9—61no—
58C3⋊D9—121no—
59C3⋊D9—121no—
60C3⋊D9—121no—
61AGL(1,ℤ/9)—183no—
62AGL(1,ℤ/9)—363no—
63C22×C32—31no—
64C22×C32—31no—
65C22×C32—32no—
66C22×C32#27211yescharacteristic
67C2×C3⋊D3—91no—
68C2×C3×D3—271no—
69C2×C3×D3—271no—
70C2×C3×D3—272no—
71C3⋊Dic3—91no—
72C3×Dic3—271no—
73C3×Dic3—271no—
74C3×Dic3—272no—
75C22×C9—33no—
76C2×D9—93no—
77C22⋊C9—33no—
78C22⋊C9—91no—
79C22⋊C9—91no—
80Dic9—93no—
81C33C3⋊S411yescharacteristic
823−1+2—33no—
833−1+2—123no—
84C3×C9—31no—
85C3×C9—121no—
86C3×C9—121no—
87C3×C9—121no—
88C3×D4—811no—
89#67—271no—
90#67—271no—
91#67—272no—
92C2×C32—31no—
93C2×C32—31no—
94C2×C32—61no—
95C2×C32—91no—
96C2×C32—92no—
97C3⋊D3—181no—
98C3×D3—541no—
99C3×D3—541no—
100C3×D3—542no—
101C2×C9—33no—
102C2×C9—63no—
103D9—183no—
104D9—363no—
105D9—1081no—
106D9—1081no—
107C22×C3—91no—
108C22×C3—811no—
109C22×C3#418311yescharacteristic
110C22×C3#418311yescharacteristic
111C22×C3#733⋊C212yes—
112C2×D3—271no—
113C2×D3—271no—
114C2×D3—272no—
115C3×C4—811no—
116Dic3—271no—
117Dic3—271no—
118Dic3—272no—
119C32—31no—
120C32—32no—
121C32—31no—
122C32#625811yescharacteristic
123C9—33no—
124C9—123no—
125C9—361no—
126C9—361no—
127D4—811noSylow
128C2×C3—31no—
129C2×C3—32no—
130C2×C3—31no—
131C2×C3—91no—
132C2×C3—181no—
133C2×C3—1621no—
134D3—541no—
135D3—542no—
136D3—541no—
137C22—811no—
138C22#6860⋊C211yescharacteristic, complemented
139C4—811no—
140C3—91no—
141C3#66366⋊C211yescharacteristic
142C3#66364⋊C212yes—
143C3#1061976211yescharacteristic
144C2—31no—
145C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757455C2
FrattiniC33C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C32#272
LCSG ▷ #11757455
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757455C2semidirect
138. C22#6860⋊C2semidirect

Maximal subgroups

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

subgroupindex
#117574552
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
#106199803
#106197463
#6860⋊C24