Finite Group Databasebeta

← #11757415⋊C2 #14516472

Subgroups — #11757415⋊C2 #14516472

Order 1944.

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

normal subgroups only

This group has 189 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#11757415C211yesmaximal, characteristic, complemented
2C3⋊(((C22⋊C9)⋊C2)⋊C3)—31nomaximal
3C3⋊(((C22⋊C9)⋊C2)⋊C3)—31nomaximal
4#10619746—31nomaximal
5#10619630—31nomaximal
6#6860⋊C2—41nomaximal
7C3×#1094D311yescharacteristic
8C3×#1094D311yescharacteristic
9C22×C32⋊C9D311yescharacteristic
10C2×#4169—31no—
11C32⋊(C22⋊C9)D311yescharacteristic
12#66316—31no—
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((C22⋊C9)⋊C2)⋊C3—93no—
20#6233—31no—
21C3⋊AGL(1,ℤ/9)—121no—
22C3⋊AGL(1,ℤ/9)—121no—
23C2×C32⋊C9—31no—
24#4169—61no—
25#4169—121no—
26C22×C33C3⋊D311yescharacteristic
27C2×C3×C3⋊D3—91no—
28C3×C3⋊Dic3—91no—
29C22×C3×C9—31no—
30C2×C3⋊D9—31no—
31#1094—33no—
32#1094—33no—
33C3×C22⋊C9—31no—
34C3×C22⋊C9—31no—
35C3×C22⋊C9—31no—
36C3⋊Dic9—31no—
37C3×3−1+2—41no—
38C3×3−1+2—41no—
39C32⋊C9—41no—
40C32⋊C9S411yescharacteristic
41#638—91no—
42C3×#67—271no—
43C3×#67—271no—
44C3×#67—271no—
45C3×#67—271no—
46(C22⋊C9)⋊C2—93no—
47(C22⋊C9)⋊C2—93no—
48(C22⋊C9)⋊C2—271no—
49#611—271no—
50C2×C33—31no—
51C3×C3⋊D3—181no—
52C2×C3×C9—31no—
53C2×C3×C9—61no—
54C3⋊D9—61no—
55C3⋊D9—121no—
56C3⋊D9—121no—
57C3⋊D9—121no—
58AGL(1,ℤ/9)—363no—
59AGL(1,ℤ/9)—363no—
60C22×C32—31no—
61C22×C32—31no—
62C22×C32—31no—
63C22×C32—31no—
64C22×C32#27211yescharacteristic
65C2×C3⋊D3—91no—
66C2×C3×D3—271no—
67C2×C3×D3—271no—
68C2×C3×D3—271no—
69C2×C3×D3—271no—
70C3⋊Dic3—91no—
71C3×Dic3—271no—
72C3×Dic3—271no—
73C3×Dic3—271no—
74C3×Dic3—271no—
75C22×C9—91no—
76C2×D9—271no—
77C22⋊C9—33no—
78C22⋊C9—33no—
79C22⋊C9—91no—
80Dic9—271no—
81C33C3⋊S411yescharacteristic
823−1+2—123no—
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—271no—
92#67—271no—
93C2×C32—31no—
94C2×C32—31no—
95C2×C32—61no—
96C2×C32—91no—
97C2×C32—91no—
98C2×C32—91no—
99C3⋊D3—181no—
100C3×D3—541no—
101C3×D3—541no—
102C3×D3—541no—
103C3×D3—541no—
104C2×C9—91no—
105C2×C9—181no—
106D9—363no—
107D9—363no—
108D9—541no—
109D9—1081no—
110C22×C3—91no—
111C22×C3—811no—
112C22×C3#418311yescharacteristic
113C22×C3#418311yescharacteristic
114C22×C3#733⋊C211yescharacteristic
115C22×C3#733⋊C211yescharacteristic
116C2×D3—271no—
117C2×D3—271no—
118C2×D3—271no—
119C2×D3—271no—
120C3×C4—811no—
121Dic3—271no—
122Dic3—271no—
123Dic3—271no—
124Dic3—271no—
125C32—31no—
126C32—31no—
127C32—31no—
128C32—31no—
129C32#625811yescharacteristic
130C9—91no—
131C9—123no—
132C9—123no—
133C9—361no—
134D4—811noSylow
135C2×C3—31no—
136C2×C3—31no—
137C2×C3—31no—
138C2×C3—31no—
139C2×C3—91no—
140C2×C3—181no—
141C2×C3—1621no—
142D3—541no—
143D3—541no—
144D3—541no—
145D3—541no—
146C22—811no—
147C22#6860⋊C211yescharacteristic, complemented
148C4—811no—
149C3—91no—
150C3#66359⋊C211yescharacteristic
151C3#1061975711yescharacteristic
152C3#66366⋊C211yescharacteristic
153C3#66364⋊C211yescharacteristic
154C2—31no—
155C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757415C2
FrattiniC33C3⋊S4
FittingC22×C32⋊C9D3
socleC22×C32#272
LCSG ▷ #11757415
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757415C2semidirect
147. C22#6860⋊C2semidirect

Maximal subgroups

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

subgroupindex
#117574152
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
#106197463
#106196303
#6860⋊C24