Finite Group Databasebeta

← #14518076

Subgroups — #14518076

Order 1944.

276 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 28 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#11757852C211yesmaximal, characteristic, complemented
2C3×(C3⋊S4)⋊C3—33nomaximal
3C3×#611⋊C3—31nomaximal
4#10619750C311yesmaximal, characteristic, complemented
5#92333—41nomaximal
6C22×C3×3−1+2D311yescharacteristic, complemented
7C2×C3×AGL(1,ℤ/9)—31no—
8C3×C22⋊H(3,𝔽3)D313yescomplemented
9C3×3−1+2⋊C4—31no—
10#66358—21no—
11#66358—23no—
12#66358C2×C311yescharacteristic, complemented
13#6911—41noSylow
14C3×C3⋊S4—33no—
15C32×#67—91no—
16(C3⋊S4)⋊C3—36no—
17(C3⋊S4)⋊C3—33no—
18#611⋊C3—33no—
19C3×#611—31no—
20C2×C3×3−1+2—31no—
21C3×AGL(1,ℤ/9)—61no—
22C3×(C3⋊D3)⋊C3—123no—
23#4185—41no—
24C22×C33C3⋊D311yescharacteristic
25C2×C32×D3—91no—
26C32×A4—33no—
27C32×Dic3—91no—
28C22×3−1+2—33no—
29C22×C3×C9—21no—
30C22×C3×C9C3×D311yescharacteristic, complemented
31C2×AGL(1,ℤ/9)—33no—
32C2×C3×D9—31no—
33C22⋊H(3,𝔽3)—23no—
34C22⋊H(3,𝔽3)—36no—
35C22⋊H(3,𝔽3)C3×D313yescomplemented
363−1+2⋊C4—33no—
37C3×Dic9—31no—
38C3×3−1+2S411yescharacteristic, complemented
39C3×H(3,𝔽3)—43no—
40#732—41no—
41#732—83no—
42#732—81no—
43C3⋊S4—33no—
44C3×S4—273no—
45C32×D4—271no—
46C3×#67—93no—
47C3×#67—91no—
48#611—31no—
49C2×C33—31no—
50C3×C3⋊D3—123no—
51C32×D3—181no—
52C2×3−1+2—33no—
53C2×3−1+2—63no—
54C2×C3×C9—31no—
55C2×C3×C9—61no—
56AGL(1,ℤ/9)—63no—
57(C3⋊D3)⋊C3—123no—
58(C3⋊D3)⋊C3—126no—
59C3×D9—61no—
60C22×C32—91no—
61C22×C32—271no—
62C22×C32#27213yes—
63C22×C32C3×C3⋊D311yescharacteristic
64C2×C3×D3—91no—
65C2×C3×D3—93no—
66C3×A4—33no—
67C3×A4—63no—
68C3×A4—93no—
69C3×A4—183no—
70C32×C4—271no—
71C3×Dic3—91no—
72C3×Dic3—93no—
73C22×C9—31no—
74C22×C9—61no—
75C2×D9—31no—
76Dic9—31no—
77C33—123no—
78C33C3⋊S411yescharacteristic
793−1+2—33no—
80H(3,𝔽3)—43no—
81H(3,𝔽3)—83no—
82H(3,𝔽3)—126no—
83C3×C9—21no—
84C3×C9C3×S411yescharacteristic, complemented
85S4—273no—
86C3×D4—271no—
87C3×D4—273no—
88#67—91no—
89C2×C32—31no—
90C2×C32—33no—
91C2×C32—91no—
92C2×C32—181no—
93C2×C32—541no—
94C3⋊D3—123no—
95C3×D3—183no—
96C3×D3—181no—
97C3×D3—1083no—
98C2×C9—31no—
99C2×C9—61no—
100C2×C9—63no—
101D9—61no—
102C22×C3—31no—
103C22×C3—33no—
104C22×C3—271no—
105C22×C3—273no—
106C22×C3C3×#27211yescharacteristic
107C2×D3—91no—
108A4—93no—
109A4—183no—
110C3×C4—271no—
111C3×C4—273no—
112Dic3—91no—
113C32—91no—
114C32—123no—
115C32—243no—
116C32—363no—
117C32—723no—
118C32#625813yes—
119C32C3×C3⋊S411yescharacteristic
120C9—31no—
121C9—61no—
122D4—271noSylow
123C2×C3—31no—
124C2×C3—31no—
125C2×C3—61no—
126C2×C3—93no—
127C2×C3—543no—
128C2×C3—541no—
129D3—181no—
130D3—1083no—
131C22—271no—
132C22#9233311yescharacteristic, complemented
133C4—271no—
134C3—31no—
135C3—33no—
136C3—363no—
137C3—723no—
138C3C3×#625811yescharacteristic
139C2—31no—
140C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#66358C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C3C3×#272
LCSG ▷ #66358
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757852C2semidirect
4. #10619750C3semidirect
6. C22×C3×3−1+2D3semidirect
8. C3×C22⋊H(3,𝔽3)D3semidirect
12. #66358C2×C3semidirect
30. C22×C3×C9C3×D3semidirect
35. C22⋊H(3,𝔽3)C3×D3semidirect
38. C3×3−1+2S4semidirect
84. C3×C9C3×S4semidirect
132. C22#92333semidirect

Maximal subgroups

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

subgroupindex
#117578522
C3×(C3⋊S4)⋊C33
C3×#611⋊C33
#106197503
#923334