Finite Group Databasebeta

← #14519002

Subgroups — #14519002

Order 1944.

1270 conjugacy classes of subgroups; only the 240 normal subgroups are shown.

normal subgroups only

This group has 1270 conjugacy classes of subgroups — too many to draw. Only its 240 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
1C22×C32×3−1+2C211yesmaximal, characteristic, complemented
2C2×C3⋊(C3⋊AGL(1,ℤ/9))C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(3−1+2⋊C4))C211yesmaximal, characteristic, complemented
4C3×#6312—31nomaximal
5#10619992C311yesmaximal, characteristic, complemented
6#10619980—312nomaximal
7C2×C32×3−1+2—21no—
8C2×C32×3−1+2C2211yescharacteristic
9C3⋊(C3⋊AGL(1,ℤ/9))—21no—
10C22×C34D311yescharacteristic
11C2×C3×C3⋊(C3⋊D3)—31no—
12C3×C3⋊(C3⋊Dic3)—31no—
13C22×C3×3−1+2—212no—
14C22×C3×3−1+2D3112yescomplemented
15C22×C32×C9—21no—
16C22×C32×C9C2×C311yescharacteristic, complemented
17C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
18C2×C3⋊AGL(1,ℤ/9)—312no—
19C3⋊(C3⋊Dic9)C2×C311yescharacteristic, complemented
20C3⋊(3−1+2⋊C4)—312no—
21C32×3−1+2D411yescharacteristic, complemented, Sylow
22#6312—31no—
23C3×#638—99no—
24C3×#638—94no—
25#6233—312no—
26#611⋊C3—99no—
27C2×C34—21no—
28C2×C34C2×D311yescharacteristic
29C3×C3⋊(C3⋊D3)—61no—
30C2×C3×3−1+2—224no—
31C2×C3×3−1+2—212no—
32C2×C3×3−1+2—212no—
33C2×C3×3−1+2C2×D3112yes—
34C2×C32×C9—22no—
35C2×C32×C9—21no—
36C2×C32×C9—21no—
37C2×C32×C9C22×C311yescharacteristic
38C3⋊(C3⋊D9)—21no—
39C3⋊AGL(1,ℤ/9)—612no—
40C22×C33—24no—
41C22×C33—39no—
42C22×C33C3×D311yescharacteristic
43C22×C33C3⋊D314yes—
44C2×C3⋊(C3⋊D3)—31no—
45C2×C3×C3⋊D3—99no—
46C2×C3×C3⋊D3—94no—
47C3⋊(C3⋊Dic3)—31no—
48C3×C3⋊Dic3—99no—
49C3×C3⋊Dic3—94no—
50C22×3−1+2—236no—
51C22×3−1+2C3⋊D319yescomplemented
52C22×C3×C9—212no—
53C22×C3×C9C3×D3112yescomplemented
54C2×C3⋊D9—312no—
55C2×AGL(1,ℤ/9)—99no—
56C3⋊Dic9—312no—
573−1+2⋊C4—99no—
58C34#6711yescharacteristic
59C3×3−1+2—212no—
60C3×3−1+2#67112yescomplemented
61C32×C9—21no—
62C32×C9C3×D411yescharacteristic, complemented
63#638—99no—
64#638—94no—
65C3×#67—2712no—
66C3×#67—271no—
67#611—99no—
68C2×C33—21no—
69C2×C33—28no—
70C2×C33—24no—
71C2×C33—24no—
72C2×C33—39no—
73C2×C33—69no—
74C2×C33C2×C3×D311yescharacteristic
75C2×C33C2×C3⋊D314yes—
76C3⋊(C3⋊D3)—61no—
77C3×C3⋊D3—189no—
78C3×C3⋊D3—184no—
79C2×3−1+2—272no—
80C2×3−1+2—29no—
81C2×3−1+2—236no—
82C2×3−1+2C2×C3⋊D319yes—
83C2×C3×C9—224no—
84C2×C3×C9—212no—
85C2×C3×C9—212no—
86C2×C3×C9C2×C3×D3112yes—
87C3⋊D9—612no—
88AGL(1,ℤ/9)—189no—
89C22×C32—24no—
90C22×C32—312no—
91C22×C32—612no—
92C22×C32AGL(1,ℤ/9)19yescomplemented
93C22×C32C3×C3⋊D314yes—
94C22×C32C3⋊(C3⋊D3)11yescharacteristic
95C2×C3⋊D3—99no—
96C2×C3⋊D3—94no—
97C2×C3×D3—2712no—
98C2×C3×D3—271no—
99C3⋊Dic3—99no—
100C3⋊Dic3—94no—
101C3×Dic3—2712no—
102C3×Dic3—271no—
103C22×C9—29no—
104C22×C9C3×C3⋊D319yescomplemented
105C2×D9—99no—
106Dic9—99no—
107C33—24no—
108C33—39no—
109C33C3×#6711yescharacteristic
110C33#63814yes—
1113−1+2—236no—
1123−1+2#63819yescomplemented
113C3×C9—212no—
114C3×C9C3×#67112yescomplemented
115C3×D4—811no—
116#67—2712no—
117#67—271no—
118C2×C32—29no—
119C2×C32—24no—
120C2×C32—28no—
121C2×C32—21no—
122C2×C32—24no—
123C2×C32—312no—
124C2×C32—612no—
125C2×C32—624no—
126C2×C32—612no—
127C2×C32C2×AGL(1,ℤ/9)19yes—
128C2×C32C2×C3×C3⋊D314yes—
129C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
130C3⋊D3—189no—
131C3⋊D3—184no—
132C3×D3—5412no—
133C3×D3—541no—
134C2×C9—218no—
135C2×C9—29no—
136C2×C9—29no—
137C2×C9C2×C3×C3⋊D319yes—
138D9—189no—
139C22×C3—31no—
140C22×C3—64no—
141C22×C3—811no—
142C22×C3C3⋊AGL(1,ℤ/9)112yescomplemented
143C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
144C2×D3—2712no—
145C2×D3—271no—
146C3×C4—811no—
147Dic3—2712no—
148Dic3—271no—
149C32—24no—
150C32—312no—
151C32—612no—
152C32#611⋊C319yescomplemented
153C32C3×#63814yes—
154C32#631211yescharacteristic
155C9—29no—
156C9C3×#63819yescomplemented
157D4—811noSylow
158C2×C3—21no—
159C2×C3—212no—
160C2×C3—31no—
161C2×C3—61no—
162C2×C3—68no—
163C2×C3—64no—
164C2×C3—1621no—
165C2×C3C2×C3⋊AGL(1,ℤ/9)112yes—
166C2×C3C2×C3×C3⋊(C3⋊D3)11yescharacteristic
167D3—541no—
168D3—5412no—
169C22—811no—
170C22C3⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic, complemented
171C4—811no—
172C3—31no—
173C3—64no—
174C3#10619980112yescomplemented
175C3C3×#631211yescharacteristic
176C2—21no—
177C2—1621no—
178C2C2×C3⋊(C3⋊AGL(1,ℤ/9))11yescharacteristic
subgroupG/H
centerC2C2×C3⋊(C3⋊AGL(1,ℤ/9))
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C3C2×C3×C3⋊(C3⋊D3)
FittingC22×C32×3−1+2C2
socleC2×C33C2×C3×D3
hypercenterC22C3⋊(C3⋊AGL(1,ℤ/9))
hypocenterC32×C9C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C32×3−1+2C2semidirect
2. C2×C3⋊(C3⋊AGL(1,ℤ/9))C2semidirect
3. C3⋊(C3⋊(3−1+2⋊C4))C2semidirect
5. #10619992C3semidirect
14. C22×C3×3−1+2D3semidirect
16. C22×C32×C9C2×C3semidirect
17. C2×C3⋊(C3⋊D9)C2×C3semidirect
19. C3⋊(C3⋊Dic9)C2×C3semidirect
21. C32×3−1+2D4semidirect
51. C22×3−1+2C3⋊D3semidirect
53. C22×C3×C9C3×D3semidirect
60. C3×3−1+2#67semidirect
62. C32×C9C3×D4semidirect
92. C22×C32AGL(1,ℤ/9)semidirect
104. C22×C9C3×C3⋊D3semidirect
112. 3−1+2#638semidirect
114. C3×C9C3×#67semidirect
142. C22×C3C3⋊AGL(1,ℤ/9)semidirect
152. C32#611⋊C3semidirect
156. C9C3×#638semidirect
170. C22C3⋊(C3⋊AGL(1,ℤ/9))semidirect
174. C3#10619980semidirect

Maximal subgroups

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

subgroupindex
C22×C32×3−1+22
C2×C3⋊(C3⋊AGL(1,ℤ/9))2
C3⋊(C3⋊(3−1+2⋊C4))2
C3×#63123
#106199923
#106199803