Finite Group Databasebeta

← #14518208

Subgroups — #14518208

Order 1944.

347 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 347 conjugacy classes of subgroups — too many to draw. Only its 39 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#11757856C211yesmaximal, characteristic, complemented
2C3×A4×C3⋊D3—31nomaximal
3C22×C3⋊AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
4#10619770C313yesmaximal, complemented
5#4169⋊C3—41nomaximal
6C33×A4D311yescharacteristic
7C22×C3×3−1+2C2×C311yescharacteristic, complemented
8C2×C3⋊AGL(1,ℤ/9)—31no—
9C2×C3⋊AGL(1,ℤ/9)—31no—
10C3×#1094—21no—
11(C3×A4)⋊C9—23no—
12(C3×A4)⋊C9C2×C313yescomplemented
13#6891—41noSylow
14C22×C3×C3⋊D3—31no—
15A4×C3⋊D3—33no—
16C3×D3×A4—91no—
17C3×D3×A4—93no—
18C22×C3⋊D9C3211yescharacteristic, complemented
19C22×AGL(1,ℤ/9)—91no—
20C32×C3⋊D3—121no—
21C2×C3×3−1+2—31no—
22C3⋊AGL(1,ℤ/9)—31no—
23C3⋊AGL(1,ℤ/9)A411yescharacteristic, complemented
24#4169—43no—
25C22×C33C3×D311yescharacteristic
26C2×C3×C3⋊D3—91no—
27C2×C3×C3⋊D3—91no—
28C32×A4—31no—
29C32×A4—33no—
30C32×A4—63no—
31C32×A4—61no—
32C32×A4C3×D313yes—
33C22×3−1+2—31no—
34C22×3−1+2—61no—
35C22×C3×C9—21no—
36C22×C3×C9C2×C3211yescharacteristic, complemented
37C2×C3⋊D9—31no—
38C2×C3⋊D9—31no—
39C2×AGL(1,ℤ/9)—93no—
40C2×AGL(1,ℤ/9)—93no—
41#1094—62no—
42#1094—61no—
43C3×C22⋊C9—23no—
44C34—41no—
45C3×3−1+2—81no—
46C3×3−1+2C2×A411yescharacteristic, complemented
47C32⋊C9—43no—
48C32⋊C9—83no—
49C22×C3⋊D3—31no—
50C22×C3×D3—93no—
51C22×C3×D3—91no—
52C2×C3×A4—271no—
53D3×A4—93no—
54D3×A4—96no—
55D3×A4—93no—
56C22×D9—91no—
57C2×C33—31no—
58C3×C3⋊D3—31no—
59C3×C3⋊D3—91no—
60C3×C3⋊D3—123no—
61C32×D3—363no—
62C32×D3—361no—
63C2×3−1+2—33no—
64C2×3−1+2—63no—
65C2×C3×C9—31no—
66C2×C3×C9—61no—
67C3⋊D9—31no—
68C3⋊D9C3×A411yescharacteristic, complemented
69AGL(1,ℤ/9)—91no—
70AGL(1,ℤ/9)—93no—
71C22×C32—21no—
72C22×C32—33no—
73C22×C32(C3⋊D3)⋊C311yescharacteristic
74C22×C32C32×D311yescharacteristic
75C2×C3⋊D3—91no—
76C2×C3⋊D3—91no—
77C2×C3×D3—271no—
78C2×C3×D3—273no—
79C2×C3×D3—271no—
80C2×C3×D3—273no—
81C3×A4—23no—
82C3×A4—31no—
83C3×A4—33no—
84C3×A4—36no—
85C3×A4—63no—
86C3×A4—63no—
87C3×A4—63no—
88C3×A4—61no—
89C3×A4—63no—
90C3×A4AGL(1,ℤ/9)13yescomplemented
91C22×C9—31no—
92C22×C9—61no—
93C2×D9—93no—
94C2×D9—93no—
95C22⋊C9—63no—
96C33—43no—
97C33—123no—
98C33—121no—
99C33—241no—
100C33—243no—
101C33D3×A411yescharacteristic
1023−1+2—31no—
1033−1+2—61no—
1043−1+2—242no—
1053−1+2—241no—
106C3×C9—21no—
107C3×C9—83no—
108C3×C9C2×C3×A411yescharacteristic, complemented
109C23×C3—271no—
110C22×D3—91no—
111C22×D3—93no—
112C2×A4—273no—
113C2×C32—31no—
114C2×C32—31no—
115C2×C32—61no—
116C2×C32—93no—
117C2×C32—1081no—
118C3⋊D3—31no—
119C3⋊D3—91no—
120C3×D3—93no—
121C3×D3—91no—
122C3×D3—273no—
123C3×D3—271no—
124C3×D3—363no—
125C3×D3—366no—
126C3×D3—363no—
127C2×C9—33no—
128C2×C9—63no—
129D9—91no—
130D9—93no—
131C22×C3—31no—
132C22×C3—61no—
133C22×C3—811no—
134C22×C3—811no—
135C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
136C22×C3C3×AGL(1,ℤ/9)13yes—
137C2×D3—271no—
138C2×D3—273no—
139C2×D3—271no—
140C2×D3—273no—
141A4—33no—
142A4—63no—
143C32—21no—
144C32—33no—
145C32—43no—
146C32—83no—
147C32—121no—
148C32—126no—
149C32—123no—
150C32—243no—
151C32—241no—
152C32—243no—
153C32—243no—
154C32—243no—
155C32(C3⋊D3)⋊A411yescharacteristic
156C32C3×D3×A411yescharacteristic
157C9—31no—
158C9—61no—
159C9—243no—
160C23—271noSylow
161C2×C3—33no—
162C2×C3—31no—
163C2×C3—91no—
164C2×C3—181no—
165C2×C3—271no—
166C2×C3—811no—
167C2×C3—1083no—
168D3—93no—
169D3—91no—
170D3—273no—
171D3—271no—
172C22—811no—
173C22—811no—
174C22#4169⋊C311yescharacteristic, complemented
175C3—31no—
176C3—61no—
177C3—123no—
178C3—243no—
179C3A4×AGL(1,ℤ/9)13yes—
180C3C3×(C3⋊D3)⋊A411yescharacteristic
181C2—31no—
182C2—271no—
183C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC32C3×D3×A4
FittingC22×C3×3−1+2C2×C3
socleC22×C32C32×D3
LCSG ▷ C22×C3×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757856C2semidirect
3. C22×C3⋊AGL(1,ℤ/9)C3semidirect
4. #10619770C3semidirect
7. C22×C3×3−1+2C2×C3semidirect
12. (C3×A4)⋊C9C2×C3semidirect
18. C22×C3⋊D9C32semidirect
23. C3⋊AGL(1,ℤ/9)A4semidirect
36. C22×C3×C9C2×C32semidirect
46. C3×3−1+2C2×A4semidirect
68. C3⋊D9C3×A4semidirect
90. C3×A4AGL(1,ℤ/9)semidirect
108. C3×C9C2×C3×A4semidirect
174. C22#4169⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117578562
C3×A4×C3⋊D33
C22×C3⋊AGL(1,ℤ/9)3
#106197703
#4169⋊C34