Finite Group Databasebeta

← #14519259

Subgroups — #14519259

Order 1944.

451 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 451 conjugacy classes of subgroups — too many to draw. Only its 58 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#11758104C211yesmaximal, characteristic, complemented
2C22×C3⋊AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
3#10620070C313yesmaximal, complemented
4C3×(C3⋊D3)⋊A4—31nomaximal
5A4×AGL(1,ℤ/9)—33nomaximal
6#4207⋊C3—41nomaximal
7C22×C3×3−1+2C2×C311yescharacteristic, complemented
8C2×C3⋊AGL(1,ℤ/9)—31no—
9C2×C3⋊AGL(1,ℤ/9)—31no—
10C3×C22⋊H(3,𝔽3)D311yescharacteristic
11C3×#1094—21no—
12#66440—26no—
13#66440—23no—
14A4×3−1+2—23no—
15A4×3−1+2D313yescomplemented
16#66436—23no—
17#66436C2×C313yescomplemented
183−1+4—41noSylow
19C22×C3×C3⋊D3—31no—
20C3×D3×A4—91no—
21C22×C3⋊D9C3211yescharacteristic, complemented
22C22×AGL(1,ℤ/9)—33no—
23(C3⋊D3)⋊A4—33no—
24A4×D9—33no—
25D9⋊A4—36no—
26C2×C3×3−1+2—31no—
27#4207—43no—
28C3⋊AGL(1,ℤ/9)—31no—
29C3⋊AGL(1,ℤ/9)A411yescharacteristic, complemented
30C3×AGL(1,ℤ/9)—123no—
31C3×(C3⋊D3)⋊C3—121no—
32C22×C33C3×D311yescharacteristic
33C2×C3×C3⋊D3—91no—
34C2×C3×C3⋊D3—91no—
35C32×A4—21no—
36C32×A4C3⋊D311yescharacteristic
37C22×3−1+2—23no—
38C22×3−1+2C3×D313yes—
39C22×C3×C9—21no—
40C22×C3×C9C2×C3211yescharacteristic, complemented
41C2×C3⋊D9—31no—
42C2×C3⋊D9—31no—
43C2×AGL(1,ℤ/9)—93no—
44C2×AGL(1,ℤ/9)—93no—
45C22⋊H(3,𝔽3)—23no—
46C22⋊H(3,𝔽3)C3×D313yes—
47#1094—22no—
48#1094—21no—
49#1094—23no—
50#1094—23no—
51C3×C22⋊C9—23no—
52C9⋊A4—26no—
53C9⋊A4—26no—
54C9⋊A4—26no—
55C9⋊A4—26no—
56C9⋊A4C3×D316yescomplemented
57C9×A4—23no—
58C9×A4—23no—
59C9×A4—23no—
60C9×A4—23no—
61C9×A4C3×D313yescomplemented
62#737—43no—
63#737—83no—
64#737—83no—
65#737—86no—
66C3×3−1+2—43no—
67C3×3−1+2—81no—
68C3×3−1+2—83no—
69C3×3−1+2C2×A411yescharacteristic, complemented
70C3×H(3,𝔽3)—41no—
71C22×C3⋊D3—31no—
72C22×C3×D3—91no—
73C22×C3×D3—271no—
74C2×C3×A4—271no—
75D3×A4—93no—
76C22×D9—33no—
77C2×C33—31no—
78C3×C3⋊D3—31no—
79C3×C3⋊D3—91no—
80C32×D3—361no—
81C2×3−1+2—33no—
82C2×3−1+2—63no—
83C2×C3×C9—31no—
84C2×C3×C9—61no—
85C3⋊D9—31no—
86C3⋊D9C3×A411yescharacteristic, complemented
87AGL(1,ℤ/9)—33no—
88AGL(1,ℤ/9)—93no—
89AGL(1,ℤ/9)—126no—
90(C3⋊D3)⋊C3—123no—
91C3×D9—123no—
92C22×C32—21no—
93C22×C32—91no—
94C22×C32C32×D311yescharacteristic
95C22×C32C3×C3⋊D311yescharacteristic
96C2×C3⋊D3—91no—
97C2×C3⋊D3—91no—
98C2×C3×D3—271no—
99C2×C3×D3—273no—
100C2×C3×D3—273no—
101C2×C3×D3—271no—
102C3×A4—23no—
103C3×A4—91no—
104C3×A4—181no—
105C3×A4C3×C3⋊D313yes—
106C22×C9—23no—
107C22×C9C32×D313yes—
108C2×D9—93no—
109C2×D9—93no—
110C22⋊C9—26no—
111C22⋊C9—23no—
112C33—41no—
113C33—81no—
114C33D3×A411yescharacteristic
1153−1+2—23no—
1163−1+2—46no—
1173−1+2—86no—
1183−1+2—86no—
1193−1+2—86no—
1203−1+2—81no—
1213−1+2—82no—
1223−1+2—83no—
1233−1+2—83no—
1243−1+2—86no—
1253−1+2D3×A413yes—
126H(3,𝔽3)—43no—
127H(3,𝔽3)—83no—
128C3×C9—21no—
129C3×C9—43no—
130C3×C9—83no—
131C3×C9—83no—
132C3×C9—83no—
133C3×C9—83no—
134C3×C9—83no—
135C3×C9C2×C3×A411yescharacteristic, complemented
136C23×C3—271no—
137C22×D3—91no—
138C22×D3—271no—
139C2×A4—273no—
140C2×C32—31no—
141C2×C32—31no—
142C2×C32—61no—
143C2×C32—93no—
144C2×C32—1081no—
145C3⋊D3—31no—
146C3⋊D3—91no—
147C3×D3—91no—
148C3×D3—271no—
149C3×D3—273no—
150C3×D3—271no—
151C3×D3—363no—
152C2×C9—33no—
153C2×C9—63no—
154D9—33no—
155D9—93no—
156C22×C3—31no—
157C22×C3—31no—
158C22×C3—61no—
159C22×C3—811no—
160C22×C3—811no—
161C22×C3C32×C3⋊D311yescharacteristic
162C2×D3—271no—
163C2×D3—273no—
164C2×D3—273no—
165C2×D3—271no—
166A4—33no—
167A4—63no—
168C32—21no—
169C32—43no—
170C32—83no—
171C32—91no—
172C32—361no—
173C32—721no—
174C32C3×D3×A411yescharacteristic
175C32A4×C3⋊D311yescharacteristic
176C9—23no—
177C9—83no—
178C9—86no—
179C9C3×D3×A413yes—
180C23—271noSylow
181C2×C3—33no—
182C2×C3—31no—
183C2×C3—91no—
184C2×C3—181no—
185C2×C3—271no—
186C2×C3—811no—
187C2×C3—1083no—
188D3—91no—
189D3—271no—
190D3—273no—
191D3—271no—
192C22—811no—
193C22—811no—
194C22#4207⋊C311yescharacteristic, complemented
195C3—31no—
196C3—31no—
197C3—61no—
198C3—123no—
199C3—243no—
200C3C3×A4×C3⋊D311yescharacteristic
201C2—31no—
202C2—271no—
203C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC3C3×A4×C3⋊D3
FittingC22×C3×3−1+2C2×C3
socleC22×C3C32×C3⋊D3
LCSG ▷ C22×C3×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11758104C2semidirect
2. C22×C3⋊AGL(1,ℤ/9)C3semidirect
3. #10620070C3semidirect
7. C22×C3×3−1+2C2×C3semidirect
15. A4×3−1+2D3semidirect
17. #66436C2×C3semidirect
21. C22×C3⋊D9C32semidirect
29. C3⋊AGL(1,ℤ/9)A4semidirect
40. C22×C3×C9C2×C32semidirect
56. C9⋊A4C3×D3semidirect
61. C9×A4C3×D3semidirect
69. C3×3−1+2C2×A4semidirect
86. C3⋊D9C3×A4semidirect
135. C3×C9C2×C3×A4semidirect
194. C22#4207⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117581042
C22×C3⋊AGL(1,ℤ/9)3
#106200703
C3×(C3⋊D3)⋊A43
A4×AGL(1,ℤ/9)3
#4207⋊C34