Finite Group Databasebeta

← #14517439

Subgroups — #14517439

Order 1944.

307 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 307 conjugacy classes of subgroups — too many to draw. Only its 72 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×#6900C211yesmaximal, characteristic, complemented
2C2×#92265C211yesmaximal, characteristic, complemented
3#11757569C211yesmaximal, characteristic, complemented
4#67×3−1+2—31nomaximal
5C3×#611⋊C3C311yesmaximal, characteristic
6#611⋊C9C312yesmaximal, complemented
7C9×#611C311yesmaximal, characteristic, complemented
8C2×#6900—21no—
9C2×#6900C2211yescharacteristic
10#92265—21no—
11C22×C3×3−1+2—21no—
12C22×C3×3−1+2D311yescharacteristic
13C22×C3×3−1+2C2×C311yescharacteristic
14C2×D3×3−1+2—31no—
15C2×C3×AGL(1,ℤ/9)C2×C311yescharacteristic
16Dic3×3−1+2—31no—
17C3×3−1+2⋊C4C2×C311yescharacteristic
18C22×C9⋊C9—22no—
19C22×C9⋊C9—21no—
20C22×C9⋊C9C2×C312yescomplemented
21C22×C92C2×C311yescharacteristic, complemented
22C2×D9⋊C9C2×C312yescomplemented
23C2×C9×D9C2×C311yescharacteristic, complemented
24Dic9⋊C9C2×C312yescomplemented
25C9×Dic9C2×C311yescharacteristic, complemented
26#6900D411yescharacteristic, complemented, Sylow
27C32×#67—31no—
28D4×3−1+2—91no—
29#611⋊C3—31no—
30C9×#67—31no—
31C9×#67—32no—
32C3×#611C3211yescharacteristic
33C2×C3×3−1+2—22no—
34C2×C3×3−1+2—21no—
35C2×C3×3−1+2—21no—
36C2×C3×3−1+2—21no—
37C2×C3×3−1+2C2×D311yescharacteristic
38C2×C3×3−1+2C22×C311yescharacteristic
39D3×3−1+2—61no—
40C3×AGL(1,ℤ/9)—21no—
41C2×C9⋊C9—24no—
42C2×C9⋊C9—22no—
43C2×C9⋊C9—22no—
44C2×C9⋊C9—22no—
45C2×C9⋊C9—21no—
46C2×C9⋊C9C22×C312yes—
47C2×C92—21no—
48C2×C92C22×C311yescharacteristic
49D9⋊C9—22no—
50C9×D9—21no—
51C22×C33C3×D311yescharacteristic
52C2×C32×D3—31no—
53C32×Dic3—31no—
54C22×3−1+2—31no—
55C22×3−1+2—31no—
56C22×3−1+2—61no—
57C22×3−1+2—63no—
58C22×3−1+2—61no—
59C22×3−1+2—91no—
60C22×C3×C9—21no—
61C22×C3×C9—21no—
62C22×C3×C9—22no—
63C22×C3×C9C3×D311yescharacteristic
64C22×C3×C9C3×D312yes—
65C22×C3×C9C2×C3211yescharacteristic
66C2×AGL(1,ℤ/9)—31no—
67C2×D3×C9—31no—
68C2×D3×C9—32no—
69C2×C3×D9C2×C3211yescharacteristic
70C4×3−1+2—91no—
713−1+2⋊C4—31no—
72C9×Dic3—31no—
73C9×Dic3—32no—
74C3×Dic9C2×C3211yescharacteristic
75C3×3−1+2—21no—
76C3×3−1+2#6711yescharacteristic
77C3×3−1+2C3×D411yescharacteristic
78C9⋊C9—22no—
79C9⋊C9—21no—
80C9⋊C9C3×D412yescomplemented
81C92C3×D411yescharacteristic, complemented
82C32×D4—91no—
83C3×#67—31no—
84C3×#67—91no—
85D4×C9—92no—
86D4×C9—91no—
87#6113−1+211yescharacteristic, complemented
88C2×C33—21no—
89C2×C33C2×C3×D311yescharacteristic
90C32×D3—61no—
91C2×3−1+2—31no—
92C2×3−1+2—31no—
93C2×3−1+2—61no—
94C2×3−1+2—61no—
95C2×3−1+2—61no—
96C2×3−1+2—62no—
97C2×3−1+2—63no—
98C2×3−1+2—62no—
99C2×3−1+2—66no—
100C2×3−1+2—61no—
101C2×3−1+2—181no—
102C2×C3×C9—22no—
103C2×C3×C9—21no—
104C2×C3×C9—21no—
105C2×C3×C9—21no—
106C2×C3×C9—22no—
107C2×C3×C9—24no—
108C2×C3×C9—22no—
109C2×C3×C9—21no—
110C2×C3×C9—22no—
111C2×C3×C9C2×C3×D311yescharacteristic
112C2×C3×C9C2×C3×D312yes—
113C2×C3×C9C22×C3211yescharacteristic
114AGL(1,ℤ/9)—61no—
115D3×C9—61no—
116D3×C9—62no—
117C3×D9—21no—
118C22×C32—31no—
119C22×C32—31no—
120C22×C32—61no—
121C22×C32—91no—
122C22×C32C32×D311yescharacteristic
123C2×C3×D3—31no—
124C2×C3×D3—91no—
125C32×C4—91no—
126C3×Dic3—31no—
127C3×Dic3—91no—
128C22×C9—23no—
129C22×C9—21no—
130C22×C9—21no—
131C22×C9—32no—
132C22×C9—62no—
133C22×C9—61no—
134C22×C9—92no—
135C22×C9—91no—
136C22×C9AGL(1,ℤ/9)11yescharacteristic, complemented
137C22×C9C2×3−1+211yescharacteristic, complemented
138C2×D9C2×3−1+211yescharacteristic, complemented
139C4×C9—92no—
140C4×C9—91no—
141Dic9C2×3−1+211yescharacteristic, complemented
142C33C3×#6711yescharacteristic
1433−1+2—31no—
1443−1+2—31no—
1453−1+2—61no—
1463−1+2—63no—
1473−1+2—61no—
148C3×C9—21no—
149C3×C9—21no—
150C3×C9—22no—
151C3×C9C3×#6711yescharacteristic
152C3×C9C3×#6712yes—
153C3×C9C32×D411yescharacteristic
154C3×D4—91no—
155C3×D4—271no—
156#67—31no—
157C2×C32—21no—
158C2×C32—31no—
159C2×C32—31no—
160C2×C32—61no—
161C2×C32—61no—
162C2×C32—61no—
163C2×C32—62no—
164C2×C32—181no—
165C2×C32C2×C32×D311yescharacteristic
166C3×D3—61no—
167C3×D3—181no—
168C2×C9—26no—
169C2×C9—22no—
170C2×C9—22no—
171C2×C9—23no—
172C2×C9—21no—
173C2×C9—21no—
174C2×C9—21no—
175C2×C9—21no—
176C2×C9—32no—
177C2×C9—62no—
178C2×C9—64no—
179C2×C9—62no—
180C2×C9—62no—
181C2×C9—61no—
182C2×C9—182no—
183C2×C9—181no—
184C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
185C2×C9C22×3−1+211yescharacteristic
186D9—21no—
187C22×C3—21no—
188C22×C3—91no—
189C22×C3—91no—
190C22×C3—271no—
191C22×C3C3×AGL(1,ℤ/9)11yescharacteristic
192C22×C3D3×3−1+211yescharacteristic
193C2×D3—31no—
194C3×C4—91no—
195C3×C4—271no—
196Dic3—31no—
197C32—31no—
198C32—31no—
199C32—61no—
200C32C32×#6711yescharacteristic
201C9—23no—
202C9—21no—
203C9—21no—
204C9—32no—
205C9—62no—
206C9—61no—
207C9#611⋊C311yescharacteristic, complemented
208C9D4×3−1+211yescharacteristic, complemented
209D4—91noSylow
210C2×C3—22no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—91no—
215C2×C3—181no—
216C2×C3—181no—
217C2×C3—541no—
218C2×C3C2×C3×AGL(1,ℤ/9)11yescharacteristic
219C2×C3C2×D3×3−1+211yescharacteristic
220D3—61no—
221C22—91no—
222C22#9226511yescharacteristic, complemented
223C4—91no—
224C3—21no—
225C3—91no—
226C3C3×#611⋊C311yescharacteristic
227C3#67×3−1+211yescharacteristic
228C2—21no—
229C2—181no—
230C2C2×#9226511yescharacteristic
subgroupG/H
centerC2×C3C2×C3×AGL(1,ℤ/9)
commutator, cosocleC2×C3×C9C22×C32
Frattini, socleC2×C32C2×C32×D3
FittingC22×#6900C2
prime radicalC3×#611⋊C3C3
hypercenterC22×C9AGL(1,ℤ/9)
hypocenterC9D4×3−1+2
LCSG ▷ C2×C3×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C22×C9

Complements

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

NH ≅ G/Ntype
1. C22×#6900C2semidirect
2. C2×#92265C2semidirect
3. #11757569C2semidirect
6. #611⋊C9C3semidirect
7. C9×#611C3semidirect
20. C22×C9⋊C9C2×C3semidirect
21. C22×C92C2×C3semidirect
22. C2×D9⋊C9C2×C3semidirect
23. C2×C9×D9C2×C3semidirect
24. Dic9⋊C9C2×C3semidirect
25. C9×Dic9C2×C3semidirect
26. #6900D4semidirect
80. C9⋊C9C3×D4semidirect
81. C92C3×D4semidirect
87. #6113−1+2semidirect
136. C22×C9AGL(1,ℤ/9)semidirect
137. C22×C9C2×3−1+2semidirect
138. C2×D9C2×3−1+2semidirect
141. Dic9C2×3−1+2semidirect
207. C9#611⋊C3semidirect
208. C9D4×3−1+2semidirect
222. C22#92265semidirect

Maximal subgroups

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

subgroupindex
C22×#69002
C2×#922652
#117575692
#67×3−1+23
C3×#611⋊C33
#611⋊C93
C9×#6113