Finite Group Databasebeta

← #14516793

Subgroups — #14516793

Order 1944.

238 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C2×#92299C211yesmaximal, characteristic, complemented
2C2×C9×AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
33−1+2×Dic9C211yesmaximal, characteristic, complemented
4#6192⋊C3—31nomaximal
5C3×#6195—31nomaximal
6#10619530C311yesmaximal, characteristic, complemented
7C2×C9×3−1+2C2211yescharacteristic
8#92299—21no—
9C9×AGL(1,ℤ/9)—21no—
10C2×C3⋊AGL(1,ℤ/9)—31no—
11C2×C3×C3⋊D9—31no—
12C2×C3×AGL(1,ℤ/9)D311yescharacteristic
13C2×C3×D3×C9—31no—
14Dic3×3−1+2—31no—
15C32×Dic9D311yescharacteristic
16C2×C9⋊D9C2×C311yescharacteristic, complemented
17C2×D9⋊C9—21no—
18C2×#4169—61no—
19C2×C9×D9C2×C311yescharacteristic, complemented
20C9×Dic9—21no—
21C9×Dic9C2×C311yescharacteristic, complemented
22C9×3−1+2D411yescharacteristic, complemented, Sylow
23C3×#626—91no—
24C3×#611—91no—
25C4⋊AGL(1,ℤ/9)—91no—
26#6195—31no—
27#6192—31no—
28C2×C3×3−1+2C2×D311yescharacteristic
29C2×C32×C9C2×D311yescharacteristic
30C3⋊AGL(1,ℤ/9)—61no—
31C3×C3⋊D9—61no—
32C3×AGL(1,ℤ/9)—21no—
33C3×D3×C9—61no—
34C2×C9⋊C9—21no—
35C2×C9⋊C9—41no—
36C2×C32⋊C9—21no—
37C2×C92—21no—
38C2×C92C22×C311yescharacteristic
39C9⋊D9—21no—
40D9⋊C9—22no—
41#4169—62no—
42C9×D9—21no—
43C2×C3×C3⋊D3—91no—
44C2×C32×D3—31no—
45C32×Dic3—31no—
46C22×C3×C9—91no—
47C2×C3⋊D9—31no—
48C2×C3⋊D9—31no—
49C2×C3⋊D9—61no—
50C2×AGL(1,ℤ/9)—21no—
51C2×AGL(1,ℤ/9)—91no—
52C2×AGL(1,ℤ/9)—181no—
53C2×AGL(1,ℤ/9)D911yescharacteristic, complemented
54C2×D3×C9—31no—
55C2×D3×C9—61no—
56C2×C3×D9—91no—
57C2×C3×D9—181no—
58C2×C3×D9C3×D311yescharacteristic
59C4×3−1+2—91no—
60C9×Dic3—31no—
61C9×Dic3—61no—
62C3×Dic9—31no—
63C3×Dic9C3×D311yescharacteristic
64C3×3−1+2#6711yescharacteristic
65C32×C9D1211yescharacteristic
66C9⋊C9—21no—
67C9⋊C9—41no—
68C32⋊C9—21no—
69C92—21no—
70C92C3×D411yescharacteristic, complemented
71C3×#67—271no—
72C3×D12—271no—
73#626—91no—
74#611—91no—
75D36—91no—
76C2×C33D3211yescharacteristic
77C3×C3⋊D3—181no—
78C32×D3—61no—
79C2×3−1+2—21no—
80C2×3−1+2—21no—
81C2×3−1+2—41no—
82C2×3−1+2C2×D911yescharacteristic
83C2×C3×C9—21no—
84C2×C3×C9—21no—
85C2×C3×C9—21no—
86C2×C3×C9—31no—
87C2×C3×C9—41no—
88C2×C3×C9—61no—
89C2×C3×C9—181no—
90C2×C3×C9C2×C3×D311yescharacteristic
91C2×C3×C9C2×C3×D311yescharacteristic
92C3⋊D9—61no—
93C3⋊D9—61no—
94C3⋊D9—62no—
95AGL(1,ℤ/9)—22no—
96AGL(1,ℤ/9)—21no—
97AGL(1,ℤ/9)—182no—
98AGL(1,ℤ/9)—181no—
99D3×C9—62no—
100D3×C9—61no—
101C3×D9—21no—
102C3×D9—181no—
103C3×D9—182no—
104C22×C32—91no—
105C2×C3⋊D3—91no—
106C2×C3×D3—31no—
107C2×C3×D3—31no—
108C2×C3×D3—61no—
109C2×C3×D3—271no—
110C2×C3×D3—271no—
111C2×C3×D3—541no—
112C32×C4—91no—
113C3×Dic3—31no—
114C3×Dic3—91no—
115C22×C9—91no—
116C22×C9—181no—
117C2×D9—91no—
118C2×D9—91no—
119C2×D9—181no—
120C2×D9—181no—
121C2×D9—541no—
122C2×D9C3×D911yescharacteristic, complemented
123C4×C9—91no—
124C4×C9—181no—
125Dic9AGL(1,ℤ/9)11yescharacteristic, complemented
126C33#62611yescharacteristic
1273−1+2—21no—
1283−1+2—21no—
1293−1+2—41no—
1303−1+2#61111yescharacteristic, complemented
131C3×C9—21no—
132C3×C9—21no—
133C3×C9—21no—
134C3×C9—31no—
135C3×C9—41no—
136C3×C9—61no—
137C3×C9C3×D1211yescharacteristic
138C3×C9C3×#6711yescharacteristic
139C3×D4—811no—
140#67—271no—
141D12—271no—
142C2×C32—21no—
143C2×C32—31no—
144C2×C32—61no—
145C2×C32—181no—
146C2×C32D3×D911yescharacteristic
147C2×C32C3×D3211yescharacteristic
148C3⋊D3—181no—
149C3×D3—62no—
150C3×D3—61no—
151C3×D3—61no—
152C3×D3—541no—
153C3×D3—542no—
154C3×D3—541no—
155C2×C9—21no—
156C2×C9—21no—
157C2×C9—21no—
158C2×C9—41no—
159C2×C9—61no—
160C2×C9—61no—
161C2×C9—121no—
162C2×C9—182no—
163C2×C9—181no—
164C2×C9C2×C3×D911yescharacteristic
165C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
166D9—21no—
167D9—182no—
168D9—182no—
169D9—181no—
170D9—181no—
171D9—542no—
172C22×C3—91no—
173C22×C3—91no—
174C22×C3—181no—
175C22×C3—811no—
176C2×D3—31no—
177C2×D3—271no—
178C2×D3—271no—
179C2×D3—541no—
180C3×C4—91no—
181C3×C4—271no—
182Dic3—31no—
183C32—21no—
184C32—31no—
185C32—61no—
186C32#619511yescharacteristic
187C32C3×#62611yescharacteristic
188C9—21no—
189C9—21no—
190C9—21no—
191C9—41no—
192C9—61no—
193C9—61no—
194C9—121no—
195C9C4⋊AGL(1,ℤ/9)11yescharacteristic, complemented
196C9C3×#61111yescharacteristic, complemented
197D4—811noSylow
198C2×C3—21no—
199C2×C3—31no—
200C2×C3—61no—
201C2×C3—181no—
202C2×C3—182no—
203C2×C3—181no—
204C2×C3—1621no—
205C2×C3C3×D3×D911yescharacteristic
206C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
207D3—61no—
208D3—542no—
209D3—541no—
210D3—541no—
211C22—91no—
212C22—811no—
213C4—91no—
214C3—21no—
215C3—31no—
216C3—61no—
217C3C3×#619511yescharacteristic
218C3#6192⋊C311yescharacteristic
219C2—181no—
220C2—1621no—
221C2D9×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC2D9×AGL(1,ℤ/9)
commutator, cosocleC2×C92C22×C3
Frattini, socleC2×C32C3×D32
FittingC2×C9×3−1+2C22
hypocenterC92C3×D4
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92299C2semidirect
2. C2×C9×AGL(1,ℤ/9)C2semidirect
3. 3−1+2×Dic9C2semidirect
6. #10619530C3semidirect
16. C2×C9⋊D9C2×C3semidirect
19. C2×C9×D9C2×C3semidirect
21. C9×Dic9C2×C3semidirect
22. C9×3−1+2D4semidirect
53. C2×AGL(1,ℤ/9)D9semidirect
70. C92C3×D4semidirect
122. C2×D9C3×D9semidirect
125. Dic9AGL(1,ℤ/9)semidirect
130. 3−1+2#611semidirect
195. C9C4⋊AGL(1,ℤ/9)semidirect
196. C9C3×#611semidirect

Maximal subgroups

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

subgroupindex
C2×#922992
C2×C9×AGL(1,ℤ/9)2
3−1+2×Dic92
#6192⋊C33
C3×#61953
#106195303