Finite Group Databasebeta

← #14516792

Subgroups — #14516792

Order 1944.

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

normal subgroups only

This group has 232 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×D9×3−1+2C211yesmaximal, characteristic, complemented
3C9×3−1+2⋊C4C211yesmaximal, characteristic, complemented
4#6195⋊C3—31nomaximal
5C3×#6192—31nomaximal
6#10619530C311yesmaximal, characteristic, complemented
7C2×C9×3−1+2C2211yescharacteristic
8#92299—21no—
9D9×3−1+2—21no—
10C2×C3⋊AGL(1,ℤ/9)—31no—
11C2×C3×C3⋊D9—31no—
12C2×D3×3−1+2—31no—
13C2×C32×D9D311yescharacteristic
14C3×3−1+2⋊C4D311yescharacteristic
15C3×C9×Dic3—31no—
16C2×C9⋊D9C2×C311yescharacteristic, complemented
17C2×#4169—61no—
18C2×C9×D9—21no—
19C2×C9×D9C2×C311yescharacteristic, complemented
20Dic9⋊C9—21no—
21C9×Dic9C2×C311yescharacteristic, complemented
22C9×3−1+2D411yescharacteristic, complemented, Sylow
23C3×#626—91no—
24#611⋊C3—91no—
25C3×D36—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—
32D3×3−1+2—61no—
33C32×D9—21no—
34C2×C9⋊C9—21no—
35C2×C9⋊C9—41no—
36C2×C32⋊C9—21no—
37C2×C92—21no—
38C2×C92C22×C311yescharacteristic
39C9⋊D9—21no—
40#4169—62no—
41C9×D9—22no—
42C9×D9—21no—
43C2×C3×C3⋊D3—91no—
44C2×C32×D3—31no—
45C32×Dic3—31no—
46C22×3−1+2—91no—
47C2×C3⋊D9—31no—
48C2×C3⋊D9—31no—
49C2×C3⋊D9—61no—
50C2×AGL(1,ℤ/9)—91no—
51C2×AGL(1,ℤ/9)—181no—
52C2×D3×C9—31no—
53C2×D3×C9—61no—
54C2×C3×D9—31no—
55C2×C3×D9—91no—
56C2×C3×D9—181no—
57C2×C3×D9C3×D311yescharacteristic
58C3×C4×C9—91no—
593−1+2⋊C4—21no—
603−1+2⋊C4D911yescharacteristic, complemented
61C9×Dic3—31no—
62C9×Dic3—61no—
63C3×Dic9C3×D311yescharacteristic
64C3×3−1+2D1211yescharacteristic
65C32×C9#6711yescharacteristic
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+2—181no—
83C2×3−1+2C2×D911yescharacteristic
84C2×C3×C9—21no—
85C2×C3×C9—21no—
86C2×C3×C9—21no—
87C2×C3×C9—31no—
88C2×C3×C9—41no—
89C2×C3×C9—61no—
90C2×C3×C9C2×C3×D311yescharacteristic
91C2×C3×C9C2×C3×D311yescharacteristic
92C3⋊D9—61no—
93C3⋊D9—61no—
94C3⋊D9—62no—
95AGL(1,ℤ/9)—182no—
96AGL(1,ℤ/9)—181no—
97D3×C9—62no—
98D3×C9—61no—
99C3×D9—21no—
100C3×D9—61no—
101C3×D9—181no—
102C3×D9—182no—
103C22×C32—91no—
104C2×C3⋊D3—91no—
105C2×C3×D3—31no—
106C2×C3×D3—91no—
107C2×C3×D3—271no—
108C2×C3×D3—271no—
109C2×C3×D3—541no—
110C32×C4—91no—
111C3×Dic3—31no—
112C3×Dic3—31no—
113C3×Dic3—61no—
114C22×C9—91no—
115C22×C9—181no—
116C2×D9—91no—
117C2×D9—91no—
118C2×D9—181no—
119C2×D9—181no—
120C2×D9—541no—
121C2×D9AGL(1,ℤ/9)11yescharacteristic, complemented
122C4×C9—91no—
123C4×C9—181no—
124Dic9C3×D911yescharacteristic, complemented
125C33#62611yescharacteristic
1263−1+2—21no—
1273−1+2—21no—
1283−1+2—41no—
1293−1+2D3611yescharacteristic, complemented
130C3×C9—21no—
131C3×C9—21no—
132C3×C9—21no—
133C3×C9—31no—
134C3×C9—41no—
135C3×C9—61no—
136C3×C9C3×D1211yescharacteristic
137C3×C9C3×#6711yescharacteristic
138C3×D4—811no—
139#67—271no—
140D12—271no—
141C2×C32—21no—
142C2×C32—31no—
143C2×C32—61no—
144C2×C32—181no—
145C2×C32D3×D911yescharacteristic
146C2×C32C3×D3211yescharacteristic
147C3⋊D3—181no—
148C3×D3—61no—
149C3×D3—181no—
150C3×D3—541no—
151C3×D3—542no—
152C3×D3—541no—
153C2×C9—21no—
154C2×C9—21no—
155C2×C9—21no—
156C2×C9—41no—
157C2×C9—61no—
158C2×C9—61no—
159C2×C9—121no—
160C2×C9—182no—
161C2×C9—181no—
162C2×C9C2×C3×D911yescharacteristic
163C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
164D9—21no—
165D9—182no—
166D9—182no—
167D9—181no—
168D9—181no—
169D9—542no—
170C22×C3—91no—
171C22×C3—271no—
172C22×C3—811no—
173C2×D3—31no—
174C2×D3—271no—
175C2×D3—271no—
176C2×D3—541no—
177C3×C4—91no—
178C3×C4—91no—
179C3×C4—181no—
180Dic3—31no—
181C32—21no—
182C32—31no—
183C32—61no—
184C32#619211yescharacteristic
185C32C3×#62611yescharacteristic
186C9—21no—
187C9—21no—
188C9—21no—
189C9—41no—
190C9—61no—
191C9—61no—
192C9—121no—
193C9C3×D3611yescharacteristic, complemented
194C9#611⋊C311yescharacteristic, complemented
195D4—811noSylow
196C2×C3—21no—
197C2×C3—31no—
198C2×C3—61no—
199C2×C3—181no—
200C2×C3—541no—
201C2×C3—1621no—
202C2×C3C3×D3×D911yescharacteristic
203C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
204D3—61no—
205D3—542no—
206D3—541no—
207D3—541no—
208C22—91no—
209C22—811no—
210C4—91no—
211C3—21no—
212C3—31no—
213C3—61no—
214C3C3×#619211yescharacteristic
215C3#6195⋊C311yescharacteristic
216C2—181no—
217C2—1621no—
218C2D9×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×D9×3−1+2C2semidirect
3. C9×3−1+2⋊C4C2semidirect
6. #10619530C3semidirect
16. C2×C9⋊D9C2×C3semidirect
19. C2×C9×D9C2×C3semidirect
21. C9×Dic9C2×C3semidirect
22. C9×3−1+2D4semidirect
60. 3−1+2⋊C4D9semidirect
70. C92C3×D4semidirect
121. C2×D9AGL(1,ℤ/9)semidirect
124. Dic9C3×D9semidirect
129. 3−1+2D36semidirect
193. C9C3×D36semidirect
194. C9#611⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#922992
C2×D9×3−1+22
C9×3−1+2⋊C42
#6195⋊C33
C3×#61923
#106195303