Finite Group Databasebeta

← #14516824

Subgroups — #14516824

Order 1944.

219 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 219 conjugacy classes of subgroups — too many to draw. Only its 40 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×#92309C211yesmaximal, characteristic, complemented
2C2×#92264C211yesmaximal, characteristic, complemented
3#11757568C211yesmaximal, characteristic, complemented
4#6195⋊C3—31nomaximal
5#6192⋊C3—31nomaximal
6#10619530C311yesmaximal, characteristic, complemented
7C2×#6896C2211yescharacteristic
8#92309—21no—
9#92264—21no—
10C2×C3⋊AGL(1,ℤ/9)—31no—
11C2×C3⋊AGL(1,ℤ/9)—31no—
12C2×D3×3−1+2—31no—
13C2×C3×AGL(1,ℤ/9)D311yescharacteristic
14Dic3×3−1+2—31no—
15C3×3−1+2⋊C4D311yescharacteristic
16C2×C9⋊D9C2×C311yescharacteristic, complemented
17C2×D9⋊C9—21no—
18C2×#4169—61no—
19C2×C9×D9C2×C311yescharacteristic, complemented
20Dic9⋊C9—21no—
21C9×Dic9C2×C311yescharacteristic, complemented
22#6896D411yescharacteristic, complemented, Sylow
23C3×#626—91no—
24#611⋊C3—91no—
25C4⋊AGL(1,ℤ/9)—91no—
26#6195—31no—
27#6192—31no—
28C2×C3×3−1+2C2×D311yescharacteristic
29C2×C3×3−1+2C2×D311yescharacteristic
30C3⋊AGL(1,ℤ/9)—61no—
31C3⋊AGL(1,ℤ/9)—61no—
32D3×3−1+2—61no—
33C3×AGL(1,ℤ/9)—21no—
34C2×C9⋊C9—21no—
35C2×C9⋊C9—21no—
36C2×C9⋊C9—41no—
37C2×C32⋊C9—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—
46C22×3−1+2—91no—
47C2×C3⋊D9—31no—
48C2×C3⋊D9—31no—
49C2×C3⋊D9—61no—
50C2×AGL(1,ℤ/9)—31no—
51C2×AGL(1,ℤ/9)—91no—
52C2×AGL(1,ℤ/9)—91no—
53C2×AGL(1,ℤ/9)—181no—
54C2×AGL(1,ℤ/9)—181no—
55C2×D3×C9—31no—
56C2×D3×C9—61no—
57C2×C3×D9C3×D311yescharacteristic
58C4×3−1+2—91no—
593−1+2⋊C4—31no—
60C9×Dic3—31no—
61C9×Dic3—61no—
62C3×Dic9C3×D311yescharacteristic
63C3×3−1+2D1211yescharacteristic
64C3×3−1+2#6711yescharacteristic
65C9⋊C9—21no—
66C9⋊C9—21no—
67C9⋊C9—41no—
68C32⋊C9—21no—
69C92C3×D411yescharacteristic, complemented
70C3×#67—271no—
71C3×D12—271no—
72#626—91no—
73#611—91no—
74D36—91no—
75C2×C33D3211yescharacteristic
76C3×C3⋊D3—181no—
77C32×D3—61no—
78C2×3−1+2—31no—
79C2×3−1+2—31no—
80C2×3−1+2—61no—
81C2×3−1+2—61no—
82C2×3−1+2—181no—
83C2×C3×C9—21no—
84C2×C3×C9—21no—
85C2×C3×C9—21no—
86C2×C3×C9—41no—
87C2×C3×C9C2×C3×D311yescharacteristic
88C2×C3×C9C2×C3×D311yescharacteristic
89C3⋊D9—61no—
90C3⋊D9—61no—
91C3⋊D9—62no—
92AGL(1,ℤ/9)—61no—
93AGL(1,ℤ/9)—181no—
94AGL(1,ℤ/9)—181no—
95AGL(1,ℤ/9)—182no—
96AGL(1,ℤ/9)—182no—
97D3×C9—62no—
98D3×C9—61no—
99C3×D9—21no—
100C22×C32—91no—
101C2×C3⋊D3—91no—
102C2×C3×D3—31no—
103C2×C3×D3—91no—
104C2×C3×D3—271no—
105C2×C3×D3—271no—
106C2×C3×D3—541no—
107C32×C4—91no—
108C3×Dic3—31no—
109C3×Dic3—91no—
110C22×C9—91no—
111C22×C9—181no—
112C2×D9—91no—
113C2×D9—91no—
114C2×D9—181no—
115C2×D9—181no—
116C2×D9—541no—
117C2×D9AGL(1,ℤ/9)11yescharacteristic, complemented
118C4×C9—91no—
119C4×C9—181no—
120Dic9AGL(1,ℤ/9)11yescharacteristic, complemented
121C33#62611yescharacteristic
1223−1+2—31no—
1233−1+2—31no—
1243−1+2—61no—
1253−1+2—61no—
126C3×C9—21no—
127C3×C9—21no—
128C3×C9—21no—
129C3×C9—41no—
130C3×C9C3×D1211yescharacteristic
131C3×C9C3×#6711yescharacteristic
132C3×D4—811no—
133#67—271no—
134D12—271no—
135C2×C32—31no—
136C2×C32—31no—
137C2×C32—61no—
138C2×C32—181no—
139C2×C32C3×D3211yescharacteristic
140C3⋊D3—181no—
141C3×D3—61no—
142C3×D3—181no—
143C3×D3—541no—
144C3×D3—541no—
145C3×D3—542no—
146C2×C9—21no—
147C2×C9—21no—
148C2×C9—61no—
149C2×C9—61no—
150C2×C9—61no—
151C2×C9—121no—
152C2×C9—182no—
153C2×C9—181no—
154C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
155C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
156D9—21no—
157D9—182no—
158D9—182no—
159D9—181no—
160D9—181no—
161D9—542no—
162C22×C3—91no—
163C22×C3—271no—
164C22×C3—811no—
165C2×D3—31no—
166C2×D3—271no—
167C2×D3—271no—
168C2×D3—541no—
169C3×C4—91no—
170C3×C4—271no—
171Dic3—31no—
172C32—31no—
173C32—31no—
174C32—61no—
175C32C3×#62611yescharacteristic
176C9—21no—
177C9—21no—
178C9—61no—
179C9—61no—
180C9—61no—
181C9—121no—
182C9C4⋊AGL(1,ℤ/9)11yescharacteristic, complemented
183C9#611⋊C311yescharacteristic, complemented
184D4—811noSylow
185C2×C3—21no—
186C2×C3—91no—
187C2×C3—181no—
188C2×C3—541no—
189C2×C3—1621no—
190C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
191C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
192D3—61no—
193D3—542no—
194D3—541no—
195D3—541no—
196C22—91no—
197C22—811no—
198C4—91no—
199C3—21no—
200C3—91no—
201C3#6192⋊C311yescharacteristic
202C3#6195⋊C311yescharacteristic
203C2—181no—
204C2—1621no—
205C2#92264⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92264⋊C2
commutator, cosocleC2×C92C22×C3
Frattini, socleC2×C32C3×D32
FittingC2×#6896C22
hypocenterC92C3×D4
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92309C2semidirect
2. C2×#92264C2semidirect
3. #11757568C2semidirect
6. #10619530C3semidirect
16. C2×C9⋊D9C2×C3semidirect
19. C2×C9×D9C2×C3semidirect
21. C9×Dic9C2×C3semidirect
22. #6896D4semidirect
69. C92C3×D4semidirect
117. C2×D9AGL(1,ℤ/9)semidirect
120. Dic9AGL(1,ℤ/9)semidirect
182. C9C4⋊AGL(1,ℤ/9)semidirect
183. C9#611⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#923092
C2×#922642
#117575682
#6195⋊C33
#6192⋊C33
#106195303