Finite Group Databasebeta

← #92299⋊C4 #14516790

Subgroups — #92299⋊C4 #14516790

Order 1944.

226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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
23−1+2×Dic9C211yesmaximal, characteristic, complemented
3C9×3−1+2⋊C4C211yesmaximal, characteristic, complemented
4(C3⋊AGL(1,ℤ/9))⋊C4—31nomaximal
5C3×(C3⋊D9)⋊C4—31nomaximal
6#10619528C311yesmaximal, characteristic, complemented
7C2×C9×3−1+2C2211yescharacteristic
8#92299C412yescomplemented
9C2×C3⋊AGL(1,ℤ/9)—31no—
10C2×C3×C3⋊D9—31no—
11Dic3×3−1+2—31no—
12C3×3−1+2⋊C4D311yescharacteristic
13C3×C9×Dic3—31no—
14C32×Dic9D311yescharacteristic
15C2×C9⋊D9C2×C311yescharacteristic
16C2×#4169—61no—
17Dic9⋊C9—21no—
18C9×Dic9—21no—
19C9×Dic9C2×C311yescharacteristic, complemented
20C9×Dic9C2×C311yescharacteristic, complemented
21C9×3−1+2C2×C411yescharacteristic, complemented, Sylow
22C3×#624—91no—
23C4×AGL(1,ℤ/9)—91no—
24C3×C4×D9—91no—
25(C3⋊D9)⋊C4—31no—
26(C3⋊D9)⋊C4—31no—
27C2×C3×3−1+2C2×D311yescharacteristic
28C2×C32×C9C2×D311yescharacteristic
29C3⋊AGL(1,ℤ/9)—32no—
30C3×C3⋊D9—32no—
31C2×C9⋊C9—21no—
32C2×C9⋊C9—41no—
33C2×C32⋊C9—21no—
34C2×C92—21no—
35C2×C92C22×C311yescharacteristic
36C9⋊D9C3×C412yescomplemented
37#4169—62no—
38C2×C3×C3⋊D3—91no—
39C32×Dic3—31no—
40C32×Dic3—31no—
41C2×C3⋊D9—31no—
42C2×C3⋊D9—31no—
43C2×C3⋊D9—61no—
44C2×AGL(1,ℤ/9)—91no—
45C2×AGL(1,ℤ/9)—181no—
46C2×C3×D9—91no—
47C2×C3×D9—181no—
48C4×3−1+2—91no—
49C3×C4×C9—91no—
503−1+2⋊C4—21no—
513−1+2⋊C4D911yescharacteristic, complemented
52C9×Dic3—31no—
53C9×Dic3—31no—
54C9×Dic3—61no—
55C9×Dic3—61no—
56C3×Dic9—31no—
57C3×Dic9C3×D311yescharacteristic
58C3×Dic9C3×D311yescharacteristic
59C3×3−1+2C4×D311yescharacteristic
60C32×C9C4×D311yescharacteristic
61C9⋊C9—21no—
62C9⋊C9—41no—
63C32⋊C9—21no—
64C92—21no—
65C92C2×C3×C411yescharacteristic, complemented
66C3×C4×D3—271no—
67C3×C4×D3—271no—
68#624—91no—
69C4×D9—91no—
70C4×D9—91no—
71C2×C33D3211yescharacteristic
72C3×C3⋊D3—92no—
73C2×3−1+2—21no—
74C2×3−1+2—21no—
75C2×3−1+2—41no—
76C2×3−1+2C2×D911yescharacteristic
77C2×C3×C9—21no—
78C2×C3×C9—21no—
79C2×C3×C9—21no—
80C2×C3×C9—31no—
81C2×C3×C9—41no—
82C2×C3×C9—61no—
83C2×C3×C9C2×C3×D311yescharacteristic
84C2×C3×C9C2×C3×D311yescharacteristic
85C3⋊D9—32no—
86C3⋊D9—32no—
87C3⋊D9—62no—
88AGL(1,ℤ/9)—92no—
89AGL(1,ℤ/9)—182no—
90C3×D9—92no—
91C3×D9—182no—
92C2×C3⋊D3—91no—
93C2×C3×D3—271no—
94C2×C3×D3—271no—
95C2×C3×D3—541no—
96C32×C4—91no—
97C32×C4—91no—
98C3×Dic3—31no—
99C3×Dic3—31no—
100C3×Dic3—31no—
101C3×Dic3—61no—
102C3×Dic3—91no—
103C2×D9—91no—
104C2×D9—91no—
105C2×D9—181no—
106C2×D9—181no—
107C2×D9—541no—
108C4×C9—91no—
109C4×C9—91no—
110C4×C9—181no—
111C4×C9—181no—
112Dic9C3×D911yescharacteristic, complemented
113Dic9AGL(1,ℤ/9)11yescharacteristic, complemented
114C33#62411yescharacteristic
1153−1+2—21no—
1163−1+2—21no—
1173−1+2—41no—
1183−1+2C4×D911yescharacteristic, complemented
119C3×C9—21no—
120C3×C9—21no—
121C3×C9—21no—
122C3×C9—31no—
123C3×C9—41no—
124C3×C9—61no—
125C3×C9C3×C4×D311yescharacteristic
126C3×C9C3×C4×D311yescharacteristic
127C2×C3×C4—811no—
128C4×D3—271no—
129C4×D3—271no—
130C2×C32—21no—
131C2×C32—31no—
132C2×C32—61no—
133C2×C32D3×D911yescharacteristic
134C2×C32C3×D3211yescharacteristic
135C3⋊D3—92no—
136C3×D3—272no—
137C3×D3—272no—
138C3×D3—542no—
139C2×C9—21no—
140C2×C9—21no—
141C2×C9—21no—
142C2×C9—41no—
143C2×C9—61no—
144C2×C9—61no—
145C2×C9—121no—
146C2×C9C2×C3×D911yescharacteristic
147C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
148D9—92no—
149D9—92no—
150D9—182no—
151D9—182no—
152D9—542no—
153C22×C3—811no—
154C2×D3—271no—
155C2×D3—271no—
156C2×D3—541no—
157C3×C4—91no—
158C3×C4—91no—
159C3×C4—91no—
160C3×C4—181no—
161C3×C4—271no—
162Dic3—31no—
163Dic3—31no—
164C32—21no—
165C32—31no—
166C32—61no—
167C32(C3⋊D9)⋊C411yescharacteristic
168C32C3×#62411yescharacteristic
169C9—21no—
170C9—21no—
171C9—21no—
172C9—41no—
173C9—61no—
174C9—61no—
175C9—121no—
176C9C3×C4×D911yescharacteristic, complemented
177C9C4×AGL(1,ℤ/9)11yescharacteristic, complemented
178C2×C4—811noSylow
179C2×C3—21no—
180C2×C3—31no—
181C2×C3—61no—
182C2×C3—812no—
183C2×C3C3×D3×D911yescharacteristic
184C2×C3D3×AGL(1,ℤ/9)11yescharacteristic
185D3—272no—
186D3—272no—
187D3—542no—
188C22—811no—
189C4—91no—
190C4—91no—
191C3—21no—
192C3—31no—
193C3—61no—
194C3C3×(C3⋊D9)⋊C411yescharacteristic
195C3(C3⋊AGL(1,ℤ/9))⋊C411yescharacteristic
196C2—812no—
197C2D9×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC2D9×AGL(1,ℤ/9)
commutator, hypocenterC92C2×C3×C4
Frattini, socleC2×C32C3×D32
FittingC2×C9×3−1+2C22
prime radicalC2×#92299C2
cosocleC2×C92C22×C3
LCSG ▷ C92
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. 3−1+2×Dic9C2semidirect
3. C9×3−1+2⋊C4C2semidirect
6. #10619528C3semidirect
8. #92299C4semidirect
19. C9×Dic9C2×C3semidirect
20. C9×Dic9C2×C3semidirect
21. C9×3−1+2C2×C4semidirect
36. C9⋊D9C3×C4semidirect
51. 3−1+2⋊C4D9semidirect
65. C92C2×C3×C4semidirect
112. Dic9C3×D9semidirect
113. Dic9AGL(1,ℤ/9)semidirect
118. 3−1+2C4×D9semidirect
176. C9C3×C4×D9semidirect
177. C9C4×AGL(1,ℤ/9)semidirect

Maximal subgroups

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

subgroupindex
C2×#922992
3−1+2×Dic92
C9×3−1+2⋊C42
(C3⋊AGL(1,ℤ/9))⋊C43
C3×(C3⋊D9)⋊C43
#106195283