Finite Group Databasebeta

← C2×#11757569 #14517438

Subgroups — C2×#11757569 #14517438

Order 1944.

307 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 307 conjugacy classes of subgroups — too many to draw. Only its 106 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
2#11757569C212yesmaximal, direct product factor
3C2×Dic3×3−1+2—31nomaximal
4C2×C3×3−1+2⋊C4C311yesmaximal, characteristic
5C2×Dic9⋊C9C312yesmaximal, complemented
6C2×C9×Dic9C311yesmaximal, characteristic, complemented
7C2×#6900C412yescomplemented
8C2×#6900C2211yescharacteristic
9C22×C3×3−1+2—21no—
10C22×C3×3−1+2D311yescharacteristic
11C22×C3×3−1+2C2×C311yescharacteristic
12Dic3×3−1+2—32no—
13C3×3−1+2⋊C4C2×C312yes—
14C22×C9⋊C9—22no—
15C22×C9⋊C9—21no—
16C22×C9⋊C9C2×C312yes—
17C22×C92C2×C311yescharacteristic
18Dic9⋊C9C2×C314yescomplemented
19C9×Dic9C2×C312yescomplemented
20#6900C2×C411yescharacteristic, complemented, Sylow
21C2×C32×Dic3—31no—
22C2×C4×3−1+2—91no—
23C2×3−1+2⋊C4—31no—
24C2×C9×Dic3—31no—
25C2×C9×Dic3—32no—
26C2×C3×Dic9C3211yescharacteristic
27C2×C3×3−1+2—22no—
28C2×C3×3−1+2—21no—
29C2×C3×3−1+2Dic312yes—
30C2×C3×3−1+2C3×C412yes—
31C2×C3×3−1+2C2×D311yescharacteristic
32C2×C3×3−1+2C22×C311yescharacteristic
33C2×C9⋊C9—24no—
34C2×C9⋊C9—22no—
35C2×C9⋊C9—22no—
36C2×C9⋊C9—21no—
37C2×C9⋊C9C3×C414yescomplemented
38C2×C9⋊C9C22×C312yes—
39C2×C92C3×C412yescomplemented
40C2×C92C22×C311yescharacteristic
41C22×C33C3×D311yescharacteristic
42C32×Dic3—32no—
43C22×3−1+2—31no—
44C22×3−1+2—31no—
45C22×3−1+2—61no—
46C22×3−1+2—63no—
47C22×3−1+2—61no—
48C22×C3×C9—21no—
49C22×C3×C9—21no—
50C22×C3×C9—22no—
51C22×C3×C9C3×D311yescharacteristic
52C22×C3×C9C3×D312yes—
53C22×C3×C9C2×C3211yescharacteristic
54C4×3−1+2—92no—
553−1+2⋊C4—32no—
56C9×Dic3—32no—
57C9×Dic3—34no—
58C3×Dic9C2×C3212yes—
59C3×3−1+2—21no—
60C3×3−1+2C2×Dic311yescharacteristic
61C3×3−1+2C2×C3×C411yescharacteristic
62C9⋊C9—22no—
63C9⋊C9—21no—
64C9⋊C9C2×C3×C412yescomplemented
65C92C2×C3×C411yescharacteristic, complemented
66C2×C32×C4—91no—
67C2×C3×Dic3—31no—
68C2×C3×Dic3—91no—
69C2×C4×C9—92no—
70C2×C4×C9—91no—
71C2×Dic93−1+211yescharacteristic, complemented
72C2×C33C3×Dic312yes—
73C2×C33C2×C3×D311yescharacteristic
74C2×3−1+2—32no—
75C2×3−1+2—31no—
76C2×3−1+2—32no—
77C2×3−1+2—31no—
78C2×3−1+2—62no—
79C2×3−1+2—61no—
80C2×3−1+2—66no—
81C2×3−1+2—63no—
82C2×3−1+2—62no—
83C2×3−1+2—61no—
84C2×C3×C9—22no—
85C2×C3×C9—21no—
86C2×C3×C9—22no—
87C2×C3×C9—24no—
88C2×C3×C9—21no—
89C2×C3×C9—22no—
90C2×C3×C9C3×Dic312yes—
91C2×C3×C9C3×Dic314yes—
92C2×C3×C9C32×C412yes—
93C2×C3×C9C2×C3×D311yescharacteristic
94C2×C3×C9C2×C3×D312yes—
95C2×C3×C9C22×C3211yescharacteristic
96C22×C32—31no—
97C22×C32—31no—
98C22×C32—61no—
99C22×C32C32×D311yescharacteristic
100C32×C4—92no—
101C3×Dic3—32no—
102C3×Dic3—92no—
103C22×C9—23no—
104C22×C9—21no—
105C22×C9—21no—
106C22×C9—32no—
107C22×C9—62no—
108C22×C9—61no—
109C22×C9AGL(1,ℤ/9)11yescharacteristic
110C22×C9C2×3−1+211yescharacteristic
111C4×C9—94no—
112C4×C9—92no—
113Dic9C2×3−1+212yescomplemented
114C33C2×C3×Dic311yescharacteristic
1153−1+2—31no—
1163−1+2—31no—
1173−1+2—61no—
1183−1+2—63no—
1193−1+2—61no—
120C3×C9—21no—
121C3×C9—21no—
122C3×C9—22no—
123C3×C9C2×C3×Dic311yescharacteristic
124C3×C9C2×C3×Dic312yes—
125C3×C9C2×C32×C411yescharacteristic
126C2×C3×C4—91no—
127C2×C3×C4—271no—
128C2×Dic3—31no—
129C2×C32—32no—
130C2×C32—32no—
131C2×C32—31no—
132C2×C32—31no—
133C2×C32—62no—
134C2×C32—61no—
135C2×C32C32×Dic312yes—
136C2×C32C2×C32×D311yescharacteristic
137C2×C9—26no—
138C2×C9—23no—
139C2×C9—22no—
140C2×C9—22no—
141C2×C9—21no—
142C2×C9—21no—
143C2×C9—34no—
144C2×C9—32no—
145C2×C9—64no—
146C2×C9—62no—
147C2×C9—62no—
148C2×C9—61no—
149C2×C93−1+2⋊C412yescomplemented
150C2×C9C4×3−1+212yescomplemented
151C2×C9C2×AGL(1,ℤ/9)11yescharacteristic
152C2×C9C22×3−1+211yescharacteristic
153C22×C3—21no—
154C22×C3—91no—
155C22×C3C3×AGL(1,ℤ/9)11yescharacteristic
156C22×C3D3×3−1+211yescharacteristic
157C3×C4—92no—
158C3×C4—272no—
159Dic3—32no—
160C32—31no—
161C32—31no—
162C32—61no—
163C32C2×C32×Dic311yescharacteristic
164C9—23no—
165C9—21no—
166C9—21no—
167C9—32no—
168C9—62no—
169C9—61no—
170C9C2×3−1+2⋊C411yescharacteristic, complemented
171C9C2×C4×3−1+211yescharacteristic, complemented
172C2×C4—91noSylow
173C2×C3—22no—
174C2×C3—21no—
175C2×C3—92no—
176C2×C3—91no—
177C2×C3C3×3−1+2⋊C412yes—
178C2×C3Dic3×3−1+212yes—
179C2×C3C2×C3×AGL(1,ℤ/9)11yescharacteristic
180C2×C3C2×D3×3−1+211yescharacteristic
181C22#9226511yescharacteristic
182C4—92no—
183C3—21no—
184C3—91no—
185C3C2×C3×3−1+2⋊C411yescharacteristic
186C3C2×Dic3×3−1+211yescharacteristic
187C2#1175756912yesdirect product factor
188C2C2×#9226511yescharacteristic
subgroupG/H
centerC22×C3C3×AGL(1,ℤ/9)
commutatorC3×C9C2×C32×C4
FrattiniC2×C32C2×C32×D3
FittingC22×#6900C2
socleC22×C32C32×D3
prime radicalC22×C33C3×D3
cosocleC2×C3×C9C22×C32
hypercenterC22×C9AGL(1,ℤ/9)
hypocenterC9C2×C4×3−1+2
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C22×C9

Complements

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

NH ≅ G/Ntype
2. #11757569C2direct (N × H)
5. C2×Dic9⋊C9C3semidirect
6. C2×C9×Dic9C3semidirect
7. C2×#6900C4semidirect
18. Dic9⋊C9C2×C3semidirect
19. C9×Dic9C2×C3semidirect
20. #6900C2×C4semidirect
37. C2×C9⋊C9C3×C4semidirect
39. C2×C92C3×C4semidirect
64. C9⋊C9C2×C3×C4semidirect
65. C92C2×C3×C4semidirect
71. C2×Dic93−1+2semidirect
113. Dic9C2×3−1+2semidirect
149. C2×C93−1+2⋊C4semidirect
150. C2×C9C4×3−1+2semidirect
170. C9C2×3−1+2⋊C4semidirect
171. C9C2×C4×3−1+2semidirect
187. C2#11757569direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#69002
#117575692
C2×Dic3×3−1+23
C2×C3×3−1+2⋊C43
C2×Dic9⋊C93
C2×C9×Dic93