Finite Group Databasebeta

← C3×#10619962 #14518922

Subgroups — C3×#10619962 #14518922

Order 1944.

702 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C32×C4×3−1+2C211yesmaximal, characteristic
2C3×C3⋊(3−1+2⋊C4)C212yesmaximal
3C32×#634—31nomaximal
4#10619962C313yesmaximal, direct product factor
5C3×#6226C311yesmaximal, characteristic, complemented
6C3×3−1+2⋊Q8—33nomaximal
7C2×C32×3−1+2C2211yescharacteristic
8C34×C4D311yescharacteristic
9C32×C3⋊Dic3—32no—
10C3×C4×3−1+2—23no—
11C3×C4×3−1+2—29no—
12C3×C4×3−1+2—23no—
13C3×C4×3−1+2D313yes—
14C3×C4×3−1+2C2×C313yes—
15C32×C4×C9—21no—
16C32×C4×C9C2×C311yescharacteristic
17C3⋊(3−1+2⋊C4)C2×C316yes—
18C3×C3⋊Dic9C2×C312yes—
19C3×3−1+2⋊C4—36no—
20C32×3−1+2Q811yescharacteristic, complemented, Sylow
21C3×#634—31no—
22C3×#634—33no—
23C32×Dic6—93no—
24C32×Dic6—91no—
25#6226C3211yescharacteristic, complemented
263−1+2⋊Q8—39no—
27C3×Dic18—33no—
28C2×C34C2×D311yescharacteristic
29C2×C3×3−1+2—23no—
30C2×C3×3−1+2—29no—
31C2×C3×3−1+2—23no—
32C2×C3×3−1+2C2×D313yes—
33C2×C3×3−1+2C22×C313yes—
34C2×C32×C9—21no—
35C2×C32×C9C22×C311yescharacteristic
36C33×C4—23no—
37C33×C4—21no—
38C33×C4—33no—
39C33×C4—63no—
40C33×C4C3×D311yescharacteristic
41C33×C4C3×D313yes—
42C33×C4C3⋊D311yescharacteristic
43C3×C3⋊Dic3—32no—
44C3×C3⋊Dic3—36no—
45C32×Dic3—96no—
46C32×Dic3—92no—
47C4×3−1+2—218no—
48C4×3−1+2—29no—
49C4×3−1+2—29no—
50C4×3−1+2C3×D319yes—
51C3×C4×C9—26no—
52C3×C4×C9—23no—
53C3×C4×C9—21no—
54C3×C4×C9—23no—
55C3×C4×C9—23no—
56C3×C4×C9C3×D313yes—
57C3×C4×C9C2×C3211yescharacteristic
58C3⋊Dic9C2×C3212yes—
593−1+2⋊C4—318no—
60C3×Dic9—36no—
61C34Dic611yescharacteristic
62C3×3−1+2—23no—
63C3×3−1+2—29no—
64C3×3−1+2—23no—
65C3×3−1+2Dic613yescomplemented
66C3×3−1+2C3×Q813yescomplemented
67C32×C9—21no—
68C32×C9C3×Q811yescharacteristic, complemented
69C32×Q8—271no—
70#634—31no—
71C3×Dic6—99no—
72C3×Dic6—93no—
73C3×Dic6—91no—
74C3×Dic6—93no—
75Dic18—33no—
76C2×C33—23no—
77C2×C33—21no—
78C2×C33—33no—
79C2×C33—63no—
80C2×C33C2×C3×D311yescharacteristic
81C2×C33C2×C3×D313yes—
82C2×C33C2×C3⋊D311yescharacteristic
83C2×3−1+2—218no—
84C2×3−1+2—29no—
85C2×3−1+2—29no—
86C2×3−1+2C2×C3×D319yes—
87C2×C3×C9—26no—
88C2×C3×C9—23no—
89C2×C3×C9—21no—
90C2×C3×C9—23no—
91C2×C3×C9—23no—
92C2×C3×C9C2×C3×D313yes—
93C2×C3×C9C22×C3211yescharacteristic
94C32×C4—23no—
95C32×C4—21no—
96C32×C4—23no—
97C32×C4—31no—
98C32×C4—39no—
99C32×C4—61no—
100C32×C4—69no—
101C32×C4—62no—
102C32×C4—61no—
103C32×C4—272no—
104C32×C4AGL(1,ℤ/9)13yes—
105C32×C4C32×D311yescharacteristic
106C32×C4C3×C3⋊D311yescharacteristic
107C32×C4C3×C3⋊D313yes—
108C3⋊Dic3—32no—
109C3×Dic3—918no—
110C3×Dic3—96no—
111C3×Dic3—92no—
112C3×Dic3—96no—
113C4×C9—29no—
114C4×C9—23no—
115C4×C9C32×D313yes—
116Dic9—36no—
117C33—23no—
118C33—21no—
119C33—33no—
120C33—63no—
121C33C3×Dic611yescharacteristic
122C33C3×Dic613yes—
123C33#63411yescharacteristic
1243−1+2—218no—
1253−1+2—29no—
1263−1+2—29no—
1273−1+2C3×Dic619yescomplemented
128C3×C9—26no—
129C3×C9—23no—
130C3×C9—21no—
131C3×C9—23no—
132C3×C9—23no—
133C3×C9C3×Dic613yescomplemented
134C3×C9C32×Q811yescharacteristic, complemented
135C3×Q8—273no—
136C3×Q8—271no—
137Dic6—93no—
138Dic6—91no—
139C2×C32—23no—
140C2×C32—21no—
141C2×C32—23no—
142C2×C32—31no—
143C2×C32—39no—
144C2×C32—61no—
145C2×C32—69no—
146C2×C32—62no—
147C2×C32—61no—
148C2×C32C2×AGL(1,ℤ/9)13yes—
149C2×C32C2×C32×D311yescharacteristic
150C2×C32C2×C3×C3⋊D311yescharacteristic
151C2×C32C2×C3×C3⋊D313yes—
152C2×C9—29no—
153C2×C9—23no—
154C2×C9C2×C32×D313yes—
155C3×C4—23no—
156C3×C4—21no—
157C3×C4—33no—
158C3×C4—63no—
159C3×C4—276no—
160C3×C4—272no—
161C3×C4C3×AGL(1,ℤ/9)13yes—
162C3×C4C3⋊AGL(1,ℤ/9)11yescharacteristic
163C3×C4C32×C3⋊D311yescharacteristic
164Dic3—96no—
165Dic3—92no—
166C32—21no—
167C32—23no—
168C32—23no—
169C32—31no—
170C32—39no—
171C32—61no—
172C32—69no—
173C32—62no—
174C32—61no—
175C323−1+2⋊Q813yescomplemented
176C32C32×Dic611yescharacteristic
177C32C3×#63411yescharacteristic
178C32C3×#63413yes—
179C9—29no—
180C9—23no—
181C9C32×Dic613yescomplemented
182Q8—271noSylow
183C2×C3—23no—
184C2×C3—21no—
185C2×C3—33no—
186C2×C3—63no—
187C2×C3C2×C3×AGL(1,ℤ/9)13yes—
188C2×C3C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
189C2×C3C2×C32×C3⋊D311yescharacteristic
190C4—272no—
191C4C3×C3⋊AGL(1,ℤ/9)11yescharacteristic
192C3—23no—
193C3—21no—
194C3—33no—
195C3—63no—
196C3C3×3−1+2⋊Q813yescomplemented
197C3#1061996211yescharacteristic, direct product factor
198C3C32×#63411yescharacteristic
199C2C2×C3×C3⋊AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
centerC2×C3C2×C3⋊AGL(1,ℤ/9)
commutator, cosocleC2×C3×C9C22×C32
FrattiniC2×C3C2×C32×C3⋊D3
FittingC32×C4×3−1+2C2
socleC2×C33C2×C3×D3
prime radicalC2×C34C2×D3
hypercenterC3×C4C3⋊AGL(1,ℤ/9)
hypocenterC3×C9C32×Q8
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
4. #10619962C3direct (N × H)
5. C3×#6226C3semidirect
20. C32×3−1+2Q8semidirect
25. #6226C32semidirect
65. C3×3−1+2Dic6semidirect
66. C3×3−1+2C3×Q8semidirect
68. C32×C9C3×Q8semidirect
127. 3−1+2C3×Dic6semidirect
133. C3×C9C3×Dic6semidirect
134. C3×C9C32×Q8semidirect
175. C323−1+2⋊Q8semidirect
181. C9C32×Dic6semidirect
196. C3C3×3−1+2⋊Q8semidirect
197. C3#10619962direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C4×3−1+22
C3×C3⋊(3−1+2⋊C4)2
C32×#6343
#106199623
C3×#62263
C3×3−1+2⋊Q83