Finite Group Databasebeta

← C2×#66316⋊C3 #14517427

Subgroups — C2×#66316⋊C3 #14517427

Order 1944.

557 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 557 conjugacy classes of subgroups — too many to draw. Only its 123 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×#6891C211yesmaximal, characteristic
2#66316⋊C3C212yesmaximal, direct product factor
3C2×C32×C3⋊Dic3—31nomaximal
4C2×C3⋊(3−1+2⋊C4)C311yesmaximal, characteristic, complemented
5C2×#66316C313yesmaximal, complemented
6C2×#6891C412yescomplemented
7C2×#6891C2211yescharacteristic
8C22×C34D311yescharacteristic
9C32×C3⋊Dic3—32no—
10C22×C3×3−1+2—21no—
11C22×C3×3−1+2C2×C311yescharacteristic
12C3⋊(3−1+2⋊C4)C2×C312yescomplemented
13C22×C32⋊C9—23no—
14C22×C32⋊C9C2×C313yes—
15#66316C2×C316yescomplemented
16#6891C2×C411yescharacteristic, complemented, Sylow
17C2×C3×C3⋊Dic3—31no—
18C2×C3×C3⋊Dic3—33no—
19C2×C32×Dic3—91no—
20C2×C32×Dic3—93no—
21C2×C3⋊Dic9C3211yescharacteristic, complemented
22C2×3−1+2⋊C4—91no—
23C2×C34Dic312yes—
24C2×C34C2×D311yescharacteristic
25C2×C3×3−1+2—22no—
26C2×C3×3−1+2—21no—
27C2×C3×3−1+2C3×C412yescomplemented
28C2×C3×3−1+2C22×C311yescharacteristic
29C2×C32⋊C9—26no—
30C2×C32⋊C9—23no—
31C2×C32⋊C9C3×C416yescomplemented
32C2×C32⋊C9C22×C313yes—
33C22×C33—31no—
34C22×C33—33no—
35C22×C33—61no—
36C22×C33—63no—
37C22×C33C3×D311yescharacteristic
38C22×C33C3×D313yes—
39C3×C3⋊Dic3—36no—
40C3×C3⋊Dic3—32no—
41C32×Dic3—92no—
42C32×Dic3—96no—
43C22×3−1+2—31no—
44C22×3−1+2—61no—
45C22×3−1+2—62no—
46C22×3−1+2—61no—
47C22×C3×C9—21no—
48C22×C3×C9—23no—
49C22×C3×C9C2×C3211yescharacteristic
50C3⋊Dic9C2×C3212yescomplemented
513−1+2⋊C4—92no—
52C34C2×Dic311yescharacteristic
53C3×3−1+2—21no—
54C3×3−1+2C2×C3×C411yescharacteristic, complemented
55C32⋊C9—23no—
56C32⋊C9C2×C3×C413yescomplemented
57C2×C32×C4—271no—
58C2×C3⋊Dic3—31no—
59C2×C3×Dic3—93no—
60C2×C3×Dic3—93no—
61C2×C3×Dic3—96no—
62C2×C3×Dic3—91no—
63C2×C3×Dic3—93no—
64C2×Dic9—91no—
65C2×C33—32no—
66C2×C33—36no—
67C2×C33—31no—
68C2×C33—33no—
69C2×C33—62no—
70C2×C33—66no—
71C2×C33—61no—
72C2×C33—63no—
73C2×C33C3×Dic312yes—
74C2×C33C3×Dic316yes—
75C2×C33C2×C3×D311yescharacteristic
76C2×C33C2×C3×D313yes—
77C2×3−1+2—32no—
78C2×3−1+2—31no—
79C2×3−1+2—62no—
80C2×3−1+2—61no—
81C2×3−1+2—64no—
82C2×3−1+2—62no—
83C2×3−1+2—62no—
84C2×3−1+2—61no—
85C2×C3×C9—22no—
86C2×C3×C9—26no—
87C2×C3×C9—21no—
88C2×C3×C9—23no—
89C2×C3×C9C32×C412yescomplemented
90C2×C3×C9C22×C3211yescharacteristic
91C22×C32—21no—
92C22×C32—23no—
93C22×C32—31no—
94C22×C32—33no—
95C22×C32—33no—
96C22×C32—36no—
97C22×C32—63no—
98C22×C32—63no—
99C22×C32—61no—
100C22×C32—63no—
101C22×C32—63no—
102C22×C32(C3⋊D3)⋊C311yescharacteristic
103C22×C32AGL(1,ℤ/9)13yes—
104C22×C32C32×D311yescharacteristic
105C32×C4—272no—
106C3⋊Dic3—32no—
107C3×Dic3—96no—
108C3×Dic3—912no—
109C3×Dic3—96no—
110C3×Dic3—92no—
111C3×Dic3—96no—
112C22×C9—31no—
113C22×C9—61no—
114C22×C9—63no—
115Dic9—92no—
116C33—31no—
117C33—33no—
118C33—61no—
119C33—63no—
120C33C2×C3×Dic311yescharacteristic
121C33C2×C3×Dic313yes—
1223−1+2—31no—
1233−1+2—61no—
1243−1+2—62no—
1253−1+2—61no—
126C3×C9—21no—
127C3×C9—23no—
128C3×C9C2×C32×C411yescharacteristic, complemented
129C2×C3×C4—271no—
130C2×C3×C4—273no—
131C2×Dic3—91no—
132C2×Dic3—93no—
133C2×C32—22no—
134C2×C32—26no—
135C2×C32—21no—
136C2×C32—23no—
137C2×C32—31no—
138C2×C32—32no—
139C2×C32—36no—
140C2×C32—36no—
141C2×C32—312no—
142C2×C32—33no—
143C2×C32—33no—
144C2×C32—36no—
145C2×C32—63no—
146C2×C32—63no—
147C2×C32—66no—
148C2×C32—66no—
149C2×C32—61no—
150C2×C32—63no—
151C2×C32—62no—
152C2×C32—66no—
153C2×C32—63no—
154C2×C32—66no—
155C2×C32(C3⋊Dic3)⋊C312yes—
156C2×C323−1+2⋊C416yescomplemented
157C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
158C2×C32C2×AGL(1,ℤ/9)13yes—
159C2×C32C32×Dic312yes—
160C2×C32C2×C32×D311yescharacteristic
161C2×C9—32no—
162C2×C9—31no—
163C2×C9—62no—
164C2×C9—66no—
165C2×C9—61no—
166C2×C9—63no—
167C22×C3—31no—
168C22×C3—33no—
169C22×C3—61no—
170C22×C3—63no—
171C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
172C22×C3C3×AGL(1,ℤ/9)13yes—
173C3×C4—272no—
174C3×C4—276no—
175Dic3—92no—
176Dic3—96no—
177C32—21no—
178C32—23no—
179C32—31no—
180C32—33no—
181C32—33no—
182C32—36no—
183C32—63no—
184C32—63no—
185C32—61no—
186C32—63no—
187C32—63no—
188C32C2×(C3⋊Dic3)⋊C311yescharacteristic
189C32C2×3−1+2⋊C413yescomplemented
190C32C2×C32×Dic311yescharacteristic
191C9—31no—
192C9—61no—
193C9—63no—
194C2×C4—271noSylow
195C2×C3—31no—
196C2×C3—33no—
197C2×C3—32no—
198C2×C3—36no—
199C2×C3—61no—
200C2×C3—63no—
201C2×C3—62no—
202C2×C3—66no—
203C2×C3C3×(C3⋊Dic3)⋊C312yes—
204C2×C3C3×3−1+2⋊C416yes—
205C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
206C2×C3C2×C3×AGL(1,ℤ/9)13yes—
207C22#4169⋊C311yescharacteristic
208C4—272no—
209C3—31no—
210C3—33no—
211C3—61no—
212C3—63no—
213C3C2×C3×(C3⋊Dic3)⋊C311yescharacteristic
214C3C2×C3×3−1+2⋊C413yes—
215C2#66316⋊C312yesdirect product factor
216C2C2×#4169⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22#4169⋊C3
commutator, hypocenterC3×C9C2×C32×C4
FrattiniC2×C32C2×C32×D3
FittingC22×#6891C2
socleC22×C32C32×D3
prime radicalC22×C34D3
cosocleC2×C3×C9C22×C32
LCSG ▷ C3×C9
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #66316⋊C3C2direct (N × H)
4. C2×C3⋊(3−1+2⋊C4)C3semidirect
5. C2×#66316C3semidirect
6. C2×#6891C4semidirect
12. C3⋊(3−1+2⋊C4)C2×C3semidirect
15. #66316C2×C3semidirect
16. #6891C2×C4semidirect
21. C2×C3⋊Dic9C32semidirect
27. C2×C3×3−1+2C3×C4semidirect
31. C2×C32⋊C9C3×C4semidirect
50. C3⋊Dic9C2×C32semidirect
54. C3×3−1+2C2×C3×C4semidirect
56. C32⋊C9C2×C3×C4semidirect
89. C2×C3×C9C32×C4semidirect
128. C3×C9C2×C32×C4semidirect
156. C2×C323−1+2⋊C4semidirect
189. C32C2×3−1+2⋊C4semidirect
215. C2#66316⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68912
#66316⋊C32
C2×C32×C3⋊Dic33
C2×C3⋊(3−1+2⋊C4)3
C2×#663163