Finite Group Databasebeta

← C22×#4184⋊C3 #14518539

Subgroups — C22×#4184⋊C3 #14518539

Order 1944.

710 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 107 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×#6910C211yesmaximal, characteristic, complemented
2C2×#4184⋊C3C216yesmaximal, direct product factor
3C22×C3×AGL(1,ℤ/9)—32nomaximal
4C22×C3×AGL(1,ℤ/9)—31nomaximal
5C22×C3×(C3⋊D3)⋊C3—31nomaximal
6C22×#4184C311yesmaximal, characteristic, complemented
7C2×#6910C2213yescomplemented
8#4184⋊C3C2214yesdirect product factor
9C22×C3×3−1+2D311yescharacteristic, complemented
10C22×C3×3−1+2D312yescomplemented
11C22×C3×H(3,𝔽3)D311yescharacteristic
12C2×C3×AGL(1,ℤ/9)—312no—
13C2×C3×AGL(1,ℤ/9)—36no—
14C2×C3×(C3⋊D3)⋊C3—36no—
15C22×#731—22no—
16C22×#731—21no—
17C22×#731—21no—
18C22×#731C2×C311yescharacteristic, complemented
19C2×#4184C2×C316yescomplemented
20#6910C2311yescharacteristic, complemented, Sylow
21C22×C3×C3⋊D3—31no—
22C22×C32×D3—91no—
23C22×AGL(1,ℤ/9)—32no—
24C22×AGL(1,ℤ/9)—32no—
25C22×AGL(1,ℤ/9)—32no—
26C22×AGL(1,ℤ/9)—31no—
27C22×AGL(1,ℤ/9)—32no—
28C22×(C3⋊D3)⋊C3—32no—
29C22×(C3⋊D3)⋊C3—31no—
30C22×C3×D9—32no—
31C22×C3×D9—31no—
32C2×C3×3−1+2C2×D313yescomplemented
33C2×C3×3−1+2C2×D316yescomplemented
34C2×C3×H(3,𝔽3)C2×D313yes—
35C3×AGL(1,ℤ/9)—38no—
36C3×AGL(1,ℤ/9)—34no—
37C3×(C3⋊D3)⋊C3—34no—
38C2×#731—26no—
39C2×#731—23no—
40C2×#731—23no—
41C2×#731C22×C313yescomplemented
42#4184C22×C314yescomplemented
43C22×C33—31no—
44C22×C33C3⋊D311yescharacteristic
45C2×C3×C3⋊D3—36no—
46C2×C32×D3—96no—
47C22×3−1+2—22no—
48C22×3−1+2—32no—
49C22×3−1+2—32no—
50C22×3−1+2—32no—
51C22×3−1+2—31no—
52C22×3−1+2C3×D312yescomplemented
53C22×H(3,𝔽3)—21no—
54C22×H(3,𝔽3)—32no—
55C22×H(3,𝔽3)C3×D311yescharacteristic
56C22×C3×C9—21no—
57C22×C3×C9—32no—
58C22×C3×C9C3×D311yescharacteristic, complemented
59C2×AGL(1,ℤ/9)—312no—
60C2×AGL(1,ℤ/9)—312no—
61C2×AGL(1,ℤ/9)—312no—
62C2×AGL(1,ℤ/9)—36no—
63C2×AGL(1,ℤ/9)—312no—
64C2×(C3⋊D3)⋊C3—312no—
65C2×(C3⋊D3)⋊C3—36no—
66C2×C3×D9—312no—
67C2×C3×D9—36no—
68C3×3−1+2C22×D311yescharacteristic, complemented
69C3×3−1+2C22×D312yescomplemented
70C3×H(3,𝔽3)C22×D311yescharacteristic
71#731—22no—
72#731—21no—
73#731—21no—
74#731C23×C311yescharacteristic, complemented
75C23×C32—271no—
76C22×C3⋊D3—31no—
77C22×C3×D3—92no—
78C22×C3×D3—91no—
79C22×C3×D3—91no—
80C22×C3×D3—271no—
81C22×D9—32no—
82C22×D9—31no—
83C2×C33—33no—
84C2×C33C2×C3⋊D313yes—
85C3×C3⋊D3—34no—
86C32×D3—94no—
87C2×3−1+2—26no—
88C2×3−1+2—36no—
89C2×3−1+2—36no—
90C2×3−1+2—36no—
91C2×3−1+2—33no—
92C2×3−1+2C2×C3×D316yescomplemented
93C2×H(3,𝔽3)—23no—
94C2×H(3,𝔽3)—36no—
95C2×H(3,𝔽3)C2×C3×D313yes—
96C2×C3×C9—23no—
97C2×C3×C9—36no—
98C2×C3×C9C2×C3×D313yescomplemented
99AGL(1,ℤ/9)—38no—
100AGL(1,ℤ/9)—38no—
101AGL(1,ℤ/9)—38no—
102AGL(1,ℤ/9)—34no—
103AGL(1,ℤ/9)—38no—
104(C3⋊D3)⋊C3—38no—
105(C3⋊D3)⋊C3—34no—
106C3×D9—38no—
107C3×D9—34no—
108C22×C32—31no—
109C22×C32—61no—
110C22×C32—91no—
111C22×C32—91no—
112C22×C32—181no—
113C22×C32—276no—
114C22×C32#27212yes—
115C22×C32#27211yescharacteristic
116C22×C32C3×C3⋊D311yescharacteristic
117C2×C3⋊D3—36no—
118C2×C3×D3—912no—
119C2×C3×D3—96no—
120C2×C3×D3—96no—
121C2×C3×D3—276no—
122C22×C9—32no—
123C22×C9—31no—
124C22×C9—61no—
125C22×C9—62no—
126C2×D9—312no—
127C2×D9—36no—
128C33—31no—
129C33C22×C3⋊D311yescharacteristic
1303−1+2—22no—
1313−1+2—32no—
1323−1+2—32no—
1333−1+2—32no—
1343−1+2—31no—
1353−1+2C22×C3×D312yescomplemented
136H(3,𝔽3)—21no—
137H(3,𝔽3)—32no—
138H(3,𝔽3)C22×C3×D311yescharacteristic
139C3×C9—21no—
140C3×C9—32no—
141C3×C9C22×C3×D311yescharacteristic, complemented
142C23×C3—271no—
143C23×C3—272no—
144C23×C3—271no—
145C22×D3—91no—
146C22×D3—271no—
147C2×C32—33no—
148C2×C32—63no—
149C2×C32—93no—
150C2×C32—93no—
151C2×C32—183no—
152C2×C32—274no—
153C2×C32C2×#27216yes—
154C2×C32C2×#27213yes—
155C2×C32C2×C3×C3⋊D313yes—
156C3⋊D3—34no—
157C3×D3—98no—
158C3×D3—94no—
159C3×D3—94no—
160C3×D3—274no—
161C2×C9—36no—
162C2×C9—33no—
163C2×C9—63no—
164C2×C9—66no—
165D9—38no—
166D9—34no—
167C22×C3—31no—
168C22×C3—32no—
169C22×C3—31no—
170C22×C3—91no—
171C22×C3—181no—
172C22×C3—276no—
173C22×C3—2712no—
174C22×C3—276no—
175C22×C3C3×#27211yescharacteristic
176C2×D3—96no—
177C2×D3—276no—
178C32—31no—
179C32—61no—
180C32—91no—
181C32—91no—
182C32—181no—
183C32C22×#27212yes—
184C32C22×#27211yescharacteristic
185C32C22×C3×C3⋊D311yescharacteristic
186C9—32no—
187C9—31no—
188C9—61no—
189C9—62no—
190C23—271noSylow
191C2×C3—33no—
192C2×C3—36no—
193C2×C3—33no—
194C2×C3—93no—
195C2×C3—183no—
196C2×C3—274no—
197C2×C3—278no—
198C2×C3—274no—
199C2×C3C2×C3×#27213yes—
200D3—94no—
201D3—274no—
202C22—276no—
203C22#4184⋊C311yescharacteristic, direct product factor
204C3—31no—
205C3—32no—
206C3—31no—
207C3—91no—
208C3—181no—
209C3C22×C3×#27211yescharacteristic
210C2—274no—
211C2C2×#4184⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22#4184⋊C3
commutator, cosocle, hypocenter#731C23×C3
FrattiniC32C22×C3×C3⋊D3
FittingC22×#6910C2
socleC22×C3C3×#272
LCSG ▷ #731
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6910C2semidirect
2. C2×#4184⋊C3C2direct (N × H)
6. C22×#4184C3semidirect
7. C2×#6910C22semidirect
8. #4184⋊C3C22direct (N × H)
9. C22×C3×3−1+2D3semidirect
10. C22×C3×3−1+2D3semidirect
18. C22×#731C2×C3semidirect
19. C2×#4184C2×C3semidirect
20. #6910C23semidirect
32. C2×C3×3−1+2C2×D3semidirect
33. C2×C3×3−1+2C2×D3semidirect
41. C2×#731C22×C3semidirect
42. #4184C22×C3semidirect
52. C22×3−1+2C3×D3semidirect
58. C22×C3×C9C3×D3semidirect
68. C3×3−1+2C22×D3semidirect
69. C3×3−1+2C22×D3semidirect
74. #731C23×C3semidirect
92. C2×3−1+2C2×C3×D3semidirect
98. C2×C3×C9C2×C3×D3semidirect
135. 3−1+2C22×C3×D3semidirect
141. C3×C9C22×C3×D3semidirect
203. C22#4184⋊C3direct (N × H)
211. C2C2×#4184⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#69102
C2×#4184⋊C32
C22×C3×AGL(1,ℤ/9)3
C22×C3×(C3⋊D3)⋊C33
C22×#41843