Finite Group Databasebeta

← C22×C3⋊#4207 #14519377

Subgroups — C22×C3⋊#4207 #14519377

Order 1944.

1545 conjugacy classes of subgroups; only the 322 normal subgroups are shown.

normal subgroups only

This group has 1545 conjugacy classes of subgroups — too many to draw. Only its 322 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×C3×#737C211yesmaximal, characteristic, complemented
2C2×C3⋊#4207C216yesmaximal, direct product factor
3C22×C3⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
4C22×#4207—39nomaximal
5C22×C3⋊AGL(1,ℤ/9)—32nomaximal
6C22×C3⋊((C3⋊D3)⋊C3)—31nomaximal
7C22×C3×C3⋊D9—31nomaximal
8C2×C3×#737C2213yescomplemented
9C3⋊#4207C2214yesdirect product factor
10C22×#737—29no—
11C22×#737D319yescomplemented
12C22×C3×3−1+2—21no—
13C22×C3×3−1+2—22no—
14C22×C3×3−1+2D312yescomplemented
15C22×C3×H(3,𝔽3)D311yescharacteristic
16C22×C32×C9—21no—
17C22×C32×C9D311yescharacteristic, complemented
18C22×C32×C9C2×C311yescharacteristic, complemented
19C2×C3⋊(C3⋊D9)C2×C316yescomplemented
20C2×#4207—354no—
21C2×C3⋊AGL(1,ℤ/9)—312no—
22C2×C3⋊((C3⋊D3)⋊C3)—36no—
23C2×C3×C3⋊D9—36no—
24C3×#737C2311yescharacteristic, complemented, Sylow
25C22×C3⋊(C3⋊D3)—31no—
26C22×C3×C3⋊D3—91no—
27C22×C3⋊D9—31no—
28C22×C3⋊D9—32no—
29C22×C3⋊D9—39no—
30C22×AGL(1,ℤ/9)—96no—
31C22×(C3⋊D3)⋊C3—93no—
32C22×C3×D9—93no—
33C2×#737—227no—
34C2×#737C2×D3127yescomplemented
35C2×C3×3−1+2—23no—
36C2×C3×3−1+2—26no—
37C2×C3×3−1+2C2×D316yescomplemented
38C2×C3×H(3,𝔽3)C2×D313yes—
39C2×C32×C9—23no—
40C2×C32×C9C2×D313yescomplemented
41C2×C32×C9C22×C313yescomplemented
42C3⋊(C3⋊D9)C22×C314yescomplemented
43#4207—336no—
44C3⋊AGL(1,ℤ/9)—38no—
45C3⋊((C3⋊D3)⋊C3)—34no—
46C3×C3⋊D9—34no—
47C22×C33—21no—
48C22×C33C3×D311yescharacteristic
49C22×C33C3⋊D311yescharacteristic
50C2×C3⋊(C3⋊D3)—36no—
51C2×C3×C3⋊D3—96no—
52C22×3−1+2—29no—
53C22×3−1+2—218no—
54C22×3−1+2—26no—
55C22×3−1+2C3⋊D316yescomplemented
56C22×H(3,𝔽3)—23no—
57C22×H(3,𝔽3)C3⋊D313yes—
58C22×C3×C9—22no—
59C22×C3×C9—21no—
60C22×C3×C9—29no—
61C22×C3×C9—23no—
62C22×C3×C9C3×D311yescharacteristic
63C22×C3×C9C3×D312yes—
64C22×C3×C9C3×D319yescomplemented
65C22×C3×C9C3⋊D313yescomplemented
66C2×C3⋊D9—36no—
67C2×C3⋊D9—312no—
68C2×C3⋊D9—354no—
69C2×AGL(1,ℤ/9)—936no—
70C2×(C3⋊D3)⋊C3—918no—
71C2×C3×D9—918no—
72#737—29no—
73#737C22×D319yescomplemented
74C3×3−1+2—21no—
75C3×3−1+2—22no—
76C3×3−1+2C22×D312yescomplemented
77C3×H(3,𝔽3)C22×D311yescharacteristic
78C32×C9—21no—
79C32×C9C22×D311yescharacteristic, complemented
80C32×C9C23×C311yescharacteristic, complemented
81C22×C3⋊D3—91no—
82C22×C3⋊D3—93no—
83C22×C3⋊D3—273no—
84C22×C3×D3—273no—
85C22×C3×D3—271no—
86C22×D9—93no—
87C22×D9—96no—
88C2×C33—23no—
89C2×C33C2×C3×D313yes—
90C2×C33C2×C3⋊D313yes—
91C3⋊(C3⋊D3)—34no—
92C3×C3⋊D3—94no—
93C2×3−1+2—227no—
94C2×3−1+2—254no—
95C2×3−1+2—218no—
96C2×3−1+2C2×C3⋊D3118yescomplemented
97C2×H(3,𝔽3)—29no—
98C2×H(3,𝔽3)C2×C3⋊D319yes—
99C2×C3×C9—26no—
100C2×C3×C9—23no—
101C2×C3×C9—227no—
102C2×C3×C9—29no—
103C2×C3×C9C2×C3×D313yes—
104C2×C3×C9C2×C3×D316yes—
105C2×C3×C9C2×C3×D3127yescomplemented
106C2×C3×C9C2×C3⋊D319yescomplemented
107C3⋊D9—34no—
108C3⋊D9—38no—
109C3⋊D9—336no—
110AGL(1,ℤ/9)—924no—
111(C3⋊D3)⋊C3—912no—
112C3×D9—912no—
113C22×C32—21no—
114C22×C32—23no—
115C22×C32—33no—
116C22×C32—33no—
117C22×C32—63no—
118C22×C32C3×C3⋊D313yes—
119C22×C32C3×C3⋊D311yescharacteristic
120C22×C32C3⋊(C3⋊D3)11yescharacteristic
121C2×C3⋊D3—96no—
122C2×C3⋊D3—918no—
123C2×C3⋊D3—2718no—
124C2×C3×D3—2718no—
125C2×C3×D3—276no—
126C22×C9—26no—
127C22×C9—23no—
128C22×C9C3×C3⋊D313yes—
129C22×C9C3×C3⋊D316yes—
130C2×D9—918no—
131C2×D9—936no—
132C33—21no—
133C33C22×C3×D311yescharacteristic
134C33C22×C3⋊D311yescharacteristic
1353−1+2—29no—
1363−1+2—218no—
1373−1+2—26no—
1383−1+2C22×C3⋊D316yescomplemented
139H(3,𝔽3)—23no—
140H(3,𝔽3)C22×C3⋊D313yes—
141C3×C9—22no—
142C3×C9—21no—
143C3×C9—29no—
144C3×C9—23no—
145C3×C9C22×C3×D311yescharacteristic
146C3×C9C22×C3×D312yes—
147C3×C9C22×C3×D319yescomplemented
148C3×C9C22×C3⋊D313yescomplemented
149C23×C3—811no—
150C22×D3—273no—
151C22×D3—271no—
152C22×D3—813no—
153C2×C32—23no—
154C2×C32—29no—
155C2×C32—39no—
156C2×C32—39no—
157C2×C32—69no—
158C2×C32C2×C3×C3⋊D319yes—
159C2×C32C2×C3×C3⋊D313yes—
160C2×C32C2×C3⋊(C3⋊D3)13yes—
161C3⋊D3—94no—
162C3⋊D3—912no—
163C3⋊D3—2712no—
164C3×D3—2712no—
165C3×D3—274no—
166C2×C9—218no—
167C2×C9—29no—
168C2×C9C2×C3×C3⋊D319yes—
169C2×C9C2×C3×C3⋊D3118yes—
170D9—912no—
171D9—924no—
172C22×C3—33no—
173C22×C3—31no—
174C22×C3—61no—
175C22×C3—63no—
176C22×C3—816no—
177C22×C3#420713yescomplemented
178C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
179C2×D3—2718no—
180C2×D3—276no—
181C2×D3—8118no—
182C32—21no—
183C32—23no—
184C32—33no—
185C32—33no—
186C32—63no—
187C32C22×C3×C3⋊D313yes—
188C32C22×C3×C3⋊D311yescharacteristic
189C32C22×C3⋊(C3⋊D3)11yescharacteristic
190C9—26no—
191C9—23no—
192C9C22×C3×C3⋊D313yes—
193C9C22×C3×C3⋊D316yes—
194C23—811noSylow
195C2×C3—39no—
196C2×C3—33no—
197C2×C3—63no—
198C2×C3—69no—
199C2×C3—814no—
200C2×C3C2×#420719yescomplemented
201C2×C3C2×C3×C3⋊(C3⋊D3)13yes—
202D3—274no—
203D3—2712no—
204D3—8112no—
205C22—816no—
206C22C3⋊#420711yescharacteristic, direct product factor
207C3—33no—
208C3—31no—
209C3—61no—
210C3—63no—
211C3C22×#420713yescomplemented
212C3C22×C3×C3⋊(C3⋊D3)11yescharacteristic
213C2—814no—
214C2C2×C3⋊#420713yesdirect product factor
subgroupG/H
center, hypercenterC22C3⋊#4207
commutator, cosocle, hypocenterC32×C9C23×C3
FrattiniC3C22×C3×C3⋊(C3⋊D3)
FittingC22×C3×#737C2
socleC22×C32C3×C3⋊D3
LCSG ▷ C32×C9
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×#737C2semidirect
2. C2×C3⋊#4207C2direct (N × H)
3. C22×C3⋊(C3⋊D9)C3semidirect
8. C2×C3×#737C22semidirect
9. C3⋊#4207C22direct (N × H)
11. C22×#737D3semidirect
14. C22×C3×3−1+2D3semidirect
17. C22×C32×C9D3semidirect
18. C22×C32×C9C2×C3semidirect
19. C2×C3⋊(C3⋊D9)C2×C3semidirect
24. C3×#737C23semidirect
34. C2×#737C2×D3semidirect
37. C2×C3×3−1+2C2×D3semidirect
40. C2×C32×C9C2×D3semidirect
41. C2×C32×C9C22×C3semidirect
42. C3⋊(C3⋊D9)C22×C3semidirect
55. C22×3−1+2C3⋊D3semidirect
64. C22×C3×C9C3×D3semidirect
65. C22×C3×C9C3⋊D3semidirect
73. #737C22×D3semidirect
76. C3×3−1+2C22×D3semidirect
79. C32×C9C22×D3semidirect
80. C32×C9C23×C3semidirect
96. C2×3−1+2C2×C3⋊D3semidirect
105. C2×C3×C9C2×C3×D3semidirect
106. C2×C3×C9C2×C3⋊D3semidirect
138. 3−1+2C22×C3⋊D3semidirect
147. C3×C9C22×C3×D3semidirect
148. C3×C9C22×C3⋊D3semidirect
177. C22×C3#4207semidirect
200. C2×C3C2×#4207semidirect
206. C22C3⋊#4207direct (N × H)
211. C3C22×#4207semidirect
214. C2C2×C3⋊#4207direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7372
C2×C3⋊#42072
C22×C3⋊(C3⋊D9)3
C22×#42073
C22×C3⋊AGL(1,ℤ/9)3
C22×C3⋊((C3⋊D3)⋊C3)3
C22×C3×C3⋊D93