Finite Group Databasebeta

← C22×#92330 #14518537

Subgroups — C22×#92330 #14518537

Order 1944.

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

normal subgroups only

This group has 640 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×#6908C211yesmaximal, characteristic, complemented
2C2×#92330C216yesmaximal, direct product factor
3C22×C3⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
4C22×#4207—31nomaximal
5C22×#4179—31nomaximal
6C22×#4177—31nomaximal
7C22×#4175—31nomaximal
8C2×#6908C2213yescomplemented
9#92330C2214yesdirect product factor
10C22×#737—21no—
11C22×#737D311yescharacteristic, complemented
12C22×C32×C9C2×C311yescharacteristic, complemented
13C2×C3⋊(C3⋊D9)C2×C316yescomplemented
14C2×#4207—36no—
15C22×#733—21no—
16C22×#732D311yescharacteristic, complemented
17C22×#731—21no—
18C22×#731D311yescharacteristic, complemented
19C22×AΣL(1,𝔽27)—21no—
20C22×AΣL(1,𝔽27)D311yescharacteristic
21C2×#4179—36no—
22C2×#4177—36no—
23C2×#4175—36no—
24#6908C2311yescharacteristic, complemented, Sylow
25C22×C3⋊(C3⋊D3)—31no—
26C22×C3⋊D9—31no—
27C22×C3⋊D9—31no—
28C22×C3⋊D9—31no—
29C22×C3⋊D9—91no—
30C22×C3⋊D9—92no—
31C22×AGL(1,ℤ/9)—92no—
32C22×(C3⋊D3)⋊C3—91no—
33C22×C3×D9—91no—
34C2×#737—23no—
35C2×#737C2×D313yescomplemented
36C2×C32×C9C22×C313yescomplemented
37C3⋊(C3⋊D9)C22×C314yescomplemented
38#4207—34no—
39C2×#733—23no—
40C2×#732C2×D313yescomplemented
41C2×#731—23no—
42C2×#731C2×D313yescomplemented
43C2×AΣL(1,𝔽27)—23no—
44C2×AΣL(1,𝔽27)C2×D313yes—
45#4179—34no—
46#4177—34no—
47#4175—34no—
48C22×C33C3×D311yescharacteristic
49C2×C3⋊(C3⋊D3)—36no—
50C22×3−1+2—21no—
51C22×3−1+2—21no—
52C22×3−1+2—21no—
53C22×3−1+2—32no—
54C22×3−1+2—62no—
55C22×H(3,𝔽3)—21no—
56C22×H(3,𝔽3)C3⋊D311yescharacteristic
57C22×C3×C9—31no—
58C22×C3×C9—32no—
59C22×C3×C9—31no—
60C22×C3×C9—61no—
61C22×C3×C9C3×D311yescharacteristic
62C22×C3×C9C3×D311yescharacteristic
63C22×C3×C9C3×D311yescharacteristic
64C2×C3⋊D9—36no—
65C2×C3⋊D9—36no—
66C2×C3⋊D9—36no—
67C2×C3⋊D9—96no—
68C2×C3⋊D9—912no—
69C2×AGL(1,ℤ/9)—912no—
70C2×(C3⋊D3)⋊C3—96no—
71C2×C3×D9—96no—
72#737—21no—
73#737C22×D311yescharacteristic, complemented
74C32×C9C23×C311yescharacteristic, complemented
75#733—21no—
76#732C22×D311yescharacteristic, complemented
77#731—21no—
78#731C22×D311yescharacteristic, complemented
79AΣL(1,𝔽27)—21no—
80AΣL(1,𝔽27)C22×D311yescharacteristic
81C22×C3⋊D3—91no—
82C22×C3⋊D3—271no—
83C22×C3⋊D3—273no—
84C22×C3×D3—271no—
85C22×D9—91no—
86C22×D9—92no—
87C22×D9—271no—
88C22×D9—271no—
89C2×C33C2×C3×D313yes—
90C3⋊(C3⋊D3)—34no—
91C2×3−1+2—23no—
92C2×3−1+2—23no—
93C2×3−1+2—23no—
94C2×3−1+2—36no—
95C2×3−1+2—66no—
96C2×H(3,𝔽3)—23no—
97C2×H(3,𝔽3)C2×C3⋊D313yes—
98C2×C3×C9—33no—
99C2×C3×C9—36no—
100C2×C3×C9—33no—
101C2×C3×C9—63no—
102C2×C3×C9C2×C3×D313yes—
103C2×C3×C9C2×C3×D313yes—
104C2×C3×C9C2×C3×D313yes—
105C3⋊D9—34no—
106C3⋊D9—34no—
107C3⋊D9—34no—
108C3⋊D9—94no—
109C3⋊D9—98no—
110AGL(1,ℤ/9)—98no—
111(C3⋊D3)⋊C3—94no—
112C3×D9—94no—
113C22×C32—31no—
114C22×C32—33no—
115C22×C32—31no—
116C22×C32—61no—
117C22×C32C3×C3⋊D311yescharacteristic
118C2×C3⋊D3—96no—
119C2×C3⋊D3—276no—
120C2×C3⋊D3—2718no—
121C2×C3×D3—276no—
122C22×C9—31no—
123C22×C9—31no—
124C22×C9—61no—
125C22×C9—61no—
126C22×C9—61no—
127C22×C9(C3⋊D3)⋊C311yescharacteristic
128C22×C9(C3⋊D3)⋊C312yes—
129C2×D9—96no—
130C2×D9—912no—
131C2×D9—276no—
132C2×D9—276no—
133C33C22×C3×D311yescharacteristic
1343−1+2—21no—
1353−1+2—21no—
1363−1+2—21no—
1373−1+2—32no—
1383−1+2—62no—
139H(3,𝔽3)—21no—
140H(3,𝔽3)C22×C3⋊D311yescharacteristic
141C3×C9—31no—
142C3×C9—32no—
143C3×C9—31no—
144C3×C9—61no—
145C3×C9C22×C3×D311yescharacteristic
146C3×C9C22×C3×D311yescharacteristic
147C3×C9C22×C3×D311yescharacteristic
148C23×C3—811no—
149C22×D3—271no—
150C22×D3—811no—
151C22×D3—813no—
152C2×C32—33no—
153C2×C32—39no—
154C2×C32—33no—
155C2×C32—63no—
156C2×C32C2×C3×C3⋊D313yes—
157C3⋊D3—94no—
158C3⋊D3—274no—
159C3⋊D3—2712no—
160C3×D3—274no—
161C2×C9—33no—
162C2×C9—33no—
163C2×C9—63no—
164C2×C9—63no—
165C2×C9—63no—
166C2×C9C2×(C3⋊D3)⋊C313yes—
167C2×C9C2×(C3⋊D3)⋊C316yes—
168D9—94no—
169D9—98no—
170D9—274no—
171D9—274no—
172C22×C3—33no—
173C22×C3—31no—
174C22×C3—91no—
175C22×C3—181no—
176C22×C3—816no—
177C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
178C2×D3—276no—
179C2×D3—816no—
180C2×D3—8118no—
181C32—33no—
182C32—31no—
183C32—31no—
184C32—61no—
185C32C22×C3×C3⋊D311yescharacteristic
186C9—31no—
187C9—31no—
188C9—61no—
189C9—61no—
190C9—61no—
191C9C22×(C3⋊D3)⋊C311yescharacteristic
192C9C22×(C3⋊D3)⋊C312yes—
193C23—811noSylow
194C2×C3—39no—
195C2×C3—33no—
196C2×C3—93no—
197C2×C3—183no—
198C2×C3—814no—
199C2×C3C2×C3⋊((C3⋊D3)⋊C3)13yes—
200D3—274no—
201D3—814no—
202D3—8112no—
203C22—816no—
204C22#9233011yescharacteristic, direct product factor
205C3—33no—
206C3—31no—
207C3—91no—
208C3—181no—
209C3C22×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
210C2—814no—
211C2C2×#9233013yesdirect product factor
subgroupG/H
center, hypercenterC22#92330
commutator, cosocle, hypocenterC32×C9C23×C3
FrattiniC32C22×C3×C3⋊D3
FittingC22×#6908C2
socleC22×C3C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C32×C9
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6908C2semidirect
2. C2×#92330C2direct (N × H)
3. C22×C3⋊(C3⋊D9)C3semidirect
8. C2×#6908C22semidirect
9. #92330C22direct (N × H)
11. C22×#737D3semidirect
12. C22×C32×C9C2×C3semidirect
13. C2×C3⋊(C3⋊D9)C2×C3semidirect
16. C22×#732D3semidirect
18. C22×#731D3semidirect
24. #6908C23semidirect
35. C2×#737C2×D3semidirect
36. C2×C32×C9C22×C3semidirect
37. C3⋊(C3⋊D9)C22×C3semidirect
40. C2×#732C2×D3semidirect
42. C2×#731C2×D3semidirect
73. #737C22×D3semidirect
74. C32×C9C23×C3semidirect
76. #732C22×D3semidirect
78. #731C22×D3semidirect
204. C22#92330direct (N × H)
211. C2C2×#92330direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#69082
C2×#923302
C22×C3⋊(C3⋊D9)3
C22×#42073
C22×#41793
C22×#41773
C22×#41753