Finite Group Databasebeta

← C3×C3⋊(C9⋊S4) #14519214

Subgroups — C3×C3⋊(C9⋊S4) #14519214

Order 1944.

771 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 771 conjugacy classes of subgroups — too many to draw. Only its 122 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×C9×A4C211yesmaximal, characteristic, complemented
2C3×C3⋊(C3⋊S4)—31nomaximal
3C3⋊(C9⋊S4)C311yesmaximal, characteristic, direct product factor
4C3×C3⋊((C22⋊C9)⋊C2)—32nomaximal
5C3×C9⋊S4—39nomaximal
6C3×#6233—31nomaximal
7C3×C3⋊(C3⋊D9)—41nomaximal
8C33×A4D311yescharacteristic
9C22×C32×C9D311yescharacteristic, complemented
10C2×C3×C3⋊D9—31no—
11C32×C22⋊C9D312yescomplemented
12C3×C9×A4—21no—
13C3×C9×A4—21no—
14C3×C9×A4—22no—
15C3×C9×A4—29no—
16C3×C9×A4D319yescomplemented
17C3×C9×A4C2×C311yescharacteristic, complemented
18C3×C3⋊Dic9—31no—
19C33×C9—41noSylow
20C3⋊(C3⋊S4)—31no—
21C3×C3⋊S4—99no—
22C3×C3⋊S4—93no—
23C3×#638—91no—
24C3⋊((C22⋊C9)⋊C2)—32no—
25C9⋊S4—39no—
26C3×(C22⋊C9)⋊C2—96no—
27#6233—31no—
28C3×#611—93no—
29C3×C3⋊(C3⋊D3)—121no—
30C2×C32×C9—31no—
31C3⋊(C3⋊D9)—41no—
32C3×C3⋊D9—61no—
33C3×C3⋊D9—129no—
34C3×C3⋊D9—122no—
35C22×C33C3⋊D311yescharacteristic
36C2×C3×C3⋊D3—91no—
37C32×A4—21no—
38C32×A4—29no—
39C32×A4—23no—
40C32×A4D919yescomplemented
41C32×A4C3×D311yescharacteristic
42C32×A4C3⋊D313yes—
43C3×C3⋊Dic3—91no—
44C22×C3×C9—21no—
45C22×C3×C9—23no—
46C22×C3×C9C3×D311yescharacteristic, complemented
47C22×C3×C9C3⋊D313yescomplemented
48C2×C3⋊D9—31no—
49C2×C3×D9—93no—
50C3×C22⋊C9—22no—
51C3×C22⋊C9—26no—
52C3×C22⋊C9C3×D312yescomplemented
53C3×C22⋊C9C3⋊D316yescomplemented
54C9×A4—29no—
55C9×A4—29no—
56C9×A4—218no—
57C9×A4C3×D319yescomplemented
58C3⋊Dic9—31no—
59C3×Dic9—93no—
60C34—41no—
61C32×C9—41no—
62C32×C9—42no—
63C32×C9—49no—
64C32×C9—82no—
65C32×C9—89no—
66C32×C9—81no—
67C32×C9—81no—
68C32×C9S411yescharacteristic, complemented
69C3⋊S4—99no—
70C3⋊S4—93no—
71C3×S4—279no—
72#638—91no—
73C3×#67—273no—
74C3×#67—271no—
75(C22⋊C9)⋊C2—96no—
76#611—93no—
77C2×C33—31no—
78C3⋊(C3⋊D3)—121no—
79C3×C3⋊D3—181no—
80C3×C3⋊D3—363no—
81C3×C3⋊D3—369no—
82C2×C3×C9—31no—
83C2×C3×C9—33no—
84C2×C3×C9—63no—
85C2×C3×C9—61no—
86C3⋊D9—61no—
87C3⋊D9—129no—
88C3⋊D9—122no—
89C3×D9—183no—
90C3×D9—366no—
91C22×C32—23no—
92C22×C32—21no—
93C22×C32C3⋊D913yescomplemented
94C22×C32C3×C3⋊D311yescharacteristic
95C22×C32C3⋊(C3⋊D3)11yescharacteristic
96C2×C3⋊D3—91no—
97C2×C3×D3—271no—
98C2×C3×D3—273no—
99C3×A4—29no—
100C3×A4—23no—
101C3×A4—227no—
102C3×A4—29no—
103C3×A4C3×D919yescomplemented
104C3×A4C3⋊D919yescomplemented
105C3×A4C3×C3⋊D313yes—
106C3⋊Dic3—91no—
107C3×Dic3—271no—
108C3×Dic3—273no—
109C22×C9—23no—
110C22×C9C3×C3⋊D313yescomplemented
111C2×D9—93no—
112C22⋊C9—26no—
113C22⋊C9C3×C3⋊D316yescomplemented
114Dic9—93no—
115C33—41no—
116C33—49no—
117C33—43no—
118C33—83no—
119C33—89no—
120C33—81no—
121C33C3⋊S411yescharacteristic
122C3×C9—21no—
123C3×C9—23no—
124C3×C9—42no—
125C3×C9—49no—
126C3×C9—46no—
127C3×C9—818no—
128C3×C9—89no—
129C3×C9—86no—
130C3×C9—82no—
131C3×C9—89no—
132C3×C9C3×S411yescharacteristic, complemented
133C3×C9C3⋊S413yescomplemented
134S4—279no—
135C3×D4—811no—
136#67—273no—
137#67—271no—
138C2×C32—31no—
139C2×C32—33no—
140C2×C32—31no—
141C2×C32—61no—
142C2×C32—63no—
143C3⋊D3—181no—
144C3⋊D3—363no—
145C3⋊D3—369no—
146C3×D3—543no—
147C3×D3—541no—
148C3×D3—1089no—
149C2×C9—33no—
150C2×C9—63no—
151D9—183no—
152D9—366no—
153C22×C3—23no—
154C22×C3—21no—
155C22×C3—811no—
156C22×C3C3×C3⋊D913yescomplemented
157C22×C3C3⋊(C3⋊D9)11yescharacteristic, complemented
158C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
159C2×D3—271no—
160C2×D3—273no—
161A4—29no—
162A4C3×C3⋊D919yescomplemented
163C3×C4—811no—
164Dic3—271no—
165Dic3—273no—
166C32—21no—
167C32—23no—
168C32—43no—
169C32—49no—
170C32—49no—
171C32—827no—
172C32—89no—
173C32—83no—
174C32—89no—
175C32C9⋊S413yescomplemented
176C32C3×C3⋊S411yescharacteristic
177C32C3⋊(C3⋊S4)11yescharacteristic
178C9—23no—
179C9—46no—
180C9—86no—
181C9C3×C3⋊S413yescomplemented
182D4—811noSylow
183C2×C3—31no—
184C2×C3—33no—
185C2×C3—31no—
186C2×C3—63no—
187C2×C3—61no—
188C2×C3—1621no—
189D3—541no—
190D3—543no—
191D3—1089no—
192C22—811no—
193C22C3×C3⋊(C3⋊D9)11yescharacteristic, complemented
194C4—811no—
195C3—23no—
196C3—21no—
197C3—49no—
198C3—89no—
199C3C3×C9⋊S413yescomplemented
200C3C3⋊(C9⋊S4)11yescharacteristic, direct product factor
201C3C3×C3⋊(C3⋊S4)11yescharacteristic
202C2—31no—
203C2—1621no—
subgroupG/H
center, hypercenterC3C3⋊(C9⋊S4)
commutator, cosocle, hypocenterC3×C9×A4C2×C3
FrattiniC3C3×C3⋊(C3⋊S4)
FittingC22×C32×C9D3
socleC22×C33C3⋊D3
LCSG ▷ C3×C9×A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C9×A4C2semidirect
3. C3⋊(C9⋊S4)C3direct (N × H)
9. C22×C32×C9D3semidirect
11. C32×C22⋊C9D3semidirect
16. C3×C9×A4D3semidirect
17. C3×C9×A4C2×C3semidirect
40. C32×A4D9semidirect
46. C22×C3×C9C3×D3semidirect
47. C22×C3×C9C3⋊D3semidirect
52. C3×C22⋊C9C3×D3semidirect
53. C3×C22⋊C9C3⋊D3semidirect
57. C9×A4C3×D3semidirect
68. C32×C9S4semidirect
93. C22×C32C3⋊D9semidirect
103. C3×A4C3×D9semidirect
104. C3×A4C3⋊D9semidirect
110. C22×C9C3×C3⋊D3semidirect
113. C22⋊C9C3×C3⋊D3semidirect
132. C3×C9C3×S4semidirect
133. C3×C9C3⋊S4semidirect
156. C22×C3C3×C3⋊D9semidirect
157. C22×C3C3⋊(C3⋊D9)semidirect
162. A4C3×C3⋊D9semidirect
175. C32C9⋊S4semidirect
181. C9C3×C3⋊S4semidirect
193. C22C3×C3⋊(C3⋊D9)semidirect
199. C3C3×C9⋊S4semidirect
200. C3C3⋊(C9⋊S4)direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C9×A42
C3×C3⋊(C3⋊S4)3
C3⋊(C9⋊S4)3
C3×C3⋊((C22⋊C9)⋊C2)3
C3×C9⋊S43
C3×#62333
C3×C3⋊(C3⋊D9)4