Finite Group Databasebeta

← C2×C9×C3⋊S4 #13049274

Subgroups — C2×C9×C3⋊S4 #13049274

Order 1296.

330 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×C3×C9×A4C211yesmaximal, characteristic, complemented
2C9×C3⋊S4C212yesmaximal, direct product factor
3C2×C3×C3⋊S4C311yesmaximal, characteristic
4C2×C9×S4—33nomaximal
5C2×C9×#67—31nomaximal
6C2×C9×C3⋊D3—41nomaximal
7C3×C9×A4C2211yescharacteristic, complemented
8C2×C32×A4C2×C311yescharacteristic
9C3×C3⋊S4C2×C312yes—
10C23×C3×C9D311yescharacteristic, complemented
11C22×D3×C9—31no—
12C2×C3×C22⋊C9—21no—
13C2×C9×A4—23no—
14C2×C9×A4D313yescomplemented
15C9×S4—36no—
16C9×#67—32no—
17C9×#67—32no—
18C2×C9×Dic3—31no—
19C2×C32×C9—41no—
20C9×C3⋊D3—42no—
21C2×C3⋊S4C911yescharacteristic, direct product factor
22C2×C3×S4—33no—
23C2×C3×#67—31no—
24C2×D4×C9—91no—
25C2×C3×C3⋊D3—41no—
26C32×A4C22×C311yescharacteristic
27C22×C3×C9—31no—
28C22×C3×C9—31no—
29C22×C3×C9C2×D311yescharacteristic, complemented
30C2×D3×C9—32no—
31C2×D3×C9—61no—
32C2×D3×C9—61no—
33C2×D3×C9—123no—
34C3×C22⋊C9—21no—
35C9×A4—23no—
36C9×A4C2×D313yescomplemented
37C9×Dic3—32no—
38C32×C9—41noSylow
39C23×C32C3×D311yescharacteristic
40C22×C3×D3—31no—
41C2×C3×A4—21no—
42C2×C3×A4—23no—
43C2×C3×A4C2×C911yescharacteristic, complemented
44C2×C3×A4C3×D313yes—
45C3⋊S4C2×C912yesdirect product factor
46C3×S4—36no—
47C3×#67—32no—
48C3×#67—32no—
49C2×C3×Dic3—31no—
50C23×C9—21no—
51C23×C9—91no—
52C23×C9C3⋊D311yescharacteristic, complemented
53C2×C22⋊C9—23no—
54D4×C9—92no—
55D4×C9—92no—
56C2×C4×C9—91no—
57C2×C33—41no—
58C3×C3⋊D3—42no—
59C2×C3×C9—31no—
60C2×C3×C9—31no—
61C2×C3×C9—43no—
62C2×C3×C9—83no—
63C2×C3×C9—81no—
64C2×C3×C9S411yescharacteristic, complemented
65D3×C9—62no—
66D3×C9—126no—
67C2×S4—33no—
68C2×C3×D4—91no—
69C2×#67—31no—
70C22×C32—31no—
71C22×C32—31no—
72C22×C32C2×C3×D311yescharacteristic
73C2×C3⋊D3—41no—
74C2×C3×D3—32no—
75C2×C3×D3—61no—
76C2×C3×D3—61no—
77C2×C3×D3—123no—
78C3×A4—21no—
79C3×A4—23no—
80C3×A4C22×C911yescharacteristic, complemented
81C3×A4C2×C3×D313yes—
82C3×Dic3—32no—
83C22×C9—21no—
84C22×C9—31no—
85C22×C9—31no—
86C22×C9—61no—
87C22×C9—61no—
88C22×C9—92no—
89C22×C9—181no—
90C22×C9—181no—
91C22×C9C2×C3⋊D311yescharacteristic, complemented
92C22⋊C9—23no—
93C4×C9—92no—
94C33—41no—
95C3×C9—43no—
96C3×C9—83no—
97C3×C9—81no—
98C3×C9C2×S411yescharacteristic, complemented
99C23×C3—21no—
100C23×C3—91no—
101C23×C3D3×C911yescharacteristic, complemented
102C23×C3C3×C3⋊D311yescharacteristic
103C22×D3—31no—
104C2×A4—23no—
105C2×A4D3×C913yescomplemented
106S4—36no—
107C3×D4—92no—
108C3×D4—92no—
109C2×C3×C4—91no—
110#67—32no—
111#67—32no—
112C2×Dic3—31no—
113C2×C32—31no—
114C2×C32—31no—
115C2×C32—41no—
116C2×C32—43no—
117C2×C32—83no—
118C2×C32—81no—
119C2×C32C3×S411yescharacteristic
120C3⋊D3—42no—
121C3×D3—62no—
122C3×D3—126no—
123C2×C9—21no—
124C2×C9—31no—
125C2×C9—31no—
126C2×C9—61no—
127C2×C9—61no—
128C2×C9—83no—
129C2×C9—182no—
130C2×C9C3⋊S411yescharacteristic, direct product factor
131C2×D4—91noSylow
132C22×C3—21no—
133C22×C3—31no—
134C22×C3—31no—
135C22×C3—31no—
136C22×C3—31no—
137C22×C3—61no—
138C22×C3—61no—
139C22×C3—92no—
140C22×C3—181no—
141C22×C3—181no—
142C22×C3C2×D3×C911yescharacteristic, complemented
143C22×C3C2×C3×C3⋊D311yescharacteristic
144C2×D3—32no—
145C2×D3—61no—
146C2×D3—61no—
147C2×D3—123no—
148A4—23no—
149A4C2×D3×C913yescomplemented
150C3×C4—92no—
151Dic3—32no—
152C32—41no—
153C32—43no—
154C32—83no—
155C32—81no—
156C32C2×C3×S411yescharacteristic
157C9—21no—
158C9—83no—
159C9C2×C3⋊S411yescharacteristic, direct product factor
160C23—91no—
161C23C9×C3⋊D311yescharacteristic, complemented
162D4—92no—
163D4—92no—
164C2×C4—91no—
165C2×C3—21no—
166C2×C3—31no—
167C2×C3—31no—
168C2×C3—31no—
169C2×C3—31no—
170C2×C3—43no—
171C2×C3—61no—
172C2×C3—61no—
173C2×C3—83no—
174C2×C3—182no—
175C2×C3C9×S411yescharacteristic, complemented
176C2×C3C3×C3⋊S411yescharacteristic
177D3—62no—
178D3—126no—
179C22—31no—
180C22—31no—
181C22—92no—
182C22—181no—
183C22—181no—
184C22C2×C9×C3⋊D311yescharacteristic, complemented
185C4—92no—
186C3—21no—
187C3—43no—
188C3—83no—
189C3C2×C9×S411yescharacteristic, complemented
190C3C2×C3×C3⋊S411yescharacteristic
191C2—31no—
192C2—31no—
193C2—182no—
194C2C9×C3⋊S411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C9C3⋊S4
commutator, hypocenterC3×A4C22×C9
FrattiniC3C2×C3×C3⋊S4
FittingC23×C3×C9D3
socleC23×C32C3×D3
prime radicalC2×C3×C3⋊S4C3
cosocleC32×A4C22×C3
LCSG ▷ C3×A4
UCSC1 ◁ C2×C9

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×A4C2semidirect
2. C9×C3⋊S4C2direct (N × H)
7. C3×C9×A4C22semidirect
10. C23×C3×C9D3semidirect
14. C2×C9×A4D3semidirect
21. C2×C3⋊S4C9direct (N × H)
29. C22×C3×C9C2×D3semidirect
36. C9×A4C2×D3semidirect
43. C2×C3×A4C2×C9semidirect
45. C3⋊S4C2×C9direct (N × H)
52. C23×C9C3⋊D3semidirect
64. C2×C3×C9S4semidirect
80. C3×A4C22×C9semidirect
91. C22×C9C2×C3⋊D3semidirect
98. C3×C9C2×S4semidirect
101. C23×C3D3×C9semidirect
105. C2×A4D3×C9semidirect
130. C2×C9C3⋊S4direct (N × H)
142. C22×C3C2×D3×C9semidirect
149. A4C2×D3×C9semidirect
159. C9C2×C3⋊S4direct (N × H)
161. C23C9×C3⋊D3semidirect
175. C2×C3C9×S4semidirect
184. C22C2×C9×C3⋊D3semidirect
189. C3C2×C9×S4semidirect
194. C2C9×C3⋊S4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9×A42
C9×C3⋊S42
C2×C3×C3⋊S43
C2×C9×S43
C2×C9×#673
C2×C9×C3⋊D34