Finite Group Databasebeta

← C2×C3×C9⋊S4 #13049276

Subgroups — C2×C3×C9⋊S4 #13049276

Order 1296.

346 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 58 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
2C3×C9⋊S4C212yesmaximal, direct product factor
3C2×C3×C3⋊S4—31nomaximal
4C2×C9⋊S4C311yesmaximal, characteristic, direct product factor
5C2×C3×(C22⋊C9)⋊C2—32nomaximal
6C2×C3×#611—31nomaximal
7C2×C3×C3⋊D9—41nomaximal
8C3×C9×A4C2211yescharacteristic, complemented
9C2×C32×A4D311yescharacteristic
10C3×C3⋊S4—32no—
11C23×C3×C9D311yescharacteristic, complemented
12C22×C3×D9—31no—
13C2×C3×C22⋊C9D312yescomplemented
14C2×C9×A4—21no—
15C2×C9×A4—21no—
16C2×C9×A4—22no—
17C2×C9×A4C2×C311yescharacteristic, complemented
18C9⋊S4C2×C312yesdirect product factor
19C3×(C22⋊C9)⋊C2—34no—
20C3×#611—32no—
21C3×#611—32no—
22C2×C3×Dic9—31no—
23C2×C32×C9—41no—
24C3×C3⋊D9—42no—
25C2×C3⋊S4—31no—
26C2×C3×S4—93no—
27C2×C3×#67—91no—
28C2×(C22⋊C9)⋊C2—32no—
29C2×#611—31no—
30C2×C3×C3⋊D3—121no—
31C32×A4C2×D311yescharacteristic
32C22×C3×C9—31no—
33C22×C3×C9—31no—
34C22×C3×C9C2×D311yescharacteristic, complemented
35C2×C3⋊D9—41no—
36C2×C3×D9—32no—
37C2×C3×D9—61no—
38C2×C3×D9—61no—
39C2×C3×D9—122no—
40C3×C22⋊C9C2×D312yescomplemented
41C9×A4—21no—
42C9×A4—21no—
43C9×A4—22no—
44C9×A4C22×C311yescharacteristic, complemented
45C3×Dic9—32no—
46C32×C9—41noSylow
47C23×C32C3⋊D311yescharacteristic
48C22×C3×D3—91no—
49C2×C3×A4—21no—
50C2×C3×A4—23no—
51C2×C3×A4D913yescomplemented
52C2×C3×A4C3×D311yescharacteristic
53C3⋊S4—32no—
54C3×S4—96no—
55C3×#67—92no—
56C3×#67—92no—
57C2×C3×Dic3—91no—
58C23×C9—21no—
59C23×C9C3×D311yescharacteristic, complemented
60C22×D9—31no—
61C2×C22⋊C9—22no—
62C2×C22⋊C9C3×D312yescomplemented
63(C22⋊C9)⋊C2—34no—
64#611—32no—
65#611—32no—
66C2×Dic9—31no—
67C2×C33—41no—
68C3×C3⋊D3—122no—
69C2×C3×C9—31no—
70C2×C3×C9—31no—
71C2×C3×C9—41no—
72C2×C3×C9—42no—
73C2×C3×C9—82no—
74C2×C3×C9—81no—
75C2×C3×C9—81no—
76C2×C3×C9S411yescharacteristic, complemented
77C3⋊D9—42no—
78C3×D9—62no—
79C3×D9—124no—
80C2×S4—93no—
81C2×C3×D4—271no—
82C2×#67—91no—
83C22×C32—31no—
84C22×C32—31no—
85C22×C32C2×C3⋊D311yescharacteristic
86C2×C3⋊D3—121no—
87C2×C3×D3—92no—
88C2×C3×D3—181no—
89C2×C3×D3—181no—
90C2×C3×D3—363no—
91C3×A4—21no—
92C3×A4—23no—
93C3×A4C2×D913yescomplemented
94C3×A4C2×C3×D311yescharacteristic
95C3×Dic3—92no—
96C22×C9—21no—
97C22×C9—31no—
98C22×C9—31no—
99C22×C9—61no—
100C22×C9—61no—
101C22×C9C2×C3×D311yescharacteristic, complemented
102C2×D9—32no—
103C2×D9—61no—
104C2×D9—61no—
105C2×D9—122no—
106C22⋊C9—22no—
107C22⋊C9C2×C3×D312yescomplemented
108Dic9—32no—
109C33—41no—
110C3×C9—41no—
111C3×C9—42no—
112C3×C9—82no—
113C3×C9—81no—
114C3×C9—81no—
115C3×C9C2×S411yescharacteristic, complemented
116C23×C3—21no—
117C23×C3—271no—
118C23×C3C3⋊D911yescharacteristic, complemented
119C23×C3C3×C3⋊D311yescharacteristic
120C22×D3—91no—
121C2×A4—23no—
122C2×A4C3×D913yescomplemented
123S4—96no—
124C3×D4—272no—
125C3×D4—272no—
126C2×C3×C4—271no—
127#67—92no—
128#67—92no—
129C2×Dic3—91no—
130C2×C32—31no—
131C2×C32—31no—
132C2×C32—41no—
133C2×C32—43no—
134C2×C32—83no—
135C2×C32—81no—
136C2×C32C3⋊S411yescharacteristic
137C3⋊D3—122no—
138C3×D3—182no—
139C3×D3—366no—
140C2×C9—21no—
141C2×C9—31no—
142C2×C9—31no—
143C2×C9—42no—
144C2×C9—61no—
145C2×C9—61no—
146C2×C9—82no—
147C2×C9C3×S411yescharacteristic, complemented
148D9—62no—
149D9—124no—
150C2×D4—271noSylow
151C22×C3—21no—
152C22×C3—31no—
153C22×C3—31no—
154C22×C3—31no—
155C22×C3—31no—
156C22×C3—61no—
157C22×C3—61no—
158C22×C3—272no—
159C22×C3—541no—
160C22×C3—541no—
161C22×C3C2×C3⋊D911yescharacteristic, complemented
162C22×C3C2×C3×C3⋊D311yescharacteristic
163C2×D3—92no—
164C2×D3—181no—
165C2×D3—181no—
166C2×D3—363no—
167A4—23no—
168A4C2×C3×D913yescomplemented
169C3×C4—272no—
170Dic3—92no—
171C32—41no—
172C32—43no—
173C32—83no—
174C32—81no—
175C32C2×C3⋊S411yescharacteristic
176C9—21no—
177C9—42no—
178C9—82no—
179C9C2×C3×S411yescharacteristic, complemented
180C23—271no—
181C23C3×C3⋊D911yescharacteristic, complemented
182D4—272no—
183D4—272no—
184C2×C4—271no—
185C2×C3—21no—
186C2×C3—31no—
187C2×C3—31no—
188C2×C3—31no—
189C2×C3—31no—
190C2×C3—43no—
191C2×C3—61no—
192C2×C3—61no—
193C2×C3—83no—
194C2×C3—542no—
195C2×C3C9⋊S411yescharacteristic, direct product factor
196C2×C3C3×C3⋊S411yescharacteristic
197D3—182no—
198D3—366no—
199C22—31no—
200C22—31no—
201C22—272no—
202C22—541no—
203C22—541no—
204C22C2×C3×C3⋊D911yescharacteristic, complemented
205C4—272no—
206C3—21no—
207C3—43no—
208C3—83no—
209C3C2×C9⋊S411yescharacteristic, direct product factor
210C3C2×C3×C3⋊S411yescharacteristic
211C2—31no—
212C2—31no—
213C2—542no—
214C2C3×C9⋊S411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3C9⋊S4
commutator, cosocle, hypocenterC9×A4C22×C3
FrattiniC3C2×C3×C3⋊S4
FittingC23×C3×C9D3
socleC23×C32C3⋊D3
LCSG ▷ C9×A4
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×A4C2semidirect
2. C3×C9⋊S4C2direct (N × H)
4. C2×C9⋊S4C3direct (N × H)
8. C3×C9×A4C22semidirect
11. C23×C3×C9D3semidirect
13. C2×C3×C22⋊C9D3semidirect
17. C2×C9×A4C2×C3semidirect
18. C9⋊S4C2×C3direct (N × H)
34. C22×C3×C9C2×D3semidirect
40. C3×C22⋊C9C2×D3semidirect
44. C9×A4C22×C3semidirect
51. C2×C3×A4D9semidirect
59. C23×C9C3×D3semidirect
62. C2×C22⋊C9C3×D3semidirect
76. C2×C3×C9S4semidirect
93. C3×A4C2×D9semidirect
101. C22×C9C2×C3×D3semidirect
107. C22⋊C9C2×C3×D3semidirect
115. C3×C9C2×S4semidirect
118. C23×C3C3⋊D9semidirect
122. C2×A4C3×D9semidirect
147. C2×C9C3×S4semidirect
161. C22×C3C2×C3⋊D9semidirect
168. A4C2×C3×D9semidirect
179. C9C2×C3×S4semidirect
181. C23C3×C3⋊D9semidirect
195. C2×C3C9⋊S4direct (N × H)
204. C22C2×C3×C3⋊D9semidirect
209. C3C2×C9⋊S4direct (N × H)
214. C2C3×C9⋊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
C3×C9⋊S42
C2×C3×C3⋊S43
C2×C9⋊S43
C2×C3×(C22⋊C9)⋊C23
C2×C3×#6113
C2×C3×C3⋊D94