Finite Group Databasebeta

← C3×A4×C3⋊D9 #14519247

Subgroups — C3×A4×C3⋊D9 #14519247

Order 1944.

671 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 671 conjugacy classes of subgroups — too many to draw. Only its 88 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×A4×C3⋊D3—31nomaximal
3C22×C3×C3⋊D9C311yesmaximal, characteristic, complemented
4A4×C3⋊D9C313yesmaximal, direct product factor
5C3×A4×D9—33nomaximal
6C32×C3⋊D9—41nomaximal
7C33×A4D311yescharacteristic
8C22×C32×C9C2×C311yescharacteristic, complemented
9C2×C3×C3⋊D9—31no—
10C2×C3×C3⋊D9—31no—
11C32×C22⋊C9—21no—
12C3×C9×A4—23no—
13C3×C9×A4—23no—
14C3×C9×A4—29no—
15C3×C9×A4D313yescomplemented
16C3×C9×A4C2×C313yescomplemented
17C33×C9—41noSylow
18C22×C3×C3⋊D3—31no—
19A4×C3⋊D3—33no—
20C3×D3×A4—93no—
21C3×D3×A4—91no—
22C22×C3⋊D9C3211yescharacteristic, complemented
23C22×C3×D9—33no—
24A4×D9—39no—
25C32×C3⋊D3—121no—
26C2×C32×C9—31no—
27C3×C3⋊D9—31no—
28C3×C3⋊D9—43no—
29C3×C3⋊D9A411yescharacteristic, direct product factor
30C32×D9—123no—
31C22×C33C3×D311yescharacteristic
32C2×C3×C3⋊D3—91no—
33C2×C3×C3⋊D3—91no—
34C32×A4—23no—
35C32×A4—21no—
36C32×A4—29no—
37C32×A4—23no—
38C32×A4D913yescomplemented
39C32×A4C3×D313yes—
40C32×A4C3⋊D311yescharacteristic
41C22×C3×C9—21no—
42C22×C3×C9—23no—
43C22×C3×C9C3×D313yescomplemented
44C22×C3×C9C2×C3211yescharacteristic, complemented
45C2×C3⋊D9—31no—
46C2×C3⋊D9—31no—
47C2×C3×D9—93no—
48C2×C3×D9—93no—
49C3×C22⋊C9—26no—
50C3×C22⋊C9—23no—
51C3×C22⋊C9—23no—
52C9×A4—218no—
53C9×A4—29no—
54C9×A4—29no—
55C9×A4C3×D319yescomplemented
56C34—41no—
57C32×C9—43no—
58C32×C9—43no—
59C32×C9—89no—
60C32×C9—83no—
61C32×C9—81no—
62C32×C9—83no—
63C32×C9C2×A411yescharacteristic, complemented
64C22×C3⋊D3—31no—
65C22×C3×D3—93no—
66C22×C3×D3—91no—
67C2×C3×A4—271no—
68D3×A4—99no—
69D3×A4—93no—
70C22×D9—33no—
71C2×C33—31no—
72C3×C3⋊D3—31no—
73C3×C3⋊D3—91no—
74C3×C3⋊D3—123no—
75C32×D3—361no—
76C32×D3—363no—
77C2×C3×C9—31no—
78C2×C3×C9—33no—
79C2×C3×C9—63no—
80C2×C3×C9—61no—
81C3⋊D9—31no—
82C3⋊D9C3×A411yescharacteristic, direct product factor
83C3×D9—33no—
84C3×D9—93no—
85C3×D9—129no—
86C22×C32—23no—
87C22×C32—21no—
88C22×C32C3×D913yescomplemented
89C22×C32C32×D311yescharacteristic
90C22×C32C3×C3⋊D311yescharacteristic
91C2×C3⋊D3—91no—
92C2×C3⋊D3—91no—
93C2×C3×D3—271no—
94C2×C3×D3—273no—
95C2×C3×D3—271no—
96C2×C3×D3—273no—
97C3×A4—26no—
98C3×A4—218no—
99C3×A4—29no—
100C3×A4—23no—
101C3×A4—21no—
102C3×A4—23no—
103C3×A4—29no—
104C3×A4—23no—
105C3×A4C3×D919yescomplemented
106C3×A4C3⋊D911yescharacteristic, direct product factor
107C3×A4C3×C3⋊D313yes—
108C22×C9—23no—
109C22×C9C32×D313yescomplemented
110C2×D9—93no—
111C2×D9—93no—
112C22⋊C9—29no—
113C33—43no—
114C33—43no—
115C33—41no—
116C33—83no—
117C33—89no—
118C33—83no—
119C33—81no—
120C33D3×A411yescharacteristic
121C3×C9—21no—
122C3×C9—23no—
123C3×C9—49no—
124C3×C9—89no—
125C3×C9—818no—
126C3×C9—86no—
127C3×C9—83no—
128C3×C9—83no—
129C3×C9—89no—
130C3×C9D3×A413yescomplemented
131C3×C9C2×C3×A411yescharacteristic, complemented
132C23×C3—271no—
133C22×D3—93no—
134C22×D3—91no—
135C2×A4—273no—
136C2×C32—31no—
137C2×C32—33no—
138C2×C32—31no—
139C2×C32—61no—
140C2×C32—63no—
141C2×C32—1081no—
142C3⋊D3—31no—
143C3⋊D3—91no—
144C3×D3—93no—
145C3×D3—91no—
146C3×D3—273no—
147C3×D3—271no—
148C3×D3—363no—
149C3×D3—369no—
150C2×C9—33no—
151C2×C9—63no—
152D9—33no—
153D9—93no—
154C22×C3—23no—
155C22×C3—21no—
156C22×C3—811no—
157C22×C3—811no—
158C22×C3C32×D913yescomplemented
159C22×C3C3×C3⋊D911yescharacteristic, complemented
160C22×C3C32×C3⋊D311yescharacteristic
161C2×D3—271no—
162C2×D3—273no—
163C2×D3—271no—
164C2×D3—273no—
165A4—29no—
166A4—23no—
167A4C3×C3⋊D913yesdirect product factor
168C32—21no—
169C32—23no—
170C32—41no—
171C32—43no—
172C32—49no—
173C32—89no—
174C32—83no—
175C32—818no—
176C32—86no—
177C32—83no—
178C32—89no—
179C32—83no—
180C32—81no—
181C32A4×D913yescomplemented
182C32C3×D3×A411yescharacteristic
183C32A4×C3⋊D311yescharacteristic
184C9—23no—
185C9—89no—
186C9C3×D3×A413yescomplemented
187C23—271noSylow
188C2×C3—31no—
189C2×C3—33no—
190C2×C3—31no—
191C2×C3—63no—
192C2×C3—61no—
193C2×C3—271no—
194C2×C3—811no—
195C2×C3—1083no—
196D3—91no—
197D3—93no—
198D3—271no—
199D3—273no—
200C22—811no—
201C22—811no—
202C22C32×C3⋊D911yescharacteristic, complemented
203C3—23no—
204C3—21no—
205C3—43no—
206C3—83no—
207C3—89no—
208C3C3×A4×D913yescomplemented
209C3A4×C3⋊D911yescharacteristic, direct product factor
210C3C3×A4×C3⋊D311yescharacteristic
211C2—31no—
212C2—271no—
213C2—811no—
subgroupG/H
center, hypercenterC3A4×C3⋊D9
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC3C3×A4×C3⋊D3
FittingC22×C32×C9C2×C3
socleC22×C33C3×D3
LCSG ▷ C22×C3×C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C9×A4C2semidirect
3. C22×C3×C3⋊D9C3semidirect
4. A4×C3⋊D9C3direct (N × H)
8. C22×C32×C9C2×C3semidirect
15. C3×C9×A4D3semidirect
16. C3×C9×A4C2×C3semidirect
22. C22×C3⋊D9C32semidirect
29. C3×C3⋊D9A4direct (N × H)
38. C32×A4D9semidirect
43. C22×C3×C9C3×D3semidirect
44. C22×C3×C9C2×C32semidirect
55. C9×A4C3×D3semidirect
63. C32×C9C2×A4semidirect
82. C3⋊D9C3×A4direct (N × H)
88. C22×C32C3×D9semidirect
105. C3×A4C3×D9semidirect
106. C3×A4C3⋊D9direct (N × H)
109. C22×C9C32×D3semidirect
130. C3×C9D3×A4semidirect
131. C3×C9C2×C3×A4semidirect
158. C22×C3C32×D9semidirect
159. C22×C3C3×C3⋊D9semidirect
167. A4C3×C3⋊D9direct (N × H)
181. C32A4×D9semidirect
186. C9C3×D3×A4semidirect
202. C22C32×C3⋊D9semidirect
208. C3C3×A4×D9semidirect
209. C3A4×C3⋊D9direct (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×A4×C3⋊D33
C22×C3×C3⋊D93
A4×C3⋊D93
C3×A4×D93
C32×C3⋊D94