Finite Group Databasebeta

← C2×A4×C3⋊D9 #13049300

Subgroups — C2×A4×C3⋊D9 #13049300

Order 1296.

450 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 69 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
2A4×C3⋊D9C212yesmaximal, direct product factor
3C2×A4×C3⋊D3—31nomaximal
4C23×C3⋊D9C311yesmaximal, characteristic, complemented
5C2×A4×D9—33nomaximal
6C2×C3×C3⋊D9—41nomaximal
7C3×C9×A4C2211yescharacteristic, complemented
8C2×C32×A4D311yescharacteristic
9A4×C3⋊D3—32no—
10C23×C3×C9C2×C311yescharacteristic, complemented
11C22×C3⋊D9—31no—
12C22×C3⋊D9—31no—
13C22×C3⋊D9—32no—
14C22×C3⋊D9C2×C312yescomplemented
15C2×C3×C22⋊C9—21no—
16C2×C9×A4—23no—
17C2×C9×A4D313yescomplemented
18A4×D9—36no—
19C2×C32×C9—41no—
20C3×C3⋊D9—42no—
21C23×C3⋊D3—31no—
22C2×D3×A4—93no—
23C2×D3×A4—91no—
24C23×D9—33no—
25C2×C3×C3⋊D3—121no—
26C32×A4C2×D311yescharacteristic
27C22×C3×C9—31no—
28C22×C3×C9—31no—
29C22×C3×C9C22×C311yescharacteristic, complemented
30C2×C3⋊D9—32no—
31C2×C3⋊D9—31no—
32C2×C3⋊D9—32no—
33C2×C3⋊D9—32no—
34C2×C3⋊D9—32no—
35C2×C3⋊D9A411yescharacteristic, direct product factor
36C2×C3×D9—123no—
37C3×C22⋊C9—21no—
38C9×A4—23no—
39C9×A4C2×D313yescomplemented
40C32×C9—41noSylow
41C23×C32C3×D311yescharacteristic
42C22×C3⋊D3—32no—
43C22×C3⋊D3—91no—
44C22×C3⋊D3—92no—
45C22×C3⋊D3—91no—
46C2×C3×A4—23no—
47C2×C3×A4—21no—
48C2×C3×A4D913yescomplemented
49C2×C3×A4C3⋊D311yescharacteristic
50D3×A4—96no—
51D3×A4—92no—
52C23×C9C3×D313yescomplemented
53C22×D9—36no—
54C22×D9—93no—
55C22×D9—96no—
56C22×D9—93no—
57C2×C22⋊C9—23no—
58C2×C33—41no—
59C3×C3⋊D3—122no—
60C2×C3×C9—31no—
61C2×C3×C9—31no—
62C2×C3×C9—43no—
63C2×C3×C9—81no—
64C2×C3×C9—83no—
65C2×C3×C9C2×A411yescharacteristic, complemented
66C3⋊D9—32no—
67C3⋊D9C2×A412yesdirect product factor
68C3×D9—126no—
69C23×D3—93no—
70C23×D3—91no—
71C22×A4—271no—
72C22×C32—31no—
73C22×C32—31no—
74C22×C32C2×C3×D311yescharacteristic
75C2×C3⋊D3—31no—
76C2×C3⋊D3—92no—
77C2×C3⋊D3—92no—
78C2×C3⋊D3—92no—
79C2×C3⋊D3—91no—
80C2×C3⋊D3—92no—
81C2×C3×D3—361no—
82C2×C3×D3—363no—
83C3×A4—23no—
84C3×A4—21no—
85C3×A4C2×D913yescomplemented
86C3×A4C2×C3⋊D311yescharacteristic
87C22×C9—33no—
88C22×C9—33no—
89C22×C9C2×C3×D313yescomplemented
90C2×D9—33no—
91C2×D9—96no—
92C2×D9—96no—
93C2×D9—96no—
94C2×D9—93no—
95C2×D9—96no—
96C22⋊C9—23no—
97C33—41no—
98C3×C9—43no—
99C3×C9—81no—
100C3×C9—83no—
101C3×C9C22×A411yescharacteristic, complemented
102C23×C3C3×D913yescomplemented
103C23×C3C3×C3⋊D311yescharacteristic
104C22×D3—96no—
105C22×D3—92no—
106C22×D3—271no—
107C22×D3—273no—
108C22×D3—272no—
109C22×D3—271no—
110C22×D3—276no—
111C22×D3—273no—
112C2×A4—23no—
113C2×A4—21no—
114C2×A4—272no—
115C2×A4C3⋊D911yescharacteristic, direct product factor
116C2×C32—31no—
117C2×C32—31no—
118C2×C32—43no—
119C2×C32—41no—
120C2×C32—83no—
121C2×C32—81no—
122C2×C32D3×A411yescharacteristic
123C3⋊D3—32no—
124C3⋊D3—92no—
125C3×D3—362no—
126C3×D3—366no—
127C2×C9—33no—
128C2×C9—33no—
129C2×C9—83no—
130C2×C9D3×A413yescomplemented
131D9—36no—
132D9—96no—
133C24—271noSylow
134C22×C3—33no—
135C22×C3—31no—
136C22×C3—33no—
137C22×C3—31no—
138C22×C3—1081no—
139C22×C3C2×C3×D913yescomplemented
140C22×C3C2×C3×C3⋊D311yescharacteristic
141C2×D3—93no—
142C2×D3—91no—
143C2×D3—272no—
144C2×D3—276no—
145C2×D3—272no—
146C2×D3—276no—
147C2×D3—272no—
148C2×D3—276no—
149C2×D3—273no—
150C2×D3—271no—
151C2×D3—272no—
152C2×D3—276no—
153A4—23no—
154A4—21no—
155A4C2×C3⋊D911yescharacteristic, direct product factor
156C32—41no—
157C32—43no—
158C32—81no—
159C32—83no—
160C32C2×D3×A411yescharacteristic
161C9—83no—
162C9C2×D3×A413yescomplemented
163C23—272no—
164C23—811no—
165C23—812no—
166C23—811no—
167C23C3×C3⋊D911yescharacteristic, complemented
168C2×C3—31no—
169C2×C3—31no—
170C2×C3—33no—
171C2×C3—33no—
172C2×C3—41no—
173C2×C3—83no—
174C2×C3—81no—
175C2×C3—1082no—
176C2×C3A4×D913yescomplemented
177C2×C3A4×C3⋊D311yescharacteristic
178D3—92no—
179D3—96no—
180D3—272no—
181D3—276no—
182C22—31no—
183C22—31no—
184C22—271no—
185C22—812no—
186C22—812no—
187C22—812no—
188C22—812no—
189C22—811no—
190C22C2×C3×C3⋊D911yescharacteristic, complemented
191C3—41no—
192C3—81no—
193C3—83no—
194C3C2×A4×D913yescomplemented
195C3C2×A4×C3⋊D311yescharacteristic
196C2—31no—
197C2—31no—
198C2—272no—
199C2—812no—
200C2A4×C3⋊D911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2A4×C3⋊D9
commutator, cosocle, hypocenterC22×C3×C9C22×C3
FrattiniC3C2×A4×C3⋊D3
FittingC23×C3×C9C2×C3
socleC23×C32C3×D3
LCSG ▷ C22×C3×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×A4C2semidirect
2. A4×C3⋊D9C2direct (N × H)
4. C23×C3⋊D9C3semidirect
7. C3×C9×A4C22semidirect
10. C23×C3×C9C2×C3semidirect
14. C22×C3⋊D9C2×C3semidirect
17. C2×C9×A4D3semidirect
29. C22×C3×C9C22×C3semidirect
35. C2×C3⋊D9A4direct (N × H)
39. C9×A4C2×D3semidirect
48. C2×C3×A4D9semidirect
52. C23×C9C3×D3semidirect
65. C2×C3×C9C2×A4semidirect
67. C3⋊D9C2×A4direct (N × H)
85. C3×A4C2×D9semidirect
89. C22×C9C2×C3×D3semidirect
101. C3×C9C22×A4semidirect
102. C23×C3C3×D9semidirect
115. C2×A4C3⋊D9direct (N × H)
130. C2×C9D3×A4semidirect
139. C22×C3C2×C3×D9semidirect
155. A4C2×C3⋊D9direct (N × H)
162. C9C2×D3×A4semidirect
167. C23C3×C3⋊D9semidirect
176. C2×C3A4×D9semidirect
190. C22C2×C3×C3⋊D9semidirect
194. C3C2×A4×D9semidirect
200. C2A4×C3⋊D9direct (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
A4×C3⋊D92
C2×A4×C3⋊D33
C23×C3⋊D93
C2×A4×D93
C2×C3×C3⋊D94