Finite Group Databasebeta

← C2×C3×A4×D9 #13049290

Subgroups — C2×C3×A4×D9 #13049290

Order 1296.

366 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 72 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×A4×D9C212yesmaximal, direct product factor
3C2×C3×D3×A4—31nomaximal
4C23×C3×D9C311yesmaximal, characteristic, complemented
5C2×A4×D9C313yesmaximal, direct product factor
6C2×C32×D9—41nomaximal
7C3×C9×A4C2211yescharacteristic, complemented
8C2×C32×A4D311yescharacteristic
9C3×D3×A4—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×A4C2×C313yescomplemented
18A4×D9C2×C316yesdirect product factor
19C2×C32×C9—41no—
20C32×D9—42no—
21C23×C3×D3—31no—
22C22×C3×A4—91no—
23C2×D3×A4—33no—
24C23×D9C3211yescharacteristic, complemented
25C2×C32×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×D9—43no—
36C2×C3×D9A411yescharacteristic, direct product factor
37C3×C22⋊C9—21no—
38C9×A4—23no—
39C9×A4C22×C313yescomplemented
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—21no—
47C2×C3×A4—23no—
48C2×C3×A4—92no—
49C2×C3×A4D911yescharacteristic, direct product factor
50C2×C3×A4C3×D313yes—
51D3×A4—36no—
52C23×C9—21no—
53C23×C9C2×C3211yescharacteristic, complemented
54C22×D9—31no—
55C22×D9—31no—
56C22×D9—32no—
57C22×D9C2×C3212yescomplemented
58C2×C22⋊C9—23no—
59C2×C33—41no—
60C32×D3—122no—
61C2×C3×C9—31no—
62C2×C3×C9—31no—
63C2×C3×C9—43no—
64C2×C3×C9—83no—
65C2×C3×C9—81no—
66C2×C3×C9C2×A411yescharacteristic, complemented
67C3×D9—32no—
68C3×D9—46no—
69C3×D9C2×A412yesdirect product factor
70C24×C3—91no—
71C23×D3—31no—
72C22×A4—93no—
73C22×C32—31no—
74C22×C32—31no—
75C22×C32—361no—
76C22×C32C2×C3×D311yescharacteristic
77C2×C3×D3—31no—
78C2×C3×D3—92no—
79C2×C3×D3—92no—
80C2×C3×D3—92no—
81C2×C3×D3—91no—
82C2×C3×D3—92no—
83C2×C3×D3—123no—
84C3×A4—21no—
85C3×A4—23no—
86C3×A4C2×D911yescharacteristic, direct product factor
87C3×A4C2×C3×D313yes—
88C22×C9—21no—
89C22×C9—31no—
90C22×C9—31no—
91C22×C9—61no—
92C22×C9—61no—
93C22×C9C22×C3211yescharacteristic, complemented
94C2×D9—32no—
95C2×D9—31no—
96C2×D9—32no—
97C2×D9—32no—
98C2×D9—32no—
99C2×D9C3×A411yescharacteristic, direct product factor
100C22⋊C9—23no—
101C33—41no—
102C3×C9—43no—
103C3×C9—83no—
104C3×C9—81no—
105C3×C9C22×A411yescharacteristic, complemented
106C23×C3—21no—
107C23×C3—92no—
108C23×C3—271no—
109C23×C3—272no—
110C23×C3—271no—
111C23×C3C3×D911yescharacteristic, complemented
112C23×C3C32×D311yescharacteristic
113C22×D3—32no—
114C22×D3—91no—
115C22×D3—92no—
116C22×D3—91no—
117C2×A4—23no—
118C2×A4—96no—
119C2×A4C3×D913yesdirect product factor
120C2×C32—31no—
121C2×C32—31no—
122C2×C32—41no—
123C2×C32—43no—
124C2×C32—83no—
125C2×C32—81no—
126C2×C32—362no—
127C2×C32D3×A411yescharacteristic
128C3×D3—32no—
129C3×D3—92no—
130C3×D3—126no—
131C2×C9—21no—
132C2×C9—31no—
133C2×C9—31no—
134C2×C9—61no—
135C2×C9—61no—
136C2×C9—83no—
137C2×C9C2×C3×A411yescharacteristic, complemented
138D9—32no—
139D9C2×C3×A412yesdirect product factor
140C24—91noSylow
141C22×C3—21no—
142C22×C3—31no—
143C22×C3—31no—
144C22×C3—31no—
145C22×C3—31no—
146C22×C3—61no—
147C22×C3—61no—
148C22×C3—91no—
149C22×C3—272no—
150C22×C3—272no—
151C22×C3—272no—
152C22×C3—272no—
153C22×C3—271no—
154C22×C3—363no—
155C22×C3C2×C3×D911yescharacteristic, complemented
156C22×C3C2×C32×D311yescharacteristic
157C2×D3—31no—
158C2×D3—92no—
159C2×D3—92no—
160C2×D3—92no—
161C2×D3—91no—
162C2×D3—92no—
163A4—23no—
164A4C2×C3×D913yesdirect product factor
165C32—41no—
166C32—43no—
167C32—83no—
168C32—81no—
169C32C2×D3×A411yescharacteristic
170C9—21no—
171C9—83no—
172C9C22×C3×A411yescharacteristic, complemented
173C23—92no—
174C23—271no—
175C23—272no—
176C23—271no—
177C23C32×D911yescharacteristic, complemented
178C2×C3—21no—
179C2×C3—31no—
180C2×C3—31no—
181C2×C3—31no—
182C2×C3—31no—
183C2×C3—43no—
184C2×C3—61no—
185C2×C3—61no—
186C2×C3—83no—
187C2×C3—92no—
188C2×C3—272no—
189C2×C3—366no—
190C2×C3A4×D911yescharacteristic, direct product factor
191C2×C3C3×D3×A411yescharacteristic
192D3—32no—
193D3—92no—
194C22—31no—
195C22—31no—
196C22—91no—
197C22—272no—
198C22—272no—
199C22—272no—
200C22—272no—
201C22—271no—
202C22C2×C32×D911yescharacteristic, complemented
203C3—21no—
204C3—43no—
205C3—83no—
206C3C2×A4×D911yescharacteristic, direct product factor
207C3C2×C3×D3×A411yescharacteristic
208C2—31no—
209C2—31no—
210C2—92no—
211C2—272no—
212C2C3×A4×D911yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3A4×D9
commutator, cosocle, hypocenterC22×C9C22×C32
FrattiniC3C2×C3×D3×A4
FittingC23×C3×C9C2×C3
socleC23×C32C3×D3
LCSG ▷ C22×C9
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×A4C2semidirect
2. C3×A4×D9C2direct (N × H)
4. C23×C3×D9C3semidirect
5. C2×A4×D9C3direct (N × H)
7. C3×C9×A4C22semidirect
10. C23×C3×C9C2×C3semidirect
14. C22×C3×D9C2×C3semidirect
17. C2×C9×A4C2×C3semidirect
18. A4×D9C2×C3direct (N × H)
24. C23×D9C32semidirect
29. C22×C3×C9C22×C3semidirect
36. C2×C3×D9A4direct (N × H)
39. C9×A4C22×C3semidirect
49. C2×C3×A4D9direct (N × H)
53. C23×C9C2×C32semidirect
57. C22×D9C2×C32semidirect
66. C2×C3×C9C2×A4semidirect
69. C3×D9C2×A4direct (N × H)
86. C3×A4C2×D9direct (N × H)
93. C22×C9C22×C32semidirect
99. C2×D9C3×A4direct (N × H)
105. C3×C9C22×A4semidirect
111. C23×C3C3×D9semidirect
119. C2×A4C3×D9direct (N × H)
137. C2×C9C2×C3×A4semidirect
139. D9C2×C3×A4direct (N × H)
155. C22×C3C2×C3×D9semidirect
164. A4C2×C3×D9direct (N × H)
172. C9C22×C3×A4semidirect
177. C23C32×D9semidirect
190. C2×C3A4×D9direct (N × H)
202. C22C2×C32×D9semidirect
206. C3C2×A4×D9direct (N × H)
212. C2C3×A4×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
C3×A4×D92
C2×C3×D3×A43
C23×C3×D93
C2×A4×D93
C2×C32×D94