Finite Group Databasebeta

← C4×#66431 #13048743

Subgroups — C4×#66431 #13048743

Order 1296.

424 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 80 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×#66431C211yesmaximal, characteristic
2C4×C9×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×C4×C3⋊D9C212yesmaximal, complemented
4#10619898C211yesmaximal, characteristic, complemented
5#10619896C212yesmaximal, complemented
6C4×#1113—31nomaximal
7C4×D3×D9—32nomaximal
8C2×C9×C3⋊D3C2211yescharacteristic
9C2×C3×C3⋊D9C2212yes—
10#66431C414yesdirect product factor
11C32×C4×C9C2211yescharacteristic, complemented
12C9×C3⋊Dic3C2211yescharacteristic, complemented
13C3×C3⋊Dic9C2212yescomplemented
14C2×#1113—31no—
15C3×C4×C3⋊D3—32no—
16C3×C4×C3⋊D3D311yescharacteristic
17#6294—31no—
18#6294—32no—
19C2×D3×D9—32no—
20C4×C3⋊D9D312yescomplemented
21C4×D3×C9—32no—
22C4×D3×C9—61no—
23C3×C4×D9—32no—
24C3×C4×D9—62no—
25D3×Dic9—32no—
26(C3⋊D9)⋊C4—32no—
27Dic3×D9—32no—
28C2×C32×C9C2311yescharacteristic
29C9×C3⋊D3C2×C412yescomplemented
30C3×C3⋊D9C2×C414yescomplemented
31C4×D32—92no—
32C4×D32—91no—
33C2×C4×D9—91no—
34C2×C3×C3⋊D3—32no—
35C2×C3×C3⋊D3C2×D311yescharacteristic
36#1113—34no—
37C33×C4C2×D311yescharacteristic
38C3×C3⋊Dic3—32no—
39C3×C3⋊Dic3C2×D311yescharacteristic
40C2×C3⋊D9C2×D312yes—
41C2×D3×C9—32no—
42C2×D3×C9—61no—
43C2×C3×D9—32no—
44C2×C3×D9—62no—
45D3×D9—38no—
46C3×C4×C9—22no—
47C3×C4×C9—21no—
48C3×C4×C9—41no—
49C3×C4×C9C2×D312yescomplemented
50C3⋊Dic9C2×D312yescomplemented
51C9×Dic3—32no—
52C9×Dic3—61no—
53C3×Dic9—32no—
54C3×Dic9—62no—
55C32×C9C22×C411yescharacteristic, complemented, Sylow
56C2×D32—92no—
57C2×D32—91no—
58C4×C3⋊D3—32no—
59C4×C3⋊D3D911yescharacteristic, complemented
60C3×C4×D3—32no—
61C3×C4×D3—61no—
62C3×C4×D3—92no—
63C3×C4×D3—92no—
64C3×C4×D3—182no—
65#624—92no—
66#624—91no—
67D3×Dic3—92no—
68D3×Dic3—92no—
69D3×Dic3—92no—
70C22×D9—91no—
71C2×C4×C9—91no—
72C2×Dic9—91no—
73C4×D9—32no—
74C4×D9—62no—
75C4×D9—92no—
76C2×C33C22×D311yescharacteristic
77C3×C3⋊D3—34no—
78C3×C3⋊D3C4×D312yes—
79C2×C3×C9—22no—
80C2×C3×C9—21no—
81C2×C3×C9—41no—
82C2×C3×C9C22×D312yes—
83C3⋊D9C4×D314yescomplemented
84D3×C9—34no—
85D3×C9—62no—
86C3×D9—34no—
87C3×D9—64no—
88C2×C4×D3—272no—
89C2×C4×D3—271no—
90C2×C3⋊D3—32no—
91C2×C3⋊D3C2×D911yescharacteristic
92C2×C3×D3—32no—
93C2×C3×D3—61no—
94C2×C3×D3—92no—
95C2×C3×D3—92no—
96C2×C3×D3—182no—
97D32—98no—
98D32—94no—
99C32×C4—22no—
100C32×C4—21no—
101C32×C4—41no—
102C32×C4C2×D911yescharacteristic, complemented
103C32×C4D3212yes—
104C3⋊Dic3—32no—
105C3⋊Dic3C2×D911yescharacteristic, complemented
106C3×Dic3—32no—
107C3×Dic3—61no—
108C3×Dic3—92no—
109C3×Dic3—92no—
110C3×Dic3—182no—
111C22×C9—91no—
112C2×D9—32no—
113C2×D9—62no—
114C2×D9—94no—
115C4×C9—22no—
116C4×C9—41no—
117C4×C9—91no—
118C4×C9D3211yescharacteristic, complemented
119Dic9—32no—
120Dic9—62no—
121C33C2×C4×D311yescharacteristic
122C3×C9—22no—
123C3×C9—21no—
124C3×C9—41no—
125C3×C9C2×C4×D312yescomplemented
126C22×D3—272no—
127C22×D3—271no—
128C2×C3×C4—91no—
129C2×C3×C4—272no—
130C2×Dic3—272no—
131C2×Dic3—271no—
132C4×D3—32no—
133C4×D3—61no—
134C4×D3—92no—
135C4×D3—92no—
136C4×D3—182no—
137C4×D3—272no—
138C4×D3—272no—
139C4×D3—272no—
140C2×C32—22no—
141C2×C32—21no—
142C2×C32—41no—
143C2×C32C22×D911yescharacteristic
144C2×C32C2×D3212yes—
145C3⋊D3—34no—
146C3⋊D3C4×D912yescomplemented
147C3×D3—34no—
148C3×D3—62no—
149C3×D3—94no—
150C3×D3—94no—
151C3×D3—184no—
152C2×C9—22no—
153C2×C9—41no—
154C2×C9—92no—
155C2×C9C2×D3211yescharacteristic
156D9—34no—
157D9—64no—
158C22×C4—811noSylow
159C22×C3—91no—
160C22×C3—272no—
161C2×D3—32no—
162C2×D3—61no—
163C2×D3—92no—
164C2×D3—92no—
165C2×D3—182no—
166C2×D3—278no—
167C2×D3—274no—
168C3×C4—21no—
169C3×C4—22no—
170C3×C4—41no—
171C3×C4—91no—
172C3×C4—272no—
173C3×C4D3×D912yescomplemented
174C3×C4#111311yescharacteristic
175Dic3—32no—
176Dic3—61no—
177Dic3—92no—
178Dic3—92no—
179Dic3—182no—
180C32—22no—
181C32—21no—
182C32—41no—
183C32C2×C4×D911yescharacteristic, complemented
184C32C4×D3212yes—
185C9—22no—
186C9—41no—
187C9C4×D3211yescharacteristic, complemented
188C23—811no—
189C2×C4—91no—
190C2×C4—272no—
191C2×C4—812no—
192C2×C4—811no—
193C2×C3—21no—
194C2×C3—22no—
195C2×C3—41no—
196C2×C3—92no—
197C2×C3—274no—
198C2×C3C2×D3×D912yes—
199C2×C3C2×#111311yescharacteristic
200D3—34no—
201D3—62no—
202D3—94no—
203D3—94no—
204D3—184no—
205C22—91no—
206C22—272no—
207C22—814no—
208C4—91no—
209C4—272no—
210C4#6643111yescharacteristic, direct product factor
211C3—21no—
212C3—22no—
213C3—41no—
214C3C4×D3×D912yescomplemented
215C3C4×#111311yescharacteristic
216C2—92no—
217C2—274no—
218C2C2×#6643111yescharacteristic
subgroupG/H
center, hypercenterC4#66431
commutator, hypocenterC32×C9C22×C4
FrattiniC2×C3C2×#1113
FittingC32×C4×C9C22
socleC2×C33C22×D3
prime radicalC2×#66431C2
cosocleC2×C32×C9C23
LCSG ▷ C32×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C9×C3⋊D3C2semidirect
3. C3×C4×C3⋊D9C2semidirect
4. #10619898C2semidirect
5. #10619896C2semidirect
10. #66431C4direct (N × H)
11. C32×C4×C9C22semidirect
12. C9×C3⋊Dic3C22semidirect
13. C3×C3⋊Dic9C22semidirect
20. C4×C3⋊D9D3semidirect
29. C9×C3⋊D3C2×C4semidirect
30. C3×C3⋊D9C2×C4semidirect
49. C3×C4×C9C2×D3semidirect
50. C3⋊Dic9C2×D3semidirect
55. C32×C9C22×C4semidirect
59. C4×C3⋊D3D9semidirect
83. C3⋊D9C4×D3semidirect
102. C32×C4C2×D9semidirect
105. C3⋊Dic3C2×D9semidirect
118. C4×C9D32semidirect
125. C3×C9C2×C4×D3semidirect
146. C3⋊D3C4×D9semidirect
173. C3×C4D3×D9semidirect
183. C32C2×C4×D9semidirect
187. C9C4×D32semidirect
210. C4#66431direct (N × H)
214. C3C4×D3×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#664312
C4×C9×C3⋊D32
C3×C4×C3⋊D92
#106198982
#106198962
C4×#11133
C4×D3×D93