Finite Group Databasebeta

← #13049712

Subgroups — #13049712

Order 1296.

1036 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 119 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⋊#1113C212yesmaximal, complemented
2C3×C4⋊(C3⋊(C3⋊D3))C212yesmaximal, complemented
3C32×C4×C3⋊D3C211yesmaximal, characteristic, complemented
4#10620156C212yesmaximal, complemented
5C4⋊#1113—34nomaximal
6D3×C4⋊(C3⋊D3)—32nomaximal
7C2×C3×C3⋊(C3⋊D3)C2214yescomplemented
8C2×C32×C3⋊D3C2211yescharacteristic
9C3⋊#1113—24no—
10C34×C4C2211yescharacteristic, complemented
11C32×C3⋊Dic3C2211yescharacteristic, complemented
12C2×#1113—38no—
13C2×D3×C3⋊D3—34no—
14C4⋊(C3⋊(C3⋊D3))D312yescomplemented
15C3×C4⋊(C3⋊D3)—32no—
16C3×C4⋊(C3⋊D3)—38no—
17C3×C4⋊(C3⋊D3)—68no—
18C3×C4×C3⋊D3D314yescomplemented
19C32×C4×D3—32no—
20C32×C4×D3—61no—
21#6295—38no—
22#6292—34no—
23C2×C34C2311yescharacteristic
24C3×C3⋊(C3⋊D3)—24no—
25C32×C3⋊D3D412yescomplemented
26C2×C4⋊(C3⋊D3)—91no—
27#3802—91no—
28D3×D12—98no—
29C2×C3⋊(C3⋊D3)C2×D314yescomplemented
30C2×C3×C3⋊D3—34no—
31C2×C3×C3⋊D3—316no—
32C2×C3×C3⋊D3—616no—
33C2×C3×C3⋊D3C2×D314yes—
34C2×C32×D3—32no—
35C2×C32×D3—61no—
36#1113—616no—
37D3×C3⋊D3—68no—
38C33×C4—21no—
39C33×C4—28no—
40C33×C4—44no—
41C33×C4C2×D312yescomplemented
42C33×C4C2×D314yescomplemented
43C3×C3⋊Dic3C2×D314yescomplemented
44C32×Dic3—32no—
45C32×Dic3—61no—
46C34C2×D411yescharacteristic, complemented, Sylow
47C22×C3⋊D3—92no—
48C2×D32—916no—
49C2×D32—92no—
50C2×C32×C4—91no—
51C4⋊(C3⋊D3)—32no—
52C4⋊(C3⋊D3)—38no—
53C4⋊(C3⋊D3)—68no—
54C4⋊(C3⋊D3)—92no—
55C4×C3⋊D3C3⋊D311yescharacteristic, complemented
56C3×D12—98no—
57C3×D12—92no—
58C3×D12—188no—
59C3×C4×D3—38no—
60C3×C4×D3—64no—
61#626—916no—
62#625—92no—
63C2×C33—21no—
64C2×C33—28no—
65C2×C33—44no—
66C2×C33C22×D312yes—
67C2×C33C22×D314yes—
68C3⋊(C3⋊D3)—24no—
69C3×C3⋊D3—64no—
70C3×C3⋊D3—616no—
71C3×C3⋊D3—1216no—
72C3×C3⋊D3D1218yescomplemented
73C32×D3—34no—
74C32×D3—62no—
75D3×D4—272no—
76C2×D12—274no—
77C22×C32—91no—
78C2×C3⋊D3—34no—
79C2×C3⋊D3—316no—
80C2×C3⋊D3—616no—
81C2×C3⋊D3—184no—
82C2×C3⋊D3C2×C3⋊D311yescharacteristic
83C2×C3×D3—38no—
84C2×C3×D3—64no—
85C2×C3×D3—916no—
86C2×C3×D3—94no—
87C2×C3×D3—1816no—
88D32—1832no—
89D32—184no—
90C32×C4—28no—
91C32×C4—28no—
92C32×C4—24no—
93C32×C4—44no—
94C32×C4—412no—
95C32×C4—44no—
96C32×C4—91no—
97C32×C4D3218yescomplemented
98C32×C4D3211yescharacteristic, complemented
99C32×C4C2×C3⋊D311yescharacteristic, complemented
100C3⋊Dic3C2×C3⋊D311yescharacteristic, complemented
101C3×Dic3—38no—
102C3×Dic3—64no—
103C33—28no—
104C33—21no—
105C33—44no—
106C33C2×D1214yescomplemented
107C33D3×D412yescomplemented
108C22×D3—274no—
109C22×D3—278no—
110C3×D4—272no—
111C2×C3×C4—94no—
112#67—274no—
113D12—92no—
114D12—98no—
115D12—188no—
116D12—278no—
117C4×D3—32no—
118C4×D3—61no—
119C2×C32—28no—
120C2×C32—28no—
121C2×C32—24no—
122C2×C32—44no—
123C2×C32—412no—
124C2×C32—44no—
125C2×C32—92no—
126C2×C32C2×D3218yes—
127C2×C32C2×D3211yescharacteristic
128C2×C32C22×C3⋊D311yescharacteristic
129C3⋊D3—64no—
130C3⋊D3—616no—
131C3⋊D3—1216no—
132C3⋊D3C4⋊(C3⋊D3)12yescomplemented
133C3×D3—316no—
134C3×D3—68no—
135C3×D3—1816no—
136C3×D3—184no—
137C3×D3—3616no—
138C2×D4—811noSylow
139C22×C3—94no—
140C22×C3—274no—
141C2×D3—32no—
142C2×D3—61no—
143C2×D3—94no—
144C2×D3—916no—
145C2×D3—1816no—
146C2×D3—548no—
147C2×D3—5416no—
148C3×C4—21no—
149C3×C4—28no—
150C3×C4—44no—
151C3×C4—94no—
152C3×C4D3×C3⋊D312yescomplemented
153C3×C4#111314yescomplemented
154Dic3—32no—
155Dic3—61no—
156C32—28no—
157C32—28no—
158C32—24no—
159C32—44no—
160C32—412no—
161C32—44no—
162C32D3×D1218yescomplemented
163C32#380211yescharacteristic, complemented
164C32C2×C4⋊(C3⋊D3)11yescharacteristic, complemented
165C23—812no—
166D4—272no—
167D4—812no—
168C2×C4—91no—
169C2×C3—21no—
170C2×C3—28no—
171C2×C3—44no—
172C2×C3—98no—
173C2×C3—544no—
174C2×C3C2×D3×C3⋊D312yes—
175C2×C3C2×#111314yes—
176D3—34no—
177D3—62no—
178D3—184no—
179D3—1816no—
180D3—3616no—
181C22—91no—
182C22—274no—
183C22—1624no—
184C4—91no—
185C4C3⋊#111311yescharacteristic, complemented
186C3—21no—
187C3—28no—
188C3—44no—
189C3D3×C4⋊(C3⋊D3)12yescomplemented
190C3C4⋊#111314yescomplemented
191C2—92no—
192C2—544no—
193C2C2×C3⋊#111311yescharacteristic
subgroupG/H
center, FrattiniC2C2×C3⋊#1113
commutator, socle, cosocleC2×C34C23
FittingC34×C4C22
hypercenterC4C3⋊#1113
hypocenterC34C2×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#1113C2semidirect
2. C3×C4⋊(C3⋊(C3⋊D3))C2semidirect
3. C32×C4×C3⋊D3C2semidirect
4. #10620156C2semidirect
7. C2×C3×C3⋊(C3⋊D3)C22semidirect
10. C34×C4C22semidirect
11. C32×C3⋊Dic3C22semidirect
14. C4⋊(C3⋊(C3⋊D3))D3semidirect
18. C3×C4×C3⋊D3D3semidirect
25. C32×C3⋊D3D4semidirect
29. C2×C3⋊(C3⋊D3)C2×D3semidirect
41. C33×C4C2×D3semidirect
42. C33×C4C2×D3semidirect
43. C3×C3⋊Dic3C2×D3semidirect
46. C34C2×D4semidirect
55. C4×C3⋊D3C3⋊D3semidirect
72. C3×C3⋊D3D12semidirect
97. C32×C4D32semidirect
98. C32×C4D32semidirect
99. C32×C4C2×C3⋊D3semidirect
100. C3⋊Dic3C2×C3⋊D3semidirect
106. C33C2×D12semidirect
107. C33D3×D4semidirect
132. C3⋊D3C4⋊(C3⋊D3)semidirect
152. C3×C4D3×C3⋊D3semidirect
153. C3×C4#1113semidirect
162. C32D3×D12semidirect
163. C32#3802semidirect
164. C32C2×C4⋊(C3⋊D3)semidirect
185. C4C3⋊#1113semidirect
189. C3D3×C4⋊(C3⋊D3)semidirect
190. C3C4⋊#1113semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#11132
C3×C4⋊(C3⋊(C3⋊D3))2
C32×C4×C3⋊D32
#106201562
C4⋊#11133
D3×C4⋊(C3⋊D3)3