Finite Group Databasebeta

← C3×C4×C3⋊#157 #13049585

Subgroups — C3×C4×C3⋊#157 #13049585

Order 1296.

364 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 58 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×C3⋊#157C212yesmaximal
2C32×C4×C3⋊D3C211yesmaximal, characteristic
3C4×C3⋊#157C311yesmaximal, characteristic, direct product factor
4C3×C4×#157—31nomaximal
5C2×C32×C3⋊D3C2211yescharacteristic
6C3×C3⋊#157C414yesdirect product factor
7C34×C4C411yescharacteristic, complemented
8C32×C3⋊Dic3C411yescharacteristic, complemented
9C2×C3⋊#157C2×C312yes—
10C2×C3×#157—32no—
11C3×C4×C3⋊D3—21no—
12C3×C4×C3⋊D3D311yescharacteristic
13C3×C4×C3⋊D3C2×C311yescharacteristic
14C32×C4×D3—62no—
15C2×C34C2×C411yescharacteristic
16C32×C3⋊D3C2×C412yes—
17C4×#157—31no—
18C3×C4×Dic3—91nomaximal
19C2×C3×C3⋊D3—21no—
20C2×C3×C3⋊D3C2×D311yescharacteristic
21C2×C3×C3⋊D3C22×C311yescharacteristic
22C2×C32×D3—62no—
23C3⋊#157C3×C414yesdirect product factor
24C3×#157—34no—
25C33×C4—21no—
26C33×C4—22no—
27C33×C4—44no—
28C33×C4—42no—
29C33×C4—42no—
30C33×C4Dic311yescharacteristic, complemented
31C33×C4C3×C411yescharacteristic, complemented
32C3×C3⋊Dic3—21no—
33C3×C3⋊Dic3Dic311yescharacteristic, complemented
34C3×C3⋊Dic3C3×C411yescharacteristic, complemented
35C32×Dic3—62no—
36C34C4211yescharacteristic, complemented, Sylow
37C2×#157—32no—
38C2×C32×C4—91no—
39C4×C3⋊D3C3×D311yescharacteristic
40C2×C3×Dic3—92no—
41C3×C4×D3—62no—
42C3×C4×D3—62no—
43C3×C4×D3—64no—
44C2×C33—21no—
45C2×C33—22no—
46C2×C33—44no—
47C2×C33—42no—
48C2×C33—42no—
49C2×C33C2×Dic311yescharacteristic
50C2×C33C2×C3×C411yescharacteristic
51C3×C3⋊D3—22no—
52C3×C3⋊D3C4×D312yes—
53C3×C3⋊D3C2×C3×C412yes—
54C32×D3—64no—
55C3×C42—271no—
56C4×Dic3—91no—
57C22×C32—91no—
58C2×C3⋊D3C2×C3×D311yescharacteristic
59C2×C3×D3—62no—
60C2×C3×D3—62no—
61C2×C3×D3—64no—
62#157—34no—
63C32×C4—24no—
64C32×C4—22no—
65C32×C4—22no—
66C32×C4—44no—
67C32×C4—44no—
68C32×C4—42no—
69C32×C4—42no—
70C32×C4—48no—
71C32×C4—42no—
72C32×C4—42no—
73C32×C4—44no—
74C32×C4—91no—
75C32×C4C3×Dic311yescharacteristic, complemented
76C32×C4#15711yescharacteristic, complemented
77C3⋊Dic3C3×Dic311yescharacteristic, complemented
78C3×Dic3—62no—
79C3×Dic3—62no—
80C3×Dic3—64no—
81C3×Dic3—94no—
82C33—21no—
83C33—22no—
84C33—44no—
85C33—42no—
86C33—42no—
87C33C4×Dic311yescharacteristic, complemented
88C33C3×C4211yescharacteristic, complemented
89C2×C3×C4—91no—
90C2×C3×C4—91no—
91C2×C3×C4—181no—
92C2×C3×C4—272no—
93C2×Dic3—92no—
94C4×D3—62no—
95C2×C32—24no—
96C2×C32—22no—
97C2×C32—22no—
98C2×C32—44no—
99C2×C32—44no—
100C2×C32—42no—
101C2×C32—42no—
102C2×C32—48no—
103C2×C32—42no—
104C2×C32—42no—
105C2×C32—44no—
106C2×C32—92no—
107C2×C32C2×C3×Dic311yescharacteristic
108C2×C32C2×#15711yescharacteristic
109C3⋊D3C3×C4×D312yes—
110C3×D3—64no—
111C3×D3—64no—
112C3×D3—68no—
113C42—271noSylow
114C22×C3—91no—
115C22×C3—91no—
116C22×C3—181no—
117C2×D3—62no—
118C3×C4—22no—
119C3×C4—21no—
120C3×C4—44no—
121C3×C4—42no—
122C3×C4—42no—
123C3×C4—91no—
124C3×C4—91no—
125C3×C4—181no—
126C3×C4—274no—
127C3×C4C3×#15711yescharacteristic, complemented
128C3×C4C3⋊#15711yescharacteristic, direct product factor
129Dic3—62no—
130Dic3—94no—
131C32—24no—
132C32—22no—
133C32—22no—
134C32—42no—
135C32—42no—
136C32—44no—
137C32—44no—
138C32—44no—
139C32—48no—
140C32—42no—
141C32—42no—
142C32C3×C4×Dic311yescharacteristic, complemented
143C32C4×#15711yescharacteristic, complemented
144C2×C4—91no—
145C2×C4—272no—
146C2×C3—22no—
147C2×C3—21no—
148C2×C3—44no—
149C2×C3—42no—
150C2×C3—42no—
151C2×C3—92no—
152C2×C3—92no—
153C2×C3—182no—
154C2×C3C2×C3×#15711yescharacteristic
155C2×C3C2×C3⋊#15711yescharacteristic
156D3—64no—
157C22—91no—
158C4—91no—
159C4—274no—
160C4C3×C3⋊#15711yescharacteristic, direct product factor
161C3—22no—
162C3—21no—
163C3—44no—
164C3—42no—
165C3—42no—
166C3C3×C4×#15711yescharacteristic, complemented
167C3C4×C3⋊#15711yescharacteristic, direct product factor
168C2—92no—
169C2C2×C3×C3⋊#15711yescharacteristic
subgroupG/H
center, hypercenterC3×C4C3⋊#157
commutator, hypocenterC33C3×C42
FrattiniC2C2×C3×C3⋊#157
FittingC34×C4C4
socleC2×C34C2×C4
prime radicalC2×C32×C3⋊D3C22
cosocleC2×C3×C3⋊D3C22×C3
LCSG ▷ C33
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
3. C4×C3⋊#157C3direct (N × H)
6. C3×C3⋊#157C4direct (N × H)
7. C34×C4C4semidirect
8. C32×C3⋊Dic3C4semidirect
23. C3⋊#157C3×C4direct (N × H)
30. C33×C4Dic3semidirect
31. C33×C4C3×C4semidirect
33. C3×C3⋊Dic3Dic3semidirect
34. C3×C3⋊Dic3C3×C4semidirect
36. C34C42semidirect
75. C32×C4C3×Dic3semidirect
76. C32×C4#157semidirect
77. C3⋊Dic3C3×Dic3semidirect
87. C33C4×Dic3semidirect
88. C33C3×C42semidirect
127. C3×C4C3×#157semidirect
128. C3×C4C3⋊#157direct (N × H)
142. C32C3×C4×Dic3semidirect
143. C32C4×#157semidirect
160. C4C3×C3⋊#157direct (N × H)
166. C3C3×C4×#157semidirect
167. C3C4×C3⋊#157direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊#1572
C32×C4×C3⋊D32
C4×C3⋊#1573
C3×C4×#1573
C3×C4×Dic39