Finite Group Databasebeta

← C22×C3×C3⋊#157 #13049876

Subgroups — C22×C3×C3⋊#157 #13049876

Order 1296.

660 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C22×C32×C3⋊D3C211yesmaximal, characteristic
2C2×C3×C3⋊#157C216yesmaximal, direct product factor
3C22×C3⋊#157C311yesmaximal, characteristic, direct product factor
4C22×C3×#157—31nomaximal
5C22×C34C411yescharacteristic, complemented
6C2×C32×C3⋊D3C413yescomplemented
7C2×C32×C3⋊D3C2213yes—
8C3×C3⋊#157C2214yesdirect product factor
9C22×C3×C3⋊D3—21no—
10C22×C3×C3⋊D3D311yescharacteristic
11C22×C3×C3⋊D3C2×C311yescharacteristic
12C22×C32×D3—62no—
13C2×C3⋊#157C2×C316yesdirect product factor
14C2×C3×#157—36no—
15C2×C34C2×C413yescomplemented
16C32×C3⋊D3C2×C413yescomplemented
17C32×C3⋊D3C2311yescharacteristic
18C22×#157—31no—
19C22×C3×Dic3—91nomaximal
20C22×C33—21no—
21C22×C33—22no—
22C22×C33—44no—
23C22×C33—42no—
24C22×C33—42no—
25C22×C33Dic311yescharacteristic, complemented
26C22×C33C3×C411yescharacteristic, complemented
27C2×C3×C3⋊D3—23no—
28C2×C3×C3⋊D3—23no—
29C2×C3×C3⋊D3Dic313yescomplemented
30C2×C3×C3⋊D3C3×C413yescomplemented
31C2×C3×C3⋊D3C2×D313yes—
32C2×C3×C3⋊D3C22×C313yes—
33C2×C32×D3—66no—
34C2×C32×D3—66no—
35C3⋊#157C22×C314yesdirect product factor
36C3×#157—34no—
37C34C22×C411yescharacteristic, complemented, Sylow
38C23×C32—91no—
39C22×C3⋊D3C3×D311yescharacteristic
40C22×C3×D3—62no—
41C22×C3×D3—62no—
42C22×C3×D3—64no—
43C2×#157—36no—
44C2×C3×Dic3—96no—
45C2×C33—23no—
46C2×C33—26no—
47C2×C33—412no—
48C2×C33—46no—
49C2×C33—46no—
50C2×C33C2×Dic313yescomplemented
51C2×C33C2×C3×C413yescomplemented
52C3×C3⋊D3—23no—
53C3×C3⋊D3—21no—
54C3×C3⋊D3C2×Dic313yescomplemented
55C3×C3⋊D3C2×C3×C413yescomplemented
56C3×C3⋊D3C22×D311yescharacteristic
57C3×C3⋊D3C23×C311yescharacteristic
58C32×D3—66no—
59C32×D3—62no—
60C22×C3×C4—271no—
61C22×Dic3—91no—
62C22×C32—24no—
63C22×C32—22no—
64C22×C32—22no—
65C22×C32—44no—
66C22×C32—44no—
67C22×C32—42no—
68C22×C32—42no—
69C22×C32—48no—
70C22×C32—42no—
71C22×C32—42no—
72C22×C32—44no—
73C22×C32—93no—
74C22×C32—93no—
75C22×C32C3×Dic311yescharacteristic, complemented
76C22×C32#15711yescharacteristic, complemented
77C2×C3⋊D3C3×Dic313yescomplemented
78C2×C3⋊D3C2×C3×D313yes—
79C2×C3×D3—66no—
80C2×C3×D3—66no—
81C2×C3×D3—66no—
82C2×C3×D3—66no—
83C2×C3×D3—612no—
84C2×C3×D3—612no—
85#157—34no—
86C3×Dic3—94no—
87C33—22no—
88C33—21no—
89C33—44no—
90C33—42no—
91C33—42no—
92C33C22×Dic311yescharacteristic, complemented
93C33C22×C3×C411yescharacteristic, complemented
94C23×C3—91no—
95C23×C3—91no—
96C23×C3—181no—
97C22×D3—62no—
98C2×C3×C4—276no—
99C2×Dic3—96no—
100C2×C32—212no—
101C2×C32—26no—
102C2×C32—26no—
103C2×C32—412no—
104C2×C32—412no—
105C2×C32—46no—
106C2×C32—46no—
107C2×C32—424no—
108C2×C32—46no—
109C2×C32—46no—
110C2×C32—412no—
111C2×C32—91no—
112C2×C32—93no—
113C2×C32C2×C3×Dic313yescomplemented
114C2×C32C2×#15713yescomplemented
115C3⋊D3C2×C3×Dic313yescomplemented
116C3⋊D3C22×C3×D311yescharacteristic
117C3×D3—66no—
118C3×D3—66no—
119C3×D3—62no—
120C3×D3—62no—
121C3×D3—612no—
122C3×D3—64no—
123C22×C4—271noSylow
124C22×C3—22no—
125C22×C3—21no—
126C22×C3—44no—
127C22×C3—42no—
128C22×C3—42no—
129C22×C3—93no—
130C22×C3—93no—
131C22×C3—93no—
132C22×C3—93no—
133C22×C3—183no—
134C22×C3—183no—
135C22×C3C3×#15711yescharacteristic, complemented
136C22×C3C3⋊#15711yescharacteristic, direct product factor
137C2×D3—66no—
138C2×D3—66no—
139C3×C4—274no—
140Dic3—94no—
141C32—24no—
142C32—22no—
143C32—22no—
144C32—42no—
145C32—42no—
146C32—44no—
147C32—44no—
148C32—44no—
149C32—48no—
150C32—42no—
151C32—42no—
152C32C22×C3×Dic311yescharacteristic, complemented
153C32C22×#15711yescharacteristic, complemented
154C23—91no—
155C2×C4—276no—
156C2×C3—26no—
157C2×C3—23no—
158C2×C3—412no—
159C2×C3—46no—
160C2×C3—46no—
161C2×C3—91no—
162C2×C3—93no—
163C2×C3—91no—
164C2×C3—93no—
165C2×C3—181no—
166C2×C3—183no—
167C2×C3C2×C3×#15713yescomplemented
168C2×C3C2×C3⋊#15713yesdirect product factor
169D3—66no—
170D3—62no—
171C22—93no—
172C22—93no—
173C22C3×C3⋊#15711yescharacteristic, direct product factor
174C4—274no—
175C3—22no—
176C3—21no—
177C3—44no—
178C3—42no—
179C3—42no—
180C3C22×C3×#15711yescharacteristic, complemented
181C3C22×C3⋊#15711yescharacteristic, direct product factor
182C2—91no—
183C2—93no—
184C2C2×C3×C3⋊#15713yesdirect product factor
subgroupG/H
center, hypercenterC22×C3C3⋊#157
commutator, hypocenterC33C22×C3×C4
FrattiniC1G
Fitting, socleC22×C34C4
prime radicalC22×C32×C3⋊D3C2
cosocleC3×C3⋊D3C23×C3
LCSG ▷ C33
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×C3⋊#157C2direct (N × H)
3. C22×C3⋊#157C3direct (N × H)
5. C22×C34C4semidirect
6. C2×C32×C3⋊D3C4semidirect
8. C3×C3⋊#157C22direct (N × H)
13. C2×C3⋊#157C2×C3direct (N × H)
15. C2×C34C2×C4semidirect
16. C32×C3⋊D3C2×C4semidirect
25. C22×C33Dic3semidirect
26. C22×C33C3×C4semidirect
29. C2×C3×C3⋊D3Dic3semidirect
30. C2×C3×C3⋊D3C3×C4semidirect
35. C3⋊#157C22×C3direct (N × H)
37. C34C22×C4semidirect
50. C2×C33C2×Dic3semidirect
51. C2×C33C2×C3×C4semidirect
54. C3×C3⋊D3C2×Dic3semidirect
55. C3×C3⋊D3C2×C3×C4semidirect
75. C22×C32C3×Dic3semidirect
76. C22×C32#157semidirect
77. C2×C3⋊D3C3×Dic3semidirect
92. C33C22×Dic3semidirect
93. C33C22×C3×C4semidirect
113. C2×C32C2×C3×Dic3semidirect
114. C2×C32C2×#157semidirect
115. C3⋊D3C2×C3×Dic3semidirect
135. C22×C3C3×#157semidirect
136. C22×C3C3⋊#157direct (N × H)
152. C32C22×C3×Dic3semidirect
153. C32C22×#157semidirect
167. C2×C3C2×C3×#157semidirect
168. C2×C3C2×C3⋊#157direct (N × H)
173. C22C3×C3⋊#157direct (N × H)
180. C3C22×C3×#157semidirect
181. C3C22×C3⋊#157direct (N × H)
184. C2C2×C3×C3⋊#157direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C3⋊D32
C2×C3×C3⋊#1572
C22×C3⋊#1573
C22×C3×#1573
C22×C3×Dic39