Finite Group Databasebeta

← #89039

Subgroups — #89039

Order 432.

452 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 70 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×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×#638C211yesmaximal, characteristic, complemented
4C32×#67C211yesmaximal, characteristic, complemented
5#6292C211yesmaximal, characteristic, complemented
6#6291C211yesmaximal, characteristic, complemented
7#6289C211yesmaximal, characteristic, complemented
8D4×C3⋊D3—31nomaximal
9#3811—34nomaximal
10C22×C33C2211yescharacteristic, complemented
11C2×C3⋊(C3⋊D3)—22no—
12C2×C3⋊(C3⋊D3)C2211yescharacteristic
13C2×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
14C2×C3×C3⋊D3C2211yescharacteristic, complemented
15C2×C32×D3C2211yescharacteristic, complemented
16D3×C3⋊D3—22no—
17C3×C3⋊Dic3C2211yescharacteristic, complemented
18C32×Dic3C2211yescharacteristic, complemented
19C22×C3⋊D3—31no—
20C22×C3⋊D3—31no—
21C22×C3⋊D3—34no—
22C22×C3⋊D3—64no—
23C2×D32—34no—
24C32×D4—31no—
25#638—31no—
26#638D311yescharacteristic, complemented
27C4⋊(C3⋊D3)—31no—
28C4×C3⋊D3—31no—
29C3×#67—34no—
30C3×#67D314yescomplemented
31#626—34no—
32#626—34no—
33#624—34no—
34C2×C33—21no—
35C2×C33C2311yescharacteristic
36C3⋊(C3⋊D3)—21no—
37C3⋊(C3⋊D3)D412yescomplemented
38C3×C3⋊D3—21no—
39C32×D3—21no—
40D3×D4—94no—
41D3×D4—91no—
42C22×C32—24no—
43C22×C32—31no—
44C22×C32C2×D314yescomplemented
45C22×C32C2×D311yescharacteristic, complemented
46C2×C3⋊D3—31no—
47C2×C3⋊D3—31no—
48C2×C3⋊D3—34no—
49C2×C3⋊D3—34no—
50C2×C3⋊D3—64no—
51C2×C3⋊D3—64no—
52C2×C3⋊D3—62no—
53C2×C3⋊D3—62no—
54C2×C3⋊D3—68no—
55C2×C3⋊D3—616no—
56C2×C3⋊D3C2×D311yescharacteristic, complemented
57C2×C3×D3—34no—
58C2×C3×D3C2×D314yescomplemented
59D32—68no—
60C32×C4—31no—
61C3⋊Dic3C2×D311yescharacteristic, complemented
62C3×Dic3—34no—
63C3×Dic3C2×D314yescomplemented
64C33C2×D411yescharacteristic, complemented, Sylow
65C22×D3—94no—
66C22×D3—94no—
67C22×D3—91no—
68C22×D3—91no—
69C22×D3—184no—
70C3×D4—34no—
71C3×D4—91no—
72#67—34no—
73#67—94no—
74#67—91no—
75#67C3⋊D311yescharacteristic, complemented
76D12—94no—
77D12—91no—
78C4×D3—94no—
79C4×D3—91no—
80C2×C32—28no—
81C2×C32—24no—
82C2×C32—21no—
83C2×C32—24no—
84C2×C32—61no—
85C2×C32C22×D314yes—
86C2×C32C22×D311yescharacteristic
87C3⋊D3—21no—
88C3⋊D3—32no—
89C3⋊D3—38no—
90C3⋊D3—68no—
91C3⋊D3—68no—
92C3⋊D3—64no—
93C3⋊D3—61no—
94C3×D3—24no—
95C3×D3—64no—
96C2×D4—271noSylow
97C22×C3—24no—
98C22×C3—34no—
99C22×C3—91no—
100C22×C3D3214yescomplemented
101C22×C3C2×C3⋊D311yescharacteristic, complemented
102C2×D3—34no—
103C2×D3—94no—
104C2×D3—91no—
105C2×D3—94no—
106C2×D3—91no—
107C2×D3—184no—
108C2×D3—184no—
109C2×D3—182no—
110C2×D3—188no—
111C2×D3—188no—
112C2×D3—182no—
113C2×D3—1816no—
114C2×D3C2×C3⋊D311yescharacteristic, complemented
115C3×C4—34no—
116C3×C4—91no—
117Dic3—34no—
118Dic3C2×C3⋊D311yescharacteristic, complemented
119C32—24no—
120C32D3×D414yescomplemented
121C32D3×D411yescharacteristic, complemented
122C23—271no—
123C23—271no—
124D4—31no—
125D4—91no—
126D4—271no—
127D4—271no—
128C2×C4—271no—
129C2×C3—28no—
130C2×C3—24no—
131C2×C3—21no—
132C2×C3—24no—
133C2×C3—64no—
134C2×C3—181no—
135C2×C3C2×D3214yes—
136C2×C3C22×C3⋊D311yescharacteristic
137D3—21no—
138D3—64no—
139D3—98no—
140D3—92no—
141D3—188no—
142D3—188no—
143D3—184no—
144D3—181no—
145C22—31no—
146C22—91no—
147C22—271no—
148C22—271no—
149C22—542no—
150C22—542no—
151C22D3×C3⋊D311yescharacteristic, complemented
152C4—31no—
153C4—91no—
154C3—24no—
155C3#381114yescomplemented
156C3D4×C3⋊D311yescharacteristic, complemented
157C2—21no—
158C2—61no—
159C2—181no—
160C2—272no—
161C2—541no—
162C2C2×D3×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC2C2×D3×C3⋊D3
commutator, socle, cosocleC2×C33C23
FittingC22×C33C22
hypercenterC22D3×C3⋊D3
hypocenterC33C2×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊(C3⋊D3)C2semidirect
2. C2×D3×C3⋊D3C2semidirect
3. C3×#638C2semidirect
4. C32×#67C2semidirect
5. #6292C2semidirect
6. #6291C2semidirect
7. #6289C2semidirect
10. C22×C33C22semidirect
13. C2×C3⋊(C3⋊D3)C22semidirect
14. C2×C3×C3⋊D3C22semidirect
15. C2×C32×D3C22semidirect
17. C3×C3⋊Dic3C22semidirect
18. C32×Dic3C22semidirect
26. #638D3semidirect
30. C3×#67D3semidirect
37. C3⋊(C3⋊D3)D4semidirect
44. C22×C32C2×D3semidirect
45. C22×C32C2×D3semidirect
56. C2×C3⋊D3C2×D3semidirect
58. C2×C3×D3C2×D3semidirect
61. C3⋊Dic3C2×D3semidirect
63. C3×Dic3C2×D3semidirect
64. C33C2×D4semidirect
75. #67C3⋊D3semidirect
100. C22×C3D32semidirect
101. C22×C3C2×C3⋊D3semidirect
114. C2×D3C2×C3⋊D3semidirect
118. Dic3C2×C3⋊D3semidirect
120. C32D3×D4semidirect
121. C32D3×D4semidirect
151. C22D3×C3⋊D3semidirect
155. C3#3811semidirect
156. C3D4×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊(C3⋊D3)2
C2×D3×C3⋊D32
C3×#6382
C32×#672
#62922
#62912
#62892
D4×C3⋊D33
#38113