Finite Group Databasebeta

← C3×#937 #64060

Subgroups — C3×#937 #64060

Order 288.

287 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 287 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C23×C3×D3C211yesmaximal, characteristic, complemented
2C2×C32×D4C211yesmaximal, characteristic, complemented
3C2×C3×#67C212yesmaximal, complemented
4C3×#217C211yesmaximal, characteristic, complemented
5C3×(C2×D3)⋊C4C212yesmaximal, complemented
6C3×#120—31nomaximal
7#937C311yesmaximal, characteristic, direct product factor
8C23×C32C2211yescharacteristic
9C23×C32C2211yescharacteristic, complemented
10C22×C3×D3—22no—
11C22×C3×D3—24no—
12C22×C3×D3C2212yes—
13C32×D4—22no—
14C2×C32×C4C2211yescharacteristic, complemented
15C3×#67—24no—
16C2×C3×Dic3C2212yescomplemented
17C24×C3—31no—
18C23×D3C2×C311yescharacteristic, complemented
19C2×C3×D4—21no—
20C2×C3×D4—32no—
21C2×C3×D4D311yescharacteristic, complemented
22C2×C3×D4C2×C311yescharacteristic, complemented
23C2×#67C2×C312yescomplemented
24C3×C22⋊C4—31no—
25C3×C22⋊C4—32no—
26#217C2×C311yescharacteristic, complemented
27(C2×D3)⋊C4C2×C312yescomplemented
28C22×C32—21no—
29C22×C32—22no—
30C22×C32—22no—
31C22×C32D412yescomplemented
32C22×C32C2311yescharacteristic
33C2×C3×D3—28no—
34C2×C3×D3—22no—
35C2×C3×D3—22no—
36C2×C3×D3D414yescomplemented
37C32×C4—21no—
38C3×Dic3—22no—
39#120—31noSylow
40C23×C3—21no—
41C23×C3—21no—
42C23×C3—32no—
43C23×C3—64no—
44C23×C3—62no—
45C23×C3C2×D311yescharacteristic
46C23×C3C2×D311yescharacteristic, complemented
47C23×C3C22×C311yescharacteristic
48C23×C3C22×C311yescharacteristic, complemented
49C22×D3—22no—
50C22×D3—24no—
51C22×D3C22×C312yes—
52C3×D4—24no—
53C3×D4—22no—
54C3×D4—22no—
55C3×D4—64no—
56C2×C3×C4—21no—
57C2×C3×C4—32no—
58C2×C3×C4C2×D311yescharacteristic, complemented
59C2×C3×C4C22×C311yescharacteristic, complemented
60#67—24no—
61C2×Dic3C22×C312yescomplemented
62C2×C32—22no—
63C2×C32—41no—
64C2×C32C2×D412yes—
65C2×C32C2×D411yescharacteristic
66C3×D3—24no—
67C24—31no—
68C2×D4—32no—
69C2×D4C3×D311yescharacteristic, complemented
70C22⋊C4—31no—
71C22⋊C4—32no—
72C22×C3—22no—
73C22×C3—22no—
74C22×C3—22no—
75C22×C3—22no—
76C22×C3—21no—
77C22×C3—22no—
78C22×C3—21no—
79C22×C3—22no—
80C22×C3—21no—
81C22×C3—34no—
82C22×C3—42no—
83C22×C3—42no—
84C22×C3—68no—
85C22×C3—62no—
86C22×C3—62no—
87C22×C3#6712yescomplemented
88C22×C3C3×D412yescomplemented
89C22×C3C22×D311yescharacteristic
90C22×C3C23×C311yescharacteristic
91C2×D3—28no—
92C2×D3—22no—
93C2×D3—22no—
94C2×D3C3×D414yescomplemented
95C3×C4—22no—
96C3×C4—21no—
97C3×C4—21no—
98C3×C4—62no—
99Dic3—22no—
100C32#12011yescharacteristic, complemented, Sylow
101C23—32no—
102C23—64no—
103C23—62no—
104C23C2×C3×D311yescharacteristic
105C23C2×C3×D311yescharacteristic, complemented
106D4—22no—
107D4—64no—
108C2×C4—32no—
109C2×C4C2×C3×D311yescharacteristic, complemented
110C2×C3—22no—
111C2×C3—22no—
112C2×C3—22no—
113C2×C3—21no—
114C2×C3—42no—
115C2×C3—42no—
116C2×C3—41no—
117C2×C3—41no—
118C2×C3—64no—
119C2×C3D3×D412yes—
120C2×C3C2×#6711yescharacteristic
121C2×C3C2×C3×D412yes—
122C2×C3C2×C3×D411yescharacteristic
123D3—24no—
124C22—22no—
125C22—22no—
126C22—21no—
127C22—34no—
128C22—68no—
129C22—62no—
130C22—62no—
131C22C3×#6712yescomplemented
132C22C22×C3×D311yescharacteristic
133C4—21no—
134C4—62no—
135C3—21no—
136C3#93711yescharacteristic, direct product factor
137C3C3×#12011yescharacteristic, complemented
138C2—22no—
139C2—41no—
140C2—64no—
141C2C3×D3×D412yes—
142C2C2×C3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D3
commutator, cosocleC22×C3C23×C3
FrattiniC22C22×C3×D3
FittingC2×C32×D4C2
socleC22×C32C23
hypercenterC2×C3×D4D3
hypocenterC3C3×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C3×D3C2semidirect
2. C2×C32×D4C2semidirect
3. C2×C3×#67C2semidirect
4. C3×#217C2semidirect
5. C3×(C2×D3)⋊C4C2semidirect
7. #937C3direct (N × H)
9. C23×C32C22semidirect
14. C2×C32×C4C22semidirect
16. C2×C3×Dic3C22semidirect
18. C23×D3C2×C3semidirect
21. C2×C3×D4D3semidirect
22. C2×C3×D4C2×C3semidirect
23. C2×#67C2×C3semidirect
26. #217C2×C3semidirect
27. (C2×D3)⋊C4C2×C3semidirect
31. C22×C32D4semidirect
36. C2×C3×D3D4semidirect
46. C23×C3C2×D3semidirect
48. C23×C3C22×C3semidirect
58. C2×C3×C4C2×D3semidirect
59. C2×C3×C4C22×C3semidirect
61. C2×Dic3C22×C3semidirect
69. C2×D4C3×D3semidirect
87. C22×C3#67semidirect
88. C22×C3C3×D4semidirect
94. C2×D3C3×D4semidirect
100. C32#120semidirect
105. C23C2×C3×D3semidirect
109. C2×C4C2×C3×D3semidirect
131. C22C3×#67semidirect
136. C3#937direct (N × H)
137. C3C3×#120semidirect

Maximal subgroups

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

subgroupindex
C23×C3×D32
C2×C32×D42
C2×C3×#672
C3×#2172
C3×(C2×D3)⋊C42
C3×#1203
#9373