Finite Group Databasebeta

← C23×C3×#157 #11724748

Subgroups — C23×C3×#157 #11724748

Order 864.

804 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C3⋊D3C211yesmaximal, characteristic
2C22×C3×#157C2114yesmaximal, direct product factor
3C23×#157C311yesmaximal, characteristic, direct product factor
4C23×C33C411yescharacteristic, complemented
5C22×C3×C3⋊D3C417yescomplemented
6C22×C3×C3⋊D3C2217yes—
7C2×C3×#157C22128yesdirect product factor
8C23×C3⋊D3C2×C311yescharacteristic
9C23×C3×D3—62no—
10C22×#157C2×C3114yesdirect product factor
11C22×C33C2×C417yescomplemented
12C2×C3×C3⋊D3C2×C4121yescomplemented
13C2×C3×C3⋊D3C2317yes—
14C3×#157C2318yesdirect product factor
15C23×C3×C4—91nomaximal
16C23×C32—22no—
17C23×C32—42no—
18C23×C32C3×C411yescharacteristic, complemented
19C22×C3⋊D3C3×C417yescomplemented
20C22×C3⋊D3C22×C317yes—
21C22×C3×D3—614no—
22C22×C3×D3—614no—
23C2×#157C22×C3128yesdirect product factor
24C2×C33C22×C417yescomplemented
25C3×C3⋊D3C22×C417yescomplemented
26C3×C3⋊D3C2411yescharacteristic
27C24×C3—91no—
28C23×D3—62no—
29C22×C3×C4—914no—
30C22×C32—214no—
31C22×C32—414no—
32C22×C32C2×C3×C417yescomplemented
33C2×C3⋊D3C2×C3×C4121yescomplemented
34C2×C3⋊D3C23×C317yes—
35C2×C3×D3—642no—
36C2×C3×D3—614no—
37#157C23×C318yesdirect product factor
38C23×C4—91noSylow
39C33C23×C411yescharacteristic, complemented, Sylow
40C23×C3—22no—
41C23×C3—42no—
42C23×C3—97no—
43C23×C3—97no—
44C23×C3#15711yescharacteristic, direct product factor
45C22×D3—614no—
46C22×D3—614no—
47C2×C3×C4—928no—
48C2×C32—214no—
49C2×C32—414no—
50C2×C32C22×C3×C417yescomplemented
51C3⋊D3C22×C3×C417yescomplemented
52C3⋊D3C24×C311yescharacteristic
53C3×D3—614no—
54C3×D3—62no—
55C24—91no—
56C22×C4—914no—
57C22×C3—214no—
58C22×C3—414no—
59C22×C3—97no—
60C22×C3—921no—
61C22×C3C2×#15717yesdirect product factor
62C2×D3—642no—
63C2×D3—614no—
64C3×C4—98no—
65C32—22no—
66C32—42no—
67C32C23×C3×C411yescharacteristic, complemented
68C23—97no—
69C23—97no—
70C23C3×#15711yescharacteristic, direct product factor
71C2×C4—928no—
72C2×C3—214no—
73C2×C3—414no—
74C2×C3—91no—
75C2×C3—97no—
76C2×C3C22×#15717yesdirect product factor
77D3—614no—
78D3—62no—
79C22—97no—
80C22—921no—
81C22C2×C3×#15717yesdirect product factor
82C4—98no—
83C3—22no—
84C3—42no—
85C3C23×#15711yescharacteristic, direct product factor
86C2—91no—
87C2—97no—
88C2C22×C3×#15717yesdirect product factor
subgroupG/H
center, hypercenterC23×C3#157
commutator, hypocenterC32C23×C3×C4
FrattiniC1G
Fitting, socleC23×C33C4
prime radicalC23×C3×C3⋊D3C2
cosocleC3⋊D3C24×C3
LCSG ▷ C32
UCSC1 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
2. C22×C3×#157C2direct (N × H)
3. C23×#157C3direct (N × H)
4. C23×C33C4semidirect
5. C22×C3×C3⋊D3C4semidirect
7. C2×C3×#157C22direct (N × H)
10. C22×#157C2×C3direct (N × H)
11. C22×C33C2×C4semidirect
12. C2×C3×C3⋊D3C2×C4semidirect
14. C3×#157C23direct (N × H)
18. C23×C32C3×C4semidirect
19. C22×C3⋊D3C3×C4semidirect
23. C2×#157C22×C3direct (N × H)
24. C2×C33C22×C4semidirect
25. C3×C3⋊D3C22×C4semidirect
32. C22×C32C2×C3×C4semidirect
33. C2×C3⋊D3C2×C3×C4semidirect
37. #157C23×C3direct (N × H)
39. C33C23×C4semidirect
44. C23×C3#157direct (N × H)
50. C2×C32C22×C3×C4semidirect
51. C3⋊D3C22×C3×C4semidirect
61. C22×C3C2×#157direct (N × H)
67. C32C23×C3×C4semidirect
70. C23C3×#157direct (N × H)
76. C2×C3C22×#157direct (N × H)
81. C22C2×C3×#157direct (N × H)
85. C3C23×#157direct (N × H)
88. C2C22×C3×#157direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C3⋊D32
C22×C3×#1572
C23×#1573
C23×C3×C49