Finite Group Databasebeta

← C2×C3⋊#1113 #10620232

Subgroups — C2×C3⋊#1113 #10620232

Order 648.

630 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 83 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⋊(C3⋊D3)C212yesmaximal, complemented
2C2×C32×C3⋊D3C211yesmaximal, characteristic, complemented
3C3⋊#1113C214yesmaximal, direct product factor
4C2×#1113—34nomaximal
5C2×D3×C3⋊D3—32nomaximal
6C2×C34C2211yescharacteristic, complemented
7C3×C3⋊(C3⋊D3)C2214yescomplemented
8C32×C3⋊D3C2212yescomplemented
9C2×C3⋊(C3⋊D3)D312yescomplemented
10C2×C3×C3⋊D3—32no—
11C2×C3×C3⋊D3—38no—
12C2×C3×C3⋊D3—68no—
13C2×C3×C3⋊D3D314yescomplemented
14C2×C32×D3—32no—
15C2×C32×D3—61no—
16#1113—316no—
17D3×C3⋊D3—38no—
18C34C2311yescharacteristic, complemented, Sylow
19C22×C3⋊D3—91no—
20C2×D32—98no—
21C2×D32—91no—
22C2×C33—21no—
23C2×C33—28no—
24C2×C33—44no—
25C2×C33C2×D312yescomplemented
26C2×C33C2×D314yescomplemented
27C3⋊(C3⋊D3)C2×D314yescomplemented
28C3×C3⋊D3—34no—
29C3×C3⋊D3—316no—
30C3×C3⋊D3—616no—
31C3×C3⋊D3C2×D318yescomplemented
32C32×D3—34no—
33C32×D3—62no—
34C22×C32—91no—
35C2×C3⋊D3—32no—
36C2×C3⋊D3—38no—
37C2×C3⋊D3—68no—
38C2×C3⋊D3—94no—
39C2×C3⋊D3C3⋊D311yescharacteristic, complemented
40C2×C3×D3—38no—
41C2×C3×D3—64no—
42C2×C3×D3—98no—
43C2×C3×D3—92no—
44C2×C3×D3—188no—
45D32—932no—
46D32—94no—
47C33—21no—
48C33—28no—
49C33—44no—
50C33C22×D312yescomplemented
51C33C22×D314yescomplemented
52C22×D3—272no—
53C22×D3—274no—
54C2×C32—28no—
55C2×C32—28no—
56C2×C32—24no—
57C2×C32—44no—
58C2×C32—412no—
59C2×C32—44no—
60C2×C32—92no—
61C2×C32D3218yescomplemented
62C2×C32D3211yescharacteristic, complemented
63C2×C32C2×C3⋊D311yescharacteristic, complemented
64C3⋊D3—34no—
65C3⋊D3—316no—
66C3⋊D3—616no—
67C3⋊D3C2×C3⋊D312yescomplemented
68C3×D3—316no—
69C3×D3—68no—
70C3×D3—916no—
71C3×D3—94no—
72C3×D3—1816no—
73C22×C3—94no—
74C22×C3—272no—
75C2×D3—32no—
76C2×D3—61no—
77C2×D3—92no—
78C2×D3—98no—
79C2×D3—188no—
80C2×D3—278no—
81C2×D3—2716no—
82C32—28no—
83C32—28no—
84C32—24no—
85C32—44no—
86C32—412no—
87C32—44no—
88C32C2×D3218yescomplemented
89C32C2×D3211yescharacteristic, complemented
90C32C22×C3⋊D311yescharacteristic, complemented
91C23—811noSylow
92C2×C3—21no—
93C2×C3—28no—
94C2×C3—44no—
95C2×C3—98no—
96C2×C3—274no—
97C2×C3D3×C3⋊D312yescomplemented
98C2×C3#111314yescomplemented
99D3—34no—
100D3—62no—
101D3—94no—
102D3—916no—
103D3—1816no—
104C22—91no—
105C22—272no—
106C22—814no—
107C3—21no—
108C3—28no—
109C3—44no—
110C3C2×D3×C3⋊D312yescomplemented
111C3C2×#111314yescomplemented
112C2—92no—
113C2—274no—
114C2C3⋊#111311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#1113
commutator, cosocle, hypocenterC34C23
FrattiniC1G
Fitting, socleC2×C34C22
LCSG ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C3⋊(C3⋊D3)C2semidirect
2. C2×C32×C3⋊D3C2semidirect
3. C3⋊#1113C2direct (N × H)
6. C2×C34C22semidirect
7. C3×C3⋊(C3⋊D3)C22semidirect
8. C32×C3⋊D3C22semidirect
9. C2×C3⋊(C3⋊D3)D3semidirect
13. C2×C3×C3⋊D3D3semidirect
18. C34C23semidirect
25. C2×C33C2×D3semidirect
26. C2×C33C2×D3semidirect
27. C3⋊(C3⋊D3)C2×D3semidirect
31. C3×C3⋊D3C2×D3semidirect
39. C2×C3⋊D3C3⋊D3semidirect
50. C33C22×D3semidirect
51. C33C22×D3semidirect
61. C2×C32D32semidirect
62. C2×C32D32semidirect
63. C2×C32C2×C3⋊D3semidirect
67. C3⋊D3C2×C3⋊D3semidirect
88. C32C2×D32semidirect
89. C32C2×D32semidirect
90. C32C22×C3⋊D3semidirect
97. C2×C3D3×C3⋊D3semidirect
98. C2×C3#1113semidirect
110. C3C2×D3×C3⋊D3semidirect
111. C3C2×#1113semidirect
114. C2C3⋊#1113direct (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⋊(C3⋊D3)2
C2×C32×C3⋊D32
C3⋊#11132
C2×#11133
C2×D3×C3⋊D33