Finite Group Databasebeta

← C3×#1655⋊C3 #11919326

Subgroups — C3×#1655⋊C3 #11919326

Order 1152.

162 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 20 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
1C3×#5464C211yesmaximal, characteristic, complemented
2C3×#1655C311yesmaximal, characteristic, complemented
3#1655⋊C3C313yesmaximal, direct product factor
4C3×#127⋊C3—41nomaximal
5C3×H(3,𝔽4)C2×C311yescharacteristic, complemented
6#5464C2×C313yescomplemented
7C3×#496—31no—
8C3×#329—31no—
9C3×C22⋊A4—81no—
10C3×C42⋊C3—41no—
11C3×C42⋊C3—81no—
12#1655C3211yescharacteristic, complemented, Sylow
13C2×C3×SD16—61no—
14C2×C3×D8—61no—
15C3×#127A411yescharacteristic, complemented
16C3×#124—31no—
17C3×#124—61no—
18C3×#120—61no—
19#127⋊C3—43no—
20C3×#97—31no—
21C2×C3×A4—161no—
22H(3,𝔽4)C2×C3211yescharacteristic, complemented
23#496—31no—
24#329—31no—
25C24×C3—21no—
26C22⋊A4—83no—
27C2×C3×Q8—31no—
28C2×C3×D4—31no—
29C2×C3×D4—61no—
30C2×C3×D4—61no—
31C3×SD16—122no—
32C3×D8—122no—
33C2×C3×C8—61no—
34C3×C22⋊C4—62no—
35C3×C22⋊C4—61no—
36C3×C42—21no—
37C3×C42C2×A411yescharacteristic
38C42⋊C3—43no—
39C42⋊C3—83no—
40C3×A4—161no—
41C3×A4—324no—
42C2×SD16—61no—
43C2×D8—61no—
44#127C3×A411yescharacteristic, complemented
45#124—31no—
46#124—61no—
47#120—61no—
48#97—31no—
49C23×C3—41no—
50C23×C3—61no—
51C23×C3—241no—
52C2×A4—163no—
53C3×Q8—121no—
54C3×D4—121no—
55C3×D4—121no—
56C3×D4—121no—
57C3×D4—241no—
58C2×C3×C4—31no—
59C2×C3×C4—61no—
60C3×C8—62no—
61C2×C32—641no—
62C24—21no—
63C2×Q8—31no—
64C2×D4—31no—
65C2×D4—61no—
66C2×D4—61no—
67SD16—122no—
68D8—122no—
69C2×C8—61no—
70C22⋊C4—62no—
71C22⋊C4—61no—
72C42—21no—
73C42C2×C3×A411yescharacteristic
74C22×C3—84no—
75C22×C3—121no—
76C22×C3—122no—
77C22×C3—241no—
78C22×C3#120⋊C311yescharacteristic
79A4—163no—
80A4—3212no—
81C3×C4—61no—
82C3×C4—121no—
83C32—641noSylow
84C23—41no—
85C23—61no—
86C23—241no—
87Q8—121no—
88D4—121no—
89D4—121no—
90D4—121no—
91D4—241no—
92C2×C4—31no—
93C2×C4—61no—
94C8—62no—
95C2×C3—31no—
96C2×C3—161no—
97C2×C3—241no—
98C2×C3—643no—
99C22—84no—
100C22—121no—
101C22—122no—
102C22—241no—
103C22C3×#120⋊C311yescharacteristic
104C4—61no—
105C4—121no—
106C3—643no—
107C3#1655⋊C311yescharacteristic, direct product factor
108C2—31no—
109C2—161no—
110C2—241no—
subgroupG/H
center, hypercenterC3#1655⋊C3
commutator, cosocle, hypocenterH(3,𝔽4)C2×C32
FrattiniC42C2×C3×A4
FittingC3×#1655C3
socleC22×C3#120⋊C3
LCSG ▷ H(3,𝔽4)
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#5464C2semidirect
2. C3×#1655C3semidirect
3. #1655⋊C3C3direct (N × H)
5. C3×H(3,𝔽4)C2×C3semidirect
6. #5464C2×C3semidirect
12. #1655C32semidirect
15. C3×#127A4semidirect
22. H(3,𝔽4)C2×C32semidirect
44. #127C3×A4semidirect
107. C3#1655⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#54642
C3×#16553
#1655⋊C33
C3×#127⋊C34