Finite Group Databasebeta

← C3×#73293 #11919656

Subgroups — C3×#73293 #11919656

Order 1152.

476 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 50 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×#2840C311yesmaximal, characteristic, complemented
2#73293C313yesmaximal, direct product factor
3C23×C3×A4—41nomaximal
4C22×C3×SL(2,𝔽3)—44nomaximal
5C3×#393—34no—
6C3×#379—31no—
7C22×C3×A4—46no—
8C22×C3×A4—41no—
9C2×C3×SL(2,𝔽3)—412no—
10#2840C3211yescharacteristic, complemented, Sylow
11C25×C3A411yescharacteristic
12C23×A4—43no—
13C22×C3×Q8A414yescomplemented
14C22×SL(2,𝔽3)—412no—
15C2×C3×C22⋊C4—36no—
16C3×#95—34no—
17C23×C32—161no—
18C2×C3×A4—43no—
19C2×C3×A4—44no—
20C3×SL(2,𝔽3)—44no—
21#393—34no—
22#379—31no—
23C24×C3—31no—
24C24×C3—31no—
25C24×C3—46no—
26C24×C3SL(2,𝔽3)11yescharacteristic, complemented
27C22×A4—418no—
28C22×A4—43no—
29C2×C3×Q8—412no—
30C22×C3×C4—34no—
31C2×SL(2,𝔽3)—436no—
32C3×C22⋊C4—126no—
33C22×C32—161no—
34C22×C32—166no—
35C3×A4—41no—
36C25C3×A411yescharacteristic
37C22×Q8C3×A414yescomplemented
38C2×C22⋊C4—36no—
39#95—34no—
40C23×C3—31no—
41C23×C3—31no—
42C23×C3—43no—
43C23×C3—44no—
44C23×C3—66no—
45C23×C3—123no—
46C23×C3—124no—
47C23×C3—163no—
48C23×C3C22⋊A411yescharacteristic
49C2×A4—49no—
50C2×A4—412no—
51C3×Q8—44no—
52C3×Q8—124no—
53C2×C3×C4—612no—
54SL(2,𝔽3)—412no—
55C2×C32—163no—
56C2×C32—164no—
57C24—31no—
58C24—31no—
59C24—46no—
60C24C3×SL(2,𝔽3)11yescharacteristic, complemented
61C2×Q8—412no—
62C22×C4—34no—
63C22⋊C4—126no—
64C22×C3—41no—
65C22×C3—63no—
66C22×C3—63no—
67C22×C3—121no—
68C22×C3—124no—
69C22×C3—124no—
70C22×C3—163no—
71C22×C3—1618no—
72C22×C3C22⋊SL(2,𝔽3)11yescharacteristic
73C22×C3#99716yes—
74A4—43no—
75C3×C4—124no—
76C32—161noSylow
77C23—31no—
78C23—31no—
79C23—43no—
80C23—44no—
81C23—66no—
82C23—123no—
83C23—124no—
84C23C3×C22⋊A411yescharacteristic
85Q8—44no—
86Q8—124no—
87C2×C4—612no—
88C2×C3—121no—
89C2×C3—121no—
90C2×C3—169no—
91C2×C3—1612no—
92C2×C3#543⋊C313yes—
93C2×C3#546514yes—
94C22—41no—
95C22—63no—
96C22—63no—
97C22—121no—
98C22—124no—
99C22—124no—
100C22C3×C22⋊SL(2,𝔽3)11yescharacteristic
101C22C3×#99716yes—
102C4—124no—
103C3—163no—
104C3#7329311yescharacteristic, direct product factor
105C2—121no—
106C2—121no—
107C2C3×#543⋊C313yes—
108C2C3×#546514yes—
subgroupG/H
center, socle, hypercenterC23×C3C22⋊A4
commutator, cosocle, hypocenter#2840C32
FrattiniC23C3×C22⋊A4
FittingC3×#2840C3
LCSG ▷ #2840
UCSC1 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C3×#2840C3semidirect
2. #73293C3direct (N × H)
10. #2840C32semidirect
13. C22×C3×Q8A4semidirect
26. C24×C3SL(2,𝔽3)semidirect
37. C22×Q8C3×A4semidirect
60. C24C3×SL(2,𝔽3)semidirect
104. C3#73293direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#28403
#732933
C23×C3×A44
C22×C3×SL(2,𝔽3)4