Finite Group Databasebeta

← C3×#73284 #11919638

Subgroups — C3×#73284 #11919638

Order 1152.

308 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 34 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×C42×Q8C311yesmaximal, characteristic, complemented
2#73284C313yesmaximal, direct product factor
3C3×C22⋊SL(2,𝔽3)—41nomaximal
4C2×C3×C42⋊C3—41nomaximal
5C3×#95⋊C3—43nomaximal
6C2×C3×C4×Q8—31no—
7C3×C4×C4⋊C4—33no—
8C3×C43—31no—
9C3×C42⋊C3—41no—
10C42×Q8C3211yescharacteristic, complemented, Sylow
11C22×C3×Q8A411yescharacteristic
12C22⋊SL(2,𝔽3)—43no—
13C3×C4×Q8—38no—
14C2×C3×C4⋊C4—33no—
15C2×C3×C42—33no—
16C2×C3×C42—33no—
17C2×C3×C42A411yescharacteristic
18C2×C42⋊C3—43no—
19C3×#95—31no—
20C3×#95A413yes—
21#95⋊C3—49no—
22C2×C3×A4—161no—
23C3×SL(2,𝔽3)—164no—
24C2×C4×Q8—31no—
25C4×C4⋊C4—33no—
26C43—31no—
27C2×C3×Q8—34no—
28C22×C3×C4—31no—
29C22×C3×C4—31no—
30C22×C3×C4—33no—
31C3×C4⋊C4—312no—
32C3×C42—31no—
33C3×C42—312no—
34C3×C42—66no—
35C3×C42SL(2,𝔽3)11yescharacteristic, complemented
36C42⋊C3—43no—
37C3×A4—161no—
38C22×Q8C3×A411yescharacteristic
39C4×Q8—38no—
40C2×C4⋊C4—33no—
41C2×C42—33no—
42C2×C42—33no—
43C2×C42C3×A411yescharacteristic
44#95—31no—
45#95C3×A413yes—
46C23×C3C22⋊A411yescharacteristic
47C2×A4—163no—
48C3×Q8—34no—
49C3×Q8C42⋊C314yescomplemented
50C2×C3×C4—32no—
51C2×C3×C4—36no—
52C2×C3×C4—32no—
53C2×C3×C4—31no—
54C2×C3×C4—31no—
55C2×C3×C4—36no—
56C2×C3×C4—66no—
57SL(2,𝔽3)—1612no—
58C2×C32—641no—
59C2×Q8—34no—
60C22×C4—31no—
61C22×C4—31no—
62C22×C4—33no—
63C4⋊C4—312no—
64C42—31no—
65C42—312no—
66C42—66no—
67C42C3×SL(2,𝔽3)11yescharacteristic, complemented
68C22×C3—31no—
69C22×C3—31no—
70C22×C3C22⋊SL(2,𝔽3)11yescharacteristic
71A4—163no—
72C3×C4—32no—
73C3×C4—32no—
74C3×C4—34no—
75C3×C4—66no—
76C32—641noSylow
77C23C3×C22⋊A411yescharacteristic
78Q8—34no—
79Q8C3×C42⋊C314yescomplemented
80C2×C4—32no—
81C2×C4—36no—
82C2×C4—32no—
83C2×C4—31no—
84C2×C4—31no—
85C2×C4—36no—
86C2×C4—66no—
87C2×C3—31no—
88C2×C3—31no—
89C2×C3—643no—
90C2×C3C22⋊(C42⋊C3)11yescharacteristic
91C22—31no—
92C22—31no—
93C22C3×C22⋊SL(2,𝔽3)11yescharacteristic
94C4—32no—
95C4—32no—
96C4—34no—
97C4—66no—
98C3—643no—
99C3#7328411yescharacteristic, direct product factor
100C2—31no—
101C2—31no—
102C2C3×C22⋊(C42⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C22⋊(C42⋊C3)
commutator, cosocle, hypocenterC42×Q8C32
FrattiniC23C3×C22⋊A4
FittingC3×C42×Q8C3
socleC23×C3C22⋊A4
LCSG ▷ C42×Q8
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C3×C42×Q8C3semidirect
2. #73284C3direct (N × H)
10. C42×Q8C32semidirect
35. C3×C42SL(2,𝔽3)semidirect
49. C3×Q8C42⋊C3semidirect
67. C42C3×SL(2,𝔽3)semidirect
79. Q8C3×C42⋊C3semidirect
99. C3#73284direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C42×Q83
#732843
C3×C22⋊SL(2,𝔽3)4
C2×C3×C42⋊C34
C3×#95⋊C34