Finite Group Databasebeta

← C3×C22⋊(#95⋊C3) #11919636

Subgroups — C3×C22⋊(#95⋊C3) #11919636

Order 1152.

728 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C22×C3×#95C311yesmaximal, characteristic, complemented
2C22⋊(#95⋊C3)C313yesmaximal, direct product factor
3C2×C3×C22⋊A4—41nomaximal
4C3×#95⋊C3—44nomaximal
5C24×C3×C4—31no—
6C2×C3×#95—34no—
7C3×C22⋊A4—41no—
8C22×#95C3211yescharacteristic, complemented, Sylow
9C25×C3A411yescharacteristic
10C2×C22⋊A4—43no—
11C23×C3×C4—38no—
12C23×C3×C4—36no—
13C23×C3×C4—68no—
14C3×#95—34no—
15C3×#95A414yescomplemented
16#95⋊C3—412no—
17C2×C3×A4—164no—
18C2×C3×A4—161no—
19C24×C4—31no—
20C2×#95—34no—
21C24×C3—31no—
22C24×C3—34no—
23C24×C3—34no—
24C24×C3—31no—
25C24×C3SL(2,𝔽3)11yescharacteristic
26C22⋊A4—43no—
27C22×C3×C4—324no—
28C22×C3×C4—34no—
29C22×C3×C4—624no—
30C22×C3×C4—624no—
31C22×C3×C4—68no—
32C3×A4—164no—
33C3×A4—161no—
34C25C3×A411yescharacteristic
35C23×C4—36no—
36C23×C4—38no—
37C23×C4—68no—
38#95—34no—
39#95C3×A414yescomplemented
40C23×C3—36no—
41C23×C3—36no—
42C23×C3—312no—
43C23×C3—312no—
44C23×C3—34no—
45C23×C3—34no—
46C23×C3—34no—
47C23×C3—31no—
48C23×C3—31no—
49C23×C3C42⋊C314yes—
50C23×C3C22⋊A411yescharacteristic
51C2×A4—163no—
52C2×A4—1612no—
53C2×C3×C4—38no—
54C2×C3×C4—68no—
55C2×C3×C4—648no—
56C2×C32—641no—
57C24—34no—
58C24—31no—
59C24—31no—
60C24—34no—
61C24C3×SL(2,𝔽3)11yescharacteristic
62C22×C4—324no—
63C22×C4—34no—
64C22×C4—624no—
65C22×C4—624no—
66C22×C4—68no—
67C22×C3—31no—
68C22×C3—34no—
69C22×C3—312no—
70C22×C3—312no—
71C22×C3—36no—
72C22×C3—34no—
73C22×C3—36no—
74C22×C3—31no—
75C22×C3—34no—
76C22×C3#95⋊C314yescomplemented
77C22×C3C22⋊SL(2,𝔽3)11yescharacteristic
78A4—163no—
79A4—1612no—
80C3×C4—68no—
81C32—641noSylow
82C23—36no—
83C23—36no—
84C23—312no—
85C23—312no—
86C23—34no—
87C23—31no—
88C23—31no—
89C23—34no—
90C23—34no—
91C23C3×C42⋊C314yes—
92C23C3×C22⋊A411yescharacteristic
93C2×C4—38no—
94C2×C4—68no—
95C2×C4—648no—
96C2×C3—31no—
97C2×C3—34no—
98C2×C3—34no—
99C2×C3—31no—
100C2×C3—643no—
101C2×C3C22⋊(C42⋊C3)11yescharacteristic
102C22—31no—
103C22—34no—
104C22—312no—
105C22—36no—
106C22—36no—
107C22—34no—
108C22—312no—
109C22—31no—
110C22—34no—
111C22C3×#95⋊C314yescomplemented
112C22C3×C22⋊SL(2,𝔽3)11yescharacteristic
113C4—68no—
114C3—643no—
115C3C22⋊(#95⋊C3)11yescharacteristic, direct product factor
116C2—31no—
117C2—31no—
118C2—34no—
119C2—34no—
120C2C3×C22⋊(C42⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C22⋊(C42⋊C3)
commutator, cosocle, hypocenterC22×#95C32
FrattiniC23C3×C22⋊A4
FittingC22×C3×#95C3
socleC25×C3A4
LCSG ▷ C22×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×#95C3semidirect
2. C22⋊(#95⋊C3)C3direct (N × H)
8. C22×#95C32semidirect
15. C3×#95A4semidirect
39. #95C3×A4semidirect
76. C22×C3#95⋊C3semidirect
111. C22C3×#95⋊C3semidirect
115. C3C22⋊(#95⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#953
C22⋊(#95⋊C3)3
C2×C3×C22⋊A44
C3×#95⋊C34