Finite Group Databasebeta

← C22⋊(#95⋊C9) #11919637

Subgroups — C22⋊(#95⋊C9) #11919637

Order 1152.

671 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 671 conjugacy classes of subgroups — too many to draw. Only its 39 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
2C2×C22⋊(C22⋊C9)—41nomaximal
3#95⋊C9—44nomaximal
4C24×C3×C4—31no—
5C2×C3×#95—34no—
6C22⋊(C22⋊C9)—41no—
7C22×#95C911yescharacteristic, complemented, Sylow
8C25×C3A411yescharacteristic
9C23×C3×C4—38no—
10C23×C3×C4—36no—
11C23×C3×C4—68no—
12C3×#95—34no—
13C3×#95A414yes—
14C2×C22⋊C9—164no—
15C2×C22⋊C9—161no—
16C24×C4—31no—
17C2×#95—34no—
18C24×C3—31no—
19C24×C3—34no—
20C24×C3—34no—
21C24×C3—31no—
22C24×C3SL(2,𝔽3)11yescharacteristic
23C22×C3×C4—324no—
24C22×C3×C4—34no—
25C22×C3×C4—624no—
26C22×C3×C4—624no—
27C22×C3×C4—68no—
28C22⋊C9—164no—
29C22⋊C9—161no—
30C25C22⋊C911yescharacteristic
31C23×C4—36no—
32C23×C4—38no—
33C23×C4—68no—
34#95—34no—
35#95C22⋊C914yescomplemented
36C23×C3—36no—
37C23×C3—36no—
38C23×C3—312no—
39C23×C3—312no—
40C23×C3—34no—
41C23×C3—34no—
42C23×C3—34no—
43C23×C3—31no—
44C23×C3—31no—
45C23×C3C42⋊C314yes—
46C23×C3C22⋊A411yescharacteristic
47C2×C3×C4—38no—
48C2×C3×C4—68no—
49C2×C3×C4—648no—
50C2×C9—641no—
51C24—34no—
52C24—31no—
53C24—34no—
54C24—31no—
55C24Q8⋊C911yescharacteristic
56C22×C4—324no—
57C22×C4—34no—
58C22×C4—624no—
59C22×C4—624no—
60C22×C4—68no—
61C22×C3—31no—
62C22×C3—34no—
63C22×C3—312no—
64C22×C3—312no—
65C22×C3—36no—
66C22×C3—34no—
67C22×C3—36no—
68C22×C3—31no—
69C22×C3—34no—
70C22×C3#95⋊C314yes—
71C22×C3C22⋊SL(2,𝔽3)11yescharacteristic
72C3×C4—68no—
73C9—641noSylow
74C23—36no—
75C23—36no—
76C23—312no—
77C23—312no—
78C23—34no—
79C23—34no—
80C23—34no—
81C23—31no—
82C23—31no—
83C23C42⋊C914yes—
84C23C22⋊(C22⋊C9)11yescharacteristic
85C2×C4—38no—
86C2×C4—68no—
87C2×C4—648no—
88C2×C3—31no—
89C2×C3—34no—
90C2×C3—34no—
91C2×C3—31no—
92C2×C3C22⋊(C42⋊C3)11yescharacteristic
93C22—31no—
94C22—34no—
95C22—312no—
96C22—34no—
97C22—36no—
98C22—312no—
99C22—36no—
100C22—31no—
101C22—34no—
102C22#95⋊C914yescomplemented
103C22C22⋊(Q8⋊C9)11yescharacteristic
104C4—68no—
105C3C22⋊(#95⋊C3)11yescharacteristic
106C2—31no—
107C2—34no—
108C2—31no—
109C2—34no—
110C2C22⋊(C42⋊C9)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3C22⋊(C42⋊C3)
commutator, hypocenterC22×#95C9
FrattiniC23×C3C22⋊A4
Fitting, cosocleC22×C3×#95C3
socle, prime radicalC25×C3A4
LCSG ▷ C22×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
7. C22×#95C9semidirect
35. #95C22⋊C9semidirect
102. C22#95⋊C9semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#953
C2×C22⋊(C22⋊C9)4
#95⋊C94