Finite Group Databasebeta

← #14516513

Subgroups — #14516513

Order 1944.

196 conjugacy classes of subgroups; only the 17 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 17 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
1#11757410C211yesmaximal, characteristic, complemented
2C3×(C3⋊D3)⋊A4—31nomaximal
3C22×#4181C311yesmaximal, characteristic, complemented
4#92161—41nomaximal
5C3×C22⋊H(3,𝔽3)D311yescharacteristic
6C3×#1094—21no—
7C22×C32⋊C9C2×C311yescharacteristic, complemented
8C2×#4181—31no—
9C2×#4181—31no—
10#6857—41noSylow
11C22×C3×C3⋊D3—31no—
12C3×D3×A4—91no—
13C22×C3×D9—91no—
14(C3⋊D3)⋊A4—33no—
15C3×(C3⋊D3)⋊C3—121no—
16C2×C32⋊C9—31no—
17#4181—31no—
18#4181A411yescharacteristic, complemented
19C22×C33C3×D311yescharacteristic
20C2×C3×C3⋊D3—91no—
21C2×C3×C3⋊D3—91no—
22C32×A4—31no—
23C22×C3×C9—31no—
24C2×C3×D9—93no—
25C2×C3×D9—93no—
26C22⋊H(3,𝔽3)—33no—
27#1094—63no—
28C3×C22⋊C9—61no—
29C3×3−1+2—81no—
30C3×H(3,𝔽3)—41no—
31C32⋊C9C2×A411yescharacteristic, complemented
32C22×C3⋊D3—31no—
33C22×C3×D3—91no—
34C22×C3×D3—271no—
35C2×C3×A4—271no—
36D3×A4—93no—
37C22×D9—91no—
38C2×C33—31no—
39C3×C3⋊D3—31no—
40C3×C3⋊D3—91no—
41C32×D3—361no—
42C2×C3×C9—33no—
43(C3⋊D3)⋊C3—123no—
44C3×D9—91no—
45C3×D9—93no—
46C22×C32—31no—
47C22×C32—31no—
48C22×C32—61no—
49C22×C32(C3⋊D3)⋊C311yescharacteristic
50C2×C3⋊D3—91no—
51C2×C3⋊D3—91no—
52C2×C3×D3—271no—
53C2×C3×D3—273no—
54C2×C3×D3—273no—
55C2×C3×D3—271no—
56C3×A4—33no—
57C3×A4—91no—
58C3×A4—181no—
59C22×C9—91no—
60C2×D9—93no—
61C2×D9—93no—
62C22⋊C9—63no—
63C33—121no—
64C33D3×A411yescharacteristic
653−1+2—243no—
66H(3,𝔽3)—123no—
67C3×C9—31no—
68C3×C9—241no—
69C23×C3—271no—
70C22×D3—91no—
71C22×D3—271no—
72C2×A4—273no—
73C2×C32—31no—
74C2×C32—33no—
75C2×C32—91no—
76C2×C32—181no—
77C2×C32—1081no—
78C3⋊D3—31no—
79C3⋊D3—91no—
80C3×D3—91no—
81C3×D3—271no—
82C3×D3—273no—
83C3×D3—271no—
84C3×D3—363no—
85C2×C9—93no—
86D9—91no—
87D9—93no—
88C22×C3—21no—
89C22×C3—91no—
90C22×C3—811no—
91C22×C3—811no—
92C22×C3#417411yescharacteristic
93C22×C3#417711yescharacteristic
94C2×D3—271no—
95C2×D3—273no—
96C2×D3—273no—
97C2×D3—271no—
98A4—93no—
99C32—31no—
100C32—31no—
101C32—61no—
102C32—123no—
103C32—361no—
104C32—721no—
105C32(C3⋊D3)⋊A411yescharacteristic
106C9—91no—
107C9—243no—
108C23—271noSylow
109C2×C3—31no—
110C2×C3—31no—
111C2×C3—61no—
112C2×C3—93no—
113C2×C3—271no—
114C2×C3—811no—
115C2×C3—1083no—
116D3—91no—
117D3—271no—
118D3—273no—
119D3—271no—
120C22—811no—
121C22—811no—
122C22#9216111yescharacteristic, complemented
123C3—21no—
124C3—91no—
125C3—363no—
126C3#1061976911yescharacteristic
127C3#1061977311yescharacteristic
128C2—31no—
129C2—271no—
130C2—811no—
subgroupG/H
center, hypercenterC3#10619769
commutator, Fitting, cosocle, hypocenterC22×C32⋊C9C2×C3
FrattiniC33D3×A4
socleC22×C32(C3⋊D3)⋊C3
LCSG ▷ C22×C32⋊C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #11757410C2semidirect
3. C22×#4181C3semidirect
7. C22×C32⋊C9C2×C3semidirect
18. #4181A4semidirect
31. C32⋊C9C2×A4semidirect
122. C22#92161semidirect

Maximal subgroups

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

subgroupindex
#117574102
C3×(C3⋊D3)⋊A43
C22×#41813
#921614