Finite Group Databasebeta

← #10619743⋊C3 #14517977

Subgroups — #10619743⋊C3 #14517977

Order 1944.

242 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 30 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#11757837C211yesmaximal, characteristic, complemented
2C3⋊(((C22⋊C9)⋊C2)⋊C3)C311yesmaximal, characteristic, complemented
3C3×#638⋊C3—31nomaximal
4#10619743C313yesmaximal, complemented
5#4179⋊C3—41nomaximal
6C22×C3×H(3,𝔽3)D311yescharacteristic
7C2×C3×(C3⋊D3)⋊C3—31no—
8C3×C22⋊H(3,𝔽3)—21no—
9C3×#1094C2×C311yescharacteristic, complemented
10C3×(C3⋊Dic3)⋊C3—31no—
11#66362—23no—
12#66362C2×C313yescomplemented
13#6911—41noSylow
14C3×#638—31no—
15C32×#67—91no—
16C3⋊((C22⋊C9)⋊C2)C3211yescharacteristic, complemented
17((C22⋊C9)⋊C2)⋊C3—91no—
18#638⋊C3—33no—
19C2×C3×H(3,𝔽3)—31no—
20C3⋊AGL(1,ℤ/9)—41no—
21C3×(C3⋊D3)⋊C3—61no—
22#4179—43no—
23C22×C33—31no—
24C22×C33C3×D311yescharacteristic
25C2×C3×C3⋊D3—31no—
26C2×C32×D3—91no—
27C32×A4—61no—
28C3×C3⋊Dic3—31no—
29C32×Dic3—91no—
30C22×H(3,𝔽3)—61no—
31C22×H(3,𝔽3)C3×D313yes—
32C2×(C3⋊D3)⋊C3—33no—
33C22⋊H(3,𝔽3)—23no—
34C22⋊H(3,𝔽3)—61no—
35C22⋊H(3,𝔽3)—61no—
36#1094—31no—
37#1094—61no—
38C3×C22⋊C9—21no—
39C3×C22⋊C9C2×C3211yescharacteristic, complemented
40(C3⋊Dic3)⋊C3—33no—
41C3×3−1+2—41no—
42C3×H(3,𝔽3)—81no—
43C3×H(3,𝔽3)S411yescharacteristic
44#732—43no—
45#732—83no—
46C32×D4—271no—
47#638—31no—
48C3×#67—93no—
49C3×#67—91no—
50C3×#67—271no—
51(C22⋊C9)⋊C2—91no—
52C2×C33—31no—
53C2×C33—31no—
54C2×C33—61no—
55C3×C3⋊D3—61no—
56C32×D3—181no—
57C2×H(3,𝔽3)—33no—
58C2×H(3,𝔽3)—63no—
59C3⋊D9—41no—
60AGL(1,ℤ/9)—361no—
61(C3⋊D3)⋊C3—63no—
62C22×C32—21no—
63C22×C32—33no—
64C22×C32—91no—
65C22×C32—91no—
66C22×C32—181no—
67C22×C32—271no—
68C22×C32(C3⋊D3)⋊C311yescharacteristic
69C22×C32C32×D311yescharacteristic
70C2×C3⋊D3—31no—
71C2×C3×D3—93no—
72C2×C3×D3—91no—
73C2×C3×D3—271no—
74C3×A4—63no—
75C3×A4—183no—
76C32×C4—271no—
77C3⋊Dic3—31no—
78C3×Dic3—93no—
79C3×Dic3—91no—
80C3×Dic3—271no—
81C22⋊C9—31no—
82C22⋊C9—61no—
83C33—31no—
84C33—241no—
85C33C3×S411yescharacteristic
863−1+2—121no—
873−1+2—241no—
88H(3,𝔽3)—61no—
89H(3,𝔽3)—83no—
90H(3,𝔽3)—241no—
91H(3,𝔽3)—241no—
92H(3,𝔽3)C3×S413yes—
93C3×C9—41no—
94C3×C9—81no—
95C3×D4—271no—
96C3×D4—273no—
97#67—91no—
98#67—271no—
99C2×C32—31no—
100C2×C32—33no—
101C2×C32—31no—
102C2×C32—61no—
103C2×C32—63no—
104C2×C32—91no—
105C2×C32—91no—
106C2×C32—181no—
107C2×C32—181no—
108C2×C32—181no—
109C2×C32—181no—
110C2×C32—181no—
111C2×C32—541no—
112C3⋊D3—61no—
113C3×D3—183no—
114C3×D3—181no—
115C3×D3—541no—
116D9—361no—
117C22×C3—31no—
118C22×C3—31no—
119C22×C3—61no—
120C22×C3—93no—
121C22×C3—271no—
122C22×C3—273no—
123C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
124C2×D3—91no—
125C2×D3—271no—
126A4—183no—
127C3×C4—271no—
128C3×C4—273no—
129Dic3—91no—
130Dic3—271no—
131C32—21no—
132C32—33no—
133C32—91no—
134C32—91no—
135C32—181no—
136C32—243no—
137C32—723no—
138C32(C3⋊S4)⋊C311yescharacteristic
139C32C32×S411yescharacteristic
140C9—121no—
141C9—241no—
142D4—271noSylow
143C2×C3—31no—
144C2×C3—31no—
145C2×C3—61no—
146C2×C3—91no—
147C2×C3—93no—
148C2×C3—181no—
149C2×C3—183no—
150C2×C3—541no—
151C2×C3—543no—
152D3—181no—
153D3—541no—
154C22—271no—
155C22#4179⋊C311yescharacteristic, complemented
156C4—271no—
157C3—31no—
158C3—31no—
159C3—61no—
160C3—93no—
161C3—723no—
162C3C3×(C3⋊S4)⋊C311yescharacteristic
163C2—31no—
164C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C22⋊C9C2×C32
FrattiniC32C32×S4
FittingC22×C3×H(3,𝔽3)D3
socleC22×C3C3×(C3⋊D3)⋊C3
LCSG ▷ C3×C22⋊C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757837C2semidirect
2. C3⋊(((C22⋊C9)⋊C2)⋊C3)C3semidirect
4. #10619743C3semidirect
9. C3×#1094C2×C3semidirect
12. #66362C2×C3semidirect
16. C3⋊((C22⋊C9)⋊C2)C32semidirect
39. C3×C22⋊C9C2×C32semidirect
155. C22#4179⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117578372
C3⋊(((C22⋊C9)⋊C2)⋊C3)3
C3×#638⋊C33
#106197433
#4179⋊C34