Finite Group Databasebeta

← #10619745⋊C3 #14517981

Subgroups — #10619745⋊C3 #14517981

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#11757841C211yesmaximal, characteristic, complemented
2C3⋊((C3⋊S4)⋊C3)C311yesmaximal, characteristic, complemented
3C3×#638⋊C3—31nomaximal
4#10619745C313yesmaximal, complemented
5#4175⋊C3—41nomaximal
6C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
7C2×C3×(C3⋊D3)⋊C3—31no—
8C3×C22⋊H(3,𝔽3)C2×C311yescharacteristic, complemented
9C3×#1094—21no—
10C3×(C3⋊Dic3)⋊C3—31no—
11#66363—23no—
12#66363C2×C313yescomplemented
13#6909—41noSylow
14C3⋊(C3⋊S4)C3211yescharacteristic, complemented
15C3×#638—31no—
16C32×#67—91no—
17(C3⋊S4)⋊C3—91no—
18#638⋊C3—33no—
19C2×C3×H(3,𝔽3)—31no—
20C3⋊((C3⋊D3)⋊C3)—41no—
21C3×(C3⋊D3)⋊C3—61no—
22#4175—43no—
23C22×C33—31no—
24C22×C33C3×D311yescharacteristic
25C2×C3×C3⋊D3—31no—
26C2×C32×D3—91no—
27C32×A4—21no—
28C32×A4C2×C3211yescharacteristic, complemented
29C3×C3⋊Dic3—31no—
30C32×Dic3—91no—
31C22×H(3,𝔽3)—61no—
32C22×H(3,𝔽3)C3×D313yes—
33C2×(C3⋊D3)⋊C3—33no—
34C22⋊H(3,𝔽3)—31no—
35C22⋊H(3,𝔽3)—61no—
36#1094—23no—
37#1094—61no—
38#1094—61no—
39C3×C22⋊C9—61no—
40(C3⋊Dic3)⋊C3—33no—
41C3×3−1+2—81no—
42C3×H(3,𝔽3)—41no—
43C3×H(3,𝔽3)S411yescharacteristic, complemented
44AΣL(1,𝔽27)—43no—
45AΣL(1,𝔽27)—83no—
46C3⋊S4—91no—
47C3⋊S4—271no—
48C32×D4—271no—
49#638—31no—
50C3×#67—93no—
51C3×#67—91no—
52C3×#67—271no—
53C2×C33—31no—
54C2×C33—31no—
55C2×C33—61no—
56C3⋊(C3⋊D3)—41no—
57C3×C3⋊D3—61no—
58C32×D3—181no—
59C2×H(3,𝔽3)—33no—
60C2×H(3,𝔽3)—63no—
61(C3⋊D3)⋊C3—63no—
62(C3⋊D3)⋊C3—361no—
63C22×C32—21no—
64C22×C32—33no—
65C22×C32—91no—
66C22×C32—91no—
67C22×C32—181no—
68C22×C32—271no—
69C22×C32(C3⋊D3)⋊C311yescharacteristic
70C22×C32C32×D311yescharacteristic
71C2×C3⋊D3—31no—
72C2×C3×D3—93no—
73C2×C3×D3—91no—
74C2×C3×D3—271no—
75C3×A4—31no—
76C3×A4—61no—
77C3×A4—91no—
78C3×A4—181no—
79C32×C4—271no—
80C3⋊Dic3—31no—
81C3×Dic3—93no—
82C3×Dic3—91no—
83C3×Dic3—271no—
84C22⋊C9—63no—
85C33—31no—
86C33—41no—
87C33—81no—
88C33C3×S411yescharacteristic
893−1+2—83no—
903−1+2—241no—
913−1+2—241no—
92H(3,𝔽3)—61no—
93H(3,𝔽3)—121no—
94H(3,𝔽3)—241no—
95H(3,𝔽3)C3×S413yes—
96C3×C9—241no—
97S4—811no—
98C3×D4—271no—
99C3×D4—273no—
100#67—91no—
101#67—271no—
102C2×C32—31no—
103C2×C32—33no—
104C2×C32—31no—
105C2×C32—61no—
106C2×C32—63no—
107C2×C32—91no—
108C2×C32—91no—
109C2×C32—181no—
110C2×C32—181no—
111C2×C32—181no—
112C2×C32—181no—
113C2×C32—181no—
114C2×C32—541no—
115C3⋊D3—61no—
116C3⋊D3—361no—
117C3⋊D3—1081no—
118C3×D3—183no—
119C3×D3—181no—
120C3×D3—541no—
121C22×C3—31no—
122C22×C3—31no—
123C22×C3—61no—
124C22×C3—93no—
125C22×C3—271no—
126C22×C3—273no—
127C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
128C2×D3—91no—
129C2×D3—271no—
130A4—91no—
131A4—181no—
132C3×C4—271no—
133C3×C4—273no—
134Dic3—91no—
135Dic3—271no—
136C32—21no—
137C32—33no—
138C32—91no—
139C32—91no—
140C32—121no—
141C32—181no—
142C32—241no—
143C32—361no—
144C32—721no—
145C32(C3⋊S4)⋊C311yescharacteristic
146C32C32×S411yescharacteristic
147C9—243no—
148D4—271noSylow
149C2×C3—31no—
150C2×C3—31no—
151C2×C3—61no—
152C2×C3—91no—
153C2×C3—93no—
154C2×C3—181no—
155C2×C3—183no—
156C2×C3—541no—
157C2×C3—543no—
158D3—181no—
159D3—541no—
160D3—3241no—
161C22—271no—
162C22#4175⋊C311yescharacteristic, complemented
163C4—271no—
164C3—31no—
165C3—31no—
166C3—61no—
167C3—93no—
168C3—361no—
169C3—721no—
170C3C3×(C3⋊S4)⋊C311yescharacteristic
171C2—31no—
172C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×A4C2×C32
FrattiniC32C32×S4
FittingC22×C3×H(3,𝔽3)D3
socleC22×C3C3×(C3⋊D3)⋊C3
LCSG ▷ C32×A4
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757841C2semidirect
2. C3⋊((C3⋊S4)⋊C3)C3semidirect
4. #10619745C3semidirect
6. C22×C3×H(3,𝔽3)D3semidirect
8. C3×C22⋊H(3,𝔽3)C2×C3semidirect
12. #66363C2×C3semidirect
14. C3⋊(C3⋊S4)C32semidirect
28. C32×A4C2×C32semidirect
43. C3×H(3,𝔽3)S4semidirect
162. C22#4175⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117578412
C3⋊((C3⋊S4)⋊C3)3
C3×#638⋊C33
#106197453
#4175⋊C34