Finite Group Databasebeta

← C3×#10619745 #14517980

Subgroups — C3×#10619745 #14517980

Order 1944.

324 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C3×#66363C211yesmaximal, characteristic, complemented
2C3×C3⋊(C3⋊S4)C311yesmaximal, characteristic, complemented
3C3×#638⋊C3—31nomaximal
4#10619745C313yesmaximal, direct product factor
5C3×#4175—41nomaximal
6C33×A4C2×C311yescharacteristic, complemented
7C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
8C2×C3×(C3⋊D3)⋊C3—31no—
9C3×#1094—21no—
10C3×(C3⋊Dic3)⋊C3—31no—
11#66363—23no—
12#66363C2×C313yescomplemented
13C3×AΣL(1,𝔽27)—41noSylow
14C3⋊(C3⋊S4)C3211yescharacteristic, complemented
15C3×C3⋊S4—91no—
16C3×C3⋊S4—93no—
17C3×#638—31no—
18C32×#67—91no—
19#638⋊C3—33no—
20C3×C3⋊(C3⋊D3)—41no—
21C2×C3×H(3,𝔽3)—31no—
22C3×(C3⋊D3)⋊C3—61no—
23#4175—43no—
24C22×C33—31no—
25C22×C33C3×D311yescharacteristic
26C2×C3×C3⋊D3—31no—
27C2×C32×D3—91no—
28C32×A4—21no—
29C32×A4—31no—
30C32×A4—33no—
31C32×A4—61no—
32C32×A4—63no—
33C32×A4C2×C3211yescharacteristic, complemented
34C3×C3⋊Dic3—31no—
35C32×Dic3—91no—
36C22×H(3,𝔽3)—61no—
37C22×H(3,𝔽3)C3×D313yescomplemented
38C2×(C3⋊D3)⋊C3—33no—
39#1094—23no—
40#1094—62no—
41C3×C22⋊C9—61no—
42(C3⋊Dic3)⋊C3—33no—
43C34—41no—
44C3×3−1+2—81no—
45C3×H(3,𝔽3)S411yescharacteristic, complemented
46AΣL(1,𝔽27)—43no—
47AΣL(1,𝔽27)—83no—
48C3⋊S4—91no—
49C3⋊S4—93no—
50C3×S4—273no—
51C32×D4—271no—
52#638—31no—
53C3×#67—93no—
54C3×#67—91no—
55C3×#67—271no—
56C2×C33—31no—
57C2×C33—31no—
58C2×C33—61no—
59C3⋊(C3⋊D3)—41no—
60C3×C3⋊D3—61no—
61C3×C3⋊D3—361no—
62C3×C3⋊D3—363no—
63C32×D3—181no—
64C2×H(3,𝔽3)—33no—
65C2×H(3,𝔽3)—63no—
66(C3⋊D3)⋊C3—63no—
67C22×C32—21no—
68C22×C32—31no—
69C22×C32—33no—
70C22×C32—61no—
71C22×C32—91no—
72C22×C32—181no—
73C22×C32—271no—
74C22×C32(C3⋊D3)⋊C311yescharacteristic
75C22×C32C32×D311yescharacteristic
76C2×C3⋊D3—31no—
77C2×C3×D3—93no—
78C2×C3×D3—91no—
79C2×C3×D3—271no—
80C3×A4—31no—
81C3×A4—33no—
82C3×A4—33no—
83C3×A4—63no—
84C3×A4—66no—
85C3×A4—63no—
86C3×A4—61no—
87C3×A4—63no—
88C32×C4—271no—
89C3⋊Dic3—31no—
90C3×Dic3—93no—
91C3×Dic3—91no—
92C3×Dic3—271no—
93C22⋊C9—63no—
94C33—31no—
95C33—41no—
96C33—81no—
97C33—123no—
98C33—121no—
99C33—241no—
100C33—243no—
101C33C3×S411yescharacteristic
1023−1+2—83no—
1033−1+2—242no—
104H(3,𝔽3)—61no—
105H(3,𝔽3)C3×S413yescomplemented
106C3×C9—241no—
107S4—273no—
108C3×D4—273no—
109C3×D4—271no—
110#67—91no—
111#67—271no—
112C2×C32—31no—
113C2×C32—33no—
114C2×C32—31no—
115C2×C32—61no—
116C2×C32—63no—
117C2×C32—91no—
118C2×C32—91no—
119C2×C32—181no—
120C2×C32—181no—
121C2×C32—181no—
122C2×C32—182no—
123C2×C32—541no—
124C3⋊D3—61no—
125C3⋊D3—361no—
126C3⋊D3—363no—
127C3×D3—183no—
128C3×D3—181no—
129C3×D3—541no—
130C3×D3—1083no—
131C22×C3—21no—
132C22×C3—31no—
133C22×C3—61no—
134C22×C3—93no—
135C22×C3—271no—
136C22×C3—273no—
137C22×C3#417511yescharacteristic, complemented
138C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
139C2×D3—91no—
140C2×D3—271no—
141A4—33no—
142A4—63no—
143C3×C4—271no—
144C3×C4—273no—
145Dic3—91no—
146Dic3—271no—
147C32—21no—
148C32—31no—
149C32—33no—
150C32—61no—
151C32—91no—
152C32—123no—
153C32—121no—
154C32—123no—
155C32—181no—
156C32—243no—
157C32—243no—
158C32—243no—
159C32—246no—
160C32—241no—
161C32(C3⋊S4)⋊C311yescharacteristic
162C32C32×S411yescharacteristic
163C9—243no—
164D4—271noSylow
165C2×C3—31no—
166C2×C3—31no—
167C2×C3—61no—
168C2×C3—91no—
169C2×C3—93no—
170C2×C3—181no—
171C2×C3—183no—
172C2×C3—543no—
173C2×C3—541no—
174D3—181no—
175D3—541no—
176D3—1083no—
177C22—271no—
178C22C3×#417511yescharacteristic, complemented
179C4—271no—
180C3—21no—
181C3—31no—
182C3—61no—
183C3—93no—
184C3—123no—
185C3—243no—
186C3#1061974511yescharacteristic, direct product factor
187C3C3×(C3⋊S4)⋊C311yescharacteristic
188C2—31no—
189C2—541no—
subgroupG/H
center, hypercenterC3#10619745
commutator, cosocle, hypocenterC32×A4C2×C32
FrattiniC32C32×S4
FittingC22×C3×H(3,𝔽3)D3
socleC22×C32(C3⋊D3)⋊C3
LCSG ▷ C32×A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#66363C2semidirect
2. C3×C3⋊(C3⋊S4)C3semidirect
4. #10619745C3direct (N × H)
6. C33×A4C2×C3semidirect
7. C22×C3×H(3,𝔽3)D3semidirect
12. #66363C2×C3semidirect
14. C3⋊(C3⋊S4)C32semidirect
33. C32×A4C2×C32semidirect
37. C22×H(3,𝔽3)C3×D3semidirect
45. C3×H(3,𝔽3)S4semidirect
105. H(3,𝔽3)C3×S4semidirect
137. C22×C3#4175semidirect
178. C22C3×#4175semidirect
186. C3#10619745direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#663632
C3×C3⋊(C3⋊S4)3
C3×#638⋊C33
#106197453
C3×#41754