Finite Group Databasebeta

← C3×#10619768 #14518172

Subgroups — C3×#10619768 #14518172

Order 1944.

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

normal subgroups only

This group has 263 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×#66358C211yesmaximal, characteristic, complemented
2C22×C3×C3⋊D9C311yesmaximal, characteristic, complemented
3C3×(C3⋊D3)⋊A4—31nomaximal
4#10619768C313yesmaximal, direct product factor
5C3×#4179—41nomaximal
6C22×C32×C9C2×C311yescharacteristic, complemented
7C2×C3×C3⋊D9—31no—
8C2×C3×C3⋊D9—31no—
9C3×C22⋊H(3,𝔽3)—21no—
10C3×C22⋊H(3,𝔽3)D311yescharacteristic
11#66358—23no—
12#66358C2×C313yescomplemented
13C3×#732—41noSylow
14C22×C3×C3⋊D3—31no—
15C3×D3×A4—91no—
16C22×C3⋊D9C3211yescharacteristic, complemented
17C22×C3×D9—91no—
18(C3⋊D3)⋊A4—33no—
19C2×C32×C9—31no—
20C3×C3⋊D9—31no—
21C3×C3⋊D9A411yescharacteristic, complemented
22C3×(C3⋊D3)⋊C3—121no—
23#4179—43no—
24C22×C33C3×D311yescharacteristic
25C2×C3×C3⋊D3—91no—
26C2×C3×C3⋊D3—91no—
27C32×A4—31no—
28C32×A4—61no—
29C22×C3×C9—21no—
30C22×C3×C9—31no—
31C22×C3×C9—61no—
32C22×C3×C9C2×C3211yescharacteristic, complemented
33C2×C3⋊D9—31no—
34C2×C3⋊D9—31no—
35C2×C3×D9—93no—
36C2×C3×D9—93no—
37C22⋊H(3,𝔽3)—23no—
38C22⋊H(3,𝔽3)—61no—
39C22⋊H(3,𝔽3)—62no—
40C22⋊H(3,𝔽3)C3×D313yes—
41C3×H(3,𝔽3)—41no—
42C3×H(3,𝔽3)—81no—
43C32×C9C2×A411yescharacteristic, complemented
44#732—43no—
45#732—83no—
46C22×C3⋊D3—31no—
47C22×C3×D3—91no—
48C22×C3×D3—271no—
49C2×C3×A4—271no—
50D3×A4—93no—
51C22×D9—91no—
52C2×C33—31no—
53C3×C3⋊D3—31no—
54C3×C3⋊D3—91no—
55C32×D3—361no—
56C2×C3×C9—31no—
57C2×C3×C9—33no—
58C2×C3×C9—63no—
59C2×C3×C9—61no—
60C3⋊D9—31no—
61C3⋊D9C3×A411yescharacteristic, complemented
62(C3⋊D3)⋊C3—123no—
63C3×D9—91no—
64C3×D9—93no—
65C22×C32—21no—
66C22×C32—31no—
67C22×C32—61no—
68C22×C32(C3⋊D3)⋊C311yescharacteristic
69C22×C32C32×D311yescharacteristic
70C2×C3⋊D3—91no—
71C2×C3⋊D3—91no—
72C2×C3×D3—271no—
73C2×C3×D3—273no—
74C2×C3×D3—273no—
75C2×C3×D3—271no—
76C3×A4—33no—
77C3×A4—63no—
78C3×A4—91no—
79C3×A4—181no—
80C3×A4—182no—
81C3×A4—181no—
82C22×C9—31no—
83C22×C9—61no—
84C2×D9—93no—
85C2×D9—93no—
86C33—121no—
87C33—241no—
88C33D3×A411yescharacteristic
89H(3,𝔽3)—43no—
90H(3,𝔽3)—83no—
91H(3,𝔽3)—241no—
92H(3,𝔽3)—242no—
93C3×C9—21no—
94C3×C9—31no—
95C3×C9—61no—
96C3×C9C2×C3×A411yescharacteristic, complemented
97C23×C3—271no—
98C22×D3—91no—
99C22×D3—271no—
100C2×A4—273no—
101C2×C32—31no—
102C2×C32—33no—
103C2×C32—31no—
104C2×C32—61no—
105C2×C32—63no—
106C2×C32—1081no—
107C3⋊D3—31no—
108C3⋊D3—91no—
109C3×D3—91no—
110C3×D3—271no—
111C3×D3—273no—
112C3×D3—271no—
113C3×D3—363no—
114C2×C9—33no—
115C2×C9—63no—
116D9—91no—
117D9—93no—
118C22×C3—21no—
119C22×C3—31no—
120C22×C3—61no—
121C22×C3—811no—
122C22×C3—811no—
123C22×C3#417911yescharacteristic, complemented
124C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
125C2×D3—271no—
126C2×D3—273no—
127C2×D3—273no—
128C2×D3—271no—
129A4—93no—
130A4—183no—
131C32—21no—
132C32—31no—
133C32—61no—
134C32—123no—
135C32—243no—
136C32—361no—
137C32—721no—
138C32—722no—
139C32—721no—
140C32(C3⋊D3)⋊A411yescharacteristic
141C32C3×D3×A411yescharacteristic
142C9—31no—
143C9—61no—
144C23—271noSylow
145C2×C3—33no—
146C2×C3—31no—
147C2×C3—31no—
148C2×C3—61no—
149C2×C3—63no—
150C2×C3—271no—
151C2×C3—811no—
152C2×C3—1083no—
153D3—91no—
154D3—271no—
155D3—273no—
156D3—271no—
157C22—811no—
158C22—811no—
159C22C3×#417911yescharacteristic, complemented
160C3—21no—
161C3—31no—
162C3—61no—
163C3—363no—
164C3—723no—
165C3#1061976811yescharacteristic, direct product factor
166C3C3×(C3⋊D3)⋊A411yescharacteristic
167C2—31no—
168C2—271no—
169C2—811no—
subgroupG/H
center, hypercenterC3#10619768
commutator, cosocle, hypocenterC22×C3×C9C2×C32
FrattiniC32C3×D3×A4
FittingC22×C32×C9C2×C3
socleC22×C32(C3⋊D3)⋊C3
LCSG ▷ C22×C3×C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#66358C2semidirect
2. C22×C3×C3⋊D9C3semidirect
4. #10619768C3direct (N × H)
6. C22×C32×C9C2×C3semidirect
12. #66358C2×C3semidirect
16. C22×C3⋊D9C32semidirect
21. C3×C3⋊D9A4semidirect
32. C22×C3×C9C2×C32semidirect
43. C32×C9C2×A4semidirect
61. C3⋊D9C3×A4semidirect
96. C3×C9C2×C3×A4semidirect
123. C22×C3#4179semidirect
159. C22C3×#4179semidirect
165. C3#10619768direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#663582
C22×C3×C3⋊D93
C3×(C3⋊D3)⋊A43
#106197683
C3×#41794