Finite Group Databasebeta

← C3×#10619769 #14518173

Subgroups — C3×#10619769 #14518173

Order 1944.

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

normal subgroups only

This group has 251 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×#66357C211yesmaximal, characteristic, complemented
2C22×C3×C3⋊D9C311yesmaximal, characteristic, complemented
3C3×(C3⋊D3)⋊A4—31nomaximal
4#10619769C313yesmaximal, direct product factor
5C3×#4177—41nomaximal
6C22×C32×C9C2×C311yescharacteristic, complemented
7C2×C3×C3⋊D9—31no—
8C2×C3×C3⋊D9—31no—
9C3×C22⋊H(3,𝔽3)D311yescharacteristic
10C3×#1094—21no—
11#66357—23no—
12#66357C2×C313yescomplemented
13C3×#731—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#4177—43no—
24C22×C33C3×D311yescharacteristic
25C2×C3×C3⋊D3—91no—
26C2×C3×C3⋊D3—91no—
27C32×A4—31no—
28C22×C3×C9—21no—
29C22×C3×C9—31no—
30C22×C3×C9—61no—
31C22×C3×C9C2×C3211yescharacteristic, complemented
32C2×C3⋊D9—31no—
33C2×C3⋊D9—31no—
34C2×C3×D9—93no—
35C2×C3×D9—93no—
36C22⋊H(3,𝔽3)—61no—
37C22⋊H(3,𝔽3)C3×D313yes—
38#1094—23no—
39#1094—62no—
40C3×C22⋊C9—61no—
41C3×3−1+2—81no—
42C3×H(3,𝔽3)—41no—
43C32×C9C2×A411yescharacteristic, complemented
44#731—43no—
45#731—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—91no—
78C3×A4—181no—
79C22×C9—31no—
80C22×C9—61no—
81C2×D9—93no—
82C2×D9—93no—
83C22⋊C9—63no—
84C33—121no—
85C33D3×A411yescharacteristic
863−1+2—83no—
873−1+2—242no—
88H(3,𝔽3)—43no—
89H(3,𝔽3)—241no—
90C3×C9—21no—
91C3×C9—31no—
92C3×C9—61no—
93C3×C9—241no—
94C3×C9C2×C3×A411yescharacteristic, complemented
95C23×C3—271no—
96C22×D3—91no—
97C22×D3—271no—
98C2×A4—273no—
99C2×C32—31no—
100C2×C32—33no—
101C2×C32—31no—
102C2×C32—61no—
103C2×C32—63no—
104C2×C32—1081no—
105C3⋊D3—31no—
106C3⋊D3—91no—
107C3×D3—91no—
108C3×D3—271no—
109C3×D3—273no—
110C3×D3—271no—
111C3×D3—363no—
112C2×C9—33no—
113C2×C9—63no—
114D9—91no—
115D9—93no—
116C22×C3—21no—
117C22×C3—31no—
118C22×C3—61no—
119C22×C3—811no—
120C22×C3—811no—
121C22×C3#417711yescharacteristic, complemented
122C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
123C2×D3—271no—
124C2×D3—273no—
125C2×D3—273no—
126C2×D3—271no—
127A4—93no—
128C32—21no—
129C32—31no—
130C32—61no—
131C32—123no—
132C32—361no—
133C32—721no—
134C32(C3⋊D3)⋊A411yescharacteristic
135C32C3×D3×A411yescharacteristic
136C9—31no—
137C9—61no—
138C9—243no—
139C23—271noSylow
140C2×C3—33no—
141C2×C3—31no—
142C2×C3—31no—
143C2×C3—61no—
144C2×C3—63no—
145C2×C3—271no—
146C2×C3—811no—
147C2×C3—1083no—
148D3—91no—
149D3—271no—
150D3—273no—
151D3—271no—
152C22—811no—
153C22—811no—
154C22C3×#417711yescharacteristic, complemented
155C3—21no—
156C3—31no—
157C3—61no—
158C3—363no—
159C3#1061976911yescharacteristic, direct product factor
160C3C3×(C3⋊D3)⋊A411yescharacteristic
161C2—31no—
162C2—271no—
163C2—811no—
subgroupG/H
center, hypercenterC3#10619769
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×#66357C2semidirect
2. C22×C3×C3⋊D9C3semidirect
4. #10619769C3direct (N × H)
6. C22×C32×C9C2×C3semidirect
12. #66357C2×C3semidirect
16. C22×C3⋊D9C32semidirect
21. C3×C3⋊D9A4semidirect
31. C22×C3×C9C2×C32semidirect
43. C32×C9C2×A4semidirect
61. C3⋊D9C3×A4semidirect
94. C3×C9C2×C3×A4semidirect
121. C22×C3#4177semidirect
154. C22C3×#4177semidirect
159. C3#10619769direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#663572
C22×C3×C3⋊D93
C3×(C3⋊D3)⋊A43
#106197693
C3×#41774