Finite Group Databasebeta

← #10619751⋊C3 #14518077

Subgroups — #10619751⋊C3 #14518077

Order 1944.

252 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 28 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#11757849C211yesmaximal, characteristic, complemented
2C3×(C3⋊S4)⋊C3—31nomaximal
3C3×((C22⋊C9)⋊C2)⋊C3—32nomaximal
4C3×#611⋊C3—31nomaximal
5#10619751C311yesmaximal, characteristic, complemented
6#4184⋊C3—41nomaximal
7C22×C3×3−1+2D311yescharacteristic, complemented
8C2×C3×AGL(1,ℤ/9)—31no—
9C3×C22⋊H(3,𝔽3)D311yescharacteristic
10C3×#1094D312yescomplemented
11C3×3−1+2⋊C4—31no—
12#66357—21no—
13#66357—21no—
14#66357—22no—
15#66357C2×C311yescharacteristic, complemented
16#6910—41noSylow
17C3×C3⋊S4—31no—
18C32×#67—91no—
19(C3⋊S4)⋊C3—32no—
20(C3⋊S4)⋊C3—31no—
21C3×(C22⋊C9)⋊C2—32no—
22((C22⋊C9)⋊C2)⋊C3—32no—
23((C22⋊C9)⋊C2)⋊C3—32no—
24((C22⋊C9)⋊C2)⋊C3—32no—
25#611⋊C3—31no—
26#611⋊C3—32no—
27C3×#611—31no—
28C2×C3×3−1+2—31no—
29C3×AGL(1,ℤ/9)—61no—
30C3×AGL(1,ℤ/9)—122no—
31C3×(C3⋊D3)⋊C3—121no—
32#4184—41no—
33C22×C33C3⋊D311yescharacteristic
34C2×C32×D3—91no—
35C32×A4—31no—
36C32×Dic3—91no—
37C22×3−1+2—32no—
38C22×3−1+2—31no—
39C22×C3×C9—21no—
40C22×C3×C9C3×D311yescharacteristic, complemented
41C2×AGL(1,ℤ/9)—32no—
42C2×AGL(1,ℤ/9)—31no—
43C2×C3×D9—31no—
44C22⋊H(3,𝔽3)—21no—
45C22⋊H(3,𝔽3)—32no—
46C22⋊H(3,𝔽3)C3×D311yescharacteristic
47#1094—22no—
48#1094—32no—
49#1094—32no—
50#1094C3×D312yescomplemented
51C3×C22⋊C9—32no—
523−1+2⋊C4—31no—
533−1+2⋊C4—32no—
54C3×Dic9—31no—
55C3×3−1+2—42no—
56C3×3−1+2S411yescharacteristic, complemented
57C3×H(3,𝔽3)—41no—
58#731—41no—
59#731—81no—
60#731—82no—
61#731—81no—
62C3⋊S4—31no—
63C3×S4—271no—
64C32×D4—271no—
65C3×#67—91no—
66C3×#67—92no—
67C3×#67—91no—
68(C22⋊C9)⋊C2—32no—
69#611—31no—
70C2×C33—31no—
71C3×C3⋊D3—121no—
72C32×D3—181no—
73C2×3−1+2—32no—
74C2×3−1+2—31no—
75C2×3−1+2—62no—
76C2×3−1+2—61no—
77C2×C3×C9—31no—
78C2×C3×C9—61no—
79AGL(1,ℤ/9)—62no—
80AGL(1,ℤ/9)—61no—
81AGL(1,ℤ/9)—122no—
82AGL(1,ℤ/9)—122no—
83AGL(1,ℤ/9)—122no—
84(C3⋊D3)⋊C3—121no—
85(C3⋊D3)⋊C3—122no—
86C3×D9—61no—
87C3×D9—122no—
88C22×C32—91no—
89C22×C32—271no—
90C22×C32#27212yes—
91C22×C32#27211yescharacteristic
92C22×C32C3×C3⋊D311yescharacteristic
93C2×C3×D3—91no—
94C2×C3×D3—92no—
95C2×C3×D3—91no—
96C3×A4—31no—
97C3×A4—61no—
98C3×A4—91no—
99C3×A4—181no—
100C32×C4—271no—
101C3×Dic3—91no—
102C3×Dic3—91no—
103C3×Dic3—92no—
104C22×C9—31no—
105C22×C9—61no—
106C2×D9—31no—
107C22⋊C9—32no—
108C22⋊C9—62no—
109Dic9—31no—
110C33—121no—
111C33C3⋊S411yescharacteristic
1123−1+2—32no—
1133−1+2—31no—
1143−1+2—42no—
1153−1+2—82no—
1163−1+2—122no—
1173−1+2—122no—
118H(3,𝔽3)—41no—
119H(3,𝔽3)—81no—
120H(3,𝔽3)—122no—
121C3×C9—21no—
122C3×C9—122no—
123C3×C9C3×S411yescharacteristic, complemented
124S4—271no—
125C3×D4—271no—
126C3×D4—272no—
127C3×D4—271no—
128#67—91no—
129C2×C32—31no—
130C2×C32—32no—
131C2×C32—31no—
132C2×C32—91no—
133C2×C32—181no—
134C2×C32—541no—
135C3⋊D3—121no—
136C3×D3—182no—
137C3×D3—181no—
138C3×D3—181no—
139C3×D3—1081no—
140C2×C9—31no—
141C2×C9—61no—
142C2×C9—62no—
143C2×C9—61no—
144D9—61no—
145D9—122no—
146C22×C3—31no—
147C22×C3—31no—
148C22×C3—32no—
149C22×C3—271no—
150C22×C3—271no—
151C22×C3—272no—
152C22×C3C3×#27211yescharacteristic
153C2×D3—91no—
154A4—91no—
155A4—181no—
156C3×C4—271no—
157C3×C4—272no—
158C3×C4—271no—
159Dic3—91no—
160C32—91no—
161C32—121no—
162C32—241no—
163C32—361no—
164C32—721no—
165C32#625812yes—
166C32#625811yescharacteristic
167C32C3×C3⋊S411yescharacteristic
168C9—31no—
169C9—61no—
170C9—122no—
171C9—242no—
172D4—271noSylow
173C2×C3—31no—
174C2×C3—31no—
175C2×C3—61no—
176C2×C3—91no—
177C2×C3—92no—
178C2×C3—541no—
179C2×C3—541no—
180C2×C3—542no—
181D3—181no—
182D3—1081no—
183C22—271no—
184C22#4184⋊C311yescharacteristic, complemented
185C4—271no—
186C3—31no—
187C3—31no—
188C3—32no—
189C3—361no—
190C3—721no—
191C3C3×#625811yescharacteristic
192C2—31no—
193C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#66357C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C3C3×#272
LCSG ▷ #66357
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757849C2semidirect
5. #10619751C3semidirect
7. C22×C3×3−1+2D3semidirect
10. C3×#1094D3semidirect
15. #66357C2×C3semidirect
40. C22×C3×C9C3×D3semidirect
50. #1094C3×D3semidirect
56. C3×3−1+2S4semidirect
123. C3×C9C3×S4semidirect
184. C22#4184⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117578492
C3×(C3⋊S4)⋊C33
C3×((C22⋊C9)⋊C2)⋊C33
C3×#611⋊C33
#106197513
#4184⋊C34