Finite Group Databasebeta

← #14518084

Subgroups — #14518084

Order 1944.

358 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 33 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#11757856C211yesmaximal, characteristic, complemented
2C32×C3⋊S4—31nomaximal
3C3×((C22⋊C9)⋊C2)⋊C3—32nomaximal
4C3×#611⋊C3—31nomaximal
5#10619754C311yesmaximal, characteristic, complemented
6#92302—41nomaximal
7C33×A4D311yescharacteristic
8C22×C3×3−1+2D311yescharacteristic, complemented
9C2×C3×AGL(1,ℤ/9)—31no—
10C3×#1094D312yescomplemented
11C3×3−1+2⋊C4—31no—
12(C3×A4)⋊C9—21no—
13(C3×A4)⋊C9—21no—
14(C3×A4)⋊C9—22no—
15(C3×A4)⋊C9C2×C311yescharacteristic, complemented
16#6891—41noSylow
17C3×C3⋊S4—33no—
18C3×C3⋊S4—31no—
19C32×S4—93no—
20C32×#67—91no—
21C3×(C22⋊C9)⋊C2—32no—
22((C22⋊C9)⋊C2)⋊C3—36no—
23#611⋊C3—33no—
24C3×#611—31no—
25C32×C3⋊D3—121no—
26C2×C3×3−1+2—31no—
27C3×AGL(1,ℤ/9)—61no—
28C3×AGL(1,ℤ/9)—122no—
29#4181—41no—
30C22×C33C3⋊D311yescharacteristic
31C2×C32×D3—91no—
32C32×A4—21no—
33C32×A4—33no—
34C32×A4—33no—
35C32×A4—63no—
36C32×A4C3×D311yescharacteristic
37C32×Dic3—91no—
38C22×3−1+2—33no—
39C22×C3×C9—21no—
40C22×C3×C9C3×D311yescharacteristic, complemented
41C2×AGL(1,ℤ/9)—33no—
42C2×C3×D9—31no—
43#1094—36no—
44C3×C22⋊C9—22no—
45C3×C22⋊C9C3×D312yescomplemented
463−1+2⋊C4—33no—
47C3×Dic9—31no—
48C34—41no—
49C3×3−1+2—42no—
50C3×3−1+2S411yescharacteristic, complemented
51C32⋊C9—41no—
52C32⋊C9—82no—
53C32⋊C9—81no—
54C32⋊C9—81no—
55C3⋊S4—31no—
56C3×S4—99no—
57C3×S4—93no—
58C32×D4—271no—
59C3×#67—93no—
60C3×#67—91no—
61(C22⋊C9)⋊C2—32no—
62#611—31no—
63C2×C33—31no—
64C3×C3⋊D3—121no—
65C3×C3⋊D3—123no—
66C32×D3—181no—
67C32×D3—363no—
68C2×3−1+2—33no—
69C2×3−1+2—63no—
70C2×C3×C9—31no—
71C2×C3×C9—61no—
72AGL(1,ℤ/9)—63no—
73AGL(1,ℤ/9)—126no—
74C3×D9—61no—
75C3×D9—122no—
76C22×C32—31no—
77C22×C32—61no—
78C22×C32—271no—
79C22×C32#27213yes—
80C22×C32C3×C3⋊D311yescharacteristic
81C2×C3×D3—91no—
82C2×C3×D3—93no—
83C3×A4—23no—
84C3×A4—31no—
85C3×A4—39no—
86C3×A4—61no—
87C3×A4—69no—
88C3×A4—61no—
89C3×A4—61no—
90C3×A4—61no—
91C3×A4AGL(1,ℤ/9)13yescomplemented
92C32×C4—271no—
93C3×Dic3—91no—
94C3×Dic3—93no—
95C22×C9—31no—
96C22×C9—61no—
97C2×D9—31no—
98C22⋊C9—32no—
99C22⋊C9—62no—
100Dic9—31no—
101C33—41no—
102C33—81no—
103C33—123no—
104C33—123no—
105C33—243no—
106C33C3⋊S411yescharacteristic
1073−1+2—33no—
1083−1+2—126no—
109C3×C9—21no—
110C3×C9—42no—
111C3×C9—82no—
112C3×C9C3×S411yescharacteristic, complemented
113S4—93no—
114C3×D4—273no—
115C3×D4—271no—
116#67—91no—
117C2×C32—31no—
118C2×C32—33no—
119C2×C32—91no—
120C2×C32—181no—
121C2×C32—541no—
122C3⋊D3—121no—
123C3×D3—183no—
124C3×D3—181no—
125C3×D3—363no—
126C3×D3—369no—
127C2×C9—31no—
128C2×C9—61no—
129C2×C9—63no—
130D9—61no—
131D9—122no—
132C22×C3—21no—
133C22×C3—33no—
134C22×C3—271no—
135C22×C3—273no—
136C22×C3C3×#27211yescharacteristic
137C22×C3C3⋊AGL(1,ℤ/9)11yescharacteristic
138C2×D3—91no—
139A4—33no—
140A4—63no—
141C3×C4—271no—
142C3×C4—273no—
143Dic3—91no—
144C32—31no—
145C32—43no—
146C32—61no—
147C32—83no—
148C32—129no—
149C32—121no—
150C32—241no—
151C32—241no—
152C32—249no—
153C32—241no—
154C32—241no—
155C32#625813yes—
156C32C3×C3⋊S411yescharacteristic
157C9—31no—
158C9—61no—
159C9—122no—
160C9—242no—
161D4—271noSylow
162C2×C3—31no—
163C2×C3—31no—
164C2×C3—61no—
165C2×C3—93no—
166C2×C3—543no—
167C2×C3—541no—
168D3—181no—
169D3—363no—
170C22—271no—
171C22#9230211yescharacteristic, complemented
172C4—271no—
173C3—21no—
174C3—33no—
175C3—123no—
176C3—243no—
177C3A4⋊AGL(1,ℤ/9)11yescharacteristic
178C3C3×#625811yescharacteristic
179C2—31no—
180C2—541no—
subgroupG/H
center, hypercenterC3A4⋊AGL(1,ℤ/9)
commutator, cosocle, hypocenter(C3×A4)⋊C9C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C32C3×C3⋊D3
LCSG ▷ (C3×A4)⋊C9
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #11757856C2semidirect
5. #10619754C3semidirect
8. C22×C3×3−1+2D3semidirect
10. C3×#1094D3semidirect
15. (C3×A4)⋊C9C2×C3semidirect
40. C22×C3×C9C3×D3semidirect
45. C3×C22⋊C9C3×D3semidirect
50. C3×3−1+2S4semidirect
91. C3×A4AGL(1,ℤ/9)semidirect
112. C3×C9C3×S4semidirect
171. C22#92302semidirect

Maximal subgroups

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

subgroupindex
#117578562
C32×C3⋊S43
C3×((C22⋊C9)⋊C2)⋊C33
C3×#611⋊C33
#106197543
#923024