Finite Group Databasebeta

← #14518110

Subgroups — #14518110

Order 1944.

313 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 313 conjugacy classes of subgroups — too many to draw. Only its 41 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#11757825C211yesmaximal, characteristic, complemented
2#10620045—33nomaximal
3C3×#6233—31nomaximal
4#10619762—33nomaximal
5#66359⋊C2—32nomaximal
6#10619751—33nomaximal
7#10619750—31nomaximal
8#92344—41nomaximal
9C22×C32×C9D311yescharacteristic, complemented
10C2×C3×C3⋊D9—31no—
11#66436D313yescomplemented
12C3×C3⋊Dic9—31no—
13#66368D313yescomplemented
14#66359D312yescomplemented
15#66358D311yescharacteristic, complemented
16#66357D313yescomplemented
17#6908—41noSylow
18C3×#638—91no—
19C9⋊S4—33no—
20(C3⋊S4)⋊C3—93no—
21((C22⋊C9)⋊C2)⋊C3—96no—
22#6233—31no—
23C3×#611—91no—
24C3×#611—91no—
25C3×#611—91no—
26C2×C32×C9—31no—
27#4207—123no—
28C3×C3⋊D9—61no—
29#733⋊C2—122no—
30#4185—121no—
31#4184—123no—
32#4183—123no—
33C22×C33C3⋊D311yescharacteristic
34C2×C3×C3⋊D3—91no—
35C3×C3⋊Dic3—91no—
36C22×C3×C9—31no—
37C22×C3×C9—61no—
38C22×C3×C9C3⋊D311yescharacteristic
39C22×C3×C9C3⋊D311yescharacteristic
40C22×C3×C9C3⋊D311yescharacteristic
41C2×C3⋊D9—31no—
42C2×C3×D9—91no—
43C2×C3×D9—91no—
44C2×C3×D9—91no—
45C22⋊H(3,𝔽3)C3⋊D313yes—
46#1094C3⋊D316yes—
47C9⋊A4—63no—
48C9×A4—33no—
49C3⋊Dic9—31no—
50C3×Dic9—91no—
51C3×Dic9—91no—
52C3×Dic9—91no—
53#737—43no—
54C32×C9S411yescharacteristic, complemented
55#733—42no—
56#732—41no—
57#731—43no—
58AΣL(1,𝔽27)—43no—
59C3⋊S4—93no—
60#638—91no—
61C3×#67—273no—
62C3×#67—271no—
63(C22⋊C9)⋊C2—96no—
64#611—91no—
65#611—91no—
66#611—91no—
67C2×C33—31no—
68C3×C3⋊D3—181no—
69C2×C3×C9—31no—
70C2×C3×C9—31no—
71C2×C3×C9—31no—
72C2×C3×C9—31no—
73C2×C3×C9—61no—
74C2×C3×C9—61no—
75C2×C3×C9—61no—
76C2×C3×C9—61no—
77C3⋊D9—61no—
78C3⋊D9—123no—
79AGL(1,ℤ/9)—366no—
80(C3⋊D3)⋊C3—363no—
81C3×D9—181no—
82C3×D9—181no—
83C3×D9—181no—
84C22×C32—31no—
85C22×C32—33no—
86C22×C32C3⋊(C3⋊D3)11yescharacteristic
87C2×C3⋊D3—91no—
88C2×C3×D3—271no—
89C2×C3×D3—273no—
90C3×A4—33no—
91C3⋊Dic3—91no—
92C3×Dic3—271no—
93C3×Dic3—273no—
94C22×C9—21no—
95C22×C9—31no—
96C22×C9—31no—
97C22×C9#27211yescharacteristic
98C2×D9—91no—
99C2×D9—91no—
100C2×D9—91no—
101C22⋊C9—36no—
102Dic9—91no—
103Dic9—91no—
104Dic9—91no—
105C33C3⋊S411yescharacteristic
1063−1+2—46no—
1073−1+2—243no—
108H(3,𝔽3)—43no—
109C3×C9—31no—
110C3×C9—61no—
111C3×C9—123no—
112C3×C9C3⋊S411yescharacteristic
113C3×C9C3⋊S411yescharacteristic
114C3×C9C3⋊S411yescharacteristic
115S4—813no—
116C3×D4—811no—
117#67—273no—
118#67—271no—
119C2×C32—31no—
120C2×C32—33no—
121C2×C32—31no—
122C2×C32—61no—
123C2×C32—63no—
124C3⋊D3—181no—
125C3⋊D3—363no—
126C3×D3—543no—
127C3×D3—541no—
128C2×C9—31no—
129C2×C9—31no—
130C2×C9—31no—
131C2×C9—61no—
132C2×C9—61no—
133C2×C9—61no—
134D9—181no—
135D9—181no—
136D9—181no—
137D9—366no—
138C22×C3—33no—
139C22×C3—31no—
140C22×C3—811no—
141C22×C3C3⋊#27211yescharacteristic
142C2×D3—271no—
143C2×D3—273no—
144A4—93no—
145C3×C4—811no—
146Dic3—271no—
147Dic3—273no—
148C32—33no—
149C32—31no—
150C32—123no—
151C32C3⋊(C3⋊S4)11yescharacteristic
152C9—21no—
153C9—31no—
154C9—31no—
155C9—126no—
156C9#625811yescharacteristic
157D4—811noSylow
158C2×C3—33no—
159C2×C3—31no—
160C2×C3—31no—
161C2×C3—63no—
162C2×C3—61no—
163C2×C3—1621no—
164D3—543no—
165D3—541no—
166D3—3243no—
167C22—811no—
168C22#9234411yescharacteristic, complemented
169C4—811no—
170C3—33no—
171C3—31no—
172C3—363no—
173C3C3⋊#625811yescharacteristic
174C2—31no—
175C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757825C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×C32×C9D3
socleC22×C3C3⋊#272
LCSG ▷ #11757825
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757825C2semidirect
9. C22×C32×C9D3semidirect
11. #66436D3semidirect
13. #66368D3semidirect
14. #66359D3semidirect
15. #66358D3semidirect
16. #66357D3semidirect
54. C32×C9S4semidirect
168. C22#92344semidirect

Maximal subgroups

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

subgroupindex
#117578252
#106200453
C3×#62333
#106197623
#66359⋊C23
#106197513
#106197503
#923444