Finite Group Databasebeta

← #11757810⋊C2 #14518105

Subgroups — #11757810⋊C2 #14518105

Order 1944.

277 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 277 conjugacy classes of subgroups — too many to draw. Only its 40 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#11757810C211yesmaximal, characteristic, complemented
2#66440⋊C2—33nomaximal
3C3×C9⋊S4—31nomaximal
4#66365⋊C2—33nomaximal
5#66366⋊C2—33nomaximal
6#66359⋊C2—31nomaximal
7#10619750—31nomaximal
8#10619685—31nomaximal
9#92344—41nomaximal
10#66440D313yescomplemented
11C3×C9×A4D311yescharacteristic, complemented
12C22×#733D311yescharacteristic, complemented
13C2×#733⋊C2—31no—
14#66366D313yescomplemented
15#66365D313yescomplemented
16#66359D311yescharacteristic, complemented
17#66358D311yescharacteristic, complemented
18#733⋊C4—31no—
19#6908—41noSylow
20C3×C3⋊S4—91no—
21C9⋊S4—31no—
22C9⋊S4—33no—
23(C3⋊S4)⋊C3—93no—
24C3×(C22⋊C9)⋊C2—91no—
25C3×(C22⋊C9)⋊C2—91no—
26((C22⋊C9)⋊C2)⋊C3—93no—
27#611⋊C3—93no—
28C3×#611—91no—
29#4207—123no—
30C3×C3⋊D9—121no—
31C2×#733—31no—
32#733⋊C2—61no—
33#733⋊C2—121no—
34#4185—121no—
35#4184—123no—
36#4183—123no—
37C32×A4C3⋊D311yescharacteristic
38C22×3−1+2C3⋊D313yes—
39C22×C3×C9C3⋊D311yescharacteristic
40C2×AGL(1,ℤ/9)—93no—
41C2×C3×D9—91no—
42C22⋊H(3,𝔽3)C3⋊D313yes—
43#1094C3⋊D313yes—
44C3×C22⋊C9C3⋊D311yescharacteristic
45C3×C22⋊C9C3⋊D311yescharacteristic
46C9⋊A4—63no—
47C9×A4—31no—
48C9×A4—33no—
49C9×A4—61no—
503−1+2⋊C4—93no—
51C3×Dic9—91no—
52#737—43no—
53C32×C9—41no—
54#733—41no—
55#733S411yescharacteristic, complemented
56#732—41no—
57#731—43no—
58AΣL(1,𝔽27)—43no—
59C3⋊S4—91no—
60C3⋊S4—93no—
61C3×S4—273no—
62C3×#67—271no—
63(C22⋊C9)⋊C2—93no—
64(C22⋊C9)⋊C2—91no—
65(C22⋊C9)⋊C2—91no—
66#611—91no—
67#611—93no—
68C3×C3⋊D3—361no—
69C2×3−1+2—33no—
70C2×C3×C9—31no—
71C3⋊D9—121no—
72C3⋊D9—123no—
73AGL(1,ℤ/9)—183no—
74AGL(1,ℤ/9)—363no—
75(C3⋊D3)⋊C3—363no—
76C3×D9—181no—
77C3×D9—361no—
78C3×D9—361no—
79C22×C32C3⋊(C3⋊D3)11yescharacteristic
80C2×C3×D3—271no—
81C3×A4—31no—
82C3×A4—33no—
83C3×A4—33no—
84C3×Dic3—271no—
85C22×C9—31no—
86C22×C9—33no—
87C2×D9—91no—
88C2×D9—93no—
89C22⋊C9—21no—
90C22⋊C9—31no—
91C22⋊C9—33no—
92C22⋊C9#27211yescharacteristic
93Dic9—91no—
94Dic9—93no—
95C33—41no—
963−1+2—43no—
973−1+2—243no—
983−1+2C3⋊S413yes—
99H(3,𝔽3)—43no—
100C3×C9—41no—
101C3×C9—41no—
102C3×C9—121no—
103C3×C9—123no—
104C3×C9—241no—
105C3×C9C3⋊S411yescharacteristic
106S4—273no—
107S4—813no—
108C3×D4—811no—
109#67—271no—
110C2×C32—31no—
111C3⋊D3—363no—
112C3⋊D3—361no—
113C3×D3—541no—
114C3×D3—1083no—
115C2×C9—91no—
116C2×C9—93no—
117D9—181no—
118D9—183no—
119D9—361no—
120D9—361no—
121D9—363no—
122C22×C3—31no—
123C22×C3—811no—
124C22×C3C3⋊#27211yescharacteristic
125C2×D3—271no—
126A4—33no—
127A4—93no—
128C3×C4—811no—
129Dic3—271no—
130C32—123no—
131C32—121no—
132C32—123no—
133C32C3⋊(C3⋊S4)11yescharacteristic
134C9—31no—
135C9—33no—
136C9—41no—
137C9—81no—
138C9—121no—
139C9—123no—
140D4—811noSylow
141C2×C3—31no—
142C2×C3—91no—
143C2×C3—1621no—
144D3—541no—
145D3—3243no—
146D3—1083no—
147C22—811no—
148C22#9234411yescharacteristic, complemented
149C4—811no—
150C3—31no—
151C3—123no—
152C3—363no—
153C3A4⋊#27211yescharacteristic
154C2—31no—
155C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757810C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×#733D3
socleC22×C3C3⋊#272
LCSG ▷ #11757810
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757810C2semidirect
10. #66440D3semidirect
11. C3×C9×A4D3semidirect
12. C22×#733D3semidirect
14. #66366D3semidirect
15. #66365D3semidirect
16. #66359D3semidirect
17. #66358D3semidirect
55. #733S4semidirect
148. C22#92344semidirect

Maximal subgroups

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

subgroupindex
#117578102
#66440⋊C23
C3×C9⋊S43
#66365⋊C23
#66366⋊C23
#66359⋊C23
#106197503
#106196853
#923444