Finite Group Databasebeta

← #14518103

Subgroups — #14518103

Order 1944.

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

normal subgroups only

This group has 286 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#11757806C211yesmaximal, characteristic, complemented
2#10620047—33nomaximal
3C3×C9⋊S4—31nomaximal
4#10619757—33nomaximal
5#10619756—33nomaximal
6#66359⋊C2—32nomaximal
7#10619683—31nomaximal
8#92344—41nomaximal
9#66437D313yescomplemented
10C3×C9×A4D311yescharacteristic, complemented
11C22×#732D311yescharacteristic, complemented
12C2×#4185—31no—
13#66363D313yescomplemented
14#66361D313yescomplemented
15#66359D312yescomplemented
16#66332—31no—
17#6908—41noSylow
18C3×C3⋊S4—91no—
19C3⋊((C22⋊C9)⋊C2)—33no—
20C9⋊S4—31no—
21C3×(C22⋊C9)⋊C2—91no—
22C3×(C22⋊C9)⋊C2—91no—
23((C22⋊C9)⋊C2)⋊C3—96no—
24#638⋊C3—93no—
25C3×#611—91no—
26#4207—123no—
27C3×C3⋊D9—121no—
28C2×#732—31no—
29#733⋊C2—122no—
30#4185—61no—
31#4184—123no—
32#4183—123no—
33C32×A4C3⋊D311yescharacteristic
34C22×H(3,𝔽3)C3⋊D313yes—
35C22×C3×C9C3⋊D311yescharacteristic
36C2×(C3⋊D3)⋊C3—93no—
37C2×C3×D9—91no—
38#1094—63no—
39#1094C3⋊D316yes—
40C3×C22⋊C9—33no—
41C3×C22⋊C9C3⋊D311yescharacteristic
42C3×C22⋊C9C3⋊D311yescharacteristic
43C9×A4—31no—
44C9×A4—61no—
45(C3⋊Dic3)⋊C3—93no—
46C3×Dic9—91no—
47#737—43no—
48C32×C9—41no—
49#733—42no—
50#732S411yescharacteristic, complemented
51#731—43no—
52AΣL(1,𝔽27)—43no—
53C3⋊S4—91no—
54C3×S4—273no—
55#638—93no—
56C3×#67—271no—
57(C22⋊C9)⋊C2—96no—
58(C22⋊C9)⋊C2—91no—
59(C22⋊C9)⋊C2—91no—
60#611—91no—
61C3×C3⋊D3—361no—
62C2×H(3,𝔽3)—33no—
63C2×C3×C9—31no—
64C3⋊D9—121no—
65C3⋊D9—123no—
66AGL(1,ℤ/9)—366no—
67(C3⋊D3)⋊C3—183no—
68C3×D9—181no—
69C3×D9—361no—
70C3×D9—361no—
71C22×C32—33no—
72C22×C32C3⋊(C3⋊D3)11yescharacteristic
73C2×C3⋊D3—93no—
74C2×C3×D3—271no—
75C3×A4—31no—
76C3×A4—33no—
77C3⋊Dic3—93no—
78C3×Dic3—271no—
79C22×C9—31no—
80C2×D9—91no—
81C22⋊C9—21no—
82C22⋊C9—31no—
83C22⋊C9—36no—
84C22⋊C9#27211yescharacteristic
85Dic9—91no—
86C33—41no—
873−1+2—46no—
883−1+2—243no—
89H(3,𝔽3)C3⋊S413yes—
90C3×C9—41no—
91C3×C9—41no—
92C3×C9—121no—
93C3×C9—123no—
94C3×C9—241no—
95C3×C9C3⋊S411yescharacteristic
96S4—273no—
97C3×D4—811no—
98#67—271no—
99#67—813no—
100C2×C32—31no—
101C2×C32—93no—
102C3⋊D3—183no—
103C3⋊D3—361no—
104C3×D3—541no—
105C3×D3—1083no—
106C2×C9—91no—
107D9—181no—
108D9—361no—
109D9—361no—
110D9—366no—
111C22×C3—31no—
112C22×C3—93no—
113C22×C3—811no—
114C22×C3C3⋊#27211yescharacteristic
115C2×D3—271no—
116C2×D3—813no—
117A4—33no—
118C3×C4—811no—
119Dic3—271no—
120Dic3—813no—
121C32—33no—
122C32—123no—
123C32—121no—
124C32C3⋊(C3⋊S4)11yescharacteristic
125C9—31no—
126C9—41no—
127C9—81no—
128C9—121no—
129C9—126no—
130D4—811noSylow
131C2×C3—31no—
132C2×C3—91no—
133C2×C3—273no—
134C2×C3—1621no—
135D3—541no—
136D3—1083no—
137D3—1623no—
138C22—811no—
139C22#9234411yescharacteristic, complemented
140C4—811no—
141C3—31no—
142C3—93no—
143C3—123no—
144C3A4⋊#27211yescharacteristic
145C2—31no—
146C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#11757806C2
FrattiniC32C3⋊(C3⋊S4)
FittingC22×#732D3
socleC22×C3C3⋊#272
LCSG ▷ #11757806
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757806C2semidirect
9. #66437D3semidirect
10. C3×C9×A4D3semidirect
11. C22×#732D3semidirect
13. #66363D3semidirect
14. #66361D3semidirect
15. #66359D3semidirect
50. #732S4semidirect
139. C22#92344semidirect

Maximal subgroups

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

subgroupindex
#117578062
#106200473
C3×C9⋊S43
#106197573
#106197563
#66359⋊C23
#106196833
#923444