Finite Group Databasebeta

← #13091647

Subgroups — #13091647

Order 1458.

536 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 67 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#10624930C211yesmaximal, characteristic, complemented, Sylow
2#4207⋊C3—32nomaximal
3#92391—31nomaximal
4C3×C3⋊((C3⋊D3)⋊C3)—31nomaximal
5C3⋊#4183C311yesmaximal, characteristic, complemented
6#4183⋊C3—36nomaximal
7C3×#4183—33nomaximal
83−1+4D312yescomplemented
9H(5,𝔽3)D311yescharacteristic, complemented
10C32×H(3,𝔽3)D311yescharacteristic, complemented
11#6909—22no—
12#6909—21no—
13#6909—26no—
14#6909D316yescomplemented
15C3×AΣL(1,𝔽27)—21no—
16C3×AΣL(1,𝔽27)—23no—
17C3×AΣL(1,𝔽27)D313yescomplemented
18C3×AΣL(1,𝔽27)C2×C311yescharacteristic, complemented
19C3×C3⋊(C3⋊D3)—31no—
20C32×C3⋊D3—91no—
21#4207—36no—
22C3⋊AGL(1,ℤ/9)—32no—
23C3⋊((C3⋊D3)⋊C3)—33no—
24C3⋊((C3⋊D3)⋊C3)—33no—
25C3⋊((C3⋊D3)⋊C3)—31no—
26C3×AGL(1,ℤ/9)—96no—
27C3×(C3⋊D3)⋊C3—91no—
28C3×(C3⋊D3)⋊C3—93no—
29C3×(C3⋊D3)⋊C3—92no—
30#4183—33no—
31#4183—36no—
32C34—21no—
33C34C3×D311yescharacteristic, complemented
34C34C3⋊D311yescharacteristic, complemented
35#737—36no—
36#737—66no—
37C3×3−1+2—22no—
38C3×3−1+2—26no—
39C3×3−1+2C3×D312yescomplemented
40C3×3−1+2C3⋊D316yescomplemented
41C3×H(3,𝔽3)—21no—
42C3×H(3,𝔽3)—23no—
43C3×H(3,𝔽3)—22no—
44C3×H(3,𝔽3)—21no—
45C3×H(3,𝔽3)—33no—
46C3×H(3,𝔽3)—33no—
47C3×H(3,𝔽3)—63no—
48C3×H(3,𝔽3)—63no—
49C3×H(3,𝔽3)C3×D311yescharacteristic, complemented
50C3×H(3,𝔽3)C3⋊D311yescharacteristic
51C3×H(3,𝔽3)C3⋊D313yescomplemented
52C3×H(3,𝔽3)C3⋊D312yescomplemented
53AΣL(1,𝔽27)—23no—
54AΣL(1,𝔽27)—26no—
55AΣL(1,𝔽27)—212no—
56AΣL(1,𝔽27)—26no—
57AΣL(1,𝔽27)—26no—
58AΣL(1,𝔽27)—23no—
59AΣL(1,𝔽27)C3×D313yescomplemented
60AΣL(1,𝔽27)C3×D316yescomplemented
61C3⋊(C3⋊D3)—31no—
62C3⋊(C3⋊D3)—31no—
63C3×C3⋊D3—93no—
64C3×C3⋊D3—91no—
65C3×C3⋊D3—93no—
66C3×C3⋊D3—92no—
67C3×C3⋊D3—91no—
68C3×C3⋊D3—273no—
69C32×D3—273no—
70C32×D3—271no—
71C3⋊D9—32no—
72AGL(1,ℤ/9)—912no—
73AGL(1,ℤ/9)—96no—
74(C3⋊D3)⋊C3—96no—
75(C3⋊D3)⋊C3—96no—
76(C3⋊D3)⋊C3—93no—
77(C3⋊D3)⋊C3—93no—
78C3×D9—96no—
79C33—21no—
80C33—21no—
81C33—22no—
82C33—31no—
83C33—31no—
84C33—33no—
85C33—33no—
86C33—61no—
87C33—63no—
88C33—63no—
89C33—61no—
90C33—93no—
91C33—93no—
92C33—183no—
93C33C3×C3⋊D311yescharacteristic
94C33C3×C3⋊D311yescharacteristic
95C33C3×C3⋊D312yes—
96C33C3⋊(C3⋊D3)11yescharacteristic
973−1+2—26no—
983−1+2—312no—
993−1+2—62no—
1003−1+2—612no—
1013−1+2—62no—
1023−1+2—62no—
1033−1+2C3×C3⋊D316yes—
104H(3,𝔽3)—23no—
105H(3,𝔽3)—23no—
106H(3,𝔽3)—36no—
107H(3,𝔽3)—36no—
108H(3,𝔽3)—61no—
109H(3,𝔽3)—66no—
110H(3,𝔽3)—66no—
111H(3,𝔽3)—61no—
112H(3,𝔽3)—62no—
113H(3,𝔽3)—61no—
114H(3,𝔽3)—61no—
115H(3,𝔽3)#27213yes—
116H(3,𝔽3)C3×C3⋊D313yes—
117C3×C9—32no—
118C3×C9—36no—
119C3×C9—66no—
120C3×C9—62no—
121C2×C32—811no—
122C3⋊D3—91no—
123C3⋊D3—92no—
124C3⋊D3—93no—
125C3⋊D3—91no—
126C3⋊D3—273no—
127C3⋊D3—811no—
128C3×D3—273no—
129C3×D3—279no—
130C3×D3—273no—
131C3×D3—271no—
132C3×D3—811no—
133C3×D3—812no—
134C3×D3—813no—
135D9—96no—
136C32—21no—
137C32—23no—
138C32—33no—
139C32—31no—
140C32—32no—
141C32—33no—
142C32—63no—
143C32—62no—
144C32—61no—
145C32—91no—
146C32—91no—
147C32—93no—
148C32—99no—
149C32—92no—
150C32—181no—
151C32—183no—
152C32—189no—
153C32—181no—
154C32—182no—
155C32—271no—
156C32—273no—
157C32—543no—
158C32—541no—
159C32C3×#27211yescharacteristic
160C32C3⋊#27213yes—
161C32C3×C3⋊(C3⋊D3)11yescharacteristic
162C9—36no—
163C9—66no—
164C2×C3—811no—
165C2×C3—813no—
166D3—273no—
167D3—271no—
168D3—811no—
169D3—812no—
170D3—813no—
171C3—33no—
172C3—31no—
173C3—31no—
174C3—33no—
175C3—61no—
176C3—63no—
177C3—92no—
178C3—93no—
179C3—181no—
180C3—182no—
181C3—183no—
182C3C3×C3⋊#27211yescharacteristic
183C2—811noSylow
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×AΣL(1,𝔽27)C2×C3
FrattiniC32C3×C3⋊(C3⋊D3)
Fitting#10624930C2
socleC3C3×C3⋊#272
LCSG ▷ C3×AΣL(1,𝔽27)
UCSC1

Complements

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

NH ≅ G/Ntype
1. #10624930C2semidirect
5. C3⋊#4183C3semidirect
8. 3−1+4D3semidirect
9. H(5,𝔽3)D3semidirect
10. C32×H(3,𝔽3)D3semidirect
14. #6909D3semidirect
17. C3×AΣL(1,𝔽27)D3semidirect
18. C3×AΣL(1,𝔽27)C2×C3semidirect
33. C34C3×D3semidirect
34. C34C3⋊D3semidirect
39. C3×3−1+2C3×D3semidirect
40. C3×3−1+2C3⋊D3semidirect
49. C3×H(3,𝔽3)C3×D3semidirect
51. C3×H(3,𝔽3)C3⋊D3semidirect
52. C3×H(3,𝔽3)C3⋊D3semidirect
59. AΣL(1,𝔽27)C3×D3semidirect
60. AΣL(1,𝔽27)C3×D3semidirect

Maximal subgroups

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

subgroupindex
#106249302
#4207⋊C33
#923913
C3×C3⋊((C3⋊D3)⋊C3)3
C3⋊#41833
#4183⋊C33
C3×#41833