Finite Group Databasebeta

← #44533719

Subgroups — #44533719

Order 31347.

560 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C43⋊H(5,𝔽3)C311yesmaximal, characteristic, complemented
2#23782892C312yesmaximal, complemented
3#23782891C312yesmaximal, complemented
4#23782883C312yesmaximal, complemented
5#23782882C311yesmaximal, characteristic, complemented
6C3×#16812508C312yesmaximal, complemented
7(C3×C43⋊C3)⋊H(3,𝔽3)C311yesmaximal, characteristic, complemented
8(C3×C43⋊C3)⋊H(3,𝔽3)C311yesmaximal, characteristic, complemented
9C43×#6909C311yesmaximal, characteristic, complemented
10C33×C43⋊C3C3211yescharacteristic, complemented
11C3×#11923958C3212yescomplemented
12C3×C32⋊(C43⋊C3)—33no—
13C3×C32⋊(C43⋊C3)—33no—
14C3×C32⋊(C43⋊C3)—33no—
15C3×C32⋊(C43⋊C3)C3211yescharacteristic
16C3×C32⋊(C43⋊C3)C3212yes—
17C3×C32⋊(C43⋊C3)C3211yescharacteristic, complemented
18C3×C32⋊(C43⋊C3)C3212yescomplemented
19H(3,𝔽3)×C43⋊C3—33no—
20H(3,𝔽3)×C43⋊C3—36no—
21#16812513—36no—
22#16812512—36no—
23#16812508—36no—
24#16812508—36no—
25#16812507—33no—
26C3×3−1+2×C43C3212yescomplemented
27C3×H(3,𝔽3)×C43C3211yescharacteristic
28C3×H(3,𝔽3)×C43C3211yescharacteristic, complemented
29C43×AΣL(1,𝔽27)—33no—
30C32×C43⋊C3—31no—
31C32×C43⋊C3—31no—
32C32×C43⋊C3—39no—
33C32×C43⋊C3—32no—
34C32×C43⋊C3—32no—
35C32×C43⋊C3—31no—
36C32×C43⋊C3—32no—
37C32×C43⋊C3—93no—
38C32×C43⋊C3H(3,𝔽3)13yescomplemented
39#11923958—32no—
40#11923958—32no—
41#11923958—32no—
42C32⋊(C43⋊C3)—318no—
43C32⋊(C43⋊C3)—32no—
44C32⋊(C43⋊C3)—32no—
45C32⋊(C43⋊C3)—31no—
46C32⋊(C43⋊C3)—32no—
47C32⋊(C43⋊C3)—31no—
48C32⋊(C43⋊C3)—32no—
49C32⋊(C43⋊C3)—32no—
50C32⋊(C43⋊C3)—32no—
51C32⋊(C43⋊C3)—32no—
52C32⋊(C43⋊C3)—99no—
53C32⋊(C43⋊C3)—99no—
54C32⋊(C43⋊C3)H(3,𝔽3)16yescomplemented
55C3×C43⋊C9—32no—
56C33×C43—31no—
57C33×C43H(3,𝔽3)13yescomplemented
58C33×C43C3311yescharacteristic
593−1+2×C43—32no—
603−1+2×C43—32no—
613−1+2×C43—32no—
62H(3,𝔽3)×C43—32no—
63H(3,𝔽3)×C43—31no—
64H(3,𝔽3)×C43—31no—
65H(3,𝔽3)×C43—32no—
66C3×C9×C43—32no—
67UT(4,𝔽3)—431nomaximal, Sylow
68C32×C43—33no—
69C32×C43—91no—
70C32×C43—93no—
71C32×C43—93no—
72C32×C43—91no—
73C32×C43C3×H(3,𝔽3)12yes—
74C32×C43C3×H(3,𝔽3)11yescharacteristic
75C32×C43C3×H(3,𝔽3)11yescharacteristic
76C3×C43⋊C3—33no—
77C3×C43⋊C3—33no—
78C3×C43⋊C3—33no—
79C3×C43⋊C3—36no—
80C3×C43⋊C3—92no—
81C3×C43⋊C3—92no—
82C3×C43⋊C3—91no—
83C3×C43⋊C3—96no—
84C3×C43⋊C3—93no—
85C3×C43⋊C3—93no—
86C3×C43⋊C3—96no—
87C3×C43⋊C3—91no—
88C3×C43⋊C3—92no—
89C3×C43⋊C3—272no—
90C3×C43⋊C3—279no—
91C9×C43—92no—
92C43⋊C9—92no—
93H(5,𝔽3)—431no—
94#6911—432no—
95#6911—432no—
96#6909—432no—
97#6909—431no—
98#6909C43⋊C311yescharacteristic, complemented
99C3×AΣL(1,𝔽27)—432no—
100C32⋊H(3,𝔽3)—431no—
101C32⋊H(3,𝔽3)—431no—
102C3×C43—31no—
103C3×C43—31no—
104C3×C43—32no—
105C3×C43—93no—
106C3×C43—271no—
107C3×C43C32⋊H(3,𝔽3)11yescharacteristic
108C43⋊C3—93no—
109C43⋊C3—93no—
110C43⋊C3—96no—
111C43⋊C3—271no—
112C43⋊C3—272no—
113C34—431no—
114C3×3−1+2—432no—
115C3×3−1+2C3×C43⋊C312yescomplemented
116C3×H(3,𝔽3)—432no—
117C3×H(3,𝔽3)—431no—
118C3×H(3,𝔽3)—432no—
119C3×H(3,𝔽3)—431no—
120C3×H(3,𝔽3)—1296no—
121C3×H(3,𝔽3)—1293no—
122C3×H(3,𝔽3)—1293no—
123C3×H(3,𝔽3)—1293no—
124C3×H(3,𝔽3)—1293no—
125C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
126C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic, complemented
127#732—1296no—
128#732—1296no—
129AΣL(1,𝔽27)—33no—
130AΣL(1,𝔽27)—1296no—
131AΣL(1,𝔽27)—1296no—
132AΣL(1,𝔽27)—1293no—
133C43UT(4,𝔽3)11yescharacteristic, complemented, Sylow
134C33—31no—
135C33—433no—
136C33—1299no—
137C33—1291no—
138C33—1291no—
139C33—1292no—
140C33—1292no—
141C33—1291no—
142C33—1292no—
143C33—3873no—
144C33C32⋊(C43⋊C3)13yescomplemented
145C33C32×C43⋊C311yescharacteristic
1463−1+2—32no—
1473−1+2—32no—
1483−1+2—32no—
1493−1+2—1292no—
1503−1+2—1292no—
1513−1+2—1292no—
152H(3,𝔽3)—32no—
153H(3,𝔽3)—31no—
154H(3,𝔽3)—32no—
155H(3,𝔽3)—31no—
156H(3,𝔽3)—436no—
157H(3,𝔽3)—12918no—
158H(3,𝔽3)—1292no—
159H(3,𝔽3)—1292no—
160H(3,𝔽3)—1292no—
161H(3,𝔽3)—1291no—
162H(3,𝔽3)—1292no—
163H(3,𝔽3)—1292no—
164H(3,𝔽3)—1292no—
165H(3,𝔽3)—1292no—
166H(3,𝔽3)—1291no—
167H(3,𝔽3)—3879no—
168H(3,𝔽3)—3879no—
169C3×C9—32no—
170C3×C9—1292no—
171C32—33no—
172C32—91no—
173C32—93no—
174C32—93no—
175C32—91no—
176C32—1293no—
177C32—1293no—
178C32—1296no—
179C32—1293no—
180C32—3873no—
181C32—3876no—
182C32—3872no—
183C32—3872no—
184C32—3873no—
185C32—3876no—
186C32—3871no—
187C32—3872no—
188C32—3871no—
189C32—11612no—
190C32—11619no—
191C32H(3,𝔽3)×C43⋊C312yes—
192C32H(3,𝔽3)×C43⋊C311yescharacteristic
193C32C3×C32⋊(C43⋊C3)11yescharacteristic
194C9—92no—
195C9—3872no—
196C3—31no—
197C3—31no—
198C3—32no—
199C3—93no—
200C3—271no—
201C3—3873no—
202C3—3873no—
203C3—3876no—
204C3—11611no—
205C3—11612no—
206C3(C3×C43⋊C3)⋊H(3,𝔽3)11yescharacteristic
subgroupG/H
centerC3(C3×C43⋊C3)⋊H(3,𝔽3)
commutator, cosocleC33×C43C33
FrattiniC33C32×C43⋊C3
FittingC43×#6909C3
socleC3×C43C32⋊H(3,𝔽3)
hypercenter#6909C43⋊C3
hypocenterC43UT(4,𝔽3)
LCSG ▷ C33×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C33 ◁ #6909

Complements

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

NH ≅ G/Ntype
1. C43⋊H(5,𝔽3)C3semidirect
2. #23782892C3semidirect
3. #23782891C3semidirect
4. #23782883C3semidirect
5. #23782882C3semidirect
6. C3×#16812508C3semidirect
7. (C3×C43⋊C3)⋊H(3,𝔽3)C3semidirect
8. (C3×C43⋊C3)⋊H(3,𝔽3)C3semidirect
9. C43×#6909C3semidirect
10. C33×C43⋊C3C32semidirect
11. C3×#11923958C32semidirect
17. C3×C32⋊(C43⋊C3)C32semidirect
18. C3×C32⋊(C43⋊C3)C32semidirect
26. C3×3−1+2×C43C32semidirect
28. C3×H(3,𝔽3)×C43C32semidirect
38. C32×C43⋊C3H(3,𝔽3)semidirect
54. C32⋊(C43⋊C3)H(3,𝔽3)semidirect
57. C33×C43H(3,𝔽3)semidirect
98. #6909C43⋊C3semidirect
115. C3×3−1+2C3×C43⋊C3semidirect
126. C3×H(3,𝔽3)C3×C43⋊C3semidirect
133. C43UT(4,𝔽3)semidirect
144. C33C32⋊(C43⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C43⋊H(5,𝔽3)3
#237828923
#237828913
#237828833
#237828823
C3×#168125083
(C3×C43⋊C3)⋊H(3,𝔽3)3
C43×#69093
UT(4,𝔽3)43