Finite Group Databasebeta

← #28354979

Subgroups — #28354979

Order 13851.

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
1C19⋊H(5,𝔽3)C311yesmaximal, characteristic, complemented
2#17987514C311yesmaximal, characteristic, complemented
3#17987514C312yesmaximal, complemented
4#17987506C312yesmaximal, complemented
5#17987504C312yesmaximal, complemented
6C3×#13095315C311yesmaximal, characteristic, complemented
7C3×#13095313C311yesmaximal, characteristic, complemented
8(C3×C19⋊C3)⋊H(3,𝔽3)C312yesmaximal, complemented
9C19×#6911C311yesmaximal, characteristic, complemented
10C33×C19⋊C3C3211yescharacteristic, complemented
11C3×#10587025C3212yescomplemented
12C3×#10587025C3211yescharacteristic, complemented
13C3×C32⋊(C19⋊C3)—33no—
14C3×C32⋊(C19⋊C3)—36no—
15C3×C32⋊(C19⋊C3)C3212yes—
16C3×C32⋊(C19⋊C3)C3211yescharacteristic
17C3×C32⋊(C19⋊C3)C3212yescomplemented
18H(3,𝔽3)×C19⋊C3—36no—
19H(3,𝔽3)×C19⋊C3—33no—
20#13095319—33no—
21#13095319—36no—
22#13095315—36no—
23#13095315—33no—
24#13095313—36no—
25#13095313—33no—
26C3×C19×3−1+2C3211yescharacteristic, complemented
27C3×C19×H(3,𝔽3)C3211yescharacteristic
28C3×C19×H(3,𝔽3)C3212yescomplemented
29C19×#732—33no—
30UT(4,𝔽3)—191nomaximal, Sylow
31C33×C19—31no—
32C33×C19—32no—
33C33×C19C3311yescharacteristic
34C32×C19⋊C3—32no—
35C32×C19⋊C3—39no—
36C32×C19⋊C3—31no—
37C32×C19⋊C3—31no—
38C32×C19⋊C3—31no—
39C32×C19⋊C3—32no—
40C32×C19⋊C3—93no—
41C32×C19⋊C3H(3,𝔽3)16yescomplemented
42C19×3−1+2—31no—
43C19×3−1+2—32no—
44C19×H(3,𝔽3)—32no—
45C19×H(3,𝔽3)—32no—
46C19×H(3,𝔽3)—32no—
47C19×H(3,𝔽3)—32no—
48C19×H(3,𝔽3)H(3,𝔽3)13yescomplemented
49C3×C9×C19—31no—
50C32⋊(C19⋊C3)—318no—
51C32⋊(C19⋊C3)—32no—
52C32⋊(C19⋊C3)—32no—
53C32⋊(C19⋊C3)—32no—
54C32⋊(C19⋊C3)—32no—
55C32⋊(C19⋊C3)—32no—
56C32⋊(C19⋊C3)—32no—
57C32⋊(C19⋊C3)—32no—
58C32⋊(C19⋊C3)—918no—
59C32⋊(C19⋊C3)H(3,𝔽3)13yescomplemented
60#10587025—32no—
61#10587025—32no—
62#10587025—32no—
63#10587025—31no—
64#10587025—32no—
65C3×#4294—32no—
66C3×#4294—31no—
67H(5,𝔽3)—191no—
68#6911—191no—
69#6911—192no—
70#6911C19⋊C311yescharacteristic, complemented
71#6909—192no—
72#6909—192no—
73C3×AΣL(1,𝔽27)—191no—
74C3×AΣL(1,𝔽27)—191no—
75C32⋊H(3,𝔽3)—192no—
76C32×C19—33no—
77C32×C19—91no—
78C32×C19—96no—
79C32×C19—92no—
80C32×C19—271no—
81C32×C19C3×H(3,𝔽3)11yescharacteristic
82C32×C19C3×H(3,𝔽3)12yes—
83C32×C19C3×H(3,𝔽3)11yescharacteristic
84C3×C19⋊C3—36no—
85C3×C19⋊C3—36no—
86C3×C19⋊C3—33no—
87C3×C19⋊C3—94no—
88C3×C19⋊C3—91no—
89C3×C19⋊C3—93no—
90C3×C19⋊C3—93no—
91C3×C19⋊C3—96no—
92C3×C19⋊C3—96no—
93C3×C19⋊C3—92no—
94C3×C19⋊C3—271no—
95C3×C19⋊C3—279no—
96C9×C19—91no—
97#4294—92no—
98#4294—91no—
99C34—191no—
100C3×3−1+2—192no—
101C3×3−1+2—191no—
102C3×3−1+2C3×C19⋊C311yescharacteristic, complemented
103C3×H(3,𝔽3)—191no—
104C3×H(3,𝔽3)—192no—
105C3×H(3,𝔽3)—192no—
106C3×H(3,𝔽3)—576no—
107C3×H(3,𝔽3)—573no—
108C3×H(3,𝔽3)—573no—
109C3×H(3,𝔽3)—576no—
110C3×H(3,𝔽3)C3×C19⋊C311yescharacteristic
111C3×H(3,𝔽3)C3×C19⋊C312yescomplemented
112#732—33no—
113#732—576no—
114#732—573no—
115AΣL(1,𝔽27)—576no—
116AΣL(1,𝔽27)—573no—
117AΣL(1,𝔽27)—576no—
118AΣL(1,𝔽27)—573no—
119C3×C19—32no—
120C3×C19—31no—
121C3×C19—31no—
122C3×C19—93no—
123C3×C19—272no—
124C3×C19C32⋊H(3,𝔽3)11yescharacteristic
125C19⋊C3—93no—
126C19⋊C3—96no—
127C19⋊C3—93no—
128C19⋊C3—272no—
129C33—31no—
130C33—32no—
131C33—196no—
132C33—579no—
133C33—571no—
134C33—572no—
135C33—571no—
136C33—572no—
137C33—571no—
138C33—1713no—
139C33C32×C19⋊C311yescharacteristic
1403−1+2—31no—
1413−1+2—32no—
1423−1+2—571no—
1433−1+2—572no—
1443−1+2—572no—
1453−1+2—572no—
1463−1+2—572no—
147H(3,𝔽3)—32no—
148H(3,𝔽3)—32no—
149H(3,𝔽3)—32no—
150H(3,𝔽3)—32no—
151H(3,𝔽3)—193no—
152H(3,𝔽3)—5718no—
153H(3,𝔽3)—572no—
154H(3,𝔽3)—572no—
155H(3,𝔽3)—572no—
156H(3,𝔽3)—572no—
157H(3,𝔽3)—572no—
158H(3,𝔽3)—572no—
159H(3,𝔽3)—572no—
160H(3,𝔽3)—17118no—
161H(3,𝔽3)C32⋊(C19⋊C3)13yescomplemented
162C3×C9—31no—
163C3×C9—572no—
164C3×C9—571no—
165C19UT(4,𝔽3)11yescharacteristic, complemented, Sylow
166C32—5131no—
167C32—5139no—
168C32—33no—
169C32—91no—
170C32—96no—
171C32—92no—
172C32—271no—
173C32—576no—
174C32—573no—
175C32—576no—
176C32—1716no—
177C32—1712no—
178C32—1716no—
179C32—1713no—
180C32—1713no—
181C32—1714no—
182C32—1711no—
183C32H(3,𝔽3)×C19⋊C311yescharacteristic
184C32H(3,𝔽3)×C19⋊C312yes—
185C32C3×C32⋊(C19⋊C3)11yescharacteristic
186C9—91no—
187C9—1712no—
188C9—1711no—
189C3—5132no—
190C3—31no—
191C3—32no—
192C3—31no—
193C3—93no—
194C3—272no—
195C3—1713no—
196C3—1716no—
197C3—1713no—
198C3(C3×C19⋊C3)⋊H(3,𝔽3)11yescharacteristic
subgroupG/H
centerC3(C3×C19⋊C3)⋊H(3,𝔽3)
commutator, cosocleC33×C19C33
FrattiniC33C32×C19⋊C3
FittingC19×#6911C3
socleC3×C19C32⋊H(3,𝔽3)
hypercenter#6911C19⋊C3
hypocenterC19UT(4,𝔽3)
LCSG ▷ C33×C19 ▷ C3×C19 ▷ C19
UCSC1 ◁ C3 ◁ C33 ◁ #6911

Complements

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

NH ≅ G/Ntype
1. C19⋊H(5,𝔽3)C3semidirect
2. #17987514C3semidirect
3. #17987514C3semidirect
4. #17987506C3semidirect
5. #17987504C3semidirect
6. C3×#13095315C3semidirect
7. C3×#13095313C3semidirect
8. (C3×C19⋊C3)⋊H(3,𝔽3)C3semidirect
9. C19×#6911C3semidirect
10. C33×C19⋊C3C32semidirect
11. C3×#10587025C32semidirect
12. C3×#10587025C32semidirect
17. C3×C32⋊(C19⋊C3)C32semidirect
26. C3×C19×3−1+2C32semidirect
28. C3×C19×H(3,𝔽3)C32semidirect
41. C32×C19⋊C3H(3,𝔽3)semidirect
48. C19×H(3,𝔽3)H(3,𝔽3)semidirect
59. C32⋊(C19⋊C3)H(3,𝔽3)semidirect
70. #6911C19⋊C3semidirect
102. C3×3−1+2C3×C19⋊C3semidirect
111. C3×H(3,𝔽3)C3×C19⋊C3semidirect
161. H(3,𝔽3)C32⋊(C19⋊C3)semidirect
165. C19UT(4,𝔽3)semidirect

Maximal subgroups

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

subgroupindex
C19⋊H(5,𝔽3)3
#179875143
#179875063
#179875043
C3×#130953153
C3×#130953133
(C3×C19⋊C3)⋊H(3,𝔽3)3
C19×#69113
UT(4,𝔽3)19