Finite Group Databasebeta

← C19⋊C3×#6911 #28356567

Subgroups — C19⋊C3×#6911 #28356567

Order 13851.

1304 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 271 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
1C3×3−1+2×C19⋊C3C311yesmaximal, characteristic, complemented
2C3×H(3,𝔽3)×C19⋊C3C313yesmaximal, complemented
3#17987515C312yesmaximal, complemented
4#17987514C316yesmaximal, complemented
5#17987513C319yesmaximal, complemented
6#17987512C319yesmaximal, complemented
7C19⋊C3×#732C319yesmaximal, complemented
8C19×#6911C311yesmaximal, characteristic, complemented
9C33×C19⋊C3—33no—
10C33×C19⋊C3C3211yescharacteristic
11C3×#10587025C3212yescomplemented
12C3×#10587022C3213yescomplemented
13C3×#10587023C3213yescomplemented
143−1+2×C19⋊C3—33no—
153−1+2×C19⋊C3—36no—
16C3×C32⋊(C19⋊C3)—36no—
17C3×C32⋊(C19⋊C3)C3216yescomplemented
18H(3,𝔽3)×C19⋊C3—36no—
19H(3,𝔽3)×C19⋊C3—36no—
20H(3,𝔽3)×C19⋊C3—36no—
21H(3,𝔽3)×C19⋊C3C3219yescomplemented
22H(3,𝔽3)×C19⋊C3C3219yescomplemented
23H(3,𝔽3)×C19⋊C3C3219yescomplemented
24C3×C9×C19⋊C3C3213yescomplemented
25#13095320C32118yescomplemented
26#13095319C32154yescomplemented
27C3×C19×3−1+2C3211yescharacteristic, complemented
28C3×C19×H(3,𝔽3)C3213yescomplemented
29C19×#732C3219yescomplemented
30C3×#6911—191nomaximal, Sylow
31C33×C19—33no—
32C33×C19C3311yescharacteristic
33C32×C19⋊C3—36no—
34C32×C19⋊C3—39no—
35C32×C19⋊C3—39no—
36C32×C19⋊C3—39no—
37C32×C19⋊C3—93no—
38C32×C19⋊C3—927no—
39C32×C19⋊C3H(3,𝔽3)13yes—
40C32×C19⋊C3H(3,𝔽3)16yes—
41C32×C19⋊C3C3311yescharacteristic
42C32×C19⋊C3C3311yescharacteristic
43C32×C19⋊C3C3311yescharacteristic
44C19×3−1+2—33no—
45C19×H(3,𝔽3)—36no—
46C19×H(3,𝔽3)C3319yescomplemented
47C3×C9×C19C3313yescomplemented
48C32⋊(C19⋊C3)—312no—
49C32⋊(C19⋊C3)—318no—
50C32⋊(C19⋊C3)—318no—
51C32⋊(C19⋊C3)—318no—
52C32⋊(C19⋊C3)C33118yescomplemented
53#10587025—36no—
54C3×#4294C3316yescomplemented
55#10587023—39no—
56#10587022—39no—
57C9×C19⋊C3—36no—
58C9×C19⋊C3—33no—
59C32×3−1+2—191no—
60C32×H(3,𝔽3)—193no—
61#6911—192no—
62#6911—196no—
63#6911—199no—
64#6911—199no—
65#6911C19⋊C311yescharacteristic, direct product factor
66C3×#732—199no—
67C32×C19—39no—
68C32×C19—91no—
69C32×C19—99no—
70C32×C19C3×H(3,𝔽3)13yes—
71C32×C19C3411yescharacteristic
72C3×C19⋊C3—39no—
73C3×C19⋊C3—33no—
74C3×C19⋊C3—318no—
75C3×C19⋊C3—96no—
76C3×C19⋊C3—91no—
77C3×C19⋊C3—91no—
78C3×C19⋊C3—927no—
79C3×C19⋊C3—927no—
80C3×C19⋊C3—918no—
81C3×C19⋊C3—927no—
82C3×C19⋊C3C3×H(3,𝔽3)12yes—
83C3×C19⋊C3C3×H(3,𝔽3)13yes—
84C3×C19⋊C3C3×H(3,𝔽3)13yes—
85C3×C19⋊C3C3×H(3,𝔽3)11yescharacteristic
86C9×C19—33no—
87#4294—36no—
88C34—191no—
89C34—573no—
90C3×3−1+2—192no—
91C3×3−1+2—193no—
92C3×3−1+2—193no—
93C3×3−1+2—573no—
94C3×3−1+2—576no—
95C3×3−1+2C3×C19⋊C311yescharacteristic, complemented
96C3×H(3,𝔽3)—196no—
97C3×H(3,𝔽3)—199no—
98C3×H(3,𝔽3)—199no—
99C3×H(3,𝔽3)—199no—
100C3×H(3,𝔽3)—576no—
101C3×H(3,𝔽3)—576no—
102C3×H(3,𝔽3)—576no—
103C3×H(3,𝔽3)—576no—
104C3×H(3,𝔽3)C3×C19⋊C313yescomplemented
105C32×C9—193no—
106#732—1954no—
107#732—1918no—
108#732C3×C19⋊C319yescomplemented
109C3×C19—33no—
110C3×C19—31no—
111C3×C19—99no—
112C3×C19C32×H(3,𝔽3)11yescharacteristic
113C19⋊C3—33no—
114C19⋊C3—33no—
115C19⋊C3—32no—
116C19⋊C3—918no—
117C19⋊C3#691113yesdirect product factor
118C33—33no—
119C33—193no—
120C33—191no—
121C33—196no—
122C33—191no—
123C33—191no—
124C33—579no—
125C33—579no—
126C33—579no—
127C33—576no—
128C33—1713no—
129C33—17127no—
130C33C32×C19⋊C311yescharacteristic
1313−1+2—33no—
1323−1+2—579no—
1333−1+2—579no—
1343−1+2—576no—
135H(3,𝔽3)—36no—
136H(3,𝔽3)—1918no—
137H(3,𝔽3)—5718no—
138H(3,𝔽3)—5718no—
139H(3,𝔽3)—5718no—
140H(3,𝔽3)—5712no—
141H(3,𝔽3)C32×C19⋊C319yescomplemented
142C3×C9—196no—
143C3×C9—573no—
144C3×C9—576no—
145C3×C9C32×C19⋊C313yescomplemented
146C19C3×#691111yescharacteristic, complemented, Sylow
147C32—39no—
148C32—91no—
149C32—99no—
150C32—191no—
151C32—192no—
152C32—193no—
153C32—193no—
154C32—579no—
155C32—573no—
156C32—5718no—
157C32—1716no—
158C32—1711no—
159C32—1711no—
160C32—17118no—
161C32—17127no—
162C32—17127no—
163C32—17127no—
164C32H(3,𝔽3)×C19⋊C313yes—
165C32C33×C19⋊C311yescharacteristic
166C9—33no—
167C9—576no—
168C3—33no—
169C3—31no—
170C3—99no—
171C3—193no—
172C3—573no—
173C3—573no—
174C3—572no—
175C3—17118no—
176C3C3×H(3,𝔽3)×C19⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C19⋊C3
commutator, cosocleC32×C19C34
FrattiniC32C33×C19⋊C3
FittingC19×#6911C3
socleC3×C19C32×H(3,𝔽3)
hypercenter#6911C19⋊C3
hypocenterC19C3×#6911
LCSG ▷ C32×C19 ▷ C3×C19 ▷ C19
UCSC1 ◁ C3 ◁ C33 ◁ #6911

Complements

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

NH ≅ G/Ntype
1. C3×3−1+2×C19⋊C3C3semidirect
2. C3×H(3,𝔽3)×C19⋊C3C3semidirect
3. #17987515C3semidirect
4. #17987514C3semidirect
5. #17987513C3semidirect
6. #17987512C3semidirect
7. C19⋊C3×#732C3semidirect
8. C19×#6911C3semidirect
11. C3×#10587025C32semidirect
12. C3×#10587022C32semidirect
13. C3×#10587023C32semidirect
17. C3×C32⋊(C19⋊C3)C32semidirect
21. H(3,𝔽3)×C19⋊C3C32semidirect
22. H(3,𝔽3)×C19⋊C3C32semidirect
23. H(3,𝔽3)×C19⋊C3C32semidirect
24. C3×C9×C19⋊C3C32semidirect
25. #13095320C32semidirect
26. #13095319C32semidirect
27. C3×C19×3−1+2C32semidirect
28. C3×C19×H(3,𝔽3)C32semidirect
29. C19×#732C32semidirect
46. C19×H(3,𝔽3)C33semidirect
47. C3×C9×C19C33semidirect
52. C32⋊(C19⋊C3)C33semidirect
54. C3×#4294C33semidirect
65. #6911C19⋊C3direct (N × H)
95. C3×3−1+2C3×C19⋊C3semidirect
104. C3×H(3,𝔽3)C3×C19⋊C3semidirect
108. #732C3×C19⋊C3semidirect
117. C19⋊C3#6911direct (N × H)
141. H(3,𝔽3)C32×C19⋊C3semidirect
145. C3×C9C32×C19⋊C3semidirect
146. C19C3×#6911semidirect

Maximal subgroups

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

subgroupindex
C3×3−1+2×C19⋊C33
C3×H(3,𝔽3)×C19⋊C33
#179875153
#179875143
#179875133
#179875123
C19⋊C3×#7323
C19×#69113
C3×#691119