Finite Group Databasebeta

← #23748553

Subgroups — #23748553

Order 9477.

960 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 960 conjugacy classes of subgroups — too many to draw. Only its 268 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×#11760454C313yesmaximal, complemented
2C3×#11760454C311yesmaximal, characteristic, complemented
3#15691681C319yesmaximal, complemented
4#15691680C319yesmaximal, complemented
5#15691670C311yesmaximal, characteristic, complemented
6#15691666C311yesmaximal, characteristic, complemented
7#15691662C313yesmaximal, complemented
8#15691657C313yesmaximal, complemented
9#15691652C319yesmaximal, complemented
10C13×#6912C311yesmaximal, characteristic, complemented
11#11760454—33no—
12#11760454—33no—
13#11760454—33no—
14#11760454—33no—
15#11760454—33no—
16#11760454—33no—
17#11760454—33no—
18#11760454—33no—
19#11760454—33no—
20#11760454C3219yescomplemented
21#11760454C3219yescomplemented
22#11760454C3219yescomplemented
23C3×#66851C3213yes—
24C3×#66851C3211yescharacteristic
25C3×#66848—33no—
26C3×#66848C3213yescomplemented
27C3×#66849—33no—
28C3×#66849C3213yescomplemented
29C3×C32⋊(C13⋊C3)C3211yescharacteristic
30C3×C32⋊(C13⋊C3)C3213yes—
31C32×C13⋊C9C3211yescharacteristic
32C3×C9×C13⋊C3—33no—
33C3×C9×C13⋊C3C3213yescomplemented
34#11760443C3219yescomplemented
35#11760441C3219yes—
36#11760439C32127yescomplemented
37#11760436C32127yescomplemented
38C3×C13×3−1+2C3213yes—
39C3×C13×3−1+2C3211yescharacteristic
40C13×#733C3219yescomplemented
41#10624929—131nomaximal, Sylow
42C33×C13C3311yescharacteristic
43C32×C13⋊C3—33no—
44C32×C13⋊C3C3313yes—
45C13×3−1+2—33no—
46C13×3−1+2—33no—
47C13×3−1+2—33no—
48C13×3−1+2C3319yes—
49C3×C9×C13—33no—
50C3×C9×C13C3313yes—
51C32⋊(C13⋊C3)—33no—
52C32⋊(C13⋊C3)—33no—
53C32⋊(C13⋊C3)—33no—
54C32⋊(C13⋊C3)C3319yes—
55#66851—33no—
56#66851—33no—
57#66851—33no—
58#66851C3319yes—
59C3×C13⋊C9—33no—
60C3×C13⋊C9H(3,𝔽3)13yes—
61C3×C13⋊C9H(3,𝔽3)13yes—
62C3×C13⋊C9H(3,𝔽3)13yes—
63C3×C13⋊C9C3313yes—
64C3×C13⋊C9C3311yescharacteristic
65C3×C13⋊C9C3311yescharacteristic
66C3×C13⋊C9C3311yescharacteristic
67#66849—39no—
68#66849—39no—
69#66849—39no—
70#66849—39no—
71#66848—39no—
72#66848—39no—
73#66848—39no—
74#66848—39no—
75C9×C13⋊C3—39no—
76C9×C13⋊C3—39no—
77C9×C13⋊C3—39no—
78C9×C13⋊C3—33no—
79C9×C13⋊C3—33no—
80C9×C13⋊C3—33no—
81C3×#737—131no—
82C3×#737—133no—
83#6913—139no—
84#6913—139no—
85#6912—131no—
86#6912C13⋊C311yescharacteristic, complemented
87#6911—131no—
88#6910—133no—
89#6909—133no—
90#6908—139no—
91C32×C13—91no—
92C32×C13C3×H(3,𝔽3)13yes—
93C32×C13C3411yescharacteristic
94C3×C13⋊C3—33no—
95C3×C13⋊C3—39no—
96C3×C13⋊C3—99no—
97C3×C13⋊C3—93no—
98C9×C13—39no—
99C9×C13—33no—
100C13⋊C9—39no—
101C13⋊C9—33no—
102C13⋊C9C3×H(3,𝔽3)11yescharacteristic
103C13⋊C9C3×H(3,𝔽3)11yescharacteristic
104C13⋊C9C3×H(3,𝔽3)13yes—
105C13⋊C9C3×H(3,𝔽3)13yes—
106C13⋊C9C3×H(3,𝔽3)11yescharacteristic
107#737—139no—
108#737—139no—
109#737—139no—
110#737—393no—
111#737—393no—
112#737—393no—
113#737—393no—
114#737—393no—
115#737—393no—
116#737—393no—
117#737—393no—
118#737—393no—
119C3×3−1+2—131no—
120C3×3−1+2—133no—
121C3×3−1+2—133no—
122C3×3−1+2—133no—
123C3×3−1+2—393no—
124C3×3−1+2—393no—
125C3×3−1+2C3×C13⋊C313yes—
126C3×3−1+2C3×C13⋊C311yescharacteristic
127C3×H(3,𝔽3)—133no—
128C3×H(3,𝔽3)—131no—
129C32×C9—131no—
130C32×C9—133no—
131C32×C9—393no—
132#733—139no—
133#733C3×C13⋊C319yescomplemented
134#732—139no—
135#731—1327no—
136AΣL(1,𝔽27)—1327no—
137C3×C13—33no—
138C3×C13—31no—
139C3×C13C32×H(3,𝔽3)11yescharacteristic
140C13⋊C3—93no—
141C13⋊C3—99no—
142C33—133no—
143C33—393no—
144C33C32×C13⋊C311yescharacteristic
1453−1+2—33no—
1463−1+2—33no—
1473−1+2—33no—
1483−1+2—139no—
1493−1+2—399no—
1503−1+2—399no—
1513−1+2—399no—
1523−1+2—399no—
1533−1+2—399no—
1543−1+2—399no—
1553−1+2—399no—
1563−1+2—399no—
1573−1+2—393no—
1583−1+2—393no—
1593−1+2—393no—
1603−1+2C32×C13⋊C319yes—
161H(3,𝔽3)—139no—
162H(3,𝔽3)—393no—
163H(3,𝔽3)—393no—
164H(3,𝔽3)—393no—
165C3×C9—33no—
166C3×C9—133no—
167C3×C9—133no—
168C3×C9—133no—
169C3×C9—131no—
170C3×C9—131no—
171C3×C9—131no—
172C3×C9—133no—
173C3×C9—393no—
174C3×C9—393no—
175C3×C9—393no—
176C3×C9—399no—
177C3×C9—399no—
178C3×C9—399no—
179C3×C9—393no—
180C3×C9C32×C13⋊C313yes—
181C13#1062492911yescharacteristic, complemented, Sylow
182C32—91no—
183C32—399no—
184C32—393no—
185C32—1173no—
186C32—1179no—
187C32H(3,𝔽3)×C13⋊C313yes—
188C32C33×C13⋊C311yescharacteristic
189C9—39no—
190C9—33no—
191C9—131no—
192C9—133no—
193C9—133no—
194C9—131no—
195C9—131no—
196C9—393no—
197C9—399no—
198C3—33no—
199C3—31no—
200C3—1179no—
201C3—1173no—
202C3C3×H(3,𝔽3)×C13⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×#6912C3
socleC3×C13C32×H(3,𝔽3)
hypercenter#6912C13⋊C3
hypocenterC13#10624929
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ #6912

Complements

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

NH ≅ G/Ntype
1. C3×#11760454C3semidirect
2. C3×#11760454C3semidirect
3. #15691681C3semidirect
4. #15691680C3semidirect
5. #15691670C3semidirect
6. #15691666C3semidirect
7. #15691662C3semidirect
8. #15691657C3semidirect
9. #15691652C3semidirect
10. C13×#6912C3semidirect
20. #11760454C32semidirect
21. #11760454C32semidirect
22. #11760454C32semidirect
26. C3×#66848C32semidirect
28. C3×#66849C32semidirect
33. C3×C9×C13⋊C3C32semidirect
34. #11760443C32semidirect
36. #11760439C32semidirect
37. #11760436C32semidirect
40. C13×#733C32semidirect
86. #6912C13⋊C3semidirect
133. #733C3×C13⋊C3semidirect
181. C13#10624929semidirect