Finite Group Databasebeta

← #23748575

Subgroups — #23748575

Order 9477.

980 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 286 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#15691697C312yesmaximal, complemented
2C3×3−1+2×C13⋊C3C311yesmaximal, characteristic, complemented
3#15691674C319yesmaximal, complemented
4#15691673C319yesmaximal, complemented
5#15691669C312yesmaximal, complemented
6#15691665C311yesmaximal, characteristic, complemented
7#15691662C312yesmaximal, complemented
8#15691660C311yesmaximal, characteristic, complemented
9#15691648C319yesmaximal, complemented
10C3×#11760436C312yesmaximal, complemented
11C3×#11760434C311yesmaximal, characteristic, complemented
12C13×3−1+4C311yesmaximal, characteristic, complemented
13C33×C13⋊C3C3211yescharacteristic
14#11760454—36no—
15#11760454—36no—
16#11760453C32118yescomplemented
17C3×#66851C3212yes—
18C3×#66851C3212yes—
19C3×#66851C3211yescharacteristic
20C3×#66851C3211yescharacteristic
21C3×#66848C3213yescomplemented
22C3×#66849C3213yescomplemented
233−1+2×C13⋊C3—33no—
243−1+2×C13⋊C3—36no—
253−1+2×C13⋊C3—36no—
26C3×C32⋊(C13⋊C3)C3212yes—
27C3×C9×C13⋊C3C3213yescomplemented
28#11760442C32118yescomplemented
29#11760440C3219yescomplemented
30#11760439C32118yescomplemented
31#11760437C3219yescomplemented
32#11760436C3216yescomplemented
33#11760436C3216yescomplemented
34#11760436C3216yescomplemented
35#11760434C3213yescomplemented
36#11760434C3213yescomplemented
37#11760434C3213yescomplemented
38C13×#737—36no—
39C13×#737C3219yescomplemented
40C3×C13×3−1+2—33no—
41C3×C13×3−1+2C3212yes—
42C3×C13×3−1+2C3211yescharacteristic
43C3×C13×H(3,𝔽3)C3211yescharacteristic
44#10624934—131nomaximal, Sylow
45C33×C13—31no—
46C33×C13C3311yescharacteristic
47C32×C13⋊C3—31no—
48C32×C13⋊C3—32no—
49C32×C13⋊C3—32no—
50C32×C13⋊C3—93no—
51C32×C13⋊C3C3311yescharacteristic
52C32×C13⋊C3C3311yescharacteristic
53C32×C13⋊C3C3311yescharacteristic
54C13×3−1+2—32no—
55C13×3−1+2—32no—
56C13×3−1+2—318no—
57C13×3−1+2H(3,𝔽3)13yes—
58C13×3−1+2H(3,𝔽3)16yes—
59C13×3−1+2C3316yes—
60C13×H(3,𝔽3)—32no—
61C13×H(3,𝔽3)C3313yes—
62C3×C9×C13—32no—
63C3×C9×C13—39no—
64C3×C9×C13C3313yes—
65C32⋊(C13⋊C3)—32no—
66C32⋊(C13⋊C3)—32no—
67C32⋊(C13⋊C3)C3316yes—
68#66851—32no—
69#66851—32no—
70#66851—31no—
71#66851—31no—
72#66851—32no—
73#66851—32no—
74#66851—32no—
75#66851—32no—
76#66851C3316yes—
77#66851C3316yes—
78C3×C13⋊C9—32no—
79C3×C13⋊C9—32no—
80C3×C13⋊C9C3313yes—
81C3×C13⋊C9C3313yes—
82#66849—39no—
83#66849—318no—
84#66848—39no—
85#66848—318no—
86C9×C13⋊C3—39no—
87C9×C13⋊C3—318no—
883−1+4—132no—
893−1+4C13⋊C311yescharacteristic, complemented
90C32×3−1+2—131no—
91#6913—139no—
92#6913—139no—
93#6912—132no—
94#6911—131no—
95#6910—132no—
96#6910—131no—
97#6908—139no—
98C3×AΣL(1,𝔽27)—132no—
99C3×AΣL(1,𝔽27)—131no—
100C32×C13—33no—
101C32×C13—91no—
102C32×C13—271no—
103C32×C13C3×H(3,𝔽3)11yescharacteristic
104C32×C13C3×H(3,𝔽3)12yes—
105C32×C13C3411yescharacteristic
106C3×C13⋊C3—31no—
107C3×C13⋊C3—33no—
108C3×C13⋊C3—36no—
109C3×C13⋊C3—31no—
110C3×C13⋊C3—31no—
111C3×C13⋊C3—96no—
112C3×C13⋊C3—93no—
113C3×C13⋊C3—91no—
114C3×C13⋊C3—91no—
115C3×C13⋊C3—272no—
116C9×C13—36no—
117C9×C13C3×H(3,𝔽3)19yes—
118C13⋊C9—36no—
119C13⋊C9—36no—
120C13⋊C9—33no—
121C13⋊C9—33no—
122C34—131no—
123#737—36no—
124#737—1318no—
125#737—396no—
126#737—396no—
127#737C3×C13⋊C319yescomplemented
128C3×3−1+2—33no—
129C3×3−1+2—131no—
130C3×3−1+2—131no—
131C3×3−1+2—133no—
132C3×3−1+2—133no—
133C3×3−1+2—132no—
134C3×3−1+2—132no—
135C3×3−1+2—393no—
136C3×3−1+2—396no—
137C3×3−1+2—396no—
138C3×3−1+2C3×C13⋊C312yes—
139C3×3−1+2C3×C13⋊C311yescharacteristic
140C3×H(3,𝔽3)—132no—
141C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
142C32×C9—133no—
143#733—1318no—
144#732—139no—
145#731—1318no—
146#731—139no—
147AΣL(1,𝔽27)—136no—
148AΣL(1,𝔽27)—136no—
149AΣL(1,𝔽27)—136no—
150AΣL(1,𝔽27)—133no—
151AΣL(1,𝔽27)—133no—
152AΣL(1,𝔽27)—133no—
153C3×C13—31no—
154C3×C13—32no—
155C3×C13—31no—
156C3×C13—93no—
157C3×C13C32×H(3,𝔽3)11yescharacteristic
158C13⋊C3—33no—
159C13⋊C3—91no—
160C13⋊C3—91no—
161C13⋊C3—96no—
162C33—31no—
163C33—131no—
164C33—131no—
165C33—131no—
166C33—392no—
167C33—392no—
168C33—391no—
169C33—1173no—
170C33C32×C13⋊C311yescharacteristic
1713−1+2—32no—
1723−1+2—32no—
1733−1+2—318no—
1743−1+2—136no—
1753−1+2—136no—
1763−1+2—392no—
1773−1+2—392no—
1783−1+2—391no—
1793−1+2—391no—
1803−1+2—392no—
1813−1+2—392no—
1823−1+2—392no—
1833−1+2—392no—
1843−1+2—399no—
1853−1+2—3918no—
1863−1+2—399no—
1873−1+2—3918no—
1883−1+2C32⋊(C13⋊C3)13yes—
1893−1+2C32⋊(C13⋊C3)16yes—
1903−1+2C32×C13⋊C316yes—
191H(3,𝔽3)—32no—
192H(3,𝔽3)—136no—
193H(3,𝔽3)—392no—
194H(3,𝔽3)—392no—
195H(3,𝔽3)C32×C13⋊C313yes—
196C3×C9—32no—
197C3×C9—39no—
198C3×C9—133no—
199C3×C9—133no—
200C3×C9—392no—
201C3×C9—392no—
202C3×C9—399no—
203C3×C9—3918no—
204C3×C9C32×C13⋊C313yes—
205C13#1062493411yescharacteristic, complemented, Sylow
206C32—33no—
207C32—91no—
208C32—271no—
209C32—393no—
210C32—391no—
211C32—396no—
212C32—391no—
213C32—391no—
214C32—3512no—
215C32—1173no—
216C32—1176no—
217C32—1171no—
218C32—1171no—
219C32C3×C32⋊(C13⋊C3)12yes—
220C32C3×C32⋊(C13⋊C3)11yescharacteristic
221C32C33×C13⋊C311yescharacteristic
222C9—36no—
223C9—393no—
224C9—393no—
225C9—396no—
226C9—396no—
227C9C3×C32⋊(C13⋊C3)19yes—
228C3—31no—
229C3—31no—
230C3—32no—
231C3—93no—
232C3—393no—
233C3—1176no—
234C3—1171no—
235C3—1171no—
236C3C32×C32⋊(C13⋊C3)11yescharacteristic
subgroupG/H
centerC3C32×C32⋊(C13⋊C3)
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×3−1+4C3
socleC3×C13C32×H(3,𝔽3)
hypercenter3−1+4C13⋊C3
hypocenterC13#10624934
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C3×3−1+2 ◁ 3−1+4

Complements

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

NH ≅ G/Ntype
1. #15691697C3semidirect
2. C3×3−1+2×C13⋊C3C3semidirect
3. #15691674C3semidirect
4. #15691673C3semidirect
5. #15691669C3semidirect
6. #15691665C3semidirect
7. #15691662C3semidirect
8. #15691660C3semidirect
9. #15691648C3semidirect
10. C3×#11760436C3semidirect
11. C3×#11760434C3semidirect
12. C13×3−1+4C3semidirect
16. #11760453C32semidirect
21. C3×#66848C32semidirect
22. C3×#66849C32semidirect
27. C3×C9×C13⋊C3C32semidirect
28. #11760442C32semidirect
29. #11760440C32semidirect
30. #11760439C32semidirect
31. #11760437C32semidirect
32. #11760436C32semidirect
33. #11760436C32semidirect
34. #11760436C32semidirect
35. #11760434C32semidirect
36. #11760434C32semidirect
37. #11760434C32semidirect
39. C13×#737C32semidirect
89. 3−1+4C13⋊C3semidirect
127. #737C3×C13⋊C3semidirect
205. C13#10624934semidirect