Finite Group Databasebeta

← #23748595

Subgroups — #23748595

Order 9477.

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

normal subgroups only

This group has 948 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×#11760454C311yesmaximal, characteristic, complemented
3#15691674C319yesmaximal, complemented
4#15691673C319yesmaximal, complemented
5#15691662C312yesmaximal, complemented
6#15691660C311yesmaximal, characteristic, complemented
7#15691657C312yesmaximal, complemented
8#15691655C311yesmaximal, characteristic, complemented
9#15691648C319yesmaximal, complemented
10C3×#11760442C312yesmaximal, complemented
11C3×#11760440C311yesmaximal, characteristic, complemented
12C13×3−1+4C311yesmaximal, characteristic, complemented
13#11760454—33no—
14#11760454—36no—
15#11760454—36no—
16#11760454—36no—
17#11760453C32118yescomplemented
18C3×#66851C3212yes—
19C3×#66851C3212yes—
20C3×#66851C3211yescharacteristic
21C3×#66848C3213yescomplemented
22C3×#66849C3213yescomplemented
233−1+2×C13⋊C3—36no—
24C3×C32⋊(C13⋊C3)C3211yescharacteristic
25C3×C32⋊(C13⋊C3)C3212yes—
26C32×C13⋊C9C3211yescharacteristic
27C3×C9×C13⋊C3C3213yescomplemented
28#11760442C3216yescomplemented
29#11760442C3216yescomplemented
30#11760442C3216yescomplemented
31#11760440C3213yes—
32#11760440C3213yes—
33#11760440C3213yes—
34#11760439C32118yescomplemented
35#11760437C3219yescomplemented
36#11760436C32118yescomplemented
37#11760434C3219yescomplemented
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#10624936—131nomaximal, Sylow
45C33×C13—31no—
46C33×C13C3311yescharacteristic
47C32×C13⋊C3—32no—
48C32×C13⋊C3C3313yes—
49C13×3−1+2—32no—
50C13×3−1+2—32no—
51C13×3−1+2—318no—
52C13×3−1+2H(3,𝔽3)13yes—
53C13×3−1+2H(3,𝔽3)16yes—
54C13×3−1+2C3316yes—
55C13×H(3,𝔽3)—32no—
56C13×H(3,𝔽3)C3313yes—
57C3×C9×C13—32no—
58C3×C9×C13—39no—
59C3×C9×C13C3313yes—
60C32⋊(C13⋊C3)—32no—
61C32⋊(C13⋊C3)—31no—
62C32⋊(C13⋊C3)—32no—
63C32⋊(C13⋊C3)—32no—
64C32⋊(C13⋊C3)C3316yes—
65#66851—32no—
66#66851—32no—
67#66851—32no—
68#66851—32no—
69#66851—32no—
70#66851—31no—
71#66851C3316yes—
72#66851C3316yes—
73C3×C13⋊C9—32no—
74C3×C13⋊C9—31no—
75C3×C13⋊C9—32no—
76C3×C13⋊C9—32no—
77C3×C13⋊C9C3313yes—
78C3×C13⋊C9C3311yescharacteristic
79C3×C13⋊C9C3311yescharacteristic
80C3×C13⋊C9C3311yescharacteristic
81#66849—318no—
82#66849—39no—
83#66848—318no—
84#66848—39no—
85C9×C13⋊C3—39no—
86C9×C13⋊C3—318no—
873−1+4—132no—
883−1+4C13⋊C311yescharacteristic, complemented
89C3×#737—131no—
90#6913—139no—
91#6913—139no—
92#6910—132no—
93#6910—131no—
94#6909—132no—
95#6909—131no—
96#6908—139no—
97C3×#733—132no—
98C3×#732—131no—
99C32×C13—33no—
100C32×C13—91no—
101C32×C13—271no—
102C32×C13C3×H(3,𝔽3)12yes—
103C32×C13C3×H(3,𝔽3)11yescharacteristic
104C32×C13C3411yescharacteristic
105C3×C13⋊C3—33no—
106C3×C13⋊C3—36no—
107C3×C13⋊C3—93no—
108C3×C13⋊C3—272no—
109C9×C13—36no—
110C9×C13C3×H(3,𝔽3)19yes—
111C13⋊C9—31no—
112C13⋊C9—36no—
113C13⋊C9—36no—
114C13⋊C9—33no—
115C13⋊C9—31no—
116C13⋊C9—31no—
117#737—36no—
118#737—1318no—
119#737—393no—
120#737—396no—
121#737—396no—
122#737—396no—
123#737C3×C13⋊C319yescomplemented
124C3×3−1+2—33no—
125C3×3−1+2—131no—
126C3×3−1+2—133no—
127C3×3−1+2—133no—
128C3×3−1+2—132no—
129C3×3−1+2—132no—
130C3×3−1+2—396no—
131C3×3−1+2C3×C13⋊C312yes—
132C3×3−1+2C3×C13⋊C311yescharacteristic
133C3×H(3,𝔽3)—132no—
134C3×H(3,𝔽3)—131no—
135C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
136C32×C9—131no—
137C32×C9—133no—
138#733—136no—
139#733—136no—
140#733—136no—
141#732—133no—
142#732—133no—
143#732—133no—
144#731—1318no—
145#731—139no—
146AΣL(1,𝔽27)—1318no—
147AΣL(1,𝔽27)—139no—
148C3×C13—31no—
149C3×C13—31no—
150C3×C13—32no—
151C3×C13—93no—
152C3×C13C32×H(3,𝔽3)11yescharacteristic
153C13⋊C3—93no—
154C13⋊C3—96no—
155C33—31no—
156C33—133no—
157C33—392no—
158C33C32×C13⋊C311yescharacteristic
1593−1+2—32no—
1603−1+2—32no—
1613−1+2—318no—
1623−1+2—136no—
1633−1+2—136no—
1643−1+2—392no—
1653−1+2—392no—
1663−1+2—392no—
1673−1+2—391no—
1683−1+2—392no—
1693−1+2—392no—
1703−1+2—399no—
1713−1+2—3918no—
1723−1+2—399no—
1733−1+2—3918no—
1743−1+2C32⋊(C13⋊C3)13yes—
1753−1+2C32⋊(C13⋊C3)16yes—
1763−1+2C32×C13⋊C316yes—
177H(3,𝔽3)—32no—
178H(3,𝔽3)—136no—
179H(3,𝔽3)—392no—
180H(3,𝔽3)—392no—
181H(3,𝔽3)—392no—
182H(3,𝔽3)—391no—
183H(3,𝔽3)C32×C13⋊C313yes—
184C3×C9—32no—
185C3×C9—39no—
186C3×C9—133no—
187C3×C9—131no—
188C3×C9—131no—
189C3×C9—131no—
190C3×C9—392no—
191C3×C9—391no—
192C3×C9—392no—
193C3×C9—392no—
194C3×C9—399no—
195C3×C9—3918no—
196C3×C9C32×C13⋊C313yes—
197C13#1062493611yescharacteristic, complemented, Sylow
198C32—33no—
199C32—91no—
200C32—271no—
201C32—396no—
202C32—393no—
203C32—3512no—
204C32—1173no—
205C32C3×C32⋊(C13⋊C3)12yes—
206C32C3×C32⋊(C13⋊C3)11yescharacteristic
207C32C33×C13⋊C311yescharacteristic
208C9—36no—
209C9—391no—
210C9—393no—
211C9—391no—
212C9—391no—
213C9—396no—
214C9—396no—
215C9C3×C32⋊(C13⋊C3)19yes—
216C3—31no—
217C3—31no—
218C3—32no—
219C3—93no—
220C3—1176no—
221C3—1173no—
222C3C32×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#10624936
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×#11760454C3semidirect
3. #15691674C3semidirect
4. #15691673C3semidirect
5. #15691662C3semidirect
6. #15691660C3semidirect
7. #15691657C3semidirect
8. #15691655C3semidirect
9. #15691648C3semidirect
10. C3×#11760442C3semidirect
11. C3×#11760440C3semidirect
12. C13×3−1+4C3semidirect
17. #11760453C32semidirect
21. C3×#66848C32semidirect
22. C3×#66849C32semidirect
27. C3×C9×C13⋊C3C32semidirect
28. #11760442C32semidirect
29. #11760442C32semidirect
30. #11760442C32semidirect
34. #11760439C32semidirect
35. #11760437C32semidirect
36. #11760436C32semidirect
37. #11760434C32semidirect
39. C13×#737C32semidirect
88. 3−1+4C13⋊C3semidirect
123. #737C3×C13⋊C3semidirect
197. C13#10624936semidirect