Finite Group Databasebeta

← #36382212

Subgroups — #36382212

Order 22599.

178 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 43 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#21419415C311yesmaximal, characteristic, complemented
2#21419415C311yesmaximal, characteristic, complemented
3#21419407C311yesmaximal, characteristic, complemented
4#21419357C311yesmaximal, characteristic, complemented
5#21419282C311yesmaximal, characteristic, complemented
6#21419282C311yesmaximal, characteristic, complemented
7#21419277C311yesmaximal, characteristic, complemented
8#21419276C311yesmaximal, characteristic, complemented
9#21419276C311yesmaximal, characteristic, complemented
10#21419266C311yesmaximal, characteristic, complemented
11#21419259C311yesmaximal, characteristic, complemented
12#21419259C311yesmaximal, characteristic, complemented
13C31×#6881C311yesmaximal, characteristic, complemented
14#14578911—31no—
15#14578911—31no—
16C3×#11719686C3211yescharacteristic
173−1+2×C31⋊C3—31no—
18#14578902C3211yescharacteristic
19#14578902C3211yescharacteristic
20#14578902C3211yescharacteristic
21#14578902C3211yescharacteristic
22#14578902C3211yescharacteristic
23#14578902C3211yescharacteristic
24#14578901—31no—
25#14578901—31no—
26#14578896—31no—
27#14578896—31no—
28#14578893—31no—
29#14578893—31no—
30#14578887C3211yescharacteristic
31#14578886—31no—
32(C31⋊C9)⋊C9—31no—
33(C3×C31⋊C3)⋊C9—31no—
34C9×C31⋊C9C3211yescharacteristic
35C31×#733C3211yescharacteristic
36C31×#732C3211yescharacteristic
37C31×#732C3211yescharacteristic
38C31×C9⋊C9C3211yescharacteristic
39C32×C31⋊C3H(3,𝔽3)11yescharacteristic
403−1+2×C31—31no—
41H(3,𝔽3)×C31—31no—
42H(3,𝔽3)×C31—31no—
43C3×C9×C31—31no—
44C3×C9×C31C3311yescharacteristic
45#11719689—31no—
46#11719689—31no—
47#11719689—31no—
48#11719689—31no—
49#11719689—31no—
50#11719689—31no—
51#11719689—92no—
52#11719689—92no—
53C3×C31⋊C9—31no—
54C3×C31⋊C9—31no—
55C3×C31⋊C9—91no—
56C3×C31⋊C9—91no—
57C3×C31⋊C9H(3,𝔽3)11yescharacteristic
58C3×C31⋊C9H(3,𝔽3)11yescharacteristic
59#11719687—91no—
60#11719686—91no—
61#11719686—91no—
62C9×C31⋊C3—91no—
63#10624854—311nomaximal, Sylow
64C32×C31—91no—
65C32×C31—91no—
66C32×C31C3×H(3,𝔽3)11yescharacteristic
67C3×C31⋊C3—31no—
68C3×C31⋊C3—91no—
69C9×C31—31no—
70C9×C31—91no—
71C9×C31—91no—
72C31⋊C9—31no—
73C31⋊C9—31no—
74C31⋊C9—91no—
75C31⋊C9—91no—
76C31⋊C9—91no—
77C31⋊C9—91no—
78C31⋊C9—91no—
79C31⋊C9—91no—
80C31⋊C9—91no—
81C31⋊C9—91no—
82#6913—311no—
83#6913—311no—
84#6912—311no—
85#6899—311no—
86#6883—311no—
87#6883—311no—
88#6882—311no—
89#6882—311no—
90#6882—311no—
91#6881C31⋊C311yescharacteristic, complemented
92#6880—311no—
93#6878—311no—
94#6878—311no—
95C3×C31—31no—
96C3×C31—271no—
97C3×C31—271no—
98C3×C31#691111yescharacteristic
99C31⋊C3—91no—
100#737—931no—
101#737—931no—
102C3×3−1+2—311no—
103C3×3−1+2—931no—
104#733—311no—
105#733—311no—
106#733—311no—
107#733—311no—
108#733—311no—
109#733—311no—
110#733—931no—
111#733—931no—
112#733C3×C31⋊C311yescharacteristic
113#732C3×C31⋊C311yescharacteristic
114#732C3×C31⋊C311yescharacteristic
115#731—931no—
116#731—931no—
117AΣL(1,𝔽27)—931no—
118AΣL(1,𝔽27)—931no—
119C9⋊C9—311no—
120C9⋊C9—931no—
121C9⋊C9—931no—
122C9⋊C9C3×C31⋊C311yescharacteristic
123C32⋊C9—931no—
124C92—311no—
125C31#1062485411yescharacteristic, complemented, Sylow
126C33—311no—
1273−1+2—31no—
1283−1+2—2791no—
1293−1+2—2791no—
1303−1+2—2791no—
1313−1+2—2792no—
1323−1+2—2792no—
1333−1+2—931no—
1343−1+2—931no—
1353−1+2—931no—
1363−1+2—931no—
1373−1+2—931no—
1383−1+2—931no—
139H(3,𝔽3)—31no—
140H(3,𝔽3)—31no—
141C3×C9—31no—
142C3×C9—2791no—
143C3×C9—2791no—
144C3×C9—2791no—
145C3×C9—311no—
146C3×C9—311no—
147C3×C9—931no—
148C3×C9—931no—
149C3×C9C32×C31⋊C311yescharacteristic
150C32—91no—
151C32—91no—
152C32—2791no—
153C32—931no—
154C32H(3,𝔽3)×C31⋊C311yescharacteristic
155C9—31no—
156C9—91no—
157C9—91no—
158C9—2791no—
159C9—2791no—
160C9—2791no—
161C9—2791no—
162C9—2791no—
163C9—2791no—
164C9—2791no—
165C9—2791no—
166C9—931no—
167C9—931no—
168C3—31no—
169C3—2791no—
170C3—271no—
171C3—271no—
172C3#2141940311yescharacteristic
subgroupG/H
centerC3#21419403
commutator, cosocleC3×C9×C31C33
FrattiniC3×C9C32×C31⋊C3
FittingC31×#6881C3
socleC3×C31#6911
hypercenter#6881C31⋊C3
hypocenterC31#10624854
LCSG ▷ C3×C9×C31 ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6881

Complements

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

NH ≅ G/Ntype
1. #21419415C3semidirect
2. #21419415C3semidirect
3. #21419407C3semidirect
4. #21419357C3semidirect
5. #21419282C3semidirect
6. #21419282C3semidirect
7. #21419277C3semidirect
8. #21419276C3semidirect
9. #21419276C3semidirect
10. #21419266C3semidirect
11. #21419259C3semidirect
12. #21419259C3semidirect
13. C31×#6881C3semidirect
91. #6881C31⋊C3semidirect
125. C31#10624854semidirect

Maximal subgroups

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

subgroupindex
#214194153
#214194073
#214193573
#214192823
#214192773
#214192763
#214192663
#214192593
C31×#68813
#1062485431