Finite Group Databasebeta

← #36382175

Subgroups — #36382175

Order 22599.

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

normal subgroups only

This group has 188 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#21419421C311yesmaximal, characteristic, complemented
2#21419416C311yesmaximal, characteristic, complemented
3#21419408C311yesmaximal, characteristic, complemented
4#21419361C311yesmaximal, characteristic, complemented
5#21419282C311yesmaximal, characteristic, complemented
6#21419279C311yesmaximal, characteristic, complemented
7#21419277C311yesmaximal, characteristic, complemented
8#21419274C311yesmaximal, characteristic, complemented
9#21419274C311yesmaximal, characteristic, complemented
10#21419269C311yesmaximal, characteristic, complemented
11#21419268C311yesmaximal, characteristic, complemented
12#21419261C311yesmaximal, characteristic, complemented
13C31×#6878C311yesmaximal, characteristic, complemented
14#14578913—31no—
15#14578911—31no—
16C3×#11719687—31no—
17C3×#11719687C3211yescharacteristic
183−1+2×C31⋊C3—31no—
19#14578902C3211yescharacteristic
20#14578902C3211yescharacteristic
21#14578902C3211yescharacteristic
22#14578902C3211yescharacteristic
23#14578902C3211yescharacteristic
24#14578901—31no—
25#14578901—31no—
26#14578900C3211yescharacteristic
27#14578898—31no—
28#14578896—31no—
29#14578895—31no—
30#14578893—31no—
31#14578887—31no—
32#14578887—31no—
33#14578887C3211yescharacteristic
34#14578887C3211yescharacteristic
35C31×#733C3211yescharacteristic
36C31×#733C3211yescharacteristic
37C31×#732C3211yescharacteristic
38C92×C31C3211yescharacteristic
39C32×C31⋊C3H(3,𝔽3)11yescharacteristic
403−1+2×C31—31no—
413−1+2×C31—31no—
42H(3,𝔽3)×C31—31no—
43C3×C9×C31—31no—
44C3×C9×C31C3311yescharacteristic
45C32⋊(C31⋊C3)—31no—
46#11719689—31no—
47#11719689—31no—
48#11719689—31no—
49#11719689—31no—
50#11719689—31no—
51#11719689—92no—
52C3×C31⋊C9—31no—
53C3×C31⋊C9—31no—
54C3×C31⋊C9—91no—
55C3×C31⋊C9H(3,𝔽3)11yescharacteristic
56C3×C31⋊C9H(3,𝔽3)11yescharacteristic
57#11719687—91no—
58#11719687—91no—
59#11719687—93no—
60#11719687—91no—
61#11719686—91no—
62#11719686—91no—
63C9×C31⋊C3—91no—
64C9×C31⋊C3—91no—
65#10624852—311nomaximal, Sylow
66C32×C31—91no—
67C32×C31C3×H(3,𝔽3)11yescharacteristic
68C3×C31⋊C3—31no—
69C3×C31⋊C3—91no—
70C3×C31⋊C3—91no—
71C9×C31—33no—
72C9×C31—31no—
73C9×C31—91no—
74C9×C31—91no—
75C31⋊C9—31no—
76C31⋊C9—31no—
77C31⋊C9—91no—
78C31⋊C9—91no—
79C31⋊C9—91no—
80C31⋊C9—91no—
81C31⋊C9—91no—
82C31⋊C9—91no—
83C31⋊C9—91no—
84#6913—311no—
85#6913—311no—
86#6912—311no—
87#6900—311no—
88#6883—311no—
89#6883—311no—
90#6882—311no—
91#6882—311no—
92#6882—311no—
93#6881—311no—
94#6880—311no—
95#6878—311no—
96#6878C31⋊C311yescharacteristic, complemented
97C3×C31—31no—
98C3×C31—271no—
99C3×C31#691111yescharacteristic
100C31⋊C3—91no—
101C31⋊C3—271no—
102#737—931no—
103#737—931no—
104C3×3−1+2—311no—
105C3×3−1+2—931no—
106C3×3−1+2—931no—
107#733—311no—
108#733—311no—
109#733—311no—
110#733—311no—
111#733—311no—
112#733—931no—
113#733—931no—
114#733C3×C31⋊C311yescharacteristic
115#733C3×C31⋊C311yescharacteristic
116#732—311no—
117#732C3×C31⋊C311yescharacteristic
118#731—931no—
119#731—931no—
120AΣL(1,𝔽27)—931no—
121AΣL(1,𝔽27)—931no—
122C9⋊C9—311no—
123C9⋊C9—311no—
124C9⋊C9—931no—
125C9⋊C9—931no—
126C92C3×C31⋊C311yescharacteristic
127C31#1062485211yescharacteristic, complemented, Sylow
128C33—311no—
1293−1+2—31no—
1303−1+2—31no—
1313−1+2—2793no—
1323−1+2—2791no—
1333−1+2—2791no—
1343−1+2—2791no—
1353−1+2—2791no—
1363−1+2—2791no—
1373−1+2—2792no—
1383−1+2—931no—
1393−1+2—931no—
1403−1+2—931no—
1413−1+2—931no—
1423−1+2—931no—
143H(3,𝔽3)—31no—
144H(3,𝔽3)—931no—
145C3×C9—31no—
146C3×C9—2791no—
147C3×C9—2791no—
148C3×C9—2791no—
149C3×C9—311no—
150C3×C9—311no—
151C3×C9—931no—
152C3×C9—931no—
153C3×C9C32×C31⋊C311yescharacteristic
154C32—91no—
155C32—2791no—
156C32—2791no—
157C32—931no—
158C32H(3,𝔽3)×C31⋊C311yescharacteristic
159C9—33no—
160C9—31no—
161C9—91no—
162C9—91no—
163C9—2791no—
164C9—2791no—
165C9—2791no—
166C9—2791no—
167C9—2791no—
168C9—2791no—
169C9—2791no—
170C9—931no—
171C9—931no—
172C3—31no—
173C3—2791no—
174C3—271no—
175C3—8371no—
176C3#2141940411yescharacteristic
subgroupG/H
centerC3#21419404
commutator, cosocleC3×C9×C31C33
FrattiniC3×C9C32×C31⋊C3
FittingC31×#6878C3
socleC3×C31#6911
hypercenter#6878C31⋊C3
hypocenterC31#10624852
LCSG ▷ C3×C9×C31 ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6878

Complements

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

NH ≅ G/Ntype
1. #21419421C3semidirect
2. #21419416C3semidirect
3. #21419408C3semidirect
4. #21419361C3semidirect
5. #21419282C3semidirect
6. #21419279C3semidirect
7. #21419277C3semidirect
8. #21419274C3semidirect
9. #21419274C3semidirect
10. #21419269C3semidirect
11. #21419268C3semidirect
12. #21419261C3semidirect
13. C31×#6878C3semidirect
96. #6878C31⋊C3semidirect
127. C31#10624852semidirect

Maximal subgroups

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

subgroupindex
#214194213
#214194163
#214194083
#214193613
#214192823
#214192793
#214192773
#214192743
#214192693
#214192683
#214192613
C31×#68783
#1062485231