Finite Group Databasebeta

← #44534593

Subgroups — #44534593

Order 31347.

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

normal subgroups only

This group has 190 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#23782907C311yesmaximal, characteristic, complemented
2#23782907C311yesmaximal, characteristic, complemented
3#23782890C311yesmaximal, characteristic, complemented
4#23782844C311yesmaximal, characteristic, complemented
5#23782769C311yesmaximal, characteristic, complemented
6#23782759C311yesmaximal, characteristic, complemented
7#23782759C311yesmaximal, characteristic, complemented
8#23782757C311yesmaximal, characteristic, complemented
9#23782757C311yesmaximal, characteristic, complemented
10#23782750C311yesmaximal, characteristic, complemented
11#23782749C311yesmaximal, characteristic, complemented
12#23782749C311yesmaximal, characteristic, complemented
13C43×#6883C311yesmaximal, characteristic, complemented
14#16812526—31no—
15#16812526—31no—
16C3×#11923956C3211yescharacteristic
17H(3,𝔽3)×C43⋊C3—31no—
18#16812515C3211yescharacteristic, complemented
19#16812515C3211yescharacteristic, complemented
20#16812513C3211yescharacteristic
21#16812513C3211yescharacteristic
22#16812513C3211yescharacteristic, complemented
23#16812513C3211yescharacteristic, complemented
24#16812512—31no—
25#16812512—31no—
26#16812511—31no—
27#16812511—31no—
28#16812508—31no—
29#16812508—31no—
30#16812500—31no—
31#16812499C3211yescharacteristic, complemented
32(C43⋊C9)⋊C9—31no—
33(C3×C43⋊C3)⋊C9—31no—
34C9×C43⋊C9C3211yescharacteristic, complemented
35C43×#733C3211yescharacteristic, complemented
36C43×#733C3211yescharacteristic, complemented
37C43×#732C3211yescharacteristic
38C43×C9⋊C9C3211yescharacteristic, complemented
39C32×C43⋊C3—91no—
40C32×C43⋊C3H(3,𝔽3)11yescharacteristic
41#11923958—31no—
42#11923958—31no—
43#11923957—91no—
44#11923957—91no—
45#11923956—91no—
46#11923956—91no—
47#11923956—91no—
48C32⋊(C43⋊C3)—31no—
49C32⋊(C43⋊C3)—31no—
50C32⋊(C43⋊C3)—31no—
51C32⋊(C43⋊C3)—31no—
52C32⋊(C43⋊C3)—92no—
53C3×C43⋊C9—31no—
54C3×C43⋊C9—31no—
55C3×C43⋊C9H(3,𝔽3)11yescharacteristic
56C3×C43⋊C9H(3,𝔽3)11yescharacteristic
57C9×C43⋊C3—91no—
58C9×C43⋊C3—91no—
593−1+2×C43—31no—
603−1+2×C43—31no—
61H(3,𝔽3)×C43—31no—
62C3×C9×C43—31no—
63C3×C9×C43C3311yescharacteristic
64#10624853—431nomaximal, Sylow
65C32×C43—91no—
66C32×C43C3×H(3,𝔽3)11yescharacteristic
67C3×C43⋊C3—31no—
68C3×C43⋊C3—91no—
69C3×C43⋊C3—91no—
70C3×C43⋊C3—91no—
71C3×C43⋊C3—91no—
72C3×C43⋊C3—91no—
73C3×C43⋊C3—273no—
74C9×C43—31no—
75C9×C43—91no—
76C9×C43—91no—
77C9×C43—91no—
78C43⋊C9—31no—
79C43⋊C9—31no—
80C43⋊C9—91no—
81C43⋊C9—91no—
82C43⋊C9—91no—
83C43⋊C9—91no—
84#6913—431no—
85#6913—431no—
86#6911—431no—
87#6899—431no—
88#6883—431no—
89#6883C43⋊C311yescharacteristic, complemented
90#6881—431no—
91#6881—431no—
92#6881—431no—
93#6881—431no—
94#6879—431no—
95#6878—431no—
96#6878—431no—
97C3×C43—31no—
98C3×C43—271no—
99C3×C43#691111yescharacteristic
100C43⋊C3—91no—
101C43⋊C3—271no—
102C43⋊C3—271no—
103C43⋊C3—271no—
104C43⋊C3—271no—
105#737—1291no—
106#737—1291no—
107C3×3−1+2—431no—
108C3×H(3,𝔽3)—1291no—
109#733—431no—
110#733—431no—
111#733C3×C43⋊C311yescharacteristic, complemented
112#733C3×C43⋊C311yescharacteristic, complemented
113#732—431no—
114#732—431no—
115#732—431no—
116#732—431no—
117#732—1291no—
118#732—1291no—
119#732C3×C43⋊C311yescharacteristic
120#731—1291no—
121#731—1291no—
122AΣL(1,𝔽27)—1291no—
123AΣL(1,𝔽27)—1291no—
124C9⋊C9—431no—
125C9⋊C9—1291no—
126C9⋊C9—1291no—
127C9⋊C9C3×C43⋊C311yescharacteristic, complemented
128C32⋊C9—1291no—
129C92—431no—
130C43#1062485311yescharacteristic, complemented, Sylow
131C33—431no—
132C33—3871no—
1333−1+2—31no—
1343−1+2—31no—
1353−1+2—1291no—
1363−1+2—1291no—
1373−1+2—3871no—
1383−1+2—3871no—
1393−1+2—3871no—
1403−1+2—3871no—
1413−1+2—3871no—
142H(3,𝔽3)—31no—
143H(3,𝔽3)—1291no—
144H(3,𝔽3)—1291no—
145H(3,𝔽3)—1291no—
146H(3,𝔽3)—1291no—
147H(3,𝔽3)—3872no—
148C3×C9—31no—
149C3×C9—431no—
150C3×C9—431no—
151C3×C9—1291no—
152C3×C9—1291no—
153C3×C9—3871no—
154C3×C9—3871no—
155C3×C9C32×C43⋊C311yescharacteristic
156C32—91no—
157C32—1291no—
158C32—3871no—
159C32—3871no—
160C32—3871no—
161C32—3871no—
162C32—3871no—
163C32—11613no—
164C32H(3,𝔽3)×C43⋊C311yescharacteristic
165C9—31no—
166C9—91no—
167C9—91no—
168C9—91no—
169C9—1291no—
170C9—1291no—
171C9—3871no—
172C9—3871no—
173C9—3871no—
174C9—3871no—
175C3—31no—
176C3—271no—
177C3—3871no—
178C3—11611no—
179C3—11611no—
180C3—11611no—
181C3—11611no—
182C3#2378289011yescharacteristic
subgroupG/H
centerC3#23782890
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6883C3
socleC3×C43#6911
hypercenter#6883C43⋊C3
hypocenterC43#10624853
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6883

Complements

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

NH ≅ G/Ntype
1. #23782907C3semidirect
2. #23782907C3semidirect
3. #23782890C3semidirect
4. #23782844C3semidirect
5. #23782769C3semidirect
6. #23782759C3semidirect
7. #23782759C3semidirect
8. #23782757C3semidirect
9. #23782757C3semidirect
10. #23782750C3semidirect
11. #23782749C3semidirect
12. #23782749C3semidirect
13. C43×#6883C3semidirect
18. #16812515C32semidirect
19. #16812515C32semidirect
22. #16812513C32semidirect
23. #16812513C32semidirect
31. #16812499C32semidirect
34. C9×C43⋊C9C32semidirect
35. C43×#733C32semidirect
36. C43×#733C32semidirect
38. C43×C9⋊C9C32semidirect
89. #6883C43⋊C3semidirect
111. #733C3×C43⋊C3semidirect
112. #733C3×C43⋊C3semidirect
127. C9⋊C9C3×C43⋊C3semidirect
130. C43#10624853semidirect

Maximal subgroups

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

subgroupindex
#237829073
#237828903
#237828443
#237827693
#237827593
#237827573
#237827503
#237827493
C43×#68833
#1062485343