Finite Group Databasebeta

← #41007389

Subgroups — #41007389

Order 26973.

186 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 46 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#733×C37⋊C3C311yesmaximal, characteristic
2#733×C37⋊C3C311yesmaximal, characteristic
3#733×C37⋊C3C311yesmaximal, characteristic
4#22582537C311yesmaximal, characteristic
5#22582520C311yesmaximal, characteristic, complemented
6#22582519C311yesmaximal, characteristic, complemented
7#22582518C311yesmaximal, characteristic, complemented
8#22582518C311yesmaximal, characteristic, complemented
9#22582517C311yesmaximal, characteristic, complemented
10#22582517C311yesmaximal, characteristic, complemented
11#22582516C311yesmaximal, characteristic, complemented
12#22582516C311yesmaximal, characteristic, complemented
13C37×#6882C311yesmaximal, characteristic, complemented
143−1+2×C37⋊C3—31no—
153−1+2×C37⋊C3—31no—
163−1+2×C37⋊C3—31no—
17C3×C9×C37⋊C3C3211yescharacteristic
18#15688521C3211yescharacteristic
19#15688521C3211yescharacteristic
20#15688521C3211yescharacteristic
21#15688521C3211yescharacteristic
22#15688521C3211yescharacteristic
23#15688521C3211yescharacteristic
24#15688520—31no—
25#15688520—31no—
26#15688520—31no—
27#15688520—31no—
28#15688520—31no—
29#15688520—31no—
30#15688506C3211yescharacteristic
31#15688505C3211yescharacteristic
32#15688504—31no—
33#15688502—31no—
34C9×#66524—31no—
35C37×#733C3211yescharacteristic
36C37×#733C3211yescharacteristic
37C37×#733C3211yescharacteristic
38C37×C9⋊C9C3211yescharacteristic
39C32×C37⋊C3H(3,𝔽3)11yescharacteristic
403−1+2×C37—31no—
413−1+2×C37—31no—
423−1+2×C37—31no—
43C3×C9×C37—31no—
44C3×C9×C37C3311yescharacteristic
45#11758608—31no—
46#11758608—31no—
47#11758608—31no—
48#11758608—31no—
49#11758608—31no—
50#11758608—31no—
51C3×#66524—31no—
52C3×#66524—31no—
53C3×#66524H(3,𝔽3)11yescharacteristic
54C3×#66524H(3,𝔽3)11yescharacteristic
55#11758606—91no—
56#11758606—91no—
57#11758606—91no—
58#11758605—91no—
59#11758605—91no—
60#11758605—91no—
61C9×C37⋊C3—31no—
62C9×C37⋊C3—31no—
63C9×C37⋊C3—31no—
64C9×C37⋊C3—91no—
65C9×C37⋊C3—91no—
66C9×C37⋊C3—91no—
67#10624847—371nomaximal, Sylow
68C32×C37C3×H(3,𝔽3)11yescharacteristic
69C3×C37⋊C3—91no—
70C3×C37⋊C3#73211yescharacteristic
71C3×C37⋊C3#73211yescharacteristic
72C3×C37⋊C3#73211yescharacteristic
73C9×C37—31no—
74C9×C37—91no—
75C9×C37—91no—
76C9×C37—91no—
77C9×C37—91no—
78#66524—31no—
79#66524—31no—
80#66524—91no—
81#66524—91no—
82#66524—91no—
83#66524—91no—
84#66524—91no—
85#66524—91no—
86#66524—91no—
87#66524—91no—
88C3×#733—371no—
89C3×#733—371no—
90C3×#733—371no—
91#6887—371no—
92#6882—371no—
93#6882—371no—
94#6882—371no—
95#6882—371no—
96#6882—371no—
97#6882—371no—
98#6882—371no—
99#6882—371no—
100#6882C37⋊C311yescharacteristic, complemented
101C3×C37—31no—
102C3×C37C3×#73211yescharacteristic
103C37⋊C3—31no—
104C37⋊C3—31no—
105C37⋊C3—31no—
106C3×3−1+2—1111no—
107C3×3−1+2—1111no—
108C3×3−1+2—1111no—
109C32×C9—371no—
110#733—371no—
111#733—371no—
112#733—371no—
113#733—371no—
114#733—371no—
115#733—371no—
116#733—1111no—
117#733—1111no—
118#733—1111no—
119#733—1111no—
120#733—1111no—
121#733—1111no—
122#733C3×C37⋊C311yescharacteristic
123#733C3×C37⋊C311yescharacteristic
124#733C3×C37⋊C311yescharacteristic
125C9⋊C9—371no—
126C9⋊C9—371no—
127C9⋊C9—1111no—
128C9⋊C9C3×C37⋊C311yescharacteristic
129C32⋊C9—1111no—
130C92—1111no—
131C37#1062484711yescharacteristic, complemented, Sylow
132C33—371no—
1333−1+2—31no—
1343−1+2—31no—
1353−1+2—31no—
1363−1+2—3331no—
1373−1+2—3331no—
1383−1+2—3331no—
1393−1+2—3331no—
1403−1+2—3331no—
1413−1+2—3331no—
1423−1+2—1111no—
1433−1+2—1111no—
1443−1+2—1111no—
1453−1+2—1111no—
1463−1+2—1111no—
1473−1+2—1111no—
148C3×C9—31no—
149C3×C9—371no—
150C3×C9—371no—
151C3×C9—3331no—
152C3×C9—3331no—
153C3×C9—3331no—
154C3×C9—1111no—
155C3×C9—1111no—
156C3×C9—1111no—
157C3×C9—1111no—
158C3×C9—1111no—
159C3×C9C32×C37⋊C311yescharacteristic
160C32—371no—
161C32—371no—
162C32—371no—
163C32—3331no—
164C32H(3,𝔽3)×C37⋊C311yescharacteristic
165C9—31no—
166C9—91no—
167C9—91no—
168C9—91no—
169C9—91no—
170C9—3331no—
171C9—3331no—
172C9—3331no—
173C9—3331no—
174C9—3331no—
175C9—3331no—
176C9—3331no—
177C9—3331no—
178C9—1111no—
179C9—1111no—
180C3—31no—
181C3—1111no—
182C3—1111no—
183C3—1111no—
184C3#732×C37⋊C311yescharacteristic
subgroupG/H
centerC3#732×C37⋊C3
commutator, cosocleC3×C9×C37C33
FrattiniC3×C9C32×C37⋊C3
FittingC37×#6882C3
socleC3×C37C3×#732
prime radicalC32×C37⋊C3H(3,𝔽3)
hypercenter#6882C37⋊C3
hypocenterC37#10624847
LCSG ▷ C3×C9×C37 ▷ C32×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6882

Complements

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

NH ≅ G/Ntype
5. #22582520C3semidirect
6. #22582519C3semidirect
7. #22582518C3semidirect
8. #22582518C3semidirect
9. #22582517C3semidirect
10. #22582517C3semidirect
11. #22582516C3semidirect
12. #22582516C3semidirect
13. C37×#6882C3semidirect
100. #6882C37⋊C3semidirect
131. C37#10624847semidirect

Maximal subgroups

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

subgroupindex
#733×C37⋊C33
#225825373
#225825203
#225825193
#225825183
#225825173
#225825163
C37×#68823
#1062484737