Finite Group Databasebeta

← #41007395

Subgroups — #41007395

Order 26973.

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

normal subgroups only

This group has 198 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, complemented
2#733×C37⋊C3C311yesmaximal, characteristic, complemented
3#732×C37⋊C3C311yesmaximal, characteristic
4#22582537C311yesmaximal, characteristic, complemented
5#22582525C311yesmaximal, characteristic, complemented
6#22582524C311yesmaximal, characteristic, complemented
7#22582523C311yesmaximal, characteristic, complemented
8#22582523C311yesmaximal, characteristic, complemented
9#22582522C311yesmaximal, characteristic, complemented
10#22582522C311yesmaximal, characteristic, complemented
11#22582521C311yesmaximal, characteristic, complemented
12#22582521C311yesmaximal, characteristic, complemented
13C37×#6883C311yesmaximal, characteristic, complemented
143−1+2×C37⋊C3—31no—
153−1+2×C37⋊C3—31no—
16H(3,𝔽3)×C37⋊C3—31no—
17C3×C9×C37⋊C3C3211yescharacteristic
18#15688521C3211yescharacteristic, complemented
19#15688521C3211yescharacteristic, complemented
20#15688521C3211yescharacteristic, complemented
21#15688521C3211yescharacteristic, complemented
22#15688520—31no—
23#15688520—31no—
24#15688520—31no—
25#15688520—31no—
26#15688519C3211yescharacteristic
27#15688519C3211yescharacteristic
28#15688518—31no—
29#15688518—31no—
30#15688506C3211yescharacteristic, complemented
31#15688505C3211yescharacteristic, complemented
32#15688504—31no—
33#15688502—31no—
34C9×#66524—31no—
35C37×#733C3211yescharacteristic, complemented
36C37×#733C3211yescharacteristic, complemented
37C37×#732C3211yescharacteristic
38C37×C9⋊C9C3211yescharacteristic, complemented
39C32×C37⋊C3—91no—
40C32×C37⋊C3H(3,𝔽3)11yescharacteristic
413−1+2×C37—31no—
423−1+2×C37—31no—
43H(3,𝔽3)×C37—31no—
44C3×C9×C37—31no—
45C3×C9×C37C3311yescharacteristic
46C32⋊(C37⋊C3)—31no—
47C32⋊(C37⋊C3)—31no—
48C32⋊(C37⋊C3)—91no—
49C32⋊(C37⋊C3)—91no—
50#11758608—31no—
51#11758608—31no—
52#11758608—31no—
53#11758608—31no—
54C3×#66524—31no—
55C3×#66524—31no—
56C3×#66524H(3,𝔽3)11yescharacteristic
57C3×#66524H(3,𝔽3)11yescharacteristic
58#11758606—91no—
59#11758606—91no—
60#11758605—91no—
61#11758605—91no—
62C9×C37⋊C3—31no—
63C9×C37⋊C3—31no—
64C9×C37⋊C3—31no—
65C9×C37⋊C3—91no—
66C9×C37⋊C3—91no—
67#10624848—371nomaximal, Sylow
68C32×C37—91no—
69C32×C37C3×H(3,𝔽3)11yescharacteristic
70C3×C37⋊C3—91no—
71C3×C37⋊C3—91no—
72C3×C37⋊C3—91no—
73C3×C37⋊C3—273no—
74C3×C37⋊C3#73211yescharacteristic
75C3×C37⋊C3#73211yescharacteristic
76C3×C37⋊C3#73211yescharacteristic
77C9×C37—31no—
78C9×C37—91no—
79C9×C37—91no—
80C9×C37—91no—
81#66524—31no—
82#66524—31no—
83#66524—91no—
84#66524—91no—
85#66524—91no—
86#66524—91no—
87#66524—91no—
88#66524—91no—
89C3×#733—371no—
90C3×#733—371no—
91C3×#732—371no—
92#6887—371no—
93#6883—371no—
94#6883—371no—
95#6883—371no—
96#6883—371no—
97#6883—371no—
98#6883—371no—
99#6883—371no—
100#6883—371no—
101#6883C37⋊C311yescharacteristic, complemented
102C3×C37—31no—
103C3×C37—271no—
104C3×C37C3×#73211yescharacteristic
105C37⋊C3—31no—
106C37⋊C3—31no—
107C37⋊C3—31no—
108C37⋊C3—271no—
109C37⋊C3—271no—
110C3×3−1+2—1111no—
111C3×3−1+2—1111no—
112C3×H(3,𝔽3)—1111no—
113C32×C9—371no—
114#733—371no—
115#733—371no—
116#733—371no—
117#733—371no—
118#733—1111no—
119#733—1111no—
120#733—1111no—
121#733—1111no—
122#733C3×C37⋊C311yescharacteristic, complemented
123#733C3×C37⋊C311yescharacteristic, complemented
124#732—371no—
125#732—371no—
126#732—1111no—
127#732—1111no—
128#732C3×C37⋊C311yescharacteristic
129C9⋊C9—371no—
130C9⋊C9—371no—
131C9⋊C9—1111no—
132C9⋊C9C3×C37⋊C311yescharacteristic, complemented
133C32⋊C9—1111no—
134C92—1111no—
135C37#1062484811yescharacteristic, complemented, Sylow
136C33—371no—
137C33—3331no—
1383−1+2—31no—
1393−1+2—31no—
1403−1+2—3331no—
1413−1+2—3331no—
1423−1+2—3331no—
1433−1+2—3331no—
1443−1+2—1111no—
1453−1+2—1111no—
1463−1+2—1111no—
1473−1+2—1111no—
148H(3,𝔽3)—31no—
149H(3,𝔽3)—3331no—
150H(3,𝔽3)—3331no—
151H(3,𝔽3)—1111no—
152H(3,𝔽3)—1111no—
153C3×C9—31no—
154C3×C9—371no—
155C3×C9—371no—
156C3×C9—3331no—
157C3×C9—3331no—
158C3×C9—1111no—
159C3×C9—1111no—
160C3×C9—1111no—
161C3×C9—1111no—
162C3×C9—1111no—
163C3×C9C32×C37⋊C311yescharacteristic
164C32—91no—
165C32—371no—
166C32—371no—
167C32—371no—
168C32—3331no—
169C32—3331no—
170C32—3331no—
171C32—9993no—
172C32H(3,𝔽3)×C37⋊C311yescharacteristic
173C9—31no—
174C9—91no—
175C9—91no—
176C9—91no—
177C9—3331no—
178C9—3331no—
179C9—3331no—
180C9—3331no—
181C9—3331no—
182C9—3331no—
183C9—1111no—
184C9—1111no—
185C3—31no—
186C3—271no—
187C3—1111no—
188C3—1111no—
189C3—1111no—
190C3—9991no—
191C3—9991no—
192C3#732×C37⋊C311yescharacteristic
subgroupG/H
centerC3#732×C37⋊C3
commutator, cosocleC3×C9×C37C33
FrattiniC3×C9C32×C37⋊C3
FittingC37×#6883C3
socleC3×C37C3×#732
prime radical#732×C37⋊C3C3
hypercenter#6883C37⋊C3
hypocenterC37#10624848
LCSG ▷ C3×C9×C37 ▷ C32×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6883

Complements

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

NH ≅ G/Ntype
1. #733×C37⋊C3C3semidirect
2. #733×C37⋊C3C3semidirect
4. #22582537C3semidirect
5. #22582525C3semidirect
6. #22582524C3semidirect
7. #22582523C3semidirect
8. #22582523C3semidirect
9. #22582522C3semidirect
10. #22582522C3semidirect
11. #22582521C3semidirect
12. #22582521C3semidirect
13. C37×#6883C3semidirect
18. #15688521C32semidirect
19. #15688521C32semidirect
20. #15688521C32semidirect
21. #15688521C32semidirect
30. #15688506C32semidirect
31. #15688505C32semidirect
35. C37×#733C32semidirect
36. C37×#733C32semidirect
38. C37×C9⋊C9C32semidirect
101. #6883C37⋊C3semidirect
122. #733C3×C37⋊C3semidirect
123. #733C3×C37⋊C3semidirect
132. C9⋊C9C3×C37⋊C3semidirect
135. C37#10624848semidirect

Maximal subgroups

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

subgroupindex
#733×C37⋊C33
#732×C37⋊C33
#225825373
#225825253
#225825243
#225825233
#225825223
#225825213
C37×#68833
#1062484837