Finite Group Databasebeta

← #41007383

Subgroups — #41007383

Order 26973.

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

normal subgroups only

This group has 210 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#732×C37⋊C3C311yesmaximal, characteristic, complemented
3#732×C37⋊C3C311yesmaximal, characteristic, complemented
4#22582537C311yesmaximal, characteristic, complemented
5#22582515C311yesmaximal, characteristic, complemented
6#22582514C311yesmaximal, characteristic, complemented
7#22582513C311yesmaximal, characteristic, complemented
8#22582513C311yesmaximal, characteristic, complemented
9#22582512C311yesmaximal, characteristic, complemented
10#22582512C311yesmaximal, characteristic, complemented
11#22582511C311yesmaximal, characteristic, complemented
12#22582511C311yesmaximal, characteristic, complemented
13C37×#6881C311yesmaximal, characteristic, complemented
143−1+2×C37⋊C3—31no—
15H(3,𝔽3)×C37⋊C3—31no—
16H(3,𝔽3)×C37⋊C3—31no—
17C3×C9×C37⋊C3C3211yescharacteristic
18#15688521C3211yescharacteristic, complemented
19#15688521C3211yescharacteristic, complemented
20#15688520—31no—
21#15688520—31no—
22#15688519C3211yescharacteristic, complemented
23#15688519C3211yescharacteristic, complemented
24#15688519C3211yescharacteristic, complemented
25#15688519C3211yescharacteristic, complemented
26#15688518—31no—
27#15688518—31no—
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×#732C3211yescharacteristic, complemented
37C37×#732C3211yescharacteristic, complemented
38C37×C9⋊C9C3211yescharacteristic, complemented
39C32×C37⋊C3—91no—
40C32×C37⋊C3—91no—
41C32×C37⋊C3H(3,𝔽3)11yescharacteristic
423−1+2×C37—31no—
43H(3,𝔽3)×C37—31no—
44H(3,𝔽3)×C37—31no—
45C3×C9×C37—31no—
46C3×C9×C37C3311yescharacteristic
47C32⋊(C37⋊C3)—31no—
48C32⋊(C37⋊C3)—31no—
49C32⋊(C37⋊C3)—31no—
50C32⋊(C37⋊C3)—31no—
51C32⋊(C37⋊C3)—91no—
52C32⋊(C37⋊C3)—91no—
53C32⋊(C37⋊C3)—91no—
54C32⋊(C37⋊C3)—91no—
55#11758608—31no—
56#11758608—31no—
57C3×#66524—31no—
58C3×#66524—31no—
59C3×#66524H(3,𝔽3)11yescharacteristic
60C3×#66524H(3,𝔽3)11yescharacteristic
61#11758606—91no—
62#11758605—91no—
63C9×C37⋊C3—31no—
64C9×C37⋊C3—31no—
65C9×C37⋊C3—31no—
66C9×C37⋊C3—91no—
67#10624846—371nomaximal, Sylow
68C32×C37—91no—
69C32×C37—91no—
70C32×C37C3×H(3,𝔽3)11yescharacteristic
71C3×C37⋊C3—91no—
72C3×C37⋊C3—91no—
73C3×C37⋊C3—91no—
74C3×C37⋊C3—91no—
75C3×C37⋊C3—91no—
76C3×C37⋊C3—273no—
77C3×C37⋊C3—273no—
78C3×C37⋊C3#73211yescharacteristic
79C3×C37⋊C3#73211yescharacteristic
80C3×C37⋊C3#73211yescharacteristic
81C9×C37—31no—
82C9×C37—91no—
83C9×C37—91no—
84#66524—31no—
85#66524—31no—
86#66524—91no—
87#66524—91no—
88#66524—91no—
89#66524—91no—
90C3×#733—371no—
91C3×#732—371no—
92C3×#732—371no—
93#6887—371no—
94#6881—371no—
95#6881—371no—
96#6881—371no—
97#6881—371no—
98#6881—371no—
99#6881—371no—
100#6881—371no—
101#6881—371no—
102#6881C37⋊C311yescharacteristic, complemented
103C3×C37—31no—
104C3×C37—271no—
105C3×C37—271no—
106C3×C37C3×#73211yescharacteristic
107C37⋊C3—31no—
108C37⋊C3—31no—
109C37⋊C3—31no—
110C37⋊C3—271no—
111C37⋊C3—271no—
112C37⋊C3—271no—
113C37⋊C3—271no—
114C3×3−1+2—1111no—
115C3×H(3,𝔽3)—1111no—
116C3×H(3,𝔽3)—1111no—
117C32×C9—371no—
118#733—371no—
119#733—371no—
120#733—1111no—
121#733—1111no—
122#733C3×C37⋊C311yescharacteristic, complemented
123#732—371no—
124#732—371no—
125#732—371no—
126#732—371no—
127#732—1111no—
128#732—1111no—
129#732—1111no—
130#732—1111no—
131#732C3×C37⋊C311yescharacteristic, complemented
132#732C3×C37⋊C311yescharacteristic, complemented
133C9⋊C9—371no—
134C9⋊C9—371no—
135C9⋊C9—1111no—
136C9⋊C9C3×C37⋊C311yescharacteristic, complemented
137C32⋊C9—1111no—
138C92—1111no—
139C37#1062484611yescharacteristic, complemented, Sylow
140C33—371no—
141C33—3331no—
142C33—3331no—
1433−1+2—31no—
1443−1+2—3331no—
1453−1+2—3331no—
1463−1+2—1111no—
1473−1+2—1111no—
148H(3,𝔽3)—31no—
149H(3,𝔽3)—31no—
150H(3,𝔽3)—3331no—
151H(3,𝔽3)—3331no—
152H(3,𝔽3)—3331no—
153H(3,𝔽3)—3331no—
154H(3,𝔽3)—1111no—
155H(3,𝔽3)—1111no—
156H(3,𝔽3)—1111no—
157H(3,𝔽3)—1111no—
158C3×C9—31no—
159C3×C9—371no—
160C3×C9—371no—
161C3×C9—3331no—
162C3×C9—1111no—
163C3×C9—1111no—
164C3×C9—1111no—
165C3×C9—1111no—
166C3×C9—1111no—
167C3×C9C32×C37⋊C311yescharacteristic
168C32—91no—
169C32—91no—
170C32—371no—
171C32—371no—
172C32—371no—
173C32—3331no—
174C32—3331no—
175C32—3331no—
176C32—3331no—
177C32—3331no—
178C32—9993no—
179C32—9993no—
180C32H(3,𝔽3)×C37⋊C311yescharacteristic
181C9—31no—
182C9—91no—
183C9—91no—
184C9—3331no—
185C9—3331no—
186C9—3331no—
187C9—3331no—
188C9—1111no—
189C9—1111no—
190C3—31no—
191C3—271no—
192C3—271no—
193C3—1111no—
194C3—1111no—
195C3—1111no—
196C3—9991no—
197C3—9991no—
198C3—9991no—
199C3—9991no—
200C3#732×C37⋊C311yescharacteristic
subgroupG/H
centerC3#732×C37⋊C3
commutator, cosocleC3×C9×C37C33
FrattiniC3×C9C32×C37⋊C3
FittingC37×#6881C3
socleC3×C37C3×#732
hypercenter#6881C37⋊C3
hypocenterC37#10624846
LCSG ▷ C3×C9×C37 ▷ C32×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6881

Complements

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

NH ≅ G/Ntype
1. #733×C37⋊C3C3semidirect
2. #732×C37⋊C3C3semidirect
3. #732×C37⋊C3C3semidirect
4. #22582537C3semidirect
5. #22582515C3semidirect
6. #22582514C3semidirect
7. #22582513C3semidirect
8. #22582513C3semidirect
9. #22582512C3semidirect
10. #22582512C3semidirect
11. #22582511C3semidirect
12. #22582511C3semidirect
13. C37×#6881C3semidirect
18. #15688521C32semidirect
19. #15688521C32semidirect
22. #15688519C32semidirect
23. #15688519C32semidirect
24. #15688519C32semidirect
25. #15688519C32semidirect
30. #15688506C32semidirect
31. #15688505C32semidirect
35. C37×#733C32semidirect
36. C37×#732C32semidirect
37. C37×#732C32semidirect
38. C37×C9⋊C9C32semidirect
102. #6881C37⋊C3semidirect
122. #733C3×C37⋊C3semidirect
131. #732C3×C37⋊C3semidirect
132. #732C3×C37⋊C3semidirect
136. C9⋊C9C3×C37⋊C3semidirect
139. C37#10624846semidirect

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
#225825153
#225825143
#225825133
#225825123
#225825113
C37×#68813
#1062484637