Finite Group Databasebeta

← #72243661

Subgroups — #72243661

Order 4374.

1669 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1669 conjugacy classes of subgroups — too many to draw. Only its 229 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#14554861C211yesmaximal, characteristic, complemented, Sylow
2#13091657—36nomaximal
3C3×#92344—32nomaximal
4#13091151—39nomaximal
5#13091139—312nomaximal
6#13091107—39nomaximal
7#13091053—32nomaximal
8#10624932D316yescomplemented
9C3×#6908D312yescomplemented
10#10624760D319yescomplemented
11#10624757D3112yescomplemented
12UT(4,𝔽3)D319yescomplemented
13#10624732D312yescomplemented
14#92391—99no—
15C3×#4207—96no—
16C32×C3⋊D9—91no—
17#92344—32no—
18C3⋊#4185—36no—
19#92333—936no—
20#4183⋊C3—936no—
21C3×#733⋊C2—94no—
22C3×#4185—92no—
23C3×#4185—912no—
24C3×#4185—96no—
25C3×#4184—96no—
26C3×#4183—96no—
27#92300—96no—
28H(5,𝔽3)C3⋊D319yescomplemented
29C3×#737C3⋊D316yescomplemented
30C33×C9C3⋊D311yescharacteristic, complemented
31#6911—618no—
32#6911C3⋊D3136yescomplemented
33#6909C3⋊D3136yescomplemented
34#6908—32no—
35#6908—66no—
36#6908—62no—
37C3×#733C3⋊D314yescomplemented
38C3×#732—36no—
39C3×#732—66no—
40C3×#732C3⋊D312yes—
41C3×#732C3⋊D3112yescomplemented
42C3×#732C3⋊D316yescomplemented
43C3×#731C3⋊D316yescomplemented
44C3×AΣL(1,𝔽27)C3⋊D316yescomplemented
45C32⋊H(3,𝔽3)C3⋊D316yescomplemented
46C32×C3⋊D3—271no—
47C3⋊#272—96no—
48#4207—96no—
49#4207—912no—
50C3⋊((C3⋊D3)⋊C3)—918no—
51C3⋊((C3⋊D3)⋊C3)—918no—
52C3×C3⋊D9—96no—
53C3×C3⋊D9—92no—
54C3×C3⋊D9—92no—
55C3×AGL(1,ℤ/9)—2712no—
56C3×(C3⋊D3)⋊C3—2718no—
57C3×(C3⋊D3)⋊C3—276no—
58C32×D9—271no—
59C32×D9—272no—
60#733⋊C2—94no—
61#4185—912no—
62#4185—936no—
63#4185—96no—
64#4185—92no—
65#4184—96no—
66#4183—96no—
67#4183—936no—
68C34C3⋊(C3⋊D3)11yescharacteristic
69#737—36no—
70#737—66no—
71#737—912no—
72C3×3−1+2—66no—
73C3×3−1+2C3⋊(C3⋊D3)112yes—
74C3×H(3,𝔽3)—318no—
75C3×H(3,𝔽3)—618no—
76C3×H(3,𝔽3)—918no—
77C3×H(3,𝔽3)—96no—
78C3×H(3,𝔽3)C3⋊(C3⋊D3)16yes—
79C3×H(3,𝔽3)C3⋊(C3⋊D3)118yes—
80C32×C9—32no—
81C32×C9—36no—
82C32×C9—62no—
83C32×C9—92no—
84C32×C9C3⋊(C3⋊D3)12yes—
85C32×C9C3⋊(C3⋊D3)11yescharacteristic
86#733—34no—
87#733—64no—
88#732—26no—
89#732—22no—
90#732—336no—
91#732—312no—
92#732—612no—
93#732—636no—
94#732—96no—
95#732#27212yescomplemented
96#731—36no—
97#731—66no—
98AΣL(1,𝔽27)—36no—
99AΣL(1,𝔽27)—66no—
100AΣL(1,𝔽27)—936no—
101C3⋊(C3⋊D3)—99no—
102C3×C3⋊D3—272no—
103C3×C3⋊D3—272no—
104C3×C3⋊D3—2718no—
105C3×C3⋊D3—276no—
106C32×D3—813no—
107C32×D3—811no—
108#272—8118no—
109C3⋊D9—91no—
110C3⋊D9—96no—
111AGL(1,ℤ/9)—2724no—
112AGL(1,ℤ/9)—2712no—
113(C3⋊D3)⋊C3—2718no—
114(C3⋊D3)⋊C3—2736no—
115(C3⋊D3)⋊C3—2712no—
116(C3⋊D3)⋊C3—276no—
117C3×D9—272no—
118C3×D9—272no—
119C3×D9—2712no—
120C3×D9—272no—
121C3×D9—274no—
122C3×D9—272no—
123C33—32no—
124C33—36no—
125C33—32no—
126C33—318no—
127C33—93no—
128C33—99no—
129C33—189no—
130C33C3⋊(C3⋊(C3⋊D3))11yescharacteristic
1313−1+2—312no—
1323−1+2—324no—
1333−1+2—186no—
1343−1+2—1812no—
135H(3,𝔽3)—26no—
136H(3,𝔽3)—312no—
137H(3,𝔽3)—336no—
138H(3,𝔽3)—318no—
139H(3,𝔽3)—1818no—
140H(3,𝔽3)—189no—
141H(3,𝔽3)—2718no—
142H(3,𝔽3)C3⋊#27216yes—
143C3×C9—22no—
144C3×C9—32no—
145C3×C9—34no—
146C3×C9—32no—
147C3×C9—312no—
148C3×C9—32no—
149C3×C9—91no—
150C3×C9—96no—
151C3×C9—182no—
152C3×C9—186no—
153C3×C9—182no—
154C3×C9C3⋊#27212yes—
155C2×C32—2431no—
156C3⋊D3—271no—
157C3⋊D3—276no—
158C3⋊D3—2718no—
159C3⋊D3—2439no—
160C3×D3—816no—
161C3×D3—816no—
162C3×D3—812no—
163C3×D3—812no—
164C3×D3—24318no—
165C3×D3—2436no—
166D9—272no—
167D9—271no—
168D9—2712no—
169C32—36no—
170C32—36no—
171C32—66no—
172C32—91no—
173C32—96no—
174C32—91no—
175C32—918no—
176C32—182no—
177C32—276no—
178C32—2718no—
179C32—819no—
180C32—1629no—
181C32C3⋊(C3⋊#272)12yes—
182C32#9240412yes—
183C9—32no—
184C9—62no—
185C9—91no—
186C9—912no—
187C2×C3—2432no—
188C2×C3—2432no—
189D3—813no—
190D3—811no—
191D3—2436no—
192D3—24318no—
193C3—32no—
194C3—32no—
195C3—93no—
196C3—96no—
197C3—186no—
198C3—2718no—
199C3#1309150211yescharacteristic
200C2—2431noSylow
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenter#14554861C2
FrattiniC33C3⋊(C3⋊(C3⋊D3))
socleC3#13091502
LCSG ▷ #14554861
UCSC1

Complements

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

NH ≅ G/Ntype
1. #14554861C2semidirect
8. #10624932D3semidirect
9. C3×#6908D3semidirect
10. #10624760D3semidirect
11. #10624757D3semidirect
12. UT(4,𝔽3)D3semidirect
13. #10624732D3semidirect
28. H(5,𝔽3)C3⋊D3semidirect
29. C3×#737C3⋊D3semidirect
30. C33×C9C3⋊D3semidirect
32. #6911C3⋊D3semidirect
33. #6909C3⋊D3semidirect
37. C3×#733C3⋊D3semidirect
41. C3×#732C3⋊D3semidirect
42. C3×#732C3⋊D3semidirect
43. C3×#731C3⋊D3semidirect
44. C3×AΣL(1,𝔽27)C3⋊D3semidirect
45. C32⋊H(3,𝔽3)C3⋊D3semidirect
95. #732#272semidirect

Maximal subgroups

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

subgroupindex
#145548612
#130916573
C3×#923443
#130911513
#130911393
#130911073
#130910533