Finite Group Databasebeta

← 3−1+2×#11923957 #44534982

Subgroups — 3−1+2×#11923957 #44534982

Order 31347.

836 conjugacy classes of subgroups; only the 316 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 316 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
1C32×#11923957C311yesmaximal, characteristic
2C3×3−1+2×C43⋊C3C311yesmaximal, characteristic
3#23782849C316yesmaximal, complemented
4#23782846C313yesmaximal, complemented
5#23782827C316yesmaximal, complemented
6#23782825C313yesmaximal, complemented
7#23782818C314yesmaximal, complemented
8#23782815C312yesmaximal, complemented
9#23782811C316yesmaximal, complemented
10#23782797C312yesmaximal
113−1+2×C43⋊C9C312yesmaximal, complemented
12C9×#11923957C313yesmaximal, complemented
13C9×3−1+2×C43C311yesmaximal, characteristic, complemented
14C33×C43⋊C3C3211yescharacteristic
15C3×#11923958C3212yes—
16C3×#11923957—39no—
17C3×#11923957C3213yes—
18C3×#11923957C3212yes—
19C3×#11923957C3211yescharacteristic
20C3×#11923957C3212yes—
21C3×#11923957C3211yescharacteristic
22C3×#11923957C3212yes—
23C3×#11923957C3216yes—
24C3×#11923957C3211yescharacteristic
25C3×#11923956C3213yes—
263−1+2×C43⋊C3—39no—
27C32×C43⋊C9C3212yes—
28C3×C9×C43⋊C3C3213yes—
29#16812500C3216yescomplemented
30#16812499C3216yescomplemented
31#16812499C3216yescomplemented
32#16812499C32112yescomplemented
33(C43⋊C9)⋊C9C32112yescomplemented
34(C43⋊C9)⋊C9C32112yescomplemented
35(C43⋊C9)⋊C9C32112yescomplemented
36C32⋊(C43⋊C9)C3214yes—
37(C3×C43⋊C3)⋊C9C3216yes—
38(C3×C43⋊C3)⋊C9C3216yes—
39C9×C43⋊C9C3216yescomplemented
40C3×3−1+2×C43C3211yescharacteristic
41C32×C9×C43C3211yescharacteristic
42C43×C9⋊C9C3216yescomplemented
43C43×C32⋊C9C3212yes—
44C92×C43C3213yescomplemented
45C32×C43⋊C3—33no—
46C32×C43⋊C3—33no—
47C32×C43⋊C3—92no—
48C32×C43⋊C3C3311yescharacteristic
49C32×C43⋊C3C3311yescharacteristic
50C32×C43⋊C3C3311yescharacteristic
51#11923958—36no—
52#11923957—36no—
53#11923957—39no—
54#11923957—33no—
55#11923957—33no—
56#11923957—36no—
57#11923957—36no—
58#11923957—96no—
59#119239573−1+219yesdirect product factor
60#11923956—39no—
61C3×C43⋊C9—36no—
62C3×C43⋊C9C33112yes—
63C3×C43⋊C9C3316yes—
64C3×C43⋊C9C3312yes—
65C3×C43⋊C9C3312yes—
66C3×C43⋊C9C3312yes—
67C9×C43⋊C3—39no—
68C33×C43C3311yescharacteristic
693−1+2×C433−1+219yescomplemented
70C3×C9×C43—33no—
71C3×C9×C43C3316yes—
72C3×C9×C43C3312yes—
73C3×C9×C43C3311yescharacteristic
74C3×C9×C43C3313yes—
753−1+22—431nomaximal, Sylow
76C32×C43—31no—
77C32×C43—32no—
78C32×C43C3×3−1+213yes—
79C32×C43C3411yescharacteristic
80C3×C43⋊C3—31no—
81C3×C43⋊C3—32no—
82C3×C43⋊C3—31no—
83C3×C43⋊C3—31no—
84C3×C43⋊C3—31no—
85C3×C43⋊C3—31no—
86C3×C43⋊C3—32no—
87C3×C43⋊C3—32no—
88C3×C43⋊C3—99no—
89C3×C43⋊C3C3×3−1+213yes—
90C9×C43—32no—
91C9×C43—36no—
92C9×C43C3×3−1+213yescomplemented
93C9×C43C3×3−1+219yescomplemented
94C43⋊C9—36no—
95C43⋊C9—32no—
96C43⋊C9—32no—
97C43⋊C9—312no—
98C43⋊C9C3×3−1+216yescomplemented
99C32×3−1+2—431no—
100C32×3−1+2—431no—
101#6900—436no—
102#6900—433no—
103#6896—436no—
104#6896—433no—
105#6894—432no—
106#6894—436no—
107#6894—434no—
108#6891—432no—
109C9×3−1+2—432no—
110C9×3−1+2—433no—
111C9×3−1+2C43⋊C311yescharacteristic, complemented
112C3×C43—33no—
113C3×C43C32×3−1+211yescharacteristic
114C3×C43C32×3−1+211yescharacteristic
115C3×C433−1+412yes—
116C43⋊C3—33no—
117C43⋊C3—91no—
118C43⋊C3—91no—
119C34—431no—
120C3×3−1+2—432no—
121C3×3−1+2—431no—
122C3×3−1+2—433no—
123C3×3−1+2—432no—
124C3×3−1+2—432no—
125C3×3−1+2—431no—
126C3×3−1+2—432no—
127C3×3−1+2—431no—
128C3×3−1+2—433no—
129C3×3−1+2—436no—
130C3×3−1+2—1299no—
131C3×3−1+2—1299no—
132C3×3−1+2C3×C43⋊C311yescharacteristic
133C32×C9—432no—
134C32×C9—433no—
135C32×C9C3×C43⋊C311yescharacteristic
136C9⋊C9—4312no—
137C9⋊C9—4312no—
138C9⋊C9—4312no—
139C9⋊C9—436no—
140C9⋊C9—436no—
141C9⋊C9—4312no—
142C9⋊C9—436no—
143C9⋊C9C3×C43⋊C316yescomplemented
144C32⋊C9—434no—
145C32⋊C9—436no—
146C32⋊C9—436no—
147C32⋊C9C3×C43⋊C312yes—
148C92—436no—
149C92C3×C43⋊C313yescomplemented
150C433−1+2211yescharacteristic, complemented, Sylow
151C33—431no—
152C33—431no—
153C33—431no—
154C33—1293no—
155C33—1293no—
156C33—3872no—
157C33C32×C43⋊C311yescharacteristic
1583−1+2—439no—
1593−1+2—1296no—
1603−1+2—1296no—
1613−1+2—1296no—
1623−1+2—1296no—
1633−1+2—1293no—
1643−1+2—1293no—
1653−1+2—1299no—
1663−1+2—1299no—
1673−1+2—3876no—
1683−1+2#1192395719yesdirect product factor
169C3×C9—33no—
170C3×C9—432no—
171C3×C9—4312no—
172C3×C9—432no—
173C3×C9—432no—
174C3×C9—436no—
175C3×C9—1296no—
176C3×C9—1299no—
177C3×C9C32×C43⋊C316yes—
178C3×C9C32×C43⋊C312yes—
179C3×C9C32×C43⋊C311yescharacteristic
180C3×C9C32×C43⋊C313yes—
181C32—31no—
182C32—32no—
183C32—433no—
184C32—1291no—
185C32—1292no—
186C32—1291no—
187C32—1291no—
188C32—1291no—
189C32—1291no—
190C32—1292no—
191C32—1292no—
192C32—3879no—
193C32C3×#1192395713yes—
194C32C33×C43⋊C311yescharacteristic
195C9—32no—
196C9—36no—
197C9—436no—
198C9—1292no—
199C9—1292no—
200C9—1296no—
201C9—12912no—
202C93−1+2×C43⋊C313yescomplemented
203C9C3×#1192395719yescomplemented
204C3—33no—
205C3—1293no—
206C3—3871no—
207C3—3871no—
208C3C3×3−1+2×C43⋊C311yescharacteristic
209C3C32×#1192395711yescharacteristic
210C3#2378292212yes—
subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
FittingC9×3−1+2×C43C3
prime radicalC33×C43⋊C3C32
hypercenterC9×3−1+2C43⋊C3
hypocenterC433−1+22
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ C9×3−1+2

Complements

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

NH ≅ G/Ntype
3. #23782849C3semidirect
4. #23782846C3semidirect
5. #23782827C3semidirect
6. #23782825C3semidirect
7. #23782818C3semidirect
8. #23782815C3semidirect
9. #23782811C3semidirect
11. 3−1+2×C43⋊C9C3semidirect
12. C9×#11923957C3semidirect
13. C9×3−1+2×C43C3semidirect
29. #16812500C32semidirect
30. #16812499C32semidirect
31. #16812499C32semidirect
32. #16812499C32semidirect
33. (C43⋊C9)⋊C9C32semidirect
34. (C43⋊C9)⋊C9C32semidirect
35. (C43⋊C9)⋊C9C32semidirect
39. C9×C43⋊C9C32semidirect
42. C43×C9⋊C9C32semidirect
44. C92×C43C32semidirect
59. #119239573−1+2direct (N × H)
69. 3−1+2×C433−1+2semidirect
92. C9×C43C3×3−1+2semidirect
93. C9×C43C3×3−1+2semidirect
98. C43⋊C9C3×3−1+2semidirect
111. C9×3−1+2C43⋊C3semidirect
143. C9⋊C9C3×C43⋊C3semidirect
149. C92C3×C43⋊C3semidirect
150. C433−1+22semidirect
168. 3−1+2#11923957direct (N × H)
202. C93−1+2×C43⋊C3semidirect
203. C9C3×#11923957semidirect

Maximal subgroups

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

subgroupindex
C32×#119239573
C3×3−1+2×C43⋊C33
#237828493
#237828463
#237828273
#237828253
#237828183
#237828153
#237828113
#237827973
3−1+2×C43⋊C93
C9×#119239573
C9×3−1+2×C433
3−1+2243