Finite Group Databasebeta

← #44534847

Subgroups — #44534847

Order 31347.

764 conjugacy classes of subgroups; only the 256 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 256 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#23782808C313yesmaximal, complemented
2#23782807C316yesmaximal, complemented
3#23782805C312yesmaximal, complemented
4#23782804C312yesmaximal, complemented
5#23782803C313yesmaximal, complemented
6#23782802C313yesmaximal, complemented
7#23782801C316yesmaximal, complemented
8#23782801C316yesmaximal, complemented
9#23782800C312yesmaximal, complemented
10#23782797C311yesmaximal, characteristic, complemented
11#23782796C311yesmaximal, characteristic, complemented
12(C3×C43⋊C3)⋊H(3,𝔽3)C311yesmaximal, characteristic
13C9×C32⋊(C43⋊C3)C312yesmaximal, complemented
14C3×(C3×C43⋊C3)⋊C9C311yesmaximal, characteristic, complemented
15C9×H(3,𝔽3)×C43C311yesmaximal, characteristic, complemented
16C33×C43⋊C3C3211yescharacteristic
17C3×#11923958C3216yescomplemented
18C3×#11923957C3213yes—
19C3×#11923957C3216yescomplemented
20C3×#11923956C3213yes—
21C3×#11923956C3216yescomplemented
22C3×C32⋊(C43⋊C3)C3212yes—
23C3×C32⋊(C43⋊C3)C3213yes—
24C3×C32⋊(C43⋊C3)C3213yes—
25C3×C32⋊(C43⋊C3)C3213yes—
26C32×C43⋊C9C3212yes—
27C3×C9×C43⋊C3C3216yescomplemented
28C32⋊(C43⋊C9)C3212yes—
29C32⋊(C43⋊C9)C3212yes—
30C32⋊(C43⋊C9)C3216yescomplemented
31C32⋊(C43⋊C9)C3216yescomplemented
32(C3×C43⋊C3)⋊C9C3212yes—
33(C3×C43⋊C3)⋊C9C3212yes—
34(C3×C43⋊C3)⋊C9C3211yescharacteristic
35(C3×C43⋊C3)⋊C9C3211yescharacteristic
36(C3×C43⋊C3)⋊C9C3212yes—
37(C3×C43⋊C3)⋊C9C3211yescharacteristic
38(C3×C43⋊C3)⋊C9C3213yes—
39(C3×C43⋊C3)⋊C9C3213yes—
40(C3×C43⋊C3)⋊C9C3213yes—
41(C3×C43⋊C3)⋊C9C3213yes—
42(C3×C43⋊C3)⋊C9C3216yescomplemented
43(C3×C43⋊C3)⋊C9C3216yescomplemented
44(C3×C43⋊C3)⋊C9C3216yescomplemented
45(C3×C43⋊C3)⋊C9C3216yescomplemented
46(C3×C43⋊C3)⋊C9C3216yescomplemented
47(C3×C43⋊C3)⋊C9C3216yescomplemented
48C3×H(3,𝔽3)×C43C3211yescharacteristic
49C32×C9×C43C3211yescharacteristic
50C32×C9×C43C3213yescomplemented
51C43×C32⋊C9C3211yescharacteristic
52C43×C32⋊C9C3211yescharacteristic
53C43×C32⋊C9C3216yescomplemented
54C32×C43⋊C3—33no—
55C32×C43⋊C3—91no—
56C32×C43⋊C3—91no—
57C32×C43⋊C3—91no—
58C32×C43⋊C3C3311yescharacteristic
59C32×C43⋊C3C3311yescharacteristic
60C32×C43⋊C3C3311yescharacteristic
61C32×C43⋊C3C3316yes—
62#11923958—96no—
63#11923957—93no—
64#11923957—96no—
65#11923956—93no—
66#11923956—96no—
67C32⋊(C43⋊C3)—36no—
68C32⋊(C43⋊C3)—93no—
69C32⋊(C43⋊C3)—93no—
70C32⋊(C43⋊C3)—93no—
71C3×C43⋊C9—92no—
72C3×C43⋊C9C3312yes—
73C3×C43⋊C9C3312yes—
74C3×C43⋊C9C3312yes—
75C3×C43⋊C9C3316yes—
76C3×C43⋊C9C3316yes—
77C9×C43⋊C3—96no—
78C33×C43C3313yes—
79C33×C43C3311yescharacteristic
80H(3,𝔽3)×C43—33no—
81C3×C9×C43—91no—
82C3×C9×C43—93no—
83C3×C9×C43C3313yes—
84C3×C9×C43C3313yes—
85C3×C9×C43C3312yes—
86C3×C9×C43C3311yescharacteristic
87#10624888—431nomaximal, Sylow
88C32×C43—31no—
89C32×C43—31no—
90C32×C43—31no—
91C32×C43—33no—
92C32×C43—33no—
93C32×C43—33no—
94C32×C43—33no—
95C32×C43#73713yes—
96C32×C43C3411yescharacteristic
97C3×C43⋊C3—36no—
98C3×C43⋊C3—31no—
99C3×C43⋊C3—31no—
100C3×C43⋊C3—31no—
101C3×C43⋊C3—36no—
102C3×C43⋊C3—31no—
103C3×C43⋊C3—31no—
104C3×C43⋊C3—31no—
105C3×C43⋊C3—31no—
106C3×C43⋊C3—31no—
107C3×C43⋊C3—36no—
108C3×C43⋊C3—36no—
109C3×C43⋊C3—31no—
110C3×C43⋊C3—31no—
111C3×C43⋊C3—31no—
112C3×C43⋊C3—31no—
113C3×C43⋊C3—99no—
114C9×C43—31no—
115C9×C43—32no—
116C9×C43—33no—
117C9×C43—33no—
118C43⋊C9—36no—
119C43⋊C9—36no—
120C43⋊C9—32no—
121C43⋊C9—32no—
122C43⋊C9—32no—
123#6893—433no—
124#6893—436no—
125C9⋊H(3,𝔽3)—432no—
126C9⋊H(3,𝔽3)—433no—
127C9⋊H(3,𝔽3)—433no—
128C9⋊H(3,𝔽3)—432no—
129C9⋊H(3,𝔽3)—432no—
130C9⋊H(3,𝔽3)—436no—
131C9⋊H(3,𝔽3)—436no—
132#6891—431no—
133#6891—431no—
134C32⋊H(3,𝔽3)—431no—
135C9×H(3,𝔽3)—432no—
136C9×H(3,𝔽3)C43⋊C311yescharacteristic, complemented
137C3×C32⋊C9—431no—
138C3×C43—33no—
139C3×C43—93no—
140C3×C43C3×#73711yescharacteristic
141C3×C43H(5,𝔽3)11yescharacteristic
142C3×C433−1+411yescharacteristic
143C3×C433−1+411yescharacteristic
144C43⋊C3—96no—
145C43⋊C3—91no—
146C43⋊C3—91no—
147C43⋊C3—91no—
148C34—431no—
149C3×3−1+2—436no—
150C3×3−1+2—433no—
151C3×3−1+2—436no—
152C3×3−1+2—433no—
153C3×3−1+2—436no—
154C3×H(3,𝔽3)—432no—
155C3×H(3,𝔽3)—433no—
156C3×H(3,𝔽3)—433no—
157C3×H(3,𝔽3)—433no—
158C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
159C32×C9—432no—
160C32×C9—436no—
161C32×C9C3×C43⋊C311yescharacteristic
162C32×C9C3×C43⋊C313yescomplemented
163C32⋊C9—432no—
164C32⋊C9—432no—
165C32⋊C9—436no—
166C32⋊C9—436no—
167C32⋊C9—431no—
168C32⋊C9—431no—
169C32⋊C9—432no—
170C32⋊C9—432no—
171C32⋊C9—431no—
172C32⋊C9—432no—
173C32⋊C9—433no—
174C32⋊C9—433no—
175C32⋊C9—433no—
176C32⋊C9—433no—
177C32⋊C9—436no—
178C32⋊C9—436no—
179C32⋊C9—436no—
180C32⋊C9—436no—
181C32⋊C9—436no—
182C32⋊C9—436no—
183C32⋊C9C3×C43⋊C311yescharacteristic
184C32⋊C9C3×C43⋊C311yescharacteristic
185C32⋊C9C3×C43⋊C316yescomplemented
186C43#1062488811yescharacteristic, complemented, Sylow
187C33—431no—
188C33—436no—
189C33—431no—
190C33—431no—
191C33—1293no—
192C33—3871no—
193C33—3871no—
194C33—3871no—
195C33C32×C43⋊C313yes—
196C33C32×C43⋊C311yescharacteristic
1973−1+2—3876no—
1983−1+2—3873no—
1993−1+2—3876no—
2003−1+2—3873no—
2013−1+2—3876no—
202H(3,𝔽3)—33no—
203H(3,𝔽3)—1296no—
204H(3,𝔽3)—3873no—
205H(3,𝔽3)—3873no—
206H(3,𝔽3)—3873no—
207C3×C9—91no—
208C3×C9—93no—
209C3×C9—436no—
210C3×C9—436no—
211C3×C9—432no—
212C3×C9—432no—
213C3×C9—432no—
214C3×C9—3876no—
215C3×C9—3872no—
216C3×C9C32×C43⋊C311yescharacteristic
217C3×C9C32×C43⋊C313yes—
218C3×C9C32×C43⋊C313yes—
219C3×C9C32×C43⋊C312yes—
220C32—31no—
221C32—31no—
222C32—31no—
223C32—33no—
224C32—33no—
225C32—33no—
226C32—33no—
227C32—1296no—
228C32—1291no—
229C32—1291no—
230C32—1291no—
231C32—1296no—
232C32—1291no—
233C32—1291no—
234C32—1291no—
235C32—1291no—
236C32—1296no—
237C32—1291no—
238C32—1291no—
239C32—1291no—
240C32—1296no—
241C32—1291no—
242C32—1291no—
243C32—3879no—
244C32#1681252513yes—
245C32C33×C43⋊C311yescharacteristic
246C9—31no—
247C9—32no—
248C9—33no—
249C9—33no—
250C9—1296no—
251C9—1296no—
252C9—1292no—
253C9—1292no—
254C9—1292no—
255C3—33no—
256C3—93no—
257C3—3876no—
258C3—3871no—
259C3—3871no—
260C3—3871no—
261C3C3×#1681252511yescharacteristic
262C3C43⋊H(5,𝔽3)11yescharacteristic
263C3#2378292111yescharacteristic
264C3#2378292211yescharacteristic
subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
FittingC9×H(3,𝔽3)×C43C3
prime radical(C3×C43⋊C3)⋊H(3,𝔽3)C3
hypercenterC9×H(3,𝔽3)C43⋊C3
hypocenterC43#10624888
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ C9×H(3,𝔽3)

Complements

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

NH ≅ G/Ntype
1. #23782808C3semidirect
2. #23782807C3semidirect
3. #23782805C3semidirect
4. #23782804C3semidirect
5. #23782803C3semidirect
6. #23782802C3semidirect
7. #23782801C3semidirect
8. #23782801C3semidirect
9. #23782800C3semidirect
10. #23782797C3semidirect
11. #23782796C3semidirect
13. C9×C32⋊(C43⋊C3)C3semidirect
14. C3×(C3×C43⋊C3)⋊C9C3semidirect
15. C9×H(3,𝔽3)×C43C3semidirect
17. C3×#11923958C32semidirect
19. C3×#11923957C32semidirect
21. C3×#11923956C32semidirect
27. C3×C9×C43⋊C3C32semidirect
30. C32⋊(C43⋊C9)C32semidirect
31. C32⋊(C43⋊C9)C32semidirect
42. (C3×C43⋊C3)⋊C9C32semidirect
43. (C3×C43⋊C3)⋊C9C32semidirect
44. (C3×C43⋊C3)⋊C9C32semidirect
45. (C3×C43⋊C3)⋊C9C32semidirect
46. (C3×C43⋊C3)⋊C9C32semidirect
47. (C3×C43⋊C3)⋊C9C32semidirect
50. C32×C9×C43C32semidirect
53. C43×C32⋊C9C32semidirect
136. C9×H(3,𝔽3)C43⋊C3semidirect
162. C32×C9C3×C43⋊C3semidirect
185. C32⋊C9C3×C43⋊C3semidirect
186. C43#10624888semidirect

Maximal subgroups

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

subgroupindex
#237828083
#237828073
#237828053
#237828043
#237828033
#237828023
#237828013
#237828003
#237827973
#237827963
(C3×C43⋊C3)⋊H(3,𝔽3)3
C9×C32⋊(C43⋊C3)3
C3×(C3×C43⋊C3)⋊C93
C9×H(3,𝔽3)×C433
#1062488843