Finite Group Databasebeta

← C43⋊C3×3−1+4 #44535402

Subgroups — C43⋊C3×3−1+4 #44535402

Order 31347.

5588 conjugacy classes of subgroups; only the 2881 normal subgroups are shown.

normal subgroups only

This group has 5588 conjugacy classes of subgroups — too many to draw. Only its 2881 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#23782924C312yesmaximal, complemented
2#23782923C3124yesmaximal, complemented
3#23782922C3127yesmaximal, complemented
4#23782921C3127yesmaximal, complemented
5#737×C43⋊C3C3127yesmaximal, complemented
6C3×3−1+2×C43⋊C3C3112yesmaximal, complemented
7C3×H(3,𝔽3)×C43⋊C3C311yesmaximal, characteristic
8C43×3−1+4C311yesmaximal, characteristic, complemented
9C33×C43⋊C3C3214yes—
10#16812526C321432yescomplemented
11#16812525C321216yescomplemented
12#16812524C32154yescomplemented
13C3×#11923958C32124yescomplemented
14C3×#11923957C32136yescomplemented
15C3×#11923956C32136yescomplemented
163−1+2×C43⋊C3C3219yes—
173−1+2×C43⋊C3C32172yescomplemented
183−1+2×C43⋊C3C32172yescomplemented
193−1+2×C43⋊C3C32172yescomplemented
203−1+2×C43⋊C3C32172yescomplemented
21C3×C32⋊(C43⋊C3)C3218yes—
22H(3,𝔽3)×C43⋊C3C3219yes—
23H(3,𝔽3)×C43⋊C3C3219yes—
24H(3,𝔽3)×C43⋊C3C3219yes—
25C3×C9×C43⋊C3C32136yescomplemented
26C43×#737C32127yescomplemented
27C3×3−1+2×C43C32112yescomplemented
28C3×H(3,𝔽3)×C43C3211yescharacteristic
29C32×C43⋊C3—912no—
30C32×C43⋊C3C33112yes—
31C32×C43⋊C3C3311yescharacteristic
32C32×C43⋊C3C33112yes—
33C32×C43⋊C3C33112yes—
34C32×C43⋊C3C3318yes—
35#11923958C33118yes—
36#11923958C331144yescomplemented
37#11923957C33127yes—
38#11923957C331216yescomplemented
39#11923956C33127yes—
40#11923956C331216yescomplemented
41C32⋊(C43⋊C3)C33172yes—
42C3×C43⋊C9C33172yescomplemented
43C9×C43⋊C3C33127yes—
44C9×C43⋊C3C331216yescomplemented
45C33×C43C3314yes—
463−1+2×C43C3319yes—
473−1+2×C43C33172yescomplemented
48H(3,𝔽3)×C43C3319yes—
49C3×C9×C43C33136yescomplemented
50C3×3−1+4—431nomaximal, Sylow
51C32×C43—94no—
52C32×C43C34112yes—
53C32×C43C3411yescharacteristic
54C3×C43⋊C3—33no—
55C3×C43⋊C3—336no—
56C3×C43⋊C3—912no—
57C3×C43⋊C3—912no—
58C3×C43⋊C3—98no—
59C3×C43⋊C3C34124yes—
60C3×C43⋊C3C3411yescharacteristic
61C3×C43⋊C3C3411yescharacteristic
62C3×C43⋊C3C3411yescharacteristic
63C9×C43C34127yes—
64C43⋊C9C34154yes—
653−1+4—4327no—
663−1+4—4327no—
673−1+4—4324no—
683−1+4—432no—
693−1+4C43⋊C311yescharacteristic, direct product factor
70C3×#737—4327no—
71C32×3−1+2—4312no—
72C32×H(3,𝔽3)—431no—
73C3×C43—31no—
74C3×C43—312no—
75C3×C43C3511yescharacteristic
76C43⋊C3—31no—
77C43⋊C3—31no—
78C43⋊C3—324no—
79C43⋊C33−1+413yesdirect product factor
80C34—434no—
81#737—43432no—
82#737—4354no—
83#737—43216no—
84#737C3×C43⋊C3127yescomplemented
85C3×3−1+2—4324no—
86C3×3−1+2—439no—
87C3×3−1+2—4372no—
88C3×3−1+2—4372no—
89C3×3−1+2—4372no—
90C3×3−1+2—4372no—
91C3×3−1+2—4336no—
92C3×3−1+2—4336no—
93C3×3−1+2C3×C43⋊C3112yescomplemented
94C3×H(3,𝔽3)—438no—
95C3×H(3,𝔽3)—439no—
96C3×H(3,𝔽3)—439no—
97C3×H(3,𝔽3)—439no—
98C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
99C32×C9—4336no—
100C43C3×3−1+411yescharacteristic, complemented, Sylow
101C33—4312no—
102C33—431no—
103C33—438no—
104C33—4312no—
105C33—4312no—
106C33—38712no—
107C33C32×C43⋊C314yes—
1083−1+2—4318no—
1093−1+2—43144no—
1103−1+2—4327no—
1113−1+2—4327no—
1123−1+2—43216no—
1133−1+2—43216no—
1143−1+2C32×C43⋊C319yes—
1153−1+2C32×C43⋊C3172yescomplemented
116H(3,𝔽3)—4372no—
117H(3,𝔽3)C32×C43⋊C319yes—
118C3×C9—4372no—
119C3×C9—4327no—
120C3×C9—43216no—
121C3×C9C32×C43⋊C3136yescomplemented
122C32—94no—
123C32—431no—
124C32—4324no—
125C32—431no—
126C32—431no—
127C32—12936no—
128C32—1293no—
129C32—3878no—
130C32—38712no—
131C32—38712no—
132C32C33×C43⋊C3112yes—
133C32C33×C43⋊C311yescharacteristic
134C9—4354no—
135C9C33×C43⋊C3127yes—
136C3—31no—
137C3—312no—
138C3—433no—
139C3—12924no—
140C3—1291no—
141C3—1291no—
142C3C34×C43⋊C311yescharacteristic
subgroupG/H
center, FrattiniC3C34×C43⋊C3
commutator, socle, cosocleC3×C43C35
FittingC43×3−1+4C3
prime radicalC3×H(3,𝔽3)×C43⋊C3C3
hypercenter3−1+4C43⋊C3
hypocenterC43C3×3−1+4
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ 3−1+4

Complements

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

NH ≅ G/Ntype
1. #23782924C3semidirect
2. #23782923C3semidirect
3. #23782922C3semidirect
4. #23782921C3semidirect
5. #737×C43⋊C3C3semidirect
6. C3×3−1+2×C43⋊C3C3semidirect
8. C43×3−1+4C3semidirect
10. #16812526C32semidirect
11. #16812525C32semidirect
12. #16812524C32semidirect
13. C3×#11923958C32semidirect
14. C3×#11923957C32semidirect
15. C3×#11923956C32semidirect
17. 3−1+2×C43⋊C3C32semidirect
18. 3−1+2×C43⋊C3C32semidirect
19. 3−1+2×C43⋊C3C32semidirect
20. 3−1+2×C43⋊C3C32semidirect
25. C3×C9×C43⋊C3C32semidirect
26. C43×#737C32semidirect
27. C3×3−1+2×C43C32semidirect
36. #11923958C33semidirect
38. #11923957C33semidirect
40. #11923956C33semidirect
42. C3×C43⋊C9C33semidirect
44. C9×C43⋊C3C33semidirect
47. 3−1+2×C43C33semidirect
49. C3×C9×C43C33semidirect
69. 3−1+4C43⋊C3direct (N × H)
79. C43⋊C33−1+4direct (N × H)
84. #737C3×C43⋊C3semidirect
93. C3×3−1+2C3×C43⋊C3semidirect
100. C43C3×3−1+4semidirect
115. 3−1+2C32×C43⋊C3semidirect
121. C3×C9C32×C43⋊C3semidirect

Maximal subgroups

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

subgroupindex
#237829243
#237829233
#237829223
#237829213
#737×C43⋊C33
C3×3−1+2×C43⋊C33
C3×H(3,𝔽3)×C43⋊C33
C43×3−1+43
C3×3−1+443