Finite Group Databasebeta

← C43×#10624896 #44531833

Subgroups — C43×#10624896 #44531833

Order 31347.

1082 conjugacy classes of subgroups; only the 482 normal subgroups are shown.

normal subgroups only

This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 482 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
1C3×C43×#737C313yesmaximal, complemented
2C32×3−1+2×C43C311yesmaximal, characteristic, complemented
3C43×#6893C316yesmaximal, complemented
4C43×C9⋊H(3,𝔽3)C316yesmaximal, complemented
5C43×C9⋊H(3,𝔽3)C3118yesmaximal, complemented
6C43×#6891C311yesmaximal, characteristic, complemented
7C43×C32⋊H(3,𝔽3)C311yesmaximal, characteristic
8C9×H(3,𝔽3)×C43C313yesmaximal, complemented
9C3×C43×C32⋊C9C311yesmaximal, characteristic, complemented
10C34×C43C3211yescharacteristic
11C43×#737—327no—
12C3×3−1+2×C43—39no—
13C3×3−1+2×C43C3212yes—
14C3×3−1+2×C43C3213yes—
15C3×3−1+2×C43C3216yes—
16C3×3−1+2×C43C3211yescharacteristic
17C3×3−1+2×C43C32118yescomplemented
18C3×H(3,𝔽3)×C43C3213yes—
19C3×H(3,𝔽3)×C43C3213yes—
20C3×H(3,𝔽3)×C43C3216yes—
21C32×C9×C43C3213yes—
22C32×C9×C43C3213yes—
23C32×C9×C43C3219yescomplemented
24C43×C32⋊C9C3211yescharacteristic
25C43×C32⋊C9C3216yes—
26C43×C32⋊C9C3212yes—
27C43×C32⋊C9C3213yes—
28C43×C32⋊C9C3216yes—
29C43×C32⋊C9C32118yescomplemented
30C43×C32⋊C9C32136yescomplemented
31C33×C43—33no—
32C33×C43—33no—
33C33×C43—92no—
34C33×C43C3312yes—
35C33×C43C3319yes—
36C33×C43C3311yescharacteristic
37C33×C43C3311yescharacteristic
383−1+2×C43—36no—
393−1+2×C43—39no—
403−1+2×C43—318no—
413−1+2×C43—354no—
423−1+2×C43H(3,𝔽3)19yescomplemented
43H(3,𝔽3)×C43—39no—
44H(3,𝔽3)×C43—39no—
45H(3,𝔽3)×C43—96no—
46C3×C9×C43—39no—
47C3×C9×C43—39no—
48C3×C9×C43—327no—
49C3×C9×C43C3313yes—
50C3×C9×C43C3316yes—
51C3×C9×C43C3319yes—
52C3×C9×C43C3316yes—
53C3×C9×C43C3313yes—
54#10624896C4311yesmaximal, characteristic, direct product factor, Sylow
55C32×C43—31no—
56C32×C43—31no—
57C32×C43—32no—
58C32×C43—32no—
59C32×C43—39no—
60C32×C43—32no—
61C32×C43—39no—
62C32×C43—32no—
63C32×C43—32no—
64C32×C43—318no—
65C32×C43—32no—
66C32×C43—99no—
67C32×C43C3×H(3,𝔽3)13yes—
68C32×C43#73713yescomplemented
69C32×C43C3411yescharacteristic
70C9×C43—33no—
71C9×C43—36no—
72C9×C43—36no—
73C9×C43—39no—
74C9×C43C3×H(3,𝔽3)19yes—
75C3×#737C3×C4313yescomplemented
76C32×3−1+2C3×C4311yescharacteristic, complemented
77#6893C3×C4316yescomplemented
78C9⋊H(3,𝔽3)C3×C4316yescomplemented
79C9⋊H(3,𝔽3)C3×C43118yescomplemented
80#6891C3×C4311yescharacteristic, complemented
81C32⋊H(3,𝔽3)C3×C4311yescharacteristic
82C9×H(3,𝔽3)C3×C4313yescomplemented
83C3×C32⋊C9C3×C4311yescharacteristic, complemented
84C3×C43—33no—
85C3×C43—33no—
86C3×C43—99no—
87C3×C43—92no—
88C3×C43C32×H(3,𝔽3)11yescharacteristic
89C3×C43C3×#73711yescharacteristic
90C3×C433−1+412yes—
91C34C32×C4311yescharacteristic
92#737—327no—
93C3×3−1+2—39no—
94C3×3−1+2C32×C4316yes—
95C3×3−1+2C32×C4312yes—
96C3×3−1+2C32×C4313yes—
97C3×3−1+2C32×C4311yescharacteristic
98C3×3−1+2C32×C43118yescomplemented
99C3×H(3,𝔽3)C32×C4313yes—
100C3×H(3,𝔽3)C32×C4313yes—
101C3×H(3,𝔽3)C32×C4316yes—
102C32×C9C32×C4313yes—
103C32×C9C32×C4313yes—
104C32×C9C32×C4319yescomplemented
105C32⋊C9C32×C4311yescharacteristic
106C32⋊C9C32×C4316yes—
107C32⋊C9C32×C4312yes—
108C32⋊C9C32×C4313yes—
109C32⋊C9C32×C4316yes—
110C32⋊C9C32×C43118yescomplemented
111C32⋊C9C32×C43136yescomplemented
112C43#1062489611yescharacteristic, direct product factor, Sylow
113C33—33no—
114C33—33no—
115C33—92no—
116C33C33×C4312yes—
117C33C33×C4319yes—
118C33C33×C4311yescharacteristic
119C33C33×C4311yescharacteristic
1203−1+2—36no—
1213−1+2—39no—
1223−1+2—318no—
1233−1+2—354no—
1243−1+2H(3,𝔽3)×C4319yescomplemented
125H(3,𝔽3)—39no—
126H(3,𝔽3)—39no—
127H(3,𝔽3)—96no—
128C3×C9—39no—
129C3×C9—39no—
130C3×C9—327no—
131C3×C9C33×C4313yes—
132C3×C9C33×C4316yes—
133C3×C9C33×C4319yes—
134C3×C9C33×C4316yes—
135C3×C9C33×C4313yes—
136C32—31no—
137C32—31no—
138C32—32no—
139C32—32no—
140C32—39no—
141C32—32no—
142C32—39no—
143C32—32no—
144C32—32no—
145C32—318no—
146C32—32no—
147C32—99no—
148C32C3×H(3,𝔽3)×C4313yes—
149C32C43×#73713yescomplemented
150C32C34×C4311yescharacteristic
151C9—33no—
152C9—36no—
153C9—36no—
154C9—39no—
155C9C3×H(3,𝔽3)×C4319yes—
156C3—33no—
157C3—33no—
158C3—99no—
159C3—92no—
160C3C32×H(3,𝔽3)×C4311yescharacteristic
161C3C3×C43×#73711yescharacteristic
162C3C43×3−1+412yes—
subgroupG/H
center, socleC32×C43C34
commutator, Frattini, cosocleC32C34×C43
prime radicalC43×C32⋊H(3,𝔽3)C3
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C43×#737C3semidirect
2. C32×3−1+2×C43C3semidirect
3. C43×#6893C3semidirect
4. C43×C9⋊H(3,𝔽3)C3semidirect
5. C43×C9⋊H(3,𝔽3)C3semidirect
6. C43×#6891C3semidirect
8. C9×H(3,𝔽3)×C43C3semidirect
9. C3×C43×C32⋊C9C3semidirect
17. C3×3−1+2×C43C32semidirect
23. C32×C9×C43C32semidirect
29. C43×C32⋊C9C32semidirect
30. C43×C32⋊C9C32semidirect
42. 3−1+2×C43H(3,𝔽3)semidirect
54. #10624896C43direct (N × H)
68. C32×C43#737semidirect
75. C3×#737C3×C43semidirect
76. C32×3−1+2C3×C43semidirect
77. #6893C3×C43semidirect
78. C9⋊H(3,𝔽3)C3×C43semidirect
79. C9⋊H(3,𝔽3)C3×C43semidirect
80. #6891C3×C43semidirect
82. C9×H(3,𝔽3)C3×C43semidirect
83. C3×C32⋊C9C3×C43semidirect
98. C3×3−1+2C32×C43semidirect
104. C32×C9C32×C43semidirect
110. C32⋊C9C32×C43semidirect
111. C32⋊C9C32×C43semidirect
112. C43#10624896direct (N × H)
124. 3−1+2H(3,𝔽3)×C43semidirect
149. C32C43×#737semidirect

Maximal subgroups

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

subgroupindex
C3×C43×#7373
C32×3−1+2×C433
C43×#68933
C43×C9⋊H(3,𝔽3)3
C43×#68913
C43×C32⋊H(3,𝔽3)3
C9×H(3,𝔽3)×C433
C3×C43×C32⋊C93
#1062489643