Finite Group Databasebeta

← #16847606

Subgroups — #16847606

Order 3968.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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#14521484C211yesmaximal, characteristic
2#14521171C211yesmaximal, characteristic, complemented
3#14521160C211yesmaximal, characteristic, complemented
4#14520871C211yesmaximal, characteristic, complemented
5#14520863C211yesmaximal, characteristic, complemented
6#14520826C211yesmaximal, characteristic, complemented
7C31×#360C211yesmaximal, characteristic, complemented
8C31×#135C2211yescharacteristic
9#11758525—21no—
10C2×D248C2211yescharacteristic
11#11758470—21no—
12C31×M32C2211yescharacteristic
13C31×#106C2211yescharacteristic
14#11758425—21no—
15#11758416C412yescomplemented
16#11758414C412yescomplemented
17#11758407C2211yescharacteristic
18#11758403C2211yescharacteristic
19#11758400C2211yescharacteristic
20#11758397—21no—
21#41×C31—21no—
22C2×D124—21no—
23C2×C4×D31—41no—
24Q16×C31C2×C411yescharacteristic, complemented
25SD16×C31—21no—
26D8×C31C2×C411yescharacteristic, complemented
27C2×C8×C31C2311yescharacteristic
28C4⋊C4×C31—21no—
29(C2×D31)⋊C4—41no—
30C4×Dic31D411yescharacteristic
31#92474—21no—
32#92474—41no—
33C2×C31⋊C8—41no—
34C2×C31⋊C8D411yescharacteristic
35D248—21no—
36D248C2×C412yes—
37C16×C31—21no—
38C31⋊C16C2×C412yescomplemented
39C22×D31—41no—
40Q8×C31—21no—
41D4×C31—21no—
42D4×C31—41no—
43C2×C4×C31—41no—
44C2×C4×C31—41no—
45C2×C4×C31C2×D411yescharacteristic
46C2×Dic31—21no—
47D124—22no—
48D124—41no—
49C4×D31—82no—
50C8×C31C22×C411yescharacteristic
51C8×C31#4111yescharacteristic
52C31⋊C8—21no—
53C31⋊C8—41no—
54AGL(1,ℤ/16)—311nomaximal, Sylow
55C22×C31—41no—
56C22×C31AGL(1,ℤ/8)11yescharacteristic
57C2×D31—42no—
58C2×D31—81no—
59C2×D31—81no—
60C4×C31—41no—
61C4×C31—81no—
62C4×C31C4×D411yescharacteristic
63C4×C31AGL(1,ℤ/8)11yescharacteristic
64Dic31—41no—
65#509—311no—
66#444—311no—
67#442—311no—
68#365—311no—
69#361—311no—
70#360D3111yescharacteristic, complemented
71#347—311no—
72C2×C31—21no—
73C2×C31—81no—
74C2×C31#44211yescharacteristic
75D31—82no—
76#135C2×D3111yescharacteristic
77C2×D8—311no—
78#131—621no—
79C4×D4—621no—
80SD32—312no—
81D16—312no—
82M32—311no—
83M32C2×D3111yescharacteristic
84#108—311no—
85#106C2×D3111yescharacteristic
86#104—621no—
87#102—621no—
88#97—311no—
89C31AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
90#41—21no—
91C2×D4—621no—
92C22×C4—1241no—
93Q16C4×D3111yescharacteristic, complemented
94SD16—21no—
95D8—312no—
96D8—621no—
97D8C4×D3111yescharacteristic, complemented
98M16—621no—
99M16—1241no—
100C2×C8—311no—
101C2×C8—1241no—
102C2×C8C22×D3111yescharacteristic
103C4⋊C4—21no—
104C22⋊C4—1241no—
105C42—311no—
106C16—21no—
107C16—312no—
108C23—1241no—
109Q8—21no—
110D4—21no—
111D4—41no—
112D4—622no—
113D4—1241no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—621no—
117C2×C4—2482no—
118C2×C4D4×D3111yescharacteristic
119C8—621no—
120C8—1241no—
121C8C2×C4×D3111yescharacteristic
122C8#9249711yescharacteristic
123C22—41no—
124C22—1242no—
125C22—2481no—
126C22—2481no—
127C22#1175848811yescharacteristic
128C4—41no—
129C4—81no—
130C4—1241no—
131C4(C22⋊D31)⋊C411yescharacteristic
132C4#1175849111yescharacteristic
133C2—21no—
134C2—81no—
135C2—2482no—
136C2#1452115811yescharacteristic
subgroupG/H
centerC2#14521158
commutatorC8×C31C22×C4
FrattiniC2×C8C22×D31
FittingC31×#360C2
socleC2×C31#442
prime radical#14521484C2
cosocleC2×C8×C31C23
hypercenter#360D31
hypocenterC31AGL(1,ℤ/16)
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #14521171C2semidirect
3. #14521160C2semidirect
4. #14520871C2semidirect
5. #14520863C2semidirect
6. #14520826C2semidirect
7. C31×#360C2semidirect
15. #11758416C4semidirect
16. #11758414C4semidirect
24. Q16×C31C2×C4semidirect
26. D8×C31C2×C4semidirect
38. C31⋊C16C2×C4semidirect
70. #360D31semidirect
89. C31AGL(1,ℤ/16)semidirect
93. Q16C4×D31semidirect
97. D8C4×D31semidirect

Maximal subgroups

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

subgroupindex
#145214842
#145211712
#145211602
#145208712
#145208632
#145208262
C31×#3602
AGL(1,ℤ/16)31