Finite Group Databasebeta

← #20245466

Subgroups — #20245466

Order 6016.

150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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#15689564C212yesmaximal
2#15689241C211yesmaximal, characteristic
3#15688944C211yesmaximal, characteristic, complemented
4#15688939C212yesmaximal, complemented
5C47×#494C211yesmaximal, characteristic, complemented
6#13094046C2211yescharacteristic
7#13094030—21no—
8#13093970—22no—
9#13093967—22no—
10#13093964C2212yes—
11#13093960C2211yescharacteristic
12#13093952—21no—
13C2×Q16×C47—21no—
14C2×Q16×C47C2212yes—
15C4⋊Q8×C47—21no—
16C4×C8×C47C2211yescharacteristic
17C2×Q8×C47—22no—
18#10625350—21no—
19Q16×C47—22no—
20Q16×C47—22no—
21Q16×C47—41no—
22Q16×C47—41no—
23C2×C8×C47D411yescharacteristic
24C2×C8×C47C2311yescharacteristic
25C4⋊C4×C47—42no—
26C42×C47D411yescharacteristic
27#10625329—21no—
28Dic188D411yescharacteristic
29D376D411yescharacteristic
30#10625325—21no—
31#10625324—41no—
32C8×D47—41no—
33C47⋊C16—22no—
34Q8×C47—42no—
35Q8×C47—42no—
36C2×C4×C47—21no—
37C2×C4×C47—42no—
38C2×C4×C47C2×D411yescharacteristic
39C22⋊D47—41no—
40D188—21no—
41C4×D47—41no—
42Dic94—21no—
43C8×C47D811yescharacteristic
44C8×C47D811yescharacteristic
45C8×C47C2×D411yescharacteristic
46C8×C47#4111yescharacteristic
47C47⋊C8—41no—
48C22×C47AGL(1,ℤ/8)11yescharacteristic
49C2×D47—41no—
50C4×C47—22no—
51C4×C47—82no—
52C4×C47#12111yescharacteristic
53C4×C47C2×D811yescharacteristic
54Dic47—41no—
55#2214—471nomaximal, Sylow
56C2×C47—21no—
57C2×C47#45911yescharacteristic
58D47—81no—
59#510—472no—
60#494D4711yescharacteristic, complemented
61#443—471no—
62#364—471no—
63#362—472no—
64C47#221411yescharacteristic, complemented, Sylow
65#135—471no—
66C2×Q16—21no—
67C2×Q16C2×D4712yes—
68#131—941no—
69C4⋊Q8—21no—
70Q32—942no—
71SD32—942no—
72M32—472no—
73#108—471no—
74#104—941no—
75C4×C8C2×D4711yescharacteristic
76#41—941no—
77C2×Q8—22no—
78Q16—22no—
79Q16—22no—
80Q16—41no—
81Q16—41no—
82Q16—471no—
83SD16—941no—
84D8—471no—
85M16—941no—
86M16—1881no—
87C2×C8—1881no—
88C2×C8C22⋊D4711yescharacteristic
89C2×C8C22×D4711yescharacteristic
90C4⋊C4—42no—
91C42C22⋊D4711yescharacteristic
92C16—942no—
93Q8—42no—
94Q8—42no—
95Q8—941no—
96D4—941no—
97D4—1881no—
98C2×C4—21no—
99C2×C4—42no—
100C2×C4—1881no—
101C2×C4C2×C22⋊D4711yescharacteristic
102C8—1881no—
103C8#1062533411yescharacteristic
104C8#1062533411yescharacteristic
105C8D4×D4711yescharacteristic
106C8#1062535211yescharacteristic
107C22—1881no—
108C22#1309405011yescharacteristic
109C4—22no—
110C4—82no—
111C4—1881no—
112C4#1309399511yescharacteristic
113C4C2×#1062533411yescharacteristic
114C2—21no—
115C2—3761no—
116C2#1568931511yescharacteristic
subgroupG/H
centerC2#15689315
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#494C2
socleC2×C47#459
hypercenter#494D47
hypocenterC47#2214
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #15688944C2semidirect
4. #15688939C2semidirect
5. C47×#494C2semidirect
60. #494D47semidirect
64. C47#2214semidirect