Finite Group Databasebeta

← #20245606

Subgroups — #20245606

Order 6016.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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#15689378C211yesmaximal, characteristic
2#15689170C211yesmaximal, characteristic
3#15688947C211yesmaximal, characteristic, complemented
4#15688946C211yesmaximal, characteristic, complemented
5#15688939C211yesmaximal, characteristic, complemented
6#15688904C211yesmaximal, characteristic
7C47×#362C211yesmaximal, characteristic, complemented
8C2×#10625324C2211yescharacteristic
9M16×D47—21no—
10#13094000—21no—
11#13093964C2211yescharacteristic
12#13093960C2211yescharacteristic
13#13093959—21no—
14#13093956C2211yescharacteristic
15#13093948—21no—
16C2×Q16×C47C2211yescharacteristic
17M32×C47C2211yescharacteristic
18#108×C47C2211yescharacteristic
19C2×Q8×C47—21no—
20C2×C4×D47D411yescharacteristic
21Q16×C47—21no—
22Q16×C47—21no—
23M16×C47—21no—
24C2×C8×C47C2311yescharacteristic
25(C2×D47)⋊C4—41no—
26C4⋊Dic47—21no—
27Dic47⋊C4—41no—
28#10625329—21no—
29C2×C47⋊C8D411yescharacteristic
30#10625324—21no—
31#10625324—21no—
32#10625324—41no—
33C8×D47—41no—
34C16×C47—21no—
35C47⋊C16—21no—
36C22×D47SD1611yescharacteristic
37Q8×C47—41no—
38Q8×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47C2×D411yescharacteristic
41C2×Dic47—41no—
42C2×Dic47SD1611yescharacteristic
43C4×D47—21no—
44C4×D47—21no—
45C8×C47—41no—
46C8×C47#4111yescharacteristic
47C8×C47#4111yescharacteristic
48C47⋊C8—21no—
49C47⋊C8—41no—
50C22×C47C2×SD1611yescharacteristic
51C2×D47—21no—
52C2×D47—41no—
53C4×C47—81no—
54C4×C47#12311yescharacteristic
55C4×C47AGL(1,ℤ/8)11yescharacteristic
56Dic47—21no—
57Dic47—81no—
58#2239—471nomaximal, Sylow
59C2×C47—21no—
60C2×C47#48111yescharacteristic
61D47—41no—
62#470—471no—
63#430—471no—
64#365—471no—
65#365—471no—
66#362—471no—
67#362D4711yescharacteristic, complemented
68#349—471no—
69C47#223911yescharacteristic, complemented, Sylow
70C2×Q16C2×D4711yescharacteristic
71C2×M16—471no—
72C2×M16—941no—
73C22⋊Q8—941no—
74M32—471no—
75M32C2×D4711yescharacteristic
76#108—471no—
77#108—941no—
78#108C2×D4711yescharacteristic
79#106—471no—
80#103—941no—
81C2×Q8—21no—
82C22×C4—471no—
83Q16—21no—
84Q16—21no—
85M16—21no—
86M16—941no—
87M16—941no—
88M16—941no—
89M16—1881no—
90C2×C8—471no—
91C2×C8—1881no—
92C2×C8C22×D4711yescharacteristic
93C4⋊C4—941no—
94C4⋊C4—1881no—
95C22⋊C4—1881no—
96C16—21no—
97C16—941no—
98C23—471no—
99Q8—41no—
100Q8—41no—
101C2×C4—41no—
102C2×C4—471no—
103C2×C4—941no—
104C2×C4—941no—
105C2×C4—1881no—
106C2×C4D4×D4711yescharacteristic
107C8—41no—
108C8—941no—
109C8—1881no—
110C8#1062535011yescharacteristic
111C8#1062535211yescharacteristic
112C22—941no—
113C22—1881no—
114C22SD16×D4711yescharacteristic
115C4—81no—
116C4—941no—
117C4—3761no—
118C4#1309400611yescharacteristic
119C4#1309404811yescharacteristic
120C2—21no—
121C2—1881no—
122C2#1568944011yescharacteristic
subgroupG/H
centerC2#15689440
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#362C2
socleC2×C47#481
hypercenter#362D47
hypocenterC47#2239
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
3. #15688947C2semidirect
4. #15688946C2semidirect
5. #15688939C2semidirect
7. C47×#362C2semidirect
67. #362D47semidirect
69. C47#2239semidirect