Finite Group Databasebeta

← #20245609

Subgroups — #20245609

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#15689382C211yesmaximal, characteristic
2#15689170C211yesmaximal, characteristic
3#15688945C211yesmaximal, characteristic, complemented
4#15688940C211yesmaximal, characteristic, complemented
5#15688938C211yesmaximal, characteristic, complemented
6#15688904C211yesmaximal, characteristic
7C47×#365C211yesmaximal, characteristic, complemented
8C2×Dic188C2211yescharacteristic
9C2×#10625324C2211yescharacteristic
10M16×D47—21no—
11#13094004—21no—
12#13093964C2211yescharacteristic
13#13093960C2211yescharacteristic
14#13093959—21no—
15#13093947—21no—
16M32×C47C2211yescharacteristic
17#108×C47C2211yescharacteristic
18#106×C47C2211yescharacteristic
19C2×C4×D47D411yescharacteristic
20C2×Dic94—21no—
21M16×C47—21no—
22C2×C8×C47C2311yescharacteristic
23C4⋊C4×C47—21no—
24(C2×D47)⋊C4—41no—
25C4⋊Dic47—41no—
26#10625329—21no—
27C2×C47⋊C8D411yescharacteristic
28Dic188—21no—
29Dic188—21no—
30#10625324—21no—
31#10625324—21no—
32#10625324—41no—
33C8×D47—41no—
34C16×C47—21no—
35C47⋊C16—21no—
36C22×D47SD1611yescharacteristic
37C2×C4×C47—41no—
38C2×C4×C47C2×D411yescharacteristic
39C2×Dic47—41no—
40C2×Dic47SD1611yescharacteristic
41C4×D47—21no—
42C4×D47—21no—
43Dic94—41no—
44Dic94—41no—
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#365D4711yescharacteristic, complemented
66#362—471no—
67#362—471no—
68#349—471no—
69C47#223911yescharacteristic, complemented, Sylow
70C2×Q16—471no—
71C2×M16—471no—
72C2×M16—941no—
73C22⋊Q8—941no—
74M32—471no—
75M32C2×D4711yescharacteristic
76#108—471no—
77#108—941no—
78#108C2×D4711yescharacteristic
79#106C2×D4711yescharacteristic
80#103—941no—
81C2×Q8—941no—
82C22×C4—471no—
83Q16—941no—
84Q16—941no—
85M16—21no—
86M16—941no—
87M16—941no—
88M16—941no—
89M16—1881no—
90C2×C8—471no—
91C2×C8—1881no—
92C2×C8C22×D4711yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—1881no—
95C22⋊C4—1881no—
96C16—21no—
97C16—941no—
98C23—471no—
99Q8—1881no—
100Q8—1881no—
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#1062535411yescharacteristic
112C22—941no—
113C22—1881no—
114C22SD16×D4711yescharacteristic
115C4—81no—
116C4—941no—
117C4—3761no—
118C4#1309400911yescharacteristic
119C4#1309405111yescharacteristic
120C2—21no—
121C2—1881no—
122C2#1568944311yescharacteristic
subgroupG/H
centerC2#15689443
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#365C2
socleC2×C47#481
hypercenter#365D47
hypocenterC47#2239
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
3. #15688945C2semidirect
4. #15688940C2semidirect
5. #15688938C2semidirect
7. C47×#365C2semidirect
65. #365D47semidirect
69. C47#2239semidirect