Finite Group Databasebeta

← #20241398

Subgroups — #20241398

Order 6016.

126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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#15689359C211yesmaximal, characteristic
2#15688886C211yesmaximal, characteristic, complemented
3C47×C22⋊C16C211yesmaximal, characteristic, complemented
4C2×D376C411yescharacteristic, complemented
5#13093998—21no—
6C2×C4⋊Dic47—21no—
7#13093958C411yescharacteristic, complemented
8#13093946—21no—
9C22×C8×C47C2211yescharacteristic
10C2×C16×C47—21no—
11C22×C4×C47D411yescharacteristic
12C2×C22⋊D47—41no—
13C22×Dic47—41no—
14C2×D188—21no—
15C2×C8×C47—41no—
16C2×C8×C47C2×C411yescharacteristic
17C2×C8×C47D411yescharacteristic
18(C2×D47)⋊C4—41no—
19C4⋊Dic47—22no—
20C4⋊Dic47—21no—
21C4⋊Dic47—41no—
22D376—41no—
23C16×C47—41no—
24C23×C47D811yescharacteristic
25C22×D47—41no—
26C2×C4×C47—21no—
27C2×C4×C47—21no—
28C2×C4×C47C22⋊C411yescharacteristic
29C2×C4×C47SD1611yescharacteristic
30C22⋊D47—81no—
31C22⋊D47—81no—
32C2×Dic47—42no—
33C2×Dic47—41no—
34C2×Dic47—81no—
35C2×Dic47—81no—
36D188—41no—
37D188—41no—
38C8×C47—21no—
39C8×C47—21no—
40C22×C47—21no—
41C22×C47—21no—
42C22×C47#10211yescharacteristic
43C22×C47D1611yescharacteristic
44C22×C47SD3211yescharacteristic
45C2×D47—81no—
46C2×D47—81no—
47C2×D47—81no—
48C4×C47—21no—
49C4×C47#9911yescharacteristic
50C4×C47#10411yescharacteristic
51Dic47—82no—
52Dic47—81no—
53#1347—471nomaximal, Sylow
54C2×C47—21no—
55C2×C47—21no—
56C2×C47#32711yescharacteristic
57C2×C47#35711yescharacteristic
58C2×C47#36011yescharacteristic
59D47—161no—
60#466—471no—
61C22⋊C16D4711yescharacteristic, complemented
62#340—471no—
63C47#134711yescharacteristic, complemented, Sylow
64C2×D8—471no—
65C22×C8C2×D4711yescharacteristic
66#121—941no—
67C2×C4⋊C4—941no—
68C2×C16—21no—
69#107—471no—
70#102—941no—
71C2×D4—941no—
72C2×D4—1881no—
73C22×C4—1881no—
74C22×C4D18811yescharacteristic
75D8—1881no—
76C2×C8—41no—
77C2×C8C4×D4711yescharacteristic
78C2×C8C22⋊D4711yescharacteristic
79C4⋊C4—942no—
80C4⋊C4—941no—
81C4⋊C4—1881no—
82C22⋊C4—1881no—
83C16—41no—
84C23—1881no—
85C23D37611yescharacteristic
86D4—3761no—
87D4—3761no—
88D4—1881no—
89D4—1881no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—3761no—
93C2×C4—3761no—
94C2×C4—1882no—
95C2×C4—1881no—
96C2×C4#1062532511yescharacteristic
97C2×C4(C2×D47)⋊C411yescharacteristic
98C8—21no—
99C8—21no—
100C22—21no—
101C22—21no—
102C22—3761no—
103C22—3761no—
104C22—3761no—
105C22#1309394611yescharacteristic
106C22D75211yescharacteristic
107C22#1309396911yescharacteristic
108C4—21no—
109C4—3762no—
110C4—3761no—
111C4#1309393811yescharacteristic
112C4#1309395011yescharacteristic
113C2—21no—
114C2—21no—
115C2—7521no—
116C2#1568885811yescharacteristic
117C2#1568892511yescharacteristic
118C2#1568893411yescharacteristic
subgroupG/H
centerC22#13093946
commutatorC2×C8×C47C2×C4
FrattiniC22×C8C2×D47
FittingC47×C22⋊C16C2
socleC22×C47#102
hypercenterC22⋊C16D47
hypocenterC47#1347
LCSG ▷ C2×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. #15688886C2semidirect
3. C47×C22⋊C16C2semidirect
4. C2×D376C4semidirect
7. #13093958C4semidirect
61. C22⋊C16D47semidirect
63. C47#1347semidirect