Finite Group Databasebeta

← #20242681

Subgroups — #20242681

Order 6016.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#15689513C212yesmaximal, complemented
2#15689489C211yesmaximal, characteristic, complemented
3#15688865C211yesmaximal, characteristic, complemented
4#15688863C212yesmaximal, complemented
5C47×#562C211yesmaximal, characteristic, complemented
6C2×#10625336—22no—
7C2×#10625334—22no—
8#13094021C2211yescharacteristic
9#13093944—22no—
10#13093935C2211yescharacteristic
11#13093935C2212yes—
12#125×C47C2211yescharacteristic
13#124×C47C2212yes—
14#123×C47—22no—
15C22⋊Q8×C47—22no—
16#121×C47—22no—
17C2×Q8×C47D412yes—
18C2×D4×C47—22no—
19C2×D4×C47D412yes—
20C22×C4×C47—22no—
21C2×D188—21no—
22C2×D188—22no—
23C4⋊C4×C47—22no—
24C4⋊C4×C47—22no—
25C4⋊C4×C47D412yes—
26C22⋊C4×C47—22no—
27C22⋊C4×C47—22no—
28C22⋊C4×C47—22no—
29C42×C47C2311yescharacteristic
30#10625336—44no—
31#10625334—44no—
32C2×C47⋊C8—22no—
33C2×C47⋊C8—21no—
34C23×C47—22no—
35C22×D47—41no—
36Q8×C47—42no—
37D4×C47—42no—
38D4×C47—82no—
39C2×C4×C47—22no—
40C2×C4×C47—22no—
41C2×C4×C47—82no—
42C2×C4×C47C2×D411yescharacteristic
43C2×C4×C47C2×D412yes—
44D188—42no—
45D188—42no—
46D188—42no—
47C47⋊C8—24no—
48C47⋊C8—41no—
49C22×C47—42no—
50C22×C47—42no—
51C22×C47—42no—
52C22×C47#12011yescharacteristic
53C2×D47—82no—
54C2×D47—81no—
55C4×C47—22no—
56C4×C47—21no—
57C4×C47—42no—
58C4×C47—42no—
59#1656—471nomaximal, Sylow
60C2×C47—82no—
61C2×C47#45312yes—
62C2×C47#45411yescharacteristic
63D47—161no—
64#562D4711yescharacteristic, complemented
65#496—472no—
66#490—471no—
67#330—471no—
68#329—472no—
69C47#165611yescharacteristic, complemented, Sylow
70C2×SD16—942no—
71C2×D8—942no—
72#127—471no—
73#125C2×D4711yescharacteristic
74#124C2×D4712yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—942no—
79#97—471no—
80#97—472no—
81C2×Q8C22⋊D4712yes—
82C2×D4—22no—
83C2×D4—941no—
84C2×D4—942no—
85C2×D4C22⋊D4712yes—
86C22×C4—22no—
87SD16—1884no—
88D8—1884no—
89C2×C8—942no—
90C2×C8—941no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D4712yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D4711yescharacteristic
98C23—22no—
99C23—1881no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—1882no—
104D4—1882no—
105D4—1882no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D4711yescharacteristic
110C2×C4C2×C22⋊D4712yes—
111C8—944no—
112C8—1881no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—3762no—
117C22—3761no—
118C22#1309399311yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—7521no—
125C2#1568929112yes—
126C2#1568929611yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#562C2
socleC22×C47#120
hypercenter#562D47
hypocenterC47#1656
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #15689513C2semidirect
2. #15689489C2semidirect
3. #15688865C2semidirect
4. #15688863C2semidirect
5. C47×#562C2semidirect
64. #562D47semidirect
69. C47#1656semidirect