Finite Group Databasebeta

← #20242683

Subgroups — #20242683

Order 6016.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689871C211yesmaximal, characteristic, complemented
2#15689512C212yesmaximal, complemented
3#15689489C211yesmaximal, characteristic, complemented
4#15688862C212yesmaximal, complemented
5C47×#330C211yesmaximal, characteristic, complemented
6C2×#10625325—22no—
7C2×D376—22no—
8#13094021C2211yescharacteristic
9#13094012C2212yes—
10#13094009—22no—
11#13094002—22no—
12#13093999—22no—
13#13093944—22no—
14#13093935C2211yescharacteristic
15#125×C47C2211yescharacteristic
16#97×C47C2212yes—
17C2×D188—21no—
18C2×D188—22no—
19C2×D188—22no—
20C2×D188D412yes—
21C2×C4×D47—22no—
22C2×Dic94D412yes—
23C2×C8×C47—22no—
24C4⋊C4×C47—22no—
25C4⋊C4×C47D412yes—
26C42×C47C2311yescharacteristic
27(C2×D47)⋊C4—22no—
28(C2×D47)⋊C4—22no—
29(C2×D47)⋊C4—22no—
30Dic47⋊C4—22no—
31C2×C47⋊C8—21no—
32D376—44no—
33#10625325—44no—
34C22×D47—22no—
35C22×D47—41no—
36C2×C4×C47—22no—
37C2×C4×C47C2×D411yescharacteristic
38C2×C4×C47C2×D412yes—
39C2×Dic47—22no—
40D188—42no—
41D188—42no—
42D188—42no—
43D188—42no—
44D188—82no—
45C4×D47—82no—
46Dic94—42no—
47C8×C47—24no—
48C47⋊C8—41no—
49C22×C47#12011yescharacteristic
50C2×D47—42no—
51C2×D47—42no—
52C2×D47—42no—
53C2×D47—82no—
54C2×D47—81no—
55C4×C47—22no—
56C4×C47—21no—
57C4×C47—42no—
58Dic47—42no—
59#1656—471nomaximal, Sylow
60C2×C47#45312yes—
61C2×C47#45411yescharacteristic
62D47—82no—
63D47—161no—
64#562—471no—
65#496—472no—
66#490—471no—
67#330D4711yescharacteristic, complemented
68#329—472no—
69C47#165611yescharacteristic, complemented, Sylow
70C2×SD16—942no—
71C2×D8—942no—
72#127—471no—
73#125C2×D4711yescharacteristic
74#124—472no—
75#123—942no—
76C22⋊Q8—942no—
77#121—942no—
78#102—942no—
79#97—471no—
80#97C2×D4712yes—
81C2×Q8—472no—
82C2×D4—472no—
83C2×D4—942no—
84C2×D4—941no—
85C2×D4—942no—
86C22×C4—942no—
87SD16—1884no—
88D8—1884no—
89C2×C8—22no—
90C2×C8—941no—
91C4⋊C4—22no—
92C4⋊C4—942no—
93C4⋊C4D18812yes—
94C22⋊C4—942no—
95C22⋊C4—942no—
96C22⋊C4—942no—
97C42C22×D4711yescharacteristic
98C23—942no—
99C23—1881no—
100Q8—1882no—
101D4—3762no—
102D4—1882no—
103D4—1882no—
104D4—1882no—
105D4—1882no—
106C2×C4—22no—
107C2×C4—942no—
108C2×C4—3762no—
109C2×C4C2×D18811yescharacteristic
110C2×C4D4×D4712yes—
111C8—24no—
112C8—1881no—
113C22—3762no—
114C22—3761no—
115C22—1882no—
116C22—1882no—
117C22—1882no—
118C22#1309399411yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—1882no—
123C2—3762no—
124C2—7521no—
125C2#1568929212yes—
126C2#1568929811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#330C2
socleC22×C47#120
hypercenter#330D47
hypocenterC47#1656
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #15689871C2semidirect
2. #15689512C2semidirect
3. #15689489C2semidirect
4. #15688862C2semidirect
5. C47×#330C2semidirect
67. #330D47semidirect
69. C47#1656semidirect