Finite Group Databasebeta

← #20242709

Subgroups — #20242709

Order 6016.

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

normal subgroups only

This group has 196 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
2#15689485C212yesmaximal, complemented
3#15688865C211yesmaximal, characteristic, complemented
4#15688862C212yesmaximal, complemented
5C47×#491C211yesmaximal, characteristic, complemented
6#13094012C2212yes—
7#13094009—22no—
8#13094002—22no—
9#13093999—22no—
10#13093947—22no—
11#13093944—22no—
12#13093935C2212yes—
13C4⋊Q8×C47C2211yescharacteristic
14#125×C47C2211yescharacteristic
15#103×C47—22no—
16#97×C47C2211yescharacteristic
17C2×Q8×C47—21no—
18C2×D188—22no—
19C2×D188D412yes—
20C2×C4×D47—22no—
21C2×Dic94D412yes—
22C2×C8×C47—21no—
23C4⋊C4×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—22no—
32C22×D47—22no—
33Q8×C47—42no—
34C2×C4×C47—22no—
35C2×C4×C47—41no—
36C2×C4×C47C2×D412yes—
37C2×C4×C47C2×D411yescharacteristic
38C2×Dic47—22no—
39D188—42no—
40D188—82no—
41C4×D47—82no—
42Dic94—42no—
43C8×C47—41no—
44C47⋊C8—42no—
45C22×C47#12011yescharacteristic
46C2×D47—42no—
47C2×D47—42no—
48C2×D47—42no—
49C4×C47—21no—
50C4×C47—22no—
51C4×C47—42no—
52C4×C47—81no—
53Dic47—42no—
54#1662—471nomaximal, Sylow
55C2×C47#45411yescharacteristic
56C2×C47#45512yes—
57D47—82no—
58#562—471no—
59#491D4711yescharacteristic, complemented
60#489—472no—
61#330—471no—
62#329—472no—
63C47#166211yescharacteristic, complemented, Sylow
64C4⋊Q8C2×D4711yescharacteristic
65#125C2×D4711yescharacteristic
66#124—472no—
67#123—942no—
68C22⋊Q8—942no—
69#121—942no—
70#103—22no—
71#103—942no—
72#102—942no—
73#97—472no—
74#97C2×D4711yescharacteristic
75C2×Q8—21no—
76C2×Q8—472no—
77C2×D4—472no—
78C2×D4—942no—
79C22×C4—942no—
80C2×C8—21no—
81C2×C8—942no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—942no—
85C4⋊C4C22⋊D4712yes—
86C22⋊C4—942no—
87C22⋊C4—942no—
88C22⋊C4—942no—
89C42C22×D4711yescharacteristic
90C23—942no—
91Q8—42no—
92Q8—1882no—
93D4—3762no—
94D4—1882no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—942no—
98C2×C4—3762no—
99C2×C4D4×D4712yes—
100C2×C4C2×C22⋊D4711yescharacteristic
101C8—41no—
102C8—1882no—
103C22—1882no—
104C22—1882no—
105C22—1882no—
106C22#1309399211yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—81no—
111C4—1882no—
112C2—3762no—
113C2#1568929511yescharacteristic
114C2#1568929912yes—
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#491C2
socleC22×C47#120
hypercenter#491D47
hypocenterC47#1662
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #15689485C2semidirect
3. #15688865C2semidirect
4. #15688862C2semidirect
5. C47×#491C2semidirect
59. #491D47semidirect
63. C47#1662semidirect