Finite Group Databasebeta

← #20242711

Subgroups — #20242711

Order 6016.

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

normal subgroups only

This group has 196 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#15689493C211yesmaximal, characteristic, complemented
2#15689482C212yesmaximal, complemented
3#15688865C211yesmaximal, characteristic, complemented
4#15688863C212yesmaximal, complemented
5C47×#562C211yesmaximal, characteristic
6#13094024C2211yescharacteristic
7#13093948—22no—
8#13093947—22no—
9#13093945—22no—
10#13093935C2212yes—
11#13093935C2211yescharacteristic
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×Dic94—21no—
22C4⋊C4×C47—22no—
23C4⋊C4×C47—22no—
24C4⋊C4×C47D412yes—
25C22⋊C4×C47—22no—
26C22⋊C4×C47—22no—
27C22⋊C4×C47—22no—
28C42×C47C2311yescharacteristic
29C4⋊Dic47—22no—
30C2×C47⋊C8—22no—
31C2×C47⋊C8—21no—
32C23×C47—22no—
33Q8×C47—42no—
34D4×C47—42no—
35D4×C47—82no—
36C2×C4×C47—22no—
37C2×C4×C47—22no—
38C2×C4×C47—82no—
39C2×C4×C47C2×D412yes—
40C2×C4×C47C2×D411yescharacteristic
41C2×Dic47—41no—
42Dic94—42no—
43C47⋊C8—41no—
44C47⋊C8—42no—
45C22×C47—42no—
46C22×C47—42no—
47C22×C47—42no—
48C22×C47#12011yescharacteristic
49C4×C47—21no—
50C4×C47—22no—
51C4×C47—42no—
52C4×C47—42no—
53Dic47—81no—
54#1662—471nomaximal, Sylow
55C2×C47—82no—
56C2×C47#45411yescharacteristic
57C2×C47#45512yes—
58#562D4711yescharacteristic
59#491—471no—
60#489—472no—
61#330—471no—
62#329—472no—
63C47#166211yescharacteristic, complemented, Sylow
64C4⋊Q8—471no—
65#125C2×D4711yescharacteristic
66#124C2×D4712yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—942no—
71#103—942no—
72#102—942no—
73#97—471no—
74#97—472no—
75C2×Q8—941no—
76C2×Q8C22⋊D4712yes—
77C2×D4—22no—
78C2×D4C22⋊D4712yes—
79C22×C4—22no—
80C2×C8—942no—
81C2×C8—941no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—942no—
85C4⋊C4C22⋊D4712yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D4711yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—1882no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—1881no—
99C2×C4C2×C22⋊D4711yescharacteristic
100C2×C4C2×C22⋊D4712yes—
101C8—1881no—
102C8—1882no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1309399311yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—3761no—
112C2—82no—
113C2#1568929611yescharacteristic
114C2#1568930112yes—
subgroupG/H
centerC22#13093993
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#562C2
socleC22×C47#120
hypercenter#562D47
hypocenterC47#1662
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. #15689493C2semidirect
2. #15689482C2semidirect
3. #15688865C2semidirect
4. #15688863C2semidirect
63. C47#1662semidirect