Finite Group Databasebeta

← #20243035

Subgroups — #20243035

Order 6016.

164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689526C211yesmaximal, characteristic
2#15689519C211yesmaximal, characteristic
3#15689475C211yesmaximal, characteristic
4#15689474C211yesmaximal, characteristic
5#15689473C211yesmaximal, characteristic
6#15688844C211yesmaximal, characteristic
7C47×#487C211yesmaximal, characteristic
8#13094024C2211yescharacteristic
9#13094024C2211yescharacteristic
10#13093957—22no—
11#13093955—22no—
12#13093949—22no—
13#13093948—22no—
14#13093947—22no—
15C4×C47⋊C8C2211yescharacteristic
16C4×C47⋊C8C2211yescharacteristic
17C4⋊Q8×C47C2211yescharacteristic
18C4⋊Q8×C47C2211yescharacteristic
19#103×C47—22no—
20C4×C8×C47C2211yescharacteristic
21C2×Q8×C47—21no—
22C2×Q8×C47—21no—
23C2×Dic94—21no—
24C2×Dic94—21no—
25C2×C8×C47D412yes—
26C4⋊C4×C47—21no—
27C4⋊C4×C47—21no—
28C4⋊C4×C47—21no—
29C4⋊C4×C47—21no—
30C42×C47C2311yescharacteristic
31C4⋊Dic47—21no—
32C4⋊Dic47—21no—
33C4⋊Dic47—21no—
34C4⋊Dic47—21no—
35C2×C47⋊C8D412yes—
36C2×C47⋊C8D412yes—
37Q8×C47—42no—
38Q8×C47—42no—
39C2×C4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47C2×D411yescharacteristic
42C2×C4×C47C2×D411yescharacteristic
43C2×C4×C47C2×D411yescharacteristic
44C2×Dic47—41no—
45C2×Dic47—41no—
46Dic94—42no—
47Dic94—42no—
48C8×C47—22no—
49C47⋊C8—22no—
50C47⋊C8—22no—
51C22×C47#12711yescharacteristic
52C4×C47—81no—
53C4×C47—81no—
54C4×C47#13512yes—
55C4×C47#13712yes—
56C4×C47#13712yes—
57Dic47—81no—
58Dic47—81no—
59#1718—471nomaximal, Sylow
60C2×C47#49511yescharacteristic
61C2×C47#49711yescharacteristic
62C2×C47#49711yescharacteristic
63#500—471no—
64#498—471no—
65#487—471no—
66#487—471no—
67#487—471no—
68#487D4711yescharacteristic
69#322—471no—
70C47#171811yescharacteristic, complemented, Sylow
71C4⋊Q8—471no—
72C4⋊Q8—471no—
73C4⋊Q8C2×D4711yescharacteristic
74C4⋊Q8C2×D4711yescharacteristic
75#107—942no—
76#106—942no—
77#103—22no—
78#103—942no—
79#103—942no—
80#103—942no—
81C4×C8—471no—
82C4×C8—471no—
83C4×C8C2×D4711yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—941no—
87C2×Q8—941no—
88C2×C8—472no—
89C2×C8—472no—
90C2×C8C22⋊D4712yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—941no—
96C4⋊C4—941no—
97C4⋊C4—941no—
98C4⋊C4—941no—
99C42C22×D4711yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—1882no—
103Q8—1882no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—1881no—
107C2×C4—1881no—
108C2×C4D4×D4711yescharacteristic
109C2×C4D4×D4711yescharacteristic
110C2×C4C2×C22⋊D4711yescharacteristic
111C8—22no—
112C8—942no—
113C8—942no—
114C22#1309402011yescharacteristic
115C4—81no—
116C4—81no—
117C4—3761no—
118C4—3761no—
119C4#1309404412yes—
120C4#1309405312yes—
121C4#1309405612yes—
122C2#1568950511yescharacteristic
123C2#1568951411yescharacteristic
124C2#1568951611yescharacteristic
subgroupG/H
centerC22#13094020
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#487C2
socleC22×C47#127
hypercenter#487D47
hypocenterC47#1718
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
70. C47#1718semidirect