Finite Group Databasebeta

← #20245257

Subgroups — #20245257

Order 6016.

148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#13093970C211yesmaximal, characteristic
2C4×Dic188C211yesmaximal, characteristic
3#15688950C211yesmaximal, characteristic
4#15688927C211yesmaximal, characteristic
5#15688926C211yesmaximal, characteristic
6#15688899C211yesmaximal, characteristic
7C4×Q16×C47C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9C4×Dic94—21no—
10#13093970C414yescomplemented
11C2×C47⋊C16C2211yescharacteristic
12C2×C47⋊C16C2211yescharacteristic
13#13093958C2211yescharacteristic
14#13093949—21no—
15C2×Q16×C47C2211yescharacteristic
16C4×Q8×C47—21no—
17#107×C47C2211yescharacteristic
18#103×C47—21no—
19C4×C8×C47C2211yescharacteristic
20C2×Q8×C47—21no—
21C2×Dic94—21no—
22Q16×C47—21no—
23Q16×C47C2×C412yes—
24C2×C8×C47D411yescharacteristic
25C2×C8×C47C2311yescharacteristic
26C4⋊C4×C47—21no—
27C4⋊C4×C47—41no—
28C42×C47—41no—
29C42×C47D411yescharacteristic
30C4⋊Dic47—21no—
31Dic47⋊C4—41no—
32C4×Dic47—41no—
33Dic188—21no—
34Dic188C2×C412yes—
35C47⋊C16—21no—
36C47⋊C16C2×C412yes—
37Q8×C47—22no—
38Q8×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47D811yescharacteristic
42C2×C4×C47D811yescharacteristic
43C2×C4×C47C2×D411yescharacteristic
44C2×Dic47—41no—
45C2×Dic47—41no—
46Dic94—22no—
47Dic94—41no—
48C8×C47—21no—
49C8×C47C22×C411yescharacteristic
50C8×C47#4111yescharacteristic
51C22×C47C2×D811yescharacteristic
52C4×C47—21no—
53C4×C47—21no—
54C4×C47—42no—
55C4×C47—81no—
56C4×C47C4×D411yescharacteristic
57C4×C47#13511yescharacteristic
58Dic47—42no—
59Dic47—81no—
60#2176—471nomaximal, Sylow
61C2×C47C4×D811yescharacteristic
62C2×C47#51011yescharacteristic
63C2×C47#51011yescharacteristic
64C2×Q32—471no—
65C4×Q16—471no—
66C4×Q16D4711yescharacteristic
67#367—471no—
68#358—471no—
69#358—471no—
70#346—471no—
71C47#217611yescharacteristic, complemented, Sylow
72C2×Q16—471no—
73C2×Q16C2×D4711yescharacteristic
74C4×Q8—21no—
75C4×Q8—941no—
76Q32—474no—
77C2×C16—471no—
78C2×C16—471no—
79#107—471no—
80#107C2×D4711yescharacteristic
81#103—21no—
82#103—941no—
83C4×C8C2×D4711yescharacteristic
84C2×Q8—21no—
85C2×Q8—941no—
86Q16—21no—
87Q16—472no—
88Q16—941no—
89Q16C4×D4712yes—
90C2×C8C22⋊D4711yescharacteristic
91C2×C8C22×D4711yescharacteristic
92C4⋊C4—21no—
93C4⋊C4—41no—
94C4⋊C4—941no—
95C4⋊C4—1881no—
96C42—41no—
97C42—1881no—
98C42C22⋊D4711yescharacteristic
99C16—472no—
100C16—941no—
101Q8—22no—
102Q8—41no—
103Q8—942no—
104Q8—1881no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—1881no—
108C2×C4—1881no—
109C2×C4#1062533411yescharacteristic
110C2×C4#1062533411yescharacteristic
111C2×C4C2×C22⋊D4711yescharacteristic
112C8—21no—
113C8C2×C4×D4711yescharacteristic
114C8#1062535011yescharacteristic
115C22C2×#1062533411yescharacteristic
116C4—21no—
117C4—21no—
118C4—42no—
119C4—81no—
120C4—3761no—
121C4—1882no—
122C4C4×C22⋊D4711yescharacteristic
123C4#1309404411yescharacteristic
124C2C4×#1062533411yescharacteristic
125C2#1568956311yescharacteristic
126C2#1568956411yescharacteristic
subgroupG/H
centerC22C2×#10625334
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC4×Q16×C47C2
socleC22×C47C2×D8
hypercenterC4×Q16D47
hypocenterC47#2176
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
10. #13093970C4semidirect
71. C47#2176semidirect