Finite Group Databasebeta

← #20245244

Subgroups — #20245244

Order 6016.

150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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
2Q16×Dic47C211yesmaximal, characteristic
3#15689217C211yesmaximal, characteristic
4#15688948C211yesmaximal, characteristic
5#15688928C211yesmaximal, characteristic
6C16×Dic47C211yesmaximal, characteristic
7C47×#358C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9Q8×Dic47—21no—
10#13093989—21no—
11#13093970C414yescomplemented
12C2×C47⋊C16C2211yescharacteristic
13#13093958C2211yescharacteristic
14#13093948—21no—
15#13093947—21no—
16C8×Dic47C2211yescharacteristic
17C2×Q16×C47C2211yescharacteristic
18C2×C16×C47C2211yescharacteristic
19#107×C47C2211yescharacteristic
20C2×Q8×C47—21no—
21C2×Dic94—21no—
22Q16×C47—21no—
23Q16×C47C2×C412yes—
24C2×C8×C47C2311yescharacteristic
25C4⋊C4×C47—21no—
26C4⋊Dic47—21no—
27C4⋊Dic47—41no—
28Dic47⋊C4—41no—
29C4×Dic47—41no—
30C4×Dic47—41no—
31C4×Dic47D411yescharacteristic
32C2×C47⋊C8D411yescharacteristic
33Dic188—21no—
34Dic188C2×C412yes—
35C16×C47—21no—
36C47⋊C16C2×C412yes—
37Q8×C47—22no—
38Q8×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47C2×D411yescharacteristic
42C2×Dic47—41no—
43C2×Dic47—41no—
44C2×Dic47D811yescharacteristic
45C2×Dic47D811yescharacteristic
46Dic94—22no—
47Dic94—41no—
48C8×C47C22×C411yescharacteristic
49C8×C47#4111yescharacteristic
50C47⋊C8—21no—
51C22×C47C2×D811yescharacteristic
52C4×C47—42no—
53C4×C47—81no—
54C4×C47C4×D411yescharacteristic
55C4×C47#13511yescharacteristic
56Dic47—21no—
57Dic47—42no—
58Dic47—81no—
59Dic47Q3212yescomplemented
60C4×Q32—471nomaximal, Sylow
61C2×C47C4×D811yescharacteristic
62C2×C47C2×Q3211yescharacteristic
63C2×C47#50811yescharacteristic
64C2×Q32—471no—
65C4×Q16—471no—
66C4×Q16—471no—
67#366—471no—
68#358—471no—
69#358D4711yescharacteristic
70C4×C16—471no—
71C47C4×Q3211yescharacteristic, complemented, Sylow
72C2×Q16—471no—
73C2×Q16C2×D4711yescharacteristic
74C4×Q8—941no—
75C4×Q8—941no—
76Q32—474no—
77C2×C16—471no—
78C2×C16C2×D4711yescharacteristic
79#107—471no—
80#107C2×D4711yescharacteristic
81#103—941no—
82#103—941no—
83C4×C8—471no—
84C2×Q8—21no—
85C2×Q8—941no—
86Q16—21no—
87Q16—472no—
88Q16—941no—
89Q16C4×D4712yes—
90C2×C8—471no—
91C2×C8C22×D4711yescharacteristic
92C4⋊C4—21no—
93C4⋊C4—941no—
94C4⋊C4—1881no—
95C4⋊C4—1881no—
96C42—471no—
97C42—1881no—
98C42—1881no—
99C16—21no—
100C16—472no—
101Q8—22no—
102Q8—41no—
103Q8—942no—
104Q8—1881no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—471no—
108C2×C4—471no—
109C2×C4—1881no—
110C2×C4—1881no—
111C2×C4D4×D4711yescharacteristic
112C8—941no—
113C8C2×C4×D4711yescharacteristic
114C8#1062535211yescharacteristic
115C22D8×D4711yescharacteristic
116C4—42no—
117C4—81no—
118C4—472no—
119C4—941no—
120C4—3761no—
121C4—1882no—
122C4(C22⋊D47)⋊C411yescharacteristic
123C4#1309404511yescharacteristic
124C2#1568920311yescharacteristic
125C2Q32×D4711yescharacteristic
126C2#1568955411yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC47×#358C2
socleC22×C47C2×D8
hypercenter#358D47
hypocenterC47C4×Q32
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
11. #13093970C4semidirect
59. Dic47Q32semidirect
71. C47C4×Q32semidirect