Finite Group Databasebeta

← C47×#1407 #20239017

Subgroups — C47×#1407 #20239017

Order 6016.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#497C211yesmaximal, characteristic
2C47×#355C211yesmaximal, characteristic
3C47×#354C211yesmaximal, characteristic
4C2×Q16×C47—21no—
5C2×SD16×C47—21no—
6C4⋊Q8×C47C411yescharacteristic, complemented
7#124×C47C2211yescharacteristic
8#101×C47—21no—
9#99×C47—21no—
10#97×C47C411yescharacteristic, complemented
11C2×Q8×C47—21no—
12C2×Q8×C47D411yescharacteristic
13C2×D4×C47D411yescharacteristic
14Q16×C47—42no—
15SD16×C47—42no—
16M16×C47—41no—
17C2×C8×C47—21no—
18C4⋊C4×C47—41no—
19C22⋊C4×C47—41no—
20C22⋊C4×C47—41no—
21C42×C47C2×C411yescharacteristic
22C23×C47—21no—
23Q8×C47—41no—
24Q8×C47—41no—
25Q8×C47—41no—
26D4×C47—41no—
27C2×C4×C47—21no—
28C2×C4×C47—21no—
29C2×C4×C47—41no—
30C2×C4×C47—81no—
31C2×C4×C47C22⋊C411yescharacteristic
32C8×C47—22no—
33C8×C47—81no—
34C22×C47—41no—
35C22×C47—81no—
36C22×C47#9911yescharacteristic
37C4×C47—21no—
38C4×C47—41no—
39C4×C47—41no—
40C4×C47—81no—
41C4×C47—161no—
42#1407C4711yesmaximal, characteristic, direct product factor, Sylow
43C2×C47—21no—
44C2×C47—81no—
45C2×C47#35311yescharacteristic
46#497C2×C4711yescharacteristic
47#355C2×C4711yescharacteristic
48#354C2×C4711yescharacteristic
49C47#140711yescharacteristic, direct product factor, Sylow
50C2×Q16—21no—
51C2×SD16—21no—
52C4⋊Q8C4×C4711yescharacteristic, complemented
53#124C22×C4711yescharacteristic
54#101—21no—
55#99—21no—
56#97C4×C4711yescharacteristic, complemented
57C2×Q8—21no—
58C2×Q8D4×C4711yescharacteristic
59C2×D4D4×C4711yescharacteristic
60Q16—42no—
61SD16—42no—
62M16—41no—
63C2×C8—21no—
64C4⋊C4—41no—
65C22⋊C4—41no—
66C22⋊C4—41no—
67C42C2×C4×C4711yescharacteristic
68C23—21no—
69Q8—41no—
70Q8—41no—
71Q8—41no—
72D4—41no—
73C2×C4—21no—
74C2×C4—21no—
75C2×C4—41no—
76C2×C4—81no—
77C2×C4C22⋊C4×C4711yescharacteristic
78C8—22no—
79C8—81no—
80C22—41no—
81C22—81no—
82C22#99×C4711yescharacteristic
83C4—21no—
84C4—41no—
85C4—41no—
86C4—81no—
87C4—161no—
88C2—21no—
89C2—81no—
90C2C47×#35311yescharacteristic
subgroupG/H
center, socleC2×C47#353
commutatorC42C2×C4×C47
Frattini, cosocle#124C22×C47
prime radicalC2×D4×C47D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C47 ◁ C2×C4×C47 ◁ #124×C47 ◁ G

Complements

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

NH ≅ G/Ntype
6. C4⋊Q8×C47C4semidirect
10. #97×C47C4semidirect
42. #1407C47direct (N × H)
49. C47#1407direct (N × H)
52. C4⋊Q8C4×C47semidirect
56. #97C4×C47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C47×#4972
C47×#3552
C47×#3542
#140747