Finite Group Databasebeta

← C47×#3556 #20241166

Subgroups — C47×#3556 #20241166

Order 6016.

890 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#564C214yesmaximal, complemented
2C47×#557C2112yesmaximal, complemented
3C47×#541C2112yesmaximal
4C47×#533C213yesmaximal
5C4⋊Q8×C47C2216yes—
6C4⋊Q8×C47C22112yes—
7#126×C47C22116yes—
8#125×C47C2216yes—
9#125×C47C22112yes—
10#125×C47C22148yes—
11C22⋊Q8×C47C22112yes—
12C4×Q8×C47C22112yes—
13C4×Q8×C47C22124yes—
14#117×C47C2216yes—
15C2×C42×C47C2211yescharacteristic
16C2×Q8×C47C23112yes—
17C22×C4×C47C2313yes—
18C4⋊C4×C47C23112yes—
19C4⋊C4×C47C23112yes—
20C4⋊C4×C47C23124yes—
21C4⋊C4×C47C23148yes—
22C22⋊C4×C47C23112yes—
23C42×C47C2313yes—
24C42×C47C2311yescharacteristic
25C42×C47C23112yes—
26C42×C47C23116yes—
27C23×C47C2411yescharacteristic
28Q8×C47—224no—
29C2×C4×C47—26no—
30C2×C4×C47C24124yes—
31C2×C4×C47C2413yes—
32C2×C4×C47C2413yes—
33C22×C47—23no—
34C22×C47C2511yescharacteristic
35C4×C47—23no—
36C4×C47—224no—
37C4×C472−1+416yes—
38#3556C4711yesmaximal, characteristic, direct product factor, Sylow
39C2×C47—41no—
40C2×C47C2×2−1+413yes—
41#564C2×C4714yescomplemented
42#557C2×C47112yescomplemented
43#541C2×C47112yes—
44#533C2×C4713yes—
45C47#355611yescharacteristic, direct product factor, Sylow
46C4⋊Q8C22×C4716yes—
47C4⋊Q8C22×C47112yes—
48#126C22×C47116yes—
49#125C22×C4716yes—
50#125C22×C47112yes—
51#125C22×C47148yes—
52C22⋊Q8C22×C47112yes—
53C4×Q8C22×C47112yes—
54C4×Q8C22×C47124yes—
55#117C22×C4716yes—
56C2×C42C22×C4711yescharacteristic
57C2×Q8C23×C47112yes—
58C22×C4C23×C4713yes—
59C4⋊C4C23×C47112yes—
60C4⋊C4C23×C47112yes—
61C4⋊C4C23×C47124yes—
62C4⋊C4C23×C47148yes—
63C22⋊C4C23×C47112yes—
64C42C23×C4713yes—
65C42C23×C4711yescharacteristic
66C42C23×C47112yes—
67C42C23×C47116yes—
68C23C24×C4711yescharacteristic
69Q8—224no—
70C2×C4—26no—
71C2×C4C24×C47124yes—
72C2×C4C24×C4713yes—
73C2×C4C24×C4713yes—
74C22—23no—
75C22C25×C4711yescharacteristic
76C4—23no—
77C4—224no—
78C42−1+4×C4716yes—
79C2—41no—
80C2C2×2−1+4×C4713yes—
subgroupG/H
center, socleC22×C47C25
commutator, Frattini, cosocleC22C25×C47
prime radicalC23×C47C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#564C2semidirect
2. C47×#557C2semidirect
38. #3556C47direct (N × H)
41. #564C2×C47semidirect
42. #557C2×C47semidirect
45. C47#3556direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#5642
C47×#5572
C47×#5412
C47×#5332
#355647