Finite Group Databasebeta

← D7×#564 #11744210

Subgroups — D7×#564 #11744210

Order 896.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#564C211yesmaximal, characteristic, complemented
2D7×#125C2115yesmaximal
3C7⋊#564C2115yesmaximal, complemented
4C7×#125C22115yes—
5D7×C4⋊C4C22130yes—
6#6453C22130yes—
7#6452C22160yes—
8C42×D7C2215yes—
9#6433C22115yes—
10C2×#564—71nomaximal, Sylow
11C2×C4×D7C23115yes—
12C7×C4⋊C4C23130yes—
13C42×C7C2315yes—
14C4⋊Dic7C23130yes—
15Dic7⋊C4C23160yes—
16C4×Dic7C23115yes—
17#564—715no—
18#564D711yescharacteristic, direct product factor
19C2×#125—715no—
20C22×D7C2411yescharacteristic
21C2×C4×C7C24115yes—
22C2×Dic7C24115yes—
23C4×D7—230no—
24#125—760no—
25#125—730no—
26#125—715no—
27#125C2×D7115yes—
28C2×C4⋊C4—730no—
29C2×C42—75no—
30C22×C7C2511yescharacteristic
31C2×D72−1+416yes—
32C4×C7—215no—
33Dic7—215no—
34C22×C4—715no—
35C4⋊C4—760no—
36C4⋊C4—730no—
37C4⋊C4C22×D7130yes—
38C42—715no—
39C42C22×D715yes—
40C2×C7C2×2−1+413yes—
41D7#56414yesdirect product factor
42C23—71no—
43C2×C4—715no—
44C2×C4—1430no—
45C2×C4C23×D7115yes—
46C7C2×#56411yescharacteristic, complemented, Sylow
47C22—76no—
48C22C24×D711yescharacteristic
49C4—215no—
50C4—1415no—
51C2—74no—
52C2D7×2−1+413yes—
subgroupG/H
center, FrattiniC22C24×D7
commutator, socle, cosocleC22×C7C25
FittingC7×#564C2
prime radicalC22×D7C24
hypercenter#564D7
hypocenterC7C2×#564
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C7×#564C2semidirect
3. C7⋊#564C2semidirect
18. #564D7direct (N × H)
41. D7#564direct (N × H)
46. C7C2×#564semidirect

Maximal subgroups

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

subgroupindex
C7×#5642
D7×#1252
C7⋊#5642
C2×#5647