Finite Group Databasebeta

← C7×#2866 #11742175

Subgroups — C7×#2866 #11742175

Order 896.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#388C217yesmaximal
2C7×#387C217yesmaximal, complemented
3C43×C7C211yesmaximal, characteristic, complemented
4C2×C7×C4⋊C4C2217yes—
5C2×C7×C22⋊C4C2217yes—
6C2×C42×C7C2217yes—
7C7×#95C22114yes—
8#2866C711yesmaximal, characteristic, direct product factor, Sylow
9C24×C7C2311yescharacteristic
10C22×C4×C7C2317yes—
11C22×C4×C7C2317yes—
12C7×C4⋊C4—214no—
13C7×C22⋊C4—214no—
14C42×C7—214no—
15#388C2×C717yes—
16#387C2×C717yescomplemented
17C43C2×C711yescharacteristic, complemented
18C23×C7—27no—
19C23×C7C2411yescharacteristic
20C2×C4×C7—214no—
21C2×C4×C7—27no—
22C2×C4×C7—214no—
23C2×C4×C7#41114yes—
24C2×C4⋊C4C22×C717yes—
25C2×C22⋊C4C22×C717yes—
26C2×C42C22×C717yes—
27#95C22×C7114yes—
28C22×C7—47no—
29C22×C7C2×#4117yes—
30C4×C7—214no—
31C4×C7—47no—
32C24C23×C711yescharacteristic
33C22×C4C23×C717yes—
34C22×C4C23×C717yes—
35C4⋊C4—214no—
36C22⋊C4—214no—
37C42—214no—
38C2×C7—81no—
39C2×C7#52917yes—
40C23—27no—
41C23C24×C711yescharacteristic
42C2×C4—214no—
43C2×C4—27no—
44C2×C4—214no—
45C2×C4C7×#41114yes—
46C7#286611yescharacteristic, direct product factor, Sylow
47C22—47no—
48C22C2×C7×#4117yes—
49C4—214no—
50C4—47no—
51C2—81no—
52C2C7×#52917yes—
subgroupG/H
center, socleC23×C7C24
commutator, Frattini, cosocleC23C24×C7
prime radicalC24×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#387C2semidirect
3. C43×C7C2semidirect
8. #2866C7direct (N × H)
16. #387C2×C7semidirect
17. C43C2×C7semidirect
46. C7#2866direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#3882
C7×#3872
C43×C72
#28667