Finite Group Databasebeta

← #28380716

Subgroups — #28380716

Order 14048.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D1756C211yesmaximal, characteristic, complemented
2C2×C22⋊D439C211yesmaximal, characteristic, complemented
3C2×C22⋊D439C211yesmaximal, characteristic, complemented
4C2×C4×D439C211yesmaximal, characteristic, complemented
5Dic439⋊C4C211yesmaximal, characteristic, complemented
6(C2×D439)⋊C4C211yesmaximal, characteristic, complemented
7C22⋊C4×C439C211yesmaximal, characteristic, complemented
8C22×D439C2211yescharacteristic
9C22×D439C2211yescharacteristic
10D1756—22no—
11C22⋊D439—22no—
12C22⋊D439—22no—
13C2×Dic439C2211yescharacteristic
14C2×Dic439C2211yescharacteristic
15C4×D439—22no—
16C23×C439C2211yescharacteristic
17C2×C4×C439C2211yescharacteristic
18C2×C4×C439C2211yescharacteristic
19C22×C439—21no—
20C22×C439—21no—
21C22×C439—21no—
22C22×C439C2311yescharacteristic
23C2×D439—21no—
24C2×D439—21no—
25C2×D439—21no—
26C2×D439—21no—
27C2×D439—21no—
28C2×D439D412yescomplemented
29C4×C439—21no—
30C4×C439—21no—
31Dic439—21no—
32Dic439D412yescomplemented
33C2×C439—41no—
34C2×C439C2×D411yescharacteristic
35C2×C439C2×D411yescharacteristic
36C2×C439#4111yescharacteristic
37D439—22no—
38D439—41no—
39C439#12111yescharacteristic, complemented, Sylow
40#121—4391nomaximal, Sylow
41C2×D4—4391no—
42C2×D4—4391no—
43C2×D4—4391no—
44C22×C4—4391no—
45C4⋊C4—4391no—
46C22⋊C4—4391no—
47C22⋊C4D43911yescharacteristic, complemented
48C23—4391no—
49C23—4391no—
50C23C2×D43911yescharacteristic
51D4—8782no—
52D4—8782no—
53D4—8782no—
54C2×C4—8782no—
55C2×C4—4391no—
56C2×C4—4391no—
57C2×C4C2×D43911yescharacteristic
58C2×C4C2×D43911yescharacteristic
59C22—21no—
60C22—21no—
61C22—21no—
62C22—8781no—
63C22—8781no—
64C22—8781no—
65C22—8781no—
66C22—8781no—
67C22—4392no—
68C22C22×D43911yescharacteristic
69C4—21no—
70C4—21no—
71C4—8781no—
72C4—4392no—
73C2—41no—
74C2—8782no—
75C2—17561no—
76C2D4×D43911yescharacteristic
77C2D4×D43911yescharacteristic
78C2#2029632911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D439
commutator, socle, cosocleC22×C439C23
FittingC22⋊C4×C439C2
hypercenterC22⋊C4D439
hypocenterC439#121
LCSG ▷ C22×C439 ▷ C439
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D1756C2semidirect
2. C2×C22⋊D439C2semidirect
3. C2×C22⋊D439C2semidirect
4. C2×C4×D439C2semidirect
5. Dic439⋊C4C2semidirect
6. (C2×D439)⋊C4C2semidirect
7. C22⋊C4×C439C2semidirect
28. C2×D439D4semidirect
32. Dic439D4semidirect
39. C439#121semidirect
47. C22⋊C4D439semidirect

Maximal subgroups

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

subgroupindex
C2×D17562
C2×C22⋊D4392
C2×C4×D4392
Dic439⋊C42
(C2×D439)⋊C42
C22⋊C4×C4392
#121439