Finite Group Databasebeta

← #37565675

Subgroups — #37565675

Order 24256.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27131354C211yesmaximal, characteristic, complemented
2#27131350C211yesmaximal, characteristic, complemented
3#27131277C211yesmaximal, characteristic, complemented
4#27131276C211yesmaximal, characteristic, complemented
5#27131272C211yesmaximal, characteristic, complemented
6C16×D379C211yesmaximal, characteristic, complemented
7SD32×C379C211yesmaximal, characteristic, complemented
8#20258607—21no—
9#20258605—21no—
10Dic1516C2211yescharacteristic
11#20258594—21no—
12#20258593—21no—
13D3032C2211yescharacteristic
14C8×D379C2211yescharacteristic
15C379⋊C16C2211yescharacteristic
16Q16×C379C2211yescharacteristic
17D8×C379C2211yescharacteristic
18C16×C379C2211yescharacteristic
19Dic758—21no—
20D1516—21no—
21D1516—41no—
22C22⋊D379—41no—
23C2×Dic379—41no—
24C4×D379—41no—
25C4×D379D411yescharacteristic
26C379⋊C8D411yescharacteristic
27Q8×C379—21no—
28D4×C379—21no—
29C8×C379C2311yescharacteristic
30C22×C379—41no—
31C2×D379—41no—
32C2×D379D811yescharacteristic
33C4×C379—41no—
34C4×C379C2×D411yescharacteristic
35Dic379—41no—
36Dic379D811yescharacteristic
37C2×C379—81no—
38C2×C379C2×D811yescharacteristic
39D379—21no—
40D379—81no—
41C379#50811yescharacteristic, complemented, Sylow
42#508—3791nomaximal, Sylow
43#135—3791no—
44#135—3791no—
45Q32—3791no—
46SD32—3791no—
47SD32D37911yescharacteristic, complemented
48D16—3791no—
49C2×C16—3791no—
50#41—7581no—
51#41—7581no—
52Q16—3791no—
53Q16C2×D37911yescharacteristic
54SD16—7581no—
55SD16—7581no—
56D8—3791no—
57D8C2×D37911yescharacteristic
58C2×C8—3791no—
59C16—3791no—
60C16C2×D37911yescharacteristic
61Q8—21no—
62Q8—7581no—
63D4—21no—
64D4—15161no—
65D4—15161no—
66D4—7581no—
67C2×C4—3791no—
68C2×C4—15161no—
69C2×C4—15161no—
70C8—3791no—
71C8C22×D37911yescharacteristic
72C22—41no—
73C22—3791no—
74C22—15161no—
75C4—41no—
76C4—3791no—
77C4—15161no—
78C4D4×D37911yescharacteristic
79C2—81no—
80C2—30321no—
81C2—7581no—
82C2D8×D37911yescharacteristic
subgroupG/H
centerC2D8×D379
commutator, cosocleC8×C379C23
FrattiniC8C22×D379
FittingSD32×C379C2
socleC2×C379C2×D8
hypercenterSD32D379
hypocenterC379#508
LCSG ▷ C8×C379 ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #27131354C2semidirect
2. #27131350C2semidirect
3. #27131277C2semidirect
4. #27131276C2semidirect
5. #27131272C2semidirect
6. C16×D379C2semidirect
7. SD32×C379C2semidirect
41. C379#508semidirect
47. SD32D379semidirect

Maximal subgroups

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

subgroupindex
#271313542
#271313502
#271312772
#271312762
#271312722
C16×D3792
SD32×C3792
#508379