Finite Group Databasebeta

← #37565674

Subgroups — #37565674

Order 24256.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27131353C211yesmaximal, characteristic, complemented
2#27131277C211yesmaximal, characteristic, complemented
3#27131275C211yesmaximal, characteristic, complemented
4#27131274C211yesmaximal, characteristic, complemented
5#27131272C211yesmaximal, characteristic, complemented
6C2×C379⋊C16C211yesmaximal, characteristic, complemented
7#135×C379C211yesmaximal, characteristic, complemented
8#20258606—21no—
9Dic1516C2211yescharacteristic
10#20258595—21no—
11D3032C2211yescharacteristic
12C379⋊C16C2211yescharacteristic
13C379⋊C16C2211yescharacteristic
14#41×C379—21no—
15Q16×C379C2211yescharacteristic
16SD16×C379—21no—
17D8×C379C2211yescharacteristic
18C2×C8×C379C2211yescharacteristic
19Dic758—21no—
20D1516—21no—
21C22⋊D379—41no—
22C4×D379—41no—
23Q8×C379—21no—
24D4×C379—21no—
25D4×C379—41no—
26C2×C4×C379—41no—
27C2×C4×C379D411yescharacteristic
28C8×C379D411yescharacteristic
29C8×C379C2311yescharacteristic
30C22×C379—41no—
31C22×C379D811yescharacteristic
32C2×D379—41no—
33C4×C379—41no—
34C4×C379D811yescharacteristic
35C4×C379C2×D411yescharacteristic
36Dic379—41no—
37C2×C379—21no—
38C2×C379—81no—
39C2×C379C2×D811yescharacteristic
40D379—81no—
41C379#50811yescharacteristic, complemented, Sylow
42#508—3791nomaximal, Sylow
43#135—3791no—
44#135D37911yescharacteristic, complemented
45Q32—3791no—
46SD32—3791no—
47SD32—3791no—
48D16—3791no—
49C2×C16—3791no—
50#41—21no—
51#41—7581no—
52Q16—3791no—
53Q16C2×D37911yescharacteristic
54SD16—21no—
55SD16—7581no—
56D8—3791no—
57D8C2×D37911yescharacteristic
58C2×C8C2×D37911yescharacteristic
59C16—3791no—
60C16—3791no—
61Q8—21no—
62Q8—7581no—
63D4—21no—
64D4—41no—
65D4—15161no—
66D4—7581no—
67C2×C4—41no—
68C2×C4—15161no—
69C2×C4C22⋊D37911yescharacteristic
70C8C22⋊D37911yescharacteristic
71C8C22×D37911yescharacteristic
72C22—41no—
73C22—15161no—
74C22#2025859111yescharacteristic
75C4—41no—
76C4—15161no—
77C4#2025859111yescharacteristic
78C4C2×C22⋊D37911yescharacteristic
79C2—21no—
80C2—81no—
81C2—30321no—
82C2C2×#2025859111yescharacteristic
subgroupG/H
centerC4#20258591
commutator, cosocleC8×C379C23
FrattiniC8C22×D379
Fitting#135×C379C2
socleC2×C379C2×D8
hypercenter#135D379
hypocenterC379#508
LCSG ▷ C8×C379 ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #27131353C2semidirect
2. #27131277C2semidirect
3. #27131275C2semidirect
4. #27131274C2semidirect
5. #27131272C2semidirect
6. C2×C379⋊C16C2semidirect
7. #135×C379C2semidirect
41. C379#508semidirect
44. #135D379semidirect

Maximal subgroups

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

subgroupindex
#271313532
#271312772
#271312752
#271312742
#271312722
C2×C379⋊C162
#135×C3792
#508379