Finite Group Databasebeta

← #31826895

Subgroups — #31826895

Order 18112.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22583632C211yesmaximal, characteristic, complemented
2#22583556C211yesmaximal, characteristic, complemented
3#22583554C211yesmaximal, characteristic, complemented
4#22583553C211yesmaximal, characteristic, complemented
5#22583551C211yesmaximal, characteristic, complemented
6C2×C283⋊C16C211yesmaximal, characteristic, complemented
7#135×C283C211yesmaximal, characteristic, complemented
8#17985392—21no—
9Dic1132C2211yescharacteristic
10#17985381—21no—
11D2264C2211yescharacteristic
12C283⋊C16C2211yescharacteristic
13C283⋊C16C2211yescharacteristic
14#41×C283—21no—
15Q16×C283C2211yescharacteristic
16SD16×C283—21no—
17D8×C283C2211yescharacteristic
18C2×C8×C283C2211yescharacteristic
19Dic566—21no—
20D1132—21no—
21C22⋊D283—41no—
22C4×D283—41no—
23Q8×C283—21no—
24D4×C283—21no—
25D4×C283—41no—
26C2×C4×C283—41no—
27C2×C4×C283D411yescharacteristic
28C8×C283D411yescharacteristic
29C8×C283C2311yescharacteristic
30C22×C283—41no—
31C22×C283D811yescharacteristic
32C2×D283—41no—
33C4×C283—41no—
34C4×C283D811yescharacteristic
35C4×C283C2×D411yescharacteristic
36Dic283—41no—
37C2×C283—21no—
38C2×C283—81no—
39C2×C283C2×D811yescharacteristic
40D283—81no—
41C283#50811yescharacteristic, complemented, Sylow
42#508—2831nomaximal, Sylow
43#135—2831no—
44#135D28311yescharacteristic, complemented
45Q32—2831no—
46SD32—2831no—
47SD32—2831no—
48D16—2831no—
49C2×C16—2831no—
50#41—21no—
51#41—5661no—
52Q16—2831no—
53Q16C2×D28311yescharacteristic
54SD16—21no—
55SD16—5661no—
56D8—2831no—
57D8C2×D28311yescharacteristic
58C2×C8C2×D28311yescharacteristic
59C16—2831no—
60C16—2831no—
61Q8—21no—
62Q8—5661no—
63D4—21no—
64D4—41no—
65D4—5661no—
66D4—11321no—
67C2×C4—41no—
68C2×C4—11321no—
69C2×C4C22⋊D28311yescharacteristic
70C8C22⋊D28311yescharacteristic
71C8C22×D28311yescharacteristic
72C22—41no—
73C22—11321no—
74C22#1798537711yescharacteristic
75C4—41no—
76C4—11321no—
77C4#1798537711yescharacteristic
78C4C2×C22⋊D28311yescharacteristic
79C2—21no—
80C2—81no—
81C2—22641no—
82C2C2×#1798537711yescharacteristic
subgroupG/H
centerC4#17985377
commutator, cosocleC8×C283C23
FrattiniC8C22×D283
Fitting#135×C283C2
socleC2×C283C2×D8
hypercenter#135D283
hypocenterC283#508
LCSG ▷ C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #22583632C2semidirect
2. #22583556C2semidirect
3. #22583554C2semidirect
4. #22583553C2semidirect
5. #22583551C2semidirect
6. C2×C283⋊C16C2semidirect
7. #135×C283C2semidirect
41. C283#508semidirect
44. #135D283semidirect

Maximal subgroups

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

subgroupindex
#225836322
#225835562
#225835542
#225835532
#225835512
C2×C283⋊C162
#135×C2832
#508283