Finite Group Databasebeta

← #34036559

Subgroups — #34036559

Order 18752.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22627646C211yesmaximal, characteristic, complemented
2#22627570C211yesmaximal, characteristic, complemented
3#22627568C211yesmaximal, characteristic, complemented
4#22627567C211yesmaximal, characteristic, complemented
5#22627565C211yesmaximal, characteristic, complemented
6C2×#17989777C211yesmaximal, characteristic, complemented
7#135×C293C211yesmaximal, characteristic, complemented
8#17989802—21no—
9Dic1172C2211yescharacteristic
10#17989791—21no—
11D2344C2211yescharacteristic
12#17989777C2211yescharacteristic
13#17989777C2211yescharacteristic
14#41×C293—21no—
15Q16×C293C2211yescharacteristic
16SD16×C293—21no—
17D8×C293C2211yescharacteristic
18C2×C8×C293C2211yescharacteristic
19Dic586—21no—
20D1172—21no—
21C22⋊D293—41no—
22C4×D293—41no—
23Q8×C293—21no—
24D4×C293—21no—
25D4×C293—41no—
26C2×C4×C293—41no—
27C2×C4×C293D411yescharacteristic
28C8×C293D411yescharacteristic
29C8×C293C2311yescharacteristic
30C22×C293—41no—
31C22×C293D811yescharacteristic
32C2×D293—41no—
33C4×C293—41no—
34C4×C293D811yescharacteristic
35C4×C293C2×D411yescharacteristic
36Dic293—41no—
37C2×C293—21no—
38C2×C293—81no—
39C2×C293C2×D811yescharacteristic
40D293—81no—
41C293#50811yescharacteristic, complemented, Sylow
42#508—2931nomaximal, Sylow
43#135—2931no—
44#135D29311yescharacteristic, complemented
45Q32—2931no—
46SD32—2931no—
47SD32—2931no—
48D16—2931no—
49C2×C16—2931no—
50#41—21no—
51#41—5861no—
52Q16—2931no—
53Q16C2×D29311yescharacteristic
54SD16—21no—
55SD16—5861no—
56D8—2931no—
57D8C2×D29311yescharacteristic
58C2×C8C2×D29311yescharacteristic
59C16—2931no—
60C16—2931no—
61Q8—21no—
62Q8—5861no—
63D4—21no—
64D4—41no—
65D4—5861no—
66D4—11721no—
67C2×C4—41no—
68C2×C4—11721no—
69C2×C4C22⋊D29311yescharacteristic
70C8C22⋊D29311yescharacteristic
71C8C22×D29311yescharacteristic
72C22—41no—
73C22—11721no—
74C22#1798978711yescharacteristic
75C4—41no—
76C4—11721no—
77C4#1798978711yescharacteristic
78C4C2×C22⋊D29311yescharacteristic
79C2—21no—
80C2—81no—
81C2—23441no—
82C2C2×#1798978711yescharacteristic
subgroupG/H
centerC4#17989787
commutator, cosocleC8×C293C23
FrattiniC8C22×D293
Fitting#135×C293C2
socleC2×C293C2×D8
hypercenter#135D293
hypocenterC293#508
LCSG ▷ C8×C293 ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #22627646C2semidirect
2. #22627570C2semidirect
3. #22627568C2semidirect
4. #22627567C2semidirect
5. #22627565C2semidirect
6. C2×#17989777C2semidirect
7. #135×C293C2semidirect
41. C293#508semidirect
44. #135D293semidirect

Maximal subgroups

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

subgroupindex
#226276462
#226275702
#226275682
#226275672
#226275652
C2×#179897772
#135×C2932
#508293