Finite Group Databasebeta

← SD32×D97 #20261157

Subgroups — SD32×D97 #20261157

Order 6208.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q16×D97C211yesmaximal, characteristic, complemented
2D8×D97C211yesmaximal, characteristic
3#15690755C211yesmaximal, characteristic, complemented
4#15690754C211yesmaximal, characteristic, complemented
5#15690753C211yesmaximal, characteristic, complemented
6C16×D97C211yesmaximal, characteristic, complemented
7SD32×C97C211yesmaximal, characteristic, complemented
8Q8×D97—21no—
9D4×D97—21no—
10Dic388C2211yescharacteristic, complemented
11#13095501—21no—
12D776C2211yescharacteristic
13#13095496—21no—
14C8×D97C2211yescharacteristic
15#13095486C2211yescharacteristic, complemented
16Q16×C97C2211yescharacteristic, complemented
17D8×C97C2211yescharacteristic
18C16×C97C2211yescharacteristic, complemented
19C22×D97—41no—
20Q8×C97—21no—
21D4×C97—21no—
22C22⋊D97—41no—
23D388—21no—
24C4×D97—41no—
25C4×D97D411yescharacteristic
26Dic194—21no—
27Dic194—41no—
28C8×C97C2311yescharacteristic
29#11715895D411yescharacteristic
30C22×C97—41no—
31C2×D97—41no—
32C2×D97—82no—
33C2×D97D811yescharacteristic
34C4×C97—41no—
35C4×C97C2×D411yescharacteristic
36Dic97—41no—
37Dic97D811yescharacteristic
38C2×C97—81no—
39C2×C97C2×D811yescharacteristic
40D97—81no—
41D97SD3212yesdirect product factor
42C97C2×SD3211yescharacteristic, complemented, Sylow
43C2×SD32—971nomaximal, Sylow
44C2×Q16—971no—
45C2×D8—971no—
46SD32—971no—
47SD32—971no—
48SD32—971no—
49SD32D9711yescharacteristic, direct product factor
50C2×C16—971no—
51C2×Q8—1941no—
52C2×D4—1941no—
53Q16—971no—
54Q16—1941no—
55Q16C2×D9711yescharacteristic, complemented
56D8—971no—
57D8—1941no—
58D8C2×D9711yescharacteristic
59C2×C8—971no—
60C16—971no—
61C16C2×D9711yescharacteristic, complemented
62C23—3881no—
63Q8—21no—
64Q8—3881no—
65Q8—1941no—
66D4—21no—
67D4—3881no—
68D4—1941no—
69C2×C4—971no—
70C2×C4—3881no—
71C8—971no—
72C8C22×D9711yescharacteristic
73C22—41no—
74C22—7762no—
75C22—971no—
76C22—3881no—
77C4—41no—
78C4—971no—
79C4—3881no—
80C4D4×D9711yescharacteristic
81C2—81no—
82C2—7761no—
83C2—972no—
84C2D8×D9711yescharacteristic
subgroupG/H
centerC2D8×D97
commutatorC8×C97C23
FrattiniC8C22×D97
FittingSD32×C97C2
socleC2×C97C2×D8
hypercenterSD32D97
hypocenterC97C2×SD32
LCSG ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. Q16×D97C2semidirect
3. #15690755C2semidirect
4. #15690754C2semidirect
5. #15690753C2semidirect
6. C16×D97C2semidirect
7. SD32×C97C2semidirect
10. Dic388C22semidirect
15. #13095486C22semidirect
16. Q16×C97C22semidirect
18. C16×C97C22semidirect
41. D97SD32direct (N × H)
42. C97C2×SD32semidirect
49. SD32D97direct (N × H)
55. Q16C2×D97semidirect
61. C16C2×D97semidirect