Finite Group Databasebeta

← #20261177

Subgroups — #20261177

Order 6208.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15690833C211yesmaximal, characteristic
2Q16×D97C211yesmaximal, characteristic, complemented
3#15690756C211yesmaximal, characteristic, complemented
4#15690755C211yesmaximal, characteristic, complemented
5#15690753C211yesmaximal, characteristic, complemented
6#15690749C211yesmaximal, characteristic, complemented
7Q32×C97C211yesmaximal, characteristic, complemented
8#13095512—21no—
9Q8×D97—21no—
10Dic388C2211yescharacteristic
11#13095501—21no—
12#13095498—21no—
13D776C2211yescharacteristic
14C8×D97C2211yescharacteristic
15#13095486C2211yescharacteristic
16Q16×C97C2211yescharacteristic
17Q16×C97C2211yescharacteristic
18C16×C97C2211yescharacteristic
19Q8×C97—21no—
20Q8×C97—21no—
21D388—21no—
22D388—41no—
23C4×D97—41no—
24C4×D97—41no—
25C4×D97D411yescharacteristic
26Dic194—21no—
27Dic194—41no—
28C8×C97C2311yescharacteristic
29#11715895D411yescharacteristic
30C2×D97—41no—
31C2×D97D811yescharacteristic
32C4×C97—41no—
33C4×C97—41no—
34C4×C97C2×D411yescharacteristic
35Dic97—41no—
36Dic97D811yescharacteristic
37C2×C97C2×D811yescharacteristic
38D97—21no—
39D97—81no—
40C97#51011yescharacteristic, complemented, Sylow
41#510—971nomaximal, Sylow
42#135—971no—
43C2×Q16—971no—
44Q32—971no—
45Q32D9711yescharacteristic, complemented
46SD32—971no—
47SD32—971no—
48M32—971no—
49#41—1941no—
50C2×Q8—1941no—
51Q16—971no—
52Q16—1941no—
53Q16C2×D9711yescharacteristic
54Q16C2×D9711yescharacteristic
55SD16—1941no—
56D8—971no—
57C2×C8—971no—
58C16—971no—
59C16C2×D9711yescharacteristic
60Q8—21no—
61Q8—21no—
62Q8—3881no—
63Q8—1941no—
64D4—3881no—
65D4—1941no—
66C2×C4—971no—
67C2×C4—3881no—
68C2×C4—3881no—
69C8—971no—
70C8C22×D9711yescharacteristic
71C22—971no—
72C22—3881no—
73C4—41no—
74C4—41no—
75C4—971no—
76C4—3881no—
77C4D4×D9711yescharacteristic
78C2—7761no—
79C2—1941no—
80C2D8×D9711yescharacteristic
subgroupG/H
centerC2D8×D97
commutatorC8×C97C23
FrattiniC8C22×D97
FittingQ32×C97C2
socleC2×C97C2×D8
hypercenterQ32D97
hypocenterC97#510
LCSG ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
2. Q16×D97C2semidirect
3. #15690756C2semidirect
4. #15690755C2semidirect
5. #15690753C2semidirect
6. #15690749C2semidirect
7. Q32×C97C2semidirect
40. C97#510semidirect
45. Q32D97semidirect