Finite Group Databasebeta

← SD32×D107 #20293049

Subgroups — SD32×D107 #20293049

Order 6848.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q16×D107C211yesmaximal, characteristic, complemented
2D8×D107C211yesmaximal, characteristic
3#16812054C211yesmaximal, characteristic, complemented
4#16812053C211yesmaximal, characteristic, complemented
5#16812052C211yesmaximal, characteristic, complemented
6C16×D107C211yesmaximal, characteristic, complemented
7SD32×C107C211yesmaximal, characteristic, complemented
8Q8×D107—21no—
9D4×D107—21no—
10Dic428C2211yescharacteristic, complemented
11#13133808—21no—
12D856C2211yescharacteristic
13#13133803—21no—
14C8×D107C2211yescharacteristic
15C107⋊C16C2211yescharacteristic, complemented
16Q16×C107C2211yescharacteristic, complemented
17D8×C107C2211yescharacteristic
18C16×C107C2211yescharacteristic, complemented
19C22×D107—41no—
20Q8×C107—21no—
21D4×C107—21no—
22C22⋊D107—41no—
23D428—21no—
24C4×D107—41no—
25C4×D107D411yescharacteristic
26Dic214—21no—
27Dic214—41no—
28C8×C107C2311yescharacteristic
29C107⋊C8D411yescharacteristic
30C22×C107—41no—
31C2×D107—41no—
32C2×D107—82no—
33C2×D107D811yescharacteristic
34C4×C107—41no—
35C4×C107C2×D411yescharacteristic
36Dic107—41no—
37Dic107D811yescharacteristic
38C2×C107—81no—
39C2×C107C2×D811yescharacteristic
40D107—81no—
41D107SD3212yesdirect product factor
42C107C2×SD3211yescharacteristic, complemented, Sylow
43C2×SD32—1071nomaximal, Sylow
44C2×Q16—1071no—
45C2×D8—1071no—
46SD32—1071no—
47SD32—1071no—
48SD32—1071no—
49SD32D10711yescharacteristic, direct product factor
50C2×C16—1071no—
51C2×Q8—2141no—
52C2×D4—2141no—
53Q16—1071no—
54Q16—2141no—
55Q16C2×D10711yescharacteristic, complemented
56D8—1071no—
57D8—2141no—
58D8C2×D10711yescharacteristic
59C2×C8—1071no—
60C16—1071no—
61C16C2×D10711yescharacteristic, complemented
62C23—4281no—
63Q8—21no—
64Q8—4281no—
65Q8—2141no—
66D4—21no—
67D4—4281no—
68D4—2141no—
69C2×C4—1071no—
70C2×C4—4281no—
71C8—1071no—
72C8C22×D10711yescharacteristic
73C22—41no—
74C22—8562no—
75C22—1071no—
76C22—4281no—
77C4—41no—
78C4—1071no—
79C4—4281no—
80C4D4×D10711yescharacteristic
81C2—81no—
82C2—8561no—
83C2—1072no—
84C2D8×D10711yescharacteristic
subgroupG/H
centerC2D8×D107
commutatorC8×C107C23
FrattiniC8C22×D107
FittingSD32×C107C2
socleC2×C107C2×D8
hypercenterSD32D107
hypocenterC107C2×SD32
LCSG ▷ C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. Q16×D107C2semidirect
3. #16812054C2semidirect
4. #16812053C2semidirect
5. #16812052C2semidirect
6. C16×D107C2semidirect
7. SD32×C107C2semidirect
10. Dic428C22semidirect
15. C107⋊C16C22semidirect
16. Q16×C107C22semidirect
18. C16×C107C22semidirect
41. D107SD32direct (N × H)
42. C107C2×SD32semidirect
49. SD32D107direct (N × H)
55. Q16C2×D107semidirect
61. C16C2×D107semidirect