Finite Group Databasebeta

← #20293064

Subgroups — #20293064

Order 6848.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16812132C211yesmaximal, characteristic, complemented
2D8×D107C211yesmaximal, characteristic, complemented
3#16812052C211yesmaximal, characteristic, complemented
4D1712C211yesmaximal, characteristic, complemented
5#16812050C211yesmaximal, characteristic, complemented
6#16812048C211yesmaximal, characteristic, complemented
7SD32×C107C211yesmaximal, characteristic, complemented
8#13133819—21no—
9D4×D107—21no—
10#13133805—21no—
11D856C2211yescharacteristic
12D856C2211yescharacteristic, complemented
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—
24D428—21no—
25D428—41no—
26C4×D107—41no—
27C4×D107D411yescharacteristic
28C8×C107C2311yescharacteristic
29C107⋊C8D411yescharacteristic
30C22×C107—41no—
31C2×D107—41no—
32C2×D107—41no—
33C2×D107—82no—
34C2×D107D811yescharacteristic
35C4×C107—41no—
36C4×C107C2×D411yescharacteristic
37Dic107D811yescharacteristic
38C2×C107—81no—
39C2×C107C2×D811yescharacteristic
40D107—21no—
41D107—81no—
42D107—81no—
43C107#50911yescharacteristic, complemented, Sylow
44#509—1071nomaximal, Sylow
45#135—1071no—
46C2×D8—1071no—
47SD32—1071no—
48SD32D10711yescharacteristic, complemented
49D16—1071no—
50D16—1071no—
51M32—1071no—
52#41—2141no—
53C2×D4—2141no—
54Q16C2×D10711yescharacteristic, complemented
55SD16—2141no—
56D8—1071no—
57D8—1071no—
58D8—2141no—
59D8C2×D10711yescharacteristic
60C2×C8—1071no—
61C16—1071no—
62C16C2×D10711yescharacteristic, complemented
63C23—4281no—
64Q8—21no—
65D4—21no—
66D4—4281no—
67D4—4281no—
68D4—2141no—
69D4—2141no—
70C2×C4—1071no—
71C2×C4—4281no—
72C8—1071no—
73C8C22×D10711yescharacteristic
74C22—41no—
75C22—8562no—
76C22—1071no—
77C22—4281no—
78C22—4281no—
79C4—41no—
80C4—1071no—
81C4D4×D10711yescharacteristic
82C2—81no—
83C2—8561no—
84C2—8561no—
85C2—2141no—
86C2D8×D10711yescharacteristic
subgroupG/H
centerC2D8×D107
commutatorC8×C107C23
FrattiniC8C22×D107
FittingSD32×C107C2
socleC2×C107C2×D8
hypercenterSD32D107
hypocenterC107#509
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. #16812132C2semidirect
2. D8×D107C2semidirect
3. #16812052C2semidirect
4. D1712C2semidirect
5. #16812050C2semidirect
6. #16812048C2semidirect
7. SD32×C107C2semidirect
12. D856C22semidirect
15. C107⋊C16C22semidirect
16. Q16×C107C22semidirect
18. C16×C107C22semidirect
43. C107#509semidirect
48. SD32D107semidirect
54. Q16C2×D107semidirect
62. C16C2×D107semidirect