Finite Group Databasebeta

← #20293058

Subgroups — #20293058

Order 6848.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16812132C211yesmaximal, characteristic, complemented
2#16812128C211yesmaximal, characteristic, complemented
3#16812055C211yesmaximal, characteristic, complemented
4#16812054C211yesmaximal, characteristic, complemented
5#16812050C211yesmaximal, characteristic, complemented
6C16×D107C211yesmaximal, characteristic, complemented
7SD32×C107C211yesmaximal, characteristic, complemented
8#13133819—21no—
9#13133817—21no—
10Dic428C2211yescharacteristic
11#13133806—21no—
12#13133805—21no—
13D856C2211yescharacteristic
14C8×D107C2211yescharacteristic
15C107⋊C16C2211yescharacteristic
16Q16×C107C2211yescharacteristic
17D8×C107C2211yescharacteristic
18C16×C107C2211yescharacteristic
19Q8×C107—21no—
20D4×C107—21no—
21C22⋊D107—41no—
22C2×Dic107—41no—
23D428—21no—
24D428—41no—
25C4×D107—41no—
26C4×D107D411yescharacteristic
27Dic214—21no—
28C8×C107C2311yescharacteristic
29C107⋊C8D411yescharacteristic
30C22×C107—41no—
31C2×D107—41no—
32C2×D107D811yescharacteristic
33C4×C107—41no—
34C4×C107C2×D411yescharacteristic
35Dic107—41no—
36Dic107D811yescharacteristic
37C2×C107—81no—
38C2×C107C2×D811yescharacteristic
39D107—21no—
40D107—81no—
41C107#50811yescharacteristic, complemented, Sylow
42#508—1071nomaximal, Sylow
43#135—1071no—
44#135—1071no—
45Q32—1071no—
46SD32—1071no—
47SD32D10711yescharacteristic, complemented
48D16—1071no—
49C2×C16—1071no—
50#41—2141no—
51#41—2141no—
52Q16—1071no—
53Q16C2×D10711yescharacteristic
54SD16—2141no—
55SD16—2141no—
56D8—1071no—
57D8C2×D10711yescharacteristic
58C2×C8—1071no—
59C16—1071no—
60C16C2×D10711yescharacteristic
61Q8—21no—
62Q8—2141no—
63D4—21no—
64D4—4281no—
65D4—4281no—
66D4—2141no—
67C2×C4—1071no—
68C2×C4—4281no—
69C2×C4—4281no—
70C8—1071no—
71C8C22×D10711yescharacteristic
72C22—41no—
73C22—1071no—
74C22—4281no—
75C4—41no—
76C4—1071no—
77C4—4281no—
78C4D4×D10711yescharacteristic
79C2—81no—
80C2—8561no—
81C2—2141no—
82C2D8×D10711yescharacteristic
subgroupG/H
centerC2D8×D107
commutatorC8×C107C23
FrattiniC8C22×D107
FittingSD32×C107C2
socleC2×C107C2×D8
hypercenterSD32D107
hypocenterC107#508
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. #16812128C2semidirect
3. #16812055C2semidirect
4. #16812054C2semidirect
5. #16812050C2semidirect
6. C16×D107C2semidirect
7. SD32×C107C2semidirect
41. C107#508semidirect
47. SD32D107semidirect