Finite Group Databasebeta

← #20293066

Subgroups — #20293066

Order 6848.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16812128C211yesmaximal, characteristic
2Q16×D107C211yesmaximal, characteristic, complemented
3Dic856C211yesmaximal, characteristic, complemented
4#16812055C211yesmaximal, characteristic, complemented
5#16812053C211yesmaximal, characteristic, complemented
6#16812048C211yesmaximal, characteristic, complemented
7SD32×C107C211yesmaximal, characteristic, complemented
8#13133817—21no—
9Q8×D107—21no—
10Dic428C2211yescharacteristic
11Dic428C2211yescharacteristic
12#13133808—21no—
13#13133806—21no—
14C8×D107C2211yescharacteristic
15C107⋊C16C2211yescharacteristic
16Q16×C107C2211yescharacteristic
17D8×C107C2211yescharacteristic
18C16×C107C2211yescharacteristic
19Q8×C107—21no—
20D4×C107—21no—
21C22⋊D107—41no—
22C2×Dic107—41no—
23C4×D107—41no—
24C4×D107D411yescharacteristic
25Dic214—21no—
26Dic214—21no—
27Dic214—41no—
28C8×C107C2311yescharacteristic
29C107⋊C8D411yescharacteristic
30C22×C107—41no—
31C2×D107D811yescharacteristic
32C4×C107—41no—
33C4×C107C2×D411yescharacteristic
34Dic107—41no—
35Dic107—41no—
36Dic107D811yescharacteristic
37C2×C107—81no—
38C2×C107C2×D811yescharacteristic
39D107—21no—
40C107#51011yescharacteristic, complemented, Sylow
41#510—1071nomaximal, Sylow
42#135—1071no—
43C2×Q16—1071no—
44Q32—1071no—
45Q32—1071no—
46SD32—1071no—
47SD32D10711yescharacteristic, complemented
48M32—1071no—
49#41—2141no—
50C2×Q8—2141no—
51Q16—1071no—
52Q16—1071no—
53Q16—2141no—
54Q16C2×D10711yescharacteristic
55SD16—2141no—
56D8C2×D10711yescharacteristic
57C2×C8—1071no—
58C16—1071no—
59C16C2×D10711yescharacteristic
60Q8—21no—
61Q8—4281no—
62Q8—2141no—
63Q8—2141no—
64D4—21no—
65D4—4281no—
66C2×C4—1071no—
67C2×C4—4281no—
68C2×C4—4281no—
69C8—1071no—
70C8C22×D10711yescharacteristic
71C22—41no—
72C22—1071no—
73C4—41no—
74C4—1071no—
75C4—4281no—
76C4—4281no—
77C4D4×D10711yescharacteristic
78C2—81no—
79C2—2141no—
80C2D8×D10711yescharacteristic
subgroupG/H
centerC2D8×D107
commutatorC8×C107C23
FrattiniC8C22×D107
FittingSD32×C107C2
socleC2×C107C2×D8
hypercenterSD32D107
hypocenterC107#510
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
2. Q16×D107C2semidirect
3. Dic856C2semidirect
4. #16812055C2semidirect
5. #16812053C2semidirect
6. #16812048C2semidirect
7. SD32×C107C2semidirect
40. C107#510semidirect
47. SD32D107semidirect