Finite Group Databasebeta

← #20293057

Subgroups — #20293057

Order 6848.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16812131C211yesmaximal, characteristic, complemented
2#16812055C211yesmaximal, characteristic, complemented
3#16812053C211yesmaximal, characteristic, complemented
4#16812052C211yesmaximal, characteristic, complemented
5#16812050C211yesmaximal, characteristic, complemented
6C2×C107⋊C16C211yesmaximal, characteristic, complemented
7#135×C107C211yesmaximal, characteristic, complemented
8#13133818—21no—
9Dic428C2211yescharacteristic
10#13133807—21no—
11D856C2211yescharacteristic
12C107⋊C16C2211yescharacteristic
13C107⋊C16C2211yescharacteristic
14#41×C107—21no—
15Q16×C107C2211yescharacteristic
16SD16×C107—21no—
17D8×C107C2211yescharacteristic
18C2×C8×C107C2211yescharacteristic
19Q8×C107—21no—
20D4×C107—21no—
21D4×C107—41no—
22C2×C4×C107—41no—
23C2×C4×C107D411yescharacteristic
24C22⋊D107—41no—
25D428—21no—
26C4×D107—41no—
27Dic214—21no—
28C8×C107D411yescharacteristic
29C8×C107C2311yescharacteristic
30C22×C107—41no—
31C22×C107D811yescharacteristic
32C2×D107—41no—
33C4×C107—41no—
34C4×C107D811yescharacteristic
35C4×C107C2×D411yescharacteristic
36Dic107—41no—
37C2×C107—21no—
38C2×C107—81no—
39C2×C107C2×D811yescharacteristic
40D107—81no—
41C107#50811yescharacteristic, complemented, Sylow
42#508—1071nomaximal, Sylow
43#135—1071no—
44#135D10711yescharacteristic, complemented
45Q32—1071no—
46SD32—1071no—
47SD32—1071no—
48D16—1071no—
49C2×C16—1071no—
50#41—21no—
51#41—2141no—
52Q16—1071no—
53Q16C2×D10711yescharacteristic
54SD16—21no—
55SD16—2141no—
56D8—1071no—
57D8C2×D10711yescharacteristic
58C2×C8C2×D10711yescharacteristic
59C16—1071no—
60C16—1071no—
61Q8—21no—
62Q8—2141no—
63D4—21no—
64D4—41no—
65D4—4281no—
66D4—2141no—
67C2×C4—41no—
68C2×C4—4281no—
69C2×C4C22⋊D10711yescharacteristic
70C8C22⋊D10711yescharacteristic
71C8C22×D10711yescharacteristic
72C22—41no—
73C22—4281no—
74C22#1313380311yescharacteristic
75C4—41no—
76C4—4281no—
77C4#1313380311yescharacteristic
78C4C2×C22⋊D10711yescharacteristic
79C2—21no—
80C2—81no—
81C2—8561no—
82C2C2×#1313380311yescharacteristic
subgroupG/H
centerC4#13133803
commutatorC8×C107C23
FrattiniC8C22×D107
Fitting#135×C107C2
socleC2×C107C2×D8
hypercenter#135D107
hypocenterC107#508
LCSG ▷ C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #16812131C2semidirect
2. #16812055C2semidirect
3. #16812053C2semidirect
4. #16812052C2semidirect
5. #16812050C2semidirect
6. C2×C107⋊C16C2semidirect
7. #135×C107C2semidirect
41. C107#508semidirect
44. #135D107semidirect