Finite Group Databasebeta

← #22549995

Subgroups — #22549995

Order 8128.

104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16861229C211yesmaximal, characteristic
2#16861217C211yesmaximal, characteristic, complemented
3#16861216C211yesmaximal, characteristic, complemented
4#16861144C211yesmaximal, characteristic, complemented
5#16861137C211yesmaximal, characteristic, complemented
6#16861120C211yesmaximal, characteristic, complemented
7#104×C127C211yesmaximal, characteristic, complemented
8#14523248C2211yescharacteristic
9#14523238C411yescharacteristic, complemented
10#14523236C411yescharacteristic, complemented
11#14523235C411yescharacteristic, complemented
12#14523233C411yescharacteristic, complemented
13#14523232—21no—
14#14523232C2211yescharacteristic
15#14523231—21no—
16C2×C127⋊C8—21no—
17C2×C127⋊C8C2211yescharacteristic
18C2×C127⋊C8C2211yescharacteristic
19C8×D127—21no—
20#41×C127C2211yescharacteristic
21M16×C127C2211yescharacteristic
22C42×C127C2211yescharacteristic
23Dic254C2×C411yescharacteristic
24D508C2×C411yescharacteristic
25C22⋊D127—21no—
26C4×D127—21no—
27C127⋊C8—21no—
28C127⋊C8C2×C411yescharacteristic
29C127⋊C8C2×C411yescharacteristic
30C127⋊C8D411yescharacteristic
31C127⋊C8D411yescharacteristic
32Q8×C127C2×C411yescharacteristic
33D4×C127—21no—
34D4×C127C2×C411yescharacteristic
35C2×C4×C127—21no—
36C2×C4×C127—21no—
37C2×C4×C127C2311yescharacteristic
38C8×C127—21no—
39C22×C127—21no—
40C22×C127#4111yescharacteristic
41C2×D127—21no—
42C4×C127—21no—
43C4×C127—41no—
44C4×C127C22×C411yescharacteristic
45C4×C127C2×D411yescharacteristic
46Dic127—21no—
47C2×C127—21no—
48C2×C127—41no—
49C2×C127C4×D411yescharacteristic
50D127—41no—
51C127#44411yescharacteristic, complemented, Sylow
52#444—1271nomaximal, Sylow
53#135—1271no—
54#131—1271no—
55#131—1271no—
56#108—1271no—
57#104—1271no—
58#104D12711yescharacteristic, complemented
59#97—1271no—
60#41—1271no—
61#41C2×D12711yescharacteristic
62Q16—1271no—
63SD16—1271no—
64SD16—1271no—
65D8—1271no—
66M16—1271no—
67M16—2541no—
68M16—2541no—
69M16C2×D12711yescharacteristic
70C2×C8—1271no—
71C2×C8—1271no—
72C2×C8—2541no—
73C2×C8—2541no—
74C42C2×D12711yescharacteristic
75Q8—1271no—
76Q8C4×D12711yescharacteristic
77D4—21no—
78D4—1271no—
79D4—2541no—
80D4C4×D12711yescharacteristic
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—2541no—
84C2×C4C22×D12711yescharacteristic
85C8—21no—
86C8—1271no—
87C8—1271no—
88C8—1271no—
89C8—1271no—
90C8—2541no—
91C22—21no—
92C22—2541no—
93C22#1452324711yescharacteristic
94C4—21no—
95C4—41no—
96C4—2541no—
97C4C2×C4×D12711yescharacteristic
98C4D4×D12711yescharacteristic
99C2—21no—
100C2—41no—
101C2—5081no—
102C2(C22⋊D127)⋊C411yescharacteristic
subgroupG/H
centerC4D4×D127
commutatorC4×C127C22×C4
FrattiniC2×C4C22×D127
Fitting#104×C127C2
socleC2×C127C4×D4
hypercenter#104D127
hypocenterC127#444
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #16861217C2semidirect
3. #16861216C2semidirect
4. #16861144C2semidirect
5. #16861137C2semidirect
6. #16861120C2semidirect
7. #104×C127C2semidirect
9. #14523238C4semidirect
10. #14523236C4semidirect
11. #14523235C4semidirect
12. #14523233C4semidirect
51. C127#444semidirect
58. #104D127semidirect