Finite Group Databasebeta

← #22549893

Subgroups — #22549893

Order 8128.

154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#14523232C211yesmaximal, characteristic, complemented
2#16861168C211yesmaximal, characteristic, complemented
3#16861136C214yesmaximal, complemented
4C2×#41×C127C211yesmaximal, characteristic
5#14523232—21no—
6#14523232C2212yescomplemented
7C2×C127⋊C8—21no—
8C4⋊Dic127—21no—
9C22⋊Dic127—21no—
10C4×Dic127C2212yescomplemented
11#41×C127—21no—
12#41×C127—21no—
13#41×C127C412yescomplemented
14#41×C127C2212yes—
15C2×Q8×C127C411yescharacteristic, complemented
16C2×D4×C127—21no—
17C2×D4×C127C411yescharacteristic, complemented
18C22×C4×C127—21no—
19C22×C4×C127C2211yescharacteristic
20C2×Dic127—22no—
21C127⋊C8—22no—
22C23×C127—21no—
23C23×C127D411yescharacteristic
24Q8×C127—21no—
25Q8×C127C2×C412yes—
26D4×C127—22no—
27D4×C127—22no—
28D4×C127—21no—
29D4×C127C2×C412yes—
30C2×C4×C127—21no—
31C2×C4×C127—22no—
32C2×C4×C127—22no—
33C2×C4×C127C2×C411yescharacteristic
34C2×C4×C127C2×C411yescharacteristic
35C2×C4×C127D411yescharacteristic
36C2×C4×C127D411yescharacteristic
37C2×C4×C127D411yescharacteristic
38C2×C4×C127C2311yescharacteristic
39C22×C127—22no—
40C22×C127—41no—
41C22×C127—42no—
42C22×C127C22⋊C411yescharacteristic
43C22×C127C22⋊C411yescharacteristic
44C22×C127C2×D411yescharacteristic
45C4×C127—22no—
46C4×C127C22⋊C411yescharacteristic
47C4×C127C22⋊C411yescharacteristic
48C4×C127C22×C411yescharacteristic
49C4×C127C2×D411yescharacteristic
50Dic127—42no—
51C2×C127—21no—
52C2×C127—21no—
53C2×C127—21no—
54C2×C127—42no—
55C2×C127C2×C22⋊C411yescharacteristic
56C127#42111yescharacteristic, complemented, Sylow
57#421—1271nomaximal, Sylow
58C2×#41D12711yescharacteristic
59C2×M16—1271no—
60#117—1271no—
61#104—1274no—
62#41—21no—
63#41—21no—
64#41Dic12712yescomplemented
65#41C2×D12712yes—
66C2×Q8Dic12711yescharacteristic, complemented
67C2×D4—21no—
68C2×D4Dic12711yescharacteristic, complemented
69C22×C4—21no—
70C22×C4C2×D12711yescharacteristic
71M16—1272no—
72M16—2541no—
73C2×C8—2541no—
74C4⋊C4—2541no—
75C22⋊C4—2541no—
76C42—1272no—
77C23—21no—
78C23C22⋊D12711yescharacteristic
79Q8—21no—
80Q8C2×Dic12712yes—
81D4—22no—
82D4—22no—
83D4—21no—
84D4C2×Dic12712yes—
85C2×C4—21no—
86C2×C4—22no—
87C2×C4—22no—
88C2×C4—2542no—
89C2×C4C2×Dic12711yescharacteristic
90C2×C4C2×Dic12711yescharacteristic
91C2×C4C22⋊D12711yescharacteristic
92C2×C4C22⋊D12711yescharacteristic
93C2×C4C22⋊D12711yescharacteristic
94C2×C4C22×D12711yescharacteristic
95C8—2542no—
96C22—22no—
97C22—41no—
98C22—42no—
99C22C22⋊Dic12711yescharacteristic
100C22C22⋊Dic12711yescharacteristic
101C22C2×C22⋊D12711yescharacteristic
102C4—22no—
103C4—5082no—
104C4C22⋊Dic12711yescharacteristic
105C4C22⋊Dic12711yescharacteristic
106C4C22×Dic12711yescharacteristic
107C4C2×C22⋊D12711yescharacteristic
108C2—21no—
109C2—21no—
110C2—21no—
111C2—42no—
112C2C2×C22⋊Dic12711yescharacteristic
subgroupG/H
centerC4C2×C22⋊D127
commutatorC4×C127C22×C4
FrattiniC2×C4C22×D127
FittingC2×#41×C127C2
socleC2×C127C2×C22⋊C4
hypercenterC2×#41D127
hypocenterC127#421
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14523232C2semidirect
2. #16861168C2semidirect
3. #16861136C2semidirect
6. #14523232C22semidirect
10. C4×Dic127C22semidirect
13. #41×C127C4semidirect
15. C2×Q8×C127C4semidirect
17. C2×D4×C127C4semidirect
56. C127#421semidirect
64. #41Dic127semidirect
66. C2×Q8Dic127semidirect
68. C2×D4Dic127semidirect