Finite Group Databasebeta

← #22549848

Subgroups — #22549848

Order 8128.

158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14523247C211yesmaximal, characteristic
2#16861165C212yesmaximal, complemented
3#16861124C211yesmaximal, characteristic, complemented
4#16861123C212yesmaximal, complemented
5#99×C127C211yesmaximal, characteristic, complemented
6#14523247—22no—
7#14523247—22no—
8C2×Dic254C411yescharacteristic, complemented
9C2×C22⋊D127C411yescharacteristic, complemented
10C2×C22⋊D127C2211yescharacteristic
11C22×Dic127C411yescharacteristic, complemented
12C22×Dic127C2211yescharacteristic
13C2×C4×D127C411yescharacteristic, complemented
14Dic127⋊C4—22no—
15C22⋊Dic127C2212yes—
16C4×Dic127—22no—
17C2×D4×C127C2211yescharacteristic
18C22⋊C4×C127C2212yes—
19C22×D127C2×C411yescharacteristic
20Dic254—22no—
21C22⋊D127—22no—
22C22⋊D127—22no—
23C2×Dic127—21no—
24C2×Dic127—21no—
25C2×Dic127—22no—
26C2×Dic127C2×C411yescharacteristic
27C2×Dic127C2×C411yescharacteristic
28C2×Dic127C2×C411yescharacteristic
29C2×Dic127D412yes—
30C2×Dic127D412yes—
31C4×D127—21no—
32C4×D127—21no—
33C23×C127C2×C411yescharacteristic
34C23×C127C2311yescharacteristic
35D4×C127—22no—
36C2×C4×C127—22no—
37C2×C4×C127C2×C411yescharacteristic
38C22×C127—21no—
39C22×C127—41no—
40C22×C127—41no—
41C22×C127C22×C411yescharacteristic
42C22×C127C2×D412yes—
43C2×D127—21no—
44C2×D127—41no—
45C4×C127—21no—
46C4×C127—42no—
47Dic127—21no—
48Dic127—42no—
49Dic127C22⋊C411yescharacteristic
50Dic127C22⋊C411yescharacteristic
51Dic127C22⋊C412yes—
52C2×C127—22no—
53C2×C127—21no—
54C2×C127—41no—
55C2×C127C2×C22⋊C411yescharacteristic
56D127—41no—
57C127#41011yescharacteristic, complemented, Sylow
58#410—1271nomaximal, Sylow
59C2×#41—1271no—
60#117—1272no—
61#99—1271no—
62#99—1272no—
63#99D12711yescharacteristic, complemented
64#41—2542no—
65#41—2542no—
66C2×Q8—1271no—
67C2×D4—1271no—
68C2×D4—1271no—
69C2×D4C2×D12711yescharacteristic
70C22×C4—1271no—
71C22×C4—1271no—
72C22×C4—1271no—
73C4⋊C4—2542no—
74C22⋊C4—1272no—
75C22⋊C4C2×D12712yes—
76C42—2542no—
77C23—1271no—
78C23C4×D12711yescharacteristic
79C23C22×D12711yescharacteristic
80Q8—2542no—
81D4—22no—
82D4—2542no—
83D4—2542no—
84C2×C4—22no—
85C2×C4—1271no—
86C2×C4—1271no—
87C2×C4—1272no—
88C2×C4—1272no—
89C2×C4—1271no—
90C2×C4—2541no—
91C2×C4—2541no—
92C2×C4—2541no—
93C2×C4—2541no—
94C2×C4—2542no—
95C2×C4C4×D12711yescharacteristic
96C22—21no—
97C22—41no—
98C22—41no—
99C22—5081no—
100C22—2541no—
101C22C2×C4×D12711yescharacteristic
102C22D4×D12712yes—
103C4—21no—
104C4—42no—
105C4—1271no—
106C4—1271no—
107C4—1272no—
108C4—5082no—
109C4—2541no—
110C2—22no—
111C2—21no—
112C2—41no—
113C2—5081no—
114C2C22⋊C4×D12711yescharacteristic
subgroupG/H
centerC2C22⋊C4×D127
commutatorC22×C127C22×C4
FrattiniC23C22×D127
Fitting#99×C127C2
socleC2×C127C2×C22⋊C4
hypercenter#99D127
hypocenterC127#410
LCSG ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #16861165C2semidirect
3. #16861124C2semidirect
4. #16861123C2semidirect
5. #99×C127C2semidirect
8. C2×Dic254C4semidirect
9. C2×C22⋊D127C4semidirect
11. C22×Dic127C4semidirect
13. C2×C4×D127C4semidirect
57. C127#410semidirect
63. #99D127semidirect