Finite Group Databasebeta

← #22550055

Subgroups — #22550055

Order 8128.

152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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#16861255C211yesmaximal, characteristic
2#16861242C211yesmaximal, characteristic, complemented
3#16861239C211yesmaximal, characteristic, complemented
4#16861197C211yesmaximal, characteristic, complemented
5#16861137C211yesmaximal, characteristic, complemented
6#16861125C211yesmaximal, characteristic, complemented
7#104×C127C211yesmaximal, characteristic, complemented
8#14523249—21no—
9#14523248—21no—
10#14523248C2211yescharacteristic
11C2×Dic254C2211yescharacteristic, complemented
12C2×D508—21no—
13C2×D508C2211yescharacteristic
14D4×D127—22no—
15D4×D127—21no—
16Dic508—21no—
17#14523238—21no—
18#14523237—21no—
19#14523236—21no—
20#14523232C2211yescharacteristic, complemented
21(C2×D127)⋊C4—22no—
22#41×C127C2211yescharacteristic
23M16×C127C2211yescharacteristic, complemented
24C42×C127C2211yescharacteristic, complemented
25C22×D127—22no—
26C22×D127D412yes—
27Dic254—21no—
28Dic254—21no—
29Dic254D411yescharacteristic
30D508—22no—
31D508—21no—
32D508—21no—
33D508D411yescharacteristic
34C22⋊D127—22no—
35C22⋊D127—21no—
36C2×Dic127—21no—
37C4×D127—22no—
38C4×D127—21no—
39C127⋊C8—21no—
40Q8×C127D411yescharacteristic
41D4×C127—21no—
42D4×C127D411yescharacteristic
43C2×C4×C127—21no—
44C2×C4×C127—21no—
45C2×C4×C127C2311yescharacteristic
46C8×C127—21no—
47C22×C127—21no—
48C22×C127C2×D411yescharacteristic
49C2×D127—22no—
50C2×D127—21no—
51C2×D127—42no—
52C2×D127—82no—
53C4×C127—21no—
54C4×C127—41no—
55C4×C127C2×D411yescharacteristic
56C4×C127C2×D411yescharacteristic
57Dic127—21no—
58Dic127—41no—
59C2×C127—21no—
60C2×C127—41no—
61C2×C127#12011yescharacteristic
62D127—42no—
63D127—41no—
64C127#45511yescharacteristic, complemented, Sylow
65#455—1271nomaximal, Sylow
66H(5,𝔽2)—1271no—
67#137—1271no—
68#137—1271no—
69#124—1271no—
70#104—1271no—
71#104D12711yescharacteristic, complemented
72#100—1271no—
73#41—1271no—
74#41—2541no—
75#41—2541no—
76#41C2×D12711yescharacteristic
77C2×Q8—1271no—
78C2×D4—1271no—
79C2×D4—2541no—
80C2×D4—2542no—
81C2×D4—2541no—
82Q16—2541no—
83Q16—2541no—
84SD16—2541no—
85SD16—2541no—
86M16—1271no—
87M16C2×D12711yescharacteristic, complemented
88C22⋊C4—2542no—
89C42C2×D12711yescharacteristic, complemented
90C23—1272no—
91C23—2542no—
92Q8—1271no—
93Q8—2541no—
94Q8—2541no—
95Q8D50811yescharacteristic
96D4—21no—
97D4—1271no—
98D4—2542no—
99D4—2542no—
100D4—2541no—
101D4—2541no—
102D4—2541no—
103D4D50811yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—2542no—
107C2×C4—2541no—
108C2×C4—2541no—
109C2×C4C22×D12711yescharacteristic
110C8—21no—
111C8—2541no—
112C22—21no—
113C22—10162no—
114C22—5082no—
115C22—2541no—
116C22—2542no—
117C22D4×D12711yescharacteristic
118C4—21no—
119C4—41no—
120C4—5081no—
121C4—2541no—
122C4D4×D12711yescharacteristic
123C4C2×D50811yescharacteristic
124C2—21no—
125C2—41no—
126C2—5081no—
127C2—5082no—
128C2#1686117911yescharacteristic
subgroupG/H
centerC2#16861179
commutatorC2×C4×C127C23
FrattiniC2×C4C22×D127
Fitting#104×C127C2
socleC2×C127#120
hypercenter#104D127
hypocenterC127#455
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #16861242C2semidirect
3. #16861239C2semidirect
4. #16861197C2semidirect
5. #16861137C2semidirect
6. #16861125C2semidirect
7. #104×C127C2semidirect
11. C2×Dic254C22semidirect
20. #14523232C22semidirect
23. M16×C127C22semidirect
24. C42×C127C22semidirect
64. C127#455semidirect
71. #104D127semidirect
87. M16C2×D127semidirect
89. C42C2×D127semidirect