Finite Group Databasebeta

← #22550047

Subgroups — #22550047

Order 8128.

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

normal subgroups only

This group has 146 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#16861256C211yesmaximal, characteristic, complemented
2#16861235C211yesmaximal, characteristic, complemented
3#16861196C211yesmaximal, characteristic, complemented
4#16861136C211yesmaximal, characteristic, complemented
5#16861135C211yesmaximal, characteristic, complemented
6#16861127C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C127C211yesmaximal, characteristic, complemented
8#14523248—21no—
9#14523248C2211yescharacteristic
10#14523247—22no—
11#14523247—21no—
12C2×Dic254—21no—
13C2×Dic254C2211yescharacteristic
14Q8×D127—21no—
15#14523236—21no—
16#14523233—21no—
17#14523232C2211yescharacteristic
18C22⋊Dic127—22no—
19C4×Dic127C2211yescharacteristic
20#41×C127C2211yescharacteristic
21C2×D4×C127C2211yescharacteristic
22SD16×C127—21no—
23D8×C127—21no—
24M16×C127C2211yescharacteristic
25Dic254—22no—
26Dic254—21no—
27Dic254—21no—
28Dic254D411yescharacteristic
29D508D411yescharacteristic
30C22⋊D127—22no—
31C22⋊D127—21no—
32C2×Dic127—22no—
33C2×Dic127—21no—
34C2×Dic127D412yes—
35C4×D127—22no—
36C4×D127—21no—
37C127⋊C8—21no—
38C23×C127—21no—
39Q8×C127D411yescharacteristic
40D4×C127—21no—
41D4×C127—21no—
42D4×C127—21no—
43D4×C127D411yescharacteristic
44C2×C4×C127—21no—
45C2×C4×C127C2311yescharacteristic
46C8×C127—21no—
47C22×C127—21no—
48C22×C127—42no—
49C22×C127—41no—
50C22×C127C2×D411yescharacteristic
51C2×D127—21no—
52C4×C127—21no—
53C4×C127C2×D411yescharacteristic
54C4×C127C2×D411yescharacteristic
55Dic127—21no—
56Dic127—22no—
57Dic127—41no—
58C2×C127—21no—
59C2×C127—41no—
60C2×C127—81no—
61C2×C127#12011yescharacteristic
62D127—41no—
63C127#45411yescharacteristic, complemented, Sylow
64#454—1271nomaximal, Sylow
652−1+4—1271no—
66AGL(1,ℤ/8)—1271no—
67AGL(1,ℤ/8)D12711yescharacteristic, complemented
68#124—1271no—
69#104—1271no—
70#104—1271no—
71#101—1271no—
72#41—1271no—
73#41—2541no—
74#41—2542no—
75#41—2541no—
76#41C2×D12711yescharacteristic
77C2×Q8—1271no—
78C2×Q8—2541no—
79C2×Q8—2541no—
80C2×D4C2×D12711yescharacteristic
81SD16—21no—
82SD16—2541no—
83D8—21no—
84D8—2541no—
85M16—1271no—
86M16C2×D12711yescharacteristic
87C22⋊C4—2542no—
88C42—1271no—
89C23—21no—
90Q8—1271no—
91Q8—2542no—
92Q8—2541no—
93Q8—2541no—
94Q8C22⋊D12711yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—1271no—
99D4—2542no—
100D4—2541no—
101D4C22⋊D12711yescharacteristic
102C2×C4—21no—
103C2×C4—1272no—
104C2×C4—2542no—
105C2×C4—2541no—
106C2×C4—2542no—
107C2×C4—2541no—
108C2×C4C22×D12711yescharacteristic
109C8—21no—
110C8—2541no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—2541no—
115C22D4×D12711yescharacteristic
116C4—21no—
117C4—5081no—
118C4—2542no—
119C4—2541no—
120C4D4×D12711yescharacteristic
121C4C2×C22⋊D12711yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—5081no—
126C2#1686117711yescharacteristic
subgroupG/H
centerC2#16861177
commutatorC2×C4×C127C23
FrattiniC2×C4C22×D127
FittingAGL(1,ℤ/8)×C127C2
socleC2×C127#120
hypercenterAGL(1,ℤ/8)D127
hypocenterC127#454
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #16861256C2semidirect
2. #16861235C2semidirect
3. #16861196C2semidirect
4. #16861136C2semidirect
5. #16861135C2semidirect
6. #16861127C2semidirect
7. AGL(1,ℤ/8)×C127C2semidirect
63. C127#454semidirect
67. AGL(1,ℤ/8)D127semidirect