Finite Group Databasebeta

← #22550060

Subgroups — #22550060

Order 8128.

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

normal subgroups only

This group has 142 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
2#16861242C211yesmaximal, characteristic, complemented
3#16861239C211yesmaximal, characteristic, complemented
4#16861209C211yesmaximal, characteristic, complemented
5#16861137C211yesmaximal, characteristic, complemented
6#16861127C211yesmaximal, characteristic, complemented
7#104×C127C211yesmaximal, characteristic, complemented
8#14523248—21no—
9#14523248C2211yescharacteristic
10#14523247—22no—
11#14523247—21no—
12C2×Dic254—21no—
13C2×Dic254C2211yescharacteristic
14C2×Dic254C2211yescharacteristic
15Q8×D127—21no—
16Dic508—21no—
17#14523238—21no—
18#14523237—21no—
19#14523236—21no—
20#14523232C2211yescharacteristic
21C4⋊Dic127—22no—
22#41×C127C2211yescharacteristic
23M16×C127C2211yescharacteristic
24C42×C127C2211yescharacteristic
25Dic254—22no—
26Dic254—21no—
27Dic254—21no—
28Dic254—21no—
29Dic254—21no—
30Dic254D411yescharacteristic
31D508D411yescharacteristic
32C22⋊D127—22no—
33C22⋊D127—21no—
34C2×Dic127—22no—
35C2×Dic127—21no—
36C2×Dic127D412yes—
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—21no—
50C4×C127—22no—
51C4×C127—21no—
52C4×C127C2×D411yescharacteristic
53C4×C127C2×D411yescharacteristic
54Dic127—21no—
55Dic127—22no—
56Dic127—41no—
57C2×C127—21no—
58C2×C127—41no—
59C2×C127#12011yescharacteristic
60D127—41no—
61C127#45611yescharacteristic, complemented, Sylow
62#456—1271nomaximal, Sylow
632−1+4—1271no—
64#137—1271no—
65#137—1271no—
66C4⋊Q8—1271no—
67#104—1271no—
68#104D12711yescharacteristic, complemented
69#101—1271no—
70#41—1271no—
71#41—2541no—
72#41—2542no—
73#41—2541no—
74#41C2×D12711yescharacteristic
75C2×Q8—1271no—
76C2×Q8—1271no—
77C2×Q8—2541no—
78C2×Q8—2541no—
79Q16—2541no—
80Q16—2541no—
81SD16—2541no—
82SD16—2541no—
83M16—1271no—
84M16C2×D12711yescharacteristic
85C4⋊C4—2542no—
86C42C2×D12711yescharacteristic
87Q8—1271no—
88Q8—2542no—
89Q8—2541no—
90Q8—2541no—
91Q8—2541no—
92Q8—2541no—
93Q8D50811yescharacteristic
94D4—21no—
95D4—1271no—
96D4—2542no—
97D4—2541no—
98D4D50811yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—1272no—
102C2×C4—2542no—
103C2×C4—2541no—
104C2×C4—2542no—
105C2×C4—2541no—
106C2×C4C22×D12711yescharacteristic
107C8—21no—
108C8—2541no—
109C22—21no—
110C22—2541no—
111C22D4×D12711yescharacteristic
112C4—22no—
113C4—21no—
114C4—5081no—
115C4—2542no—
116C4—2541no—
117C4D4×D12711yescharacteristic
118C4C2×D50811yescharacteristic
119C2—21no—
120C2—41no—
121C2—5081no—
122C2#1686117911yescharacteristic
subgroupG/H
centerC2#16861179
commutatorC2×C4×C127C23
FrattiniC2×C4C22×D127
Fitting#104×C127C2
socleC2×C127#120
hypercenter#104D127
hypocenterC127#456
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. #16861209C2semidirect
5. #16861137C2semidirect
6. #16861127C2semidirect
7. #104×C127C2semidirect
61. C127#456semidirect
68. #104D127semidirect