Finite Group Databasebeta

← C127×#7524 #44571197

Subgroups — C127×#7524 #44571197

Order 32512.

134 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 30 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
1C127×#1658C211yesmaximal, characteristic
2C127×#1412C211yesmaximal, characteristic
3C127×#1355C211yesmaximal, characteristic
4#564×C127C411yescharacteristic, complemented
5#490×C127—21no—
6#490×C127C2211yescharacteristic
7#353×C127—21no—
8#347×C127—21no—
9#330×C127—21no—
10#330×C127C411yescharacteristic, complemented
11#127×C127D411yescharacteristic
12#125×C127—21no—
13#125×C127—41no—
14#125×C127—41no—
15#125×C127—41no—
16#125×C127C2×C411yescharacteristic
17M32×C127—41no—
18#102×C127—41no—
19#102×C127—41no—
20#102×C127—41no—
21#99×C127—41no—
22#97×C127—21no—
23#97×C127D411yescharacteristic
24C2×D4×C127—21no—
25C2×D4×C127—41no—
26C2×C8×C127—21no—
27C2×C8×C127—41no—
28C4⋊C4×C127—21no—
29C4⋊C4×C127—21no—
30C4⋊C4×C127—21no—
31C4⋊C4×C127—41no—
32C4⋊C4×C127—41no—
33C4⋊C4×C127—41no—
34C4⋊C4×C127—41no—
35C4⋊C4×C127—41no—
36C4⋊C4×C127—41no—
37C22⋊C4×C127—81no—
38C42×C127—41no—
39C42×C127C22⋊C411yescharacteristic
40C16×C127—42no—
41C23×C127—41no—
42D4×C127—81no—
43D4×C127—82no—
44C2×C4×C127—21no—
45C2×C4×C127—41no—
46C2×C4×C127—41no—
47C2×C4×C127—41no—
48C2×C4×C127—161no—
49C2×C4×C127#9911yescharacteristic
50C8×C127—41no—
51C8×C127—81no—
52C22×C127—81no—
53C22×C127—161no—
54C22×C127AΣL(1,𝔽16)11yescharacteristic
55C4×C127—21no—
56C4×C127—41no—
57C4×C127—81no—
58C4×C127—81no—
59C4×C127—81no—
60C4×C127—321no—
61#7524C12711yesmaximal, characteristic, direct product factor, Sylow
62C2×C127—21no—
63C2×C127—161no—
64C2×C127#140411yescharacteristic
65#1658C2×C12711yescharacteristic
66#1412C2×C12711yescharacteristic
67#1355C2×C12711yescharacteristic
68C127#752411yescharacteristic, direct product factor, Sylow
69#564C4×C12711yescharacteristic, complemented
70#490—21no—
71#490C22×C12711yescharacteristic
72#353—21no—
73#347—21no—
74#330—21no—
75#330C4×C12711yescharacteristic, complemented
76#127D4×C12711yescharacteristic
77#125—21no—
78#125—41no—
79#125—41no—
80#125—41no—
81#125C2×C4×C12711yescharacteristic
82M32—41no—
83#102—41no—
84#102—41no—
85#102—41no—
86#99—41no—
87#97—21no—
88#97D4×C12711yescharacteristic
89C2×D4—21no—
90C2×D4—41no—
91C2×C8—21no—
92C2×C8—41no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—41no—
100C4⋊C4—41no—
101C4⋊C4—41no—
102C22⋊C4—81no—
103C42—41no—
104C42C22⋊C4×C12711yescharacteristic
105C16—42no—
106C23—41no—
107D4—81no—
108D4—82no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—161no—
114C2×C4#99×C12711yescharacteristic
115C8—41no—
116C8—81no—
117C22—81no—
118C22—161no—
119C22AΣL(1,𝔽16)×C12711yescharacteristic
120C4—21no—
121C4—41no—
122C4—81no—
123C4—81no—
124C4—81no—
125C4—321no—
126C2—21no—
127C2—161no—
128C2C127×#140411yescharacteristic
subgroupG/H
center, socleC2×C127#1404
commutator#125C2×C4×C127
Frattini, cosocle#490C22×C127
prime radical#127×C127D4
LCSG ▷ #125 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ C42×C127 ◁ #490×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. #564×C127C4semidirect
10. #330×C127C4semidirect
61. #7524C127direct (N × H)
68. C127#7524direct (N × H)
69. #564C4×C127semidirect
75. #330C4×C127semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C127×#16582
C127×#14122
C127×#13552
#7524127