Finite Group Databasebeta

← C127×#7526 #44571199

Subgroups — C127×#7526 #44571199

Order 32512.

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

normal subgroups only

This group has 126 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×#1663C211yesmaximal, characteristic
2C127×#1413C211yesmaximal, characteristic
3C127×#1356C211yesmaximal, characteristic
4#564×C127C411yescharacteristic
5#501×C127—21no—
6#491×C127C2211yescharacteristic
7#356×C127—21no—
8#347×C127—21no—
9#330×C127—21no—
10#330×C127C411yescharacteristic
11C4⋊Q8×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#107×C127—41no—
19#106×C127—41no—
20#103×C127—41no—
21#101×C127—41no—
22#97×C127—21no—
23#97×C127D411yescharacteristic
24C2×Q8×C127—21no—
25M16×C127—81no—
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—
37C4⋊C4×C127—41no—
38C42×C127—41no—
39C42×C127C22⋊C411yescharacteristic
40C16×C127—42no—
41Q8×C127—81no—
42C2×C4×C127—21no—
43C2×C4×C127—41no—
44C2×C4×C127—41no—
45C2×C4×C127—41no—
46C2×C4×C127—41no—
47C2×C4×C127#9911yescharacteristic
48C8×C127—41no—
49C8×C127—42no—
50C8×C127—161no—
51C22×C127AΣL(1,𝔽16)11yescharacteristic
52C4×C127—21no—
53C4×C127—41no—
54C4×C127—81no—
55C4×C127—81no—
56C4×C127—81no—
57C4×C127—81no—
58#7526C12711yesmaximal, characteristic, direct product factor, Sylow
59C2×C127—21no—
60C2×C127#140411yescharacteristic
61#1663C2×C12711yescharacteristic
62#1413C2×C12711yescharacteristic
63#1356C2×C12711yescharacteristic
64C127#752611yescharacteristic, direct product factor, Sylow
65#564C4×C12711yescharacteristic
66#501—21no—
67#491C22×C12711yescharacteristic
68#356—21no—
69#347—21no—
70#330—21no—
71#330C4×C12711yescharacteristic
72C4⋊Q8D4×C12711yescharacteristic
73#125—21no—
74#125—41no—
75#125—41no—
76#125—41no—
77#125C2×C4×C12711yescharacteristic
78M32—41no—
79#107—41no—
80#106—41no—
81#103—41no—
82#101—41no—
83#97—21no—
84#97D4×C12711yescharacteristic
85C2×Q8—21no—
86M16—81no—
87C2×C8—21no—
88C2×C8—41no—
89C4⋊C4—21no—
90C4⋊C4—21no—
91C4⋊C4—21no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C42—41no—
100C42C22⋊C4×C12711yescharacteristic
101C16—42no—
102Q8—81no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4#99×C12711yescharacteristic
109C8—41no—
110C8—42no—
111C8—161no—
112C22AΣL(1,𝔽16)×C12711yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—81no—
117C4—81no—
118C4—81no—
119C2—21no—
120C2C127×#140411yescharacteristic
subgroupG/H
center, socleC2×C127#1404
commutator#125C2×C4×C127
Frattini, cosocle#491C22×C127
prime radicalC22×C127AΣL(1,𝔽16)
LCSG ▷ #125 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ C42×C127 ◁ #491×C127 ◁ G

Complements

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

NH ≅ G/Ntype
58. #7526C127direct (N × H)
64. C127#7526direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#16632
C127×#14132
C127×#13562
#7526127