Finite Group Databasebeta

← C127×#7518 #44571191

Subgroups — C127×#7518 #44571191

Order 32512.

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

normal subgroups only

This group has 148 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×#1630C211yesmaximal, characteristic
2C127×#1410C211yesmaximal, characteristic
3C127×#1359C211yesmaximal, characteristic
4#559×C127C411yescharacteristic
5#492×C127C2211yescharacteristic
6#477×C127—21no—
7#364×C127—21no—
8#356×C127—21no—
9#331×C127C411yescharacteristic
10Q8⋊C8×C127—21no—
11C2×SD16×C127—41no—
12C4⋊Q8×C127D411yescharacteristic
13#127×C127C2×C411yescharacteristic
14#124×C127—41no—
15#123×C127—41no—
16C4×Q8×C127—21no—
17C4×D4×C127—41no—
18M32×C127—41no—
19#107×C127—41no—
20C4⋊C8×C127—21no—
21#103×C127—41no—
22#101×C127—41no—
23C4×C8×C127D411yescharacteristic
24C2×Q8×C127—21no—
25C2×Q8×C127—21no—
26C2×D4×C127—21no—
27C2×D4×C127—41no—
28C22×C4×C127—41no—
29SD16×C127—81no—
30SD16×C127—81no—
31M16×C127—81no—
32C2×C8×C127—21no—
33C2×C8×C127—41no—
34C4⋊C4×C127—21no—
35C4⋊C4×C127—41no—
36C4⋊C4×C127—41no—
37C22⋊C4×C127—42no—
38C22⋊C4×C127—41no—
39C42×C127—41no—
40C42×C127C22⋊C411yescharacteristic
41C16×C127—81no—
42C23×C127—41no—
43Q8×C127—41no—
44Q8×C127—41no—
45Q8×C127—81no—
46D4×C127—81no—
47D4×C127—81no—
48D4×C127—81no—
49C2×C4×C127—21no—
50C2×C4×C127—41no—
51C2×C4×C127—41no—
52C2×C4×C127—41no—
53C2×C4×C127—161no—
54C2×C4×C127#9911yescharacteristic
55C8×C127—21no—
56C8×C127—21no—
57C8×C127—81no—
58C8×C127—161no—
59C22×C127—82no—
60C22×C127—81no—
61C22×C127AΣL(1,𝔽16)11yescharacteristic
62C4×C127—21no—
63C4×C127—21no—
64C4×C127—21no—
65C4×C127—81no—
66C4×C127—81no—
67C4×C127—81no—
68#7518C12711yesmaximal, characteristic, direct product factor, Sylow
69C2×C127—21no—
70C2×C127—161no—
71C2×C127#140211yescharacteristic
72#1630C2×C12711yescharacteristic
73#1410C2×C12711yescharacteristic
74#1359C2×C12711yescharacteristic
75C127#751811yescharacteristic, direct product factor, Sylow
76#559C4×C12711yescharacteristic
77#492C22×C12711yescharacteristic
78#477—21no—
79#364—21no—
80#356—21no—
81#331C4×C12711yescharacteristic
82Q8⋊C8—21no—
83C2×SD16—41no—
84C4⋊Q8D4×C12711yescharacteristic
85#127C2×C4×C12711yescharacteristic
86#124—41no—
87#123—41no—
88C4×Q8—21no—
89C4×D4—41no—
90M32—41no—
91#107—41no—
92C4⋊C8—21no—
93#103—41no—
94#101—41no—
95C4×C8D4×C12711yescharacteristic
96C2×Q8—21no—
97C2×Q8—21no—
98C2×D4—21no—
99C2×D4—41no—
100C22×C4—41no—
101SD16—81no—
102SD16—81no—
103M16—81no—
104C2×C8—21no—
105C2×C8—41no—
106C4⋊C4—21no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C22⋊C4—42no—
110C22⋊C4—41no—
111C42—41no—
112C42C22⋊C4×C12711yescharacteristic
113C16—81no—
114C23—41no—
115Q8—41no—
116Q8—41no—
117Q8—81no—
118D4—81no—
119D4—81no—
120D4—81no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—161no—
126C2×C4#99×C12711yescharacteristic
127C8—21no—
128C8—21no—
129C8—81no—
130C8—161no—
131C22—82no—
132C22—81no—
133C22AΣL(1,𝔽16)×C12711yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—81no—
138C4—81no—
139C4—81no—
140C2—21no—
141C2—161no—
142C2C127×#140211yescharacteristic
subgroupG/H
center, socleC2×C127#1402
commutator#127C2×C4×C127
Frattini, cosocle#492C22×C127
prime radical#127×C127C2×C4
LCSG ▷ #127 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ C42×C127 ◁ #492×C127 ◁ G

Complements

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

NH ≅ G/Ntype
68. #7518C127direct (N × H)
75. C127#7518direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#16302
C127×#14102
C127×#13592
#7518127