Finite Group Databasebeta

← C127×#13717 #44577390

Subgroups — C127×#13717 #44577390

Order 32512.

170 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 66 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×#2218C211yesmaximal, characteristic
2C127×#2161C211yesmaximal, characteristic, complemented
3C127×#1426C212yesmaximal, complemented
4C127×#1419C212yesmaximal, complemented
5C127×#1400C211yesmaximal, characteristic, complemented
6C2×D16×C127C2211yescharacteristic
7C2×M32×C127C2211yescharacteristic
8#466×C127—21no—
9C2×#108×C127—21no—
10M64×C127C2212yes—
11#368×C127—21no—
12#368×C127C2212yes—
13#367×C127C2211yescharacteristic
14#357×C127—21no—
15C2×D8×C127—21no—
16C2×M16×C127—41no—
17C22×C8×C127D411yescharacteristic
18#121×C127—41no—
19D16×C127—22no—
20M32×C127—22no—
21C2×C16×C127D411yescharacteristic
22C2×C16×C127C2311yescharacteristic
23#108×C127—22no—
24#108×C127—41no—
25#107×C127—21no—
26#102×C127—41no—
27C32×C127—22no—
28C2×D4×C127—41no—
29C2×D4×C127—81no—
30C22×C4×C127D811yescharacteristic
31D8×C127—41no—
32D8×C127—41no—
33M16×C127—42no—
34M16×C127—81no—
35C2×C8×C127—21no—
36C2×C8×C127—21no—
37C2×C8×C127—81no—
38C2×C8×C127D811yescharacteristic
39C2×C8×C127C2×D411yescharacteristic
40C4⋊C4×C127—41no—
41C22⋊C4×C127—81no—
42C16×C127—21no—
43C16×C127#4112yes—
44C23×C127—81no—
45C23×C127SD3211yescharacteristic
46D4×C127—81no—
47D4×C127—81no—
48D4×C127—162no—
49C2×C4×C127—21no—
50C2×C4×C127—21no—
51C2×C4×C127—81no—
52C2×C4×C127SD3211yescharacteristic
53C2×C4×C127C2×D811yescharacteristic
54C8×C127—21no—
55C8×C127—82no—
56C8×C127#12311yescharacteristic
57C8×C127#13711yescharacteristic
58C22×C127—21no—
59C22×C127—41no—
60C22×C127—161no—
61C22×C127—161no—
62C22×C127—161no—
63C22×C127C2×SD3211yescharacteristic
64C4×C127—21no—
65C4×C127—161no—
66C4×C127#48011yescharacteristic
67C4×C127#50911yescharacteristic
68#13717C12711yesmaximal, characteristic, direct product factor, Sylow
69C2×C127—21no—
70C2×C127—41no—
71C2×C127—321no—
72C2×C127#223311yescharacteristic
73#2218C2×C12711yescharacteristic
74#2161C2×C12711yescharacteristic, complemented
75#1426C2×C12712yescomplemented
76#1419C2×C12712yescomplemented
77#1400C2×C12711yescharacteristic, complemented
78C127#1371711yescharacteristic, direct product factor, Sylow
79C2×D16C22×C12711yescharacteristic
80C2×M32C22×C12711yescharacteristic
81#466—21no—
82C2×#108—21no—
83M64C22×C12712yes—
84#368—21no—
85#368C22×C12712yes—
86#367C22×C12711yescharacteristic
87#357—21no—
88C2×D8—21no—
89C2×M16—41no—
90C22×C8D4×C12711yescharacteristic
91#121—41no—
92D16—22no—
93M32—22no—
94C2×C16D4×C12711yescharacteristic
95C2×C16C23×C12711yescharacteristic
96#108—22no—
97#108—41no—
98#107—21no—
99#102—41no—
100C32—22no—
101C2×D4—41no—
102C2×D4—81no—
103C22×C4D8×C12711yescharacteristic
104D8—41no—
105D8—41no—
106M16—42no—
107M16—81no—
108C2×C8—21no—
109C2×C8—21no—
110C2×C8—81no—
111C2×C8D8×C12711yescharacteristic
112C2×C8C2×D4×C12711yescharacteristic
113C4⋊C4—41no—
114C22⋊C4—81no—
115C16—21no—
116C16#41×C12712yes—
117C23—81no—
118C23SD32×C12711yescharacteristic
119D4—81no—
120D4—81no—
121D4—162no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—81no—
125C2×C4SD32×C12711yescharacteristic
126C2×C4C2×D8×C12711yescharacteristic
127C8—21no—
128C8—82no—
129C8#123×C12711yescharacteristic
130C8#137×C12711yescharacteristic
131C22—21no—
132C22—41no—
133C22—161no—
134C22—161no—
135C22—161no—
136C22C2×SD32×C12711yescharacteristic
137C4—21no—
138C4—161no—
139C4#480×C12711yescharacteristic
140C4#509×C12711yescharacteristic
141C2—21no—
142C2—41no—
143C2—321no—
144C2C127×#223311yescharacteristic
subgroupG/H
center, socleC2×C127#2233
commutator, Frattini, cosocleC2×C16C23×C127
prime radicalC127×#2218C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C22×C8×C127 ◁ C2×M32×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2161C2semidirect
3. C127×#1426C2semidirect
4. C127×#1419C2semidirect
5. C127×#1400C2semidirect
68. #13717C127direct (N × H)
74. #2161C2×C127semidirect
75. #1426C2×C127semidirect
76. #1419C2×C127semidirect
77. #1400C2×C127semidirect
78. C127#13717direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22182
C127×#21612
C127×#14262
C127×#14192
C127×#14002
#13717127