Finite Group Databasebeta

← C127×#7337 #44571010

Subgroups — C127×#7337 #44571010

Order 32512.

154 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 54 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×#2113C211yesmaximal, characteristic
2C127×#1400C212yesmaximal, complemented
3C2×#131×C127C411yescharacteristic
4C2×M32×C127C2211yescharacteristic
5C22×C16×C127C411yescharacteristic
6M64×C127—22no—
7C22⋊C16×C127—22no—
8C2×#41×C127C811yescharacteristic
9#131×C127—41no—
10#131×C127—41no—
11C2×M16×C127—21no—
12C2×M16×C127C811yescharacteristic
13C22×C8×C127—21no—
14C22×C8×C127C2×C411yescharacteristic
15M32×C127—41no—
16C2×C16×C127—21no—
17C2×C16×C127—41no—
18C2×C16×C127D412yes—
19C32×C127—42no—
20#41×C127—41no—
21#41×C127—41no—
22C2×Q8×C127C1611yescharacteristic
23C2×D4×C127—21no—
24C2×D4×C127C1611yescharacteristic
25C22×C4×C127—21no—
26C22×C4×C127C2×C811yescharacteristic
27M16×C127—42no—
28M16×C127—41no—
29C2×C8×C127—21no—
30C2×C8×C127—21no—
31C2×C8×C127—21no—
32C2×C8×C127—41no—
33C2×C8×C127—41no—
34C2×C8×C127C22⋊C411yescharacteristic
35C2×C8×C127M1611yescharacteristic
36C16×C127—22no—
37C16×C127—41no—
38C23×C127—21no—
39C23×C127M3211yescharacteristic
40Q8×C127—41no—
41D4×C127—41no—
42D4×C127—42no—
43C2×C4×C127—21no—
44C2×C4×C127—21no—
45C2×C4×C127—21no—
46C2×C4×C127—41no—
47C2×C4×C127—41no—
48C2×C4×C127C22⋊C811yescharacteristic
49C2×C4×C127C2×C1611yescharacteristic
50C8×C127—21no—
51C8×C127—41no—
52C8×C127#9911yescharacteristic
53C8×C127#10011yescharacteristic
54C22×C127—21no—
55C22×C127—41no—
56C22×C127—42no—
57C22×C127—41no—
58C22×C127C22⋊C1611yescharacteristic
59C4×C127—21no—
60C4×C127—41no—
61C4×C127#32311yescharacteristic
62C4×C127#34911yescharacteristic
63#7337C12711yesmaximal, characteristic, direct product factor, Sylow
64C2×C127—21no—
65C2×C127—41no—
66C2×C127—81no—
67C2×C127#131411yescharacteristic
68#2113C2×C12711yescharacteristic
69#1400C2×C12712yescomplemented
70C127#733711yescharacteristic, direct product factor, Sylow
71C2×#131C4×C12711yescharacteristic
72C2×M32C22×C12711yescharacteristic
73C22×C16C4×C12711yescharacteristic
74M64—22no—
75C22⋊C16—22no—
76C2×#41C8×C12711yescharacteristic
77#131—41no—
78#131—41no—
79C2×M16—21no—
80C2×M16C8×C12711yescharacteristic
81C22×C8—21no—
82C22×C8C2×C4×C12711yescharacteristic
83M32—41no—
84C2×C16—21no—
85C2×C16—41no—
86C2×C16D4×C12712yes—
87C32—42no—
88#41—41no—
89#41—41no—
90C2×Q8C16×C12711yescharacteristic
91C2×D4—21no—
92C2×D4C16×C12711yescharacteristic
93C22×C4—21no—
94C22×C4C2×C8×C12711yescharacteristic
95M16—42no—
96M16—41no—
97C2×C8—21no—
98C2×C8—21no—
99C2×C8—21no—
100C2×C8—41no—
101C2×C8—41no—
102C2×C8C22⋊C4×C12711yescharacteristic
103C2×C8M16×C12711yescharacteristic
104C16—22no—
105C16—41no—
106C23—21no—
107C23M32×C12711yescharacteristic
108Q8—41no—
109D4—41no—
110D4—42no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4C22⋊C8×C12711yescharacteristic
117C2×C4C2×C16×C12711yescharacteristic
118C8—21no—
119C8—41no—
120C8#99×C12711yescharacteristic
121C8#100×C12711yescharacteristic
122C22—21no—
123C22—41no—
124C22—42no—
125C22—41no—
126C22C22⋊C16×C12711yescharacteristic
127C4—21no—
128C4—41no—
129C4#323×C12711yescharacteristic
130C4#349×C12711yescharacteristic
131C2—21no—
132C2—41no—
133C2—81no—
134C2C127×#131411yescharacteristic
subgroupG/H
centerC8×C127#99
commutatorC2×C4C2×C16×C127
Frattini, cosocleC2×M32C22×C127
socleC2×C127#1314
prime radicalC2×#41×C127C8
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C8×C127 ◁ C2×C8×C127 ◁ C2×M32×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1400C2semidirect
63. #7337C127direct (N × H)
69. #1400C2×C127semidirect
70. C127#7337direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21132
C127×#14002
#7337127