Finite Group Databasebeta

← C127×#2214 #30635166

Subgroups — C127×#2214 #30635166

Order 16256.

150 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 60 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
1#510×C127C212yesmaximal
2#494×C127C211yesmaximal, characteristic, complemented
3#443×C127C211yesmaximal, characteristic
4#364×C127C211yesmaximal, characteristic, complemented
5#362×C127C212yesmaximal, complemented
6#135×C127C2211yescharacteristic
7C2×Q16×C127—21no—
8C2×Q16×C127C2212yes—
9#131×C127—21no—
10C4⋊Q8×C127—21no—
11Q32×C127—22no—
12SD32×C127—22no—
13M32×C127C2212yes—
14#108×C127C2211yescharacteristic
15#104×C127—21no—
16C4×C8×C127C2211yescharacteristic
17#41×C127—21no—
18C2×Q8×C127—22no—
19Q16×C127—22no—
20Q16×C127—22no—
21Q16×C127—41no—
22Q16×C127—41no—
23Q16×C127D411yescharacteristic
24SD16×C127—21no—
25D8×C127D411yescharacteristic
26M16×C127—21no—
27M16×C127—41no—
28C2×C8×C127—41no—
29C2×C8×C127D411yescharacteristic
30C2×C8×C127C2311yescharacteristic
31C4⋊C4×C127—42no—
32C42×C127D411yescharacteristic
33C16×C127—22no—
34Q8×C127—21no—
35Q8×C127—42no—
36Q8×C127—42no—
37D4×C127—21no—
38D4×C127—41no—
39C2×C4×C127—21no—
40C2×C4×C127—41no—
41C2×C4×C127—42no—
42C2×C4×C127C2×D411yescharacteristic
43C8×C127—41no—
44C8×C127D811yescharacteristic
45C8×C127D811yescharacteristic
46C8×C127C2×D411yescharacteristic
47C8×C127#4111yescharacteristic
48C22×C127—41no—
49C22×C127AGL(1,ℤ/8)11yescharacteristic
50C4×C127—22no—
51C4×C127—41no—
52C4×C127—82no—
53C4×C127#12111yescharacteristic
54C4×C127C2×D811yescharacteristic
55C2×C127—21no—
56C2×C127—81no—
57C2×C127#45911yescharacteristic
58#2214C12711yesmaximal, characteristic, direct product factor, Sylow
59C127#221411yescharacteristic, direct product factor, Sylow
60#510C2×C12712yes—
61#494C2×C12711yescharacteristic, complemented
62#443C2×C12711yescharacteristic
63#364C2×C12711yescharacteristic, complemented
64#362C2×C12712yescomplemented
65#135C22×C12711yescharacteristic
66C2×Q16—21no—
67C2×Q16C22×C12712yes—
68#131—21no—
69C4⋊Q8—21no—
70Q32—22no—
71SD32—22no—
72M32C22×C12712yes—
73#108C22×C12711yescharacteristic
74#104—21no—
75C4×C8C22×C12711yescharacteristic
76#41—21no—
77C2×Q8—22no—
78Q16—22no—
79Q16—22no—
80Q16—41no—
81Q16—41no—
82Q16D4×C12711yescharacteristic
83SD16—21no—
84D8D4×C12711yescharacteristic
85M16—21no—
86M16—41no—
87C2×C8—41no—
88C2×C8D4×C12711yescharacteristic
89C2×C8C23×C12711yescharacteristic
90C4⋊C4—42no—
91C42D4×C12711yescharacteristic
92C16—22no—
93Q8—21no—
94Q8—42no—
95Q8—42no—
96D4—21no—
97D4—41no—
98C2×C4—21no—
99C2×C4—41no—
100C2×C4—42no—
101C2×C4C2×D4×C12711yescharacteristic
102C8—41no—
103C8D8×C12711yescharacteristic
104C8D8×C12711yescharacteristic
105C8C2×D4×C12711yescharacteristic
106C8#41×C12711yescharacteristic
107C22—41no—
108C22AGL(1,ℤ/8)×C12711yescharacteristic
109C4—22no—
110C4—41no—
111C4—82no—
112C4#121×C12711yescharacteristic
113C4C2×D8×C12711yescharacteristic
114C2—21no—
115C2—81no—
116C2#459×C12711yescharacteristic
subgroupG/H
center, socleC2×C127#459
commutator, Frattini, cosocleC2×C8C23×C127
prime radical#135×C127C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #494×C127C2semidirect
4. #364×C127C2semidirect
5. #362×C127C2semidirect
58. #2214C127direct (N × H)
59. C127#2214direct (N × H)
61. #494C2×C127semidirect
63. #364C2×C127semidirect
64. #362C2×C127semidirect

Maximal subgroups

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

subgroupindex
#510×C1272
#494×C1272
#443×C1272
#364×C1272
#362×C1272
#2214127