Finite Group Databasebeta

← C127×#7066 #44570739

Subgroups — C127×#7066 #44570739

Order 32512.

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

normal subgroups only

This group has 176 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×#1843C211yesmaximal, characteristic
2C127×#1322C212yesmaximal
3C2×C4⋊C8×C127—22no—
4C2×C4⋊C8×C127C411yescharacteristic
5C2×C4⋊C8×C127C2211yescharacteristic
6#376×C127C411yescharacteristic
7C22⋊C16×C127—22no—
8C22×C8×C127—21no—
9C22×C8×C127D412yes—
10C2×C42×C127—21no—
11C2×C42×C127C2×C411yescharacteristic
12C2×C16×C127—42no—
13C4⋊C8×C127—41no—
14C4⋊C8×C127—44no—
15C4⋊C8×C127—41no—
16#95×C127—21no—
17#95×C127C812yes—
18C22×C4×C127—22no—
19C22×C4×C127C22⋊C411yescharacteristic
20C22×C4×C127C2×C811yescharacteristic
21C22×C4×C127M1611yescharacteristic
22C2×C8×C127—22no—
23C2×C8×C127—42no—
24C2×C8×C127—42no—
25C2×C8×C127—41no—
26C42×C127—22no—
27C42×C127—22no—
28C42×C127—21no—
29C42×C127—21no—
30C16×C127—82no—
31C23×C127C22⋊C811yescharacteristic
32C2×C4×C127—21no—
33C2×C4×C127—21no—
34C2×C4×C127—24no—
35C2×C4×C127—21no—
36C2×C4×C127—21no—
37C2×C4×C127—22no—
38C2×C4×C127—42no—
39C2×C4×C127—42no—
40C2×C4×C127—41no—
41C2×C4×C127#9911yescharacteristic
42C2×C4×C127#10111yescharacteristic
43C8×C127—42no—
44C8×C127—81no—
45C22×C127—21no—
46C22×C127—21no—
47C22×C127#32411yescharacteristic
48C22×C127#35012yes—
49C4×C127—21no—
50C4×C127—44no—
51C4×C127—41no—
52C4×C127—41no—
53C4×C127#35311yescharacteristic
54C4×C127#35611yescharacteristic
55#7066C12711yesmaximal, characteristic, direct product factor, Sylow
56C2×C127—22no—
57C2×C127#132311yescharacteristic
58C2×C127#132511yescharacteristic
59C2×C127#132811yescharacteristic
60#1843C2×C12711yescharacteristic
61#1322C2×C12712yes—
62C127#706611yescharacteristic, direct product factor, Sylow
63C2×C4⋊C8—22no—
64C2×C4⋊C8C4×C12711yescharacteristic
65C2×C4⋊C8C22×C12711yescharacteristic
66#376C4×C12711yescharacteristic
67C22⋊C16—22no—
68C22×C8—21no—
69C22×C8D4×C12712yes—
70C2×C42—21no—
71C2×C42C2×C4×C12711yescharacteristic
72C2×C16—42no—
73C4⋊C8—41no—
74C4⋊C8—41no—
75C4⋊C8—44no—
76#95—21no—
77#95C8×C12712yes—
78C22×C4—22no—
79C22×C4C22⋊C4×C12711yescharacteristic
80C22×C4C2×C8×C12711yescharacteristic
81C22×C4M16×C12711yescharacteristic
82C2×C8—22no—
83C2×C8—42no—
84C2×C8—42no—
85C2×C8—41no—
86C42—22no—
87C42—22no—
88C42—21no—
89C42—21no—
90C16—82no—
91C23C22⋊C8×C12711yescharacteristic
92C2×C4—21no—
93C2×C4—21no—
94C2×C4—24no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—22no—
98C2×C4—42no—
99C2×C4—42no—
100C2×C4—41no—
101C2×C4#99×C12711yescharacteristic
102C2×C4#101×C12711yescharacteristic
103C8—42no—
104C8—81no—
105C22—21no—
106C22—21no—
107C22#324×C12711yescharacteristic
108C22#350×C12712yes—
109C4—21no—
110C4—44no—
111C4—41no—
112C4—41no—
113C4#353×C12711yescharacteristic
114C4#356×C12711yescharacteristic
115C2—22no—
116C2C127×#132311yescharacteristic
117C2C127×#132511yescharacteristic
118C2C127×#132811yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C2×C8×C127
Frattini, cosocleC2×C4⋊C8C22×C127
socleC22×C127#324
prime radicalC23×C127C22⋊C8
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×C4⋊C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
55. #7066C127direct (N × H)
62. C127#7066direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#18432
C127×#13222
#7066127