Finite Group Databasebeta

← C127×#2062 #30635014

Subgroups — C127×#2062 #30635014

Order 16256.

314 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 92 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#543×C127C211yesmaximal, characteristic
2#385×C127C213yesmaximal
3#342×C127C213yesmaximal
4C23×C4×C127C2211yescharacteristic
5C22⋊Q8×C127—23no—
6C22⋊Q8×C127—23no—
7C2×C4⋊C4×C127—23no—
8C2×C22⋊C4×C127C2213yes—
9C2×C22⋊C4×C127C2213yes—
10#95×C127—23no—
11C24×C127C2311yescharacteristic
12C2×Q8×C127—21no—
13C2×Q8×C127—21no—
14C22×C4×C127—23no—
15C22×C4×C127—23no—
16C22×C4×C127—42no—
17C22×C4×C127D413yes—
18C22×C4×C127D413yes—
19C4⋊C4×C127—23no—
20C4⋊C4×C127—23no—
21C4⋊C4×C127—46no—
22C22⋊C4×C127—26no—
23C22⋊C4×C127—23no—
24C22⋊C4×C127Q816yescomplemented
25C23×C127—41no—
26C23×C127—41no—
27C23×C127C2×D413yes—
28C23×C127C2×Q813yes—
29C23×C127#4111yescharacteristic
30Q8×C127—81no—
31Q8×C127—81no—
32C2×C4×C127—26no—
33C2×C4×C127—23no—
34C2×C4×C127—23no—
35C2×C4×C127—26no—
36C2×C4×C127—43no—
37C2×C4×C127—43no—
38C2×C4×C127—43no—
39C2×C4×C127—41no—
40C2×C4×C127—43no—
41C2×C4×C127—43no—
42C22×C127—23no—
43C22×C127—23no—
44C22×C127—43no—
45C22×C127—41no—
46C22×C127#12011yescharacteristic
47C22×C127C22⋊Q813yes—
48C22×C127C4⋊Q813yes—
49C4×C127—46no—
50C4×C127—42no—
51C4×C127—43no—
52C4×C127—43no—
53C2×C127—23no—
54C2×C127—23no—
55C2×C127#39511yescharacteristic
56C2×C127B(4,𝔽2)11yescharacteristic
57C2×C127#45811yescharacteristic
58#2062C12711yesmaximal, characteristic, direct product factor, Sylow
59C127#206211yescharacteristic, direct product factor, Sylow
60#543C2×C12711yescharacteristic
61#385C2×C12713yes—
62#342C2×C12713yes—
63C23×C4C22×C12711yescharacteristic
64C22⋊Q8—23no—
65C22⋊Q8—23no—
66C2×C4⋊C4—23no—
67C2×C22⋊C4C22×C12713yes—
68C2×C22⋊C4C22×C12713yes—
69#95—23no—
70C24C23×C12711yescharacteristic
71C2×Q8—21no—
72C2×Q8—21no—
73C22×C4—23no—
74C22×C4—23no—
75C22×C4—42no—
76C22×C4D4×C12713yes—
77C22×C4D4×C12713yes—
78C4⋊C4—23no—
79C4⋊C4—23no—
80C4⋊C4—46no—
81C22⋊C4—26no—
82C22⋊C4—23no—
83C22⋊C4Q8×C12716yescomplemented
84C23—41no—
85C23—41no—
86C23C2×D4×C12713yes—
87C23C2×Q8×C12713yes—
88C23#41×C12711yescharacteristic
89Q8—81no—
90Q8—81no—
91C2×C4—26no—
92C2×C4—23no—
93C2×C4—23no—
94C2×C4—26no—
95C2×C4—43no—
96C2×C4—43no—
97C2×C4—43no—
98C2×C4—41no—
99C2×C4—43no—
100C2×C4—43no—
101C22—23no—
102C22—23no—
103C22—43no—
104C22—41no—
105C22#120×C12711yescharacteristic
106C22C22⋊Q8×C12713yes—
107C22C4⋊Q8×C12713yes—
108C4—46no—
109C4—42no—
110C4—43no—
111C4—43no—
112C2—23no—
113C2—23no—
114C2#395×C12711yescharacteristic
115C2B(4,𝔽2)×C12711yescharacteristic
116C2#458×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#120
commutator, Frattini, cosocleC24C23×C127
prime radicalC24×C127C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
24. C22⋊C4×C127Q8semidirect
58. #2062C127direct (N × H)
59. C127#2062direct (N × H)
83. C22⋊C4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
#543×C1272
#385×C1272
#342×C1272
#2062127