Finite Group Databasebeta

← C127×#2644 #30635596

Subgroups — C127×#2644 #30635596

Order 16256.

420 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 184 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#397×C127C216yesmaximal, complemented
2#396×C127C212yesmaximal, complemented
3#390×C127C213yesmaximal
4#389×C127C213yesmaximal, complemented
5#376×C127C211yesmaximal, characteristic, complemented
6C22×D4×C127C2211yescharacteristic
7C2×C4⋊C4×C127C2213yes—
8C2×C4⋊C4×C127C2216yes—
9C2×C22⋊C4×C127C2216yes—
10C2×C22⋊C4×C127C2216yes—
11C2×C42×C127C2213yes—
12#95×C127C2211yescharacteristic
13#95×C127C2213yes—
14#95×C127C2216yes—
15C24×C127C2312yes—
16C2×D4×C127—26no—
17C22×C4×C127C2313yes—
18C22×C4×C127C2313yes—
19C22×C4×C127C2316yes—
20C22×C4×C127C2311yescharacteristic
21C4⋊C4×C127—26no—
22C4⋊C4×C127—46no—
23C22⋊C4×C127—46no—
24C22⋊C4×C127—46no—
25C42×C127—26no—
26C23×C127—26no—
27C23×C127—26no—
28C23×C127—22no—
29C23×C127C2411yescharacteristic
30D4×C127—44no—
31C2×C4×C127—23no—
32C2×C4×C127—23no—
33C2×C4×C127—26no—
34C2×C4×C127—23no—
35C2×C4×C127—23no—
36C2×C4×C127—26no—
37C2×C4×C127—26no—
38C2×C4×C127—23no—
39C2×C4×C127—23no—
40C2×C4×C127#4116yes—
41C22×C127—42no—
42C22×C127—46no—
43C22×C127—46no—
44C22×C127C2×#4113yes—
45C22×C127H(5,𝔽2)13yes—
46C22×C1272−1+411yescharacteristic
47C4×C127—43no—
48C4×C127—46no—
49C4×C127—43no—
50C4×C127#12614yes—
51C2×C127—82no—
52C2×C127C2×#12611yescharacteristic
53C2×C127#54013yes—
54C2×C127#54213yes—
55#2644C12711yesmaximal, characteristic, direct product factor, Sylow
56C127#264411yescharacteristic, direct product factor, Sylow
57#397C2×C12716yescomplemented
58#396C2×C12712yescomplemented
59#390C2×C12713yes—
60#389C2×C12713yescomplemented
61#376C2×C12711yescharacteristic, complemented
62C22×D4C22×C12711yescharacteristic
63C2×C4⋊C4C22×C12713yes—
64C2×C4⋊C4C22×C12716yes—
65C2×C22⋊C4C22×C12716yes—
66C2×C22⋊C4C22×C12716yes—
67C2×C42C22×C12713yes—
68#95C22×C12711yescharacteristic
69#95C22×C12713yes—
70#95C22×C12716yes—
71C24C23×C12712yes—
72C2×D4—26no—
73C22×C4C23×C12713yes—
74C22×C4C23×C12713yes—
75C22×C4C23×C12716yes—
76C22×C4C23×C12711yescharacteristic
77C4⋊C4—26no—
78C4⋊C4—46no—
79C22⋊C4—46no—
80C22⋊C4—46no—
81C42—26no—
82C23—26no—
83C23—26no—
84C23—22no—
85C23C24×C12711yescharacteristic
86D4—44no—
87C2×C4—23no—
88C2×C4—23no—
89C2×C4—26no—
90C2×C4—23no—
91C2×C4—23no—
92C2×C4—26no—
93C2×C4—26no—
94C2×C4—23no—
95C2×C4—23no—
96C2×C4#41×C12716yes—
97C22—42no—
98C22—46no—
99C22—46no—
100C22C2×#41×C12713yes—
101C22H(5,𝔽2)×C12713yes—
102C222−1+4×C12711yescharacteristic
103C4—43no—
104C4—46no—
105C4—43no—
106C4#126×C12714yes—
107C2—82no—
108C2C2×#126×C12711yescharacteristic
109C2#540×C12713yes—
110C2#542×C12713yes—
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #397×C127C2semidirect
2. #396×C127C2semidirect
4. #389×C127C2semidirect
5. #376×C127C2semidirect
55. #2644C127direct (N × H)
56. C127#2644direct (N × H)
57. #397C2×C127semidirect
58. #396C2×C127semidirect
60. #389C2×C127semidirect
61. #376C2×C127semidirect

Maximal subgroups

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

subgroupindex
#397×C1272
#396×C1272
#390×C1272
#389×C1272
#376×C1272
#2644127