Finite Group Databasebeta

← C127×#1689 #30634641

Subgroups — C127×#1689 #30634641

Order 16256.

166 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 68 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#494×C127C211yesmaximal, characteristic, complemented
2#474×C127C212yesmaximal
3#436×C127C211yesmaximal, characteristic
4#334×C127C211yesmaximal, characteristic, complemented
5#332×C127C212yesmaximal, complemented
6C2×Q16×C127—21no—
7C2×Q16×C127—21no—
8C2×M16×C127—21no—
9C4⋊Q8×C127C2212yes—
10C4×D4×C127C2211yescharacteristic
11#107×C127—22no—
12C4⋊C8×C127C2211yescharacteristic
13C4⋊C8×C127C2212yes—
14#102×C127—22no—
15C22⋊C8×C127—21no—
16C4×C8×C127C2211yescharacteristic
17C2×Q8×C127—22no—
18C2×D4×C127D411yescharacteristic
19C22×C4×C127—21no—
20Q16×C127—42no—
21Q16×C127—42no—
22M16×C127—42no—
23C2×C8×C127—21no—
24C2×C8×C127—22no—
25C2×C8×C127D411yescharacteristic
26C2×C8×C127D411yescharacteristic
27C4⋊C4×C127—22no—
28C4⋊C4×C127—22no—
29C4⋊C4×C127D411yescharacteristic
30C22⋊C4×C127—21no—
31C42×C127C2311yescharacteristic
32C23×C127—21no—
33Q8×C127—42no—
34Q8×C127—42no—
35D4×C127—22no—
36C2×C4×C127—21no—
37C2×C4×C127—41no—
38C2×C4×C127—41no—
39C2×C4×C127—42no—
40C2×C4×C127C2×D411yescharacteristic
41C2×C4×C127C2×D411yescharacteristic
42C2×C4×C127#4111yescharacteristic
43C8×C127—21no—
44C8×C127—41no—
45C8×C127—42no—
46C8×C127D812yes—
47C22×C127—41no—
48C22×C127—41no—
49C22×C127—41no—
50C22×C127#12111yescharacteristic
51C4×C127—21no—
52C4×C127—41no—
53C4×C127—82no—
54C4×C127C2×D811yescharacteristic
55C4×C127AGL(1,ℤ/8)11yescharacteristic
56C4×C127#13712yes—
57C2×C127—81no—
58C2×C127#45911yescharacteristic
59C2×C127#47011yescharacteristic
60C2×C127#47311yescharacteristic
61#1689C12711yesmaximal, characteristic, direct product factor, Sylow
62C127#168911yescharacteristic, direct product factor, Sylow
63#494C2×C12711yescharacteristic, complemented
64#474C2×C12712yes—
65#436C2×C12711yescharacteristic
66#334C2×C12711yescharacteristic, complemented
67#332C2×C12712yescomplemented
68C2×Q16—21no—
69C2×Q16—21no—
70C2×M16—21no—
71C4⋊Q8C22×C12712yes—
72C4×D4C22×C12711yescharacteristic
73#107—22no—
74C4⋊C8C22×C12711yescharacteristic
75C4⋊C8C22×C12712yes—
76#102—22no—
77C22⋊C8—21no—
78C4×C8C22×C12711yescharacteristic
79C2×Q8—22no—
80C2×D4D4×C12711yescharacteristic
81C22×C4—21no—
82Q16—42no—
83Q16—42no—
84M16—42no—
85C2×C8—21no—
86C2×C8—22no—
87C2×C8D4×C12711yescharacteristic
88C2×C8D4×C12711yescharacteristic
89C4⋊C4—22no—
90C4⋊C4—22no—
91C4⋊C4D4×C12711yescharacteristic
92C22⋊C4—21no—
93C42C23×C12711yescharacteristic
94C23—21no—
95Q8—42no—
96Q8—42no—
97D4—22no—
98C2×C4—21no—
99C2×C4—41no—
100C2×C4—41no—
101C2×C4—42no—
102C2×C4C2×D4×C12711yescharacteristic
103C2×C4C2×D4×C12711yescharacteristic
104C2×C4#41×C12711yescharacteristic
105C8—21no—
106C8—41no—
107C8—42no—
108C8D8×C12712yes—
109C22—41no—
110C22—41no—
111C22—41no—
112C22#121×C12711yescharacteristic
113C4—21no—
114C4—41no—
115C4—82no—
116C4C2×D8×C12711yescharacteristic
117C4AGL(1,ℤ/8)×C12711yescharacteristic
118C4#137×C12712yes—
119C2—81no—
120C2#459×C12711yescharacteristic
121C2#470×C12711yescharacteristic
122C2#473×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#121
commutator, Frattini, cosocleC42C23×C127
prime radicalC2×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #494×C127C2semidirect
4. #334×C127C2semidirect
5. #332×C127C2semidirect
61. #1689C127direct (N × H)
62. C127#1689direct (N × H)
63. #494C2×C127semidirect
66. #334C2×C127semidirect
67. #332C2×C127semidirect

Maximal subgroups

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

subgroupindex
#494×C1272
#474×C1272
#436×C1272
#334×C1272
#332×C1272
#1689127