Finite Group Databasebeta

← C127×#1667 #30634619

Subgroups — C127×#1667 #30634619

Order 16256.

204 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 72 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#493×C127C211yesmaximal, characteristic, complemented
2#459×C127C212yesmaximal, complemented
3C8×D4×C127C211yesmaximal, characteristic, complemented
4#335×C127C211yesmaximal, characteristic, complemented
5#331×C127C212yesmaximal, complemented
6C2×D8×C127—22no—
7C2×D8×C127—21no—
8C2×D8×C127—21no—
9C22×C8×C127—21no—
10#127×C127C2212yes—
11C4×D4×C127C2211yescharacteristic
12C4⋊C8×C127C2211yescharacteristic
13C4⋊C8×C127C2212yes—
14#102×C127—22no—
15C22⋊C8×C127—21no—
16C4×C8×C127C2211yescharacteristic
17C2×D4×C127—22no—
18C2×D4×C127—22no—
19C2×D4×C127—22no—
20C2×D4×C127D411yescharacteristic
21C22×C4×C127—21no—
22D8×C127—42no—
23D8×C127—44no—
24D8×C127—42no—
25C2×C8×C127—21no—
26C2×C8×C127—22no—
27C2×C8×C127—42no—
28C2×C8×C127D411yescharacteristic
29C2×C8×C127D411yescharacteristic
30C4⋊C4×C127D411yescharacteristic
31C22⋊C4×C127—21no—
32C42×C127C2311yescharacteristic
33C23×C127—21no—
34C23×C127—42no—
35D4×C127—21no—
36D4×C127—42no—
37D4×C127—42no—
38D4×C127—42no—
39D4×C127—42no—
40D4×C127—82no—
41D4×C127D812yescomplemented
42C2×C4×C127—21no—
43C2×C4×C127—41no—
44C2×C4×C127—41no—
45C2×C4×C127C2×D411yescharacteristic
46C2×C4×C127C2×D411yescharacteristic
47C2×C4×C127#4111yescharacteristic
48C8×C127—21no—
49C8×C127—41no—
50C8×C127—42no—
51C8×C127D812yescomplemented
52C22×C127—22no—
53C22×C127—41no—
54C22×C127—41no—
55C22×C127—82no—
56C22×C127—82no—
57C22×C127—82no—
58C22×C127#12111yescharacteristic
59C4×C127—21no—
60C4×C127—41no—
61C4×C127C2×D811yescharacteristic
62C4×C127C2×D811yescharacteristic
63C4×C127#13511yescharacteristic
64C4×C127AGL(1,ℤ/8)11yescharacteristic
65C2×C127—42no—
66C2×C127—162no—
67C2×C127#45911yescharacteristic
68C2×C127#46611yescharacteristic
69C2×C127#47211yescharacteristic
70#1667C12711yesmaximal, characteristic, direct product factor, Sylow
71C127#166711yescharacteristic, direct product factor, Sylow
72#493C2×C12711yescharacteristic, complemented
73#459C2×C12712yescomplemented
74C8×D4C2×C12711yescharacteristic, complemented
75#335C2×C12711yescharacteristic, complemented
76#331C2×C12712yescomplemented
77C2×D8—22no—
78C2×D8—21no—
79C2×D8—21no—
80C22×C8—21no—
81#127C22×C12712yes—
82C4×D4C22×C12711yescharacteristic
83C4⋊C8C22×C12711yescharacteristic
84C4⋊C8C22×C12712yes—
85#102—22no—
86C22⋊C8—21no—
87C4×C8C22×C12711yescharacteristic
88C2×D4—22no—
89C2×D4—22no—
90C2×D4—22no—
91C2×D4D4×C12711yescharacteristic
92C22×C4—21no—
93D8—42no—
94D8—44no—
95D8—42no—
96C2×C8—21no—
97C2×C8—22no—
98C2×C8—42no—
99C2×C8D4×C12711yescharacteristic
100C2×C8D4×C12711yescharacteristic
101C4⋊C4D4×C12711yescharacteristic
102C22⋊C4—21no—
103C42C23×C12711yescharacteristic
104C23—21no—
105C23—42no—
106D4—21no—
107D4—42no—
108D4—42no—
109D4—42no—
110D4—42no—
111D4—82no—
112D4D8×C12712yescomplemented
113C2×C4—21no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4C2×D4×C12711yescharacteristic
117C2×C4C2×D4×C12711yescharacteristic
118C2×C4#41×C12711yescharacteristic
119C8—21no—
120C8—41no—
121C8—42no—
122C8D8×C12712yescomplemented
123C22—22no—
124C22—41no—
125C22—41no—
126C22—82no—
127C22—82no—
128C22—82no—
129C22#121×C12711yescharacteristic
130C4—21no—
131C4—41no—
132C4C2×D8×C12711yescharacteristic
133C4C2×D8×C12711yescharacteristic
134C4#135×C12711yescharacteristic
135C4AGL(1,ℤ/8)×C12711yescharacteristic
136C2—42no—
137C2—162no—
138C2#459×C12711yescharacteristic
139C2#466×C12711yescharacteristic
140C2#472×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#121
commutator, Frattini, cosocleC42C23×C127
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. #493×C127C2semidirect
2. #459×C127C2semidirect
3. C8×D4×C127C2semidirect
4. #335×C127C2semidirect
5. #331×C127C2semidirect
41. D4×C127D8semidirect
51. C8×C127D8semidirect
70. #1667C127direct (N × H)
71. C127#1667direct (N × H)
72. #493C2×C127semidirect
73. #459C2×C127semidirect
74. C8×D4C2×C127semidirect
75. #335C2×C127semidirect
76. #331C2×C127semidirect
112. D4D8×C127semidirect
122. C8D8×C127semidirect

Maximal subgroups

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

subgroupindex
#493×C1272
#459×C1272
C8×D4×C1272
#335×C1272
#331×C1272
#1667127