Finite Group Databasebeta

← C127×#8533 #44572206

Subgroups — C127×#8533 #44572206

Order 32512.

656 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 150 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×#3556C211yesmaximal, characteristic
2C127×#1994C213yesmaximal
3C127×#1561C213yesmaximal
4#564×C127C414yescomplemented
5#557×C127—26no—
6#541×C127—26no—
7#533×C127C2213yes—
8#423×C127C2213yes—
9C43×C127C2211yescharacteristic
10#339×C127—26no—
11#332×C127—26no—
12C2×M16×C127—23no—
13C4⋊Q8×C127—26no—
14C4⋊Q8×C127D416yes—
15#126×C127—28no—
16#125×C127—26no—
17#125×C127—224no—
18#125×C127C2×C416yes—
19C22⋊Q8×C127—26no—
20C4×Q8×C127—212no—
21C4×Q8×C127—26no—
22#117×C127D416yes—
23C2×C42×C127—23no—
24C2×C42×C127C2311yescharacteristic
25C4⋊C8×C127—26no—
26C2×Q8×C127—26no—
27C22×C4×C127—41no—
28C22×C4×C127C2×D413yes—
29M16×C127—46no—
30C2×C8×C127—43no—
31C4⋊C4×C127—224no—
32C4⋊C4×C127—212no—
33C4⋊C4×C127—26no—
34C4⋊C4×C127C22⋊C4112yes—
35C22⋊C4×C127—26no—
36C42×C127—28no—
37C42×C127—26no—
38C42×C127—26no—
39C42×C127—43no—
40C42×C127C22×C411yescharacteristic
41C42×C127C2×D413yes—
42C23×C127#12011yescharacteristic
43Q8×C127—46no—
44Q8×C127—46no—
45C2×C4×C127—23no—
46C2×C4×C127—23no—
47C2×C4×C127—212no—
48C2×C4×C127—46no—
49C2×C4×C127C2×C22⋊C413yes—
50C2×C4×C127#12013yes—
51C8×C127—83no—
52C22×C127—23no—
53C22×C127#37911yescharacteristic
54C4×C127—23no—
55C4×C127—44no—
56C4×C127—412no—
57C4×C127#45413yes—
58C4×C127#45613yes—
59#8533C12711yesmaximal, characteristic, direct product factor, Sylow
60C2×C127—41no—
61C2×C127#179313yes—
62#3556C2×C12711yescharacteristic
63#1994C2×C12713yes—
64#1561C2×C12713yes—
65C127#853311yescharacteristic, direct product factor, Sylow
66#564C4×C12714yescomplemented
67#557—26no—
68#541—26no—
69#533C22×C12713yes—
70#423C22×C12713yes—
71C43C22×C12711yescharacteristic
72#339—26no—
73#332—26no—
74C2×M16—23no—
75C4⋊Q8—26no—
76C4⋊Q8D4×C12716yes—
77#126—28no—
78#125—26no—
79#125—224no—
80#125C2×C4×C12716yes—
81C22⋊Q8—26no—
82C4×Q8—212no—
83C4×Q8—26no—
84#117D4×C12716yes—
85C2×C42—23no—
86C2×C42C23×C12711yescharacteristic
87C4⋊C8—26no—
88C2×Q8—26no—
89C22×C4—41no—
90C22×C4C2×D4×C12713yes—
91M16—46no—
92C2×C8—43no—
93C4⋊C4—224no—
94C4⋊C4—212no—
95C4⋊C4—26no—
96C4⋊C4C22⋊C4×C127112yes—
97C22⋊C4—26no—
98C42—28no—
99C42—26no—
100C42—26no—
101C42—43no—
102C42C22×C4×C12711yescharacteristic
103C42C2×D4×C12713yes—
104C23#120×C12711yescharacteristic
105Q8—46no—
106Q8—46no—
107C2×C4—23no—
108C2×C4—23no—
109C2×C4—212no—
110C2×C4—46no—
111C2×C4C2×C22⋊C4×C12713yes—
112C2×C4#120×C12713yes—
113C8—83no—
114C22—23no—
115C22#379×C12711yescharacteristic
116C4—23no—
117C4—44no—
118C4—412no—
119C4#454×C12713yes—
120C4#456×C12713yes—
121C2—41no—
122C2C127×#179313yes—
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. #564×C127C4semidirect
59. #8533C127direct (N × H)
65. C127#8533direct (N × H)
66. #564C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35562
C127×#19942
C127×#15612
#8533127