Finite Group Databasebeta

← C127×#10583 #44574256

Subgroups — C127×#10583 #44574256

Order 32512.

406 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2844C211yesmaximal, characteristic
2C127×#1847C213yesmaximal
3C127×#1295C213yesmaximal
4C2×#107×C127—23no—
5C2×#106×C127—23no—
6C2×#97×C127C2213yes—
7#400×C127—23no—
8#395×C127—23no—
9#384×C127C2211yescharacteristic
10#382×C127C2213yes—
11C22×Q8×C127—21no—
12C22×C8×C127—23no—
13C2×C4⋊C4×C127—23no—
14C2×C4⋊C4×C127—23no—
15C2×C4⋊C4×C127D413yes—
16C2×C4⋊C4×C127D413yes—
17C2×C42×C127C2311yescharacteristic
18#107×C127—46no—
19#106×C127—46no—
20#97×C127—23no—
21#97×C127Q816yescomplemented
22#95×C127—23no—
23#95×C127—21no—
24#95×C127—26no—
25C2×Q8×C127—83no—
26C22×C4×C127—23no—
27C22×C4×C127—23no—
28C22×C4×C127—41no—
29C22×C4×C127C2×D413yes—
30C2×C8×C127—26no—
31C2×C8×C127—26no—
32C2×C8×C127—26no—
33C4⋊C4×C127—43no—
34C4⋊C4×C127—43no—
35C4⋊C4×C127—43no—
36C4⋊C4×C127—43no—
37C4⋊C4×C127—83no—
38C42×C127C2×Q813yes—
39C42×C127#4111yescharacteristic
40C23×C127#12011yescharacteristic
41Q8×C127—84no—
42C2×C4×C127—23no—
43C2×C4×C127—23no—
44C2×C4×C127—43no—
45C2×C4×C127—43no—
46C2×C4×C127—46no—
47C2×C4×C127—46no—
48C2×C4×C127—83no—
49C2×C4×C127C22⋊Q813yes—
50C2×C4×C127C4⋊Q813yes—
51C8×C127—212no—
52C22×C127#39511yescharacteristic
53C22×C127#45313yes—
54C22×C127#45613yes—
55C4×C127—23no—
56C4×C127—23no—
57C4×C127—83no—
58C4×C127—83no—
59C4×C127—161no—
60#10583C12711yesmaximal, characteristic, direct product factor, Sylow
61C2×C127#165511yescharacteristic
62C2×C127#166013yes—
63C2×C127#206013yes—
64#2844C2×C12711yescharacteristic
65#1847C2×C12713yes—
66#1295C2×C12713yes—
67C127#1058311yescharacteristic, direct product factor, Sylow
68C2×#107—23no—
69C2×#106—23no—
70C2×#97C22×C12713yes—
71#400—23no—
72#395—23no—
73#384C22×C12711yescharacteristic
74#382C22×C12713yes—
75C22×Q8—21no—
76C22×C8—23no—
77C2×C4⋊C4—23no—
78C2×C4⋊C4—23no—
79C2×C4⋊C4D4×C12713yes—
80C2×C4⋊C4D4×C12713yes—
81C2×C42C23×C12711yescharacteristic
82#107—46no—
83#106—46no—
84#97—23no—
85#97Q8×C12716yescomplemented
86#95—23no—
87#95—21no—
88#95—26no—
89C2×Q8—83no—
90C22×C4—23no—
91C22×C4—23no—
92C22×C4—41no—
93C22×C4C2×D4×C12713yes—
94C2×C8—26no—
95C2×C8—26no—
96C2×C8—26no—
97C4⋊C4—43no—
98C4⋊C4—43no—
99C4⋊C4—43no—
100C4⋊C4—43no—
101C4⋊C4—83no—
102C42C2×Q8×C12713yes—
103C42#41×C12711yescharacteristic
104C23#120×C12711yescharacteristic
105Q8—84no—
106C2×C4—23no—
107C2×C4—23no—
108C2×C4—43no—
109C2×C4—43no—
110C2×C4—46no—
111C2×C4—46no—
112C2×C4—83no—
113C2×C4C22⋊Q8×C12713yes—
114C2×C4C4⋊Q8×C12713yes—
115C8—212no—
116C22#395×C12711yescharacteristic
117C22#453×C12713yes—
118C22#456×C12713yes—
119C4—23no—
120C4—23no—
121C4—83no—
122C4—83no—
123C4—161no—
124C2C127×#165511yescharacteristic
125C2C127×#166013yes—
126C2C127×#206013yes—
subgroupG/H
center, socle, prime radicalC23×C127#120
commutator, Frattini, cosocleC2×C42C23×C127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
21. #97×C127Q8semidirect
60. #10583C127direct (N × H)
67. C127#10583direct (N × H)
85. #97Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#28442
C127×#18472
C127×#12952
#10583127