Finite Group Databasebeta

← C127×#10339 #44574012

Subgroups — C127×#10339 #44574012

Order 32512.

738 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2483C213yesmaximal
2C127×#1819C213yesmaximal
3C127×#1304C211yesmaximal, characteristic
4C22×C22⋊C4×C127C2213yes—
5#397×C127—26no—
6#385×C127—26no—
7#381×C127—26no—
8#379×C127C2211yescharacteristic
9#379×C127C2213yes—
10#342×C127—26no—
11C25×C127C2311yescharacteristic
12C23×C4×C127D416yes—
13C2×C4⋊C4×C127—26no—
14C2×C22⋊C4×C127—23no—
15C2×C22⋊C4×C127—26no—
16C2×C22⋊C4×C127—26no—
17C2×C22⋊C4×C127—26no—
18C2×C22⋊C4×C127—23no—
19C2×C22⋊C4×C127—23no—
20C2×C22⋊C4×C127D416yes—
21#95×C127—26no—
22#95×C127—212no—
23C24×C127—46no—
24C24×C127C2×D413yes—
25C24×C127C2×D413yes—
26C24×C127#4111yescharacteristic
27C22×C4×C127—26no—
28C22×C4×C127—26no—
29C22×C4×C127—26no—
30C22×C4×C127—26no—
31C22×C4×C127—412no—
32C22×C4×C127—41no—
33C4⋊C4×C127—86no—
34C22⋊C4×C127—412no—
35C22⋊C4×C127—43no—
36C22⋊C4×C127—46no—
37C22⋊C4×C127—43no—
38C22⋊C4×C127—46no—
39C22⋊C4×C127—46no—
40C23×C127—212no—
41C23×C127—26no—
42C23×C127—43no—
43C23×C127—46no—
44C23×C127—43no—
45C23×C127—88no—
46C23×C127#12013yes—
47C23×C127#12113yes—
48C23×C127#12711yescharacteristic
49C2×C4×C127—412no—
50C2×C4×C127—412no—
51C2×C4×C127—46no—
52C2×C4×C127—46no—
53C2×C4×C127—412no—
54C2×C4×C127—86no—
55C2×C4×C127—83no—
56C22×C127—26no—
57C22×C127—26no—
58C22×C127—23no—
59C22×C127—23no—
60C22×C127—412no—
61C22×C127—86no—
62C22×C127—82no—
63C22×C127#39211yescharacteristic
64C22×C127#45816yes—
65C4×C127—86no—
66C4×C127—86no—
67C4×C127—161no—
68#10339C12711yesmaximal, characteristic, direct product factor, Sylow
69C2×C127—26no—
70C2×C127—41no—
71C2×C127—43no—
72C2×C127#202213yes—
73#2483C2×C12713yes—
74#1819C2×C12713yes—
75#1304C2×C12711yescharacteristic
76C127#1033911yescharacteristic, direct product factor, Sylow
77C22×C22⋊C4C22×C12713yes—
78#397—26no—
79#385—26no—
80#381—26no—
81#379C22×C12711yescharacteristic
82#379C22×C12713yes—
83#342—26no—
84C25C23×C12711yescharacteristic
85C23×C4D4×C12716yes—
86C2×C4⋊C4—26no—
87C2×C22⋊C4—23no—
88C2×C22⋊C4—26no—
89C2×C22⋊C4—26no—
90C2×C22⋊C4—26no—
91C2×C22⋊C4—23no—
92C2×C22⋊C4—23no—
93C2×C22⋊C4D4×C12716yes—
94#95—26no—
95#95—212no—
96C24—46no—
97C24C2×D4×C12713yes—
98C24C2×D4×C12713yes—
99C24#41×C12711yescharacteristic
100C22×C4—26no—
101C22×C4—26no—
102C22×C4—26no—
103C22×C4—26no—
104C22×C4—412no—
105C22×C4—41no—
106C4⋊C4—86no—
107C22⋊C4—412no—
108C22⋊C4—43no—
109C22⋊C4—46no—
110C22⋊C4—43no—
111C22⋊C4—46no—
112C22⋊C4—46no—
113C23—212no—
114C23—26no—
115C23—43no—
116C23—46no—
117C23—43no—
118C23—88no—
119C23#120×C12713yes—
120C23#121×C12713yes—
121C23#127×C12711yescharacteristic
122C2×C4—412no—
123C2×C4—412no—
124C2×C4—46no—
125C2×C4—46no—
126C2×C4—412no—
127C2×C4—86no—
128C2×C4—83no—
129C22—26no—
130C22—26no—
131C22—23no—
132C22—23no—
133C22—412no—
134C22—86no—
135C22—82no—
136C22#392×C12711yescharacteristic
137C22#458×C12716yes—
138C4—86no—
139C4—86no—
140C4—161no—
141C2—26no—
142C2—41no—
143C2—43no—
144C2C127×#202213yes—
subgroupG/H
center, socleC22×C127#392
commutator, Frattini, cosocleC25C23×C127
prime radicalC25×C127C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
68. #10339C127direct (N × H)
76. C127#10339direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#24832
C127×#18192
C127×#13042
#10339127