Finite Group Databasebeta

← C47×#10339 #26050037

Subgroups — C47×#10339 #26050037

Order 12032.

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
1C47×#2483C213yesmaximal
2C47×#1819C213yesmaximal
3C47×#1304C211yesmaximal, characteristic
4C22×C22⋊C4×C47C2213yes—
5C47×#397—26no—
6C47×#385—26no—
7C47×#381—26no—
8C47×#379C2211yescharacteristic
9C47×#379C2213yes—
10C47×#342—26no—
11C25×C47C2311yescharacteristic
12C23×C4×C47D416yes—
13C2×C4⋊C4×C47—26no—
14C2×C22⋊C4×C47—23no—
15C2×C22⋊C4×C47—26no—
16C2×C22⋊C4×C47—26no—
17C2×C22⋊C4×C47—26no—
18C2×C22⋊C4×C47—23no—
19C2×C22⋊C4×C47—23no—
20C2×C22⋊C4×C47D416yes—
21#95×C47—26no—
22#95×C47—212no—
23C24×C47—46no—
24C24×C47C2×D413yes—
25C24×C47C2×D413yes—
26C24×C47#4111yescharacteristic
27C22×C4×C47—26no—
28C22×C4×C47—26no—
29C22×C4×C47—26no—
30C22×C4×C47—26no—
31C22×C4×C47—412no—
32C22×C4×C47—41no—
33C4⋊C4×C47—86no—
34C22⋊C4×C47—412no—
35C22⋊C4×C47—43no—
36C22⋊C4×C47—46no—
37C22⋊C4×C47—43no—
38C22⋊C4×C47—46no—
39C22⋊C4×C47—46no—
40C23×C47—212no—
41C23×C47—26no—
42C23×C47—43no—
43C23×C47—46no—
44C23×C47—43no—
45C23×C47—88no—
46C23×C47#12013yes—
47C23×C47#12113yes—
48C23×C47#12711yescharacteristic
49C2×C4×C47—412no—
50C2×C4×C47—412no—
51C2×C4×C47—46no—
52C2×C4×C47—46no—
53C2×C4×C47—412no—
54C2×C4×C47—86no—
55C2×C4×C47—83no—
56#10339C4711yesmaximal, characteristic, direct product factor, Sylow
57C22×C47—26no—
58C22×C47—26no—
59C22×C47—23no—
60C22×C47—23no—
61C22×C47—412no—
62C22×C47—86no—
63C22×C47—82no—
64C22×C47#39211yescharacteristic
65C22×C47#45816yes—
66C4×C47—86no—
67C4×C47—86no—
68C4×C47—161no—
69#2483C2×C4713yes—
70#1819C2×C4713yes—
71#1304C2×C4711yescharacteristic
72C2×C47—26no—
73C2×C47—41no—
74C2×C47—43no—
75C2×C47#202213yes—
76C22×C22⋊C4C22×C4713yes—
77#397—26no—
78#385—26no—
79#381—26no—
80#379C22×C4711yescharacteristic
81#379C22×C4713yes—
82#342—26no—
83C47#1033911yescharacteristic, direct product factor, Sylow
84C25C23×C4711yescharacteristic
85C23×C4D4×C4716yes—
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×C4716yes—
94#95—26no—
95#95—212no—
96C24—46no—
97C24C2×D4×C4713yes—
98C24C2×D4×C4713yes—
99C24#41×C4711yescharacteristic
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×C4713yes—
120C23#121×C4713yes—
121C23#127×C4711yescharacteristic
122C2×C4—412no—
123C2×C4—412no—
124C2×C4—46no—
125C2×C4—412no—
126C2×C4—46no—
127C2×C4—86no—
128C2×C4—83no—
129C22—26no—
130C22—26no—
131C22—23no—
132C22—23no—
133C22—412no—
134C22—86no—
135C22—82no—
136C22C47×#39211yescharacteristic
137C22C47×#45816yes—
138C4—86no—
139C4—86no—
140C4—161no—
141C2—26no—
142C2—41no—
143C2—43no—
144C2C47×#202213yes—
subgroupG/H
center, socleC22×C47#392
commutator, Frattini, cosocleC25C23×C47
prime radicalC25×C47C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
56. #10339C47direct (N × H)
83. C47#10339direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#24832
C47×#18192
C47×#13042
#1033947