Finite Group Databasebeta

← #26119244

Subgroups — #26119244

Order 12032.

738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 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#20247669C213yesmaximal
2#20243460C213yesmaximal
3C47×#1304C211yesmaximal, characteristic
4C22×C22⋊Dic47C2213yes—
5#15689048—26no—
6#15688998—26no—
7#15688984—26no—
8#15688979C2211yescharacteristic
9#15688889—26no—
10C47×#379C2213yes—
11C23×Dic47D416yes—
12C2×C4⋊Dic47—26no—
13C2×C22⋊Dic47—26no—
14C2×C22⋊Dic47—26no—
15C2×C22⋊Dic47—23no—
16C2×C22⋊Dic47—23no—
17C2×C22⋊Dic47—23no—
18C47⋊#95—26no—
19C47⋊#95—212no—
20C25×C47C2311yescharacteristic
21C2×C22⋊C4×C47—26no—
22C2×C22⋊C4×C47D416yes—
23C24×C47—46no—
24C24×C47C2×D413yes—
25C24×C47C2×D413yes—
26C24×C47#4111yescharacteristic
27C22×C4×C47—26no—
28C22×Dic47—26no—
29C22×Dic47—26no—
30C22×Dic47—26no—
31C22×Dic47—412no—
32C22×Dic47—41no—
33C22⋊C4×C47—412no—
34C22⋊C4×C47—46no—
35C22⋊Dic47—43no—
36C22⋊Dic47—46no—
37C22⋊Dic47—43no—
38C22⋊Dic47—46no—
39C4⋊Dic47—86no—
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—46no—
51C2×Dic47—412no—
52C2×Dic47—46no—
53C2×Dic47—412no—
54C2×Dic47—86no—
55C2×Dic47—83no—
56#10339—471nomaximal, 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—
67Dic47—86no—
68Dic47—161no—
69#2483—473no—
70#1819—473no—
71#1304D4711yescharacteristic
72C2×C47—26no—
73C2×C47—41no—
74C2×C47—43no—
75C2×C47#202213yes—
76C22×C22⋊C4—473no—
77#397—946no—
78#385—946no—
79#381—946no—
80#379—471no—
81#379C2×D4713yes—
82#342—946no—
83C47#1033911yescharacteristic, complemented, Sylow
84C25C22×D4711yescharacteristic
85C23×C4—476no—
86C2×C4⋊C4—946no—
87C2×C22⋊C4—26no—
88C2×C22⋊C4—943no—
89C2×C22⋊C4—946no—
90C2×C22⋊C4—946no—
91C2×C22⋊C4—943no—
92C2×C22⋊C4—943no—
93C2×C22⋊C4D18816yes—
94#95—946no—
95#95—9412no—
96C24—46no—
97C24C2×D18813yes—
98C24D4×D4713yes—
99C24#1062535411yescharacteristic
100C22×C4—26no—
101C22×C4—946no—
102C22×C4—946no—
103C22×C4—946no—
104C22×C4—1881no—
105C22×C4—18812no—
106C4⋊C4—3766no—
107C22⋊C4—412no—
108C22⋊C4—46no—
109C22⋊C4—1886no—
110C22⋊C4—1883no—
111C22⋊C4—1886no—
112C22⋊C4—1883no—
113C23—212no—
114C23—26no—
115C23—43no—
116C23—46no—
117C23—43no—
118C23—88no—
119C23#1309399413yes—
120C23#1309399913yes—
121C23#1309402111yescharacteristic
122C2×C4—412no—
123C2×C4—46no—
124C2×C4—3766no—
125C2×C4—3763no—
126C2×C4—18812no—
127C2×C4—1886no—
128C2×C4—18812no—
129C22—26no—
130C22—26no—
131C22—23no—
132C22—23no—
133C22—412no—
134C22—86no—
135C22—82no—
136C22#1568903311yescharacteristic
137C22#1568931416yes—
138C4—86no—
139C4—3766no—
140C4—7521no—
141C2—26no—
142C2—41no—
143C2—43no—
144C2#2024452013yes—
subgroupG/H
centerC22#15689033
commutator, prime radical, cosocleC25×C47C23
FrattiniC25C22×D47
FittingC47×#1304C2
socleC22×C47#392
hypercenter#1304D47
hypocenterC47#10339
LCSG ▷ C25×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
83. C47#10339semidirect

Maximal subgroups

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

subgroupindex
#202476692
#202434602
C47×#13042
#1033947