Finite Group Databasebeta

← #26104152

Subgroups — #26104152

Order 12032.

138 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 25 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#20242987C211yesmaximal, characteristic
2#20241555C211yesmaximal, characteristic
3C47×#1409C211yesmaximal, characteristic
4#15689521C411yescharacteristic, complemented
5#15689475—21no—
6#15689469—21no—
7#15688922—21no—
8C8×C47⋊C8C411yescharacteristic, complemented
9C47×#492C2211yescharacteristic
10C47×#353—21no—
11#13094024—21no—
12#13093956—41no—
13#13093947—42no—
14#13093945—42no—
15#13093943—41no—
16C4×C47⋊C8—21no—
17C2×SD16×C47—41no—
18C4⋊Q8×C47D411yescharacteristic
19#127×C47D411yescharacteristic
20#99×C47—41no—
21C4×C8×C47C2×C411yescharacteristic
22C2×Q8×C47—21no—
23C2×D4×C47—21no—
24C2×D4×C47—41no—
25C2×Dic94—41no—
26SD16×C47—82no—
27C2×C8×C47—21no—
28C4⋊C4×C47—41no—
29C22⋊C4×C47—81no—
30C42×C47C22⋊C411yescharacteristic
31C4⋊Dic47—41no—
32C4⋊Dic47—41no—
33#10625329—81no—
34C2×C47⋊C8—22no—
35C23×C47—41no—
36Q8×C47—81no—
37D4×C47—81no—
38D4×C47—82no—
39C2×C4×C47—21no—
40C2×C4×C47—41no—
41C2×C4×C47—161no—
42C2×C4×C47#9911yescharacteristic
43C2×Dic47—81no—
44Dic94—82no—
45C8×C47—22no—
46C47⋊C8—42no—
47C47⋊C8—161no—
48#7536—471nomaximal, Sylow
49C22×C47—81no—
50C22×C47—161no—
51C22×C47#35311yescharacteristic
52C4×C47—22no—
53C4×C47—21no—
54C4×C47—81no—
55C4×C47—321no—
56Dic47—161no—
57#1708—471no—
58#1410—471no—
59#1409D4711yescharacteristic
60C2×C47—21no—
61C2×C47—161no—
62C2×C47#140911yescharacteristic
63#498—471no—
64#492C2×D4711yescharacteristic
65#487—941no—
66#486—941no—
67#356—941no—
68#353—21no—
69C82—471no—
70C47#753611yescharacteristic, complemented, Sylow
71C2×SD16—41no—
72C4⋊Q8—941no—
73C4⋊Q8D18811yescharacteristic
74#127C22⋊D4711yescharacteristic
75#106—1881no—
76#103—1882no—
77#102—1882no—
78#101—1881no—
79#99—41no—
80C4×C8—941no—
81C4×C8C4×D4711yescharacteristic
82C2×Q8—21no—
83C2×Q8—1881no—
84C2×D4—21no—
85C2×D4—41no—
86SD16—82no—
87M16—3761no—
88C2×C8—21no—
89C2×C8—942no—
90C4⋊C4—41no—
91C4⋊C4—1881no—
92C4⋊C4—1881no—
93C22⋊C4—81no—
94C42(C2×D47)⋊C411yescharacteristic
95C23—41no—
96Q8—81no—
97Q8—3762no—
98D4—81no—
99D4—82no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—161no—
103C2×C4—3761no—
104C2×C4#1309393811yescharacteristic
105C8—22no—
106C8—1882no—
107C8—7521no—
108C22—81no—
109C22—161no—
110C22#1568891511yescharacteristic
111C4—22no—
112C4—21no—
113C4—81no—
114C4—321no—
115C4—7521no—
116C2—21no—
117C2—161no—
118C2#2024155211yescharacteristic
subgroupG/H
centerC2#20241552
commutatorC4×C8×C47C2×C4
Frattini#492C2×D47
FittingC47×#1409C2
socleC2×C47#1409
prime radical#127×C47D4
cosocleC47×#492C22
hypercenter#1409D47
hypocenterC47#7536
LCSG ▷ C4×C8×C47 ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1409

Complements

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

NH ≅ G/Ntype
4. #15689521C4semidirect
8. C8×C47⋊C8C4semidirect
70. C47#7536semidirect

Maximal subgroups

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

subgroupindex
#202429872
#202415552
C47×#14092
#753647