Finite Group Databasebeta

← #26104151

Subgroups — #26104151

Order 12032.

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

normal subgroups only

This group has 150 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#20242974C211yesmaximal, characteristic
2#20241553C211yesmaximal, characteristic
3C47×#1410C211yesmaximal, characteristic
4#15689521C411yescharacteristic, complemented
5#15689519—21no—
6#15689495—21no—
7#15688916—21no—
8C8×C47⋊C8C411yescharacteristic, complemented
9C47×#492C2211yescharacteristic
10C47×#356—21no—
11C2×#10625335—42no—
12#13094024—21no—
13#13093956—41no—
14#13093955—42no—
15#13093939—41no—
16C4×C47⋊C8—21no—
17C2×SD16×C47—41no—
18C4⋊Q8×C47D411yescharacteristic
19#127×C47D411yescharacteristic
20#101×C47—41no—
21C4×C8×C47C2×C411yescharacteristic
22C2×Q8×C47—21no—
23C2×D4×C47—21no—
24C2×D4×C47—41no—
25C2×Dic94—41no—
26SD16×C47—82no—
27M16×C47—81no—
28C2×C8×C47—21no—
29C4⋊C4×C47—41no—
30C42×C47C22⋊C411yescharacteristic
31C22⋊Dic47—81no—
32#10625335—84no—
33C4⋊Dic47—41no—
34C4⋊Dic47—41no—
35C2×C47⋊C8—22no—
36C23×C47—41no—
37Q8×C47—81no—
38D4×C47—81no—
39D4×C47—82no—
40C2×C4×C47—21no—
41C2×C4×C47—41no—
42C2×C4×C47#9911yescharacteristic
43C2×Dic47—81no—
44C2×Dic47—161no—
45Dic94—82no—
46C8×C47—22no—
47C8×C47—161no—
48C47⋊C8—24no—
49#7535—471nomaximal, Sylow
50C22×C47—81no—
51C22×C47—161no—
52C22×C47#35311yescharacteristic
53C4×C47—22no—
54C4×C47—21no—
55C4×C47—81no—
56Dic47—161no—
57Dic47—321no—
58#1705—471no—
59#1410D4711yescharacteristic
60#1409—471no—
61C2×C47—21no—
62C2×C47—161no—
63C2×C47#140911yescharacteristic
64#498—471no—
65#498—941no—
66#492—941no—
67#492C2×D4711yescharacteristic
68#356—21no—
69#353—941no—
70C82—471no—
71C47#753511yescharacteristic, complemented, Sylow
72C2×SD16—41no—
73C2×SD16—1882no—
74C4⋊Q8—941no—
75C4⋊Q8C22⋊D4711yescharacteristic
76#127D18811yescharacteristic
77#106—1882no—
78#106—1881no—
79#101—41no—
80#99—1881no—
81C4×C8—941no—
82C4×C8C4×D4711yescharacteristic
83C2×Q8—21no—
84C2×Q8—1881no—
85C2×D4—21no—
86C2×D4—41no—
87SD16—82no—
88SD16—3764no—
89M16—81no—
90C2×C8—21no—
91C2×C8—942no—
92C4⋊C4—41no—
93C4⋊C4—1881no—
94C4⋊C4—1881no—
95C22⋊C4—3761no—
96C42(C2×D47)⋊C411yescharacteristic
97C23—41no—
98Q8—81no—
99Q8—3762no—
100D4—81no—
101D4—82no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—3761no—
105C2×C4—7521no—
106C2×C4#1309393811yescharacteristic
107C8—22no—
108C8—161no—
109C8—944no—
110C22—81no—
111C22—161no—
112C22#1568891511yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—15041no—
117C4—7521no—
118C2—21no—
119C2—161no—
120C2#2024155211yescharacteristic
subgroupG/H
centerC2#20241552
commutatorC4×C8×C47C2×C4
Frattini#492C2×D47
FittingC47×#1410C2
socleC2×C47#1409
prime radical#127×C47D4
cosocleC47×#492C22
hypercenter#1410D47
hypocenterC47#7535
LCSG ▷ C4×C8×C47 ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1410

Complements

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

NH ≅ G/Ntype
4. #15689521C4semidirect
8. C8×C47⋊C8C4semidirect
71. C47#7535semidirect

Maximal subgroups

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

subgroupindex
#202429742
#202415532
C47×#14102
#753547