Finite Group Databasebeta

← #26104126

Subgroups — #26104126

Order 12032.

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

normal subgroups only

This group has 126 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#20242714C211yesmaximal, characteristic
2#20241423C211yesmaximal, characteristic
3C47×#1413C211yesmaximal, characteristic
4C47⋊#564C411yescharacteristic
5#15689529—21no—
6#15688901—21no—
7#15688865C411yescharacteristic
8#15688864—21no—
9C47×#491C2211yescharacteristic
10C47×#356—21no—
11#13094016—21no—
12#13094015—41no—
13#13094014—41no—
14#13094014—41no—
15#13093964—41no—
16#13093957—41no—
17#13093955—41no—
18#13093935—21no—
19C4⋊Q8×C47D411yescharacteristic
20#125×C47C2×C411yescharacteristic
21#103×C47—41no—
22#101×C47—41no—
23#97×C47D411yescharacteristic
24C2×Q8×C47—21no—
25M16×C47—81no—
26C2×C8×C47—21no—
27C4⋊C4×C47—21no—
28C4⋊C4×C47—41no—
29C4⋊C4×C47—41no—
30C42×C47C22⋊C411yescharacteristic
31C4⋊Dic47—21no—
32C4⋊Dic47—21no—
33C4⋊Dic47—41no—
34Dic47⋊C4—41no—
35Dic47⋊C4—41no—
36Dic47⋊C4—41no—
37Dic47⋊C4—41no—
38C4×Dic47—41no—
39C2×C47⋊C8—41no—
40C47⋊C16—42no—
41Q8×C47—81no—
42C2×C4×C47—21no—
43C2×C4×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47#9911yescharacteristic
46C2×Dic47—41no—
47C2×Dic47—41no—
48C8×C47—41no—
49C8×C47—161no—
50C47⋊C8—42no—
51#7526—471nomaximal, Sylow
52C22×C47AΣL(1,𝔽16)11yescharacteristic
53C4×C47—21no—
54C4×C47—41no—
55C4×C47—81no—
56C4×C47—81no—
57Dic47—81no—
58Dic47—81no—
59#1663—471no—
60#1413D4711yescharacteristic
61#1356—471no—
62C2×C47—21no—
63C2×C47#140411yescharacteristic
64#564—471no—
65#501—941no—
66#491C2×D4711yescharacteristic
67#356—21no—
68#347—941no—
69#330—471no—
70#330—941no—
71C47#752611yescharacteristic, complemented, Sylow
72C4⋊Q8C22⋊D4711yescharacteristic
73#125—941no—
74#125—1881no—
75#125—1881no—
76#125—1881no—
77#125C4×D4711yescharacteristic
78M32—1881no—
79#107—1881no—
80#106—1881no—
81#103—41no—
82#101—41no—
83#97—941no—
84#97D18811yescharacteristic
85C2×Q8—21no—
86M16—81no—
87C2×C8—21no—
88C2×C8—1881no—
89C4⋊C4—21no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—941no—
93C4⋊C4—941no—
94C4⋊C4—1881no—
95C4⋊C4—1881no—
96C4⋊C4—1881no—
97C4⋊C4—1881no—
98C4⋊C4—1881no—
99C42—1881no—
100C42(C2×D47)⋊C411yescharacteristic
101C16—1882no—
102Q8—81no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—1881no—
107C2×C4—1881no—
108C2×C4#1309393811yescharacteristic
109C8—41no—
110C8—161no—
111C8—1882no—
112C22#1568890911yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—81no—
117C4—3761no—
118C4—3761no—
119C2—21no—
120C2#2024153811yescharacteristic
subgroupG/H
centerC2#20241538
commutator#125×C47C2×C4
Frattini#491C2×D47
FittingC47×#1413C2
socleC2×C47#1404
prime radicalC22×C47AΣL(1,𝔽16)
cosocleC47×#491C22
hypercenter#1413D47
hypocenterC47#7526
LCSG ▷ #125×C47 ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1413

Complements

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

NH ≅ G/Ntype
71. C47#7526semidirect

Maximal subgroups

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

subgroupindex
#202427142
#202414232
C47×#14132
#752647