Finite Group Databasebeta

← #26104103

Subgroups — #26104103

Order 12032.

148 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 27 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#20241555C211yesmaximal, characteristic
2#20241429C211yesmaximal, characteristic
3C47×#1630C211yesmaximal, characteristic
4#15688944—21no—
5#15688922—21no—
6C47×#559C411yescharacteristic
7C47×#492C2211yescharacteristic
8C47×#477—21no—
9C47×#331C411yescharacteristic
10C47×Q8⋊C8—21no—
11#13093964—41no—
12#13093943—41no—
13C2×SD16×C47—41no—
14C4⋊Q8×C47D411yescharacteristic
15#127×C47C2×C411yescharacteristic
16#124×C47—41no—
17#123×C47—41no—
18C4×Q8×C47—21no—
19C4×D4×C47—41no—
20#107×C47—41no—
21C4⋊C8×C47—21no—
22#103×C47—41no—
23C4×C8×C47D411yescharacteristic
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—41no—
28C22×C4×C47—41no—
29SD16×C47—81no—
30SD16×C47—81no—
31C2×C8×C47—21no—
32C2×C8×C47—41no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—41no—
35C4⋊C4×C47—41no—
36C22⋊C4×C47—42no—
37C22⋊C4×C47—41no—
38C42×C47—41no—
39C42×C47C22⋊C411yescharacteristic
40#10625329—81no—
41C47⋊C16—81no—
42C23×C47—41no—
43Q8×C47—41no—
44Q8×C47—41no—
45Q8×C47—81no—
46D4×C47—81no—
47D4×C47—81no—
48D4×C47—81no—
49C2×C4×C47—21no—
50C2×C4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—161no—
54C2×C4×C47#9911yescharacteristic
55C8×C47—21no—
56C8×C47—21no—
57C8×C47—81no—
58C47⋊C8—161no—
59#7518—471nomaximal, Sylow
60C22×C47—82no—
61C22×C47—81no—
62C22×C47AΣL(1,𝔽16)11yescharacteristic
63C4×C47—21no—
64C4×C47—21no—
65C4×C47—21no—
66C4×C47—81no—
67C4×C47—81no—
68C4×C47—81no—
69#1630D4711yescharacteristic
70#1410—471no—
71#1359—471no—
72C2×C47—21no—
73C2×C47—161no—
74C2×C47#140211yescharacteristic
75#559Dic4711yescharacteristic
76#492C2×D4711yescharacteristic
77#477—21no—
78#364—941no—
79#356—941no—
80#331Dic4711yescharacteristic
81Q8⋊C8—21no—
82C47#751811yescharacteristic, complemented, Sylow
83C2×SD16—41no—
84C4⋊Q8C22⋊D4711yescharacteristic
85#127C2×Dic4711yescharacteristic
86#124—41no—
87#123—41no—
88C4×Q8—21no—
89C4×D4—41no—
90M32—1881no—
91#107—41no—
92C4⋊C8—21no—
93#103—41no—
94#101—1881no—
95C4×C8C22⋊D4711yescharacteristic
96C2×Q8—21no—
97C2×Q8—21no—
98C2×D4—21no—
99C2×D4—41no—
100C22×C4—41no—
101SD16—81no—
102SD16—81no—
103M16—3761no—
104C2×C8—21no—
105C2×C8—41no—
106C4⋊C4—21no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C22⋊C4—42no—
110C22⋊C4—41no—
111C42—41no—
112C42C22⋊Dic4711yescharacteristic
113C16—3761no—
114C23—41no—
115Q8—41no—
116Q8—41no—
117Q8—81no—
118D4—81no—
119D4—81no—
120D4—81no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—161no—
126C2×C4#1309393911yescharacteristic
127C8—21no—
128C8—21no—
129C8—81no—
130C8—7521no—
131C22—82no—
132C22—81no—
133C22#1568891011yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—81no—
138C4—81no—
139C4—81no—
140C2—21no—
141C2—161no—
142C2#2024153311yescharacteristic
subgroupG/H
centerC2#20241533
commutator, prime radical#127×C47C2×C4
Frattini#492C2×D47
FittingC47×#1630C2
socleC2×C47#1402
cosocleC47×#492C22
hypercenter#1630D47
hypocenterC47#7518
LCSG ▷ #127×C47 ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1630

Complements

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

NH ≅ G/Ntype
82. C47#7518semidirect

Maximal subgroups

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

subgroupindex
#202415552
#202414292
C47×#16302
#751847