Finite Group Databasebeta

← #26104123

Subgroups — #26104123

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#20242709C211yesmaximal, characteristic
2#20241423C211yesmaximal, characteristic, complemented
3C47×#1413C211yesmaximal, characteristic, complemented
4#15689871C411yescharacteristic
5#15689485—21no—
6#15688901—21no—
7#15688865C411yescharacteristic
8#15688862—21no—
9C47×#491C2211yescharacteristic
10C47×#356—21no—
11#13094012—21no—
12#13094009—41no—
13#13094002—41no—
14#13093999—41no—
15#13093964—41no—
16#13093947—41no—
17#13093944—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—
25C2×D188—21no—
26C2×D188—41no—
27C2×C4×D47—41no—
28C2×Dic94—21no—
29M16×C47—81no—
30C2×C8×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—41no—
33C4⋊C4×C47—41no—
34C42×C47C22⋊C411yescharacteristic
35(C2×D47)⋊C4—41no—
36(C2×D47)⋊C4—41no—
37(C2×D47)⋊C4—41no—
38Dic47⋊C4—41no—
39C2×C47⋊C8—41no—
40C47⋊C16—42no—
41C22×D47—41no—
42Q8×C47—81no—
43C2×C4×C47—21no—
44C2×C4×C47—41no—
45C2×C4×C47—41no—
46C2×C4×C47#9911yescharacteristic
47C2×Dic47—41no—
48D188—81no—
49D188—161no—
50C4×D47—161no—
51Dic94—81no—
52C8×C47—41no—
53C8×C47—161no—
54C47⋊C8—81no—
55#7525—471nomaximal, Sylow
56C22×C47AΣL(1,𝔽16)11yescharacteristic
57C2×D47—81no—
58C2×D47—81no—
59C2×D47—81no—
60C4×C47—21no—
61C4×C47—41no—
62C4×C47—81no—
63C4×C47—81no—
64Dic47—81no—
65#1662—471no—
66#1413D4711yescharacteristic, complemented
67#1356—471no—
68C2×C47—21no—
69C2×C47#140411yescharacteristic
70D47—161no—
71#562—471no—
72#491C2×D4711yescharacteristic
73#489—941no—
74#356—21no—
75#347—941no—
76#330—471no—
77#329—941no—
78C47#752511yescharacteristic, complemented, Sylow
79C4⋊Q8C22⋊D4711yescharacteristic
80#125C4×D4711yescharacteristic
81#124—941no—
82#123—1881no—
83C22⋊Q8—1881no—
84#121—1881no—
85M32—1881no—
86#103—41no—
87#103—1881no—
88#102—1881no—
89#101—41no—
90#97—941no—
91#97D18811yescharacteristic
92C2×Q8—21no—
93C2×Q8—941no—
94C2×D4—941no—
95C2×D4—1881no—
96C22×C4—1881no—
97M16—81no—
98C2×C8—21no—
99C2×C8—1881no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—1881no—
104C22⋊C4—1881no—
105C22⋊C4—1881no—
106C22⋊C4—1881no—
107C42(C2×D47)⋊C411yescharacteristic
108C16—1882no—
109C23—1881no—
110Q8—81no—
111Q8—3761no—
112D4—3761no—
113D4—7521no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—1881no—
118C2×C4—7521no—
119C2×C4#1309393811yescharacteristic
120C8—41no—
121C8—161no—
122C8—3761no—
123C22—3761no—
124C22—3761no—
125C22—3761no—
126C22#1568890911yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—3761no—
132C2—21no—
133C2—7521no—
134C2#2024153811yescharacteristic
subgroupG/H
centerC2#20241538
commutator#125×C47C2×C4
Frattini#491C2×D47
FittingC47×#1413C2
socleC2×C47#1404
prime radical#15689871C4
cosocleC47×#491C22
hypercenter#1413D47
hypocenterC47#7525
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
2. #20241423C2semidirect
3. C47×#1413C2semidirect
66. #1413D47semidirect
78. C47#7525semidirect

Maximal subgroups

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

subgroupindex
#202427092
#202414232
C47×#14132
#752547