Finite Group Databasebeta

← #26104131

Subgroups — #26104131

Order 12032.

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

normal subgroups only

This group has 164 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#20243052C211yesmaximal, characteristic
2#20241553C211yesmaximal, characteristic, complemented
3C47×#1410C211yesmaximal, characteristic, complemented
4#15689500C411yescharacteristic, complemented
5#15689499—21no—
6#15689471—21no—
7#15688916—21no—
8#15688844C411yescharacteristic, complemented
9C47×#492C2211yescharacteristic
10C47×#356—21no—
11C2×D376—41no—
12C2×#10625334—42no—
13#13094021—21no—
14#13093944—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×D188—41no—
26C2×D188—41no—
27C2×D188—41no—
28SD16×C47—82no—
29M16×C47—81no—
30C2×C8×C47—21no—
31C4⋊C4×C47—41no—
32C42×C47C22⋊C411yescharacteristic
33C22⋊Dic47—81no—
34#10625334—84no—
35C2×C47⋊C8—22no—
36D376—82no—
37C23×C47—41no—
38C22×D47—81no—
39Q8×C47—81no—
40D4×C47—81no—
41D4×C47—82no—
42C2×C4×C47—21no—
43C2×C4×C47—41no—
44C2×C4×C47#9911yescharacteristic
45C2×Dic47—161no—
46D188—82no—
47D188—82no—
48D188—82no—
49C8×C47—22no—
50C8×C47—161no—
51C47⋊C8—42no—
52#7527—471nomaximal, Sylow
53C22×C47—81no—
54C22×C47—161no—
55C22×C47#35311yescharacteristic
56C2×D47—161no—
57C2×D47—161no—
58C2×D47—161no—
59C4×C47—22no—
60C4×C47—21no—
61C4×C47—81no—
62Dic47—321no—
63#1721—471no—
64#1410D4711yescharacteristic, complemented
65#1409—471no—
66C2×C47—21no—
67C2×C47—161no—
68C2×C47#140811yescharacteristic
69D47—321no—
70#493—471no—
71#493—941no—
72#492C2×D4711yescharacteristic
73#486—941no—
74#356—21no—
75#353—941no—
76#322—471no—
77C47#752711yescharacteristic, complemented, Sylow
78C2×SD16—41no—
79C2×D8—1881no—
80C2×D8—1882no—
81C4⋊Q8C22⋊D4711yescharacteristic
82#127—941no—
83#127D18811yescharacteristic
84#102—1882no—
85#101—41no—
86#99—1881no—
87C4×C8—941no—
88C4×C8C4×D4711yescharacteristic
89C2×Q8—21no—
90C2×D4—21no—
91C2×D4—41no—
92C2×D4—1881no—
93C2×D4—1881no—
94C2×D4—1881no—
95SD16—82no—
96D8—3762no—
97D8—3764no—
98M16—81no—
99C2×C8—21no—
100C2×C8—942no—
101C4⋊C4—41no—
102C22⋊C4—3761no—
103C42(C2×D47)⋊C411yescharacteristic
104C23—41no—
105C23—3761no—
106Q8—81no—
107D4—81no—
108D4—82no—
109D4—3762no—
110D4—3762no—
111D4—3762no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—7521no—
115C2×C4#1309393811yescharacteristic
116C8—22no—
117C8—161no—
118C8—1882no—
119C22—81no—
120C22—161no—
121C22—7521no—
122C22—7521no—
123C22—7521no—
124C22#1568891511yescharacteristic
125C4—22no—
126C4—21no—
127C4—81no—
128C4—15041no—
129C2—21no—
130C2—161no—
131C2—15041no—
132C2#2024155011yescharacteristic
subgroupG/H
centerC2#20241550
commutatorC4×C8×C47C2×C4
Frattini#492C2×D47
FittingC47×#1410C2
socleC2×C47#1408
prime radical#20243052C2
cosocleC47×#492C22
hypercenter#1410D47
hypocenterC47#7527
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
2. #20241553C2semidirect
3. C47×#1410C2semidirect
4. #15689500C4semidirect
8. #15688844C4semidirect
64. #1410D47semidirect
77. C47#7527semidirect

Maximal subgroups

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

subgroupindex
#202430522
#202415532
C47×#14102
#752747