Finite Group Databasebeta

← #20241413

Subgroups — #20241413

Order 6016.

154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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#15689059C211yesmaximal, characteristic
2#15688890C211yesmaximal, characteristic
3C47×#323C211yesmaximal, characteristic
4C2×C4⋊Dic47C411yescharacteristic, complemented
5C2×Dic47⋊C4—21no—
6C2×C22⋊Dic47—21no—
7C2×C22⋊Dic47—21no—
8C47⋊#95C411yescharacteristic, complemented
9C2×C22⋊C4×C47C2211yescharacteristic
10C22⋊C8×C47—21no—
11C24×C47D411yescharacteristic
12C22×C4×C47C2×C411yescharacteristic
13C22×C4×C47D411yescharacteristic
14C22×Dic47—21no—
15C22×Dic47—21no—
16C22×Dic47—41no—
17C2×C8×C47—41no—
18C22⋊C4×C47—41no—
19C22⋊Dic47—22no—
20C22⋊Dic47—42no—
21C22⋊Dic47—41no—
22C4⋊Dic47—41no—
23Dic47⋊C4—42no—
24C23×C47—21no—
25C23×C47—21no—
26C23×C47—41no—
27C23×C47—41no—
28C23×C47C22⋊C411yescharacteristic
29C23×C47SD1611yescharacteristic
30C23×C47Q1611yescharacteristic
31C2×C4×C47—21no—
32C2×C4×C47—21no—
33C2×C4×C47—41no—
34C2×C4×C47—41no—
35C2×Dic47—22no—
36C2×Dic47—41no—
37C2×Dic47—41no—
38C2×Dic47—41no—
39C2×Dic47—42no—
40C2×Dic47—41no—
41C2×Dic47—41no—
42C2×Dic47—81no—
43C2×Dic47—81no—
44C8×C47—81no—
45C22×C47—21no—
46C22×C47—21no—
47C22×C47—21no—
48C22×C47—21no—
49C22×C47—41no—
50C22×C47—41no—
51C22×C47—41no—
52C22×C47—41no—
53C22×C47—81no—
54C22×C47#9911yescharacteristic
55C22×C47#10311yescharacteristic
56C22×C47#10411yescharacteristic
57C4×C47—41no—
58C4×C47—41no—
59Dic47—42no—
60Dic47—82no—
61Dic47—81no—
62#1352—471nomaximal, Sylow
63C2×C47—21no—
64C2×C47—21no—
65C2×C47—41no—
66C2×C47—41no—
67C2×C47#32811yescharacteristic
68C2×C47#35211yescharacteristic
69C2×C47#35311yescharacteristic
70#399—471no—
71#342—471no—
72#323D4711yescharacteristic
73C47#135211yescharacteristic, complemented, Sylow
74C2×C4⋊C4—471no—
75C2×C4⋊C4—941no—
76C2×C22⋊C4—941no—
77C2×C22⋊C4—941no—
78C2×C22⋊C4C2×D4711yescharacteristic
79C22⋊C8—21no—
80#95—471no—
81C24D18811yescharacteristic
82C22×C4—941no—
83C22×C4—941no—
84C22×C4—1881no—
85C22×C4C4×D4711yescharacteristic
86C22×C4C22⋊D4711yescharacteristic
87C2×C8—41no—
88C4⋊C4—1881no—
89C4⋊C4—1882no—
90C22⋊C4—41no—
91C22⋊C4—942no—
92C22⋊C4—1882no—
93C22⋊C4—1881no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23#1062532511yescharacteristic
99C23Dic18811yescharacteristic
100C23(C2×D47)⋊C411yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—942no—
106C2×C4—3761no—
107C2×C4—3761no—
108C2×C4—1882no—
109C2×C4—1881no—
110C2×C4—1881no—
111C2×C4—1881no—
112C2×C4—1881no—
113C2×C4—1881no—
114C8—81no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#1309393811yescharacteristic
125C22#1309394911yescharacteristic
126C22#1309395011yescharacteristic
127C4—41no—
128C4—41no—
129C4—3762no—
130C4—3761no—
131C4—1882no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#1568886111yescharacteristic
137C2#1568891411yescharacteristic
138C2#1568891511yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC22×C4×C47C2×C4
FrattiniC2×C22⋊C4C2×D47
FittingC47×#323C2
socleC22×C47#99
hypercenter#323D47
hypocenterC47#1352
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic47C4semidirect
8. C47⋊#95C4semidirect
73. C47#1352semidirect