Finite Group Databasebeta

← #20241409

Subgroups — #20241409

Order 6016.

162 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 37 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#15688890C211yesmaximal, characteristic
2#15688847C211yesmaximal, characteristic
3C47×#393C211yesmaximal, characteristic
4C2×C22⋊Dic47—21no—
5C22⋊(C47⋊C8)—21no—
6C22×Q8×C47C411yescharacteristic, complemented
7C2×C22⋊C4×C47—21no—
8C2×C22⋊C4×C47C2211yescharacteristic
9#95×C47—21no—
10#95×C47C411yescharacteristic, complemented
11C24×C47D411yescharacteristic
12C2×Q8×C47—42no—
13C2×Q8×C47—41no—
14C22×C4×C47—21no—
15C22×C4×C47—21no—
16C22×C4×C47C2×C411yescharacteristic
17C22×C4×C47D411yescharacteristic
18C22×Dic47—41no—
19C22⋊C4×C47—41no—
20C22⋊C4×C47—42no—
21C22⋊Dic47—22no—
22C22⋊Dic47—41no—
23C2×C47⋊C8—41no—
24C23×C47—21no—
25C23×C47—21no—
26C23×C47—41no—
27C23×C47—41no—
28C23×C47C22⋊C411yescharacteristic
29C23×C47SD1611yescharacteristic
30C23×C47Q1611yescharacteristic
31Q8×C47—42no—
32Q8×C47—42no—
33C2×C4×C47—22no—
34C2×C4×C47—21no—
35C2×C4×C47—21no—
36C2×C4×C47—41no—
37C2×C4×C47—41no—
38C2×C4×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47—41no—
41C2×C4×C47—41no—
42C2×C4×C47—41no—
43C2×Dic47—42no—
44C2×Dic47—81no—
45C2×Dic47—81no—
46C47⋊C8—81no—
47C22×C47—21no—
48C22×C47—21no—
49C22×C47—21no—
50C22×C47—21no—
51C22×C47—41no—
52C22×C47—41no—
53C22×C47—41no—
54C22×C47—41no—
55C22×C47—81no—
56C22×C47#9911yescharacteristic
57C22×C47#10311yescharacteristic
58C22×C47#10411yescharacteristic
59C4×C47—42no—
60C4×C47—41no—
61C4×C47—41no—
62C4×C47—81no—
63Dic47—82no—
64#1351—471nomaximal, Sylow
65C2×C47—21no—
66C2×C47—21no—
67C2×C47—41no—
68C2×C47—41no—
69C2×C47#32811yescharacteristic
70C2×C47AΣL(1,𝔽16)11yescharacteristic
71C2×C47#35411yescharacteristic
72#393D4711yescharacteristic
73#342—471no—
74#323—471no—
75C47#135111yescharacteristic, complemented, Sylow
76C22×Q8Dic4711yescharacteristic, complemented
77C2×C22⋊C4—21no—
78C2×C22⋊C4—941no—
79C2×C22⋊C4C2×D4711yescharacteristic
80C22⋊C8—941no—
81#95—21no—
82#95Dic4711yescharacteristic, complemented
83C24C22⋊D4711yescharacteristic
84C2×Q8—42no—
85C2×Q8—41no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—1881no—
89C22×C4C2×Dic4711yescharacteristic
90C22×C4C22⋊D4711yescharacteristic
91C2×C8—1881no—
92C22⋊C4—41no—
93C22⋊C4—42no—
94C22⋊C4—942no—
95C22⋊C4—1881no—
96C23—21no—
97C23—21no—
98C23—41no—
99C23—41no—
100C23#1062533611yescharacteristic
101C23#1062533711yescharacteristic
102C23C22⋊Dic4711yescharacteristic
103Q8—42no—
104Q8—42no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—3761no—
116C2×C4—3761no—
117C2×C4—1882no—
118C8—3761no—
119C22—21no—
120C22—21no—
121C22—21no—
122C22—21no—
123C22—41no—
124C22—41no—
125C22—41no—
126C22—41no—
127C22—81no—
128C22#1309393911yescharacteristic
129C22#1309394811yescharacteristic
130C22#1309395111yescharacteristic
131C4—42no—
132C4—41no—
133C4—41no—
134C4—81no—
135C4—3762no—
136C2—21no—
137C2—21no—
138C2—41no—
139C2—41no—
140C2#1568886011yescharacteristic
141C2#1568891011yescharacteristic
142C2#1568891811yescharacteristic
subgroupG/H
centerC22#13093939
commutatorC22×C4×C47C2×C4
FrattiniC2×C22⋊C4C2×D47
FittingC47×#393C2
socleC22×C47#99
hypercenter#393D47
hypocenterC47#1351
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #393

Complements

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

NH ≅ G/Ntype
6. C22×Q8×C47C4semidirect
10. #95×C47C4semidirect
75. C47#1351semidirect
76. C22×Q8Dic47semidirect
82. #95Dic47semidirect