Finite Group Databasebeta

← #20254163

Subgroups — #20254163

Order 6016.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#13094003C212yesmaximal
2#15689459C214yesmaximal, complemented
3#15689364C214yesmaximal, complemented
4#15689281C214yesmaximal, complemented
5C2×C22⋊C8×C47C211yesmaximal, characteristic
6C22×Dic94C2212yes—
7C2×Dic188C2214yescomplemented
8#13094003—22no—
9#13094003—22no—
10#13094003C2214yes—
11#13094003C2214yes—
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4—22no—
14C2×C22⋊Dic47—22no—
15#13093958C2214yescomplemented
16#13093949C2218yescomplemented
17C23×C4×C47C2211yescharacteristic
18C22×C8×C47C2212yes—
19C22⋊C8×C47C2214yes—
20C24×C47D411yescharacteristic
21C22×C4×C47—42no—
22C22×C4×C47D412yes—
23C22×C4×C47D411yescharacteristic
24C22×C4×C47C2311yescharacteristic
25C22×C4×C47C2312yes—
26C22×Dic47—22no—
27C22×Dic47—22no—
28C2×Dic94—22no—
29C2×Dic94—44no—
30C2×Dic94C2314yes—
31C2×C8×C47—42no—
32C2×C8×C47C2314yes—
33C22⋊Dic47—24no—
34C22⋊Dic47—24no—
35C4⋊Dic47—22no—
36C4⋊Dic47C2314yes—
37Dic47⋊C4—24no—
38Dic47⋊C4—24no—
39Dic188—44no—
40C23×C47—41no—
41C23×C47—41no—
42C23×C47Q1614yescomplemented
43C23×C47C2×D411yescharacteristic
44C23×C47C2×D412yes—
45C2×C4×C47—22no—
46C2×C4×C47—24no—
47C2×C4×C47—41no—
48C2×C4×C47—42no—
49C2×C4×C47C2×D411yescharacteristic
50C2×C4×C47C2×D412yes—
51C2×C4×C47C2411yescharacteristic
52C2×Dic47—24no—
53C2×Dic47—24no—
54C2×Dic47—44no—
55C2×Dic47—44no—
56Dic94—28no—
57Dic94—44no—
58C8×C47—24no—
59C22×C47—22no—
60C22×C47—21no—
61C22×C47—22no—
62C22×C47—21no—
63C22×C47—44no—
64C22×C47C2×Q1612yes—
65C22×C47C2×Q1614yes—
66C22×C47C22×D411yescharacteristic
67C4×C47—22no—
68C4×C47—21no—
69C4×C47H(5,𝔽2)12yes—
70Dic47—44no—
71Dic47—44no—
72#3189—471nomaximal, Sylow
73C2×C47—24no—
74C2×C47—22no—
75C2×C47#53411yescharacteristic
76C2×C47C22×Q1611yescharacteristic
77C2×C47#57511yescharacteristic
78C2×C22⋊Q8—472no—
79#484—474no—
80#467—474no—
81#451—474no—
82C2×C22⋊C8D4711yescharacteristic
83C47#318911yescharacteristic, complemented, Sylow
84C22×Q8—472no—
85C23×C4C2×D4711yescharacteristic
86C2×Q16—474no—
87C22×C8C2×D4712yes—
88C22⋊Q8—474no—
89C22⋊Q8—474no—
90C22⋊Q8—942no—
91C22⋊Q8—942no—
92C2×C4⋊C4—472no—
93C2×C4⋊C4—942no—
94C2×C22⋊C4—942no—
95#107—474no—
96#103—478no—
97C22⋊C8C2×D4714yes—
98C24D18811yescharacteristic
99C2×Q8—474no—
100C2×Q8—942no—
101C2×Q8—1884no—
102C22×C4—42no—
103C22×C4—942no—
104C22×C4—942no—
105C22×C4D18812yes—
106C22×C4D18811yescharacteristic
107C22×C4C22×D4712yes—
108C22×C4C22×D4711yescharacteristic
109Q16—1884no—
110C2×C8—42no—
111C2×C8C22×D4714yes—
112C4⋊C4—474no—
113C4⋊C4—944no—
114C4⋊C4—944no—
115C4⋊C4—942no—
116C22⋊C4—944no—
117C22⋊C4—944no—
118C23—41no—
119C23—41no—
120C23Dic18814yescomplemented
121C23C2×D18811yescharacteristic
122C23C2×D18812yes—
123Q8—948no—
124Q8—1884no—
125C2×C4—22no—
126C2×C4—24no—
127C2×C4—41no—
128C2×C4—42no—
129C2×C4—944no—
130C2×C4—944no—
131C2×C4—1884no—
132C2×C4—1884no—
133C2×C4C2×D18811yescharacteristic
134C2×C4C2×D18812yes—
135C2×C4C23×D4711yescharacteristic
136C8—24no—
137C22—22no—
138C22—21no—
139C22—22no—
140C22—21no—
141C22—44no—
142C22C2×Dic18812yes—
143C22C2×Dic18814yes—
144C22C22×D18811yescharacteristic
145C4—22no—
146C4—21no—
147C4—1884no—
148C4—1884no—
149C4#1309406912yes—
150C2—24no—
151C2—22no—
152C2#1568968511yescharacteristic
153C2C22×Dic18811yescharacteristic
154C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C22⋊C8×C47C2
socleC22×C47C22×D4
hypercenterC2×C22⋊C8D47
hypocenterC47#3189
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #15689459C2semidirect
3. #15689364C2semidirect
4. #15689281C2semidirect
7. C2×Dic188C22semidirect
15. #13093958C22semidirect
16. #13093949C22semidirect
42. C23×C47Q16semidirect
83. C47#3189semidirect
120. C23Dic188semidirect