Finite Group Databasebeta

← #20244475

Subgroups — #20244475

Order 6016.

474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C22×#10625336C212yesmaximal, complemented
2C2×#13094021C211yesmaximal, characteristic
3C2×#13093944C212yesmaximal, complemented
4#15688878C211yesmaximal, characteristic, complemented
5C47×#391C211yesmaximal, characteristic, complemented
6C22×D188—22no—
7C22×D188C2212yes—
8C2×#10625336—24no—
9C2×#10625336—24no—
10C2×#10625336—24no—
11C22×C47⋊C8C2212yes—
12#13094021—24no—
13#13093944—24no—
14C22×Q8×C47C2211yescharacteristic
15C2×C4⋊C4×C47C2211yescharacteristic
16C2×C42×C47C2211yescharacteristic
17#95×C47—22no—
18C23×D47—22no—
19C2×Q8×C47—21no—
20C2×Q8×C47—22no—
21C2×Q8×C47—22no—
22C2×Q8×C47D412yescomplemented
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47D412yes—
26C22×C4×C47C2311yescharacteristic
27C2×D188—22no—
28C2×D188—22no—
29C2×D188—22no—
30C2×D188—22no—
31C2×D188—28no—
32C2×D188—22no—
33C2×D188—44no—
34C2×D188—44no—
35C2×D188D414yes—
36C4⋊C4×C47—22no—
37C42×C47—22no—
38#10625336—216no—
39C2×C47⋊C8—22no—
40C2×C47⋊C8—22no—
41C2×C47⋊C8D414yescomplemented
42C23×C47C2×D411yescharacteristic
43C22×D47—24no—
44C22×D47—42no—
45C22×D47—42no—
46C22×D47—44no—
47C22×D47—44no—
48Q8×C47—24no—
49Q8×C47—42no—
50C2×C4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—42no—
57C2×C4×C47SD1614yescomplemented
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D412yes—
60C2×C4×C47C2×D412yes—
61C2×C4×C47#4111yescharacteristic
62D188—24no—
63D188—24no—
64D188—416no—
65D188—42no—
66D188—42no—
67C47⋊C8—24no—
68C22×C47#12011yescharacteristic
69C22×C47#12111yescharacteristic
70C22×C47#12711yescharacteristic
71C22×C47C2×SD1612yes—
72C22×C47AGL(1,ℤ/8)12yes—
73C2×D47—44no—
74C2×D47—48no—
75C2×D47—84no—
76C2×D47—82no—
77C2×D47—82no—
78C4×C47—24no—
79C4×C47—42no—
80C4×C47—81no—
81C4×C47#12012yes—
82C4×C47#12112yes—
83#2014—471nomaximal, Sylow
84C2×C47#39211yescharacteristic
85C2×C47#45012yes—
86C2×C47#46012yes—
87C2×C47#49211yescharacteristic
88C2×C47#49611yescharacteristic
89D47—84no—
90C22×SD16—472no—
91C2×#127—471no—
92C2×#102—472no—
93#391D4711yescharacteristic, complemented
94#336—471no—
95C47#201411yescharacteristic, complemented, Sylow
96C22×Q8C2×D4711yescharacteristic
97C22×D4—472no—
98C22×D4—942no—
99C2×SD16—944no—
100C2×SD16—944no—
101C2×SD16—944no—
102C22×C8—472no—
103#127—944no—
104C2×C4⋊C4C2×D4711yescharacteristic
105C2×C42C2×D4711yescharacteristic
106#102—944no—
107#95—22no—
108C24—942no—
109C2×Q8—21no—
110C2×Q8—22no—
111C2×Q8—22no—
112C2×Q8D18812yescomplemented
113C2×D4—474no—
114C2×D4—948no—
115C2×D4—942no—
116C2×D4—942no—
117C2×D4—942no—
118C2×D4—942no—
119C2×D4—942no—
120C2×D4—1884no—
121C2×D4—1884no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4C22⋊D4712yes—
125C22×C4C22×D4711yescharacteristic
126SD16—9416no—
127C2×C8—474no—
128C2×C8—942no—
129C2×C8—942no—
130C4⋊C4—22no—
131C42—22no—
132C23—944no—
133C23—1882no—
134C23—1882no—
135C23—1884no—
136C23—1884no—
137C23C2×C22⋊D4711yescharacteristic
138Q8—24no—
139Q8—42no—
140D4—944no—
141D4—944no—
142D4—18816no—
143D4—1882no—
144D4—1882no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—42no—
152C2×C4#1062533614yescomplemented
153C2×C4C2×D18811yescharacteristic
154C2×C4#1062535011yescharacteristic
155C2×C4D4×D4712yes—
156C2×C4D4×D4712yes—
157C8—944no—
158C22—3762no—
159C22—3762no—
160C22—3764no—
161C22—1888no—
162C22—1884no—
163C22#1309399211yescharacteristic
164C22#1309399811yescharacteristic
165C22#1309402011yescharacteristic
166C22C2×#1062533612yes—
167C22#1309404912yes—
168C4—24no—
169C4—42no—
170C4—81no—
171C4#1309399412yes—
172C4#1309399712yes—
173C2—3764no—
174C2#1568903211yescharacteristic
175C2#1568927312yes—
176C2#1568932312yes—
177C2#1568949711yescharacteristic
178C2#1568951311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#391C2
socleC23×C47C2×D4
hypercenter#391D47
hypocenterC47#2014
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C22×#10625336C2semidirect
3. C2×#13093944C2semidirect
4. #15688878C2semidirect
5. C47×#391C2semidirect
22. C2×Q8×C47D4semidirect
41. C2×C47⋊C8D4semidirect
57. C2×C4×C47SD16semidirect
93. #391D47semidirect
95. C47#2014semidirect
112. C2×Q8D188semidirect
152. C2×C4#10625336semidirect