Finite Group Databasebeta

← #20244458

Subgroups — #20244458

Order 6016.

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

normal subgroups only

This group has 510 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×#10625334C212yesmaximal, complemented
2C2×#13094021C211yesmaximal, characteristic, complemented
3C2×#13093944C212yesmaximal, complemented
4#15688878C211yesmaximal, characteristic, complemented
5C47×#390C211yesmaximal, characteristic, complemented
6C22×D188—22no—
7C22×D188C2212yes—
8C2×#10625334—24no—
9C2×#10625334—24no—
10C2×#10625334—24no—
11C22×C47⋊C8C2212yes—
12#13094021—24no—
13#13093944—24no—
14C22×D4×C47C2211yescharacteristic
15C2×C4⋊C4×C47C2211yescharacteristic
16C2×C22⋊C4×C47—22no—
17C2×C42×C47C2211yescharacteristic
18C24×C47—21no—
19C23×D47—22no—
20C2×D4×C47—22no—
21C2×D4×C47—22no—
22C2×D4×C47—21no—
23C2×D4×C47D412yescomplemented
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—
37C22⋊C4×C47—44no—
38C42×C47—22no—
39#10625334—216no—
40C2×C47⋊C8—22no—
41C2×C47⋊C8—22no—
42C2×C47⋊C8D414yescomplemented
43C23×C47—22no—
44C23×C47—41no—
45C23×C47—41no—
46C23×C47—42no—
47C23×C47—42no—
48C23×C47C2×D411yescharacteristic
49C22×D47—24no—
50C22×D47—42no—
51C22×D47—42no—
52C22×D47—44no—
53C22×D47—44no—
54D4×C47—24no—
55D4×C47—42no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—41no—
59C2×C4×C47—42no—
60C2×C4×C47D814yescomplemented
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D412yes—
63C2×C4×C47C2×D412yes—
64C2×C4×C47#4111yescharacteristic
65D188—24no—
66D188—24no—
67D188—416no—
68D188—42no—
69D188—42no—
70C47⋊C8—24no—
71C22×C47—42no—
72C22×C47—44no—
73C22×C47—82no—
74C22×C47—81no—
75C22×C47—81no—
76C22×C47#12011yescharacteristic
77C22×C47#12111yescharacteristic
78C22×C47#12711yescharacteristic
79C22×C47C2×D812yes—
80C22×C47AGL(1,ℤ/8)12yes—
81C2×D47—44no—
82C2×D47—48no—
83C2×D47—84no—
84C2×D47—82no—
85C2×D47—82no—
86C4×C47—24no—
87C4×C47—81no—
88C4×C47#12012yes—
89C4×C47#12112yes—
90#2011—471nomaximal, Sylow
91C2×C47—82no—
92C2×C47#39211yescharacteristic
93C2×C47#44712yes—
94C2×C47#45912yes—
95C2×C47#49311yescharacteristic
96C2×C47#49611yescharacteristic
97D47—84no—
98C22×D8—472no—
99C2×#127—471no—
100C2×#102—472no—
101#390D4711yescharacteristic, complemented
102#336—471no—
103C47#201111yescharacteristic, complemented, Sylow
104C22×D4—472no—
105C22×D4—942no—
106C22×D4C2×D4711yescharacteristic
107C2×D8—944no—
108C2×D8—944no—
109C2×D8—944no—
110C22×C8—472no—
111#127—944no—
112C2×C4⋊C4C2×D4711yescharacteristic
113C2×C22⋊C4—22no—
114C2×C42C2×D4711yescharacteristic
115#102—944no—
116C24—21no—
117C24—942no—
118C2×D4—21no—
119C2×D4—22no—
120C2×D4—22no—
121C2×D4—474no—
122C2×D4—948no—
123C2×D4—942no—
124C2×D4—942no—
125C2×D4—942no—
126C2×D4—942no—
127C2×D4—942no—
128C2×D4—1884no—
129C2×D4—1884no—
130C2×D4D18812yescomplemented
131C22×C4—21no—
132C22×C4C22⋊D4712yes—
133C22×C4C22×D4711yescharacteristic
134D8—9416no—
135C2×C8—474no—
136C2×C8—942no—
137C2×C8—942no—
138C4⋊C4—22no—
139C22⋊C4—44no—
140C42—22no—
141C23—22no—
142C23—41no—
143C23—41no—
144C23—42no—
145C23—42no—
146C23—944no—
147C23—1882no—
148C23—1882no—
149C23—1884no—
150C23—1884no—
151C23C2×C22⋊D4711yescharacteristic
152D4—24no—
153D4—42no—
154D4—944no—
155D4—944no—
156D4—18816no—
157D4—1882no—
158D4—1882no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4#1062533414yescomplemented
164C2×C4C2×D18811yescharacteristic
165C2×C4#1062535011yescharacteristic
166C2×C4D4×D4712yes—
167C2×C4D4×D4712yes—
168C8—944no—
169C22—42no—
170C22—44no—
171C22—81no—
172C22—82no—
173C22—81no—
174C22—3762no—
175C22—3762no—
176C22—3764no—
177C22—1888no—
178C22—1884no—
179C22#1309399211yescharacteristic
180C22#1309399811yescharacteristic
181C22#1309402011yescharacteristic
182C22C2×#1062533412yes—
183C22#1309404912yes—
184C4—24no—
185C4—81no—
186C4#1309399412yes—
187C4#1309399712yes—
188C2—82no—
189C2—3764no—
190C2#1568903211yescharacteristic
191C2#1568925612yes—
192C2#1568931812yes—
193C2#1568949911yescharacteristic
194C2#1568951311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#390C2
socleC23×C47C2×D4
hypercenter#390D47
hypocenterC47#2011
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C22×#10625334C2semidirect
2. C2×#13094021C2semidirect
3. C2×#13093944C2semidirect
4. #15688878C2semidirect
5. C47×#390C2semidirect
23. C2×D4×C47D4semidirect
42. C2×C47⋊C8D4semidirect
60. C2×C4×C47D8semidirect
101. #390D47semidirect
103. C47#2011semidirect
130. C2×D4D188semidirect
163. C2×C4#10625334semidirect