Finite Group Databasebeta

← #20243351

Subgroups — #20243351

Order 6016.

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

normal subgroups only

This group has 548 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
1#15689959C211yesmaximal, characteristic
2#15689139C212yesmaximal, complemented
3#15689120C212yesmaximal, complemented
4#15689097C211yesmaximal, characteristic, complemented
5C47×#408C211yesmaximal, characteristic, complemented
6#13094072C412yescomplemented
7#13094071—22no—
8#13094070—22no—
9#13094069—22no—
10#13094069C412yescomplemented
11C2×#10625350—22no—
12C2×#10625350C2212yes—
13#41×D47—24no—
14#13093983C2212yescomplemented
15#13093950—24no—
16#13093949—22no—
17#13093946—22no—
18#13093939—22no—
19C2×#41×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic, complemented
21C22×C8×C47C2211yescharacteristic, complemented
22C22⋊C8×C47—22no—
23#41×C47—22no—
24#41×C47—22no—
25C2×Q8×C47C2×C411yescharacteristic
26C2×D4×C47C2×C411yescharacteristic
27C2×D4×C47D412yes—
28C22×C4×C47D412yes—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—24no—
31C2×C22⋊D47—22no—
32#10625354—24no—
33Q8×D47—24no—
34#10625352—28no—
35#10625352—24no—
36D4×D47—28no—
37D4×D47—24no—
38#10625350—24no—
39#10625350—24no—
40#10625350—24no—
41#10625350—22no—
42#10625350—22no—
43#10625350C2×C414yes—
44#10625350D414yes—
45C2×D188—22no—
46C2×D188D412yes—
47C2×C4×D47—24no—
48C2×C4×D47—22no—
49C2×Dic94—22no—
50C2×Dic94D412yes—
51M16×C47—22no—
52C2×C8×C47—22no—
53C2×C8×C47—21no—
54C2×C8×C47—21no—
55C22⋊Dic47—22no—
56C4⋊Dic47—22no—
57C4×Dic47—22no—
58C23×C47C22⋊C412yes—
59C23×C47C2×D411yescharacteristic
60C22×D47—24no—
61C22×D47—22no—
62Q8×C47—22no—
63D4×C47—24no—
64D4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47C22⋊C412yes—
68C2×C4×C47C22×C411yescharacteristic
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D411yescharacteristic
72C22⋊D47—28no—
73C22⋊D47—24no—
74C22⋊D47—24no—
75C2×Dic47—24no—
76C2×Dic47—22no—
77C2×Dic47—42no—
78D188—24no—
79D188—22no—
80D188C22⋊C414yes—
81C4×D47—28no—
82C4×D47—24no—
83C4×D47—24no—
84Dic94—24no—
85Dic94—22no—
86Dic94C22⋊C414yes—
87C8×C47—41no—
88C8×C47—41no—
89C22×C47—22no—
90C22×C47—41no—
91C22×C47—42no—
92C22×C47C2×C22⋊C411yescharacteristic
93C22×C47#12012yes—
94C2×D47—24no—
95C2×D47—82no—
96C2×D47—84no—
97C4×C47—22no—
98C4×C47C2×C22⋊C412yes—
99C4×C47#12011yescharacteristic
100C4×C47#12011yescharacteristic
101Dic47—24no—
102Dic47—82no—
103#1794—471nomaximal, Sylow
104C2×C47—22no—
105C2×C47—21no—
106C2×C47—42no—
107C2×C47#37911yescharacteristic
108D47—44no—
109#585—471no—
110#421—472no—
111#416—472no—
112#410—471no—
113#408D4711yescharacteristic, complemented
114C47#179411yescharacteristic, complemented, Sylow
1152−1+4—472no—
1162−1+4—942no—
117H(5,𝔽2)—472no—
118H(5,𝔽2)—942no—
119H(5,𝔽2)—942no—
120C2×#41—472no—
121C2×#41—944no—
122C2×#41—942no—
123C2×#41C2×D4711yescharacteristic
124C2×M16C2×D4711yescharacteristic, complemented
125C22×C8C2×D4711yescharacteristic, complemented
126#117—472no—
127#104—944no—
128#103—942no—
129#102—942no—
130#99—942no—
131C22⋊C8—22no—
132#41—22no—
133#41—22no—
134#41—474no—
135#41—474no—
136#41—944no—
137#41—944no—
138#41—944no—
139#41—948no—
140#41—944no—
141#41—944no—
142#41—942no—
143#41—942no—
144C2×Q8—472no—
145C2×Q8—942no—
146C2×Q8—944no—
147C2×Q8C4×D4711yescharacteristic
148C2×D4—472no—
149C2×D4—942no—
150C2×D4—944no—
151C2×D4—948no—
152C2×D4—944no—
153C2×D4—942no—
154C2×D4C4×D4711yescharacteristic
155C2×D4D18812yes—
156C22×C4—944no—
157C22×C4—942no—
158C22×C4C22⋊D4712yes—
159C22×C4C22×D4711yescharacteristic
160M16—22no—
161C2×C8—22no—
162C2×C8—21no—
163C2×C8—21no—
164C4⋊C4—942no—
165C22⋊C4—942no—
166C42—942no—
167C23—944no—
168C23—942no—
169C23(C2×D47)⋊C412yes—
170C23C2×D18811yescharacteristic
171Q8—22no—
172Q8—474no—
173Q8—944no—
174Q8—942no—
175D4—24no—
176D4—22no—
177D4—474no—
178D4—944no—
179D4—948no—
180D4—944no—
181D4—944no—
182D4—942no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—948no—
186C2×C4—944no—
187C2×C4—942no—
188C2×C4—944no—
189C2×C4—944no—
190C2×C4—1882no—
191C2×C4(C2×D47)⋊C412yes—
192C2×C4C2×C4×D4711yescharacteristic
193C2×C4D4×D4712yes—
194C2×C4D4×D4712yes—
195C2×C4C2×C22⋊D4711yescharacteristic
196C8—41no—
197C8—41no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—944no—
202C22—3762no—
203C22—3764no—
204C22C2×(C2×D47)⋊C411yescharacteristic
205C22#1309399412yes—
206C4—22no—
207C4—944no—
208C4—3762no—
209C4C22⋊C4×D4712yes—
210C4#1309399211yescharacteristic
211C4#1309399211yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—1884no—
216C2#1568897811yescharacteristic
subgroupG/H
centerC4#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#408C2
socleC2×C47#379
hypercenter#408D47
hypocenterC47#1794
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #15689139C2semidirect
3. #15689120C2semidirect
4. #15689097C2semidirect
5. C47×#408C2semidirect
6. #13094072C4semidirect
10. #13094069C4semidirect
14. #13093983C22semidirect
20. C2×M16×C47C22semidirect
21. C22×C8×C47C22semidirect
113. #408D47semidirect
114. C47#1794semidirect
124. C2×M16C2×D47semidirect
125. C22×C8C2×D47semidirect