Finite Group Databasebeta

← #20252755

Subgroups — #20252755

Order 6016.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13094072C211yesmaximal, characteristic, complemented
2#15689923C212yesmaximal, complemented
3#15689697C211yesmaximal, characteristic, complemented
4#15689308C214yesmaximal, complemented
5#15689298C214yesmaximal, complemented
6#15689139C212yesmaximal, complemented
7C2×#101×C47C211yesmaximal, characteristic, complemented
8#13094072—22no—
9#13094072—24no—
10#13094072C2214yes—
11C2×#10625354—22no—
12C2×#10625350—22no—
13C2×#10625350C2212yes—
14C2×#10625350C2211yescharacteristic
15C2×Q8×D47—22no—
16#13094057—22no—
17#13094057C2214yescomplemented
18#13094052—22no—
19#13094052C2214yescomplemented
20#13094046—24no—
21#13094022C2212yescomplemented
22#13094013C2212yescomplemented
23#13094007—22no—
24#13094000—22no—
25#13093983C2211yescharacteristic
26#13093950C2218yescomplemented
27C22×Q8×C47C2211yescharacteristic
28C2×M16×C47C2212yes—
29#101×C47C2214yescomplemented
30C2×Q8×C47—22no—
31C2×Q8×C47—22no—
32C2×Q8×C47D412yes—
33C2×Q8×C47C2312yes—
34C22×C4×C47D412yes—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—22no—
37C2×C22⋊D47—21no—
38#10625354—28no—
39#10625354—28no—
40Q8×D47—28no—
41Q8×D47—28no—
42#10625350—28no—
43#10625350—28no—
44#10625350—22no—
45#10625350—22no—
46#10625350—22no—
47#10625350—22no—
48#10625350D414yes—
49#10625350C2314yes—
50C2×D188—22no—
51C2×D188D412yes—
52C2×D188C2311yescharacteristic
53C2×C4×D47—24no—
54C2×C4×D47—22no—
55C2×C4×D47—21no—
56C2×Dic94—22no—
57C2×Dic94D412yes—
58C2×Dic94C2311yescharacteristic
59M16×C47—22no—
60M16×C47C2314yes—
61C2×C8×C47—22no—
62C22⋊Dic47—21no—
63(C2×D47)⋊C4—24no—
64C4⋊Dic47—21no—
65Dic47⋊C4—24no—
66C4×Dic47C2312yes—
67Dic188—24no—
68D376—24no—
69#10625325—24no—
70#10625325—24no—
71C23×C47C2×D411yescharacteristic
72C22×D47—22no—
73C22×D47—21no—
74Q8×C47—24no—
75Q8×C47—24no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D414yes—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2411yescharacteristic
83C22⋊D47—24no—
84C22⋊D47—24no—
85C22⋊D47—41no—
86C22⋊D47—41no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—21no—
90D188—28no—
91D188—22no—
92D188—22no—
93D188C2×D414yes—
94C4×D47—216no—
95C4×D47—24no—
96C4×D47—24no—
97C4×D47—42no—
98Dic94—28no—
99Dic94—22no—
100Dic94—22no—
101Dic94C2×D414yes—
102C8×C47—24no—
103C22×C47—41no—
104C22×C47#12011yescharacteristic
105C22×C47#12011yescharacteristic
106C22×C47C22×D411yescharacteristic
107C2×D47—24no—
108C2×D47—44no—
109C2×D47—42no—
110C2×D47—41no—
111C4×C47—24no—
112C4×C47#12012yes—
113C4×C47C22×D412yes—
114Dic47—24no—
115Dic47—42no—
116Dic47—41no—
117#3020—471nomaximal, Sylow
118C2×C47—21no—
119C2×C47—21no—
120C2×C47—21no—
121C2×C47C2×#12011yescharacteristic
122D47—44no—
123D47—81no—
124C2×2−1+4—471no—
125#575—472no—
126#536—471no—
127#456—474no—
128#454—474no—
129#421—472no—
130C2×#101D4711yescharacteristic, complemented
131C47#302011yescharacteristic, complemented, Sylow
1322−1+4—474no—
1332−1+4—944no—
1342−1+4—942no—
135C2×#41—472no—
136C2×#41—471no—
137C2×#41—942no—
138C2×#41—942no—
139C22×Q8—942no—
140C22×Q8C2×D4711yescharacteristic
141#137—474no—
142#137—942no—
143AGL(1,ℤ/8)—474no—
144AGL(1,ℤ/8)—942no—
145#135—944no—
146C2×M16C2×D4712yes—
147C4⋊Q8—472no—
148#124—472no—
149#123—942no—
150C22⋊Q8—942no—
151#117—471no—
152#104—478no—
153#101C2×D4714yescomplemented
154#41—474no—
155#41—474no—
156#41—948no—
157#41—948no—
158#41—948no—
159#41—942no—
160#41—948no—
161#41—942no—
162#41—942no—
163#41—942no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—472no—
167C2×Q8—471no—
168C2×Q8—942no—
169C2×Q8—948no—
170C2×Q8—948no—
171C2×Q8D18812yes—
172C2×Q8C22×D4712yes—
173C2×D4—472no—
174C2×D4—471no—
175C2×D4—942no—
176C2×D4—942no—
177C2×D4—941no—
178C22×C4—944no—
179C22×C4—942no—
180C22×C4—941no—
181C22×C4D18812yes—
182C22×C4C22×D4711yescharacteristic
183Q16—944no—
184SD16—944no—
185SD16—944no—
186D8—944no—
187M16—22no—
188M16C22×D4714yes—
189C2×C8—22no—
190C4⋊C4—944no—
191C4⋊C4—941no—
192C22⋊C4—941no—
193C22⋊C4—944no—
194C42—472no—
195C23—942no—
196C23—941no—
197C23C2×D18811yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—474no—
201Q8—948no—
202Q8—942no—
203Q8—942no—
204D4—474no—
205D4—948no—
206D4—944no—
207D4—944no—
208D4—942no—
209D4—942no—
210D4—1881no—
211D4—1881no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—9416no—
215C2×C4—942no—
216C2×C4—944no—
217C2×C4—944no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—1882no—
221C2×C4C2×D18814yes—
222C2×C4C2×D18811yescharacteristic
223C2×C4D4×D4712yes—
224C2×C4D4×D4712yes—
225C2×C4C23×D4711yescharacteristic
226C8—24no—
227C22—41no—
228C22—944no—
229C22—1882no—
230C22—1884no—
231C22—1881no—
232C22#1309399411yescharacteristic
233C22#1309399411yescharacteristic
234C22C22×D18811yescharacteristic
235C4—24no—
236C4—944no—
237C4—1882no—
238C4—1881no—
239C4#1309399412yes—
240C4C2×D4×D4712yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—3761no—
245C2—1884no—
246C2C2×#1309399411yescharacteristic
subgroupG/H
centerC2C2×#13093994
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#101×C47C2
socleC2×C47C2×#120
hypercenterC2×#101D47
hypocenterC47#3020
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#13094072C2semidirect
2. #15689923C2semidirect
3. #15689697C2semidirect
4. #15689308C2semidirect
5. #15689298C2semidirect
6. #15689139C2semidirect
7. C2×#101×C47C2semidirect
17. #13094057C22semidirect
19. #13094052C22semidirect
21. #13094022C22semidirect
22. #13094013C22semidirect
26. #13093950C22semidirect
29. #101×C47C22semidirect
130. C2×#101D47semidirect
131. C47#3020semidirect
153. #101C2×D47semidirect