Finite Group Databasebeta

← #20243888

Subgroups — #20243888

Order 6016.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689923C211yesmaximal, characteristic
2C4×#10625350C211yesmaximal, characteristic, complemented
3#15689141C211yesmaximal, characteristic, complemented
4C2×#13093952C211yesmaximal, characteristic, complemented
5#15689096C211yesmaximal, characteristic, complemented
6#15688895C211yesmaximal, characteristic, complemented
7C47×#339C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625350C2211yescharacteristic
10#13094057—21no—
11#13094057C412yescomplemented
12#13094052—21no—
13#13094052C412yescomplemented
14#13094046—22no—
15C2×#10625329C2211yescharacteristic
16C4×Dic94—21no—
17C4×D188—21no—
18C4×C22⋊D47—22no—
19#13093983C2211yescharacteristic
20#13093981—21no—
21C42×D47—21no—
22#13093952—22no—
23#13093952—21no—
24#13093952—21no—
25#13093938—22no—
26C2×M16×C47C2211yescharacteristic
27#117×C47C2211yescharacteristic
28C2×C42×C47C2211yescharacteristic
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—21no—
32C2×C22⋊D47—21no—
33#10625350—21no—
34#10625350—21no—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38#10625350—21no—
39#10625350C2×C412yes—
40#10625350D412yes—
41C2×D188C2×C411yescharacteristic, complemented
42C2×D188D411yescharacteristic
43C2×C4×D47—21no—
44C2×C4×D47—22no—
45C2×C4×D47—21no—
46C2×Dic94C2×C411yescharacteristic, complemented
47C2×Dic94D411yescharacteristic
48M16×C47—21no—
49M16×C47C2×C412yescomplemented
50C2×C8×C47—21no—
51C4⋊C4×C47—21no—
52C22⋊C4×C47—21no—
53C42×C47—21no—
54C42×C47—21no—
55C42×C47D411yescharacteristic
56C42×C47D411yescharacteristic
57C22⋊Dic47D412yes—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—21no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62C4×Dic47—21no—
63#10625329—21no—
64#10625329—21no—
65C2×C47⋊C8—21no—
66Dic188—22no—
67D376—22no—
68#10625325—22no—
69#10625325—22no—
70C23×C47C2×D411yescharacteristic
71C22×D47—21no—
72C22×D47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—42no—
76C2×C4×C47—41no—
77C2×C4×C47C22×C411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C22⋊D47—22no—
84C22⋊D47—22no—
85C22⋊D47—41no—
86C22⋊D47—41no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90D188—21no—
91D188—21no—
92D188—21no—
93D188C22⋊C412yes—
94C4×D47—22no—
95C4×D47—22no—
96C4×D47—44no—
97C4×D47—41no—
98C4×D47—41no—
99Dic94—21no—
100Dic94—21no—
101Dic94—21no—
102Dic94C22⋊C412yes—
103C8×C47—22no—
104C47⋊C8—41no—
105C22×C47—41no—
106C22×C47C4×D411yescharacteristic
107C22×C47#12011yescharacteristic
108C22×C47#12111yescharacteristic
109C2×D47—22no—
110C2×D47—42no—
111C2×D47—41no—
112C2×D47—81no—
113C4×C47—22no—
114C4×C47—41no—
115C4×C47—81no—
116C4×C47C2×C22⋊C411yescharacteristic
117C4×C47C4×D411yescharacteristic
118C4×C47#12111yescharacteristic
119C4×C47#12311yescharacteristic
120Dic47—22no—
121Dic47—42no—
122Dic47—41no—
123#1906—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—21no—
127C2×C47#38611yescharacteristic
128D47—42no—
129D47—81no—
130#575—471no—
131C4×#41—471no—
132#421—471no—
133C2×#104—471no—
134#410—471no—
135#344—471no—
136#339D4711yescharacteristic, complemented
137C47#190611yescharacteristic, complemented, Sylow
138C2×#41—471no—
139C2×#41—471no—
140#137—472no—
141#137—941no—
142AGL(1,ℤ/8)—472no—
143AGL(1,ℤ/8)—941no—
144#135—942no—
145C2×M16—471no—
146C2×M16C2×D4711yescharacteristic
147C4×Q8—941no—
148C4×D4—941no—
149C4×D4—942no—
150#117—471no—
151#117—941no—
152#117C2×D4711yescharacteristic
153C2×C42—941no—
154C2×C42C2×D4711yescharacteristic
155#104—942no—
156#104—941no—
157#104—941no—
158#99—942no—
159#41—472no—
160#41—472no—
161#41—941no—
162#41—941no—
163#41—941no—
164#41—941no—
165#41—941no—
166#41—941no—
167C2×Q8—471no—
168C2×Q8—471no—
169C2×D4—471no—
170C2×D4—471no—
171C2×D4—941no—
172C2×D4—941no—
173C22×C4—21no—
174C22×C4—942no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178Q16—942no—
179SD16—942no—
180SD16—942no—
181D8—942no—
182M16—21no—
183M16—941no—
184M16—941no—
185M16C4×D4712yescomplemented
186C2×C8—21no—
187C2×C8—941no—
188C4⋊C4—21no—
189C4⋊C4—942no—
190C4⋊C4—941no—
191C22⋊C4—21no—
192C22⋊C4—472no—
193C22⋊C4—942no—
194C42—21no—
195C42—21no—
196C42—942no—
197C42—941no—
198C42D18811yescharacteristic
199C42D18811yescharacteristic
200C23—941no—
201C23—941no—
202C23D4×D4711yescharacteristic
203Q8—472no—
204Q8—941no—
205Q8—941no—
206Q8—941no—
207D4—472no—
208D4—942no—
209D4—942no—
210D4—941no—
211D4—941no—
212D4—941no—
213D4—1881no—
214D4—1881no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—941no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—1884no—
225C2×C4—1881no—
226C2×C4—1881no—
227C2×C4C2×C4×D4711yescharacteristic
228C2×C4C2×D18811yescharacteristic
229C2×C4#1062535011yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4D4×D4711yescharacteristic
232C2×C4#1062535411yescharacteristic
233C8—22no—
234C8—1881no—
235C22—41no—
236C22—942no—
237C22—3761no—
238C22—1882no—
239C22—1881no—
240C22#1309398611yescharacteristic
241C22#1309399411yescharacteristic
242C22#1309399711yescharacteristic
243C4—22no—
244C4—41no—
245C4—81no—
246C4—942no—
247C4—1882no—
248C4—1881no—
249C4C22⋊C4×D4711yescharacteristic
250C4C4×D18811yescharacteristic
251C4#1309399911yescharacteristic
252C4#1309400911yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—3761no—
257C2—1882no—
258C2#1568900111yescharacteristic
subgroupG/H
centerC4#13093999
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC2×C47#386
hypercenter#339D47
hypocenterC47#1906
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C4×#10625350C2semidirect
3. #15689141C2semidirect
4. C2×#13093952C2semidirect
5. #15689096C2semidirect
6. #15688895C2semidirect
7. C47×#339C2semidirect
11. #13094057C4semidirect
13. #13094052C4semidirect
41. C2×D188C2×C4semidirect
46. C2×Dic94C2×C4semidirect
49. M16×C47C2×C4semidirect
136. #339D47semidirect
137. C47#1906semidirect
185. M16C4×D47semidirect